2,492 research outputs found
Asymptotic Normality of the Maximum Pseudolikelihood Estimator for Fully Visible Boltzmann Machines
Boltzmann machines (BMs) are a class of binary neural networks for which
there have been numerous proposed methods of estimation. Recently, it has been
shown that in the fully visible case of the BM, the method of maximum
pseudolikelihood estimation (MPLE) results in parameter estimates which are
consistent in the probabilistic sense. In this article, we investigate the
properties of MPLE for the fully visible BMs further, and prove that MPLE also
yields an asymptotically normal parameter estimator. These results can be used
to construct confidence intervals and to test statistical hypotheses. We
support our theoretical results by showing that the estimator behaves as
expected in a simulation study
Mixtures of Spatial Spline Regressions
We present an extension of the functional data analysis framework for
univariate functions to the analysis of surfaces: functions of two variables.
The spatial spline regression (SSR) approach developed can be used to model
surfaces that are sampled over a rectangular domain. Furthermore, combining SSR
with linear mixed effects models (LMM) allows for the analysis of populations
of surfaces, and combining the joint SSR-LMM method with finite mixture models
allows for the analysis of populations of surfaces with sub-family structures.
Through the mixtures of spatial splines regressions (MSSR) approach developed,
we present methodologies for clustering surfaces into sub-families, and for
performing surface-based discriminant analysis. The effectiveness of our
methodologies, as well as the modeling capabilities of the SSR model are
assessed through an application to handwritten character recognition
Multipair Full-Duplex Relaying with Massive Arrays and Linear Processing
We consider a multipair decode-and-forward relay channel, where multiple
sources transmit simultaneously their signals to multiple destinations with the
help of a full-duplex relay station. We assume that the relay station is
equipped with massive arrays, while all sources and destinations have a single
antenna. The relay station uses channel estimates obtained from received pilots
and zero-forcing (ZF) or maximum-ratio combining/maximum-ratio transmission
(MRC/MRT) to process the signals. To reduce significantly the loop interference
effect, we propose two techniques: i) using a massive receive antenna array; or
ii) using a massive transmit antenna array together with very low transmit
power at the relay station. We derive an exact achievable rate in closed-form
for MRC/MRT processing and an analytical approximation of the achievable rate
for ZF processing. This approximation is very tight, especially for large
number of relay station antennas. These closed-form expressions enable us to
determine the regions where the full-duplex mode outperforms the half-duplex
mode, as well as, to design an optimal power allocation scheme. This optimal
power allocation scheme aims to maximize the energy efficiency for a given sum
spectral efficiency and under peak power constraints at the relay station and
sources. Numerical results verify the effectiveness of the optimal power
allocation scheme. Furthermore, we show that, by doubling the number of
transmit/receive antennas at the relay station, the transmit power of each
source and of the relay station can be reduced by 1.5dB if the pilot power is
equal to the signal power, and by 3dB if the pilot power is kept fixed, while
maintaining a given quality-of-service
Periods for flat algebraic connections
In previous work, we established a duality between the algebraic de Rham
cohomology of a flat algebraic connection on a smooth quasi-projective surface
over the complex numbers and the rapid decay homology of the dual connection
relying on a conjecture by C. Sabbah, which has been proved recently by T.
Mochizuki for algebraic connections in any dimension. In the present article,
we verify that Mochizuki's results allow to generalize these duality results to
arbitrary dimensions also
Thermal kinetic inductance detectors for ground-based millimeter-wave cosmology
We show measurements of thermal kinetic inductance detectors (TKID) intended
for millimeter wave cosmology in the 200-300 GHz atmospheric window. The TKID
is a type of bolometer which uses the kinetic inductance of a superconducting
resonator to measure the temperature of the thermally isolated bolometer
island. We measure bolometer thermal conductance, time constant and noise
equivalent power. We also measure the quality factor of our resonators as the
bath temperature varies to show they are limited by effects consistent with
coupling to two level systems.Comment: 8 pages, 4 figures. Submitted to Journal of Low Temperature Physic
Homological perturbation theory for nonperturbative integrals
We use the homological perturbation lemma to produce explicit formulas
computing the class in the twisted de Rham complex represented by an arbitrary
polynomial. This is a non-asymptotic version of the method of Feynman diagrams.
In particular, we explain that phenomena usually thought of as particular to
asymptotic integrals in fact also occur exactly: integrals of the type
appearing in quantum field theory can be reduced in a totally algebraic fashion
to integrals over an Euler--Lagrange locus, provided this locus is understood
in the scheme-theoretic sense, so that imaginary critical points and
multiplicities of degenerate critical points contribute.Comment: 22 pages. Minor revisions from previous versio
Simple Combined Model for Nonlinear Excitations in DNA
We propose a new simple model for DNA denaturation bases on the pendulum
model of Englander\cite{A1} and the microscopic model of Peyrard {\it et
al.},\cite{A3} so called "combined model". The main parameters of our model
are: the coupling constant along each strand, the mean stretching
of the hydrogen bonds, the ratio of the damping constant and driven force
. We show that both the length of unpaired bases and the velocity
of kinks depend on not only the coupling constant but also the
temperature . Our results are in good agreement with previous works.Comment: 6 pages, 10 figures, submitted to Phys. Rev.
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