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## Statistical physics of equilibrium and nonequilibrium models : a computational approach

Fonte: Universidade de Trás-os-Montes e Alto Douro
Publicador: Universidade de Trás-os-Montes e Alto Douro

Tipo: Tese de Doutorado

ENG

Relevância na Pesquisa

16.03%

Tese de Doutoramento em Física; O mote central desta tese é o estudo, por métodos computacionais, de sistemas de muitos corpos que evoluem tanto por estados de equilíbrio como por estados não-equilíbrio.
Nos sistemas que evoluem por estados de equilíbrio termodinâmico foram estudados sistemas poliméricos. Nesta área, o estudo dividiu-se em sistemas fortemente diluídos de polímeros ramificados e em sistemas fortemente densos e fundidos de polímeros lineares. Para os sistemas fortemente diluídos, fez-se uma análise da estrutura geométrica dos polímeros embebidos em redes regulares, estruturas essas denominadas animais e árvores, em redes em situações fortemente direccionadas ou dirigidas. O estudo centrou-se na análise de parâmetros não-universais presentes na expressão assimptótica do número configuracional destas estruturas, bem como nas expressões que fornecem informação sobre as suas características geométricas através do cálculo do quadrado da distância média dos monómeros, nas direcções paralela e perpendicular á direcção dirigida, a partir das séries exactas das propriedades indicadas e da simulação das estruturas pelo método de Monte Carlo. Para a obtenção das séries, foi empregue o algoritmo de enumeração de Mertens para a geração configuracional de estruturas diluídas num solvente forte para um número fixo de monómeros. As enumerações foram descriminadas segundo as valências de cada monómero da estrutura do polímero ramificado...

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## Illumination pattern optimization for fluorescence tomography: theory and simulation studies

Fonte: PubMed
Publicador: PubMed

Tipo: Artigo de Revista Científica

EN

Relevância na Pesquisa

15.71%

Fluorescence molecular tomography is a powerful tool for 3D visualization of molecular targets and pathways in vivo in small animals. Owing to the high degrees of absorption and scattering of light through tissue, the fluorescence tomographic inverse problem is inherently ill-posed. In order to improve source localization and the conditioning of the light propagation model, multiple sets of data are acquired by illuminating the animal surface with different spatial patterns of near-infrared light. However, the choice of these patterns in most experimental setups is ad hoc and suboptimal. This paper presents a systematic approach for designing efficient illumination patterns for fluorescence tomography. Our objective here is to determine how to optimally illuminate the animal surface so as to maximize the information content in the acquired data. We achieve this by improving the conditioning of the Fisher information matrix. We parameterize the spatial illumination patterns and formulate our problem as a constrained optimization problem that, for a fixed number of illumination patterns, yields the optimal set of patterns. For geometric insight, we used our method to generate a set of three optimal patterns for an optically homogeneous...

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## The Nearly Neutral and Selection Theories of Molecular Evolution Under the Fisher Geometrical Framework: Substitution Rate, Population Size, and Complexity

Fonte: Genetics Society of America
Publicador: Genetics Society of America

Tipo: Artigo de Revista Científica

Publicado em /06/2012
EN

Relevância na Pesquisa

56.02%

The general theories of molecular evolution depend on relatively arbitrary assumptions about the relative distribution and rate of advantageous, deleterious, neutral, and nearly neutral mutations. The Fisher geometrical model (FGM) has been used to make distributions of mutations biologically interpretable. We explored an FGM-based molecular model to represent molecular evolutionary processes typically studied by nearly neutral and selection models, but in which distributions and relative rates of mutations with different selection coefficients are a consequence of biologically interpretable parameters, such as the average size of the phenotypic effect of mutations and the number of traits (complexity) of organisms. A variant of the FGM-based model that we called the static regime (SR) represents evolution as a nearly neutral process in which substitution rates are determined by a dynamic substitution process in which the population’s phenotype remains around a suboptimum equilibrium fitness produced by a balance between slightly deleterious and slightly advantageous compensatory substitutions. As in previous nearly neutral models, the SR predicts a negative relationship between molecular evolutionary rate and population size; however...

