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A unified metric is given for the evaluation of object tracking systems. The metric is inspired by KL-divergence or relative entropy, which is commonly used to evaluate clustering techniques. Since tracking problems are fundamentally…
In many statistical modeling frameworks, goodness-of-fit tests are typically administered to the estimated residuals. In the time series setting, whiteness of the residuals is assessed using the sample autocorrelation function. For many…
A general method of minimization using correlation coefficients and order statistics is evaluated relative to least squares procedures in the estimation of parameters for normal data in simple linear regression.
We present separability criteria based on local symmetric measurements. These experimental plausible criteria are shown to be more efficient in detecting entanglement than the current counterparts by detailed examples. Furthermore, we…
We consider a new type of defect in the scope of linear elasticity theory, using geometrical methods. This defect is produced by a spherically symmetric dislocation, or ball dislocation. We derive the induced metric as well as the affine…
We present a sequential version of the kernelized Stein discrepancy goodness-of-fit test, which allows for conducting goodness-of-fit tests for unnormalized densities that are continuously monitored and adaptively stopped. That is, the…
The statistical properties of local alignment algorithms with gaps are analyzed theoretically for uncorrelated and correlated DNA sequences. In the vicinity of the log-linear phase transition, the statistics of alignment with gaps is shown…
Scattering can rapidly degrade our ability to form an optical image, to the point where only speckle-like patterns can be measured. Truly non-invasive imaging through a strongly scattering obstacle is difficult, and usually reliant on a…
The conformance testing problem for dynamical systems asks, given two dynamical models (e.g., as Simulink diagrams), whether their behaviors are "close" to each other. In the semi-formal approach to conformance testing, the two systems are…
The notion of concept drift refers to the phenomenon that the distribution, which is underlying the observed data, changes over time; as a consequence machine learning models may become inaccurate and need adjustment. Many unsupervised…
Concept drift -- the change of the distribution over time -- poses significant challenges for learning systems and is of central interest for monitoring. Understanding drift is thus paramount, and drift localization -- determining which…
We introduce two forms of correlations on two $d$-level (qudit) systems for entanglement detection. The correlations can be measured via experimentally tractable two local measurement settings and their separable bounds are determined by…
In this thesis we analyse three aspects of Conformal Field Theories (CFTs). First, we consider correlation functions of descendant states in two-dimensional CFTs. We discuss a recursive formula to calculate them and provide a computer…
It is well known that correlations in microarray data represent a serious nuisance deteriorating the performance of gene selection procedures. This paper is intended to demonstrate that the correlation structure of microarray data provides…
A prescription is presented for a new and practical correlation coefficient, $\phi_K$, based on several refinements to Pearson's hypothesis test of independence of two variables. The combined features of $\phi_K$ form an advantage over…
The theoretical description of observables at collider experiments relies on factorization theorems separating perturbative dynamics from universal non-perturbative matrix elements. Despite significant recent progress in extending these…
Usually, density functional models are considered approximations to density functional theory, However, there is no systematic connection between the two, and this can make us doubt about a linkage. This attitude can be further enforced by…
Recently, a connection between quantum coherence and quantum steering was established and criteria for quantum steering or in other words, nonlocal advantage of quantum coherence (NAQC) were derived for two-qubit states. Here, we derive a…
The flexibility of short DNA chains is investigated via computation of the average correlation function between dimers which defines the persistence length. Path integration techniques have been applied to confine the phase space available…
`Trackability', the ability of systems to follow arbitrary reference commands, is investigated in this work. Controllability is not useful in explaining the tracking behavior of system outputs, a gap that is often overlooked. Trackability…