224 research outputs found
A Measure of Space for Computing over the Reals
We propose a new complexity measure of space for the BSS model of
computation. We define LOGSPACE\_W and PSPACE\_W complexity classes over the
reals. We prove that LOGSPACE\_W is included in NC^2\_R and in P\_W, i.e. is
small enough for being relevant. We prove that the Real Circuit Decision
Problem is P\_R-complete under LOGSPACE\_W reductions, i.e. that LOGSPACE\_W is
large enough for containing natural algorithms. We also prove that PSPACE\_W is
included in PAR\_R
Separation of complexity classes in Koiran's weak model
AbstractWe continue the study of complexity classes over the weak model introduced by P. Koiran. In particular we provide several separations of complexity classes, the most remarkable being the strict inclusion of P in NP. Other separations concern classes defined by weak polynomial time over parallel or alternating machines as well as over nondeterministic machines whose guesses are required to be 0 or 1
A parabolic approach to the control of opinion spreading
We analyze the problem of controlling to consensus a nonlinear system
modeling opinion spreading. We derive explicit exponential estimates on the
cost of approximately controlling these systems to consensus, as a function of
the number of agents N and the control time-horizon T. Our strategy makes use
of known results on the controllability of spatially discretized semilinear
parabolic equations. Both systems can be linked through time-rescalin
Singular Cucker-Smale Dynamics
The existing state of the art for singular models of flocking is overviewed,
starting from microscopic model of Cucker and Smale with singular communication
weight, through its mesoscopic mean-filed limit, up to the corresponding
macroscopic regime. For the microscopic Cucker-Smale (CS) model, the
collision-avoidance phenomenon is discussed, also in the presence of bonding
forces and the decentralized control. For the kinetic mean-field model, the
existence of global-in-time measure-valued solutions, with a special emphasis
on a weak atomic uniqueness of solutions is sketched. Ultimately, for the
macroscopic singular model, the summary of the existence results for the
Euler-type alignment system is provided, including existence of strong
solutions on one-dimensional torus, and the extension of this result to higher
dimensions upon restriction on the smallness of initial data. Additionally, the
pressureless Navier-Stokes-type system corresponding to particular choice of
alignment kernel is presented, and compared - analytically and numerically - to
the porous medium equation
The Impatient May Use Limited Optimism to Minimize Regret
Discounted-sum games provide a formal model for the study of reinforcement
learning, where the agent is enticed to get rewards early since later rewards
are discounted. When the agent interacts with the environment, she may regret
her actions, realizing that a previous choice was suboptimal given the behavior
of the environment. The main contribution of this paper is a PSPACE algorithm
for computing the minimum possible regret of a given game. To this end, several
results of independent interest are shown. (1) We identify a class of
regret-minimizing and admissible strategies that first assume that the
environment is collaborating, then assume it is adversarial---the precise
timing of the switch is key here. (2) Disregarding the computational cost of
numerical analysis, we provide an NP algorithm that checks that the regret
entailed by a given time-switching strategy exceeds a given value. (3) We show
that determining whether a strategy minimizes regret is decidable in PSPACE
Structure preserving schemes for mean-field equations of collective behavior
In this paper we consider the development of numerical schemes for mean-field
equations describing the collective behavior of a large group of interacting
agents. The schemes are based on a generalization of the classical Chang-Cooper
approach and are capable to preserve the main structural properties of the
systems, namely nonnegativity of the solution, physical conservation laws,
entropy dissipation and stationary solutions. In particular, the methods here
derived are second order accurate in transient regimes whereas they can reach
arbitrary accuracy asymptotically for large times. Several examples are
reported to show the generality of the approach.Comment: Proceedings of the XVI International Conference on Hyperbolic
Problem
Congestion in a macroscopic model of self-driven particles modeling gregariousness
International audienceWe analyze a macroscopic model with a maximal density constraint which describes short range repulsion in biological systems. This system aims at modeling finite-size particles which cannot overlap and repel each other when they are too close. The parts of the fluid where the maximal density is reached behave like incompressible fluids while lower density regions are compressible. This paper investigates the transition between the compressible and incompressible regions. To capture this transition, we study a one-dimensional Riemann problem and introduce a perturbation problem which regularizes the compressible-incompressible transition. Specific difficulties related to the non-conservativity of the problem are discussed
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