Exact temporal evolution for some non-linear diffusion process

Exact solutions to FokkerPlanck equations with nonlinear drift are considered. Applications of these exact solutions for concrete models are studied. We arrive at the conclusion that for certain drifts we obtain divergent moments (and infinite relaxation time) if the diffusion process can be extended without any obstacle to the whole space. But if we introduce a potential barrier that limits the diffusion process, moments converge with a finite relaxation time.

Variational localized-site cluster expansions. X. Dimerization in linear Heisenberg chains

Ground-state instability to bond alternation in long linear chains is considered from the point of view of valence-bond (VB) theory. This instability is viewed as the consequence of a long-range order (LRO) which is expected if the ground state is reasonably described in terms of the Kekulé states (with nearest-neighbor singlet pairing). It is argued that the bond alternation and associated LRO predicted by this simple, VB picture is retained for certain linear Heisenberg models; many-body VB calculations on spin s=1 / 2 and s=1 chains are carried out in a test of this argument.

To select or to weigh: a comparative study of linear combination schemes for superparent-one-dependence estimators

We conduct a large-scale comparative study on linearly combining superparent-one-dependence estimators (SPODEs), a popular family of seminaive Bayesian classifiers. Altogether, 16 model selection and weighing schemes, 58 benchmark data sets, and various statistical tests are employed. This paper's main contributions are threefold. First, it formally presents each scheme's definition, rationale, and time complexity and hence can serve as a comprehensive reference for researchers interested in ensemble learning. Second, it offers bias-variance analysis for each scheme's classification error performance. Third, it identifies effective schemes that meet various needs in practice. This leads to accurate and fast classification algorithms which have an immediate and significant impact on real-world applications. Another important feature of our study is using a variety of statistical tests to evaluate multiple learning methods across multiple data sets.

Analysis of linear networks with inconsistent initial conditions

This paper presents a new method to analyze timeinvariant linear networks allowing the existence of inconsistent initial conditions. This method is based on the use of distributions and state equations. Any time-invariant linear network can be analyzed. The network can involve any kind of pure or controlled sources. Also, the transferences of energy that occur at t=O are determined, and the concept of connection energy is introduced. The algorithms are easily implemented in a computer program.

Linear least squares estimation of the first order moving average parameter

We propose an iterative procedure to minimize the sum of squares function which avoids the nonlinear nature of estimating the first order moving average parameter and provides a closed form of the estimator. The asymptotic properties of the method are discussed and the consistency of the linear least squares estimator is proved for the invertible case. We perform various Monte Carlo experiments in order to compare the sample properties of the linear least squares estimator with its nonlinear counterpart for the conditional and unconditional cases. Some examples are also discussed

A theoretical and practical study on linear reforms of dual taxes

[cat] En aquest treball extenem les reformes lineals introduïdes per Pfähler (1984) al cas d’impostos duals. Estudiem l’efecte relatiu que els retalls lineals duals d’un impost dual tenen sobre la distribució de la desigualtat -es pot fer un estudi simètric per al cas d’augments d’impostos-. Tambe introduïm mesures del grau de progressivitat d’impostos duals i mostrem que estan connectades amb el criteri de dominació de Lorenz. Addicionalment, estudiem l’elasticitat de la càrrega fiscal de cadascuna de les reformes proposades. Finalment, gràcies a un model de microsimulació i una gran base de dades que conté informació sobre l’IRPF espanyol de l’any 2004, 1) comparem l’efecte que diferents reformes tindrien sobre l’impost dual espanyol i 2) estudiem quina redistribució de la riquesa va suposar la reforma dual de l’IRPF (Llei ’35/2006’) respecte l’anterior impost.

Utilization of dietary glucose in the metabolic syndrome

This review is focused on the fate of dietary glucose under conditions of chronically high energy (largely fat) intake, evolving into the metabolic syndrome. We are adapted to carbohydrate-rich diets similar to those of our ancestors. Glucose is the main energy staple, but fats are our main energy reserves. Starvation drastically reduces glucose availability, forcing the body to shift to fatty acids as main energy substrate, sparing glucose and amino acids. We are not prepared for excess dietary energy, our main defenses being decreased food intake and increased energy expenditure, largely enhanced metabolic activity and thermogenesis. High lipid availability is a powerful factor decreasing glucose and amino acid oxidation. Present-day diets are often hyperenergetic, high on lipids, with abundant protein and limited amounts of starchy carbohydrates. Dietary lipids favor their metabolic processing, saving glucose, which additionally spares amino acids. The glucose excess elicits hyperinsulinemia, which may derive, in the end, into insulin resistance. The available systems of energy disposal could not cope with the excess of substrates, since they are geared for saving not for spendthrift, which results in an unbearable overload of the storage mechanisms. Adipose tissue is the last energy sink, it has to store the energy that cannot be used otherwise. However, adipose tissue growth also has limits, and the excess of energy induces inflammation, helped by the ineffective intervention of the immune system. However, even under this acute situation, the excess of glucose remains, favoring its final conversion to fat. The sum of inflammatory signals and deranged substrate handling induce most of the metabolic syndrome traits: insulin resistance, obesity, diabetes, liver steatosis, hyperlipidemia and their compounded combined effects. Thus, a maintained excess of energy in the diet may result in difficulties in the disposal of glucose, eliciting inflammation and the development of the metabolic syndrome

Treatment patterns and health care resource utilization in a 1-year observational cohort study of outpatients with schizophrenia at risk of nonadherence treated with long-acting injectable antipsychotics

