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We present a range of applications of localisation for constrained transports for pairs of probability measures in order with respect to a lattice cone. These examples comprise irreducible convex paving for martingale transports in…
An approximate projection onto the tangent cone to the variety of third-order tensors of bounded tensor-train rank is proposed and proven to satisfy a better angle condition than the one proposed by Kutschan (2019). Such an approximate…
Parabolic equations with homogeneous Dirichlet conditions on the boundary are studied in a setting where the solutions are required to have a prescribed change of the profile in fixed time, instead of a Cauchy condition. It is shown that…
This report aims at establishing a theoretical framework for dealing with the reconstruction problem of a small acoustic inclusion. The objective is to introduce the new concept of time-dependent polarization tensors for the Helmholtz…
We prove an existence and uniqueness result for Neumann boundary problem of a parabolic partial differential equation (PDE for short) with a singular nonlinear divergence term which can only be understood in a weak sense. A probabilistic…
This paper studies the long-time behavior of optimal solutions for a class of linear-convex optimal control problems. We focus on a partial exponential turnpike property, established without imposing controllability or stabilizability…
A class of time-optimal control problems governed by semilinear parabolic equations with mixed pointwise constraints and final point constraints is considered. By introducing the so-called locally optimal solution to time-optimal control…
We study inverse boundary problems for evolutionary PDEs using only a single passive boundary observation, where data from an unknown internal source propagate through an unknown medium without active inputs. The goal is the simultaneous…
In this paper we provide some new sufficient conditions that ensure the existence of the solution of a weak vector equilibrium problem in Hausdorff topological vector spaces ordered by a cone. Further, we introduce a dual problem and we…
We prove a well-posedness result for two pseudo-parabolic problems, which can be seen as two models for the same electrical conduction phenomenon in heterogeneous media, neglecting the magnetic field. One of the problems is the…
This paper shows that the problem of testing hypotheses in moment condition models without any assumptions about identification may be considered as a problem of testing with an infinite-dimensional nuisance parameter. We introduce a…
We study Bayesian posterior consistency in parametric density models with proper priors, challenging the perception that the problem is settled. Classical results established consistency via MLE convergence under regularity and…
In recent years much effort has been concentrated towards achieving polynomial time lower bounds on algorithms for solving various well-known problems. A useful technique for showing such lower bounds is to prove them conditionally based on…
In this paper, we present an overview of constrained PARAFAC models where the constraints model linear dependencies among columns of the factor matrices of the tensor decomposition, or alternatively, the pattern of interactions between…
This paper provides a nonparametric analysis for several classes of models, with cases such as classical measurement error, regression with errors in variables, factor models and other models that may be represented in a form involving…
Determinantal varieties -- the sets of bounded-rank matrices or tensors -- have attracted growing interest in low-rank optimization. The tangent cone to low-rank sets is widely studied and underpins a range of geometric methods. The…
As an improvement to the recently proposed procedure for the determination of the stress state beneath axisymmetric tangential contacts in Hertz-Mindlin approximation via an appropriate superposition of solutions for the respective…
The aim of this paper is to study time-fractional pseudo-parabolic type equations generated by the Dunkl operator. The forward problem is considered and its well-posedness is established. In particular, a prior estimates are obtained in the…
We propose a new abstract formalism for probabilistic timed systems, Parametric Interval Probabilistic Timed Automata, based on an extension of Parametric Timed Automata and Interval Markov Chains. In this context, we consider the…
We apply the linking method for cones in normed spaces to p-Laplace equations with various nonlinear boundary conditions. Some existence results are obtained.