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Axioms
Volume 3
Issue 1
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Axioms, Volume 3, Issue 1 (March 2014) – 11 articles , Pages 1-139

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291 KiB  
Article
Ricci Curvature on Polyhedral Surfaces via Optimal Transportation
by Benoît Loisel and Pascal Romon
Axioms 2014, 3(1), 119-139; https://doi.org/10.3390/axioms3010119 - 6 Mar 2014
Cited by 27 | Viewed by 5435
Abstract
The problem of correctly defining geometric objects, such as the curvature, is a hard one in discrete geometry. In 2009, Ollivier defined a notion of curvature applicable to a wide category of measured metric spaces, in particular to graphs. He named it coarse [...] Read more.
The problem of correctly defining geometric objects, such as the curvature, is a hard one in discrete geometry. In 2009, Ollivier defined a notion of curvature applicable to a wide category of measured metric spaces, in particular to graphs. He named it coarse Ricci curvature because it coincides, up to some given factor, with the classical Ricci curvature, when the space is a smooth manifold. Lin, Lu and Yau and Jost and Liu have used and extended this notion for graphs, giving estimates for the curvature and, hence, the diameter, in terms of the combinatorics. In this paper, we describe a method for computing the coarse Ricci curvature and give sharper results, in the specific, but crucial case of polyhedral surfaces. Full article
(This article belongs to the Special Issue Discrete Differential Geometry and Its Applications to Imaging and Graphics)
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<p>Generic description of <math display="inline"> <mrow> <mtext>star</mtext> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>∪</mo> <mtext>star</mtext> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </math>.</p> Full article ">Figure 2
<p>Rectangular parallelepiped.</p> Full article ">
183 KiB  
Article
Optimization Models for Reaction Networks: Information Divergence, Quadratic Programming and Kirchhoff’s Laws
by Julio Michael Stern and Fabio Nakano
Axioms 2014, 3(1), 109-118; https://doi.org/10.3390/axioms3010109 - 5 Mar 2014
Cited by 3 | Viewed by 4353
Abstract
This article presents a simple derivation of optimization models for reaction networks leading to a generalized form of the mass-action law, and compares the formal structure of Minimum Information Divergence, Quadratic Programming and Kirchhoff type network models. These optimization models are used in [...] Read more.
This article presents a simple derivation of optimization models for reaction networks leading to a generalized form of the mass-action law, and compares the formal structure of Minimum Information Divergence, Quadratic Programming and Kirchhoff type network models. These optimization models are used in related articles to develop and illustrate the operation of ontology alignment algorithms and to discuss closely connected issues concerning the epistemological and statistical significance of sharp or precise hypotheses in empirical science. Full article
315 KiB  
Article
Increasing Personal Value Congruence in Computerized Decision Support Using System Feedback
by Bryan Hosack and David Paradice
Axioms 2014, 3(1), 84-108; https://doi.org/10.3390/axioms3010084 - 25 Feb 2014
Cited by 3 | Viewed by 6537
Abstract
The Theory of Universals in Values (TUV), a reliable and validated conceptualization of personal values used in psychology, is used to examine the effect of system feedback delivered by a Decision Support System (DSS) on personal values. The results indicate that value-based decision-making [...] Read more.
