Power law size distribution of supercritical random trees

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We propose a new convex integration scheme in fluid mechanics, and we provide an application to the two-dimensional Euler equations. We prove the flexibility and nonuniqueness of L∞L2 weak solutions with vorticity in L∞Lp for some p>1, surpassing for the first time the critical scaling of the standard convex integration technique. To achieve this, we introduce several new ideas, including: a new family of building blocks built from the Lamb–Chaplygin dipole; a new method to cancel the error based on time av

The stochastic gradient descent (SGD) method is a widely used approach for solving stochastic optimization problems, but its convergence is typically slow. Existing variance reduction techniques, such as SAGA, improve convergence by leveraging stored gradient information; however, they are restricted to settings where the objective functional is a finite sum, and their performance degrades when the number of terms in the sum is large. In this work, we propose a novel approach which is well suited when the o

We propose additive regression models for response densities, which may be observed only via a sample from the conditional density given scalar covariates - or even a single observation, nicely linking our functional regression approach to distributional regression models for scalar data. We formulate our models in Bayes Hilbert spaces to incorporate nonnegativity and integration to one constraints for densities. Considering densities and Bayes Hilbert spaces with respect to an arbitrary finite measure allo

In this project, we study and compare two methods to solve stochastic ordinary differential equations. The first is the Monte Carlo method and the second uses Polynomial Chaos. In the first part, we will solve a stochastic ordinary differential equation by both a crude Monte Carlo method and a Quasi-Monte Carlo method. Convergence analysis of the two different methods is performed. Generation of samples according to different probability distributions is studied in detail. In the second part, we will approx

We present a method for multimodal fusion based on the estimated reliability of each individual modality. Our method uses an information theoretic measure, the entropy derived from the state probability distribution for each stream, as an estimate of reliability. Our application is audio-visual speech recognition. The two modalities, audio and video, are weighted at each time instant according to their reliability. In this way, the weights vary dynamically and are able to adapt to any type of noise in each

We present an on-the-fly abstraction technique for infinite-state continuous-time Markov chains. We consider Markov chains that are specified by a finite set of transition classes. Such models naturally represent biochemical reactions and therefore play an important role in the stochastic modeling of biological systems. We approximate the transient probability distributions at various time instances by solving a sequence of dynamically constructed abstract models, each depending on the previous one. Each ab

Odorant receptors are an excellent example of natural superiority in binding specific, small and hydrophobic molecules, and therefore are of particular interest in the development of a sensor platform for G protein-coupled receptors (GPCRs). Odorant receptors (OR5) of Rattus norvegicus were incorporated into model membranes by in vitro synthesis and vectorial incorporation for achieving natural receptor function. The vectorial insertion of OR5 into the planar membrane and their lateral distribution, their i

In this paper, we present a new approach towards high performance speech/music discrimination on realistic tasks related to the automatic transcription of broadcast news. In the approach presented here, the (local) Probability Density Function (PDF) estimators trained on clean, microphone, speech (as used in a standard large vocabulary speech recognition system) are used as a channel model at the output of which the entropy and ``dynamism'' will be measured and integrated over time through a 2-state (speech

Methods to improve noise robustness of speech recognition systems often result in degradation of recognition performance for clean speech. Recently proposed Phase AutoCorrelation (PAC) \cite{ikbal03,ikbal03a} based features, showing noticeable improvement in noise robustness, also suffer from this draw back. In this paper, we try to alleviate this problem by using the PAC based features along with regular speech features in a multi-stream framework. The multi-stream system uses entropy of the posterior prob

Several authors have proposed studying randomly forced turbulent hows (e.g., E. A. Novikov, Soviet Physics JETP, 20(5), 1290 1965). More recently, theoretical investigations (e.g., renormalization group) have focused on whim-noise forced Navier-Stokes equations (V. Yakhot and S. A. Orszag, J.Sci.Comput. 1(1), 3 1986), The present article aims to provide an appropriate numerical method for the simulation of randomly forced turbulent systems. The spatial discretization is based on the classical Fourier spectr

Recent neurobiophysics experiments based on synchrotron spectromicroscopy indicated that aluminium is selectively accumulated by GABAergic neurons and glial cells rather than by granule cells. Does a similar cell specificity occur in the accumulation of other metals? We provide experimental evidence to the contrary: cobalt is found in granule cells at least with equal probability as in glial cells and GABAergic neurons. This result also confirms that neurobiophysics studies based on surface physics techniqu

Optimal channel networks are fractal structures that bear a striking resemblance to real rivers. They are obtained by minimizing an energy functional associated with spanning trees. We show that large network development effectively occurs al zero temperature since the entropy scales subdominantly with system size compared to the energy. Thus these networks develop under generic conditions and freeze into a static scale-free structure. We suggest a link of optimal channel networks with self-organized critic

We present measurements for the resistivity of

c' axis oriented YBa2Cu3O7-δ (YBCO) films grown on (100) SrTiO3 substrates by both laser ablation and ion beam sputtering. The effect of the magnetic field on the resistivity is investigated with the field parallel to the

c' axis. The zero field transition widths vary from 1 K to 4 K in different films. However the data exhibits 3d X-Y critical scaling having introduced an `effective' magnetic field characteristic of the length scale of the disorder in the f

Power law size distribution of supercritical random trees

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Flexibility of two-dimensional Euler flows with integrable vorticity

Stochastic gradient with least-squares control variates

Bayes Hilbert Space Additive Density-on-scalar Regression Based on Individual Observations

Solving Stochastic Ordinary Differential Equations by Monte Carlo and Polynomial Chaos

Audio-visual reliability estimates using stream entropy for speech recognition

Sliding Window Abstraction for Infinite Markov Chains

Imaging of G protein-coupled receptors in solid-supported planar membranes at the single molecule level

Speech/Music Discrimination using Entropy and Dynamism Features in a HMM Classification Framework

Phase AutoCorrelation (PAC) features in Entropy based Multi-Stream for Robust Speech Recognition

Numerical simulation of randomly forced turbulent flows

Synchrotron spectromicroscopy of cobalt accumulation in granule cells, glial cells and GABAergic neurons

Thermodynamics of fractal networks

3d X-Y scaling of the resistivity and the effect of disorder in YBa2Cu3O7-δ thin films