Related papers: Scale Holography
The AdS/CFT correspondence is useful primarily when the number of colours, $N_{\textsf{c}}$, characterising the boundary field theory, is "large", and when the mass of the bulk black hole that is usually present is "large" relative to the…
Topological techniques are powerful tools for characterizing the complexity of many dynamical systems, including the commonly studied area-preserving maps of the plane. However, the extension of many topological techniques to higher…
Scale-free networks are abundant in nature and society, describing such diverse systems as the world wide web, the web of human sexual contacts, or the chemical network of a cell. All models used to generate a scale-free topology are…
In this paper we explore ideas of holography and strings living in the $d+1$ dimensional Anti-de Sitter space $AdS_{d+1}$ in a unified framework borrowed from twistor theory. In our treatise of correspondences between geometric structures…
Finite-size scaling is a key tool in statistical physics, used to infer critical behavior in finite systems. Here we use the analogous concept of finite-time scaling to describe the bifurcation diagram at finite times in discrete dynamical…
This paper studies first the differential inequalities that make it possible to build a global theory of pseudo-holomorphic functions in the case of one or several complex variables. In the case of one complex dimension, we prove that the…
We present a new technique in order to quantify the dynamics of spatially extended systems. Using a test on the existence of unstable periodic orbits, we identify intermediate spatial scales, wherein the dynamics is characterized by maximum…
One of the key issues in holography is going beyond $\mathrm{AdS}$ and defining quantum gravity in spacetimes with a null boundary. Recent examples of this type involve linear dilaton asymptotics and are related to the $T \overline{T}$…
In this thesis I explore the generality of the holographic principle in 2+1 (bulk) dimensions by looking at the possibility of having holographic correspondences for non-AdS (higher-spin) spacetimes. The first part focuses on Lobachevsky…
We introduce the notion of scale to generalize and compare different invariants of metric spaces and their measures. Several versions of scales are introduced such as Hausdorff, packing, box, local and quantization. They moreover are…
We review recent developments in holographic hydrodynamics. We start from very basic discussion on hydrodynamic systems and motivate why string theory is an essential tool to deal with these systems when they are strongly coupled. The main…
We explain how to relate the ideas of Carroll geometry, matrix theory on instantonic objects, and infinite boost limits of M-theory. Based on these new insights, we explore the implications for possible holographic constructions involving a…
We introduce the notion of angular values for deterministic linear difference equations and random linear cocycles. We measure the principal angles between subspaces of fixed dimension as they evolve under nonautonomous or random linear…
This paper introduces a new concept of one-dimensional hologram which represents one line image, and a new kind of display structure using it. This one-dimensional hologram is similar to a superpositioned diffraction lattice. And the…
Various scaling relations of the entanglement entropy are reviewed. Based on the scaling, I would like to point out similarity of mathematical formulation among recent topics in wide research area. In particular, the scaling plays crucial…
Space filling curves are widely used in Computer Science. In particular Hilbert curves and their generalisations to higher dimension are used as an indexing method because of their nice locality properties. This article generalises this…
This is a survey on local dynamics of holomorphic maps in one and several complex variables, discussing in particular normal forms and the structure of local stable sets in the non-hyperbolic case, and including several proofs and a vast…
This work approaches the multidimensional scaling problem from a novel angle. We introduce a scalable method based on the h-plot, which inherently accommodates asymmetric proximity data. Instead of embedding the objects themselves, the…
This paper introduces a new fundamental characteristic, \ie, the dynamic range, from real-world metric tools to deep visual recognition. In metrology, the dynamic range is a basic quality of a metric tool, indicating its flexibility to…
In many instances of holographic correspondences between a d dimensional boundary theory and a d+1 dimensional bulk, a direct argument in the boundary theory implies that there must exist a simple and precise relation between the Euclidean…