Related papers: Improved error bounds for quantization based numer…
We consider a class of nonlinear elliptic problems associated with models in biophysics, which are described by the Poisson-Boltzmann equation (PBE). We prove mathematical correctness of the problem, study a suitable class of…
Parameter estimation for non-stationary stochastic differential equations (SDE) with an arbitrary nonlinear drift, and nonlinear diffusion is accomplished in combination with a non-parametric clustering methodology. Such a model-based…
We consider a system of semilinear partial differential equations (PDEs) with a nonlinearity depending on both the solution and its gradient. The Neumann boundary condition depends on the solution in a nonlinear manner. The uniform…
In this paper, we study an asymptotic approximation of the Fisher information for the estimation of a scalar parameter using quantized measurements. We show that, as the number of quantization intervals tends to infinity, the loss of Fisher…
This paper is concerned with linear quadratic optimal control problems for mean-field backward stochastic differential equations (MF-BSDEs, for short) with deterministic coefficients. The optimality system, which is a linear mean-field…
Errors in the data and the forward operator of an inverse problem can be handily modelled using partial order in Banach lattices. We present some existing results of the theory of regularisation in this novel framework, where errors are…
In this paper, we develop {finite-time horizon} causal filters using the nonanticipative rate distortion theory. We apply the {developed} theory to {design optimal filters for} time-varying multidimensional Gauss-Markov processes, subject…
We consider the problem of solving a distributed optimization problem using a distributed computing platform, where the communication in the network is limited: each node can only communicate with its neighbours and the channel has a…
We establish upper bounds for the $L^p$-quantization error, p in (1, 2+d), induced by the recursive Markovian quantization of a d-dimensional diffusion discretized via the Euler scheme. We introduce a hybrid recursive quantization scheme,…
In this study, we propose a global optimization algorithm based on quantizing the energy level of an objective function in an NP-hard problem. According to the white noise hypothesis for a quantization error with a dense and uniform…
Free-boundary diffeomorphism optimization, an important and widely occurring task in geometric modeling, computer graphics, and biological imaging, requires simultaneously determining a planar target domain and a locally bijective map with…
In this paper, we propose a quantized learning equation with a monotone increasing resolution of quantization and stochastic analysis for the proposed algorithm. According to the white noise hypothesis for the quantization error with dense…
We study fundamental limits of first-order stochastic optimization in a range of nonconvex settings, including L-smooth functions satisfying Quasar-Convexity (QC), Quadratic Growth (QG), and Restricted Secant Inequalities (RSI). While the…
Belief propagation (BP) decoding of quantum low density parity check (QLDPC) codes is often implemented using overcomplete stabilizer (OS) representations, where redundant parity checks are introduced to improve finite length performance.…
This work unifies pseudo-time and inexact regularization techniques for nonmonotone classes of partial differential equations, into a regularized pseudo-time framework. Convergence of the residual at the predicted rate is investigated…
We consider the problem of numerically approximating the solutions to an elliptic partial differential equation (PDE) for which the boundary conditions are lacking. To alleviate this missing information, we assume to be given measurement…
An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…
We study a stochastic optimal control problem for forward-backward control systems with quadratic generators. In order to establish the first and second-order variational and adjoint equations, we obtain a new estimate for one-dimensional…
We derive novel algorithms for optimization problems constrained by partial differential equations describing multiscale particle dynamics, including non-local integral terms representing interactions between particles. In particular, we…
The problem of optimally measuring an analytic function of unknown local parameters each linearly coupled to a qubit sensor is well understood, with applications ranging from field interpolation to noise characterization. Here, we resolve a…