20,610 research outputs found
Ninth and Tenth Order Virial Coefficients for Hard Spheres in D Dimensions
We evaluate the virial coefficients B_k for k<=10 for hard spheres in
dimensions D=2,...,8. Virial coefficients with k even are found to be negative
when D>=5. This provides strong evidence that the leading singularity for the
virial series lies away from the positive real axis when D>=5. Further analysis
provides evidence that negative virial coefficients will be seen for some k>10
for D=4, and there is a distinct possibility that negative virial coefficients
will also eventually occur for D=3.Comment: 33 pages, 12 figure
Factor Graphs for Quantum Probabilities
A factor-graph representation of quantum-mechanical probabilities (involving
any number of measurements) is proposed. Unlike standard statistical models,
the proposed representation uses auxiliary variables (state variables) that are
not random variables. All joint probability distributions are marginals of some
complex-valued function , and it is demonstrated how the basic concepts of
quantum mechanics relate to factorizations and marginals of .Comment: To appear in IEEE Transactions on Information Theory, 201
Strong coupling expansion for finite temperature Yang-Mills theory in the confined phase
We perform euclidean strong coupling expansions for Yang Mills theory on the
lattice at finite temperature. After setting up the formalism for general
SU(N), we compute the first few terms of the series for the free energy density
and the lowest screening mass in the case of SU(2). To next-to-leading order
the free energy series agrees with that of an ideal gas of glueballs. This
demonstrates that in the confined phase the quasi-particles indeed correspond
to the T=0 hadron excitations, as commonly assumed in hadron resonance gas
models. Our result also fixes the lower integration constant for Monte Carlo
calculations of the thermodynamic pressure via the integral method. In accord
with Monte Carlo results, we find screening masses to be nearly temperature
independent in the confined phase. This and the exponential smallness of the
pressure can be understood as genuine strong coupling effects. Finally, we
analyse Pade approximants to estimate the critical couplings of the phase
transition, which for our short series are only ~25% accurate. However, up to
these couplings the equation of state agrees quantitatively with numerical
results on N_t=1-4 lattices.Comment: 18 pages, 4 figures, Nt=1 results added, references added, version
published in JHE
Effects of many-electron jumps in relaxation and conductivity of Coulomb glasses
A numerical study of the energy relaxation and conductivity of the Coulomb
glass is presented. The role of many-electron transitions is studied by two
complementary methods: a kinetic Monte Carlo algorithm and a master equation in
configuration space method. A calculation of the transition rate for
two-electron transitions is presented, and the proper extension of this to
multi-electron transitions is discussed. It is shown that two-electron
transitions are important in bypassing energy barriers which effectively block
sequential one-electron transitions. The effect of two-electron transitions is
also discussed.Comment: 8 pages, 6 figure
Under-dominance constrains the evolution of negative autoregulation in diploids
Regulatory networks have evolved to allow gene expression to rapidly track changes in the environment as well as to buffer perturbations and maintain cellular homeostasis in the absence of change. Theoretical work and empirical investigation in Escherichia coli have shown that negative autoregulation confers both rapid response times and reduced intrinsic noise, which is reflected in the fact that almost half of Escherichia coli transcription factors are negatively autoregulated. However, negative autoregulation is rare amongst the transcription factors of Saccharomyces cerevisiae. This difference is surprising because E. coli and S. cerevisiae otherwise have similar profiles of network motifs. In this study we investigate regulatory interactions amongst the transcription factors of Drosophila melanogaster and humans, and show that they have a similar dearth of negative autoregulation to that seen in S. cerevisiae. We then present a model demonstrating that this stiking difference in the noise reduction strategies used amongst species can be explained by constraints on the evolution of negative autoregulation in diploids. We show that regulatory interactions between pairs of homologous genes within the same cell can lead to under-dominance - mutations which result in stronger autoregulation, and decrease noise in homozygotes, paradoxically can cause increased noise in heterozygotes. This severely limits a diploid's ability to evolve negative autoregulation as a noise reduction mechanism. Our work offers a simple and general explanation for a previously unexplained difference between the regulatory architectures of E. coli and yeast, Drosophila and humans. It also demonstrates that the effects of diploidy in gene networks can have counter-intuitive consequences that may profoundly influence the course of evolution
Sequential Monte Carlo for Graphical Models
We propose a new framework for how to use sequential Monte Carlo (SMC)
algorithms for inference in probabilistic graphical models (PGM). Via a
sequential decomposition of the PGM we find a sequence of auxiliary
distributions defined on a monotonically increasing sequence of probability
spaces. By targeting these auxiliary distributions using SMC we are able to
approximate the full joint distribution defined by the PGM. One of the key
merits of the SMC sampler is that it provides an unbiased estimate of the
partition function of the model. We also show how it can be used within a
particle Markov chain Monte Carlo framework in order to construct
high-dimensional block-sampling algorithms for general PGMs
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