Related papers: Some Combinatorial Aspects of Discrete Non-linear …

The logistic map is a nonlinear difference equation well studied in the literature, used to model self-limiting growth in certain populations. It is known that, under certain regularity conditions, the stochastic logistic map, where the…

This work focuses on developing a data-driven framework using Koopman operator theory for system identification and linearization of nonlinear systems for control. Our proposed method presents a deep learning framework with recursive…

Mathematical theory of selection is developed within the frameworks of general models of inhomogeneous populations with continuous time. Methods that allow us to study the distribution dynamics under natural selection and to construct…

A classical problem describing the collective motion of cells, is the movement driven by consumption/depletion of a nutrient. Here we analyze one of the simplest such model written as a coupled Partial Differential Equation/Ordinary…

The discretization of optimal transport problems often leads to large linear programs with sparse solutions. We derive error estimates for the approximation of the problem using convex combinations of Dirac measures and devise an active-set…

Although there is a rapidly growing literature on dynamic connectivity methods, the primary focus has been on separate network estimation for each individual, which fails to leverage common patterns of information. We propose novel…

Regularization method and Bayesian inverse method are two dominating ways for solving inverse problems generated from various fields, e.g., seismic exploration and medical imaging. The two methods are related with each other by the MAP…

The use of data assimilation for the merging of observed data with dynamical models is becoming standard in modern physics. If a parametric model is known, methods such as Kalman filtering have been developed for this purpose. If no model…

We derive and analyse a new variant of the iteratively regularized Landweber iteration, for solving linear and nonlinear ill-posed inverse problems. The method takes into account training data, which are used to estimate the interior of a…

Estimating the ratio of two probability densities from finitely many samples, is a central task in machine learning and statistics. In this work, we show that a large class of kernel methods for density ratio estimation suffers from error…

We introduce an efficient combination of polyhedral analysis and predicate partitioning. Template polyhedral analysis abstracts numerical variables inside a program by one polyhedron per control location, with a priori fixed directions for…

This paper addresses mechanisms for boundedly rational decision makers in discrete choice problem. First, we introduce two mathematical models of population dynamics with conformity biases. We next analyze the models in terms of…

We study partially linear models when the outcome of interest and some of the covariates are observed in two different datasets that cannot be linked. This type of data combination problem arises very frequently in empirical microeconomics.…

This paper focuses on inverse problems arising in studying multi-population aggregations. The goal is to reconstruct the diffusion coefficient, advection coefficient, and interaction kernels of the aggregation system, which characterize the…

Koopman analysis provides a general framework from which to analyze a nonlinear dynamical system in terms of a linear operator acting on an infinite-dimensional observable space. This theoretical framework provides a rigorous underpinning…

Population annealing is an efficient sequential Monte Carlo algorithm for simulating equilibrium states of systems with rough free energy landscapes. The theory of population annealing is presented, and systematic and statistical errors are…

Non-standard Lagrangians do not display any discernible energy-like terms, yet they give the same equations of motion as standard Lagrangians, which have easily identifiable energy-like terms. A new method to derive non-standard Lagrangians…

The goal of robust motion planning consists of designing open-loop controls which optimally steer a system to a specific target region while mitigating uncertainties and disturbances which affect the dynamics. Recently, stochastic optimal…

We present a Hamiltonian approach for the wellknown Eigen model of the Darwin selection dynamics. Hamiltonization is carried out by means of the embedding of the population variable space, describing behavior of the system, into the space…

To check the satisfiability of (non-linear) real arithmetic formulas, modern satisfiability modulo theories (SMT) solving algorithms like NLSAT depend heavily on single cell construction, the task of generalizing a sample point to a…