Related papers: A General Solution to Bellman's Lost-in-a-forest P…

In this paper we present a general scheme to generate constructive solutions to the Riemann--Hilbert problem via middle convolution and illustrate this approach for a Fuchsian system with four singular points.

We develop a universal model based on the classical complex matter fields that allow the optimal mapping of many real-life NP-hard combinatorial optimisation problems into the problem of minimising a spin Hamiltonian. We explicitly…

A systematic derivation of Boltzmann equation is presented in the framework of closed-time-path formalism. Introducing a new type of probe, the expectation value of number operator is calculated as a functional of source. Then solving for…

Resource allocation problems are usually solved with specialized methods exploiting their general sparsity and problem-specific algebraic structure. We show that the sparsity structure alone yields a closed-form Newton search direction for…

We present here a new and universal approach for the study of random and/or trees, unifying in one framework many different models, including some novel ones not yet understood in the literature. An and/or tree is a Boolean expression…

This paper establishes a rigorous connection between regularized discrete-time reinforcement learning (RL) and continuous-time stochastic optimal control. Specifically, classical RL algorithms are typically solving a regularized…

We discuss several connections between discrete and continuous random trees. In the discrete setting, we focus on Galton-Watson trees under various conditionings. In particular, we present a simple approach to Aldous' theorem giving the…

The Generalized Traveling Salesman Problem (GTSP) is a well-known combinatorial optimization problem with a host of applications. It is an extension of the Traveling Salesman Problem (TSP) where the set of cities is partitioned into…

The present article introduces a generalization of the (multisymplectic) Hamiltonian field theory for a Lagrangian density, allowing the formulation of this kind of field theories for variational problem of more general nature than those…

We analyze combinatorial optimization problems with ordinal, i.e., non-additive, objective functions that assign categories (like good, medium and bad) rather than cost coefficients to the elements of feasible solutions. We review different…

Dynamic mean field theory is applied to the problem of forest fires. The starting point is the Monte Carlo simulation in a lattice of million cells. The statistics of the clusters is obtained by means of the Hoshen--Kopelman algorithm. We…

We outline an approach to the inverse problem of Calder\'on that highlights the role of microlocal normal forms and propagation of singularities and extends a number of earlier results also in the anisotropic case. The main result states…

After showing the efficiency of feedforward networks to estimate control in high dimension in the global optimization of some storages problems, we develop a modification of an algorithm based on some dynamic programming principle. We show…

Motion planning is a fundamental problem and focuses on finding control inputs that enable a robot to reach a goal region while safely avoiding obstacles. However, in many situations, the state of the system may not be known but only…

A general formalism to solve nonlinear differential equations is given. Solutions are found and reduced to those of second order nonlinear differential equations in one variable. The approach is uniformized in the geometry and solves…

In this study, we consider the guidance control problem of the sheepdog system, which involves the guidance of the flock using the characteristics of the sheepdog and sheep. Sheepdog systems require a strategy to guide sheep agents to a…

This paper discusses basic results and recent developments on variational regularization methods, as developed for inverse problems. In a typical setup we review basic properties needed to obtain a convergent regularization scheme and…

Understanding the evolution of a set of genes or species is a fundamental problem in evolutionary biology. The problem we study here takes as input a set of trees describing {possibly discordant} evolutionary scenarios for a given set of…

We consider the problem of recovering a signal from nonlinear transformations, under convex constraints modeling a priori information. Standard feasibility and optimization methods are ill-suited to tackle this problem due to the…

We study an extensive class of movement minimization problems which arise from many practical scenarios but so far have little theoretical study. In general, these problems involve planning the coordinated motion of a collection of agents…