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We address the problem to infer physical material parameters and boundary conditions from the observed motion of a homogeneous deformable object via the solution of an inverse problem. Parameters are estimated from potentially unreliable…
We discuss the identification of a time-dependent potential in a time-fractional diffusion model from a boundary measurement taken at a single point. Theoretically, we establish a conditional Lipschitz stability for this inverse problem.…
It is surprising that last two decades many works in time series data mining and clustering were concerned with measures of similarity of time series but not with measures of association that can be used for measuring possible direct and…
We consider continuous-time models with a large panel of moment conditions, where the structural parameter depends on a set of characteristics, whose effects are of interest. The leading example is the linear factor model in financial…
Statistical learning theory has largely focused on learning and generalization given independent and identically distributed (i.i.d.) samples. Motivated by applications involving time-series data, there has been a growing literature on…
Bounds are developed for the condition number of the linear finite element equations of an anisotropic diffusion problem with arbitrary meshes. They depend on three factors. The first, factor proportional to a power of the number of mesh…
In the context of elasticity theory, rigidity theorems allow to derive global properties of a deformation from local ones. This paper presents a new asymptotic version of rigidity, applicable to elastic bodies with sufficiently stiff…
We derive theorems which outline explicit mechanisms by which anomalous scaling for the probability density function of the sum of many correlated random variables asymptotically prevails. The results characterize general anomalous scaling…
We propose a new approach to temporal inference, inspired by the Pearlian causal inference paradigm - though quite different from Pearl's approach formally. Rather than using directed acyclic graphs, we make use of factored sets, which are…
We describe how geometrical methods can be applied to a system with explicitly time-dependent second-class constraints so as to cast it in Hamiltonian form on its physical phase space. Examples of particular interest are systems which…
Statistical divergences are important tools in data analysis, information theory, and statistical physics, and there exist well known inequalities on their bounds. However, in many circumstances involving temporal evolution, one needs…
Power law or generalized polynomial regressions with unknown real-valued exponents and coefficients, and weakly dependent errors, are considered for observations over time, space or space--time. Consistency and asymptotic normality of…
Diffusion models struggle to produce samples that respect constraints, a common requirement in scientific applications. Recent approaches have introduced regularization terms in the loss or guidance methods during sampling to enforce such…
This paper focuses on causal structure estimation from time series data in which measurements are obtained at a coarser timescale than the causal timescale of the underlying system. Previous work has shown that such subsampling can lead to…
High dimensional time series datasets are becoming increasingly common in various fields such as economics, finance, meteorology, and neuroscience. Given this ubiquity of time series data, it is surprising that very few works on variable…
Using factorization we determine the allowed domains of the ratios of form factors, $x = A_2(0)/A_1(0)$ and $y = V(0)/A_1(0)$, from the experimentally measured ratio $R_h \equiv \Gamma(D_s^+ \ra \phi \rho^+)/\Gamma(D_s^+ \ra \phi \pi^+)$…
One of the most criticized features of Bayesian statistics is the fact that credible intervals, especially when open likelihoods are involved, may strongly depend on the prior shape and range. Many analyses involving open likelihoods are…
In this paper, we establish novel data-dependent upper bounds on the generalization error through the lens of a "variable-size compressibility" framework that we introduce newly here. In this framework, the generalization error of an…
We propose a series-based nonparametric specification test for a regression function when data are spatially dependent, the `space' being of a general economic or social nature. Dependence can be parametric, parametric with increasing…
In the current density functional theory of linear and nonlinear time-dependent phenomena, the treatment of exchange and correlation beyond the level of the adiabatic local density approximation is shown to lead to the appearance of…