11,164 research outputs found
Retrieval behavior and thermodynamic properties of symmetrically diluted Q-Ising neural networks
The retrieval behavior and thermodynamic properties of symmetrically diluted
Q-Ising neural networks are derived and studied in replica-symmetric mean-field
theory generalizing earlier works on either the fully connected or the
symmetrical extremely diluted network. Capacity-gain parameter phase diagrams
are obtained for the Q=3, Q=4 and state networks with uniformly
distributed patterns of low activity in order to search for the effects of a
gradual dilution of the synapses. It is shown that enlarged regions of
continuous changeover into a region of optimal performance are obtained for
finite stochastic noise and small but finite connectivity. The de
Almeida-Thouless lines of stability are obtained for arbitrary connectivity,
and the resulting phase diagrams are used to draw conclusions on the behavior
of symmetrically diluted networks with other pattern distributions of either
high or low activity.Comment: 21 pages, revte
Rise of correlations of transformation strains in random polycrystals
We investigate the statistics of the transformation strains that arise in random martensitic polycrystals as boundary conditions cause its component crystallites to undergo martensitic phase transitions. In our laminated polycrystal model the orientation of the n grains (crystallites)
is given by an uncorrelated random array of the orientation angles Ξ_i, i = 1, . . . ,n. Under imposed boundary conditions the polycrystal grains may undergo a martensitic transformation. The associated transformation strains Δ_i, i = 1, . . . ,n depend on the array of orientation angles, and they can be obtained as a solution to a nonlinear optimization problem. While the random variables Ξ_i,
i = 1, . . . ,n are uncorrelated, the random variables Δ_i, i = 1, . . . ,n may be correlated. This issue is
central in our considerations. We investigate it in following three different scaling limits: (i) Infinitely
long grains (laminated polycrystal of height L = â); (ii) Grains of finite but large height (L » 1); and (iii) Chain of short grains (L = l_0/(2n), l_0 « 1). With references to de Finettiâs theorem, Rieszâ
rearrangement inequality, and near neighbor approximations, our analyses establish that under the
scaling limits (i), (ii), and (iii) the arrays of transformation strains arising from given boundary
conditions exhibit no correlations, long-range correlations, and exponentially decaying short-range
correlations, respectivel
Symmetrically normalized instrumental-variable estimation using panel data
In this paper we discuss the estimation of panel data models with sequential moment restrictions using symmetrically normalized GMM estimators. These estimators are asymptotically equivalent to standard GMM but are invariant to normalization and tend to have a smaller finite sample bias. They also have a very different behaviour compared to standard GMM when the instruments are poor. We study the properties of SN-GMM estimators in relation to GMM, minimum distance and pseudo maximum likelihood estimators for various versions of the AR(1) model with individual effects by mean of simulations. The emphasis is not in assessing the value of enforcing particular restrictions in the model; rather, we wish to evaluate the effects in small samples of using alternative estimating criteria that produce asymptotically equivalent estimators for fixed T and large N. Finally, as an empĂrical illustration, we estimate by SN-GMM employment and wage equations using panels of UK and Spanish firms
Optimal sensing for fish school identification
Fish schooling implies an awareness of the swimmers for their companions. In
flow mediated environments, in addition to visual cues, pressure and shear
sensors on the fish body are critical for providing quantitative information
that assists the quantification of proximity to other swimmers. Here we examine
the distribution of sensors on the surface of an artificial swimmer so that it
can optimally identify a leading group of swimmers. We employ Bayesian
experimental design coupled with two-dimensional Navier Stokes equations for
multiple self-propelled swimmers. The follower tracks the school using
information from its own surface pressure and shear stress. We demonstrate that
the optimal sensor distribution of the follower is qualitatively similar to the
distribution of neuromasts on fish. Our results show that it is possible to
identify accurately the center of mass and even the number of the leading
swimmers using surface only information
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