**Previous months:**

2009 - 0908(1)

2010 - 1003(2) - 1004(2) - 1008(1)

2011 - 1101(3) - 1106(3) - 1108(1) - 1109(1) - 1112(2)

2012 - 1202(1) - 1208(3) - 1210(2) - 1211(1) - 1212(3)

2013 - 1301(1) - 1302(2) - 1303(6) - 1305(2) - 1306(6) - 1308(1) - 1309(1) - 1310(4) - 1311(1) - 1312(1)

2014 - 1403(3) - 1404(3) - 1405(25) - 1406(2) - 1407(2) - 1408(3) - 1409(3) - 1410(3) - 1411(1) - 1412(2)

2015 - 1501(2) - 1502(4) - 1503(3) - 1504(4) - 1505(2) - 1506(1) - 1507(1) - 1508(1) - 1509(5) - 1510(6) - 1511(1)

2016 - 1601(12) - 1602(4) - 1603(7) - 1604(1) - 1605(8) - 1606(6) - 1607(6) - 1608(3) - 1609(3) - 1610(2) - 1611(3) - 1612(4)

2017 - 1701(3) - 1702(4) - 1703(1) - 1704(1) - 1706(2) - 1707(5) - 1708(4) - 1709(1) - 1710(4) - 1711(1) - 1712(7)

2018 - 1801(4) - 1802(5) - 1803(2) - 1804(3) - 1805(5) - 1806(1) - 1807(6) - 1808(3) - 1809(4) - 1810(6) - 1811(1)

Any replacements are listed farther down

[252] **viXra:1810.0227 [pdf]**
*submitted on 2018-10-14 09:18:20*

**Authors:** Yuly Shipilevsky

**Comments:** 9 Pages.

We introduce and suggest to research a special class of optimization problems,
wherein an objective function is a real-valued complex variables function
and constraints comprising complex-valued complex variables functions

**Category:** Data Structures and Algorithms

[251] **viXra:1810.0197 [pdf]**
*submitted on 2018-10-12 17:56:39*

**Authors:** Young TAB-LO

**Comments:** 1 Page.

N/A

**Category:** Data Structures and Algorithms

[250] **viXra:1810.0189 [pdf]**
*submitted on 2018-10-13 04:56:51*

**Authors:** George Rajna

**Comments:** 64 Pages.

The Pentagon on Friday said there has been a cyber breach of Defense Department travel records that compromised the personal information and credit card data of U.S. military and civilian personnel. [41] Quantum secure direct communication transmits secret information directly without encryption. [40] Physicists at The City College of New York have used atomically thin two-dimensional materials to realize an array of quantum emitters operating at room temperature that can be integrated into next generation quantum communication systems. [39] Research in the quantum optics lab of Prof. Barak Dayan in the Weizmann Institute of Science may be bringing the development of such computers one step closer by providing the "quantum gates" that are required for communication within and between such quantum computers. [38] Calculations of a quantum system's behavior can spiral out of control when they involve more than a handful of particles. [37] Researchers from the University of North Carolina at Chapel Hill have reached a new milestone on the way to optical computing, or the use of light instead of electricity for computing. [36] The key technical novelty of this work is the creation of semantic embeddings out of structured event data. [35] The researchers have focussed on a complex quantum property known as entanglement, which is a vital ingredient in the quest to protect sensitive data. [34] Cryptography is a science of data encryption providing its confidentiality and integrity. [33] Researchers at the University of Sheffield have solved a key puzzle in quantum physics that could help to make data transfer totally secure. [32]

**Category:** Data Structures and Algorithms

[249] **viXra:1810.0103 [pdf]**
*submitted on 2018-10-07 18:13:41*

**Authors:** Colin James III

**Comments:** 1 Page. © Copyright 2018 by Colin James III All rights reserved. Respond to the author by email at: info@ersatz-systems dot com.

The optimization paradigm is not tautologous, hence refuting complex programming as that paradigm as a new class.

**Category:** Data Structures and Algorithms

[248] **viXra:1810.0096 [pdf]**
*submitted on 2018-10-06 08:08:06*

**Authors:** Mesut Kavak

**Comments:** 2 Pages.

I have been working for a time about basic laws of directing the universe [1,2]. It seems that the most basic and impressive principle which causes any physical phenomenon is the Uncertainty Principle of Heisenberg [3], that existence have any property because of the uncertainty. During this process, while I was thinking about conservation of information I noticed, that information cannot be lost; but at a point, it becomes completely unrecognizable according to us as there is no alternative. Any information and the information searched for become the same after a point relatively to us. The sensitivity increases forever but its loss. Each sensitivity level also has higher level; so actually an absolute protection seems possible.

**Category:** Data Structures and Algorithms

[247] **viXra:1810.0073 [pdf]**
*submitted on 2018-10-05 18:20:15*

**Authors:** Yuly Shipilevsky

**Comments:** 9 Pages.

We introduce and suggest to research a special class of optimization problems,
wherein an objective function is a real-valued complex variables function
and constraints comprising complex-valued complex variables functions.

**Category:** Data Structures and Algorithms

[246] **viXra:1809.0601 [pdf]**
*submitted on 2018-09-30 07:15:47*

**Authors:** Yuly Shipilevsky

**Comments:** 6 Pages.

We introduce and suggest to research a special class of optimization problems,
wherein an objective function is a real-valued complex variables function
and constraints comprising complex-valued complex variables functions.

**Category:** Data Structures and Algorithms

[245] **viXra:1809.0324 [pdf]**
*submitted on 2018-09-15 08:18:55*

**Authors:** George Rajna

**Comments:** 46 Pages.

Workflow management systems allow users to prepare, produce and analyze scientific processes to help simplify complex simulations. [27] Now, a team of A*STAR researchers and colleagues has developed a detector that can successfully pick out where human actions will occur in videos, in almost real-time. [26] A team of researchers affiliated with several institutions in Germany and the U.S. has developed a deep learning algorithm that can be used for motion capture of animals of any kind. [25] In 2016, when we inaugurated our new IBM Research lab in Johannesburg, we took on this challenge and are reporting our first promising results at Health Day at the KDD Data Science Conference in London this month. [24] The research group took advantage of a system at SLAC's Stanford Synchrotron Radiation Lightsource (SSRL) that combines machine learning—a form of artificial intelligence where computer algorithms glean knowledge from enormous amounts of data—with experiments that quickly make and screen hundreds of sample materials at a time. [23] Researchers at the UCLA Samueli School of Engineering have demonstrated that deep learning, a powerful form of artificial intelligence, can discern and enhance microscopic details in photos taken by smartphones. [22] Such are the big questions behind one of the new projects underway at the MIT-IBM Watson AI Laboratory, a collaboration for research on the frontiers of artificial intelligence. [21] The possibility of cognitive nuclear-spin processing came to Fisher in part through studies performed in the 1980s that reported a remarkable lithium isotope dependence on the behavior of mother rats. [20] And as will be presented today at the 25th annual meeting of the Cognitive Neuroscience Society (CNS), cognitive neuroscientists increasingly are using those emerging artificial networks to enhance their understanding of one of the most elusive intelligence systems, the human brain. [19] U.S. Army Research Laboratory scientists have discovered a way to leverage emerging brain-like computer architectures for an age-old number-theoretic problem known as integer factorization. [18]

**Category:** Data Structures and Algorithms

[244] **viXra:1809.0204 [pdf]**
*submitted on 2018-09-10 17:59:12*

**Authors:** Yuly Shipilevsky

**Comments:** 20 Pages.

We develop two different polynomial-time integer factorization algorithms.
We reduce integer factorization problem to equivalent problem of minimizing
a quadratic polynomial with integer coefficients over the integer points
in a quadratically constrained two-dimensional region.
Next, we reduce those minimization problem to the polynomial-time minimizing
a quadratic polynomial with integer coefficients over the integer
points in a special two-dimensional rational polyhedron.
Next, we reduce integer factorization problem to the problem of enumeration
of vertices of integer hull of a special two-dimensional rational polyhedron,
solvable in time polynomial by Hartmann's algorithm.
Finally, as we show that there exists an NP-hard minimization problem,
equivalent to the original minimization problem, we conclude that P = NP.

**Category:** Data Structures and Algorithms

[243] **viXra:1809.0070 [pdf]**
*submitted on 2018-09-05 07:47:16*

**Authors:** Shravan Mohan

**Comments:** 10 Pages.

This preliminary note presents a heuristic for determining rank constrained solutions to
linear matrix equations (LME). The method proposed here is based on minimizing a non-
convex quadratic functional, which will hence-forth be termed as the Low-Rank-Functional
(LRF). Although this method lacks a formal proof/comprehensive analysis, for example in
terms of a probabilistic guarantee for converging to a solution, the proposed idea is intuitive
and has been seen to perform well in simulations. To that end, many numerical examples are
provided to corroborate the idea.

**Category:** Data Structures and Algorithms

[242] **viXra:1808.0651 [pdf]**
*submitted on 2018-08-29 08:12:31*

**Authors:** John R. Berryhill

**Comments:** 6 Pages. License Creative Commons 4.0

Historically as well as mathematically, the octonions were derived from the quaternions, and the quaternions from the complex numbers. A proper C++ implementation of these numerical types should reflect these relationships. This brief note describes how the author's previously published C++ Quaternion class serves as the natural foundation for a C++ Octonion class.

**Category:** Data Structures and Algorithms

[241] **viXra:1808.0286 [pdf]**
*submitted on 2018-08-19 22:31:41*

**Authors:** Terence Chi-Shen Tao

**Comments:** 7 Pages.

According to the Green-Tao theorem that a small number of sequences contains an isoquant sequence of arbitrary length
The isometric sequence is infinite
And in such a structure, p = np

**Category:** Data Structures and Algorithms

[240] **viXra:1808.0143 [pdf]**
*submitted on 2018-08-12 07:01:09*

**Authors:** 문예강

**Comments:** 5 Pages.

In this article, Describe about an integer sorting algorithm that is better than radix sort and more general than counting sort.
It works like quick sort in worst case.

**Category:** Data Structures and Algorithms

[239] **viXra:1807.0507 [pdf]**
*submitted on 2018-07-29 07:51:50*

**Authors:** John Archie Gillis

**Comments:** 22 Pages.

Recursive compression of random data is generally deemed to be an impossible process that defies the laws of physics (Shannon Entropy). This paper explains why this perception is incorrect and provides a proof that explains how such a compression system may be achieved. The practicality of the method has yet to be determined.

**Category:** Data Structures and Algorithms

[238] **viXra:1807.0506 [pdf]**
*submitted on 2018-07-29 08:10:25*

**Authors:** John Archie Gillis

**Comments:** 37 Pages.

The present methods take a novel approach to solving NP-Complete problems and provide steps that a computational device and software program can follow to accurately solve NP-class problems without the use of heuristics or brute force methods.

**Category:** Data Structures and Algorithms

[237] **viXra:1807.0413 [pdf]**
*submitted on 2018-07-23 13:10:53*

**Authors:** Caesar Chad, Neo Liu, Leon Lau, Joseph Sadove

**Comments:** 34 Pages.

BITCONCH chain proposed an innovative POR (Proof Of Reputation) reputation consensus algorithm, which solved the pain point that the blockchain is difficult to maintain both high throughput and decentralization. Based on social graphs, BITCONCH Chain mathematically models social, time, and contribution activities to build a decentralized reputation system. Each user has the opportunity to establish a high reputation value. The higher the user's reputation, the lower the transaction cost (or even free). The more opportunities that are selected as trust nodes to participate in the consensus, the greater the benefits. High-reputation users are defined as “mutual trust nodes”, and small micro-transactions will start “payment channels” for high-speed offline transactions.
The reputation system and system incentive system will effectively promote the continued enthusiasm of business developers and ordinary users, and contribute to the construction of the business ecosystem. Business developers with traffic are more likely to get high reputation values, and the chances of being elected to a trusted full node are higher. Ordinary users can increase reputation by actively engaging in social interactions and actively using business applications in the ecosystem, increasing the chances of being selected as trusted light nodes.
The Bitconch chain uses a DAG directed acyclic graph data structure to maintain the system's positive scalability. Support smartphone light node client to resist the decentralization of the system and maintain dispersion. Zero-knowledge verification, latticed data storage, quantum-level encryption algorithms, and improved BVM virtual machines make Bitconch chain more reliable and provide a friendly DApp and sidechain development environment to meet certain applications. Technical requirements for large file storage, low transaction costs, user information protection, sidechain and smart contract iterations, and bug fixes.
BITCONCH chain is a decentralized distributed network with no block and no chain, which solves two difficulties in the application of blockchain: scalability and decentralization. Bitconch chain, which can be applied to the commercial application needs of users above 10 million, is the most feasible blockchain ecosystem for high-frequency small micro-transactions and social applications.

