This paper serves as a bridge between quantum computing and analogical modeling (a general theory for predicting categories of behavior in varying contexts). Since its formulation in the early 1980s, analogical modeling has been successfully applie...
It is still unclear how an evolutionary algorithm (EA) searches a fitness landscape, and on what fitness landscapes a particular EA will do well. The validity of the building-block hypothesis, a major tenet of traditional genetic algorithm theory,...
Points: 451 | Comments: 19 | Author: oska
We formulate an info-clustering paradigm based on a multivariate information measure, called multivariate mutual information, that naturally extends Shannon's mutual information between two random variables to the multivariate case involving more tha...
Solid ionic conductors are essential components of batteries and fuel cells. In many cases, ionic conduction through crystalline materials with substitutional disorder can be modeled with atomic-scale lattice model percolation simulations. The ionic...
We extend the theory and the algorithms of Border Bases to systems of Laurent polynomial equations, defining "toric" roots. Instead of introducing new variables and new relations to saturate by the variable inverses, we propose a more efficient appro...
Here we study the problem of generalizing one of the main tools of Groebner basis theory, namely the flat deformation to the leading term ideal, to the border basis setting. After showing that the straightforward approach based on the deformation t...
We propose $\textbf{E}$lectric $\textbf{C}$urrent $\textbf{D}$iscrete $\textbf{D}$ata $\textbf{G}$eneration (ECD$^{2}$G), a pioneering method for data generation in discrete settings that is grounded in electrical engineering theory. Our approach dra...
Eigen mode selection ought to be a practical issue in some real game systems, as it is a practical issue in the dynamics behaviour of a building, bridge, or molecular, because of the mathematical similarity in theory. However, its reality and accurac...
We examined the chromo-natural inflation in the context of warm inflation with variable dissipation coefficient. The dynamical equations of this model are obtained. We studied the cosmological perturbation theory in this model. The sources of density...
Points: 291 | Comments: 370 | Author: morby
In this paper, we construct a sequence $(c_k)_{k\in\mathbb{N}}$ of symplectic capacities based on the Chiu-Tamarkin complex $C_{T,\ell}$, a $\mathbb{Z}/\ell$-equivariant invariant coming from the microlocal theory of sheaves. We compute $(c_k)_{k\in\...
We study conditions on a commutative ring R which are equivalent to the following requirement; whenever X is a projective scheme over S = Spec(R) of fiber dimension \leq d for some integer d \geq 0, there is a finite morphism from X to P^d_S over S s...
Stochastic Gradient Descent (SGD) and its variants are mainstream methods for training deep networks in practice. SGD is known to find a flat minimum that often generalizes well. However, it is mathematically unclear how deep learning can select a fl...
Points: 632 | Comments: 798 | Author: doctaj
We give an overview of several of the mathematical works of Gilles Lachaud and provide a historical context. This is interspersed with some personal anecdotes highlighting many facets of his personality....
Gravity constrains the range of validity of quantum field theory. As has been pointed out by Cohen, Kaplan, and Nelson (CKN), such effects lead to interdependent ultraviolet (UV) and infrared (IR) cutoffs that may stabilize the dark energy of the uni...
Recently, an increasing interest in UV/IR mixing phenomena has drawn attention to the range of validity of standard quantum field theory. Here we explore the consequences of such a limited range of validity in the context of radiative models for neut...
Adolf Hurwitz is rather famous for his celebrated contributions to Riemann surfaces, modular forms, diophantine equations and approximation as well as to certain aspects of algebra. His early work on an important generalization of Dirichlet's $L$-ser...
We give a brief account of supersymmetric Born-Infeld theories with extended supersymmetry, including those with partially broken supersymmetry. Some latest developments in this area are presented. One of them is N=3 supersymmetric Born-Infeld theo...