Self-consistent theory of current and voltage noise in multimode ballistic conductors

Electron transport in a self-consistent potential along a ballistic two-terminal conductor has been investigated. We have derived general formulas which describe the nonlinear current-voltage characteristics, differential conductance, and low-frequency current and voltage noise assuming an arbitrary distribution function and correlation properties of injected electrons. The analytical results have been obtained for a wide range of biases: from equilibrium to high values beyond the linear-response regime. The particular case of a three-dimensional Fermi-Dirac injection has been analyzed. We show that the Coulomb correlations are manifested in the negative excess voltage noise, i.e., the voltage fluctuations under high-field transport conditions can be less than in equilibrium.

Developing a numerical inverse-theory-based extraction of orientation-dependent relaxation rates from partially- relaxed spectra

Second-rank tensor interactions, such as quadrupolar interactions between the spin- 1 deuterium nuclei and the electric field gradients created by chemical bonds, are affected by rapid random molecular motions that modulate the orientation of the molecule with respect to the external magnetic field. In biological and model membrane systems, where a distribution of dynamically averaged anisotropies (quadrupolar splittings, chemical shift anisotropies, etc.) is present and where, in addition, various parts of the sample may undergo a partial magnetic alignment, the numerical analysis of the resulting Nuclear Magnetic Resonance (NMR) spectra is a mathematically ill-posed problem. However, numerical methods (de-Pakeing, Tikhonov regularization) exist that allow for a simultaneous determination of both the anisotropy and orientational distributions. An additional complication arises when relaxation is taken into account. This work presents a method of obtaining the orientation dependence of the relaxation rates that can be used for the analysis of the molecular motions on a broad range of time scales. An arbitrary set of exponential decay rates is described by a three-term truncated Legendre polynomial expansion in the orientation dependence, as appropriate for a second-rank tensor interaction, and a linear approximation to the individual decay rates is made. Thus a severe numerical instability caused by the presence of noise in the experimental data is avoided. At the same time, enough flexibility in the inversion algorithm is retained to achieve a meaningful mapping from raw experimental data to a set of intermediate, model-free

A Theory of Random Consumer Demand

This paper presents a new theory of random consumer demand. The primitive is a collection of probability distributions, rather than a binary preference. Various assumptions constrain these distributions, including analogues of common assumptions about preferences such as transitivity, monotonicity and convexity. Two results establish a complete representation of theoretically consistent random demand. The purpose of this theory of random consumer demand is application to empirical consumer demand problems. To this end, the theory has several desirable properties. It is intrinsically stochastic, so the econometrician can apply it directly without adding extrinsic randomness in the form of residuals. Random demand is parsimoniously represented by a single function on the consumption set. Finally, we have a practical method for statistical inference based on the theory, described in McCausland (2004), a companion paper.

Bayesian Analysis for a Theory of Random Consumer Demand: The Case of Indivisible Goods

McCausland (2004a) describes a new theory of random consumer demand. Theoretically consistent random demand can be represented by a \"regular\" \"L-utility\" function on the consumption set X. The present paper is about Bayesian inference for regular L-utility functions. We express prior and posterior uncertainty in terms of distributions over the indefinite-dimensional parameter set of a flexible functional form. We propose a class of proper priors on the parameter set. The priors are flexible, in the sense that they put positive probability in the neighborhood of any L-utility function that is regular on a large subset bar(X) of X; and regular, in the sense that they assign zero probability to the set of L-utility functions that are irregular on bar(X). We propose methods of Bayesian inference for an environment with indivisible goods, leaving the more difficult case of indefinitely divisible goods for another paper. We analyse individual choice data from a consumer experiment described in Harbaugh et al. (2001).

Semiclassical theory of shot noise in ballistic n+in+ semiconductor structures: relevance of Pauli and long range Coulomb interactions

We work out a semiclassical theory of shot noise in ballistic n+-i-n+ semiconductor structures aiming at studying two fundamental physical correlations coming from Pauli exclusion principle and long-range Coulomb interaction. The theory provides a unifying scheme which, in addition to the current-voltage characteristics, describes the suppression of shot noise due to Pauli and Coulomb correlations in the whole range of system parameters and applied bias. The whole scenario is summarized by a phase diagram in the plane of two dimensionless variables related to the sample length and contact chemical potential. Here different regions of physical interest can be identified where only Coulomb or only Pauli correlations are active, or where both are present with different relevance. The predictions of the theory are proven to be fully corroborated by Monte Carlo simulations.

Self-consistent theory of current and voltage noise in multimode ballistic conductors

Electron transport in a self-consistent potential along a ballistic two-terminal conductor has been investigated. We have derived general formulas which describe the nonlinear current-voltage characteristics, differential conductance, and low-frequency current and voltage noise assuming an arbitrary distribution function and correlation properties of injected electrons. The analytical results have been obtained for a wide range of biases: from equilibrium to high values beyond the linear-response regime. The particular case of a three-dimensional Fermi-Dirac injection has been analyzed. We show that the Coulomb correlations are manifested in the negative excess voltage noise, i.e., the voltage fluctuations under high-field transport conditions can be less than in equilibrium.

