31,513 research outputs found
The first non-zero Neumann p-fractional eigenvalue
In this work we study the asymptotic behavior of the first non-zero Neumann p-fractional eigenvalue λ1(s,p) as s → 1- and as p → ∞. We show that there exists a constant K such that K(1-s)λ1(s,p) goes to the first non-zero Neumann eigenvalue of the p-Laplacian. While in the limit case p → ∞, we prove that λ-(1,s)1/p goes to an eigenvalue of the Hölder ∞-Laplacian.Fil: del Pezzo, Leandro Martin. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones CientÃficas y Técnicas; ArgentinaFil: Salort, Ariel Martin. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; Argentin
The thermodynamics of human reaction times
I present a new approach for the interpretation of reaction time (RT) data from behavioral experiments. From a physical perspective, the entropy of the RT distribution provides a model-free estimate of the amount of processing performed by the cognitive system. In this way, the focus is shifted from the conventional interpretation of individual RTs being either long or short, into their distribution being\ud
more or less complex in terms of entropy. The new approach enables the estimation of the cognitive processing load without reference to the informational content of the stimuli themselves, thus providing a more appropriate estimate of the cognitive impact of dierent sources of information that are carried by experimental stimuli or tasks. The paper introduces the formulation of the theory, followed by an empirical validation using a database of human RTs in lexical tasks (visual lexical decision and word\ud
naming). The results show that this new interpretation of RTs is more powerful than the traditional one. The method provides theoretical estimates of the processing loads elicited by individual stimuli. These loads sharply distinguish the responses from different tasks. In addition, it provides upper-bound estimates for the speed at which the system processes information. Finally, I argue that the theoretical proposal, and the associated empirical evidence, provide strong arguments for an adaptive system that systematically adjusts its operational processing speed to the particular demands of each stimulus. This\ud
finding is in contradiction with Hick's law, which posits a relatively constant processing speed within an experimental context
Exact goodness-of-fit testing for the Ising model
The Ising model is one of the simplest and most famous models of interacting
systems. It was originally proposed to model ferromagnetic interactions in
statistical physics and is now widely used to model spatial processes in many
areas such as ecology, sociology, and genetics, usually without testing its
goodness of fit. Here, we propose various test statistics and an exact
goodness-of-fit test for the finite-lattice Ising model. The theory of Markov
bases has been developed in algebraic statistics for exact goodness-of-fit
testing using a Monte Carlo approach. However, finding a Markov basis is often
computationally intractable. Thus, we develop a Monte Carlo method for exact
goodness-of-fit testing for the Ising model which avoids computing a Markov
basis and also leads to a better connectivity of the Markov chain and hence to
a faster convergence. We show how this method can be applied to analyze the
spatial organization of receptors on the cell membrane.Comment: 20 page
Efficiency in the cake-eating problem with quasi-geometric discounting
This paper shows that any equilibrium allocation in the cake-eating problem with quasi-geometric discounting is not Pareto efficient. However, efficiency can be established by introducing a planner who controls the initial endowment and makes transfers over time. It is shown than any Pareto efficient allocation can be supported by a perfect equilibrium with transfers.Pareto efficiency
Simulating accelerated atoms coupled to a quantum field
We show an analogy between static quantum emitters coupled to a single mode
of a quantum field and accelerated Unruh-DeWitt detectors. We envision a way to
simulate a variety of relativistic quantum field settings beyond the reach of
current computational power, such as high number of qubits coupled to a quantum
field following arbitrary non-inertial trajectories. Our scheme may be
implemented with trapped ions and circuit QED set-ups.Comment: 5 pages, 2 figures, revtex 4-
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