The Theory of Universals in Values (TUV), a reliable and validated conceptualization of personal values used in psychology, is used to examine the effect of system feedback delivered by a Decision Support System (DSS) on personal values. The results indicate that value-based decision-making behavior can be influenced by DSS feedback to address value congruence in decision-making. User behavior was shown to follow the outcomes expected by operant theory when feedback was supportive and to follow the outcomes of reactance theory when feedback was challenging. This result suggests that practitioners and Information System (IS) researchers should consider user values when designing computerized decision feedback to adjust a system’s design such that the potential user backlash is avoided or congruence between organizational and personal values is achieved. Full article
(This article belongs to the Special Issue Axioms of Decision Support System)
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<p>Relationships among the Value Constructs [<a href="#B18-axioms-03-00084" class="html-bibr">18</a>].</p> Full article ">Figure 2
<p>Task with Challenging Feedback.</p> Full article ">Figure 3
<p>Portrait Values Questionnaire (PVQ) Smallest Space Analysis.</p> Full article ">Figure 4
<p>The Effect of Feedback Type on Allocation Behavior between Decisions.</p> Full article ">Figure 5
<p>The Effect of Feedback and Value Congruency on Allocation Behavior between Decisions.</p> Full article ">
23 KiB  
Editorial
Acknowledgement to Reviewers of Axioms in 2013
by Axioms Editorial Office
Axioms 2014, 3(1), 82-83; https://doi.org/10.3390/axioms3010082 - 25 Feb 2014
Viewed by 3454
Abstract
The editors of Axioms would like to express their sincere gratitude to the following reviewers for assessing manuscripts in 2013. [...] Full article
533 KiB  
Article
Canonical Coordinates for Retino-Cortical Magnification
by Luc Florack
Axioms 2014, 3(1), 70-81; https://doi.org/10.3390/axioms3010070 - 24 Feb 2014
Viewed by 5954
Abstract
A geometric model for a biologically-inspired visual front-end is proposed, based on an isotropic, scale-invariant two-form field. The model incorporates a foveal property typical of biological visual systems, with an approximately linear decrease of resolution as a function of eccentricity, and by a [...] Read more.
A geometric model for a biologically-inspired visual front-end is proposed, based on an isotropic, scale-invariant two-form field. The model incorporates a foveal property typical of biological visual systems, with an approximately linear decrease of resolution as a function of eccentricity, and by a physical size constant that measures the radius of the geometric foveola, the central region characterized by maximal resolving power. It admits a description in singularity-free canonical coordinates generalizing the familiar log-polar coordinates and reducing to these in the asymptotic case of negligibly-sized geometric foveola or, equivalently, at peripheral locations in the visual field. It has predictive power to the extent that quantitative geometric relationships pertaining to retino-cortical magnification along the primary visual pathway, such as receptive field size distribution and spatial arrangement in retina and striate cortex, can be deduced in a principled manner. The biological plausibility of the model is demonstrated by comparison with known facts of human vision. Full article
(This article belongs to the Special Issue Discrete Differential Geometry and Its Applications to Imaging and Graphics)
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<p>Schematic representation of the optic pathways from each of the four quadrants of view for both eyes. Adapted from Wikimedia Commons, original illustration by Ratznium. LGN, lateral geniculate nucleus.</p> Full article ">Figure 2
