463 research outputs found
Universal Parametric Correlations of Eigenfunctions in Chaotic and Disordered Systems
This paper establishes the universality of parametric correlations of
eigenfunctions in chaotic and weakly disordered systems. We demonstrate this
universality in the framework of the gaussian random matrix process and obtain
predictions for a number of parametric correlators, one of them analytically.
We present numerical evidence from different models that verifies our
predictions.Comment: 11 pages, RevTeX, 2 uuencoded Postscript figure
Learning a hierarchical belief network of independent factor analyzers
Abstract Many belief networks have been proposed that are composed of binary units. However, for tasks such as object and speech recognition which produce real-valued data, binary network models are usually inadequate. Independent component analysis (ICA) learns a model from real data, but the descriptive power of this model is severly limited. We begin by describing the independent factor analysis (IFA) technique, which overcomes some of the limitations of ICA. We then create a multilayer network by cascading singlelayer IFA models. At each level, the IFA network extracts realvalued latent variables that are non-linear functions of the input data with a highly adaptive functional form, resulting in a hierarchical distributed representation of these data. Whereas exact maximum-likelihood learning of the network is intractable, we derive an algorithm that maximizes a lower bound on the likelihood, based on a variational approach
Active inference, evidence accumulation, and the urn task
Deciding how much evidence to accumulate before making a decision is a problem we and other animals often face, but one that is not completely understood. This issue is particularly important because a tendency to sample less information (often known as reflection impulsivity) is a feature in several psychopathologies, such as psychosis. A formal understanding of information sampling may therefore clarify the computational anatomy of psychopathology. In this theoretical letter, we consider evidence accumulation in terms of active (Bayesian) inference using a generic model of Markov decision processes. Here, agents are equipped with beliefs about their own behavior--in this case, that they will make informed decisions. Normative decision making is then modeled using variational Bayes to minimize surprise about choice outcomes. Under this scheme, different facets of belief updating map naturally onto the functional anatomy of the brain (at least at a heuristic level). Of particular interest is the key role played by the expected precision of beliefs about control, which we have previously suggested may be encoded by dopaminergic neurons in the midbrain. We show that manipulating expected precision strongly affects how much information an agent characteristically samples, and thus provides a possible link between impulsivity and dopaminergic dysfunction. Our study therefore represents a step toward understanding evidence accumulation in terms of neurobiologically plausible Bayesian inference and may cast light on why this process is disordered in psychopathology
Spectroscopy of bulk and few-layer superconducting NbSe with van der Waals tunnel junctions
Tunnel junctions, a well-established platform for high-resolution
spectroscopy of superconductors, require defect-free insulating barriers with
clean engagement to metals on both sides. Extending the range of materials
accessible to tunnel junction fabrication, beyond the limited selection which
allows high-quality oxide formation, requires the development of alternative
fabrication techniques. Here we show that van-der-Waals (vdW) tunnel barriers,
fabricated by stacking layered semiconductors on top of the transition metal
dichalcogenide (TMD) superconductor NbSe, sustain a stable, low noise
tunneling current, and exhibit strong suppression of sub-gap tunneling. We
utilize the technique to measure the spectra of bulk (20 nm) and ultrathin (3-
and 4-layer) devices at 70 mK. The spectra exhibit two distinct energy gaps,
the larger of which decreases monotonously with thickness and , in
agreement with BCS theory. The spectra are analyzed using a two-band model
modified to account for depairing. We show that in the bulk, the smaller gap
exhibits strong depairing in an in-plane magnetic field, consistent with a high
Fermi velocity. In the few-layer devices, depairing of the large gap is
negligible, consistent with out-of-plane spin-locking due to Ising spin-orbit
coupling. Our results demonstrate the utility of vdW tunnel junctions in
mapping the intricate spectral evolution of TMD superconductors over a range of
magnetic fields.Comment: This submission contains the first part of arxiv:1703.07677 with the
addition of spectra taken on this devices. The second part of 1703.07677 will
be published separatel
The Perturbed Static Path Approximation at Finite Temperature: Observables and Strength Functions
We present an approximation scheme for calculating observables and strength
functions of finite fermionic systems at finite temperature such as hot nuclei.
The approach is formulated within the framework of the Hubbard-Stratonovich
transformation and goes beyond the static path approximation and the RPA by
taking into account small amplitude time-dependent fluctuations around each
static value of the auxiliary fields. We show that this perturbed static path
approach can be used systematically to obtain good approximations for
observable expectation values and for low moments of the strength function. The
approximation for the strength function itself, extracted by an analytic
continuation from the imaginary-time response function, is not always reliable,
and we discuss the origin of the discrepancies and possible improvements. Our
results are tested in a solvable many-body model.Comment: 37 pages, 8 postscript figures included, RevTe
Variational approximation for mixtures of linear mixed models
Mixtures of linear mixed models (MLMMs) are useful for clustering grouped
data and can be estimated by likelihood maximization through the EM algorithm.
The conventional approach to determining a suitable number of components is to
compare different mixture models using penalized log-likelihood criteria such
as BIC.We propose fitting MLMMs with variational methods which can perform
parameter estimation and model selection simultaneously. A variational
approximation is described where the variational lower bound and parameter
updates are in closed form, allowing fast evaluation. A new variational greedy
algorithm is developed for model selection and learning of the mixture
components. This approach allows an automatic initialization of the algorithm
and returns a plausible number of mixture components automatically. In cases of
weak identifiability of certain model parameters, we use hierarchical centering
to reparametrize the model and show empirically that there is a gain in
efficiency by variational algorithms similar to that in MCMC algorithms.
Related to this, we prove that the approximate rate of convergence of
variational algorithms by Gaussian approximation is equal to that of the
corresponding Gibbs sampler which suggests that reparametrizations can lead to
improved convergence in variational algorithms as well.Comment: 36 pages, 5 figures, 2 tables, submitted to JCG
Self-consistent quantal treatment of decay rates within the perturbed static path approximation
The framework of the Perturbed Static Path Approximation (PSPA) is used to
calculate the partition function of a finite Fermi system from a Hamiltonian
with a separable two body interaction. Therein, the collective degree of
freedom is introduced in self-consistent fashion through a Hubbard-Stratonovich
transformation. In this way all transport coefficients which dominate the decay
of a meta-stable system are defined and calculated microscopically. Otherwise
the same formalism is applied as in the Caldeira-Leggett model to deduce the
decay rate from the free energy above the so called crossover temperature
.Comment: 17 pages, LaTex, no figures; final version, accepted for publication
in PRE; e-mail: [email protected]
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