13,971 research outputs found
Birth/birth-death processes and their computable transition probabilities with biological applications
Birth-death processes track the size of a univariate population, but many
biological systems involve interaction between populations, necessitating
models for two or more populations simultaneously. A lack of efficient methods
for evaluating finite-time transition probabilities of bivariate processes,
however, has restricted statistical inference in these models. Researchers rely
on computationally expensive methods such as matrix exponentiation or Monte
Carlo approximation, restricting likelihood-based inference to small systems,
or indirect methods such as approximate Bayesian computation. In this paper, we
introduce the birth(death)/birth-death process, a tractable bivariate extension
of the birth-death process. We develop an efficient and robust algorithm to
calculate the transition probabilities of birth(death)/birth-death processes
using a continued fraction representation of their Laplace transforms. Next, we
identify several exemplary models arising in molecular epidemiology,
macro-parasite evolution, and infectious disease modeling that fall within this
class, and demonstrate advantages of our proposed method over existing
approaches to inference in these models. Notably, the ubiquitous stochastic
susceptible-infectious-removed (SIR) model falls within this class, and we
emphasize that computable transition probabilities newly enable direct
inference of parameters in the SIR model. We also propose a very fast method
for approximating the transition probabilities under the SIR model via a novel
branching process simplification, and compare it to the continued fraction
representation method with application to the 17th century plague in Eyam.
Although the two methods produce similar maximum a posteriori estimates, the
branching process approximation fails to capture the correlation structure in
the joint posterior distribution
A Formalization of The Natural Gradient Method for General Similarity Measures
In optimization, the natural gradient method is well-known for likelihood
maximization. The method uses the Kullback-Leibler divergence, corresponding
infinitesimally to the Fisher-Rao metric, which is pulled back to the parameter
space of a family of probability distributions. This way, gradients with
respect to the parameters respect the Fisher-Rao geometry of the space of
distributions, which might differ vastly from the standard Euclidean geometry
of the parameter space, often leading to faster convergence. However, when
minimizing an arbitrary similarity measure between distributions, it is
generally unclear which metric to use. We provide a general framework that,
given a similarity measure, derives a metric for the natural gradient. We then
discuss connections between the natural gradient method and multiple other
optimization techniques in the literature. Finally, we provide computations of
the formal natural gradient to show overlap with well-known cases and to
compute natural gradients in novel frameworks
Spin Injection into a Luttinger Liquid
We study the effect of spin injection into a Luttinger liquid. The
spin-injection-detection setup of Johnson and Silsbee is considered; here spins
injected into the Luttinger liquid induce, across an interface with a
ferromagnetic metal, either a spin-dependent current () or a
spin-dependent boundary voltage (). We find that the spin-charge
separation nature of the Luttinger liquid affects and in a very
different fashion. In particular, in the Ohmic regime, depends on the
spin transport properties of the Luttinger liquid in essentially the same way
as it would in the case of a Fermi liquid. The implications of our results for
the spin-injection-detection experiments in the high cuprates are
discussed.Comment: 4 pages, REVTEX, 2 figures. Minor changes and corrections to typos.
To appear in Phys. Rev. Let
Andreev Reflection and Spin Injection into and wave Superconductors
We study the effect of spin injection into and wave superconductors,
with an emphasis on the interplay between boundary and bulk spin transport
properties. The quantities of interest include the amount of non-equilibrium
magnetization (), as well as the induced spin-dependent current () and
boundary voltage (). In general, the Andreev reflection makes each of the
three quantities depend on a different combination of the boundary and bulk
contributions. The situation simplifies either for half-metallic ferromagnets
or in the strong barrier limit, where both and depend solely on the
bulk spin transport/relaxation properties. The implications of our results for
the on-going spin injection experiments in high cuprates are discussed.Comment: 4 pages, REVTEX, 1 figure included; typos correcte
Correlation Induced Insulator to Metal Transitions
We study a spinless two-band model at half-filling in the limit of infinite
dimensions. The ground state of this model in the non-interacting limit is a
band-insulator. We identify transitions to a metal and to a charge-Mott
insulator, using a combination of analytical, Quantum Monte Carlo, and zero
temperature recursion methods. The metallic phase is a non-Fermi liquid state
with algebraic local correlation functions with universal exponents over a
range of parameters.Comment: 12 pages, REVTE
Kosterlitz-Thouless Transition and Short Range Spatial Correlations in an Extended Hubbard Model
We study the competition between intersite and local correlations in a
spinless two-band extended Hubbard model by taking an alternative limit of
infinite dimensions. We find that the intersite density fluctuations suppress
the charge Kondo energy scale and lead to a Fermi liquid to non-Fermi liquid
transition for repulsive on-site density-density interactions. In the absence
of intersite interactions, this transition reduces to the known
Kosterlitz-Thouless transition. We show that a new line of non-Fermi liquid
fixed points replace those of the zero intersite interaction problem.Comment: 11 pages, 2 figure
Mixed-valent regime of the two-channel Anderson impurity as a model for UBe_13
We investigate the mixed-valent regime of a two-configuration Anderson
impurity model for uranium ions, with separate quadrupolar and magnetic
doublets. With a new Monte Carlo approach and the non-crossing approximation we
find: (i) A non-Fermi-liquid fixed point with two-channel Kondo model critical
behavior; (ii) Distinct energy scales for screening the low-lying and excited
doublets; (iii) A semi-quantitative explanation of magnetic-susceptibility data
for UThBe assuming 60-70% quadrupolar doublet ground-state
weight, supporting the quadrupolar-Kondo interpretation.Comment: 4 Pages, 3 eps figures; submitted to Phys. Rev. Let
Fixed-point elimination in the intuitionistic propositional calculus
It is a consequence of existing literature that least and greatest
fixed-points of monotone polynomials on Heyting algebras-that is, the algebraic
models of the Intuitionistic Propositional Calculus-always exist, even when
these algebras are not complete as lattices. The reason is that these extremal
fixed-points are definable by formulas of the IPC. Consequently, the
-calculus based on intuitionistic logic is trivial, every -formula
being equivalent to a fixed-point free formula. We give in this paper an
axiomatization of least and greatest fixed-points of formulas, and an algorithm
to compute a fixed-point free formula equivalent to a given -formula. The
axiomatization of the greatest fixed-point is simple. The axiomatization of the
least fixed-point is more complex, in particular every monotone formula
converges to its least fixed-point by Kleene's iteration in a finite number of
steps, but there is no uniform upper bound on the number of iterations. We
extract, out of the algorithm, upper bounds for such n, depending on the size
of the formula. For some formulas, we show that these upper bounds are
polynomial and optimal
Screening Breakdown on the Route toward the Metal-Insulator Transition in Modulation Doped Si/SiGe Quantum Wells
Exploiting the spin resonance of two-dimensional (2D) electrons in SiGe/Si
quantum wells we determine the carrier-density-dependence of the magnetic
susceptibility. Assuming weak interaction we evaluate the density of states at
the Fermi level D(E_F), and the screening wave vector, q_TF. Both are constant
at higher carrier densities n, as for an ideal 2D carrier gas. For n < 3e11
cm-2, they decrease and extrapolate to zero at n = 7e10 cm-2. Calculating the
mobility from q_TF yields good agreement with experimental values justifying
the approach. The decrease in D(E_F) is explained by potential fluctuations
which lead to tail states that make screening less efficient and - in a
positive feedback - cause an increase of the potential fluctuations. Even in
our high mobility samples the fluctuations exceed the electron-electron
interaction leading to the formation of puddles of mobile carriers with at
least 1 micrometer diameter.Comment: 4 pages, 3 figure
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