Microscopic models of hardness

Simulation of Pedestrian Dynamics with Macroscopic and Microscopic Mathematical Models

Here, we collect two parts of a research project on the pedestrian flow modeling. Rapid growth in the volume of public transport and the need for its reasonable, efficient planning have made the description and modeling of transport and pedestrian behaviors as important research topics in the past twenty years. First, we present a macroscopic model for the pedestrian flow based on continuum mec...

Microscopic models of quasicrystals

Hierarchical Hardness Models for SAT

Empirical hardness models predict a solver’s runtime for a given instance of an NP-hard problem based on efficiently computable features. Previous research in the SAT domain has shown that better prediction accuracy and simpler models can be obtained when models are trained separately on satisfiable and unsatisfiable instances. We extend this work by training separate hardness models for each c...

Hardness of parameter estimation in graphical models

We consider the problem of learning the canonical parameters specifying an undirected graphical model (Markov random field) from the mean parameters. For graphical models representing a minimal exponential family, the canonical parameters are uniquely determined by the mean parameters, so the problem is feasible in principle. The goal of this paper is to investigate the computational feasibilit...

Macroscopic Limits of Microscopic Models

Many physical systems are comprised of several discrete elements, the equations of motion of each element being known. If the system has a large number of degrees of freedom, it may be possible to treat it as a continuous system. In this event, one might wish to derive the equations of motion of the continuous (macroscopic) system by taking a suitable limit of the equations governing the discre...