Related papers: Jaggedness of Path Integral Trajectories
The use of random sampling in decision-making and control has become popular with the ease of access to graphic processing units that can generate and calculate multiple random trajectories for real-time robotic applications. In contrast to…
Importance sampling of trajectories has proved a uniquely successful strategy for exploring rare dynamical behaviors of complex systems in an unbiased way. Carrying out this sampling, however, requires an ability to propose changes to…
Path integrals can be rigorously defined only in low dimensional systems where the small distance limit can be taken. Particularly non-trivial models in more than four dimensions can only be handled with considerable amount of speculation.…
Much like the action, diffeomorphism invariance can be used to fix the form of the path integral measure in quantum gravity. Moreover, since there is a redundancy between what constitutes "the action" and what constitutes "the measure" one…
We introduce and analyze a new quantity, the path integral ideal, governing the flow of generic discrete theories to the continuum limit and greatly increasing their convergence. The said flow is classified according to the degree of…
Paths are important structural elements in complex networks because they are finite (unlike walks), related to effective node coverage (minimum spanning trees), and can be understood as being dual to star connectivity. This article…
The equivalence between the path integrals for first order gravity and the standard torsion-free, metric gravity in 3+1 dimensions is analyzed. Starting with the path integral for first order gravity, the correct measure for the path…
With recent advances in sensing and tracking technology, trajectory data is becoming increasingly pervasive and analysis of trajectory data is becoming exceedingly important. A fundamental problem in analyzing trajectory data is that of…
The path integral formulation of constrained systems leads to obtain the equations of motion as total differential equations in many variables. If these equations are integrable then one can constuct a valid and a canonical phase space…
Cyclomatic complexity is an incompletely specified but mathematically principled software metric that can be usefully applied to both source and binary code. We consider the application of path homology as a stronger analogue of cyclomatic…
Path integration is a respected form of quantization that all theoretical quantum physicists should welcome. This elaboration begins with simple examples of three different versions of path integration. After an important clarification of…
On the basis of the canonical quantization procedure of a system defined on a cubic lattice, we propose a new method, in which resolutions of unity expressed in terms of eigenvectors are naturally provided, to find eigenvectors of field…
The graph-navigability problem concerns how one can find as short paths as possible between a pair of vertices, given an incomplete picture of a graph. We study the navigability of graphs where the vertices are tagged by a number (between 1…
A key overall goal of biomolecular simulations is the characterization of "mechanism" -- the pathways through configuration space of processes such as conformational transitions and binding. Some amount of heterogeneity is intrinsic to the…
Path integrals represent a powerful route to quantization: they calculate probabilities by summing over classical configurations of variables such as fields, assigning each configuration a phase equal to the action of that configuration.…
Solutions to linear controlled differential equations can be expressed in terms of iterated path integrals of the driving path. This collection of iterated integrals encodes essentially all information about the driving path. While upper…
In the context of two illustrative examples from supersymmetric quantum mechanics we show that the semi-classical analysis of the path integral requires complexification of the configuration space and action, and the inclusion of complex…
The integral with respect to a multidimensional stochastic measure, for which we assume only $\sigma$-additivity in probability, is studied. The continuity and differentiability of its realizations are established.
The parallel computational complexity of the quadratic map is studied. A parallel algorithm is described that generates typical pseudotrajectories of length t in a time that scales as log t and increases slowly in the accuracy demanded of…
Path integrals for particles in curved spaces can be used to compute trace anomalies in quantum field theories, and more generally to study properties of quantum fields coupled to gravity in first quantization. While their construction in…