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Most data processing techniques, applied to biomedical and sociological time series, are only valid for random fluctuations that are stationary in time. Unfortunately, these data are often non stationary and the use of techniques of…
We provide a detailed proof of Proposition 3.1 in the paper titled ``Backstepping control of a class of space-time-varying linear parabolic PDEs via time invariant kernel functions''. In the paper titled ``Backstepping control of a class of…
There is an emerging trend in applying deep learning methods to control complex nonlinear systems. This paper considers enhancing the runtime safety of nonlinear systems controlled by neural networks in the presence of disturbance and…
In the multiple testing problem with independent tests, the classical linear step-up procedure controls the false discovery rate (FDR) at level $\pi_0\alpha$, where $\pi_0$ is the proportion of true null hypotheses and $\alpha$ is the…
Graph representations offer powerful and intuitive ways to describe data in a multitude of application domains. Here, we consider stochastic processes generating graphs and propose a methodology for detecting changes in stationarity of such…
We consider the prediction problem of a continuous-time stochastic process on an entire time-interval in terms of its recent past. The approach we adopt is based on functional kernel nonparametric regression estimation techniques where…
We aim at estimating in a non-parametric way the density $\pi$ of the stationary distribution of a $d$-dimensional stochastic differential equation $(X_t)_{t \in [0, T]}$, for $d \ge 2$, from the discrete observations of a finite sample…
We obtain an elementary invariance principle for multi-dimensional Brownian sheet where the underlying random fields are not necessarily independent or stationary. Possible applications include unit-root tests for spatial as well as panel…
Method for detection and visualization of trends, periodicities, local peculiarities in measurement series (dL-method) based on DFA technology (Detrended fluctuation analysis) is proposed. The essence of the method lies in reflecting the…
Statistical inference for non-stationary data is hindered by the failure of classical central limit theorems (CLTs), not least because there is no fixed Gaussian limit to converge to. To resolve this, we introduce relative weak convergence,…
We propose an adaptive control strategy for the simultaneous estimation of topology and synchronization in complex dynamical networks with unknown, time-varying topology. Our approach transforms the problem of time-varying topology…
Let $(U_n(t))_{t\in\R^d}$ be the empirical process associated to an $\R^d$-valued stationary process $(X_i)_{i\ge 0}$. We give general conditions, which only involve processes $(f(X_i))_{i\ge 0}$ for a restricted class of functions $f$,…
The rapid validation of newly predicted materials through autonomous synthesis requires real-time adaptive control methods that exploit physics knowledge, a capability that is lacking in most systems. Here, we demonstrate an approach to…
Recently, a framework for controller design of sampled-data nonlinear systems via their approximate discrete-time models has been proposed in the literature. In this paper we develop novel tools that can be used within this framework and…
To deploy and operate deep neural models in production, the quality of their predictions, which might be contaminated benignly or manipulated maliciously by input distributional deviations, must be monitored and assessed. Specifically, we…
The goal of the paper is to develop a specific application of the convex optimization based hypothesis testing techniques developed in A. Juditsky, A. Nemirovski, "Hypothesis testing via affine detectors," Electronic Journal of Statistics…
Stationarity is a cornerstone property that facilitates the analysis and processing of random signals in the time domain. Although time-varying signals are abundant in nature, in many practical scenarios the information of interest resides…
Based on dynamical density functional theory (DDFT) we consider a non-equilibrium system of interacting colloidal particles driven by a constant tilting force through a periodic, symmetric "washboard" potential. We demonstrate that, despite…
In this work, we define a practical identifiability criterion, (e, q)-identifiability, based on a parameter e, reflecting the noise in observed variables, and a parameter q, reflecting the mean-square error of the parameter estimator. This…
An emerging way of tackling the dimensionality issues arising in the modeling of a multivariate process is to assume that the inherent data structure can be captured by a graph. Nevertheless, though state-of-the-art graph-based methods have…