**Category:** Data Structures and Algorithms

[236] **viXra:1807.0269 [pdf]**
*submitted on 2018-07-16 11:19:08*

**Authors:** George Rajna

**Comments:** 53 Pages.

Cryptography is a science of data encryption providing its confidentiality and integrity. [33] Researchers at the University of Sheffield have solved a key puzzle in quantum physics that could help to make data transfer totally secure. [32] "The realization of such all-optical single-photon devices will be a large step towards deterministic multi-mode entanglement generation as well as high-fidelity photonic quantum gates that are crucial for all-optical quantum information processing," says Tanji-Suzuki. [31] Researchers at ETH have now used attosecond laser pulses to measure the time evolution of this effect in molecules. [30] A new benchmark quantum chemical calculation of C2, Si2, and their hydrides reveals a qualitative difference in the topologies of core electron orbitals of organic molecules and their silicon analogues. [29] A University of Central Florida team has designed a nanostructured optical sensor that for the first time can efficiently detect molecular chirality—a property of molecular spatial twist that defines its biochemical properties. [28] UCLA scientists and engineers have developed a new process for assembling semiconductor devices. [27] A new experiment that tests the limit of how large an object can be before it ceases to behave quantum mechanically has been proposed by physicists in the UK and India. [26] Phonons are discrete units of vibrational energy predicted by quantum mechanics that correspond to collective oscillations of atoms inside a molecule or a crystal. [25] This achievement is considered as an important landmark for the realization of practical application of photon upconversion technology. [24]

**Category:** Data Structures and Algorithms

[235] **viXra:1807.0090 [pdf]**
*submitted on 2018-07-03 11:17:42*

**Authors:** Pedram Ahmadi

**Comments:** 121 Pages.

Today Designing efficient interfaces plays an important role in world wide web. People are highly attracted to websites that gives them more useful information at lowest time intervals. Websites always have a lack of enough strategies to keep users involved and satisfied. Now user experience design comes up to mind to solve these difficulties with new ideas and practices. The UX Design uses usability and accessibility methods to improve the interaction between users and websites. This thesis focuses on web navigation types to make them more appropriate in the way of providing useful contents.

**Category:** Data Structures and Algorithms

[234] **viXra:1807.0026 [pdf]**
*submitted on 2018-07-02 02:25:42*

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 40 Pages. Meu trabalho de Métodos em Pesquisa Operacional (PM015), IMECC-UNICAMP.

Usando um novo conceito de linguagem variável, já provei anteriormente que P≠NP, mas tal prova não utilizou nenhum dos problemas clássicos conhecidos como NP-completos, a exemplo de SAT (satisfatibilidade, satisfiability), caixeiro-viajante (travelling-salesman), soma de subconjuntos (subset-sum), da mochila (knapsack), programação linear inteira (integer linear programming), etc. Tal prova não implica que sendo P≠NP então devemos ter NP-completo ∉P, ou seja, os mencionados famosos problemas difíceis podem ainda ser resolvidos em tempo polinomial, sem precisar encerrar a pesquisa nesta direção. Tal como ocorre com o método simplex, que pode resolver em tempo polinomial a grande maioria dos problemas de programação linear, também é possível resolver SAT em tempo polinomial na maioria das vezes, que é o que eu mostro neste trabalho.

**Category:** Data Structures and Algorithms

[233] **viXra:1806.0225 [pdf]**
*submitted on 2018-06-19 06:33:05*

**Authors:** Robert DiGregorio

**Comments:** 2 Pages.

A problem exists that’s hard to solve but easy to verify a solution for.

**Category:** Data Structures and Algorithms

[232] **viXra:1805.0502 [pdf]**
*submitted on 2018-05-29 04:16:47*

**Authors:** Babak Hosseini, Barbara Hammer

**Comments:** 4 Pages. Pre-print introduction for a section of recently submitted article, as provided by the authors.

We propose the Non-negative Quadratic Pursuit (NQP) algorithm to approximately minimize a quadratic function in the presence of the $l0$-norm constraint. It is a quadratic generalization of matching pursuit method which is reformulated in a non-negative framework. Although the optimization problem is NP-hard, NQP provides an approximate solution to the problem which is locally optimal, but acceptable in the general literature.
In this document, we explain the algorithm's exact steps along with its convergence proof and complexity analysis.

**Category:** Data Structures and Algorithms

[231] **viXra:1805.0399 [pdf]**
*submitted on 2018-05-21 20:28:48*

**Authors:** Yuly Shipilevsky

**Comments:** 18 Pages.

We reduce integer factorization problem to the equivalent problem of minimizing
a quadratic polynomial with integer coefficients over the integer
points in a quadratically constrained two-dimensional region.
Next, we reduce integer factorization problem to the problem of enumeration
of vertices of integer hull of a special two-dimensional rational polyhedron,
solvable in time polynomial by Hartmann's algorithm.
Finally, as we show that there exists an NP-hard minimization problem,
equivalent to the original minimization problem, we conclude that P = NP.

**Category:** Data Structures and Algorithms

[230] **viXra:1805.0248 [pdf]**
*submitted on 2018-05-12 21:38:04*

**Authors:** Bai Yang

**Comments:** 26 Pages.

SOA (Service Oriented Architecture) and micro SOA (Micro Service) have the advantages of high cohesion and low coupling, but at the same time they also bring complicated implementation, maintenance, high network load, and weak consistency. At the same time, they also increase product development and operation costs. This article attempts to use an improved approach by a kind of plug-in isolation mechanism that avoids the above issues as much as possible while preserving the benefits of SOA.
In addition, this paper also proposes a new strong consistent distributed coordination algorithm for improving the low performance and high overhead (at least three network broadcasts and multiple disk I/O requests per request) problem of existing Paxos/Raft algorithms. This algorithm, at the expense of data reliability, completely eliminates the above overhead and provides the same level of strong agreement and high availability guarantees as the Paxos/Raft algorithm.

**Category:** Data Structures and Algorithms

[229] **viXra:1805.0131 [pdf]**
*submitted on 2018-05-06 07:42:44*

**Authors:** IlNam Ri, SongIl Choe, Hun Kim

**Comments:** 11 Pages.

In recent years, with the rapid development of cloud computing and IoT, the demand for big data has increased and the need for large data center and enterprise data center has been actively promoted. (1,3)
In this paper, a system design method that integrates and manages various information systems in the data centers of enterprise units is dealt with.
Since the production facilities of medium-scale units are managed by various detention facilities and control devices, an integrated monitoring system should be established to manage them collectively. (2)
Therefore, the paper suggests a standard design for proposing an integrated model face-to-face configuration of various facilities to be managed in enterprise units and an integrated monitoring system for environmental facilities, do.
And we try to evaluate the effectiveness of the system by analyzing the failure information transmission time of the integrated monitoring system.

**Category:** Data Structures and Algorithms

[228] **viXra:1805.0038 [pdf]**
*submitted on 2018-05-02 00:18:33*

**Authors:** IlNam Ri, SongIl Choe, Hun Kim

**Comments:** 10 Pages.

Ajax (Asynchronos Javascript And XML), one of the world's most widely used Web 2.0
technologies, is devoid of the traditional Web page approach.(1) This technology is becoming an
indispensable element in Web apps as it supports asynchronous communication that allows the user to
proceed with the conversation.(3,4)
Today 's reality is getting closer to the virtual reality by the dissemination of intelligent devices, the new
Internet of Things, cloud computing and the development of information society.
In the field of business services, we also need to improve the size and service quality of our web apps, and
Ajax technology is constantly expanding.(5)
In the fields of stocks, finance, auctions, etc. that deal with large-scale, real-time data, it is important for
business service providers to transmit information to users as soon as possible.
This Paper describes one way of using Ajax components to realize asynchronous communication of Web
service providers on the Internet.
Ajax components consist of an Ajax core that supports Epoll and an Ajax library that supports asynchronous communication, and provides an application interface to define and implement various push functions.(2)Web service applications developed using Ajax components can provide various push services by using
asynchronous communication with client by using Epoll method.

**Category:** Data Structures and Algorithms

[227] **viXra:1804.0299 [pdf]**
*submitted on 2018-04-22 08:32:08*

**Authors:** George Rajna

**Comments:** 48 Pages.

Scientists at the Max Planck Institute for Brain Research in Frankfurt have now shown how the new model can be used to investigate multiple properties in parallel. [28] Scientists at the Department of Energy's Oak Ridge National Laboratory are conducting fundamental physics research that will lead to more control over mercurial quantum systems and materials. [27] Physicists in Italy have designed a " quantum battery " that they say could be built using today's solid-state technology. [26] Researches of scientists from South Ural State University are implemented within this area. [25] Following three years of extensive research, Hebrew University of Jerusalem (HU) physicist Dr. Uriel Levy and his team have created technology that will enable computers and all optic communication devices to run 100 times faster through terahertz microchips. [24] When the energy efficiency of electronics poses a challenge, magnetic materials may have a solution. [23] An exotic state of matter that is dazzling scientists with its electrical properties, can also exhibit unusual optical properties, as shown in a theoretical study by researchers at A*STAR. [22] The breakthrough was made in the lab of Andrea Alù, director of the ASRC's Photonics Initiative. Alù and his colleagues from The City College of New York, University of Texas at Austin and Tel Aviv University were inspired by the seminal work of three British researchers who won the 2016 Noble Prize in Physics for their work, which teased out that particular properties of matter (such as electrical conductivity) can be preserved in certain materials despite continuous changes in the matter's form or shape. [21] Researchers at the University of Illinois at Urbana-Champaign have developed a new technology for switching heat flows 'on' or 'off'. [20] Thermoelectric materials can use thermal differences to generate electricity. Now there is an inexpensive and environmentally friendly way of producing them with the simplest tools: a pencil, photocopy paper, and conductive paint. [19] A team of researchers with the University of California and SRI International has developed a new type of cooling device that is both portable and efficient. [18]

**Category:** Data Structures and Algorithms

[226] **viXra:1804.0076 [pdf]**
*submitted on 2018-04-05 21:48:59*

**Authors:** Yuly Shipilevsky

**Comments:** 17 Pages.

We reduce integer factorization problem to the equivalent problem of minimizing
a quadratic polynomial with integer coefficients over the integer
points in a quadratically constrained two-dimensional region.
Next, we reduce integer factorization problem to the problem of enumeration
of vertices of integer hull of a special two-dimensional rational polyhedron,
solvable in time polynomial by Hartmann's algorithm.
Finally, as we show that there exists an NP-hard minimization problem,
equivalent to the original minimization problem, we conclude that P = NP.

**Category:** Data Structures and Algorithms

[225] **viXra:1804.0062 [pdf]**
*submitted on 2018-04-05 04:11:14*

**Authors:** Stefan Ćertić

**Comments:** 14 Pages. Keywords: internet, 2FA, data security, attacks, breaches.

Corporative giants of the internet, such as Google, Facebook, Various Banks have being using
the two-factor authentication technique to ensure security to its users. Although, this companies don’t make this kind operations by themselves, they hire third part companies to do so, integrating the API products for onwards delivery. Because of this, technique have serious breaches that can be explored by a ill-intentioned company. The third part companies stays between the client and the website being in a privileged place to attack any unsuspecting victim.

**Category:** Data Structures and Algorithms

[224] **viXra:1803.0673 [pdf]**
*submitted on 2018-03-26 09:19:32*

**Authors:** Song−Il Choe, Il−Nam Li, Chang−Su Paek, Jun−Hyok Choe, Su−Bom Yun

**Comments:** 18 Pages.

Abstract-Task scheduling is one of the most challenging aspects in cloud computing nowadays,
which plays an important role to improve the overall performance and services of the cloud such
as response time, cost, makespan, throughput etc. Recently, a cloud task scheduling algorithm
based on the Symbiotic Organisms Search (SOS) not only have fewer specific parameters, but also
take a little time complexity. Symbiotic Organism Search (SOS) is a newly developed metaheuristic
optimization technique for solving numerical optimization problems. In this paper, the basic
SOS algorithm is reduced and a chaotic local search(CLS) is integrated into the reduced SOS to
improve the convergence rate of the basic SOS algorithm. Also, Simulated Annealing (SA) is
combined in order to asist the SOS in avoiding being trapped into local minimum. The performance
of the proposed SA-CLS-SOS algorithm is evaluated by extensive simulation using MATLAB simulation
framework and compared with SOS, SA-SOS and CLS-SOS. Results of simulation showed that improved
hybrid SOS performs better than SOS, SA-SOS and CLS-SOS in terms of convergence speed and makespan
time.