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## MR Measurement of Alloy Magnetic Susceptibility: Towards Developing Tissue-Susceptibility Matched Metals

Fonte: PubMed
Publicador: PubMed

Tipo: Artigo de Revista Científica

EN

Relevância na Pesquisa

25.71%

Magnetic resonance imaging (MRI) can be used to relate structure to function mapped with
high-temporal resolution electrophysiological recordings using metal electrodes. Additionally, MRI
may be used to guide the placement of electrodes or conductive cannula in the brain. However, the
magnetic susceptibility mismatch between implanted metals and surrounding brain tissue can severely
distort MR images and spectra, particularly in high magnetic fields. In this study, we present a
modified MR method of characterizing the magnetic susceptibility of materials that can be used to
develop biocompatible, metal alloys that match the susceptibility of host tissue in order to
eliminate MR distortions proximal to the implant. This method was applied at 4.7 T and 11.1 T to
measure the susceptibility of a model solid-solution alloy of Cu and Sn, which is inexpensive but not biocompatible. MR-derived relative susceptibility values of four different compositions of Cu-Sn
alloy deviated by less than 3.1% from SQUID magnetometry absolute susceptibility
measurements performed up to 7 T. These results demonstrate that the magnetic susceptibility varies
linearly with atomic percentage in these solid-solution alloys, but are not simply the weighted
average of Cu and Sn magnetic susceptibilities. Therefore susceptibility measurements are necessary
when developing susceptibility-matched...

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## Fisher’s Geometrical Model Emerges as a Property of Complex Integrated Phenotypic Networks

Fonte: Genetics Society of America
Publicador: Genetics Society of America

Tipo: Artigo de Revista Científica

EN

Relevância na Pesquisa

46.04%

Models relating phenotype space to fitness (phenotype–fitness landscapes) have seen important developments recently. They can roughly be divided into mechanistic models (e.g., metabolic networks) and more heuristic models like Fisher’s geometrical model. Each has its own drawbacks, but both yield testable predictions on how the context (genomic background or environment) affects the distribution of mutation effects on fitness and thus adaptation. Both have received some empirical validation. This article aims at bridging the gap between these approaches. A derivation of the Fisher model “from first principles” is proposed, where the basic assumptions emerge from a more general model, inspired by mechanistic networks. I start from a general phenotypic network relating unspecified phenotypic traits and fitness. A limited set of qualitative assumptions is then imposed, mostly corresponding to known features of phenotypic networks: a large set of traits is pleiotropically affected by mutations and determines a much smaller set of traits under optimizing selection. Otherwise, the model remains fairly general regarding the phenotypic processes involved or the distribution of mutation effects affecting the network. A statistical treatment and a local approximation close to a fitness optimum yield a landscape that is effectively the isotropic Fisher model or its extension with a single dominant phenotypic direction. The fit of the resulting alternative distributions is illustrated in an empirical data set. These results bear implications on the validity of Fisher’s model’s assumptions and on which features of mutation fitness effects may vary (or not) across genomic or environmental contexts.

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## Integration of enzyme immobilised single-walled carbon nanotube arrays into microchannels for glucose detection

Fonte: Electrochemical Science Group
Publicador: Electrochemical Science Group

Tipo: Artigo de Revista Científica

Publicado em //2013
EN

Relevância na Pesquisa

25.82%

#Microfluidic devices#glucose oxidase#carbon nanotube arrays#glucose detection#ferrocenecarboxylic acid

Microfluidic devices for glucose detection have been constructed and developed by integration of covalently immobilised single-walled carbon nanotube arrays functionalised with glucose oxidase into a poly (dimethylsiloxane)-based microfluidic channel. With biocompatible ferrocenecarboxylic acid as electron transfer mediator, these microfluidic devices were tested systematically for electrochemical glucose detection by changing some geometrical parameters such as the width of detecting electrode as well as electrode gap between the enzyme electrode and the detecting electrode. Numerical simulations were also carried out using a finite difference model and used to further understand the concentration profiles in michochannels. The experimental results showed that glucose can be detected with a linear response up to a concentration of 5 mmol L⁻¹. Compared to reported glucose detection techniques, our microfluidic devices have some advantages such as simple design, repeated use and low cost.; Jingxian Yu, Sinéad M Matthews, Kamran Yunus, Joseph G Shapter and Adrian C Fisher

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## Fisher information under decoherence in Bloch representation

