Related papers: Finite sample breakdown point of Tukey's halfspace…
We present the new results on stability and semi-classical limit in a semiconductor full quantum hydrodynamic (FQHD) model with non-flat doping profile. The FQHD model can be used to analyze the thermal and quantum influences on the…
This paper is concerned with the study of Aubry-Mather and weak KAM theories for contact Hamiltonian systems with Hamiltonians $H(x,u,p)$ defined on $T^*M\times\mathbb{R}$, satisfying Tonelli conditions with respect to $p$ and…
A stationary Stokes problem with a piecewise constant viscosity coefficient in multiple subdomains is considered in the paper. For standard finite element pairs, a robust inf-sup condition is required to show the robustness of the…
This thesis belongs to the area of General Topology and, in particular, to the field of study of uniform spaces. It is divided in three parts where the related topics Bourbaki-completeness and Samuel realcompactification are studied. In the…
We offer a survey of recent results on covariance estimation for heavy-tailed distributions. By unifying ideas scattered in the literature, we propose user-friendly methods that facilitate practical implementation. Specifically, we…
Quantum many-body simulation provides a straightforward way to understand fundamental physics and connect with quantum information applications. However, suffering from exponentially growing Hilbert space size, characterization in terms of…
Recent results from Higgs boson and supersymmetry searches at the Large Hadron Collider provide strong new motivations for supersymmetric theories with heavy superpartners. We reconsider focus point supersymmetry (FP SUSY), in which all…
Data depth is a statistical function that generalizes order and quantiles to the multivariate setting and beyond, with applications spanning over descriptive and visual statistics, anomaly detection, testing, etc. The celebrated halfspace…
We introduce a robust estimator of the location parameter for the change-point in the mean based on the Wilcoxon statistic and establish its consistency for $L_1$ near epoch dependent processes. It is shown that the consistency rate depends…
We study distributions of persistent homology barcodes associated to taking subsamples of a fixed size from metric measure spaces. We show that such distributions provide robust invariants of metric measure spaces, and illustrate their use…
The topic of robustness is experiencing a resurgence of interest in the statistical and machine learning communities. In particular, robust algorithms making use of the so-called median of means estimator were shown to satisfy strong…
We establish a stability result for the Shannon-McMillan-Breiman theorem on the one-sided finite shift space. For any shift-invariant probability measure P and any data-dependent parsing whose number of blocks is sublinear in N almost…
We introduce a novel longitudinal mixed model for analyzing complex multidimensional functional data, addressing challenges such as high-resolution, structural complexities, and computational demands. Our approach integrates dimension…
We develop algorithms for detecting multiple changepoints in functional data when the number of changepoints is unknown (unsupervised case), when it is specified apriori (supervised case), and when certain bounds are available…
A sequence of invertible matrices given by a small random perturbation around a fixed diagonal partially hyperbolic matrix induces a random dynamics on the Grassmann manifolds. Under suitable weak conditions it is known to have a unique…
The Tukey (or halfspace) depth extends nonparametric methods toward multivariate data. The multivariate analogues of the quantiles are the central regions of the Tukey depth, defined as sets of points in the $d$-dimensional space whose…
Finite Sample Smeariness (FSS) has been recently discovered. It means that the distribution of sample Fr\'echet means of underlying rather unsuspicious random variables can behave as if it were smeary for quite large regimes of finite…
The problem of establishing out-of-sample bounds for the values of an unkonwn ground-truth function is considered. Kernels and their associated Hilbert spaces are the main formalism employed herein along with an observational model where…
The stickiness effect is a fundamental feature of quasi-integrable Hamiltonian systems. We propose the use of an entropy-based measure of the recurrence plots (RP), namely, the entropy of the distribution of the recurrence times (estimated…
The primary objective of this paper is to demonstrate that problems related to stability and robust control in the harmonic context can be effectively addressed by formulating them as semidefinite optimization problems, invoking the concept…