Axioms

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Open AccessArticle

Summary of Data Farming

by Gary Horne and Klaus-Peter Schwierz

Axioms 2016, 5(1), 8; https://doi.org/10.3390/axioms5010008 - 01 Mar 2016

Cited by 4 | Viewed by 5020

Data Farming is a process that has been developed to support decision-makers by answering questions that are not currently addressed. Data farming uses an inter-disciplinary approach that includes modeling and simulation, high performance computing, and statistical analysis to examine questions of interest with [...] Read more.

Data Farming is a process that has been developed to support decision-makers by answering questions that are not currently addressed. Data farming uses an inter-disciplinary approach that includes modeling and simulation, high performance computing, and statistical analysis to examine questions of interest with a large number of alternatives. Data farming allows for the examination of uncertain events with numerous possible outcomes and provides the capability of executing enough experiments so that both overall and unexpected results may be captured and examined for insights. Harnessing the power of data farming to apply it to our questions is essential to providing support not currently available to decision-makers. This support is critically needed in answering questions inherent in the scenarios we expect to confront in the future as the challenges our forces face become more complex and uncertain. This article was created on the basis of work conducted by Task Group MSG-088 “Data Farming in Support of NATO”, which is being applied in MSG-124 “Developing Actionable Data Farming Decision Support for NATO” of the Science and Technology Organization, North Atlantic Treaty Organization (STO NATO). Full article

(This article belongs to the Special Issue Data Farming: Mathematical Foundations and Applications)

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Open AccessArticle

Tactical Size Unit as Distribution in a Data Farming Environment

by Esa Lappi and Bernt Åkesson

Axioms 2016, 5(1), 7; https://doi.org/10.3390/axioms5010007 - 22 Feb 2016

Cited by 1 | Viewed by 4149

Abstract

In agent based models, the agents are usually platforms (individual soldiers, tanks, helicopters, etc.), not military units. In the Sandis software, the agents can be platoon size units. As there are about 30 soldiers in a platoon, there is a need for [...] Read more.

In agent based models, the agents are usually platforms (individual soldiers, tanks, helicopters, etc.), not military units. In the Sandis software, the agents can be platoon size units. As there are about 30 soldiers in a platoon, there is a need for strength distribution in simulations. The contribution of this paper is a conceptual model of the platoon level agent, the needed mathematical models and concepts, and references earlier studies of how simulations have been conducted in a data farming environment with platoon/squad size unit agents with strength distribution. Full article

(This article belongs to the Special Issue Data Farming: Mathematical Foundations and Applications)

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Open AccessArticle

Entropy Production Rate of a One-Dimensional Alpha-Fractional Diffusion Process

by Yuri Luchko

Axioms 2016, 5(1), 6; https://doi.org/10.3390/axioms5010006 - 05 Feb 2016

Cited by 31 | Viewed by 4663

Abstract

In this paper, the one-dimensional α-fractional diffusion equation is revisited. This equation is a particular case of the time- and space-fractional diffusion equation with the quotient of the orders of the time- and space-fractional derivatives equal to one-half. First, some integral representations [...] Read more.

In this paper, the one-dimensional α-fractional diffusion equation is revisited. This equation is a particular case of the time- and space-fractional diffusion equation with the quotient of the orders of the time- and space-fractional derivatives equal to one-half. First, some integral representations of its fundamental solution including the Mellin-Barnes integral representation are derived. Then a series representation and asymptotics of the fundamental solution are discussed. The fundamental solution is interpreted as a probability density function and its entropy in the Shannon sense is calculated. The entropy production rate of the stochastic process governed by the α-fractional diffusion equation is shown to be equal to one of the conventional diffusion equation. Full article

(This article belongs to the Special Issue Special Functions: Fractional Calculus and the Pathway for Entropy Dedicated to Professor Dr. A.M. Mathai on the occasion of his 80th Birthday)

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Open AccessArticle

Modular Nuclearity: A Generally Covariant Perspective

by Gandalf Lechner and Ko Sanders

Axioms 2016, 5(1), 5; https://doi.org/10.3390/axioms5010005 - 29 Jan 2016

Cited by 6 | Viewed by 4844

Abstract

A quantum field theory in its algebraic description may admit many irregular states. So far, selection criteria to distinguish physically reasonable states have been restricted to free fields (Hadamard condition) or to flat spacetimes (e.g., Buchholz-Wichmann nuclearity). We propose instead to use a [...] Read more.

