[6] **viXra:1306.0213 [pdf]**
*submitted on 2013-06-26 04:41:30*

**Authors:** José Francisco García Juliá

**Comments:** 2 Pages.

The information hiding principle can be applied completely using the Modula language.

**Category:** Data Structures and Algorithms

[5] **viXra:1306.0193 [pdf]**
*replaced on 2013-06-28 01:21:51*

**Authors:** Dhananjay P. Mehendale

**Comments:** 4 pages. Sorting algorithm is added.

The unstructured search problem asks for search of some predefined number, called target, from given unstructured list of numbers. In this paper we propose a novel classical algorithm with complexity ~O(Log N) for searching the target from unstructured list of numbers. We propose a new algorithm, which achieves improvement of exponential order over existing algorithms. Suppose N is the largest number in the list then we consider N dimensional vector space with Euclidean basis. With each of the numbers in the given unstructured list we associate the unique basis vector among the vectors that form together the Euclidean basis. For example suppose j is a number in the list then we associate with this number j the unique basis vector in the above mentioned N-dimensional vector space, namely, |j> = transpose(0, 0, 0, … , 0, 0, 1, 0, 0, … , 0, 0, 0), where the there is entry 1 only at j-th place and every where else there is entry 0. We then divide the given list of numbers in two roughly equal parts (i.e. we divide the given bag containing scrambled numbers in two roughly equal parts and put them in two separate bags, Bag 1 and Bag 2). We represent the list of numbers in Bag 1, Bag 2 in the form of equally weighted superposition of basis vectors associated with the numbers contained in these bags, namely, we represent list in Bag 1 (Bag 2) as a single state formed by equally weighted superposition using orthonormal states forming Euclidean basis corresponding to numbers in the bag B1 (bag B2), namely, |Psi-1> (|Psi-2>). Let t be the target number. It will be represented as |t>. We then find the value of scalar product of target state |t> with |Psi-1> (or Psi-2>). It will revel us whether t belongs to Bag 1 (or Bag 2) which essentially enables us to carry out the binary search and to achieve above mentioned ~O(Log N) complexity!Also, representing list as superposition provides sorting of numbers instantly! One needs to read vector from left to right and prepare the desired sorted list!

**Category:** Data Structures and Algorithms

[4] **viXra:1306.0128 [pdf]**
*submitted on 2013-06-17 01:49:37*

**Authors:** Dietmar Hildenbrand, Eckhard Hitzer

**Comments:** 6 Pages. 6 figures, 1 table. In Braz, J. (ed.), GRAPP 2008, 3rd Int. Conf. on Computer Graphics Theory and Applications. Proc.: Funchal, Madeira, Portugal, January 22-25, 2008, Porto: INSTICC Press, pp. 99-106 (2008). DOI: 10.1.1.151.7539

This paper presents some basics for the analysis of point clouds using the geometrically intuitive mathematical
framework of conformal geometric algebra. In this framework it is easy to compute with osculating circles
for the description of local curvature. Also methods for the fitting of spheres as well as bounding spheres are
presented. In a nutshell, this paper provides a starting point for shape analysis based on this new, geometrically
intuitive and promising technology.
Keywords: geometric algebra, geometric computing, point clouds, osculating circle, fitting of spheres, bounding spheres.

**Category:** Data Structures and Algorithms

[3] **viXra:1306.0120 [pdf]**
*submitted on 2013-06-17 03:19:30*

**Authors:** Eckhard Hitzer, Ginanjar Utama

**Comments:** 13 Pages. 3 figures, 5 tables. Mem. Fac. Eng. Univ. Fukui 53(1), pp. 47-59 (2005).

This paper first briefly reviews the algebraic background of the conformal (homogeneous) model of Euclidean space in Clifford geometric algebra R_4,1= Cl(4,1), concentrating on the subalgebra structure. The subalgebras include space-time algebra (STA), Dirac and Pauli algebras, as well as real and complex quaternion algebras, etc. The concept of the Horosphere is introduced along with the definition of subspaces that intuitively correspond to three dimensional Euclidean geometric objects. Algebraic expressions for the motions of these objects and their set theoretic operations are given. It is shown how 3D Euclidean information on positions, orientations and radii can be extracted.
The second main part of the paper concentrates on the GeometricAlgebra Java package implementation of the Clifford geometric algebra R_4,1 = Cl(4,1) and the homogeneous model of 3D Euclidean space. Details are exemplified by looking at the structure and code of the basic MultiVector class and of the 3D Euclidean object model class Sphere. Finally code optimization issues and the ongoing open source project implementation are discussed.

**Category:** Data Structures and Algorithms

[2] **viXra:1306.0068 [pdf]**
*submitted on 2013-06-11 02:23:10*

**Authors:** Shreyak Chakraborty

**Comments:** 4 Pages.

We introduce the alpha version of a C++ Computational Framework to simulate life processes
in the body of a living multicellular
organism by virtually replicating the data flow of the actual living being in real time.
LivMach Framework is an open source project on Sourceforge.net
We use various data structures to effectively simulate all components of a living organism
's body. Due to the
absence of a Graphical User Interface(GUI), we use special indicator statements to display
the flow of data
between various parts of the virtual body.
Using this code,one can simulate the complete physical,mental and psychological behaviour of
simple and complex
multicellular organisms on low cost machines.

**Category:** Data Structures and Algorithms

[1] **viXra:1306.0058 [pdf]**
*replaced on 2013-10-20 14:40:22*

**Authors:** Laszlo B. Kish, Derek Abbott, Claes-Goran Granqvist

**Comments:** 33 Pages. Accepted for publication at PLOS ONE

Recently, Bennett and Riedel (BR) (http://arxiv.org/abs/1303.7435v1) argued that thermodynamics is not essential in the Kirchhoff-law–Johnson-noise (KLJN) classical physical cryptographic exchange method in an effort to disprove the security of the KLJN scheme. They attempted to demonstrate this by introducing a dissipation-free deterministic key exchange method with two batteries and two switches. In the present paper, we first show that BR’s scheme is unphysical and that some elements of its assumptions violate basic protocols of secure communication. All our analyses are based on a technically-unlimited Eve with infinitely accurate and fast measurements limited only by the laws of physics and statistics. For non-ideal situations and at active (invasive) attacks, the uncertainly principle between measurement duration and statistical errors makes it impossible for Eve to extract the key regardless of the accuracy or speed of her measurements. To show that thermodynamics and noise are essential for the security, we crack the BR system with 100% success via passive attacks, in ten different ways, and demonstrate that the same cracking methods do not function for the KLJN scheme that employs Johnson noise to provide security underpinned by the Second Law of Thermodynamics. We also present a critical analysis of some other claims by BR; for example, we prove that their equations for describing zero security do not apply to the KLJN scheme. Finally we give mathematical security proofs for each BR-attack against the KLJN scheme and conclude that the information theoretic (unconditional) security of the KLJN method has not been successfully challenged.

**Category:** Data Structures and Algorithms