**Category:** Data Structures and Algorithms

[223] **viXra:1803.0173 [pdf]**
*submitted on 2018-03-12 09:00:13*

**Authors:** George Rajna

**Comments:** 67 Pages.

Researchers have discovered that input-output maps, which are widely used throughout science and engineering to model systems ranging from physics to finance, are strongly biased toward producing simple outputs. [38] A QEG team has provided unprecedented visibility into the spread of information in large quantum mechanical systems, via a novel measurement methodology and metric described in a new article in Physics Review Letters. [37] Researchers from Würzburg and London have succeeded in controlling the coupling of light and matter at room temperature. [36] Researchers have, for the first time, integrated two technologies widely used in applications such as optical communications, bio-imaging and Light Detection and Ranging (LIDAR) systems that scan the surroundings of self-driving cars and trucks. [35] The unique platform, which is referred as a 4-D microscope, combines the sensitivity and high time-resolution of phase imaging with the specificity and high spatial resolution of fluorescence microscopy. [34] The experiment relied on a soliton frequency comb generated in a chip-based optical microresonator made from silicon nitride. [33] This scientific achievement toward more precise control and monitoring of light is highly interesting for miniaturizing optical devices for sensing and signal processing. [32] It may seem like such optical behavior would require bending the rules of physics, but in fact, scientists at MIT, Harvard University, and elsewhere have now demonstrated that photons can indeed be made to interact-an accomplishment that could open a path toward using photons in quantum computing, if not in light sabers. [31] Optical highways for light are at the heart of modern communications. But when it comes to guiding individual blips of light called photons, reliable transit is far less common. [30] Theoretical physicists propose to use negative interference to control heat flow in quantum devices. [29] Particle physicists are studying ways to harness the power of the quantum realm to further their research. [28]

**Category:** Data Structures and Algorithms

[222] **viXra:1802.0337 [pdf]**
*submitted on 2018-02-24 01:14:54*

**Authors:** Robert DiGregorio

**Comments:** 2 Pages.

Using a new technique called the power key, it’s possible to imply P ≠ NP using a proof by logical contradiction.

**Category:** Data Structures and Algorithms

[221] **viXra:1802.0336 [pdf]**
*submitted on 2018-02-24 03:08:38*

**Authors:** Nicolas Bourbaki, Jr

**Comments:** 1 Page.

We prove that P != NP using a simple and elegant method.

**Category:** Data Structures and Algorithms

[220] **viXra:1802.0118 [pdf]**
*submitted on 2018-02-10 16:11:01*

**Authors:** Szostek Roman

**Comments:** 24 Pages. New system (algorithm) settlement of sports competitions called R-Sport (in Polish).

Celem rozgrywek sportowych jest wyłonienie spośród grupy drużyn, bądź zawodników, drużyny najlepszej, czyli mistrza. Dlatego pomiędzy poszczególnymi drużynami muszą zostać rozegrane mecze. O tym, kto zostanie mistrzem decydują wyniki wszystkich spotkań. Zasady obowiązujące w trakcie sezonu tworzą System Rozgrywek Sportowych.
W dokumencie tym został opisany nowy System Rozgrywek Sportowych. System ten pozwala na sprawiedliwe i efektywne wyłonienie zwycięzcy całego sezonu. Posiada on zalety, których nie posiadają inne, znane i stosowane obecnie Systemy Rozgrywek Sportowych.
R-Sport jest Systemem Rozgrywek Sportowych, który pozwala przeprowadzić rozgrywki ligowe na wiele sposobów.

**Category:** Data Structures and Algorithms

[219] **viXra:1802.0045 [pdf]**
*submitted on 2018-02-04 12:01:59*

**Authors:** Bebereche Bogdan-Ionut

**Comments:** 1 Page.

.

**Category:** Data Structures and Algorithms

[218] **viXra:1801.0334 [pdf]**
*submitted on 2018-01-25 10:09:43*

**Authors:** George Rajna

**Comments:** 54 Pages.

As cloud storage becomes more common, data security is an increasing concern. [34] Scientists of the National Research Nuclear University MEPhI (Russia) have proposed a scheme for optical encoding of information based on the formation of wave fronts, and which works with spatially incoherent illumination. [33] A joint China-Austria team has performed quantum key distribution between the quantum-science satellite Micius and multiple ground stations located in Xinglong (near Beijing), Nanshan (near Urumqi), and Graz (near Vienna). [32] In the race to build a computer that mimics the massive computational power of the human brain, researchers are increasingly turning to memristors, which can vary their electrical resistance based on the memory of past activity. [31] Engineers worldwide have been developing alternative ways to provide greater memory storage capacity on even smaller computer chips. Previous research into two-dimensional atomic sheets for memory storage has failed to uncover their potential— until now. [30] Scientists used spiraling X-rays at the Lab) to observe, for the first time, a property that gives handedness to swirling electric patterns – dubbed polar vortices – in a synthetically layered material. [28] To build tomorrow's quantum computers, some researchers are turning to dark excitons, which are bound pairs of an electron and the absence of an electron called a hole. [27] Concerning the development of quantum memories for the realization of global quantum networks, scientists of the Quantum Dynamics Division led by Professor Gerhard Rempe at the Max Planck Institute of Quantum Optics (MPQ) have now achieved a major breakthrough: they demonstrated the long-lived storage of a photonic qubit on a single atom trapped in an optical resonator. [26] Achieving strong light-matter interaction at the quantum level has always been a central task in quantum physics since the emergence of quantum information and quantum control. [25]

**Category:** Data Structures and Algorithms

[217] **viXra:1801.0279 [pdf]**
*submitted on 2018-01-22 08:16:07*

**Authors:** George Rajna

**Comments:** 26 Pages.

Behind every self-driving car, self-learning robot and smart building hides a variety of advanced algorithms that control learning and decision making. [17] Quantum computers can be made to utilize effects such as quantum coherence and entanglement to accelerate machine learning. [16] Neural networks learn how to carry out certain tasks by analyzing large amounts of data displayed to them. [15] Who is the better experimentalist, a human or a robot? When it comes to exploring synthetic and crystallization conditions for inorganic gigantic molecules, actively learning machines are clearly ahead, as demonstrated by British Scientists in an experiment with polyoxometalates published in the journal Angewandte Chemie. [14] Machine learning algorithms are designed to improve as they encounter more data, making them a versatile technology for understanding large sets of photos such as those accessible from Google Images. Elizabeth Holm, professor of materials science and engineering at Carnegie Mellon University, is leveraging this technology to better understand the enormous number of research images accumulated in the field of materials science. [13] With the help of artificial intelligence, chemists from the University of Basel in Switzerland have computed the characteristics of about two million crystals made up of four chemical elements. The researchers were able to identify 90 previously unknown thermodynamically stable crystals that can be regarded as new materials. [12] The artificial intelligence system's ability to set itself up quickly every morning and compensate for any overnight fluctuations would make this fragile technology much more useful for field measurements, said co-lead researcher Dr Michael Hush from UNSW ADFA. [11] Quantum physicist Mario Krenn and his colleagues in the group of Anton Zeilinger from the Faculty of Physics at the University of Vienna and the Austrian Academy of Sciences have developed an algorithm which designs new useful quantum experiments. As the computer does not rely on human intuition, it finds novel unfamiliar solutions. [10] Researchers at the University of Chicago's Institute for Molecular Engineering and the University of Konstanz have demonstrated the ability to generate a quantum logic operation, or rotation of the qubit, that-surprisingly—is intrinsically resilient to noise as well as to variations in the strength or duration of the control. Their achievement is based on a geometric concept known as the Berry phase and is implemented through entirely optical means within a single electronic spin in diamond. [9]

**Category:** Data Structures and Algorithms

[216] **viXra:1801.0274 [pdf]**
*submitted on 2018-01-21 13:58:08*

**Authors:** Zhengjun Cao, Jeffrey Uhlmann, Lihua Liu

**Comments:** 5 Pages.

We remark that Deutsch-Jozsa algorithm has confused two unitary transformations: one is performed on a pure state, the other is performed on a superposition. In the past decades, no constructive specifications on the essential unitary operator performed on the superposition have been found. We think the Deutsch-Jozsa algorithm needs more constructive specifications so as to check its correctness.

**Category:** Data Structures and Algorithms

[215] **viXra:1801.0100 [pdf]**
*submitted on 2018-01-08 22:06:09*

**Authors:** Yuly Shipilevsky

**Comments:** 12 Pages.

We reduce integer factorization problem to the NP-hard problem of minimizing
a quadratic polynomial with integer coefficients over the integer points
in a quadratically constrained two-dimensional region.
Next, we reduce integer factorization problem to the problem of enumeration
of vertices of integer hull of a special two-dimensional rational polyhedron,
solvable in time polynomial by Hartmann's algorithm.
Finally, as we find a polynomial-time algorithm to solve an NP-hard problem,
we conclude that P = NP

**Category:** Data Structures and Algorithms

[214] **viXra:1712.0587 [pdf]**
*submitted on 2017-12-23 16:09:27*

**Authors:** Brian Beckman

**Comments:** 31 Pages. Creative Commons 4.0 license: https://creativecommons.org/licenses/by/4.0/

Kalman Folding 5 presents an Extended Kalman Filter in Mathematica. Python is much more accessible to average practitioners. In this follow-up article, we write a very general, foldable EKF in Python, verify it against Mathematica using sympy, Python's package for symbolic mathematics. We apply it to a spinning dashpot and demonstrate both state estimation and system identification from observing only one angle over time. It is remarkable that a complete dynamical description of eight states and parameters can be recovered from measurements of a single, scalar value.

**Category:** Data Structures and Algorithms

[213] **viXra:1712.0528 [pdf]**
*submitted on 2017-12-21 01:38:25*

**Authors:** Sanjeev Saxena

**Comments:** 11 Pages.

An extremely simple, description of Karmarkar's algorithm with very few technical terms is given.

**Category:** Data Structures and Algorithms

[212] **viXra:1712.0510 [pdf]**
*submitted on 2017-12-20 04:40:22*

**Authors:** Mai Ben-Adar Bessos, Amir Herzberg

**Comments:** 18 Pages.

We investigate a new threat: networks of stealthy
routers (S-Routers), communicating across a restricted area. The ‘classical’ approach of transmission-detection by triangulation fails, since S-Routers use short-range, low-energy communication, detectable only by nearby devices.
We investigate algorithms to intercept S-Routers, using one or more mobile devices, called Interceptors. Given a source of
communication, Interceptors find the destination, by intercepting packet-relaying by S-Routers along the path. We evaluate the algorithms analytically and experimentally (simulations), including against a parametric, optimized S-Routers algorithm. Our main result is a (centralized) Interceptors algorithm bounding the outcome to O(Nlog^2(N), where N is the number of S-Routers. We later improve the bound to O(Nlog(N)log(log(N))), for the case where the transmission schedule of the S-Routers is continuous.

**Category:** Data Structures and Algorithms

[211] **viXra:1712.0407 [pdf]**
*submitted on 2017-12-13 01:25:52*

**Authors:** Sanjeev Saxena

**Comments:** 8 Pages.

In this paper, ellipsoid method for linear programming is derived
using only minimal knowledge of algebra and matrices.
Unfortunately, most authors first describe the algorithm, then
later prove its correctness, which requires a good knowledge of
linear algebra.

**Category:** Data Structures and Algorithms

[210] **viXra:1712.0374 [pdf]**
*submitted on 2017-12-09 10:21:20*

**Authors:** Steven David Young

**Comments:** 16 Pages. A proposal to Improve Tor Hidden Services

A system that incorporates distributed means of communication as well as steganographic storage techniques while remaining as similar as possible to an existing trusted platform such as Tor could provide a model for a next generation anonymous communication system that is less susceptible to common vulnerabilities, such as an adversarial Global Network Observer.

**Category:** Data Structures and Algorithms

[209] **viXra:1712.0137 [pdf]**
*submitted on 2017-12-05 14:10:05*

**Authors:** M. J. Dudziak, M. Tsepeleva

**Comments:** 6 Pages. submitted to CoDIT 2018 *Theassaloniki, Greece, April, 2018)

NeoPlexus is a newly established permanent program of international collaborative scientific research and application development. It is focused upon the design, construction and application of a new architecture and family of computing machines that are adept at solving problems of control involving extreme complex systems (XCS) for which conventional numerical computing methods and machines are fundamentally inadequate. The GCM involves a different foundation of computing from classical Turing Machines including qubit-based quantum computers and it incorporates geometrical and specifically topological dynamics. The target for implementation is to construct molecular-scale platform using protein-polymer conjugates and MEMS-type microfluidics.

**Category:** Data Structures and Algorithms

[208] **viXra:1712.0081 [pdf]**
*submitted on 2017-12-04 07:40:22*

**Authors:** Timothy W. Jones

**Comments:** 19 Pages.

Using simple arithmetic of the prime numbers, a model of nutritional content of food need and content is created. This model allows for the dynamics of natural languages to be specified as a game theoretical construct. The goal of this model is to evolve human culture.

**Category:** Data Structures and Algorithms

[207] **viXra:1711.0118 [pdf]**
*submitted on 2017-11-02 14:57:59*

**Authors:** Sathish Kumar Vijayakumar

**Comments:** 10 Pages.

Sorting is one of the most researched topics of Computer Science and it is one of the essential operations across computing devices. Given the ubiquitous presence of computers, sorting algorithms utilize significant percentage of computation times across the globe. In this paper we present a sorting algorithm with worst case time complexity of O(n).

