2 State of the art in robot motion algorithms 3 2.1 Global path-planners . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.1.1 Grid methods (cell decomposition) . . . . . . . . . . . . . 3 2.1.2 Roadmap methods . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Local and reactive algorithms . . . . . . . . . . . . . . . . . . . . 4 2.2.1 Potential Field Methods (PF) . . . . . . . . . . . . ....

Spin foam models are the path integral counterparts to loop quantized canonical theories. In the last few years several spin foam models of gravity have been proposed, most of which live on finite simplicial lattice spacetime. The lattice truncates the presumably infinite set of gravitational degrees of freedom down to a finite set. Models that can accomodate an infinite set of degrees of freed...

Last years there was an essential progress in calculations of Feynman integrals. It seems that most important results have been obtained for two-loop four-point massless Feynman diagrams: in on-shall case (see [1,2]) and for a class of offshall legs (see [3]). A review of the results can be found in [4]. Moreover, very recently results for a class of these diagrams have been obtained [5] in the...

We present a new method for the momentum expansion of Feynman integrals with arbitrary masses and any number of loops and external momenta. By using the parametric representation we derive a generating function for the coefficients of the small momentum expansion of an arbitrary diagram. The method is applicable for the expansion w.r.t. all or a subset of external momenta. The coefficients of t...

Using Path Integral Monte Carlo, we have calculated exchange frequencies as electrons undergo ring exchanges of 2, 3, and 4 electrons in a “clean” 3D Wigner crystal (bcc lattice) as a function of density. We find pair exchange dominates and estimate the critical temperature for the transition to antiferromagnetic ordering to be roughly 1310−8 Ry at melting. In contrast to the situation in 2D, t...

In this paper, we propose a novel algorithm to construct common base domains for cross-parameterization constrained by anchor points. Based on the common base domains, a bijective mapping between given models can be established. Experimental results show that the distortion in a cross-parameterization generated on our common base domains is much smaller than that of a mapping on domains constru...

Consider the continuum of points along the edges of a network, an embedded undirected graph with positive edge weights. Distance between these points can be measured as shortest path distance along the edges of the network. We introduce two new concepts to capture farthest-point information in this metric space. The first, eccentricity diagrams, are used to encode the distance towards farthest ...

The differential-reduction algorithm, which allows one to express generalized hypergeometric functions with parameters of arbitrary values in terms of such functions with parameters whose values differ from the original ones by integers, is discussed in the context of evaluating Feynman diagrams. Where this is possible, we compare our results with those obtained using standard techniques. It is...

Spin foam models are the path integral counterparts to loop quantized canonical theories. In the last few years several spin foam models of gravity have been proposed, most of which live on finite simplicial lattice spacetime. The lattice truncates the presumably infinite set of gravitational degrees of freedom down to a finite set. Models that can accomodate an infinite set of degrees of freed...

The operator approach to analytical evaluation of multi-loop Feynman diagrams is proposed. We show that the known analytical methods of evaluation of massless Feynman integrals, such as the integration by parts method and the method of ”uniqueness” (which is based on the star-triangle relation), can be drastically simplified by using this operator approach. To demonstrate the advantages of the ...