<p>Retino-cortical magnification, <math display="inline"> <mrow> <msup> <mi>V</mi> <mo>′</mo> </msup> <mrow> <mo>(</mo> <mi>t</mi> <mo>,</mo> <mi>T</mi> <mo>)</mo> </mrow> </mrow> </math> (<b>left</b>), and its integral, <math display="inline"> <mrow> <mi>V</mi> <mo>(</mo> <mi>t</mi> <mo>,</mo> <mi>T</mi> <mo>)</mo> </mrow> </math> (<b>right</b>), as a function of dimensionless eccentricity, <span class="html-italic">t</span>, illustrated for the case <math display="inline"> <mrow> <mi>T</mi> <mo>=</mo> <mn>95</mn> </mrow> </math> (dashed vertical line); recall Equations (<a href="#FD12-axioms-03-00070" class="html-disp-formula">12</a>)–(<a href="#FD15-axioms-03-00070" class="html-disp-formula">15</a>). The peak on the left occurs at <math display="inline"> <mrow> <msub> <mi>t</mi> <mo>+</mo> </msub> <mo>=</mo> <mn>1</mn> </mrow> </math> and marks the border <math display="inline"> <mrow> <msub> <mi>ρ</mi> <mo>+</mo> </msub> <mo>=</mo> <mi>a</mi> </mrow> </math> of the geometric foveola. The half maximum on the right is reached at <math display="inline"> <mrow> <msub> <mi>t</mi> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </msub> <mspace width="-0.166667em"/> <mo>≈</mo> <mspace width="-0.166667em"/> <msqrt> <mi>T</mi> </msqrt> </mrow> </math>, corresponding to the geometric equipartitioning radius (left vertical line), <math display="inline"> <mrow> <msub> <mi>ρ</mi> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </msub> <mspace width="-0.166667em"/> <mo>≈</mo> <mspace width="-0.166667em"/> <msqrt> <mrow> <mi>a</mi> <mspace width="0.166667em"/> <mi>R</mi> </mrow> </msqrt> </mrow> </math>. With our choice of parameters (motivated in the text), the tiny geometric foveola has a relative processing capacity <math display="inline"> <mrow> <mi>v</mi> <mo>(</mo> <msub> <mi>t</mi> <mo>+</mo> </msub> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mi>T</mi> <mo>=</mo> <mn>95</mn> <mo>)</mo> <mo>≈</mo> <mn>8</mn> <mo>%</mo> </mrow> </math>; recall Equation (<a href="#FD13-axioms-03-00070" class="html-disp-formula">13</a>).</p> Full article ">Figure 3
<p>Retino-cortical mapping of macaque monkey. (<b>Left</b>) Retina with spoke-wheel stimulus. (<b>Right</b>) Stimulus image retinotopically mapped onto the posterior part of (hemifield) striate cortex, a.k.a. calcarine sulcus. Source: Tootell <span class="html-italic">et al.</span> [<a href="#B21-axioms-03-00070" class="html-bibr">21</a>].</p> Full article ">Figure 4
<p>The canonical <math display="inline"> <mrow> <mo>(</mo> <mi>p</mi> <mo>,</mo> <mi>q</mi> <mo>)</mo> </mrow> </math>-domain is the region between the graphs of <math display="inline"> <mrow> <msub> <mi>q</mi> <mrow> <mo>±</mo> <mfrac> <mi>π</mi> <mn>2</mn> </mfrac> </mrow> </msub> <mspace width="-0.166667em"/> <mo>=</mo> <mspace width="-0.166667em"/> <mo>±</mo> <mfrac> <mi>π</mi> <mn>2</mn> </mfrac> <mo form="prefix">tanh</mo> <mi>p</mi> </mrow> </math> and the lines <math display="inline"> <mrow> <mi>p</mi> <mspace width="-0.166667em"/> <mo>=</mo> <mspace width="-0.166667em"/> <mn>0</mn> </mrow> </math> and <math display="inline"> <mrow> <mi>p</mi> <mspace width="-0.166667em"/> <mo>=</mo> <mspace width="-0.166667em"/> <mrow> <mi>arcsinh</mi> </mrow> <mspace width="0.166667em"/> <mi>T</mi> </mrow> </math>. On the <b>left</b>, <math display="inline"> <mrow> <mo>(</mo> <mi>t</mi> <mo>,</mo> <mi>ϕ</mi> <mo>)</mo> </mrow> </math> are dimensionless radial and azimuthal coordinates. On the <b>right</b>, the canonical <math display="inline"> <mrow> <mo>(</mo> <mi>p</mi> <mo>,</mo> <mi>q</mi> <mo>)</mo> </mrow> </math>-coordinates are plotted as Cartesian coordinates, with <span class="html-italic">p</span> on the horizontal axis. Recall Equation (<a href="#FD28-axioms-03-00070" class="html-disp-formula">28</a>), and compare with <a href="#axioms-03-00070-f003" class="html-fig">Figure 3</a>.</p> Full article ">
161 KiB  
Communication
On Transcendental Numbers
by Florin F. Nichita
Axioms 2014, 3(1), 64-69; https://doi.org/10.3390/axioms3010064 - 21 Feb 2014
Cited by 4 | Viewed by 4565
Abstract
Transcendental numbers play an important role in many areas of science. This paper contains a short survey on transcendental numbers and some relations among them. New inequalities for transcendental numbers are stated in Section 2 and proved in Section 4. Also, in relationship [...] Read more.