**Category:** Data Structures and Algorithms

[206] **viXra:1710.0266 [pdf]**
*submitted on 2017-10-23 06:45:18*

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 8 Pages. In english and portuguese. A better translation of the my article published at Transactions on Mathematics (TM) Vol. 3, No. 1, January 2017, pp. 34-37.

An original proof of P is not equal to NP.

**Category:** Data Structures and Algorithms

[205] **viXra:1710.0201 [pdf]**
*submitted on 2017-10-15 11:44:37*

**Authors:** Shivam Bansal

**Comments:** 8 Pages.

There are a lot of educational videos online which are in English and inaccessible to 80% population of the world. This paper presents a process to translate a video into another language by creating its transcript and using TTS to produce synthesized fragments of speech. It introduces an algorithm which synthesyses intelligent, synchronized, and easily understandable audio by combining those fragments of speech. This algorithm is also compared to an algorithm from another research paper on the basis of performance.

**Category:** Data Structures and Algorithms

[204] **viXra:1710.0104 [pdf]**
*submitted on 2017-10-09 12:57:09*

**Authors:** Yuly Shipilevsky

**Comments:** 11 Pages.

polynomial-time algorithm for integer factorization, wherein integer factorization
reduced to a polynomial-time integer minimization problem over the
integer points in a two-dimensional rational polyhedron with conclusion that
P = NP and a polynomial-time algorithm for integer factorization using enumeration
of vertices of integer hull of those two-dimensional rational polyhedron

**Category:** Data Structures and Algorithms

[203] **viXra:1710.0101 [pdf]**
*submitted on 2017-10-09 16:11:25*

**Authors:** Eirini Molla, Theodoros Tzouramanis, Stefanos Gritzalis

**Comments:** 24 Pages. 37 figures, 2 tables, 60 references

Due to the increasing demand for cloud services and the threat of privacy invasion, the user is suggested to encrypt the data before it is outsourced to the remote server. The safe storage and efficient retrieval of d-dimensional data on an untrusted server has therefore crucial importance. The paper proposes a new encryption model which offers spatial order-preservation for d-dimensional data (SOPE model). The paper studies the operations for the construction of the encrypted database and suggests algorithms that exploit unique properties that this new model offers for the efficient execution of a whole range of well-known queries over the encrypted d-dimensional data. The new model utilizes wellknown database indices, such as the B+-tree and the R-tree, as backbone structures in their traditional form, as it suggests no modifications to them for loading the data and for the efficient execution of the supporting query algorithms. An extensive experimental study that is also presented in the paper indicates the effectiveness and practicability of the proposed encryption model for real-life d-dimensional data applications.

**Category:** Data Structures and Algorithms

[202] **viXra:1709.0006 [pdf]**
*submitted on 2017-09-01 10:34:42*

**Authors:** George Rajna

**Comments:** 31 Pages.

A group of scientists from the Max Planck Institutes in Halle and Dresden have discovered a new kind of magnetic nano-object in a novel material that could serve as a magnetic bit with cloaking properties to make a magnetic disk drive with no moving parts - a Racetrack Memory - a reality in the near future. [19]
Jarvis Loh, Gan Chee Kwan and Khoo Khoong Hong from the Agency for Science, Technology and Research (A*STAR) Institute of High Performance Computing, Singapore, have modeled these minute spin spirals in nanoscopic crystal layers. [18]
Some of the world's leading technology companies are trying to build massive quantum computers that rely on materials super-cooled to near absolute zero, the theoretical temperature at which atoms would cease to move. [17]
While technologies that currently run on classical computers, such as Watson, can help find patterns and insights buried in vast amounts of existing data, quantum computers will deliver solutions to important problems where patterns cannot be seen because the data doesn't exist and the possibilities that you need to explore to get to the answer are too enormous to ever be processed by classical computers. [16]
Through a collaboration between the University of Calgary, The City of Calgary and researchers in the United States, a group of physicists led by Wolfgang Tittel, professor in the Department of Physics and Astronomy at the University of Calgary have successfully demonstrated teleportation of a photon (an elementary particle of light) over a straight-line distance of six kilometers using The City of Calgary's fiber optic cable infrastructure. [15]
Optical quantum technologies are based on the interactions of atoms and photons at the single-particle level, and so require sources of single photons that are highly indistinguishable – that is, as identical as possible. Current single-photon sources using semiconductor quantum dots inserted into photonic structures produce photons that are ultrabright but have limited indistinguishability due to charge noise, which results in a fluctuating electric field. [14]
A method to produce significant amounts of semiconducting nanoparticles for light-emitting displays, sensors, solar panels and biomedical applications has gained momentum with a demonstration by researchers at the Department of Energy's Oak Ridge National Laboratory. [13]
A source of single photons that meets three important criteria for use in quantum-information systems has been unveiled in China by an international team of physicists. Based on a quantum dot, the device is an efficient source of photons that emerge as solo particles that are indistinguishable from each other. The researchers are now trying to use the source to create a quantum computer based on "boson sampling". [11]
With the help of a semiconductor quantum dot, physicists at the University of Basel have developed a new type of light source that emits single photons. For the first time, the researchers have managed to create a stream of identical photons. [10]

**Category:** Data Structures and Algorithms

[201] **viXra:1708.0473 [pdf]**
*submitted on 2017-08-30 20:26:27*

**Authors:** Yuly Shipilevsky

**Comments:** 10 Pages.

A polynomial-time algorithm for integer factorization, wherein integer factorization
reduced to a polynomial-time integer minimization problem over the
integer points in a two-dimensional rational polyhedron with conclusion that
P = NP

**Category:** Data Structures and Algorithms

[200] **viXra:1708.0373 [pdf]**
*submitted on 2017-08-26 08:20:39*

**Authors:** Wolfgang Fischl, Georg Gottlob, Reinhard Pichler

**Comments:** 16 Pages.

The authors have recently shown that recognizing low fractional hypertree-width (fhw) is NP-complete
in the general case and that the problem becomes tractable if the hypergraphs under consideration have degree and intersection width bounded by a constant, i.e., every vertex is contained in only constantly many different edges and the intersection of two edges contains only constantly many vertices. In this article, we show that bounded degree alone suffices to ensure tractability.

**Category:** Data Structures and Algorithms

[199] **viXra:1708.0117 [pdf]**
*submitted on 2017-08-10 13:08:30*

**Authors:** George Rajna

**Comments:** 33 Pages.

Concepts for information storage and logical processing based on magnetic domain walls have great potential for implementation in future information and communications technologies." [21] Research at the National Institute of Standards and Technology (NIST) suggests it also may be true in the microscopic world of computer memory, where a team of scientists may have found that subtlety solves some of the issues with a novel memory switch. [20] Los Alamos National Laboratory has produced the first known material capable of single-photon emission at room temperature and at telecommunications wavelengths. [19] In their paper published in Nature, the team demonstrates that photons can become an accessible and powerful quantum resource when generated in the form of colour-entangled quDits. [18] But in the latest issue of Physical Review Letters, MIT researchers describe a new technique for enabling photon-photon interactions at room temperature, using a silicon crystal with distinctive patterns etched into it. [17] Kater Murch's group at Washington University in St. Louis has been exploring these questions with an artificial atom called a qubit. [16] Researchers have studied how light can be used to observe the quantum nature of an electronic material. [15] An international team of researchers led by the National Physical Laboratory (NPL) and the University of Bern has revealed a new way to tune the functionality of next-generation molecular electronic devices using graphene. [14] Researchers at the Department of Physics, University of Jyväskylä, Finland, have created a theory that predicts the properties of nanomagnets manipulated with electric currents. This theory is useful for future quantum technologies. [13] Quantum magnetism, in which – unlike magnetism in macroscopic-scale materials, where electron spin orientation is random – atomic spins self-organize into one-dimensional rows that can be simulated using cold atoms trapped along a physical structure that guides optical spectrum electromagnetic waves known as a photonic crystal waveguide. [12]

**Category:** Data Structures and Algorithms

[198] **viXra:1708.0034 [pdf]**
*submitted on 2017-08-04 01:51:06*

**Authors:** Nicholas R. Wright

**Comments:** 8 Pages.

We use the whole order approach to solve the problem of P versus NP. The relation of the whole order within a beautiful order is imperative to understanding the total order. We also show several techniques observed by the minimum element, we call a logical minimum. The perfect zero-knowledge technique will deliver exactly the same. We conclude with a demonstration of the halting problem.

**Category:** Data Structures and Algorithms

[197] **viXra:1707.0371 [pdf]**
*submitted on 2017-07-28 06:39:26*

**Authors:** George Rajna

**Comments:** 43 Pages.

Over millennia, nature has evolved an incredible information storage medium – DNA. It evolved to store genetic information, blueprints for building proteins, but DNA can be used for many more purposes than just that. [23] Based on early research involving the storage of movies and documents in DNA, Microsoft is developing an apparatus that uses biology to replace tape drives, researchers at the company say. [22] Our brains are often compared to computers, but in truth, the billions of cells in our bodies may be a better analogy. The squishy sacks of goop may seem a far cry from rigid chips and bundled wires, but cells are experts at taking inputs, running them through a complicated series of logic gates and producing the desired programmed output. [21] At Caltech, a group of researchers led by Assistant Professor of Bioengineering Lulu Qian is working to create circuits using not the usual silicon transistors but strands of DNA. [20] Researchers have introduced a new type of "super-resolution" microscopy and used it to discover the precise walking mechanism behind tiny structures made of DNA that could find biomedical and industrial applications. [19] Genes tell cells what to do—for example, when to repair DNA mistakes or when to die—and can be turned on or off like a light switch. Knowing which genes are switched on, or expressed, is important for the treatment and monitoring of disease. Now, for the first time, Caltech scientists have developed a simple way to visualize gene expression in cells deep inside the body using a common imaging technology. [18] Researchers at The University of Manchester have discovered that a potential new drug reduces the number of brain cells destroyed by stroke and then helps to repair the damage. [17]

**Category:** Data Structures and Algorithms

[196] **viXra:1707.0247 [pdf]**
*submitted on 2017-07-18 07:46:50*

**Authors:** A. A. Salama, Mohamed Eisa, A. E. Fawzy

**Comments:** 6 Pages.

In this paper, we propose a two-phase Content-Based Retrieval System for images embedded in the Neutrosophic domain. In this first phase, we extract a set of features to represent the content of each image in the training database. In the second phase, a similarity measurement is used to determine the distance between the image under consideration (query image), and each image in the training database, using their feature vectors constructed in the first phase. Hence, the N most similar images are retrieved.

**Category:** Data Structures and Algorithms

[195] **viXra:1707.0091 [pdf]**
*submitted on 2017-07-06 04:33:07*

**Authors:** George Rajna

**Comments:** 54 Pages.

Now, researchers at Stanford University and MIT have built a new chip to overcome this hurdle. [28]
In the quest to make computers faster and more efficient, researchers have been exploring the field of spintronics—shorthand for spin electronics—in hopes of controlling the natural spin of the electron to the benefit of electronic devices. [27]
When two researchers from the Swiss Federal Institute of Technology (ETH Zurich) announced in April that they had successfully simulated a 45-qubit quantum circuit, the science community took notice: it was the largest ever simulation of a quantum computer, and another step closer to simulating "quantum supremacy"—the point at which quantum computers become more powerful than ordinary computers. [26]
Researchers from the University of Pennsylvania, in collaboration with Johns Hopkins University and Goucher College, have discovered a new topological material which may enable fault-tolerant quantum computing. [25]
The central idea of TQC is to encode qubits into states of topological phases of matter (see Collection on Topological Phases). [24]
One promising approach to building them involves harnessing nanometer-scale atomic defects in diamond materials. [23]
Based on early research involving the storage of movies and documents in DNA, Microsoft is developing an apparatus that uses biology to replace tape drives, researchers at the company say. [22]
Our brains are often compared to computers, but in truth, the billions of cells in our bodies may be a better analogy. The squishy sacks of goop may seem a far cry from rigid chips and bundled wires, but cells are experts at taking inputs, running them through a complicated series of logic gates and producing the desired programmed output. [21]
At Caltech, a group of researchers led by Assistant Professor of Bioengineering Lulu Qian is working to create circuits using not the usual silicon transistors but strands of DNA. [20]
Researchers have introduced a new type of "super-resolution" microscopy and used it to discover the precise walking mechanism behind tiny structures made of DNA that could find biomedical and industrial applications. [19]
Genes tell cells what to do—for example, when to repair DNA mistakes or when to die—and can be turned on or off like a light switch. Knowing which genes are switched on, or expressed, is important for the treatment and monitoring of disease. Now, for the first time, Caltech scientists have developed a simple way to visualize gene expression in cells deep inside the body using a common imaging technology. [18]

**Category:** Data Structures and Algorithms

[194] **viXra:1707.0074 [pdf]**
*submitted on 2017-07-05 07:51:08*

**Authors:** Theophanes Raptis

**Comments:** 47 Pages.

We utilize a previously reported methodological framework [5], to find a general set of mappings for any satisfiability (SAT) problem to a set of arithmetized codes allowing a classification hierarchy enumerable via integer partition functions. This reveals a unique unsatisfiability criterion via the introduction of certain universal indicator functions associating the validity of any such problem with a mapping between Mersenne integers and their complements in an inclusive hierarchy of exponential intervals. Lastly, we present means to reduce the complexity of the original problem to that of a special set of binary sequences and their bit block analysis via a reduction of any expression to a type of a Sequential Dynamical System (SDS) using the technique of clause equalization. We specifically notice the apparent analogy of certain dynamical properties behind such problems with resonances and coherencies of multi-periodic systems leading to the possibility of certain fast analog or natural implementations of dedicated SAT-machines. A Matlab toolbox is also offered as additional aid in exploring certain simple examples.

