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Reset control is known to be able to outperform PID and the like linear controllers. However, in motion control systems, quantization can cause severe performance degradation. This paper shows the application of time regularization to…
This paper presents a synthesis on the mathematical work done on level crossings of stationary Gaussian processes, with some extensions. The main results [(factorial) moments, representation into the Wiener Chaos, asymptotic results, rate…
Mappings from biological sequences (DNA, RNA, protein) to quantitative measures of sequence functionality play an important role in contemporary biology. We are interested in the related tasks of (i) inferring predictive…
We characterize all multi-dimensional real self-similar Gaussian Markov processes. Three types of covariance matrix functions occur: white-noise type functions, covariances that can be expressed by continuous matrix semigroups, and…
The dynamics of quantum systems can be approximated by the time propagation of Gaussian wave packets. Applying a time dependent variational principle, the time evolution of the parameters of the coupled Gaussian wave packets can be…
In this paper, we analyze Gaussian processes using statistical mechanics. Although the input is originally multidimensional, we simplify our model by considering the input as one-dimensional for statistical mechanical analysis. Furthermore,…
Gaussian processes are a natural way of defining prior distributions over functions of one or more input variables. In a simple nonparametric regression problem, where such a function gives the mean of a Gaussian distribution for an…
This note is devoted to a discussion of the potential links and differences between three topics: regularization by noise, convex integration, spontaneous stochasticity. All of them deal with the effect on large scales of a small-scale…
In geostatistics, traditional spatial models often rely on the Gaussian Process (GP) to fit stationary covariances to data. It is well known that this approach becomes computationally infeasible when dealing with large data volumes,…
The accurate prediction of time-changing variances is an important task in the modeling of financial data. Standard econometric models are often limited as they assume rigid functional relationships for the variances. Moreover, function…
In regression-based analyses of group-level neuroimage data researchers typically fit a series of marginal general linear models to image outcomes at each spatially-referenced pixel. Spatial regularization of effects of interest is usually…
The link between Gaussian random fields and Markov random fields is well established based on a stochastic partial differential equation in Euclidean spaces, where the Mat\'ern covariance functions are essential. However, the Mat\'ern…
Many scientific and economic problems involve the analysis of high-dimensional time series datasets. However, theoretical studies in high-dimensional statistics to date rely primarily on the assumption of independent and identically…
We put forward a functional renormalisation group approach for the direct computation of real time correlation functions, also applicable at finite temperature and density. We construct a general class of regulators that preserve the…
We consider the nonparametric functional estimation of the drift of a Gaussian process via minimax and Bayes estimators. In this context, we construct superefficient estimators of Stein type for such drifts using the Malliavin integration…
In many areas of science one aims to estimate latent sub-population mean curves based only on observations of aggregated population curves. By aggregated curves we mean linear combination of functional data that cannot be observed…
We generalize fast Gaussian process leave-one-out formulae to multiple-fold cross-validation, highlighting in turn the covariance structure of cross-validation residuals in both Simple and Universal Kriging frameworks. We illustrate how…
Gaussian bounds on noise correlation of functions play an important role in hardness of approximation, in quantitative social choice theory and in testing. The author (2008) obtained sharp gaussian bounds for the expected correlation of…
This paper consists of two parts. In the first part, we focus on the average of a functional over shifted Gaussian homogeneous noise and as the averaging domain covers the whole space, we establish a Breuer-Major type Gaussian fluctuation…
Time-translation symmetry strongly constrains physical dynamics, yet systematic characterization for continuous-variable systems lags behind its discrete-variable counterpart. We close this gap by providing a rigorous classification of…