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 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.
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 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.
Axioms2014, 3(1), 84-108; doi:10.3390/axioms3010084 - published online 25 February 2014 Show/Hide Abstract
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 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.
Axioms2014, 3(1), 70-81; doi:10.3390/axioms3010070 - published online 24 February 2014 Show/Hide Abstract
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 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.
Axioms2014, 3(1), 64-69; doi:10.3390/axioms3010064 - published online 21 February 2014 Show/Hide Abstract
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 with these topics, we study the exponential function axioms related to the Yang-Baxter equation.