Purpose: To describe (1) the clinical profiles and the patterns of use of long-acting injectable (LAI) antipsychotics in patients with schizophrenia at risk of nonadherence with oral antipsychotics, and in those who started treatment with LAI antipsychotics, (2) health care resource utilization and associated costs. Patients and methods: A total of 597 outpatients with schizophrenia at risk of nonadherence, according to the psychiatrist's clinical judgment, were recruited at 59 centers in a noninterventional prospective observational study of 1-year follow-up when their treatment was modified. In a post hoc analysis, the profiles of patients starting LAI or continuing with oral antipsychotics were described, and descriptive analyses of treatments, health resource utilization, and direct costs were performed in those who started an LAI antipsychotic. Results: Therapy modifications involved the antipsychotic medications in 84.8% of patients, mostly because of insufficient efficacy of prior regimen. Ninety-two (15.4%) patients started an LAI antipsychotic at recruitment. Of these, only 13 (14.1%) were prescribed with first-generation antipsychotics. During 1 year, 16.3% of patients who started and 14.9% of patients who did not start an LAI antipsychotic at recruitment relapsed, contrasting with the 20.9% who had been hospitalized only within the prior 6 months. After 1 year, 74.3% of patients who started an LAI antipsychotic continued concomitant treatment with oral antipsychotics. The mean (median) total direct health care cost per patient per month during the study year among the patients starting any LAI antipsychotic at baseline was 1,407 ( 897.7). Medication costs (including oral and LAI antipsychotics and concomitant medication) represented almost 44%, whereas nonmedication costs accounted for more than 55% of the mean total direct health care costs. Conclusion: LAI antipsychotics were infrequently prescribed in spite of a psychiatrist-perceived risk of nonadherence to oral antipsychotics. Mean medication costs were lower than nonmedication costs.

Enhanced pulse propagation in non-linear arrays of oscillators

The propagation of a pulse in a nonlinear array of oscillators is influenced by the nature of the array and by its coupling to a thermal environment. For example, in some arrays a pulse can be speeded up while in others a pulse can be slowed down by raising the temperature. We begin by showing that an energy pulse (one dimension) or energy front (two dimensions) travels more rapidly and remains more localized over greater distances in an isolated array (microcanonical) of hard springs than in a harmonic array or in a soft-springed array. Increasing the pulse amplitude causes it to speed up in a hard chain, leaves the pulse speed unchanged in a harmonic system, and slows down the pulse in a soft chain. Connection of each site to a thermal environment (canonical) affects these results very differently in each type of array. In a hard chain the dissipative forces slow down the pulse while raising the temperature speeds it up. In a soft chain the opposite occurs: the dissipative forces actually speed up the pulse, while raising the temperature slows it down. In a harmonic chain neither dissipation nor temperature changes affect the pulse speed. These and other results are explained on the basis of the frequency vs energy relations in the various arrays

Polydispersity index from linear viscoelastic data: Unimodal and bimodal linear polymer melts

This article describes a method for determining the polydispersity index Ip2=Mz/Mw of the molecular weight distribution (MWD) of linear polymeric materials from linear viscoelastic data. The method uses the Mellin transform of the relaxation modulus of a simple molecular rheological model. One of the main features of this technique is that it enables interesting MWD information to be obtained directly from dynamic shear experiments. It is not necessary to achieve the relaxation spectrum, so the ill-posed problem is avoided. Furthermore, a determinate shape of the continuous MWD does not have to be assumed in order to obtain the polydispersity index. The technique has been developed to deal with entangled linear polymers, whatever the form of the MWD is. The rheological information required to obtain the polydispersity index is the storage G′(ω) and loss G″(ω) moduli, extending from the terminal zone to the plateau region. The method provides a good agreement between the proposed theoretical approach and the experimental polydispersity indices of several linear polymers for a wide range of average molecular weights and polydispersity indices. It is also applicable to binary blends.

SAT Modulo Linear Arithmetic for Solving Polynomial

Polynomial constraint solving plays a prominent role in several areas of hardware and software analysis and verification, e.g., termination proving, program invariant generation and hybrid system verification, to name a few. In this paper we propose a new method for solving non-linear constraints based on encoding the problem into an SMT problem considering only linear arithmetic. Unlike other existing methods, our method focuses on proving satisfiability of the constraints rather than on proving unsatisfiability, which is more relevant in several applications as we illustrate with several examples. Nevertheless, we also present new techniques based on the analysis of unsatisfiable cores that allow one to efficiently prove unsatisfiability too for a broad class of problems. The power of our approach is demonstrated by means of extensive experiments comparing our prototype with state-of-the-art tools on benchmarks taken both from the academic and the industrial world.

A non-linear VAD for noisy environments

This paper deals with non-linear transformations for improving the performance of an entropy-based voice activity detector (VAD). The idea to use a non-linear transformation has already been applied in the field of speech linear prediction, or linear predictive coding (LPC), based on source separation techniques, where a score function is added to classical equations in order to take into account the true distribution of the signal. We explore the possibility of estimating the entropy of frames after calculating its score function, instead of using original frames. We observe that if the signal is clean, the estimated entropy is essentially the same; if the signal is noisy, however, the frames transformed using the score function may give entropy that is different in voiced frames as compared to nonvoiced ones. Experimental evidence is given to show that this fact enables voice activity detection under high noise, where the simple entropy method fails.