Geometric Hamiltonian formulation of a variational problem depending on the covariant acceleration

We consider a second-order variational problem depending on the covariant acceleration, which is related to the notion of Riemannian cubic polynomials. This problem and the corresponding optimal control problem are described in the context of higher order tangent bundles using geometric tools. The main tool, a presymplectic variant of Pontryagin’s maximum principle, allows us to study the dynamics of the control problem.

Nonlinear, nonhomogeneous parametric Neumann problems

We consider a parametric nonlinear Neumann problem driven by a nonlinear nonhomogeneous differential operator and with a Caratheodory reaction $f\left( t,x\right) $ which is $p-$superlinear in $x$ without satisfying the usual in such cases Ambrosetti-Rabinowitz condition. We prove a bifurcation type result describing the dependence of the positive solutions on the parameter $\lambda>0,$ we show the existence of a smallest positive solution $\overline{u}_{\lambda}$ and investigate the properties of the map $\lambda\rightarrow\overline{u}_{\lambda}.$ Finally we also show the existence of nodal solutions.

On the axiomatic approach to the maximum entropy principle of inference

Recent axiomatic derivations of the maximum entropy principle from consistency conditions are critically examined. We show that proper application of consistency conditions alone allows a wider class of functionals, essentially of the form ∝ dx p(x)[p(x)/g(x)] s , for some real numbers, to be used for inductive inference and the commonly used form − ∝ dx p(x)ln[p(x)/g(x)] is only a particular case. The role of the prior densityg(x) is clarified. It is possible to regard it as a geometric factor, describing the coordinate system used and it does not represent information of the same kind as obtained by measurements on the system in the form of expectation values.

A maximum likelihood framework for protein design

Affiliation: Claudia Kleinman, Nicolas Rodrigue & Hervé Philippe : Département de biochimie, Faculté de médecine, Université de Montréal

Maximum Entropy Discrimination

We present a general framework for discriminative estimation based on the maximum entropy principle and its extensions. All calculations involve distributions over structures and/or parameters rather than specific settings and reduce to relative entropy projections. This holds even when the data is not separable within the chosen parametric class, in the context of anomaly detection rather than classification, or when the labels in the training set are uncertain or incomplete. Support vector machines are naturally subsumed under this class and we provide several extensions. We are also able to estimate exactly and efficiently discriminative distributions over tree structures of class-conditional models within this framework. Preliminary experimental results are indicative of the potential in these techniques.

Are the maximum hardness and minimum polarizability principles always obeyed in nontotally symmetric vibrations?

An overview is given on a study which showed that not only in chemical reactions but also in the favorable case of nontotally symmetric vibrations where the chemical and external potentials keep approximately constant, the generalized maximum hardness principle (GMHP) and generalized minimum polarizability principle (GMPP) may not be obeyed. A method that allows an accurate determination of the nontotally symmetric molecular distortions with more marked GMPP or anti-GMPP character through diagonalization of the polarizability Hessian matrix is introduced

Two maximum entropy-based algorithms for running quantile estimation in nonstationary data streams

The need to estimate a particular quantile of a distribution is an important problem that frequently arises in many computer vision and signal processing applications. For example, our work was motivated by the requirements of many semiautomatic surveillance analytics systems that detect abnormalities in close-circuit television footage using statistical models of low-level motion features. In this paper, we specifically address the problem of estimating the running quantile of a data stream when the memory for storing observations is limited. We make the following several major contributions: 1) we highlight the limitations of approaches previously described in the literature that make them unsuitable for nonstationary streams; 2) we describe a novel principle for the utilization of the available storage space; 3) we introduce two novel algorithms that exploit the proposed principle in different ways; and 4) we present a comprehensive evaluation and analysis of the proposed algorithms and the existing methods in the literature on both synthetic data sets and three large real-world streams acquired in the course of operation of an existing commercial surveillance system. Our findings convincingly demonstrate that both of the proposed methods are highly successful and vastly outperform the existing alternatives. We show that the better of the two algorithms (data-aligned histogram) exhibits far superior performance in comparison with the previously described methods, achieving more than 10 times lower estimate errors on real-world data, even when its available working memory is an order of magnitude smaller.

Kinetics of the polarization reversal process in a non-constant applied electric field and the generalized superposition principle

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

EMG activity of trunk stabilizer muscles during Centering Principle of Pilates Method

This study aimed to analyze the electromyographic (EMG) activity of iliocostalis lumborum (IL), internal oblique (IO) and multifidus (MU) and the antagonist cocontraction (IO/MU and IO/IL) during the performance of Centering Principle of Pilates Method. Participating in this study were eighteen young and physically fit volunteers, without experience in Pilates Method, divided in two groups: low back pain group (LBPG, n = 8) and control group (CG, n = 10). Two isometric contractions of IO muscles (Centering Principle) were performed in upright sitting posture. EMG signal amplitude was calculated by Root Mean Square (RMS), which was normalized by RMS maximum value. The common area method to calculate the antagonist cocontraction index was used. MU and IO activation and IO/MU cocontraction (. p < 0.05) were higher in CG. The CG therefore showed a higher stabilizer muscles recruitment than LBPG during the performance of Centering Principle of Pilates Method. © 2012 Elsevier Ltd.

The optimization principle in phylogenetic analysis tends to give incorrect topologies when the number of nucleotides or amino acids used is small

In the maximum parsimony (MP) and minimum evolution (ME) methods of phylogenetic inference, evolutionary trees are constructed by searching for the topology that shows the minimum number of mutational changes required (M) and the smallest sum of branch lengths (S), respectively, whereas in the maximum likelihood (ML) method the topology showing the highest maximum likelihood (A) of observing a given data set is chosen. However, the theoretical basis of the optimization principle remains unclear. We therefore examined the relationships of M, S, and A for the MP, ME, and ML trees with those for the true tree by using computer simulation. The results show that M and S are generally greater for the true tree than for the MP and ME trees when the number of nucleotides examined (n) is relatively small, whereas A is generally lower for the true tree than for the ML tree. This finding indicates that the optimization principle tends to give incorrect topologies when n is small. To deal with this disturbing property of the optimization principle, we suggest that more attention should be given to testing the statistical reliability of an estimated tree rather than to finding the optimal tree with excessive efforts. When a reliability test is conducted, simplified MP, ME, and ML algorithms such as the neighbor-joining method generally give conclusions about phylogenetic inference very similar to those obtained by the more extensive tree search algorithms.

Integration of ice-core, marine and terrestrial records for the Australian Last Glacial Maximum and Termination: a contribution from the OZ INTIMATE group

The degree to which Southern Hemisphere climatic changes during the end of the last glacial period and early Holocene (30-8 ka) were influenced or initiated by events occurring in the high latitudes of the Northern Hemisphere is a complex issue. There is conflicting evidence for the degree of hemispheric 'teleconnection' and an unresolved debate as to the principle forcing mechanism(s). The available hypotheses are difficult to test robustly, however, because the few detailed palaeoclimatic records in the Southern Hemisphere are widely dispersed and lack duplication. Here we present climatic and environmental reconstructions from across Australia, a key region of the Southern Hemisphere because of the range of environments it covers and the potentially important role regional atmospheric and oceanic controls play in global climate change. We identify a general scheme of events for the end of the last glacial period and early Holocene but a detailed reconstruction proved problematic. Significant progress in climate quantification and geochronological control is now urgently required to robustly investigate change through this period. Copyright (c) 2006 John Wiley & Sons, Ltd.