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Generalized dimensions of multifractal measures are usually seen as static objects, related to the scaling properties of suitable partition functions, or moments of measures of cells. When these measures are invariant for the flow of a…
Recently, a new framework for solving the hierarchy problem has been proposed which does not rely on low energy supersymmetry or technicolor. The gravitational and gauge interactions unite at the electroweak scale, and the observed weakness…
Model complexity is an important factor to consider when selecting among graphical models. When all variables are observed, the complexity of a model can be measured by its standard dimension, i.e. the number of independent parameters. When…
Continuous-Variable (CV) devices are a promising platform for demonstrating large-scale quantum information protocols. In this framework, we define a general quantum computational model based on a CV hardware. It consists of vacuum input…
We consider a fractal with a variable fractal dimension, which is a generalization of the well known triadic Cantor set. In contrast with the usual Cantor set, the fractal dimension is controlled using a scaling factor, and can vary from…
The fractal dimension is a central quantity in nonlinear dynamics and can be estimated via several different numerical techniques. In this review paper we present a self-contained and comprehensive introduction to the fractal dimension. We…
In this paper we develop combinatorial techniques for the case of string algebras with the aim to give a characterization of string complexes with infinite minimal projective resolution. These complexes will be called \textit{periodic…
Centrality analysis in dynamical network systems is essential for understanding system behavior. In finite-dimensional settings, controllability scores -- namely, the Volumetric Controllability Score (VCS) and the Average Energy…
We study the properties of singular values of mixing matrices embedded within an experimentally determined interval matrix. We argue that any physically admissible mixing matrix needs to have the property of being a contraction. This…
The Gap Forcing Theorem, a key contribution of this paper, implies essentially that after any reverse Easton iteration of closed forcing, such as the Laver preparation, every supercompactness measure on a supercompact cardinal extends a…
We introduce and study the spherical dimension, a natural topological relaxation of the VC dimension that unifies several results in learning theory where topology plays a key role in the proofs. The spherical dimension is defined by…
Let $\Gamma^\infty$ be the set of all universally Baire sets of reals. Inspired by recent work of the second author and Nam Trang, we introduce a new technique for establishing generic absoluteness results for models containing…
The purpose of this paper is to study the fractal phenomena in large data sets and the associated questions of dimension reduction. We examine situations where the classical Principal Component Analysis is not effective in identifying the…
In this Thesis we investigate properties of stability, rigidity and unitarity of the string landscape in ten and lower dimensions. The dissertation explores these aspects by intertwining a detailed analysis of string vacua, with and without…
We describe new families of random fractals, referred to as "V-variable", which are intermediate between the notions of deterministic and of standard random fractals. The parameter V describes the degree of "variability" : at each…
Delle Rose et al.~(COLT'23) introduced an effective version of the Vapnik-Chervonenkis dimension, and showed that it characterizes improper PAC learning with total computable learners. In this paper, we introduce and study a similar…
Size-Change Termination (SCT) is a method of proving program termination based on the impossibility of infinite descent. To this end we use a program abstraction in which transitions are described by Monotonicity Constraints over (abstract)…
Instantaneous quantum computing is a sub-universal quantum complexity class, whose circuits have proven to be hard to simulate classically in the Discrete-Variable (DV) realm. We extend this proof to the Continuous-Variable (CV) domain by…
The problem of computing the dimension of a left/right ideal in a group algebra F[G] of a finite group G over a field F is considered. The ideal dimension is related to the rank of a matrix originating from a regular left/right…
In this work, we aim to advance the development of a fractal theory for sets of integers. The core idea is to utilize the fractal structure of $p$-adic integers, where $p$ is a prime number, and compare this with conventional densities and…