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Register a new userWavelet differentiation of a noisy signal
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Several differentiating algorithms of the noisy signals are considered. The proposed wavelet based technique is compared with others based on the Fourier transform and the finite differences. The accuracy of the calculations for different algorithms is estimated for two model examples.
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We study the dynamics of a class of Hamiltonian systems with dissipation, coupled to noise, in a singular (small mass) limit. We derive the homogenized equation for the position degrees of freedom in the limit, including the presence of a {em noise-induced drift} term. We prove convergence to the solution of the homogenized equation in probability and, under stronger assumptions, in an $L^p$-norm. Applications cover the overdamped limit of particle motion in a time-dependent electromagnetic field, on a manifold with time-dependent metric, and the dynamics of nuclear matter.
A survey of recents advances in the theory of Heun operators is offered. Some of the topics covered include: quadratic algebras and orthogonal polynomials, differential and difference Heun operators associated to Jacobi and Hahn polynomials, connections with time and band limiting problems in signal processing.
In this paper we make progress on the unsupervised task of mining arbitrarily shaped clusters in highly noisy datasets, which is a task present in many real-world applications. Based on the fundamental work that first applies a wavelet transform to data clustering, we propose an adaptive clustering algorithm, denoted as AdaWave, which exhibits favorable characteristics for clustering. By a self-adaptive thresholding technique, AdaWave is parameter free and can handle data in various situations. It is deterministic, fast in linear time, order-insensitive, shape-insensitive, robust to highly noisy data, and requires no pre-knowledge on data models. Moreover, AdaWave inherits the ability from the wavelet transform to cluster data in different resolutions. We adopt the grid labeling data structure to drastically reduce the memory consumption of the wavelet transform so that AdaWave can be used for relatively high dimensional data. Experiments on synthetic as well as natural datasets demonstrate the effectiveness and efficiency of our proposed method.
Signal transduction networks can form highly interconnected systems within cells due to network crosstalk, the sharing of input signals between multiple downstream responses. To better understand the evolutionary design principles underlying such networks, we study the evolution of crosstalk and the emergence of specificity for two parallel signaling pathways that arise via gene duplication and are subsequently allowed to diverge. We focus on a sequence based evolutionary algorithm and evolve the network based on two physically motivated fitness functions related to information transmission. Surprisingly, we find that the two fitness functions lead to very different evolutionary outcomes, one with a high degree of crosstalk and the other without.
Particle physics experiments such as those run in the Large Hadron Collider result in huge quantities of data, which are boiled down to a few numbers from which it is hoped that a signal will be detected. We discuss a simple probability model for this and derive frequentist and noninformative Bayesian procedures for inference about the signal. Both are highly accurate in realistic cases, with the frequentist procedure having the edge for interval estimation, and the Bayesian procedure yielding slightly better point estimates. We also argue that the significance, or $p$-value, function based on the modified likelihood root provides a comprehensive presentation of the information in the data and should be used for inference.
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