Related papers: On the Convergence Time of a Natural Dynamics for …
In this paper we study dynamics inspired by Physarum polycephalum (a slime mold) for solving linear programs [NTY00, IJNT11, JZ12]. These dynamics are arrived at by a local and mechanistic interpretation of the inner workings of the slime…
Physarum Polycephalum is a slime mold that can solve shortest path problems. A mathematical model based on Physarum's behavior, known as the Physarum Directed Dynamics, can solve positive linear programs. In this paper, we present a family…
We present two results on slime mold computations. In wet-lab experiments (Nature'00) by Nakagaki et al. the slime mold Physarum polycephalum demonstrated its ability to solve shortest path problems. Biologists proposed a mathematical…
Physarum Polycephalum is a slime mold that is apparently able to solve shortest path problems. A mathematical model has been proposed by biologists to describe the feedback mechanism used by the slime mold to adapt its tubular channels…
In this paper we present a connection between two dynamical systems arising in entirely different contexts: one in signal processing and the other in biology. The first is the famous Iteratively Reweighted Least Squares (IRLS) algorithm…
The phase space flow of a dynamical system leading to the solution of Linear Programming (LP) problems is explored as an example of complexity analysis in an analog computation framework. An ensemble of LP problems with $n$ variables and…
Physarum polycephalum is a large single amoeba cell, which in its plasmodial phase,forages and connects nearby food sources with protoplasmic tubes. The organism forages for food by growing these tubes towards detected food stuffs, this…
We consider linear programming (LP) problems in infinite dimensional spaces that are in general computationally intractable. Under suitable assumptions, we develop an approximation bridge from the infinite-dimensional LP to tractable finite…
Recent work [Ran22] formulated a class of optimal control problems involving positive linear systems, linear stage costs, and elementwise constraints on control. It was shown that the problem admits linear optimal cost and the associated…
The slime mould Physarum polycephalum displays adaptive transport dynamics and network formation that have inspired its use as a model of biological computation. We develop a Lagrangian formulation of Physarum's adaptive dynamics on…
The paper aims at the development of an apparatus for analysis and construction of near optimal solutions of singularly perturbed (SP) optimal controls problems (that is, problems of optimal control of SP systems) considered on the infinite…
We formulate and study the infinite dimensional linear programming (LP) problem associated with the deterministic discrete time long-run average criterion optimal control problem. Along with its dual, this LP problem allows one to…
A supply chain is a system which moves products from a supplier to customers. The supply chains are ubiquitous. They play a key role in all economic activities. Inspired by biological principles of nutrients' distribution in protoplasmic…
A natural optimization model that formulates many online resource allocation and revenue management problems is the online linear program (LP) in which the constraint matrix is revealed column by column along with the corresponding…
A numerical method is developed to solve linear semi-infinite programming problem (LSIP) in which the iterates produced by the algorithm are feasible for the original problem. This is achieved by constructing a sequence of standard linear…
In this work we study and expand a model describing the dynamics of a unicellular slime mold, Physarum Polycephalum (PP), which was proposed to simulate the ability of PP to find the shortest path connecting two food sources in a maze. The…
There is a recent interest on first-order methods for linear programming (LP). In this paper,we propose a stochastic algorithm using variance reduction and restarts for solving sharp primal-dual problems such as LP. We show that the…
In this article, we address a class of non convex, integer, non linear mathematical programs using dynamic programming. The mathematical program considered, whose properties are studied in this article, may be used to model the optimal…
The linear programming (LP) approach has a long history in the theory of approximate dynamic programming. When it comes to computation, however, the LP approach often suffers from poor scalability. In this work, we introduce a relaxed…
We develop a new numerical method for approximating the infinite time reachable set of strictly stable linear control systems. By solving a linear program with a constraint that incorporates the system dynamics, we compute a polytope with…