Data Structures and Algorithms

1607 Submissions

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

Technologies to Support, Enhance and Protect Social Networking Freedoms During Periods of Social Unrest and Political Disruption

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

Kalman Folding 4: Streams and Observables

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

Multistep Transformation Method for Discrete and Continuous Time Enzyme Kinetics

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

Kalman Folding 5: Non-Linear Models and the EKF

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

Kalman Folding 7: A Small Streams Library

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

Kalman Folding 3: Derivations

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