Related papers: Procedure to produce discretized path composed by …
The motivation for this thesis was to recast quantum self-testing [MY98,MY04] in operational terms. The result is a category-theoretic framework for discussing the following general question: How do different implementations of the same…
This paper investigates the use of multiple directions of stratification as a variance reduction technique for Monte Carlo simulations of path-dependent options driven by Gaussian vectors. The precision of the method depends on the choice…
The identification of physical degrees of freedom is sometimes obscured in the path integral formalism, and this makes it difficult to impose some constraints or to do some approximations. I review a number of cases where the difficulty is…
In this paper we introduce a path complex that can be regarded as a generalization of the notion of a simplicial complex. The main motivation for considering path complexes comes from directed graphs(digraphs). We obtain a new notion of the…
Classic distributed control problems have an interesting dichotomy: they are either trivial or undecidable. If we allow the controllers to fully synchronize, then synthesis is trivial. In this case, controllers can effectively act as a…
Recently, it was found that a new set of simple techniques allow one to conveniently express ordinary integrals through differentiation. These techniques add to the general toolbox for integration and integral transforms such as the Fourier…
In the graph stream model of computation, an algorithm processes the edges of an input graph in one or more sequential passes while using a memory sublinear in the input size. This model poses significant challenges for constructing long…
In this paper, we consider the problem of reconstructing a directed graph using path queries. In this query model of learning, a graph is hidden from the learner, and the learner can access information about it with path queries. For a…
To produce cartographic maps, simplification is typically used to reduce complexity of the map to a legible level. With schematic maps, however, this simplification is pushed far beyond the legibility threshold and is instead constrained by…
This paper introduces an approach to endow generative diffusion processes the ability to satisfy and certify compliance with constraints and physical principles. The proposed method recast the traditional sampling process of generative…
The semiclassical approximation to the coherent state propagator requires complex classical trajectories in order to satisfy the associated boundary conditions, but finding these trajectories in practice is a difficult task that may…
We discuss in detail the uniform discretization approach to the quantization of totally constrained theories. This approach allows to construct the continuum theory of interest as a well defined, controlled, limit of well behaved discrete…
Quantum geometry on a discrete set means a directed graph with a weight associated to each arrow defining the quantum metric. However, these `lattice spacing' weights do not have to be independent of the direction of the arrow. We use this…
Denoising Diffusion Probabilistic Models (DDPMs) are powerful generative deep learning models that have been very successful at image generation, and, very recently, in path planning and control. In this paper, we investigate how to…
We prove a quantitative version of the curve selection lemma. Denoting by $s,d,k$ a bound on the number, the degree and the number of variables of the polynomials describing a semi-algebraic set $S$ and a point $x$ in $\bar S$, we find a…
This work studies path planning in two-dimensional space, in the presence of polygonal obstacles. We specifically address the problem of building a roadmap graph, that is, an abstract representation of all the paths that can potentially be…
The degree of symmetry of a combinatorial object, such as a lattice path, is a measure of how symmetric the object is. It typically ranges from zero, if the object is completely asymmetric, to its size, if it is completely symmetric. We…
We introduce stripe-like quasi-nondiffracting lattices that can be generated via spatial spectrum engineering. The complexity of the spatial shapes of such lattices and the distance of their almost diffractionless propagation depend on the…
We propose an extrapolation technique that allows accuracy improvement of the discrete dipole approximation computations. The performance of this technique was studied empirically based on extensive simulations for 5 test cases using many…
Smooth parametrization consists in a subdivision of the mathematical objects under consideration into simple pieces, and then parametric representation of each piece, while keeping control of high order derivatives. The main goal of the…