6,556 research outputs found
Path Puzzles: Discrete Tomography with a Path Constraint is Hard
We prove that path puzzles with complete row and column information--or
equivalently, 2D orthogonal discrete tomography with Hamiltonicity
constraint--are strongly NP-complete, ASP-complete, and #P-complete. Along the
way, we newly establish ASP-completeness and #P-completeness for 3-Dimensional
Matching and Numerical 3-Dimensional Matching.Comment: 16 pages, 8 figures. Revised proof of Theorem 2.4. 2-page abstract
appeared in Abstracts from the 20th Japan Conference on Discrete and
Computational Geometry, Graphs, and Games (JCDCGGG 2017
Self-Evaluation Applied Mathematics 2003-2008 University of Twente
This report contains the self-study for the research assessment of the Department of Applied Mathematics (AM) of the Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) at the University of Twente (UT). The report provides the information for the Research Assessment Committee for Applied Mathematics, dealing with mathematical sciences at the three universities of technology in the Netherlands. It describes the state of affairs pertaining to the period 1 January 2003 to 31 December 2008
A Model for Optimal Human Navigation with Stochastic Effects
We present a method for optimal path planning of human walking paths in
mountainous terrain, using a control theoretic formulation and a
Hamilton-Jacobi-Bellman equation. Previous models for human navigation were
entirely deterministic, assuming perfect knowledge of the ambient elevation
data and human walking velocity as a function of local slope of the terrain.
Our model includes a stochastic component which can account for uncertainty in
the problem, and thus includes a Hamilton-Jacobi-Bellman equation with
viscosity. We discuss the model in the presence and absence of stochastic
effects, and suggest numerical methods for simulating the model. We discuss two
different notions of an optimal path when there is uncertainty in the problem.
Finally, we compare the optimal paths suggested by the model at different
levels of uncertainty, and observe that as the size of the uncertainty tends to
zero (and thus the viscosity in the equation tends to zero), the optimal path
tends toward the deterministic optimal path
On the Relationship between Convex Bodies Related to Correlation Experiments with Dichotomic Observables
In this paper we explore further the connections between convex bodies
related to quantum correlation experiments with dichotomic variables and
related bodies studied in combinatorial optimization, especially cut polyhedra.
Such a relationship was established in Avis, Imai, Ito and Sasaki (2005 J.
Phys. A: Math. Gen. 38 10971-87) with respect to Bell inequalities. We show
that several well known bodies related to cut polyhedra are equivalent to
bodies such as those defined by Tsirelson (1993 Hadronic J. S. 8 329-45) to
represent hidden deterministic behaviors, quantum behaviors, and no-signalling
behaviors. Among other things, our results allow a unique representation of
these bodies, give a necessary condition for vertices of the no-signalling
polytope, and give a method for bounding the quantum violation of Bell
inequalities by means of a body that contains the set of quantum behaviors.
Optimization over this latter body may be performed efficiently by semidefinite
programming. In the second part of the paper we apply these results to the
study of classical correlation functions. We provide a complete list of tight
inequalities for the two party case with (m,n) dichotomic observables when
m=4,n=4 and when min{m,n}<=3, and give a new general family of correlation
inequalities.Comment: 17 pages, 2 figure
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