**Category:** Data Structures and Algorithms

[193] **viXra:1706.0419 [pdf]**
*submitted on 2017-06-21 12:49:53*

**Authors:** George Rajna

**Comments:** 22 Pages.

Chemists at Case Western Reserve University have found a way to possibly store digital data in half the space current systems require. [12] Using lasers to make data storage faster than ever. [11] Some three-dimensional materials can exhibit exotic properties that only exist in "lower" dimensions. For example, in one-dimensional chains of atoms that emerge within a bulk sample, electrons can separate into three distinct entities, each carrying information about just one aspect of the electron's identity—spin, charge, or orbit. The spinon, the entity that carries information about electron spin, has been known to control magnetism in certain insulating materials whose electron spins can point in any direction and easily flip direction. Now, a new study just published in Science reveals that spinons are also present in a metallic material in which the orbital movement of electrons around the atomic nucleus is the driving force behind the material's strong magnetism. [10] Currently studying entanglement in condensed matter systems is of great interest. This interest stems from the fact that some behaviors of such systems can only be explained with the aid of entanglement. [9] Researchers from the Norwegian University of Science and Technology (NTNU) and the University of Cambridge in the UK have demonstrated that it is possible to directly generate an electric current in a magnetic material by rotating its magnetization. [8] This paper explains the magnetic effect of the electric current from the observed effects of the accelerating electrons, causing naturally the experienced changes of the electric field potential along the electric wire. The accelerating electrons explain not only the Maxwell Equations and the Special Relativity, but the Heisenberg Uncertainty Relation, the wave particle duality and the electron's spin also, building the bridge between the Classical and Quantum Theories. The changing acceleration of the electrons explains the created negative electric field of the magnetic induction, the changing relativistic mass and the Gravitational Force, giving a Unified Theory of the physical forces. Taking into account the Planck Distribution Law of the electromagnetic oscillators also, we can explain the electron/proton mass rate and the Weak and Strong Interactions.

**Category:** Data Structures and Algorithms

[192] **viXra:1706.0294 [pdf]**
*submitted on 2017-06-16 05:46:25*

**Authors:** Yu Yunlong, Ru Le

**Comments:** 4 Pages.

Aiming at the special circumstance in which UAVs swarm are used in the mode of battlefield extending, a message delivery scheme called AWJPMMD (ARIMA-WNN Joint Prediction Model based Message Delivery) is proposed. In this scheme, the LET (Link Expiration Time) of the center node and the proxy node is calculated by high precision GPS information, then the LET at next moment is predicted by ARIMA-WNN (Autoregressive Integrated Moving Average model - Wavelet Neural Network) Joint Prediction Model. Finally, the process of message delivery is affected by the predicted value of LET and other parameters. The target information is sent to the UAVs ground station in form of store-and-forward by the message delivery process. Simulation shows that this scheme can provide higher message delivery ratio and this scheme is more stable.

**Category:** Data Structures and Algorithms

[191] **viXra:1704.0175 [pdf]**
*submitted on 2017-04-13 07:02:31*

**Authors:** Q.P.Wimblik

**Comments:** 2 Pages.

Vertex Coloring can be reduced to a set of 2 color vertex coloring problems.
This is achieved by utilizing an ability to account for every positive integer with a unique pair of smaller integers.

**Category:** Data Structures and Algorithms

[190] **viXra:1703.0105 [pdf]**
*submitted on 2017-03-12 04:14:12*

**Authors:** Dhara Joshi1, Krishna Dalsaniya2, Chintan Patel3

**Comments:** 5 Pages.

With the fast advancement in the field of network security everything gets the chance to be possible on web. Remote user authentication is an imperative system in the networks framework to check the exactitude of remote user over the public channel. In this authentication procedure, server checks accreditation of the user that user is authentic and legal one or not. For that Server and user commonly confirm each other and make a same session key for encryption of upcoming conversations. There are two types of authentication: Single server and Multi server. To overcome the drawback of single server authentication (remembering id and pswd for accessing each of the server), the concept of Multi server comes, in which user first register with RC, and whatever servers are registerd under RC can be accessed by user by providing single id and pswd for all. Here We review US patent [US 9264425 B1] scheme which is based on Multi server authentication, we provide mathematical analysis of the same with some attacks found on it.

**Category:** Data Structures and Algorithms

[189] **viXra:1702.0321 [pdf]**
*submitted on 2017-02-26 11:24:32*

**Authors:** Michail Zak

**Comments:** 11 Pages.

The challenge of this paper is to relate quantum-inspired dynamics represented by a self- supervised system, to solutions of noncomputable problems. In the self-supervised systems, the role of actuators is played by the probability produced by the corresponding Liouville equation. Following the Madelung equation that belongs to this class, non- Newtonian properties such as randomness, entanglement, and probability interference typical for quantum systems have been described in [1]. It has been demonstrated there, that such systems exist in the mathematical world: they are presented by ODE coupled with their Liouville equation, but they belong neither to Newtonian nor to quantum physics. The central point of this paper is the application of the self-supervised systems to solve traveling salesman problem.

**Category:** Data Structures and Algorithms

[188] **viXra:1702.0261 [pdf]**
*submitted on 2017-02-20 21:15:53*

**Authors:** Michail Zak

**Comments:** 11 Pages.

The challenge of this paper is to relate quantum-inspired dynamics represented by a self-supervised system, to solutions of noncomputable problems. In the self-supervised systems, the role of actuators is played by the probability produced by the corresponding Liouville equation. Following the Madelung equation that belongs to this class, non-Newtonian properties such as randomness, entanglement, and probability interference typical for quantum systems have been described in [1]. It has been demonstrated there, that such systems exist in the mathematical world: they are presented by ODE coupled with their Liouville equation, but they belong neither to Newtonian nor to quantum physics. The central point of this paper is the application of the self-supervised systems to finding global maximum of functions that is no-where differential, but everywhere continuous (such as Weierstrass functions)

**Category:** Data Structures and Algorithms

[187] **viXra:1702.0060 [pdf]**
*submitted on 2017-02-04 06:12:29*

**Authors:** George Rajna

**Comments:** 36 Pages.

The researchers, in their paper published in Science Advances, say this freedom allows quantum computers to store many different states of the system being simulated in different superpositions, using less memory overall than in a classical computer. [26] The advancement of quantum computing faces a tremendous challenge in improving the reproducibility and robustness of quantum circuits. One of the biggest problems in this field is the presence of noise intrinsic to all these devices, the origin of which has puzzled scientists for many decades. [25] Characterising quantum channels with non-separable states of classical light the researchers demonstrate the startling result that sometimes Nature cannot tell the difference between particular types of laser beams and quantum entangled photons. [24] Physicists at Princeton University have revealed a device they've created that will allow a single electron to transfer its quantum information to a photon. [23] A strong, short light pulse can record data on a magnetic layer of yttrium iron garnet doped with Co-ions. This was discovered by researchers from Radboud University in the Netherlands and Bialystok University in Poland. The novel mechanism outperforms existing alternatives, allowing the fastest read-write magnetic recording accompanied by unprecedentedly low heat load. [22] It goes by the unwieldy acronym STT-MRAM, which stands for spin-transfer torque magnetic random access memory. [21] Memory chips are among the most basic components in computers. The random access memory is where processors temporarily store their data, which is a crucial function. Researchers from Dresden and Basel have now managed to lay the foundation for a new memory chip concept. [20] Researchers have built a record energy-efficient switch, which uses the interplay of electricity and a liquid form of light, in semiconductor microchips. The device could form the foundation of future signal processing and information technologies, making electronics even more efficient. [19] The magnetic structure of a skyrmion is symmetrical around its core; arrows indicate the direction of spin. [18]

**Category:** Data Structures and Algorithms

[186] **viXra:1701.0573 [pdf]**
*submitted on 2017-01-22 21:38:03*

**Authors:** Mildred Bennet, Timothy Sato, Frank West

**Comments:** 6 Pages.

Many end-users would agree that, had it
not been for systems, the improvement of
fiber-optic cables might never have occurred.
Given the current status of self-learning symmetries,
physicists clearly desire the deployment
of courseware, which embodies the compelling
principles of unstable operating systems.
We construct a novel methodology for
the evaluation of hash tables, which we call
MOP.

**Category:** Data Structures and Algorithms

[185] **viXra:1701.0572 [pdf]**
*submitted on 2017-01-22 21:57:46*

**Authors:** R. Salvato, G. Casey

**Comments:** 6 Pages.

Many experts would agree that, had it not
been for the study of context-free grammar,
the understanding of the UNIVAC computer
might never have occurred. This is crucial
to the success of our work. In fact, few analysts
would disagree with the visualization of
spreadsheets, which embodies the important
principles of software engineering. In order
to realize this intent, we describe new robust
modalities (Destrer), which we use to validate
that architecture and wide-area networks can
collude to realize this intent

**Category:** Data Structures and Algorithms

[184] **viXra:1701.0089 [pdf]**
*submitted on 2017-01-03 10:03:01*

**Authors:** George Rajna

**Comments:** 28 Pages.

Memory chips are among the most basic components in computers. The random access memory is where processors temporarily store their data, which is a crucial function. Researchers from Dresden and Basel have now managed to lay the foundation for a new memory chip concept. [20] Researchers have built a record energy-efficient switch, which uses the interplay of electricity and a liquid form of light, in semiconductor microchips. The device could form the foundation of future signal processing and information technologies, making electronics even more efficient. [19] The magnetic structure of a skyrmion is symmetrical around its core; arrows indicate the direction of spin. [18] According to current estimates, dozens of zettabytes of information will be stored electronically by 2020, which will rely on physical principles that facilitate the use of single atoms or molecules as basic memory cells. [17] EPFL scientists have developed a new perovskite material with unique properties that can be used to build next-generation hard drives. [16] Scientists have fabricated a superlattice of single-atom magnets on graphene with a density of 115 terabits per square inch, suggesting that the configuration could lead to next-generation storage media. [15] Now a researcher and his team at Tyndall National Institute in Cork have made a 'quantum leap' by developing a technical step that could enable the use of quantum computers sooner than expected. [14] A method to produce significant amounts of semiconducting nanoparticles for light-emitting displays, sensors, solar panels and biomedical applications has gained momentum with a demonstration by researchers at the Department of Energy's Oak Ridge National Laboratory. [13] A source of single photons that meets three important criteria for use in quantum-information systems has been unveiled in China by an international team of physicists. Based on a quantum dot, the device is an efficient source of photons that emerge as solo particles that are indistinguishable from each other. The researchers are now trying to use the source to create a quantum computer based on "boson sampling". [11] With the help of a semiconductor quantum dot, physicists at the University of Basel have developed a new type of light source that emits single photons.

**Category:** Data Structures and Algorithms

[183] **viXra:1612.0368 [pdf]**
*submitted on 2016-12-29 05:24:47*

**Authors:** Domenico Oricchio

**Comments:** 1 Page.

A server can distribute signed files using the pretty good privacy program, using a universal standard client that have known public key and known private key.

**Category:** Data Structures and Algorithms

[182] **viXra:1612.0185 [pdf]**
*submitted on 2016-12-09 20:47:27*

**Authors:** Taha Sochi

**Comments:** 17 Pages.

Area detectors are used in many scientific and technological applications such as particle and radiation physics. Thanks to the recent technological developments, the radiation sources are becoming increasingly brighter and the detectors become faster and more efficient. The result is a sharp increase in the size of data collected in a typical experiment. This situation imposes a bottleneck on data processing capabilities, and could pose a real challenge to scientific research in certain areas. This article proposes a number of simple techniques to facilitate rapid and efficient extraction of data obtained from these detectors. These techniques are successfully implemented and tested in a computer program to deal with the extraction of X-ray diffraction patterns from EDF image files obtained from CCD detectors.

**Category:** Data Structures and Algorithms

[181] **viXra:1612.0179 [pdf]**
*submitted on 2016-12-09 21:07:59*

**Authors:** Taha Sochi

**Comments:** 17 Pages.

In this article we discuss general strategies and computer algorithms to test the connectivity of unstructured networks which consist of a number of segments connected through randomly distributed nodes.

**Category:** Data Structures and Algorithms

[180] **viXra:1612.0079 [pdf]**
*submitted on 2016-12-06 17:35:29*

**Authors:** Yuly Shipilevsky

**Comments:** 9 Pages. This is a new paper and I changed the title. Thanks.

A polynomial-time algorithm for integer factorization, wherein integer factorization reduced to a polynomial-time integer minimization problem over the integer points in a two-dimensional polyhedron.