Stochastic perturbations to dynamical systems: a response theory approach

Using the formalism of the Ruelle response theory, we study how the invariant measure of an Axiom A dynamical system changes as a result of adding noise, and describe how the stochastic perturbation can be used to explore the properties of the underlying deterministic dynamics. We first find the expression for the change in the expectation value of a general observable when a white noise forcing is introduced in the system, both in the additive and in the multiplicative case. We also show that the difference between the expectation value of the power spectrum of an observable in the stochastically perturbed case and of the same observable in the unperturbed case is equal to the variance of the noise times the square of the modulus of the linear susceptibility describing the frequency-dependent response of the system to perturbations with the same spatial patterns as the considered stochastic forcing. This provides a conceptual bridge between the change in the fluctuation properties of the system due to the presence of noise and the response of the unperturbed system to deterministic forcings. Using Kramers-Kronig theory, it is then possible to derive the real and imaginary part of the susceptibility and thus deduce the Green function of the system for any desired observable. We then extend our results to rather general patterns of random forcing, from the case of several white noise forcings, to noise terms with memory, up to the case of a space-time random field. Explicit formulas are provided for each relevant case analysed. As a general result, we find, using an argument of positive-definiteness, that the power spectrum of the stochastically perturbed system is larger at all frequencies than the power spectrum of the unperturbed system. We provide an example of application of our results by considering the spatially extended chaotic Lorenz 96 model. These results clarify the property of stochastic stability of SRB measures in Axiom A flows, provide tools for analysing stochastic parameterisations and related closure ansatz to be implemented in modelling studies, and introduce new ways to study the response of a system to external perturbations. Taking into account the chaotic hypothesis, we expect that our results have practical relevance for a more general class of system than those belonging to Axiom A.

Random Prism: a noise-tolerant alternative to Random Forests

Ensemble learning can be used to increase the overall classification accuracy of a classifier by generating multiple base classifiers and combining their classification results. A frequently used family of base classifiers for ensemble learning are decision trees. However, alternative approaches can potentially be used, such as the Prism family of algorithms that also induces classification rules. Compared with decision trees, Prism algorithms generate modular classification rules that cannot necessarily be represented in the form of a decision tree. Prism algorithms produce a similar classification accuracy compared with decision trees. However, in some cases, for example, if there is noise in the training and test data, Prism algorithms can outperform decision trees by achieving a higher classification accuracy. However, Prism still tends to overfit on noisy data; hence, ensemble learners have been adopted in this work to reduce the overfitting. This paper describes the development of an ensemble learner using a member of the Prism family as the base classifier to reduce the overfitting of Prism algorithms on noisy datasets. The developed ensemble classifier is compared with a stand-alone Prism classifier in terms of classification accuracy and resistance to noise.

NOISE and ULTRAVIOLET DIVERGENCES IN SIMULATIONS of GINZBURG-LANDAU-LANGEVIN TYPE of EQUATIONS

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Analog Model for Quantum Gravity Effects: Phonons in Random Fluids

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Numerical study of the Ginzburg-Landau-Langevin equation: coherent structures and noise perturbation theory

Pós-graduação em Física - IFT

Foundations of stochastic geometry and theory of random sets

The first section of this chapter starts with the Buffon problem, which is one of the oldest in stochastic geometry, and then continues with the definition of measures on the space of lines. The second section defines random closed sets and related measurability issues, explains how to characterize distributions of random closed sets by means of capacity functionals and introduces the concept of a selection. Based on this concept, the third section starts with the definition of the expectation and proves its convexifying effect that is related to the Lyapunov theorem for ranges of vector-valued measures. Finally, the strong law of large numbers for Minkowski sums of random sets is proved and the corresponding limit theorem is formulated. The chapter is concluded by a discussion of the union-scheme for random closed sets and a characterization of the corresponding stable laws.

Signal or Noise? Information Theory and the Novel

In the context of a hostile funding environment, universities are increasingly asked to justify their output in narrowly defined economic terms, and this can be difficult in Humanities or Arts faculties where productivity is rarely reducible to a simple financial indicator. This can lead to a number of immediate consequences that I have no need to rehearse here, but can also result in some interesting tensions within the academic community itself. First is that which has become known as the ‘Science Wars’: the increasingly acrimonious exchanges between scientists and scientific academics and cultural critics or theorists about who has the right to describe the world. Much has already been said—and much remains to be said—about this issue, but it is not my intention to discuss it here. Rather, I will look at a second area of contestation: the incorporation of scientific theory into literary or cultural criticism. Much of this work comes from a genuine commitment to interdisciplinarity, and an appreciation of insights that a fresh perspective can bring to a familiar object. However, some can be seen as cynical attempts to lend literary studies the sort of empirical legitimacy of the sciences. In particular, I want to look at a number of critics who have applied information theory to the literary work. In this paper, I will examine several instances of this sort of criticism, and then, through an analysis of a novel by American author Richard Powers, Three Farmers on Their Way to a Dance, show how this sort of criticism merely reduces the meaningful analysis of a complex literary text.