Related papers: Scale Holography
Scaling relations for the mass, angular momentum and other properties of a wide range of self-similar structures in the universe are seen to have universal features. As a consequence of the ideas elaborated in earlier papers these relations…
We develop a linear-algebraic framework for dimensional analysis in systems with constraints, particularly when variables are numerous or related by implicit relations so that direct elimination is impractical. By expressing both…
This is the first paper in a series on new higher categorical structures called higher Segal spaces. For every d > 0, we introduce the notion of a d-Segal space which is a simplicial space satisfying locality conditions related to…
The motion of a scalar particle in (d+1)-dimensional AdS space may be described in terms of the Cartesian coordinates that span the (d+2)-dimensional space in which the AdS space is embedded. Upon quantization, the mass hyperboloid defined…
Digital holography measures the complex optical field and transfer matrix of a device, polarization-diversity is often achieved through spatial multiplexing. We introduce angular multiplexing, to increase flexibility in the optical setup.…
Consider two families of closed oriented curves in a d-manifold. At each point of intersecction of a curve of one family with a curve of the other family, form a new closed curve by going around the first curve and then going around the…
The evolution of a large class of biological, physical and engineering systems can be studied through both dynamical systems theory and Hamiltonian mechanics. The former theory, in particular its specialization to study systems with…
This paper is about the tiling dynamical systems approach to the study of aperiodic order. We compare and contrast four related types of systems: ordinary (one-dimensional) symbolic systems, one-dimensional tiling systems, multidimensional…
Using a new version of the holographic principle, a constant term was introduced, which conduces to the description of the standard cosmological LCDM model, and unifies under the same concept the dark matter and dark energy phenomena. The…
Digital holography numerically restores three-dimensional image information using optically captured diffractive waves. The required bandwidth is larger than that of hologram pixel at a closer distance in the Fresnel diffraction regime,…
Many complex systems involve direct interactions among more than two entities and can be represented by hypergraphs, in which hyperedges encode higher-order interactions among an arbitrary number of nodes. To analyze structures and dynamics…
Hole-ography is a prescription relating the areas of surfaces in an AdS bulk to the differential entropy of a family of intervals in the dual CFT. In (2+1) bulk dimensions, or in higher dimensions when the bulk features a sufficient degree…
Hyperspaces form a powerful tool in some branches of mathematics: lots of fractal and other geometric objects can be viewed as fixed points of some functions in suitable hyperspaces - as well as interesting classes of formal languages in…
Multidimensional scaling is an important dimension reduction tool in statistics and machine learning. Yet few theoretical results characterizing its statistical performance exist, not to mention any in high dimensions. By considering a…
We study the low-energy dynamics of systems with exact and approximate higher-form symmetries using gauge/gravity duality. These symmetries are realised holographically via Maxwell-type theories for massless and massive $p$-forms in AlAdS…
We propose a local renormalization group procedure where length scale is changed in spacetime dependent way. Combining this scheme with an earlier observation that high energy modes in renormalization group play the role of dynamical…
String Newton-Cartan holography is a new example of gauge/gravity duality relating non-relativistic string theory and gauge theories. We review how to construct a family of string and $p$-brane Newton-Cartan holographic dualities by…
With the rapid adoption of machine learning techniques for large-scale applications in science and engineering comes the convergence of two grand challenges in visualization. First, the utilization of black box models (e.g., deep neural…
When the cosmological "constant" is derived from modern five-dimensional relativity, exact solutions imply that for small systems it scales in proportion to the square of the mass. However, a duality transformation implies that for large…
The non-commutative geometry is revisited from the perspective of a generalized D p-brane. In particular, we analyze the open bosonic string world-sheet description and show that an effective non-commutative description on a D p-brane…