Related papers: Numerical Solution of an Inverse Problem in Size-S…
We study the problem of instance segmentation in biological images with crowded and compact cells. We formulate this task as an integer program where variables correspond to cells and constraints enforce that cells do not overlap. To solve…
We shall investigate randomized algorithms for solving large-scale linear inverse problems with general regularizations. We first present some techniques to transform inverse problems of general form into the ones of standard form, then…
Starting from the dynamical system model capturing the splitting-differentiation process of populations, we extend this notion to show how the speciation mechanism from a single species leads to the consideration of several well known…
The problem of object restoration in the case of spatially incoherent illumination is considered. A regularized solution to the inverse problem is obtained through a probabilistic approach, and a numerical algorithm based on the statistical…
We consider a heat equation and a wave equation in a spatial interval over a time interval. This article deals with inverse problems of determining sizes of spatial intervals by extra boundary data of solutions of the governing equations.…
By the use of Perron-Frobenius theory, simple proofs are given of the Fundamental Theorem of Demography and of a theorem of Cushing and Yicang on the net reproductive rate occurring in matrix models of population dynamics. The latter result…
Inverse problems arise in a variety of imaging applications including computed tomography, non-destructive testing, and remote sensing. The characteristic features of inverse problems are the non-uniqueness and instability of their…
In this article we study the problem of recovering the unknown solution of a linear ill-posed problem, via iterative regularization methods. We review the problem of projection-regularization from a statistical point of view. A basic…
Regularization techniques are widely employed in optimization-based approaches for solving ill-posed inverse problems in data analysis and scientific computing. These methods are based on augmenting the objective with a penalty function,…
We study the coupled dynamics of two populations of random replicators by means of statistical mechanics methods, and focus on the effects of relative population size, strategy correlations and heterogeneities in the respective co-operation…
A fundamental problem of statistical data analysis, distribution density estimation by experimental data, is considered. A new method with optimal asymptotic behavior, the root density estimator, is developed. The method proposed may be…
In this paper we consider new regularization methods for linear inverse problems of dynamic type. These methods are based on dynamic programming techniques for linear quadratic optimal control problems. Two different approaches are…
The Giardin\`a-Kurchan-Peliti algorithm is a numerical procedure that uses population dynamics in order to calculate large deviation functions associated to the distribution of time-averaged observables. To study the numerical errors of…
A new numerical method to solve an inverse source problem for the radiative transfer equation involving the absorption and scattering terms, with incomplete data, is proposed. No restrictive assumption on those absorption and scattering…
In this paper, we consider the inverse source problem for the time-fractional diffusion equation, which has been known to be an ill-posed problem. To deal with the ill-posedness of the problem, we propose to transform the problem into a…
Solving the inverse problem is the key step in evaluating the capacity of a physical model to describe real phenomena. In medical image computing, it aligns with the classical theme of image-based model personalization. Traditionally, a…
In this paper, we consider the problem of partitioning a small data sample of size $n$ drawn from a mixture of $2$ sub-gaussian distributions. Our work is motivated by the application of clustering individuals according to their population…
This paper explores an idealized dynamic population sizing strategy for solving additive decomposable problems of uniform scale. The method is designed on top of the foundations of existing population sizing theory for this class of…
The Cell Formation Problem has been studied as an optimization problem in manufacturing for more than 90 years. It consists of grouping machines and parts into manufacturing cells in order to maximize loading of cells and minimize movement…
We analyze a size-structured branching process in which individual cells grow exponentially according to a Feller square-root process and divide under general size-control mechanisms. We obtain exact expressions for the asymptotic…