**Category:** Data Structures and Algorithms

[179] **viXra:1611.0352 [pdf]**
*submitted on 2016-11-26 05:11:34*

**Authors:** Robert Deloin

**Comments:** 16 Pages.

Collatz' conjecture (stated in 1937 by Collatz and also named Thwaites conjecture, or Syracuse, 3n+1 or oneness problem) can be described as follows:
Take any positive whole number N. If N is even, divide it by 2. If it is odd, multiply it by 3 and add 1. Repeat this process to the result over
and over again. Collatz' conjecture is the supposition that for any positive integer N, the sequence will invariably reach the value 1.
The main contribution of this paper is to present a new approach to Collatz' conjecture. The key idea of this new approach is to clearly differentiate
the role of the division by two and the role of what we will name here the jump: a = 3n + 1.
With this approach, the proof of the conjecture is given as well as generalizations for jumps of the form qn + r and for jumps being polynomials
of degree m >1.

**Category:** Data Structures and Algorithms

[178] **viXra:1611.0328 [pdf]**
*submitted on 2016-11-24 06:35:11*

**Authors:** George Rajna

**Comments:** 22 Pages.

EPFL scientists have developed a new perovskite material with unique properties that can be used to build next-generation hard drives. [16] Scientists have fabricated a superlattice of single-atom magnets on graphene with a density of 115 terabits per square inch, suggesting that the configuration could lead to next-generation storage media. [15] Now a researcher and his team at Tyndall National Institute in Cork have made a 'quantum leap' by developing a technical step that could enable the use of quantum computers sooner than expected. [14] A method to produce significant amounts of semiconducting nanoparticles for light-emitting displays, sensors, solar panels and biomedical applications has gained momentum with a demonstration by researchers at the Department of Energy's Oak Ridge National Laboratory. [13] A source of single photons that meets three important criteria for use in quantum-information systems has been unveiled in China by an international team of physicists. Based on a quantum dot, the device is an efficient source of photons that emerge as solo particles that are indistinguishable from each other. The researchers are now trying to use the source to create a quantum computer based on "boson sampling". [11] With the help of a semiconductor quantum dot, physicists at the University of Basel have developed a new type of light source that emits single photons. For the first time, the researchers have managed to create a stream of identical photons. [10] Optical photons would be ideal carriers to transfer quantum information over large distances. Researchers envisage a network where information is processed in certain nodes and transferred between them via photons. [9] While physicists are continually looking for ways to unify the theory of relativity, which describes large-scale phenomena, with quantum theory, which describes small-scale phenomena, computer scientists are searching for technologies to build the quantum computer using Quantum Information. In August 2013, the achievement of "fully deterministic" quantum teleportation, using a hybrid technique, was reported. On 29 May 2014, scientists announced a reliable way of transferring data by quantum teleportation. Quantum teleportation of data had been done before but with highly unreliable methods. The accelerating electrons explain not only the Maxwell Equations and the Special Relativity, but the Heisenberg Uncertainty Relation, the Wave-Particle Duality and the electron's spin also, building the Bridge between the Classical and Quantum Theories. The Planck Distribution Law of the electromagnetic oscillators explains the electron/proton mass rate and the Weak and Strong Interactions by the diffraction patterns. The Weak Interaction changes the diffraction patterns by moving the electric charge from one side to the other side of the diffraction pattern, which violates the CP and Time reversal symmetry. The diffraction patterns and the locality of the self-maintaining electromagnetic potential explains also the Quantum Entanglement, giving it as a natural part of the Relativistic Quantum Theory and making possible to build the Quantum Computer with the help of Quantum Information.

**Category:** Data Structures and Algorithms

[177] **viXra:1611.0088 [pdf]**
*submitted on 2016-11-07 07:25:12*

**Authors:** George Rajna

**Comments:** 29 Pages.

Dynamic programming is a technique that can yield relatively efficient solutions to computational problems in economics, genomic analysis, and other fields. But adapting it to computer chips with multiple "cores," or processing units, requires a level of programming expertise that few economists and biologists have. [16] Researchers at Lancaster University's Data Science Institute have developed a software system that can for the first time rapidly self-assemble into the most efficient form without needing humans to tell it what to do. [15] Physicists have shown that quantum effects have the potential to significantly improve a variety of interactive learning tasks in machine learning. [14] A Chinese team of physicists have trained a quantum computer to recognise handwritten characters, the first demonstration of " quantum artificial intelligence ". Physicists have long claimed that quantum computers have the potential to dramatically outperform the most powerful conventional processors. The secret sauce at work here is the strange quantum phenomenon of superposition, where a quantum object can exist in two states at the same time. [13] One of biology's biggest mysteries-how a sliced up flatworm can regenerate into new organisms-has been solved independently by a computer. The discovery marks the first time that a computer has come up with a new scientific theory without direct human help. [12] A team of researchers working at the University of California (and one from Stony Brook University) has for the first time created a neural-network chip that was built using just memristors. In their paper published in the journal Nature, the team describes how they built their chip and what capabilities it has. [11] A team of researchers used a promising new material to build more functional memristors, bringing us closer to brain-like computing. Both academic and industrial laboratories are working to develop computers that operate more like the human brain. Instead of operating like a conventional, digital system, these new devices could potentially function more like a network of neurons. [10] Cambridge Quantum Computing Limited (CQCL) has built a new Fastest Operating System aimed at running the futuristic superfast quantum computers. [9] IBM scientists today unveiled two critical advances towards the realization of a practical quantum computer. For the first time, they showed the ability to detect and measure both kinds of quantum errors simultaneously, as well as demonstrated a new, square quantum bit circuit design that is the only physical architecture that could successfully scale to larger dimensions. [8] Physicists at the Universities of Bonn and Cambridge have succeeded in linking two completely different quantum systems to one another. In doing so, they have taken an important step forward on the way to a quantum computer. To accomplish their feat the researchers used a method that seems to function as well in the quantum world as it does for us people: teamwork. The results have now been published in the "Physical Review Letters". [7] While physicists are continually looking for ways to unify the theory of relativity, which describes large-scale phenomena, with quantum theory, which describes small-scale phenomena, computer scientists are searching for technologies to build the quantum computer. The accelerating electrons explain not only the Maxwell Equations and the Special Relativity, but the Heisenberg Uncertainty Relation, the Wave-Particle Duality and the electron's spin also, building the Bridge between the Classical and Quantum Theories. The Planck Distribution Law of the electromagnetic oscillators explains the electron/proton mass rate and the Weak and Strong Interactions by the diffraction patterns. The Weak Interaction changes the diffraction patterns by moving the electric charge from one side to the other side of the diffraction pattern, which violates the CP and Time reversal symmetry. The diffraction patterns and the locality of the self-maintaining electromagnetic potential explains also the Quantum Entanglement, giving it as a natural part of the Relativistic Quantum Theory and making possible to build the Quantum Computer.

**Category:** Data Structures and Algorithms

[176] **viXra:1610.0351 [pdf]**
*submitted on 2016-10-29 09:23:20*

**Authors:** George Rajna

**Comments:** 30 Pages.

A revolutionary and emerging class of energy-harvesting computer systems require neither a battery nor a power outlet to operate, instead operating by harvesting energy from their environment. [18]
In 1959 renowned physicist Richard Feynman, in his talk "Plenty of Room at the Bottom," spoke of a future in which tiny machines could perform huge feats. Like many forward-looking concepts, his molecule and atom-sized world remained for years in the realm of science fiction. [17]
The race towards quantum computing is heating up. Faster, brighter, more exacting – these are all terms that could be applied as much to the actual science as to the research effort going on in labs around the globe. [16]
For the first time, scientists now have succeeded in placing a complete quantum optical structure on a chip, as outlined Nature Photonics. This fulfills one condition for the use of photonic circuits in optical quantum computers. [15]
The intricately sculpted device made by Paul Barclay and his team of physicists is so tiny it can only be seen under a microscope. But their diamond microdisk could lead to huge advances in computing, telecommunications, and other fields. [14]
Researchers from the Institute for Quantum Computing at the University of Waterloo and the National Research Council of Canada (NRC) have, for the first time, converted the color and bandwidth of ultrafast single photons using a room-temperature quantum memory in diamond. [13]
One promising approach for scalable quantum computing is to use an all-optical architecture, in which the qubits are represented by photons and manipulated by mirrors and beam splitters. So far, researchers have demonstrated this method, called Linear Optical Quantum Computing, on a very small scale by performing operations using just a few photons. In an attempt to scale up this method to larger numbers of photons, researchers in a new study have developed a way to fully integrate single-photon sources inside optical circuits, creating integrated quantum circuits that may allow for scalable optical quantum computation. [12]
Spin-momentum locking might be applied to spin photonics, which could hypothetically harness the spin of photons in devices and circuits. Whereas microchips use electrons to perform computations and process information, photons are limited primarily to communications, transmitting data over optical fiber. However, using the spin of light waves could make possible devices that integrate electrons and photons to perform logic and memory operations. [11]

**Category:** Data Structures and Algorithms

[175] **viXra:1610.0326 [pdf]**
*submitted on 2016-10-27 07:48:22*

**Authors:** Miaomiaomiao

**Comments:** 47 Pages. I AM NOT THE AUTHOR

Note of matrix multiplication

**Category:** Data Structures and Algorithms

[174] **viXra:1609.0421 [pdf]**
*submitted on 2016-09-29 08:00:08*

**Authors:** Emshanov Dima

**Comments:** 15 Pages.

This article contains a description representing the logical formula 3-SAT as a conjunction of two polynomial logical formulas.

**Category:** Data Structures and Algorithms

[173] **viXra:1609.0370 [pdf]**
*submitted on 2016-09-26 06:59:01*

**Authors:** Trung Kien Vu, Sungoh Kwon

**Comments:** Preprint submitted to Computer Networks, 10 pages, 15 figures

In this paper, we propose an ad-hoc on-demand distance vector routing algorithm for mobile ad-hoc networks taking
into account node mobility. Changeable topology of such mobile ad-hoc networks provokes overhead messages in
order to search available routes and maintain found routes. The overheadmessages impede data delivery from sources
to destination and deteriorate network performance. To overcome such a challenge, our proposed algorithm estimates
link duration based neighboring node mobility and chooses the most reliable route. The proposed algorithm also
applies the estimate for route maintenance to lessen the number of overhead messages. Via simulations, the proposed
algorithmis verified in variousmobile environments. In the low mobility environment, by reducing routemaintenance
messages, the proposed algorithm significantly improves network performance such as packet data rate and end-toend
delay. In the high mobility environment, the reduction of route discovery message enhances network performance
since the proposed algorithm provides more reliable routes.

**Category:** Data Structures and Algorithms

[172] **viXra:1609.0044 [pdf]**
*submitted on 2016-09-03 16:15:57*

**Authors:** Brian Beckman

**Comments:** 7 Pages.

This paper fills in some blanks left between part 1 of this series, Kalman Folding (http://vixra.org/abs/1606.0328), and the rest of the papers in the series. In part 1, we present basic Kalman filtering as a functional fold, highlighting the advantages of this form for hardening code in a test environment. In that paper, we motivated the Kalman filter as a natural extension of the running average and variance, writing both as functional folds computed in constant memory. We expressed the running statistics as recurrence relations, where the new statistic is the old statistic plus a correction. We write the correction as a gain factor times some transform of a residual. The residual is the difference between the current (old) statistic and the incoming (new) observation. In both expressions, for brevity, we left derivations to the reader. Here, we present those derivations in full “school-level” detail, along with some basic explanation of the programming language that mechanizes the computations.

**Category:** Data Structures and Algorithms

[171] **viXra:1608.0230 [pdf]**
*submitted on 2016-08-21 11:20:24*

**Authors:** Fu Yuhua

**Comments:** 5 Pages.

Based on creating generalized and hybrid set and library with neutrosophy and quad-stage method, this paper presents the concept of "computer information library clusters" (CILC). There are various ways and means to form CILC. For example, CILC can be considered as the "total-library", and consists of several "sub-libraries". As another example, in CILC, a "total-library" can be set up, and a number of "sub-libraries" are side by side with the "total-library". Specially, for CILC, the operation functions can be added; for example, according to "natural science computer information library clusters" (natural science CILC), and applying "variation principle of library (or sub-library)", “partial and temporary unified theory of natural science so far” with different degrees can be established. Referring to the concept of “natural science CILC”, the concepts of “social science CILC”, “natural science and social science CILC”, and the like, can be presented. While, referreing to the concept of “computer information library clusters”, the concepts of “computer and non-computer information library clusters”, “earth information library clusters”, “solar system information library clusters”, “Milky Way galaxy information library clusters”, “universe information library clusters”, and the like, can be presented.