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

25.88%

The dynamics of two variants of quantum Fisher information under decoherence
are investigated from a geometrical point of view. We first derive the explicit
formulas of these two quantities for a single qubit in terms of the Bloch
vector. Moreover, we obtain analytical results for them under three different
decoherence channels, which are expressed as affine transformation matrices.
Using the hierarchy equation method, we numerically study the dynamics of both
the two information in a dissipative model and compare the numerical results
with the analytical ones obtained by applying the rotating-wave approximation.
We further express the two information quantities in terms of the Bloch vector
for a qudit, by expanding the density matrix and Hermitian operators in a
common set of generators of the Lie algebra $\mathfrak{su}(d)$. By calculating
the dynamical quantum Fisher information, we find that the collisional
dephasing significantly diminishes the precision of phase parameter with the
Ramsey interferometry.; Comment: 16 pages, 4 figures

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## Asymptotic Accuracy of Bayes Estimation for Latent Variables with Redundancy

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

15.95%

Hierarchical parametric models consisting of observable and latent variables
are widely used for unsupervised learning tasks. For example, a mixture model
is a representative hierarchical model for clustering. From the statistical
point of view, the models can be regular or singular due to the distribution of
data. In the regular case, the models have the identifiability; there is
one-to-one relation between a probability density function for the model
expression and the parameter. The Fisher information matrix is positive
definite, and the estimation accuracy of both observable and latent variables
has been studied. In the singular case, on the other hand, the models are not
identifiable and the Fisher matrix is not positive definite. Conventional
statistical analysis based on the inverse Fisher matrix is not applicable.
Recently, an algebraic geometrical analysis has been developed and is used to
elucidate the Bayes estimation of observable variables. The present paper
applies this analysis to latent-variable estimation and determines its
theoretical performance. Our results clarify behavior of the convergence of the
posterior distribution. It is found that the posterior of the
observable-variable estimation can be different from the one in the
latent-variable estimation. Because of the difference...

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## Geometrical Aspects on Parameter estimation of stochastic gravitational wave background: beyond the Fisher analysis

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 22/06/2012

Relevância na Pesquisa

25.71%

The maximum likelihood method is often used for parameter estimation in
gravitational wave astronomy. Recently, an interesting approach was proposed by
Vallisneri to evaluate the distributions of parameter estimation errors
expected for the method. This approach is to statistically analyze the local
peaks of the likelihood surface, and works efficiently even for signals with
low signal-to-noise ratios. Focusing special attention to geometric structure
of the likelihood surface, we follow the proposed approach and derive formulae
for a simplified model of data analysis where the target signal has only one
intrinsic parameter, along with its overall amplitude. Then we apply our
formulae to correlation analysis of stochastic gravitational wave background
with a power-law spectrum. We report qualitative trends of the formulae using
numerical results specifically obtained for correlation analysis with two
Advanced-LIGO detectors.; Comment: 23 pages, to be published in PRD

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## An information criterion for model selection with missing data via complete-data divergence

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

25.78%

We derive an information criterion for selecting a parametric model of
complete-data distribution when only incomplete or partially observed data is
available. Compared with AIC, the new criterion has an additional penalty term
for missing data expressed by the Fisher information matrices of complete data
and incomplete data. We prove that the new criterion is an asymptotically
unbiased estimator of the complete-data divergence, namely, the expected
Kullback-Leibler divergence between the true distribution and the estimated
distribution for complete data, whereas AIC is that for the incomplete data.
Information criteria PDIO (Shimodaira 1994) and AICcd (Cavanaugh and Shumway
1998) have been previously proposed for estimating the complete-data
divergence, and these two criteria have the same penalty term. The additional
penalty term of the new criterion for missing data turns out to be only the
half of what is claimed in PDIO and AICcd. We observe in a simulation study
that the new criterion is unbiased while the other two criteria are biased.
Before starting the argument of model selection, we review the geometrical view
of alternating minimizations of the EM algorithm, which plays an important role
for the derivation of the new criterion.

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## Effects of cosmological model assumptions on galaxy redshift survey measurements

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

25.91%

The clustering of galaxies observed in future redshift surveys will provide a
wealth of cosmological information. Matching the signal at different redshifts
constrains the dark energy driving the acceleration of the expansion of the
Universe. In tandem with these geometrical constraints, redshift-space
distortions (RSD) depend on the build up of large-scale structure. As pointed
out by many authors measurements of these effects are intrinsically coupled. We
investigate this link, and argue that it strongly depends on the cosmological
assumptions adopted when analysing data. Using representative assumptions for
the parameters of the Euclid survey in order to provide a baseline future
experiment, we show how the derived constraints change due to different model
assumptions. We argue that even the assumption of a Friedman-Robertson-Walker
(FRW) space-time is sufficient to reduce the importance of the coupling to a
significant degree. Taking this idea further, we consider how the data would
actually be analysed and argue that we should not expect to be able to
simultaneously constrain multiple deviations from the standard $\Lambda$CDM
model. We therefore consider different possible ways in which the Universe
could deviate from the $\Lambda$CDM model...

