21,394 research outputs found
Quantitative isoperimetric inequalities for log-convex probability measures on the line
The purpose of this paper is to analyze the isoperimetric inequality for
symmetric log-convex probability measures on the line. Using geometric
arguments we first re-prove that extremal sets in the isoperimetric inequality
are intervals or complement of intervals (a result due to Bobkov and Houdr\'e).
Then we give a quantitative form of the isoperimetric inequality, leading to a
somehow anomalous behavior. Indeed, it could be that a set is very close to be
optimal, in the sense that the isoperimetric inequality is almost an equality,
but at the same time is very far (in the sense of the symmetric difference
between sets) to any extremal sets! From the results on sets we derive
quantitative functional inequalities of weak Cheeger type
Exploring the bulk of tidal charged micro-black holes
We study the bulk corresponding to tidal charged brane-world black holes. We
employ a propagating algorithm which makes use of the three-dimensional
multipole expansion and analytically yields the metric elements as functions of
the five-dimensional coordinates and of the ADM mass, tidal charge and brane
tension. Since the projected brane equations cannot determine how the charge
depends on the mass, our main purpose is to select the combinations of these
parameters for which black holes of microscopic size possess a regular bulk.
Our results could in particular be relevant for a better understanding of
TeV-scale black holes.Comment: Latex, 15 pages, 1 table, 5 figures; Section 3.2 extended, typos
corrected, no change in conclusion
Incomplete markets with no Hart points
We provide a geometric test of whether a general equilibrium incomplete markets (GEI) economy has Hart points---points at which the rank of the securities payoff matrix drops. Condition (H) says that, at each nonterminal node, there is an affine set (of appropriate dimension) that intersects all of a well-specified set of convex polyhedra. If the economy has Hart points, then Condition (H) is satisfied; consequently, if condition (H) fails, the economy has no Hart points. The shapes of the convex polyhedra are determined by the number of physical goods and the dividends of the securities, but are independent of the endowments and preferences of the agents. Condition (H) fails, and thus there are no Hart points, in interesting classes of economies with only short-lived securities, including economies obtained by discretizing an economy with a continuum of states and sufficiently diverse payoffs.Incomplete Markets, GEI model, Hart points
The q-gradient method for global optimization
The q-gradient is an extension of the classical gradient vector based on the
concept of Jackson's derivative. Here we introduce a preliminary version of the
q-gradient method for unconstrained global optimization. The main idea behind
our approach is the use of the negative of the q-gradient of the objective
function as the search direction. In this sense, the method here proposed is a
generalization of the well-known steepest descent method. The use of Jackson's
derivative has shown to be an effective mechanism for escaping from local
minima. The q-gradient method is complemented with strategies to generate the
parameter q and to compute the step length in a way that the search process
gradually shifts from global in the beginning to almost local search in the
end. For testing this new approach, we considered six commonly used test
functions and compared our results with three Genetic Algorithms (GAs)
considered effective in optimizing multidimensional unimodal and multimodal
functions. For the multimodal test functions, the q-gradient method
outperformed the GAs, reaching the minimum with a better accuracy and with less
function evaluations.Comment: 12 pages, 1 figur
Quantum Dissipation in a Neutrino System Propagating in Vacuum and in Matter
Considering the neutrino state like an open quantum system, we analyze its
propagation in vacuum or in matter. After defining what can be called
decoherence and relaxation effects, we show that in general the probabilities
in vacuum and in constant matter can be written in a similar way, which is not
an obvious result in this approach. From this result, we analyze the situation
where neutrinos evolution satisfies the adiabatic limit and use this formalim
to study solar neutrinos. We show that the decoherence effect may not be
bounded by the solar neutrino data and review some results in the literature.
We discuss the current results where solar neutrinos were used to put bounds on
decoherence effects through a model-dependent approach. We conclude explaining
how and why this models are not general and we reinterpret these constraints.Comment: new version: title was changend and was added a table. To appear at
Nucl. Physic.
Odor-driven attractor dynamics in the antennal lobe allow for simple and rapid olfactory pattern classification
The antennal lobe plays a central role for odor processing in insects, as demonstrated by electrophysiological and imaging experiments. Here we analyze the detailed temporal evolution of glomerular activity patterns in the antennal lobe of honeybees. We represent these spatiotemporal patterns as trajectories in a multidimensional space, where each dimension accounts for the activity of one glomerulus. Our data show that the trajectories reach odor-specific steady states (attractors) that correspond to stable activity patterns at about 1 second after stimulus onset. As revealed by a detailed mathematical investigation, the trajectories are characterized by different phases: response onset, steady-state plateau, response offset, and periods of spontaneous activity. An analysis based on support-vector machines quantifies the odor specificity of the attractors and the optimal time needed for odor discrimination. The results support the hypothesis of a spatial olfactory code in the antennal lobe and suggest a perceptron-like readout mechanism that is biologically implemented in a downstream network, such as the mushroom body
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