A quantum field theory in its algebraic description may admit many irregular states. So far, selection criteria to distinguish physically reasonable states have been restricted to free fields (Hadamard condition) or to flat spacetimes (e.g., Buchholz-Wichmann nuclearity). We propose instead to use a modular ℓp -condition, which is an extension of a strengthened modular nuclearity condition to generally covariant theories. The modular nuclearity condition was previously introduced in Minkowski space, where it played an important role in constructive two dimensional algebraic QFT’s. We show that our generally covariant extension of this condition makes sense for a vast range of theories, and that it behaves well under causal propagation and taking mixtures. In addition we show that our modular ℓp -condition holds for every quasi-free Hadamard state of a free scalar quantum field (regardless of mass or scalar curvature coupling). However, our condition is not equivalent to the Hadamard condition. Full article

(This article belongs to the Special Issue Infinite-dimensional Analysis: Multi-variable Operator Theory, Representation Theory, and Applications)

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Open AccessArticle

Data Farming Process and Initial Network Analysis Capabilities

by Gary Horne and Theodore Meyer

Axioms 2016, 5(1), 4; https://doi.org/10.3390/axioms5010004 - 27 Jan 2016

Cited by 3 | Viewed by 4384

Abstract

Data Farming, network applications and approaches to integrate network analysis and processes to the data farming paradigm are presented as approaches to address complex system questions. Data Farming is a quantified approach that examines questions in large possibility spaces using modeling and simulation. [...] Read more.

Data Farming, network applications and approaches to integrate network analysis and processes to the data farming paradigm are presented as approaches to address complex system questions. Data Farming is a quantified approach that examines questions in large possibility spaces using modeling and simulation. It evaluates whole landscapes of outcomes to draw insights from outcome distributions and outliers. Social network analysis and graph theory are widely used techniques for the evaluation of social systems. Incorporation of these techniques into the data farming process provides analysts examining complex systems with a powerful new suite of tools for more fully exploring and understanding the effect of interactions in complex systems. The integration of network analysis with data farming techniques provides modelers with the capability to gain insight into the effect of network attributes, whether the network is explicitly defined or emergent, on the breadth of the model outcome space and the effect of model inputs on the resultant network statistics. Full article

(This article belongs to the Special Issue Data Farming: Mathematical Foundations and Applications)

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Graphical abstract

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Open AccessEditorial

Acknowledgement to Reviewers of Axioms in 2015

by Axioms Editorial Office

Axioms 2016, 5(1), 3; https://doi.org/10.3390/axioms5010003 - 25 Jan 2016

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Abstract

The editors of Axioms would like to express their sincere gratitude to the following reviewers for assessing manuscripts in 2015. [...] Full article

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Open AccessArticle

Non-Abelian Pseudocompact Groups

by W. W. Comfort and Dieter Remus

Axioms 2016, 5(1), 2; https://doi.org/10.3390/axioms5010002 - 12 Jan 2016

Cited by 3 | Viewed by 4103

Abstract

Here are three recently-established theorems from the literature. (A) (2006) Every non-metrizable compact abelian group K has 2^|K| -many proper dense pseudocompact subgroups. (B) (2003) Every non-metrizable compact abelian group K admits 2^{2^|K|} -many strictly finer pseudocompact topological group refinements. [...] Read more.

Here are three recently-established theorems from the literature. (A) (2006) Every non-metrizable compact abelian group K has 2^|K| -many proper dense pseudocompact subgroups. (B) (2003) Every non-metrizable compact abelian group K admits 2^{2^|K|} -many strictly finer pseudocompact topological group refinements. (C) (2007) Every non-metrizable pseudocompact abelian group has a proper dense pseudocompact subgroup and a strictly finer pseudocompact topological group refinement. (Theorems (A), (B) and (C) become false if the non-metrizable hypothesis is omitted.) With a detailed view toward the relevant literature, the present authors ask: What happens to (A), (B), (C) and to similar known facts about pseudocompact abelian groups if the abelian hypothesis is omitted? Are the resulting statements true, false, true under certain natural additional hypotheses, etc.? Several new results responding in part to these questions are given, and several specific additional questions are posed. Full article

(This article belongs to the Special Issue Topological Groups: Yesterday, Today, Tomorrow)

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Open AccessArticle

On some Integral Representations of Certain G-Functions

by Seemon Thomas

Axioms 2016, 5(1), 1; https://doi.org/10.3390/axioms5010001 - 31 Dec 2015

Cited by 2 | Viewed by 3229

Abstract

This is a brief exposition of some statistical techniques utilized to obtain several useful integral equations involving G-functions. Full article

(This article belongs to the Special Issue Special Functions: Fractional Calculus and the Pathway for Entropy Dedicated to Professor Dr. A.M. Mathai on the occasion of his 80th Birthday)