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## Information Geometry, One, Two, Three (and Four)

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 15/08/2003

Relevância na Pesquisa

15.8%

Although the notion of entropy lies at the core of statistical mechanics, it
is not often used in statistical mechanical models to characterize phase
transitions, a role more usually played by quantities such as various order
parameters, specific heats or suscept ibilities. The relative entropy induces a
metric, the so-called information or Fisher-Rao m etric, on the space of
parameters and the geometrical invariants of this metric carry information
about the phase structure of the model.
In various models the scalar curvature, ${\cal R}$, of the information metric
has been found to diverge at the phase transition point and a plausible scaling
relation postulated. For spin models the necessity of calculating in non-zero
field has limited analytic consideration to one-dimensional, mean-field and
Bethe lattice Ising models. We report on previous papers in which we extended
the list somewhat in the current note by considering the {\it one}-dime nsional
Potts model, the {\it two}-dimensional Ising model coupled to two-dimensional
quantum gravity and the {\it three}-dimensional spherical model. We note that
similar ideas have been ap plied to elucidate possible critical behaviour in
families of black hole solutions in
{\it four} space-time dimensions.

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## A Widely Applicable Bayesian Information Criterion

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 30/08/2012

Relevância na Pesquisa

15.8%

A statistical model or a learning machine is called regular if the map taking
a parameter to a probability distribution is one-to-one and if its Fisher
information matrix is always positive definite. If otherwise, it is called
singular. In regular statistical models, the Bayes free energy, which is
defined by the minus logarithm of Bayes marginal likelihood, can be
asymptotically approximated by the Schwarz Bayes information criterion (BIC),
whereas in singular models such approximation does not hold.
Recently, it was proved that the Bayes free energy of a singular model is
asymptotically given by a generalized formula using a birational invariant, the
real log canonical threshold (RLCT), instead of half the number of parameters
in BIC. Theoretical values of RLCTs in several statistical models are now being
discovered based on algebraic geometrical methodology. However, it has been
difficult to estimate the Bayes free energy using only training samples,
because an RLCT depends on an unknown true distribution.
In the present paper, we define a widely applicable Bayesian information
criterion (WBIC) by the average log likelihood function over the posterior
distribution with the inverse temperature $1/\log n$, where $n$ is the number
of training samples. We mathematically prove that WBIC has the same asymptotic
expansion as the Bayes free energy...

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## Statistical Geometry in Quantum Mechanics

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

15.76%

A statistical model M is a family of probability distributions, characterised
by a set of continuous parameters known as the parameter space. This possesses
natural geometrical properties induced by the embedding of the family of
probability distributions into the Hilbert space H. By consideration of the
square-root density function we can regard M as a submanifold of the unit
sphere in H. Therefore, H embodies the `state space' of the probability
distributions, and the geometry of M can be described in terms of the embedding
of in H. The geometry in question is characterised by a natural Riemannian
metric (the Fisher-Rao metric), thus allowing us to formulate the principles of
classical statistical inference in a natural geometric setting. In particular,
we focus attention on the variance lower bounds for statistical estimation, and
establish generalisations of the classical Cramer-Rao and Bhattacharyya
inequalities. The statistical model M is then specialised to the case of a
submanifold of the state space of a quantum mechanical system. This is pursued
by introducing a compatible complex structure on the underlying real Hilbert
space, which allows the operations of ordinary quantum mechanics to be
reinterpreted in the language of real Hilbert space geometry. The application
of generalised variance bounds in the case of quantum statistical estimation
leads to a set of higher order corrections to the Heisenberg uncertainty
relations for canonically conjugate observables.; Comment: 32 pages...