Transcendental numbers play an important role in many areas of science. This paper contains a short survey on transcendental numbers and some relations among them. New inequalities for transcendental numbers are stated in Section 2 and proved in Section 4. Also, in relationship with these topics, we study the exponential function axioms related to the Yang-Baxter equation. Full article
330 KiB  
Article
A Hybrid Artificial Reputation Model Involving Interaction Trust, Witness Information and the Trust Model to Calculate the Trust Value of Service Providers
by Gurdeep Singh Ransi and Ziad Kobti
Axioms 2014, 3(1), 50-63; https://doi.org/10.3390/axioms3010050 - 19 Feb 2014
Cited by 1 | Viewed by 5521
Abstract
Agent interaction in a community, such as the online buyer-seller scenario, is often uncertain, as when an agent comes in contact with other agents they initially know nothing about each other. Currently, many reputation models are developed that help service consumers select better [...] Read more.
Agent interaction in a community, such as the online buyer-seller scenario, is often uncertain, as when an agent comes in contact with other agents they initially know nothing about each other. Currently, many reputation models are developed that help service consumers select better service providers. Reputation models also help agents to make a decision on who they should trust and transact with in the future. These reputation models are either built on interaction trust that involves direct experience as a source of information or they are built upon witness information also known as word-of-mouth that involves the reports provided by others. Neither the interaction trust nor the witness information models alone succeed in such uncertain interactions. In this paper we propose a hybrid reputation model involving both interaction trust and witness information to address the shortcomings of existing reputation models when taken separately. A sample simulation is built to setup buyer-seller services and uncertain interactions. Experiments reveal that the hybrid approach leads to better selection of trustworthy agents where consumers select more reputable service providers, eventually helping consumers obtain more gains. Furthermore, the trust model developed is used in calculating trust values of service providers. Full article
(This article belongs to the Special Issue Axioms of Decision Support System)
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<p>Framework for centralized Reputation Systems. “Adapted from [<a href="#B1-axioms-03-00050" class="html-bibr">1</a>]”. (<b>a</b>) Past interaction between agents is shown; (<b>b</b>) Present interaction between agents is shown.</p> Full article ">Figure 2
<p>Framework for Distributed Reputation Systems. “Adapted from [<a href="#B1-axioms-03-00050" class="html-bibr">1</a>]”. (<b>a</b>) Past interaction is between agents is shown; (<b>b</b>) Present interaction between agents is shown.</p> Full article ">Figure 3
<p>Overview of the hybrid model having both direct and indirect sources of information.</p> Full article ">Figure 4
<p>Experimental Results involving hybrid and witness as source of information.</p> Full article ">Figure 5
<p>Experimental Results involving hybrid and witness as source of information.</p> Full article ">Figure 6
<p>Shows trust values of all providers for camera as a product from Amazon<sup>®</sup> website.</p> Full article ">
133 KiB  
Concept Paper
The Three Laws of Thought, Plus One: The Law of Comparisons
by Thomas L. Saaty
Axioms 2014, 3(1), 46-49; https://doi.org/10.3390/axioms3010046 - 10 Feb 2014
Cited by 1 | Viewed by 46366
Abstract
The rules of logic are nearly 2500 years old and date back to Plato and Aristotle who set down the three laws of thought: identity, non-contradiction, and excluded middle. The use of language and logic has been adequate for us to develop mathematics, [...] Read more.
The rules of logic are nearly 2500 years old and date back to Plato and Aristotle who set down the three laws of thought: identity, non-contradiction, and excluded middle. The use of language and logic has been adequate for us to develop mathematics, prove theorems, and create scientific knowledge. However, the laws of thought are incomplete. We need to extend our logical system by adding to the very old laws of thought an essential yet poorly understood law. It is a necessary law of thought that resides in our biology even deeper than the other three laws. It is related to the rudiments of how we as living beings, and even nonliving things, respond to influences as stimuli. It helps us discriminate between being ourselves and sensing that there is something else that is not ourselves that even amoebas seem to know. It is the intrinsic ability to sense and distinguish. This fourth law is the law of comparisons. Although it has been missing from our logical deductions it underlies the other three laws of thought because without it we cannot know what is and what is not. Full article
(This article belongs to the Special Issue Axioms of Decision Support System)
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<p>Plato (Left) Holding the Timaeus and Aristotle Holding the Ethics, a Painting by Raphael Sanzio at the School of Athens.</p> Full article ">
301 KiB  
Article
Second-Order Risk Constraints in Decision Analysis
by Love Ekenberg, Mats Danielson, Aron Larsson and David Sundgren
Axioms 2014, 3(1), 31-45; https://doi.org/10.3390/axioms3010031 - 17 Jan 2014
Cited by 13 | Viewed by 4606
Abstract
Recently, representations and methods aimed at analysing decision problems where probabilities and values (utilities) are associated with distributions over them (second-order representations) have been suggested. In this paper we present an approach to how imprecise information can be modelled by means of second-order [...] Read more.
