Related papers: Bowen's equations for upper metric mean dimension …
We discuss possible observational manifestations of static, spherically symmetric solutions of a class of multidimensional theories of gravity, which includes the low energy limits of supergravities and superstring theories as special…
In this paper, we prove the boundedness of the Bergman projection on weighted mixed norm spaces of the upper-half space for some weights that are constructed using the logarithm function and growth functions. Our necessary and sufficient…
We introduce several new functions that measure the distance between two points $x$ and $y$ in a domain $G\subsetneq\mathbb{R}^n$ by using the arithmetic or the logarithmic mean of the Euclidean distances from the points $x$ and $y$ to the…
We devise a new embedding technique, which we call measured descent, based on decomposing a metric space locally, at varying speeds, according to the density of some probability measure. This provides a refined and unified framework for the…
We establish improved mean value estimates associated with the number of integer solutions of certain systems of diagonal equations, in some instances attaining the sharpest conjectured conclusions. This is the first occasion on which…
A geometric theory for spacetimes whose world lines associated with physical particles have an upper bound for the proper acceleration is developed. After some fundamental remarks on the requirements that the classical dynamics for point…
Bayesian optimization (BO) is a powerful approach for seeking the global optimum of expensive black-box functions and has proven successful for fine tuning hyper-parameters of machine learning models. However, BO is practically limited to…
The problem of measurement in quantum mechanics is reanalyzed within a general, strictly probabilistic framework (without reduction postulate). Based on a novel comprehensive definition of measurement the natural emergence of objective…
We develop a variational principle between mean dimension theory and rate distortion theory. We consider a minimax problem about the rate distortion dimension with respect to two variables (metrics and measures). We prove that the minimax…
The generalized Busemann-Petty problem asks whether origin-symmetric convex bodies with lower-dimensional smaller sections necessarily have smaller volume. We study the weighted version of this problem corresponding to the physical…
Variational mean field approximations tend to struggle with contemporary overparametrized deep neural networks. Where a Bayesian treatment is usually associated with high-quality predictions and uncertainties, the practical reality has been…
Three hyperbolic type metrics including the triangular ratio metric, the $j^*$-metric and the M\"obius metric are studied in an annular ring. The Euclidean midpoint rotation is introduced as a method to create upper and lower bounds for…
We discuss class of doubled geometry models with diagonal metrics. Based on the analysis of known examples we formulate a hypothesis that supports treating them as modified bimetric gravity theories. Certain steps towards the generic case…
Recently the authors have explored new concepts of plurisubharmonicity and pseudoconvexity, with much of the attendant analysis, in the context of calibrated manifolds. Here a much broader extension is made. This development covers a wide…
A Bayesian approach is developed to determine quantum mechanical potentials from empirical data. Bayesian methods, combining empirical measurements and "a priori" information, provide flexible tools for such empirical learning problems. The…
Associated to any finite metric space are a large number of objects and quantities which provide some degree of structural or geometric information about the space. In this paper we show that in the setting of subsets of weighted Hamming…
In this paper, we establish novel data-dependent upper bounds on the generalization error through the lens of a "variable-size compressibility" framework that we introduce newly here. In this framework, the generalization error of an…
We prove a Tb theorem on quasimetric spaces equipped with what we call an upper doubling measure. This is a property that encompasses both the doubling measures and those satisfying the upper power bound \mu(B(x,r)) \le Cr^d. Our spaces are…
In this review articel we study the gaugings of extended supergravity theories in various space-time dimensions. These theories describe the low-energy limit of non-trivial string compactifications. For each theory under consideration we…
We introduce a new type of means. It is new in two ways: its domain consists of sets and its values are sets too. We investigate the properties and behavior of such generalization. We also present many naturally arisen examples for such…