Related papers: On the Dimensional Reduction Procedure
The scalar modes of the geometry induced by dimensional decoupling are investigated. In the context of the low energy string effective action, solutions can be found where the spatial part of the background geometry is the direct product of…
In the introduction, we will discuss the symmetries of QCD, its breaking in the physical vacuum and its restoration at finite temperature and/or density. Then we will discuss what exact relations can be made between chiral symmetry…
Dimensionality reduction techniques map values from a high dimensional space to one with a lower dimension. The result is a space which requires less physical memory and has a faster distance calculation. These techniques are widely used…
The off-shell entropy for a massless scalar field in a D-dimensional Rindler-like space-time is investigated within the conical Euclidean approach in the manifold $C_\be\times\M^N$, $C_\be$ being the 2-dimensional cone, making use of the…
We give a short proof of a strong version of the short time asymptotic expansion of heat kernels associated to Laplace type operators acting on sections of vector bundles over compact Riemannian manifolds, including exponential decay of the…
A variety of problems in computational physics and engineering require the convolution of the heat kernel (a Gaussian) with either discrete sources, densities supported on boundaries, or continuous volume distributions. We present a unified…
A brief overview of dimensional reductions for diffeomorphism invariant theories is given. The distinction between the physical idea of compactification and the mathematical problem of a consistent truncation is discussed, and the typical…
It is shown that the classical motion of massive particles in hyperbolic spaces $H^D$ has a bounded character in $D-1$ coordinates. Studying the Dirac equation, it is found that a bounded character of the classical motion corresponds to the…
In this paper, we consider the following symmetric non-local Dirichlet forms of pure jump type on metric measure space $(M,d,\mu)$: $$\mathcal{E}(f,g)=\int_{M\times M} (f(x)-f(y))(g(x)-g(y))\,J(dx,dy),$$ where $J(dx,dy)$ is a symmetric…
The exact solution for a system with two-particle annihilation and decoagulation has been studied. The spectrum of the Hamiltonian of the system is found. It is shown that the steady state is two-fold degenerate. The average number density…
Focusing on the real-time dynamics of the reduced density matrix of the multidimensional Caldeira-Leggett model, several techniques are adopted in this paper to reduce the spatial and temporal dimensionality, combined into an efficient…
Explicit and semi-explicit geometric integration schemes for dissipative perturbations of Hamiltonian systems are analyzed. The dissipation is characterized by a small parameter $\epsilon$, and the schemes under study preserve the…
Modern density functional approximations achieve moderate accuracy at low computational cost for many electronic structure calculations. Some background is given relating the gradient expansion of density functional theory to the WKB…
Computing persistent homology using Gaussian kernels is useful in the domains of topological data analysis and machine learning as shown by Phillips, Wang and Zheng [SoCG 2015]. However, contrary to the case of computing persistent homology…
In this paper, we consider the following symmetric Dirichlet forms on a metric measure space $(M,d,\mu)$: $$\mathcal{E}(f,g) = \mathcal{E}(^{(c)}(f,g)+\int_{M\times M} (f(x)-f(y))(g(x)-g(y))\,J(dx,dy),$$ where $\mathcal{E}(^{(c)}$ is a…
Hyperspectral imaging is a powerful technology that is plagued by large dimensionality. Herein, we explore a way to combat that hindrance via non-contiguous and contiguous (simpler to realize sensor) band grouping for dimensionality…
It has been shown previously, that the spatial thermal variation of a thermal medium can be recast as a variation in the Euclidean metric. It is now extended to temporal variations in temperature, for a non-relativistic thermal bath, which…
We consider the problem of numerically integrating functions with hyperplane discontinuities over the entire Euclidean space in many dimensions. We describe a simple process through which the Euclidean space is partitioned into simplices on…
Dimensional regularization is used to derive the equations of motion of two point masses in harmonic coordinates. At the third post-Newtonian (3PN) approximation, it is found that the dimensionally regularized equations of motion contain a…
In this paper we revisit the kernel density estimation problem: given a kernel $K(x, y)$ and a dataset of $n$ points in high dimensional Euclidean space, prepare a data structure that can quickly output, given a query $q$, a…