Recently, representations and methods aimed at analysing decision problems where probabilities and values (utilities) are associated with distributions over them (second-order representations) have been suggested. In this paper we present an approach to how imprecise information can be modelled by means of second-order distributions and how a risk evaluation process can be elaborated by integrating procedures for numerically imprecise probabilities and utilities. We discuss some shortcomings of the use of the principle of maximising the expected utility and of utility theory in general, and offer remedies by the introduction of supplementary decision rules based on a concept of risk constraints taking advantage of second-order distributions. Full article
(This article belongs to the Special Issue Axioms of Decision Support System)
218 KiB  
Review
Business Decision-Making Using Geospatial Data: A Research Framework and Literature Review
by Michael A. Erskine, Dawn G. Gregg, Jahangir Karimi and Judy E. Scott
Axioms 2014, 3(1), 10-30; https://doi.org/10.3390/axioms3010010 - 23 Dec 2013
Cited by 12 | Viewed by 8369
Abstract
Organizations that leverage their increasing volume of geospatial data have the potential to enhance their strategic and organizational decisions. However, literature describing the best techniques to make decisions using geospatial data and the best approaches to take advantage of geospatial data’s unique visualization [...] Read more.
Organizations that leverage their increasing volume of geospatial data have the potential to enhance their strategic and organizational decisions. However, literature describing the best techniques to make decisions using geospatial data and the best approaches to take advantage of geospatial data’s unique visualization capabilities is limited. This paper reviews the use of geospatial visualization and its effects on decision performance, which is one of the many components of decision-making when using geospatial data. Additionally, this paper proposes a comprehensive model allowing researchers to better understand decision-making using geospatial data and provides a robust foundation for future research. Finally, this paper makes an argument for further research of information-presentation, task-characteristics, user-characteristics and their effects on decision-performance when utilizing geospatial data. Full article
(This article belongs to the Special Issue Axioms of Decision Support System)
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<p>Conceptual geospatial decision-making model.</p> Full article ">
247 KiB  
Communication
A Method for Negotiating Various Customer Requirements for Public Service Design
by Yoshiki Shimomura, Yutaro Nemoto, Fumiya Akasaka and Koji Kimita
Axioms 2014, 3(1), 1-9; https://doi.org/10.3390/axioms3010001 - 20 Dec 2013
Cited by 1 | Viewed by 5252
Abstract
A method for public service design, which enables designers to realize high-value added service design by considering plural different customer groups in parallel, is proposed. In General, service designs focus on specific customers. However, because of the diversity of customer requirements, it is [...] Read more.
A method for public service design, which enables designers to realize high-value added service design by considering plural different customer groups in parallel, is proposed. In General, service designs focus on specific customers. However, because of the diversity of customer requirements, it is difficult to design a public service that addresses the requirements of all customers. To achieve higher customer satisfaction, it is imperative to summarize the requirements of various customers and design a service by considering customers belonging to different categories. In this article, we propose a method that enables highly public service development by considering groups of various customers and minimizing customer dissatisfaction by adopting a group-decision-making approach. As a consequence, improvement of effectiveness of highly public service development can be expected. Full article
(This article belongs to the Special Issue Axioms of Decision Support System)
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<p>Distribution of the personas.</p> Full article ">
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