247 research outputs found
Minimax Estimation of Nonregular Parameters and Discontinuity in Minimax Risk
When a parameter of interest is nondifferentiable in the probability, the
existing theory of semiparametric efficient estimation is not applicable, as it
does not have an influence function. Song (2014) recently developed a local
asymptotic minimax estimation theory for a parameter that is a
nondifferentiable transform of a regular parameter, where the nondifferentiable
transform is a composite map of a continuous piecewise linear map with a single
kink point and a translation-scale equivariant map. The contribution of this
paper is two fold. First, this paper extends the local asymptotic minimax
theory to nondifferentiable transforms that are a composite map of a Lipschitz
continuous map having a finite set of nondifferentiability points and a
translation-scale equivariant map. Second, this paper investigates the
discontinuity of the local asymptotic minimax risk in the true probability and
shows that the proposed estimator remains to be optimal even when the risk is
locally robustified not only over the scores at the true probability, but also
over the true probability itself. However, the local robustification does not
resolve the issue of discontinuity in the local asymptotic minimax risk
Quantum and frustration effects on fluctuations of the inverse compressibility in two-dimensional Coulomb glasses
We consider interacting electrons in a two-dimensional quantum Coulomb glass
and investigate by means of the Hartree-Fock approximation the combined effects
of the electron-electron interaction and the transverse magnetic field on
fluctuations of the inverse compressibility. Preceding systematic study of the
system in the absence of the magnetic field identifies the source of the
fluctuations, interplay of disorder and interaction, and effects of hopping.
Revealed in sufficiently clean samples with strong interactions is an unusual
right-biased distribution of the inverse compressibility, which is neither of
the Gaussian nor of the Wigner-Dyson type. While in most cases weak magnetic
fields tend to suppress fluctuations, in relatively clean samples with weak
interactions fluctuations are found to grow with the magnetic field. This is
attributed to the localization properties of the electron states, which may be
measured by the participation ratio and the inverse participation number. It is
also observed that at the frustration where the Fermi level is degenerate,
localization or modulation of electrons is enhanced, raising fluctuations.
Strong frustration in general suppresses effects of the interaction on the
inverse compressibility and on the configuration of electrons.Comment: 15 pages, 18 figures, To appear in Phys. Rev.
Anatomy of nuclear shape transition in the relativistic mean field theory
A detailed microscopic study of the temperature dependence of the shapes of
some rare-earth nuclei is made in the relativistic mean field theory. Analyses
of the thermal evolution of the single-particle orbitals and their occupancies
leading to the collapse of the deformation are presented. The role of the
non-linear field on the shape transition in different nuclei is also
investigated; in its absence the shape transition is found to be sharper.Comment: REVTEX file (13pages), 12 figures, Phys. Rev. C(in press),
\documentstyle[aps,preprint]{revtex
Adaptive response and enlargement of dynamic range
Many membrane channels and receptors exhibit adaptive, or desensitized,
response to a strong sustained input stimulus, often supported by protein
activity-dependent inactivation. Adaptive response is thought to be related to
various cellular functions such as homeostasis and enlargement of dynamic range
by background compensation. Here we study the quantitative relation between
adaptive response and background compensation within a modeling framework. We
show that any particular type of adaptive response is neither sufficient nor
necessary for adaptive enlargement of dynamic range. In particular a precise
adaptive response, where system activity is maintained at a constant level at
steady state, does not ensure a large dynamic range neither in input signal nor
in system output. A general mechanism for input dynamic range enlargement can
come about from the activity-dependent modulation of protein responsiveness by
multiple biochemical modification, regardless of the type of adaptive response
it induces. Therefore hierarchical biochemical processes such as methylation
and phosphorylation are natural candidates to induce this property in signaling
systems.Comment: Corrected typos, minor text revision
Caloric curves and critical behavior in nuclei
Data from a number of different experimental measurements have been used to
construct caloric curves for five different regions of nuclear mass. These
curves are qualitatively similar and exhibit plateaus at the higher excitation
energies. The limiting temperatures represented by the plateaus decrease with
increasing nuclear mass and are in very good agreement with results of recent
calculations employing either a chiral symmetry model or the Gogny interaction.
This agreement strongly favors a soft equation of state. Evidence is presented
that critical excitation energies and critical temperatures for nuclei can be
determined over a large mass range when the mass variations inherent in many
caloric curve measurements are taken into account.Comment: In response to referees comments we have improved the discussion of
the figures and added a new figure showing the relationship between the
effective level density and the excitation energy. The discussion has been
reordered and comments are made on recent data which support the hypothesis
of a mass dependence of caloric curve
Coulomb blockade conductance peak fluctuations in quantum dots and the independent particle model
We study the combined effect of finite temperature, underlying classical
dynamics, and deformations on the statistical properties of Coulomb blockade
conductance peaks in quantum dots. These effects are considered in the context
of the single-particle plus constant-interaction theory of the Coulomb
blockade. We present numerical studies of two chaotic models, representative of
different mean-field potentials: a parametric random Hamiltonian and the smooth
stadium. In addition, we study conductance fluctuations for different
integrable confining potentials. For temperatures smaller than the mean level
spacing, our results indicate that the peak height distribution is nearly
always in good agreement with the available experimental data, irrespective of
the confining potential (integrable or chaotic). We find that the peak bunching
effect seen in the experiments is reproduced in the theoretical models under
certain special conditions. Although the independent particle model fails, in
general, to explain quantitatively the short-range part of the peak height
correlations observed experimentally, we argue that it allows for an
understanding of the long-range part.Comment: RevTex 3.1, 34 pages (including 13 EPS and PS figures), submitted to
Phys. Rev.
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Overview of mathematical approaches used to model bacterial chemotaxis I: the single cell
Mathematical modeling of bacterial chemotaxis systems has been influential and insightful in helping to understand experimental observations. We provide here a comprehensive overview of the range of mathematical approaches used for modeling, within a single bacterium, chemotactic processes caused by changes to external gradients in its environment. Specific areas of the bacterial system which have been studied and modeled are discussed in detail, including the modeling of adaptation in response to attractant gradients, the intracellular phosphorylation cascade, membrane receptor clustering, and spatial modeling of intracellular protein signal transduction. The importance of producing robust models that address adaptation, gain, and sensitivity are also discussed. This review highlights that while mathematical modeling has aided in understanding bacterial chemotaxis on the individual cell scale and guiding experimental design, no single model succeeds in robustly describing all of the basic elements of the cell. We conclude by discussing the importance of this and the future of modeling in this area
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