[6] **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

[5] **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

[4] **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

[3] **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

[2] **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

[1] **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