Computing symmetry groups of polyhedra

Knowing the symmetries of a polyhedron can be very useful for the analysis of its structure as well as for practical polyhedral computations. In this note, we study symmetry groups preserving the linear, projective and combinatorial structure of a polyhedron. In each case we give algorithmic methods to compute the corresponding group and discuss some practical experiences. For practical purposes the linear symmetry group is the most important, as its computation can be directly translated into a graph automorphism problem. We indicate how to compute integral subgroups of the linear symmetry group that are used for instance in integer linear programming.Comment: 20 pages, 1 figure; containing a corrected and improved revisio

Superposition in nonlinear wave and evolution equations

Real and bounded elliptic solutions suitable for applying the Khare-Sukhatme superposition procedure are presented and used to generate superposition solutions of the generalized modified Kadomtsev-Petviashvili equation (gmKPE) and the nonlinear cubic-quintic Schroedinger equation (NLCQSE).Comment: submitted to International Journal of Theoretical Physics, 23 pages, 2 figures, style change

Exploiting Polyhedral Symmetries in Social Choice

A large amount of literature in social choice theory deals with quantifying the probability of certain election outcomes. One way of computing the probability of a specific voting situation under the Impartial Anonymous Culture assumption is via counting integral points in polyhedra. Here, Ehrhart theory can help, but unfortunately the dimension and complexity of the involved polyhedra grows rapidly with the number of candidates. However, if we exploit available polyhedral symmetries, some computations become possible that previously were infeasible. We show this in three well known examples: Condorcet's paradox, Condorcet efficiency of plurality voting and in Plurality voting vs Plurality Runoff.Comment: 14 pages; with minor improvements; to be published in Social Choice and Welfar

Measurement of 1323 and 1487 keV resonances in 15N({\alpha}, {\gamma})19F with the recoil separator ERNA

The origin of fluorine is a widely debated issue. Nevertheless, the ^{15}N({\alpha},{\gamma})^{19}F reaction is a common feature among the various production channels so far proposed. Its reaction rate at relevant temperatures is determined by a number of narrow resonances together with the DC component and the tails of the two broad resonances at E_{c.m.} = 1323 and 1487 keV. Measurement through the direct detection of the 19F recoil ions with the European Recoil separator for Nuclear Astrophysics (ERNA) were performed. The reaction was initiated by a 15N beam impinging onto a 4He windowless gas target. The observed yield of the resonances at Ec.m. = 1323 and 1487 keV is used to determine their widths in the {\alpha} and {\gamma} channels. We show that a direct measurement of the cross section of the ^{15}N({\alpha},{\gamma})^{19}F reaction can be successfully obtained with the Recoil Separator ERNA, and the widths {\Gamma}_{\gamma} and {\Gamma}_{\alpha} of the two broad resonances have been determined. While a fair agreement is found with earlier determination of the widths of the 1487 keV resonance, a significant difference is found for the 1323 keV resonance {\Gamma}_{\alpha} . The revision of the widths of the two more relevant broad resonances in the 15N({\alpha},{\gamma})19F reaction presented in this work is the first step toward a more firm determination of the reaction rate. At present, the residual uncertainty at the temperatures of the ^{19}F stellar nucleosynthesis is dominated by the uncertainties affecting the Direct Capture component and the 364 keV narrow resonance, both so far investigated only through indirect experiments.Comment: 8 pages, 11 figures. Accepted for publication in PR

The Scientific Case for Brain Simulators

A key element of the European Union’s Human Brain Project (HBP) and other large-scale brain research projects is the simulation of large-scale model networks of neurons. Here, we argue why such simulations will likely be indispensable for bridging the scales between the neuron and system levels in the brain, and why a set of brain simulators based on neuron models at different levels of biological detail should therefore be developed. To allow for systematic refinement of candidate network models by comparison with experiments, the simulations should be multimodal in the sense that they should predict not only action potentials, but also electric, magnetic, and optical signals measured at the population and system levels

Essential role of glucose transporter GLUT3 for post-implantation embryonic development

Deletion of glucose transporter gene Slc2a3 (GLUT3) has previously been reported to result in embryonic lethality. Here, we define the exact time point of growth arrest and subsequent death of the embryo. Slc2a3−/− morulae and blastocysts developed normally, implanted in vivo, and formed egg-cylinder-stage embryos that appeared normal until day 6·0. At day 6·5, apoptosis was detected in the ectodermal cells of Slc2a3−/− embryos resulting in severe disorganization and growth retardation at day 7·5 and complete loss of embryos at day 12·5. GLUT3 was detected in placental cone, in the visceral ectoderm and in the mesoderm of 7·5-day-old wild-type embryos. Our data indicate that GLUT3 is essential for the development of early post-implanted embryos

Exploring language as the “in-between”

Assuming a performative notion of language, this contribution addresses how language functions as a symbolic means and asks for its function for the dialogical self. In accordance with a non-individualistic notion, individuals are related to each other within and by virtue of an in-between. This in-between is called “spacetime of language”: a dynamic evolving across time, perceived as linguistic forms with their chronotopology and the positionings of the performers (self as-whom to other as-whom). With respect to the linguistic forms, the specificity of language functioning is described by Bühler’s term of displacement. The effect of displacement is to generate sharedness by inducing a movement the partners follow, going beyond their actual, sensitive contact. Symbolic displacement, expanding Bühler’s notion, is particularly interesting with regard to the dialogical self: it permits the social construction of several perspectives on self, other, and reality—positions and voices informing the self’s performances

Structural Information in Two-Dimensional Patterns: Entropy Convergence and Excess Entropy

We develop information-theoretic measures of spatial structure and pattern in more than one dimension. As is well known, the entropy density of a two-dimensional configuration can be efficiently and accurately estimated via a converging sequence of conditional entropies. We show that the manner in which these conditional entropies converge to their asymptotic value serves as a measure of global correlation and structure for spatial systems in any dimension. We compare and contrast entropy-convergence with mutual-information and structure-factor techniques for quantifying and detecting spatial structure.Comment: 11 pages, 5 figures, http://www.santafe.edu/projects/CompMech/papers/2dnnn.htm

Neuron splitting in compute-bound parallel network simulations enables runtime scaling with twice as many processors

Neuron tree topology equations can be split into two subtrees and solved on different processors with no change in accuracy, stability, or computational effort; communication costs involve only sending and receiving two double precision values by each subtree at each time step. Splitting cells is useful in attaining load balance in neural network simulations, especially when there is a wide range of cell sizes and the number of cells is about the same as the number of processors. For compute-bound simulations load balance results in almost ideal runtime scaling. Application of the cell splitting method to two published network models exhibits good runtime scaling on twice as many processors as could be effectively used with whole-cell balancing