**Category:** Data Structures and Algorithms

[170] **viXra:1608.0098 [pdf]**
*submitted on 2016-08-09 15:04:41*

**Authors:** Leorge Takeuchi

**Comments:** 16 Pages.

Quicksort, invented by Tony Hoare in 1959, is one of the fastest sorting algorithms. However, conventional
implementations have some weak points, including the following: swaps to exchange two elements are redundant,
deep recursive calls may encounter stack overflow, and the case of repeated many elements in input data is a well-
known issue. This paper improves quicksort to make it more secure and faster using new or known ideas in C
language.

**Category:** Data Structures and Algorithms

[169] **viXra:1608.0044 [pdf]**
*submitted on 2016-08-04 22:35:27*

**Authors:** Sidharth Ghoshal

**Comments:** 10 Pages.

Documented is an algorithm,
It is intimately related to a question about piecewise linear cobordisms. IF the conjecture is true then this algorithm is polynomial time. IF it is not, the this algorithm "might be" but probably won't be. Contact a local topologist for updates in this computational crisis.

**Category:** Data Structures and Algorithms

[168] **viXra:1607.0457 [pdf]**
*submitted on 2016-07-24 21:42:26*

**Authors:** Martin Dudziak

**Comments:** 22 Pages.

We address the topic of internet and communications integrity and continuity during times of social unrest and disturbance where a variety of actions can lead to short-term or long-term disruption of conventional, public and private internet and wireless networks. The internet disruptions connected with WikiLeaks in 2010, those in Egypt and Libya during protests and revolution commencing in January of 2011, and long-standing controls upon internet access and content imposed within China and other nations, are considered as specific and contemporary examples. We examine alternatives that have been proposed by which large numbers of individuals can maintain “connectivity without borders.” We review the strengths and weaknesses of such alternatives, the countermeasures that can be employed against such connectivity, and a number of innovative measures that can be used to overcome such countermeasures.

**Category:** Data Structures and Algorithms

[167] **viXra:1607.0141 [pdf]**
*submitted on 2016-07-10 15:52:42*

**Authors:** Brian Beckman

**Comments:** 11 Pages.

In Kalman Folding, Part 1, we present basic, static Kalman filtering
as a functional fold, highlighting the unique advantages of this form for
deploying test-hardened code verbatim in harsh, mission-critical environments.
In that paper, all examples folded over arrays in memory for convenience and
repeatability. That is an example of developing filters in a friendly
environment.
Here, we prototype a couple of less friendly environments and demonstrate
exactly the same Kalman accumulator function at work. These less friendly
environments are
- lazy streams, where new observations are computed on demand but never fully
realized in memory, thus not available for inspection in a debugger
- asynchronous observables, where new observations are delivered at arbitrary
times from an external source, thus not available for replay once consumed by
the filter

**Category:** Data Structures and Algorithms

[166] **viXra:1607.0109 [pdf]**
*submitted on 2016-07-09 08:03:25*

**Authors:** Z. Vosika, G. Lazović

**Comments:** 7 Pages.

In this paper we develop the new physicalmathematical time scale kinetic approach-model applied
on organic and non-organic particles motion. Concretely,
here, at first, this new research approach is based on
enzyme particles dynamics results. At the beginning, a
time scale is defined to be an arbitrary closed subset of the
real numbers R, with the standard inherited topology.
Mathematical examples of time scales include real
numbers R, natural numbers N, integers Z, the Cantor set
(i.e. fractals), and any finite union of closed intervals of R.
Calculus on time scales (TSC) was established in 1988 by
Stefan Hilger. TSC, by construction, is used to describe the
complex process. This method may utilized for description
of physical (classical mechanics), material (crystal growth
kinetics, physical chemistry kinetics - for example,
kinetics of barium-titanate synthesis), (bio)chemical or
similar systems and represents major challenge for
contemporary scientists. In this sense, the MichaelisMenten (MM) mechanism is the one of the best known and
simplest nonlinear biochemical network which deserves
appropriate attention. Generally speaking, such processes
may be described of discrete time scale. Reasonably it
could be assumed that such a scenario is possible for MM
mechanism. In this work, discrete time MM kinetics
(dtMM) with time various step h, is investigated. Instead of
the first derivative by time used first backward difference
h. Physical basics for new time scale approach is a new
statistical thermodynamics, natural generalization of
Tsallis non-extensive or similar thermodynamics. A
reliable new algorithm of novel difference transformation
method, namely multi-step difference transformation
method (MSDETM) for solving system of nonlinear
ordinary difference equations is proposed. If h tends to
zero, MSDETM transformed into multi-step differential
transformation method (MSDTM). In the spirit of TSC,
MSDETM describes analogously MSDTM.

**Category:** Data Structures and Algorithms

[165] **viXra:1607.0084 [pdf]**
*submitted on 2016-07-07 09:50:50*

**Authors:** Brian Beckman

**Comments:** 11 Pages.

We exhibit a foldable Extended Kalman Filter that internally integrates
non-linear equations of motion with a nested fold of generic
integrators over lazy streams in constant memory.
Functional form allows us to switch integrators easily and to diagnose filter
divergence accurately, achieving orders of magnitude better speed than
the source example from the literature. As with all Kalman folds, we can move
the vetted code verbatim, without even recompilation, from the lab to the field.

**Category:** Data Structures and Algorithms

[164] **viXra:1607.0083 [pdf]**
*submitted on 2016-07-07 09:52:55*

**Authors:** Brian Beckman

**Comments:** 9 Pages.

In Kalman Folding 5: Non-Linear Models and the EKF, we present an
Extended Kalman Filter as a fold over a lazy stream of observations that uses a
nested fold over a lazy stream of states to integrate non-linear equations of
motion. In Kalman Folding 4: Streams and Observables, we present a
handful of stream operators, just enough to demonstrate Kalman folding over
observables.
In this paper, we enrich the collection of operators, adding takeUntil,
last, and map. We then show how to use them to integrate differential
equations in state-space form in two different ways and to generate test cases
for the non-linear EKF from paper 5.

**Category:** Data Structures and Algorithms

[163] **viXra:1607.0059 [pdf]**
*submitted on 2016-07-05 23:28:11*

**Authors:** Brian Beckman

**Comments:** 14 Pages.

In Kalman Folding, Part 1, we present basic, static Kalman filtering
as a functional fold, highlighting the unique advantages of this form for
deploying test-hardened code verbatim in harsh, mission-critical environments.
The examples in that paper are all static, meaning that the states of the model
do not depend on the independent variable, often physical time.
Here, we present mathematical derivations of the basic, static filter. These are
semi-formal sketches that leave many details to the reader, but highlight all
important points that must be rigorously proved. These derivations have several
novel arguments and we strive for much higher clarity and simplicity than is
found in most treatments of the topic.

**Category:** Data Structures and Algorithms

[162] **viXra:1606.0348 [pdf]**
*submitted on 2016-06-30 20:27:15*

**Authors:** Brian Beckman

**Comments:** 7 Pages.

In Kalman Folding, Part 1, we present basic, static Kalman filtering
as a functional fold, highlighting the unique advantages of this form for
deploying test-hardened code verbatim in harsh, mission-critical environments.
The examples in that paper are all static, meaning that the states of the model
do not depend on the independent variable, often physical time.
Here, we present a dynamic Kalman filter in the same, functional form. This
filter can handle many dynamic, time-evolving applications including some
tracking and navigation problems, and is easilly extended to nonlinear and
non-Gaussian forms, the Extended Kalman Filter (EKF) and Unscented Kalman Filter
(UKF) respectively. Those are subjects of other papers in this Kalman-folding
series. Here, we reproduce a tracking example from a well known reference, but
in functional form, highlighting the advantages of that form.

**Category:** Data Structures and Algorithms

[161] **viXra:1606.0328 [pdf]**
*submitted on 2016-06-29 14:21:33*

**Authors:** Brian Beckman

**Comments:** 19 Pages.

Kalman filtering is commonplace in engineering, but less familiar to software
developers. It is the central tool for estimating states of a model, one
observation at a time. It runs fast in constant memory. It is the mainstay of
tracking and navigation, but it is equally applicable to econometrics,
recommendations, control: any application where we update models over time.
By writing a Kalman filter as a functional fold, we can test code in friendly
environments and then deploy identical code with confidence in unfriendly
environments. In friendly environments, data are deterministic, static, and
present in memory. In unfriendly, real-world environments,
data are unpredictable, dynamic, and arrive asynchronously.
The flexibility to deploy exactly the code that was tested is especially
important for numerical code like filters. Detecting, diagnosing and correcting
numerical issues without repeatable data sequences is impractical. Once code is
hardened, it can be critical to deploy exactly the same code, to the binary
level, in production, because of numerical brittleness. Functional form makes it
easy to test and deploy exactly the same code because it minimizes the coupling
between code and environment.

**Category:** Data Structures and Algorithms

[160] **viXra:1606.0182 [pdf]**
*submitted on 2016-06-17 22:40:41*

**Authors:** Ramesh Chandra Bagadi

**Comments:** 18 Pages.

In this research investigation, the author has presented a theory of ‘Universal
Relative Metric That Generates A Field Super-Set To The Fields Generated By
Various Distinct Relative Metrics’.

**Category:** Data Structures and Algorithms

[159] **viXra:1606.0157 [pdf]**
*submitted on 2016-06-15 07:29:20*

**Authors:** Ramesh Chandra Bagadi

**Comments:** 14 Pages.

In this research investigation, the author has presented a theory of ‘The Universal
Irreducible Any Field Generating Metric’.

**Category:** Data Structures and Algorithms

[158] **viXra:1606.0156 [pdf]**
*submitted on 2016-06-15 07:30:06*

**Authors:** Ramesh Chandra Bagadi

**Comments:** 14 Pages.

In this research investigation, the author has presented a theory of ‘The Universal
Irreducible Any Field Generating Metric’.

**Category:** Data Structures and Algorithms

[157] **viXra:1606.0147 [pdf]**
*submitted on 2016-06-15 00:16:12*

**Authors:** Ramesh Chandra Bagadi

**Comments:** 14 Pages.

In this research investigation, the author has presented a theory of ‘Universal Natural Memory Embedding’.

**Category:** Data Structures and Algorithms

[98] **viXra:1811.0062 [pdf]**
*replaced on 2018-11-05 06:35:15*

**Authors:** Robert DiGregorio

**Comments:** 2 Pages. fix typos and clarify

We prove that class P ≠ class co-NP.

**Category:** Data Structures and Algorithms

[97] **viXra:1807.0026 [pdf]**
*replaced on 2018-08-09 13:48:59*

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 40 Pages. A primeira versão deste artigo foi meu trabalho de Métodos em Pesquisa Operacional (PM015), IMECC-UNICAMP.

Usando um novo conceito de linguagem variável, já provei anteriormente que P≠NP, mas tal prova não utilizou nenhum dos problemas clássicos conhecidos como NP-completos, a exemplo de SAT (satisfatibilidade, satisfiability), caixeiro-viajante (travelling-salesman), soma de subconjuntos (subset-sum), da mochila (knapsack), programação linear inteira (integer linear programming), etc. Tal prova não implica que sendo P≠NP então devemos ter NP-completo ∉P, ou seja, os mencionados famosos problemas difíceis podem ainda ser resolvidos em tempo polinomial, sem precisar encerrar a pesquisa nesta direção. Tal como ocorre com o método simplex, que pode resolver em tempo polinomial a grande maioria dos problemas de programação linear, também é possível resolver SAT em tempo polinomial na maioria das vezes, que é o que eu mostro neste trabalho.

**Category:** Data Structures and Algorithms

[96] **viXra:1807.0026 [pdf]**
*replaced on 2018-07-20 12:41:10*

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 40 Pages. A primeira versão deste artigo foi meu trabalho de Métodos em Pesquisa Operacional (PM015), IMECC-UNICAMP.

Usando um novo conceito de linguagem variável, já provei anteriormente que P≠NP, mas tal prova não utilizou nenhum dos problemas clássicos conhecidos como NP-completos, a exemplo de SAT (satisfatibilidade, satisfiability), caixeiro-viajante (travelling-salesman), soma de subconjuntos (subset-sum), da mochila (knapsack), programação linear inteira (integer linear programming), etc. Tal prova não implica que sendo P≠NP então devemos ter NP-completo ∉P, ou seja, os mencionados famosos problemas difíceis podem ainda ser resolvidos em tempo polinomial, sem precisar encerrar a pesquisa nesta direção. Tal como ocorre com o método simplex, que pode resolver em tempo polinomial a grande maioria dos problemas de programação linear, também é possível resolver SAT em tempo polinomial na maioria das vezes, que é o que eu mostro neste trabalho.

**Category:** Data Structures and Algorithms

[95] **viXra:1807.0026 [pdf]**
*replaced on 2018-07-12 18:01:28*

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 40 Pages. A primeira versão deste artigo foi meu trabalho de Métodos em Pesquisa Operacional (PM015), IMECC-UNICAMP.

