Related papers: The ghost and weak dimensions of rings and ring sp…
Dynamical networks are powerful tools for modeling a broad range of complex systems, including financial markets, brains, and ecosystems. They encode how the basic elements (nodes) of these systems interact altogether (via links) and evolve…
In their paper, Bazzoni and Glaz conjecture that the weak global dimension of a Gaussian ring is $0,1$ or $\infty$. In this paper, we prove their conjecture.
In many linear inverse problems, we want to estimate an unknown vector belonging to a high-dimensional (or infinite-dimensional) space from few linear measurements. To overcome the ill-posed nature of such problems, we use a low-dimension…
In this non-specialist review I look at how weak lensing can provide information on the dark sector of the Universe. The review concentrates on what can be learned about Dark Matter, Dark Energy and Dark Gravity, and why. On Dark Matter,…
This work investigates the dark matters structures that form on the smallest cosmological scales. We find that the types and abundances of structures which form at approximately Earth-mass scales are very sensitive to the nature of dark…
The previous version of this article was a first attempt to confront the Dark Gravity theory to cosmological data. However, more recent developments lead to the conclusion that the cosmological principle is probably not valid in Dark…
This chapter explores the notion of "dimension" of a set. Various power laws by which an Euclidean space can be characterized are used to define dimensions, which then explore different aspects of the set. Also discussed are the…
In this paper we review the main theoretical and experimental achievements in the field of Dark Matter from the Cosmological and Astrophysical point of view. We revisit it from the very first surveys of local astrophysical matter, up to the…
In this paper, we study the rings with zero Gorenstein weak dimensions, which we call them Gorenstein Von Neumann regular rings.
The strong global dimension of a ring is the supremum of the length of perfect complexes that are indecomposable in the derived category. In this note we characterize the noetherian commutative rings that have finite strong global…
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…
This is a survey of what is known and/or conjectured about the prime and primitive spectra of quantum algebras, of quantized coordinate rings in particular. The topological structure of these spectra, their relations to classical affine…
There is a non-trivial four-derivative extension of the gravitational spectrum that is free of ghosts and phenomenologically viable. It is the so called $R^2$-gravity since it is defined by the only addition of a term proportional to the…
This article briefly summarizes and reviews the motivations for - and the present status of - the proposal that the small size of the observed Dark Energy density can be understood in terms of the dynamical relaxation of two large extra…
Ghost imaging is a developing imaging technique that employs random masks to image a sample. Ghost projection utilizes ghost-imaging concepts to perform the complementary procedure of projection of a desired image. The key idea underpinning…
General Relativity (GR) is an effective field theory valid in the infrared regime. Quadratic curvature extensions intended to probe ultraviolet physics generically propagate a massive spin-$2$ ghost and are therefore non-unitary. One route…
Computational ghost imaging retrieves the spatial information of a scene using a single pixel detector. By projecting a series of known random patterns and measuring the back reflected intensity for each one, it is possible to reconstruct a…
In this paper, we define weakly coherent rings, and examine the transfer of these rings to homomorphic image, trivial ring extension, localization, and direct product. These results provide examples of weakly coherent rings that are not…
We prove some basic results on the dimension theory of algebraic stacks, and on the multiplicities of their irreducible components, for which we do not know a reference.
We study the deflection of light in the background of a "wiggly" cosmic string, and investigate whether it is possible to detect cosmic strings by means of weak gravitational lensing. For straight strings without small-scale structure there…