Voting and the Cardinal Aggregation of Judgments

The paper elaborates the idea that voting is an instance of the aggregation of judgments, this being a more general concept than the aggregation of preferences. To aggregate judgments one must first measure them. I show that such aggregation has been unproblematic whenever it has been based on an independent and unrestricted scale. The scales analyzed in voting theory are either context dependent or subject to unreasonable restrictions. This is the real source of the diverse 'paradoxes of voting' that would better be termed 'voting pathologies'. The theory leads me to advocate what I term evaluative voting. It can also be called utilitarian voting as it is based on having voters express their cardinal preferences. The alternative that maximizes the sum wins. This proposal operationalizes, in an election context, the abstract cardinal theories of collective choice due to Fleming and Harsanyi. On pragmatic grounds, I argue for a three valued scale for general elections

Modularity and Optimality in Social Choice

Marengo and the second author have developed in the last years a geometric model of social choice when this takes place among bundles of interdependent elements, showing that by bundling and unbundling the same set of constituent elements an authority has the power of determining the social outcome. In this paper we will tie the model above to tournament theory, solving some of the mathematical problems arising in their work and opening new questions which are interesting not only from a mathematical and a social choice point of view, but also from an economic and a genetic one. In particular, we will introduce the notion of u-local optima and we will study it from both a theoretical and a numerical/probabilistic point of view; we will also describe an algorithm that computes the universal basin of attraction of a social outcome in O(M^3 logM) time (where M is the number of social outcomes).Comment: 42 pages, 4 figures, 8 tables, 1 algorithm

Enhanced second harmonic generation from resonant GaAs gratings

We study second harmonic generation in nonlinear, GaAs gratings. We find large enhancement of conversion efficiency when the pump field excites the guided mode resonances of the grating. Under these circumstances the spectrum near the pump wavelength displays sharp resonances characterized by dramatic enhancements of local fields and favorable conditions for second harmonic generation, even in regimes of strong linear absorption at the harmonic wavelength. In particular, in a GaAs grating pumped at 1064nm, we predict second harmonic conversion efficiencies approximately five orders of magnitude larger than conversion rates achievable in either bulk or etalon structures of the same material.Comment: 8 page

Seven-body central configurations: a family of central configurations in the spatial seven-body problem

The main result of this paper is the existence of a new family of central configurations in the Newtonian spatial seven-body problem. This family is unusual in that it is a simplex stacked central configuration, i.e the bodies are arranged as concentric three and two dimensional simplexes.Comment: 15 pages 5 figure

Statistical mechanics of voting

Decision procedures aggregating the preferences of multiple agents can produce cycles and hence outcomes which have been described heuristically as `chaotic'. We make this description precise by constructing an explicit dynamical system from the agents' preferences and a voting rule. The dynamics form a one dimensional statistical mechanics model; this suggests the use of the topological entropy to quantify the complexity of the system. We formulate natural political/social questions about the expected complexity of a voting rule and degree of cohesion/diversity among agents in terms of random matrix models---ensembles of statistical mechanics models---and compute quantitative answers in some representative cases.Comment: 9 pages, plain TeX, 2 PostScript figures included with epsf.tex (ignore the under/overfull \vbox error messages

On the Global Existence of Bohmian Mechanics

We show that the particle motion in Bohmian mechanics, given by the solution of an ordinary differential equation, exists globally: For a large class of potentials the singularities of the velocity field and infinity will not be reached in finite time for typical initial values. A substantial part of the analysis is based on the probabilistic significance of the quantum flux. We elucidate the connection between the conditions necessary for global existence and the self-adjointness of the Schr\"odinger Hamiltonian.Comment: 35 pages, LaTe

Total immersion : Designing for affective symbiosis in a virtual reality game with haptics, biosensors, and emotive agents

Peer reviewe

Dynamical principles in neuroscience

Dynamical modeling of neural systems and brain functions has a history of success over the last half century. This includes, for example, the explanation and prediction of some features of neural rhythmic behaviors. Many interesting dynamical models of learning and memory based on physiological experiments have been suggested over the last two decades. Dynamical models even of consciousness now exist. Usually these models and results are based on traditional approaches and paradigms of nonlinear dynamics including dynamical chaos. Neural systems are, however, an unusual subject for nonlinear dynamics for several reasons: (i) Even the simplest neural network, with only a few neurons and synaptic connections, has an enormous number of variables and control parameters. These make neural systems adaptive and flexible, and are critical to their biological function. (ii) In contrast to traditional physical systems described by well-known basic principles, first principles governing the dynamics of neural systems are unknown. (iii) Many different neural systems exhibit similar dynamics despite having different architectures and different levels of complexity. (iv) The network architecture and connection strengths are usually not known in detail and therefore the dynamical analysis must, in some sense, be probabilistic. (v) Since nervous systems are able to organize behavior based on sensory inputs, the dynamical modeling of these systems has to explain the transformation of temporal information into combinatorial or combinatorial-temporal codes, and vice versa, for memory and recognition. In this review these problems are discussed in the context of addressing the stimulating questions: What can neuroscience learn from nonlinear dynamics, and what can nonlinear dynamics learn from neuroscience?This work was supported by NSF Grant No. NSF/EIA-0130708, and Grant No. PHY 0414174; NIH Grant No. 1 R01 NS50945 and Grant No. NS40110; MEC BFI2003-07276, and Fundación BBVA

A genetic approach for long term virtual organization distribution

Electronic versíon of an article published as International Journal on Artificial Intelligent Tools, Volume 20, issue 2, 2011. 10.1142/S0218213011000152. © World Scientific Publishing Company[EN] An agent-based Virtual Organization is a complex entity where dynamic collections of agents agree to share resources in order to accomplish a global goal or offer a complex service. An important problem for the performance of the Virtual Organization is the distribution of the agents across the computational resources. The final distribution should provide a good load balancing for the organization. In this article, a genetic algorithm is applied to calculate a proper distribution across hosts in an agent-based Virtual Organization. Additionally, an abstract multi-agent system architecture which provides infrastructure for Virtual Organization distribution is introduced. The developed genetic solution employs an elitist crossover operator where one of the children inherits the most promising genetic material from the parents with higher probability. In order to validate the genetic proposal, the designed genetic algorithm has been successfully compared to several heuristics in different scenarios. © 2011 World Scientific Publishing Company.This work is supported by TIN2008-04446, TIN2009-13839-C03-01, CSD2007-00022 and FPU grant AP2008-00600 of the Spanish government, and PROMETEO 2008/051 of the Generalitat Valenciana.Sánchez Anguix, V.; Valero Cubas, S.; García Fornes, AM. (2011). A genetic approach for long term virtual organization distribution. International Journal on Artificial Intelligence Tools. 20(2):271-295. https://doi.org/10.1142/S0218213011000152S27129520