**Category:** Data Structures and Algorithms

[94] **viXra:1802.0337 [pdf]**
*replaced on 2018-03-02 02:39:44*

**Authors:** Robert DiGregorio

**Comments:** 3 Pages.

A problem exists that’s hard to solve but easy to verify a solution for.

**Category:** Data Structures and Algorithms

[93] **viXra:1802.0337 [pdf]**
*replaced on 2018-02-27 13:36:30*

**Authors:** Robert DiGregorio

**Comments:** 3 Pages.

A problem exists that’s hard to solve but easy to verify a solution for.

**Category:** Data Structures and Algorithms

[92] **viXra:1802.0337 [pdf]**
*replaced on 2018-02-26 18:50:42*

**Authors:** Robert DiGregorio

**Comments:** 3 Pages.

Using sorting keys, we prove that P ≠ NP.

**Category:** Data Structures and Algorithms

[91] **viXra:1802.0337 [pdf]**
*replaced on 2018-02-25 18:57:08*

**Authors:** Robert DiGregorio

**Comments:** 2 Pages.

Using a new tool called a “sorting key” it’s possible to imply that P ≠ NP.

**Category:** Data Structures and Algorithms

[90] **viXra:1802.0337 [pdf]**
*replaced on 2018-02-25 05:21:23*

**Authors:** Robert DiGregorio

**Comments:** 2 Pages.

Using a new tool called a “sorting key” it’s possible to imply that P ≠ NP.

**Category:** Data Structures and Algorithms

[89] **viXra:1802.0337 [pdf]**
*replaced on 2018-02-24 14:08:46*

**Authors:** Robert DiGregorio

**Comments:** 2 Pages.

Using a new tool called a “sorting key” it’s possible to imply that P ≠ NP.

**Category:** Data Structures and Algorithms

[88] **viXra:1802.0288 [pdf]**
*replaced on 2018-02-23 01:14:55*

**Authors:** Stephen P. Smith, Karin Meyer, Bruce Tier

**Comments:** 19 Pages.

A QR algorithm was designed using sparse matrix techniques for likelihood evaluation in REML. The efficiency of the algorithm depends on how the order of columns in the mixed model array are arranged. Three heuristic orderings were considered. The QR algorithm was tested successfully in likelihood evaluation, but vector processing was needed to finish the procedure because of excess fill-ins. The improvements made for the QR algorithm also applied to the competing absorption approach, and hence absorption was found to be more competitive than the QR algorithm in terms of computing time and memory requirements. Absorption was made 52 times faster than a first generation absorption algorithm.

**Category:** Data Structures and Algorithms

[87] **viXra:1712.0407 [pdf]**
*replaced on 2017-12-28 01:10:10*

**Authors:** Sanjeev Saxena

**Comments:** 8 Pages. Minor corrections

In this paper, ellipsoid method for linear programming is derived using only minimal knowledge of algebra and matrices.
Unfortunately, most authors first describe the algorithm, then later prove its correctness, which requires a good knowledge of linear algebra.

**Category:** Data Structures and Algorithms

[86] **viXra:1711.0118 [pdf]**
*replaced on 2017-12-18 07:09:12*

**Authors:** Sathish Kumar Vijayakumar

**Comments:** 12 Pages.

Sorting is one of the most researched topics of Computer Science and it is one of the essential operations across computing devices. Given the ubiquitous presence of computers, sorting algorithms utilize significant percentage of computation times across the globe. In this paper we present a non-comparison based sorting algorithm with average case time complexity of O(n) without any assumptions on the nature of the input data.

**Category:** Data Structures and Algorithms

[85] **viXra:1711.0118 [pdf]**
*replaced on 2017-11-21 12:58:56*

**Authors:** Sathish Kumar Vijayakumar

**Comments:** 13 Pages. Hi though sorting is one of the vastly researched area, this paper brings out the best time complexity of them all. My linkedin profile is as follows http://linkedin.com/in/sathish-kumar-b7434579. Please feel free to post your queries.

Sorting is one of the most researched topics of Computer Science and it is one of the essential operations across computing devices. Given the ubiquitous presence of computers, sorting algorithms utilize significant percentage of computation times across the globe. In this paper we present a sorting algorithm with average case time complexity of O(n) without any assumptions on the nature of the input data.

**Category:** Data Structures and Algorithms

[84] **viXra:1711.0118 [pdf]**
*replaced on 2017-11-03 10:00:49*

**Authors:** Sathish Kumar Vijayakumar

**Comments:** 12 Pages. Hi though sorting is one of the vastly researched area, this paper brings out the best time complexity of them all. My linkedin profile is as follows http://linkedin.com/in/sathish-kumar-b7434579. Please feel free to post your queries.

Sorting is one of the most researched topics of Computer Science and it is one of the essential operations across computing devices. Given the ubiquitous presence of computers, sorting algorithms utilize significant percentage of computation times across the globe. In this paper we present a sorting algorithm with worst case time complexity of O(n) without any assumptions on the nature of the input data.

**Category:** Data Structures and Algorithms

[83] **viXra:1708.0373 [pdf]**
*replaced on 2018-07-25 09:30:51*

**Authors:** Wolfgang Fischl, Georg Gottlob, Reinhard Pichler

**Comments:** 17 Pages.

The authors have recently shown that recognizing low fractional hypertree-width (fhw) is NP-complete
in the general case and that the problem becomes tractable if the hypergraphs under consideration have degree and intersection width bounded by a constant, i.e., every vertex is contained in only constantly many different edges and the intersection of two edges contains only constantly many vertices. In this article, we show that bounded degree alone suffices to ensure tractability.

**Category:** Data Structures and Algorithms

[82] **viXra:1708.0034 [pdf]**
*replaced on 2018-02-14 22:49:05*

**Authors:** Nicholas R. Wright

**Comments:** 8 Pages. Changed Moore's Law from "<" to ">".

We use the whole order approach to solve the problem of P versus NP. The relation of the whole order within a beautiful order is imperative to understanding the total order. We also show several techniques observed by the minimum element, we call a logical minimum. The perfect zero-knowledge technique will deliver exactly the same. We conclude with a demonstration of the halting problem.

**Category:** Data Structures and Algorithms

[81] **viXra:1708.0034 [pdf]**
*replaced on 2017-10-11 04:03:46*

**Authors:** Nicholas R. Wright

**Comments:** 8 Pages. Cambria Math font

We use the whole order approach to solve the problem of P versus NP. The relation of the whole order within a beautiful order is imperative to understanding the total order. We also show several techniques observed by the minimum element, we call a logical minimum. The perfect zero-knowledge technique will deliver exactly the same. We conclude with a demonstration of the halting problem.

**Category:** Data Structures and Algorithms

[80] **viXra:1707.0356 [pdf]**
*replaced on 2017-08-27 17:15:18*

**Authors:** Alexandre Harvey-Tremblay

**Comments:** 25 Pages.

In this paper, I investigate a prefix-free universal Turing machine (UTM) running multiple programs in parallel according to a scheduler. I found that if, over the course of the computation, the scheduler adjusts the work done on programs so as to maximize the entropy in the calculation of the halting probability Omega, the system will follow many laws analogous to the laws of physics. As the scheduler maximizes entropy, the result relies on algorithmic thermodynamics which connects the halting probability of a prefix-free UTM to the Gibb's ensemble of statistical physics (which also maximizes entropy). My goal with this paper is to show specifically, that special relativity and general relativity can be derived from algorithmic thermodynamics under a certain choice of thermodynamic observables applied to the halting probability.

**Category:** Data Structures and Algorithms

[79] **viXra:1707.0239 [pdf]**
*replaced on 2017-08-13 18:09:20*

**Authors:** Stephen P. Smith

**Comments:** 19 Pages.

The bordering method of the Cholesky decomposition is backward differentiated to derive a method of calculating first derivatives. The result is backward differentiated again and an algorithm for calculating second derivatives results. Applying backward differentiation twice also generates an algorithm for conducting forward differentiation. The differentiation methods utilize three main modules: a generalization of forward substitution for calculating the forward derivatives; a generalization of backward substitution for calculating the backward derivatives; and an additional module involved with the calculation of second derivatives. Separating the methods into three modules lends itself to optimization where software can be developed for special cases that are suitable for sparse matrix manipulation, vector processing and/or blocking strategies that utilize matrix partitions. Surprisingly, the same derivative algorithms fashioned for the Cholesky decomposition of a positive definite matrix can be used again for matrices that are indefinite. The only differences are very minor adjustments involving an initialization step that leads into backward differentiation and a finalization step that follows forward differentiation.

**Category:** Data Structures and Algorithms

[78] **viXra:1707.0074 [pdf]**
*replaced on 2017-07-11 13:15:48*

**Authors:** Theophanes Raptis

**Comments:** 47 Pages. Typo correction in eq. (29a-b) and (35a-b)

We utilize a previously reported methodological framework [5], to find a general set of mappings for any satisfiability (SAT) problem to a set of arithmetized codes allowing a classification hierarchy enumerable via integer partition functions. This reveals a unique unsatisfiability criterion via the introduction of certain universal indicator functions associating the validity of any such problem with a mapping between Mersenne integers and their complements in an inclusive hierarchy of exponential intervals. Lastly, we present means to reduce the complexity of the original problem to that of a special set of binary sequences and their bit block analysis via a reduction of any expression to a type of a Sequential Dynamical System (SDS) using the technique of clause equalization. We specifically notice the apparent analogy of certain dynamical properties behind such problems with resonances and coherencies of multi-periodic systems leading to the possibility of certain fast analog or natural implementations of dedicated SAT-machines. A Matlab toolbox is also offered as additional aid in exploring certain simple examples.

**Category:** Data Structures and Algorithms

[77] **viXra:1702.0156 [pdf]**
*replaced on 2017-02-20 14:49:06*

**Authors:** Stephen P Smith

**Comments:** 12 Pages.

This paper describes the backward differentiation of the Cholesky decomposition by the bordering method. The backward differentiation of the Cholesky decomposition by the inner product form and the outer product form have been described elsewhere. It is found that the resulting algorithm can be adapted to vector processing, as is also true of the algorithms developed from the inner product form and outer product form. The three approaches can also be fashioned to treat sparse matrices, but this is done by enforcing the same sparse structure found for the Cholesky decomposition on a secondary work space.

**Category:** Data Structures and Algorithms

[76] **viXra:1608.0098 [pdf]**
*replaced on 2017-12-15 10:49:02*

**Authors:** Leorge Takeuchi

**Comments:** 18 Pages. Some explanation was added.

Quicksort, invented by Tony Hoare in 1959, is one of the fastest sorting algorithms. However, conventional
implementations have some weak points, including the following: swaps to exchange two elements are redundant,
deep recursive calls may encounter stack overflow, and the case of repeated many elements in input data is a well-
known issue. This paper improves quicksort to make it more secure and faster using new or known ideas in C
language.

**Category:** Data Structures and Algorithms

[75] **viXra:1608.0098 [pdf]**
*replaced on 2016-08-11 23:42:15*

**Authors:** Leorge Takeuchi

**Comments:** 16 Pages. Two link addresses (URI) were wrong.

Quicksort, invented by Tony Hoare in 1959, is one of the fastest sorting algorithms. However, conventional
implementations have some weak points, including the following: swaps to exchange two elements are redundant,
deep recursive calls may encounter stack overflow, and the case of repeated many elements in input data is a well-
known issue. This paper improves quicksort to make it more secure and faster using new or known ideas in C
language.

**Category:** Data Structures and Algorithms

[74] **viXra:1607.0059 [pdf]**
*replaced on 2016-07-06 11:01:24*

**Authors:** Brian Beckman

**Comments:** 14 Pages. Minor corrections to original version

In Kalman Folding, Part 1, we present basic, static Kalman filtering
as a functional fold, highlighting the unique advantages of this form for
deploying test-hardened code verbatim in harsh, mission-critical environments.
The examples in that paper are all static, meaning that the states of the model
do not depend on the independent variable, often physical time.
Here, we present mathematical derivations of the basic, static filter. These are
semi-formal sketches that leave many details to the reader, but highlight all
important points that must be rigorously proved. These derivations have several
novel arguments and we strive for much higher clarity and simplicity than is
found in most treatments of the topic.

**Category:** Data Structures and Algorithms

[73] **viXra:1606.0348 [pdf]**
*replaced on 2016-07-06 16:57:41*

**Authors:** Brian Beckman

**Comments:** 7 Pages.

In Kalman Folding, Part 1, we present basic, static Kalman filtering as a functional fold, highlighting the unique advantages of this form for deploying test-hardened code verbatim in harsh, mission-critical environments. The examples in that paper are all static, meaning that the states of the model do not depend on the independent variable, often physical time. Here, we present a dynamic Kalman filter in the same, functional form. This filter can handle many dynamic, time-evolving applications including some tracking and navigation problems, and is easilly extended to nonlinear and non-Gaussian forms, the Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF) respectively. Those are subjects of other papers in this Kalman-folding series. Here, we reproduce a tracking example from a well known reference, but in functional form, highlighting the advantages of that form.

**Category:** Data Structures and Algorithms