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## On the Enlargement by Pr\"ufer Objects of the Cluster Category of type $A_\infty$

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 18/11/2014

Relevância na Pesquisa

25.71%

In a paper by Holm and Jorgensen, the cluster category $\mathscr{D}$ of type
$A_\infty$, with Auslander-Reiten quiver $\mathbb{Z} A_\infty$, is introduced.
Slices in the Auslander-Reiten quiver of $\mathscr{D}$ give rise to direct
systems; the homotopy colimit of such direct systems can be computed and these
"Pr\"ufer objects" can be adjoined to form a larger category. It is this larger
category, $\overline{\mathscr{D}},$ which is the main object of study in this
paper. We show that $\overline{\mathscr{D}}$ inherits a nice geometrical
structure from $\mathscr{D}$; "arcs" between non-neighbouring integers on the
number line correspond to indecomposable objects, and in the case of
$\overline{\mathscr{D}}$ we also have arcs to infinity which correspond to the
Pr\"ufer objects. During the course of this paper, we show that
$\overline{\mathscr{D}}$ is triangulated, compute homs, investigate the
geometric model, and we conclude by computing the cluster tilting subcategories
of $\overline{\mathscr{D}}$.; Comment: 36 pages

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## Critical behavior of the geometrical spin clusters and interfaces in the two-dimensional thermalized bond Ising model

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 29/02/2012

Relevância na Pesquisa

26.06%

The fractal dimensions and the percolation exponents of the geometrical spin
clusters of like sign at criticality, are obtained numerically for an Ising
model with temperature-dependent annealed bond dilution, also known as the
thermalized bond Ising model (TBIM), in two dimensions. For this purpose, a
modified Wolff single-cluster Monte Carlo simulation is used to generate
equilibrium spin configurations on square lattices in the critical region. A
tie-breaking rule is employed to identify non-intersecting spin cluster
boundaries along the edges of the dual lattice. The values obtained for the
fractal dimensions of the spanning geometrical clusters $D_{c}$, and their
interfaces $D_{I}$, are in perfect agreement with those reported for the
standard two-dimensional ferromagnetic Ising model. Furthermore, the variance
of the winding angles, results in a diffusivity $\kappa=3$ for the
two-dimensional thermalized bond Ising model, thus placing it in the
universality class of the regular Ising model. A finite-size scaling analysis
of the largest geometrical clusters, results in a reliable estimation of the
critical percolation exponents for the geometrical clusters in the limit of an
infinite lattice size. The percolation exponents thus obtained...

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## Reaction-subdiffusion front propagation in a comblike model of spiny dendrites

Fonte: Universidade Autônoma de Barcelona
Publicador: Universidade Autônoma de Barcelona

Tipo: Artigo de Revista Científica
Formato: application/pdf

Publicado em //2013
ENG

Relevância na Pesquisa

25.76%

Fractional reaction-diffusion equations are derived by exploiting the geometrical similarities between a comb structure and a spiny dendrite. In the framework of the obtained equations, two scenarios of reaction transport in spiny dendrites are explored, where both a linear reaction in spines and nonlinear Fisher-Kolmogorov-Petrovskii-Piskunov reactions along dendrites are considered. In the framework of fractional subdiffusive comb model, we develop a Hamilton-Jacobi approach to estimate the overall velocity of the reaction front propagation. One of the main effects observed is the failure of the front propagation for both scenarios due to either the reaction inside the spines or the interaction of the reaction with the spines. In the first case the spines are the source of reactions, while in the latter case, the spines are a source of a damping mechanism.

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## RATES OF FITNESS DECLINE AND REBOUND SUGGEST PERVASIVE EPISTASIS

Fonte: Wiley
Publicador: Wiley

Tipo: Artigo de Revista Científica

Publicado em /01/2014
ENG

Relevância na Pesquisa

55.9%

Unraveling the factors that determine the rate of adaptation is a major question in evolutionary biology. One key parameter is the effect of a new mutation on fitness, which invariably depends on the environment and genetic background. The fate of a mutation also depends on population size, which determines the amount of drift it will experience. Here, we manipulate both population size and genotype composition and follow adaptation of 23 distinct Escherichia coli genotypes. These have previously accumulated mutations under intense genetic drift and encompass a substantial fitness variation. A simple rule is uncovered: the net fitness change is negatively correlated with the fitness of the genotype in which new mutations appear--a signature of epistasis. We find that Fisher's geometrical model can account for the observed patterns of fitness change and infer the parameters of this model that best fit the data, using Approximate Bayesian Computation. We estimate a genomic mutation rate of 0.01 per generation for fitness altering mutations, albeit with a large confidence interval, a mean fitness effect of mutations of -0.01, and an effective number of traits nine in mutS(-) E. coli. This framework can be extended to confront a broader range of models with data and test different classes of fitness landscape models.; LAO/ITQB...

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