Related papers: Holography, Pade Approximants and Deconstruction
We consider Lorentzian correlation functions in theories with non-relativistic Schrodinger symmetry. We employ the method developed by Skenderis and van Rees in which the contour in complex time defining a given correlation function is…
In previous work, we introduced a method for modeling a configuration of objects in 2D and 3D images using a mathematical "medial/skeletal linking structure." In this paper, we show how these structures allow us to capture positional…
We study a fourth-order derivative scalar field configuration in a fixed Lifshitz background. Using an auxiliary field we rewrite the equations of motion as two coupled second order equations. We specialize to the limit that the mass of the…
To gain insight into the mechanisms behind machine learning methods, it is crucial to establish connections among the features describing data points. However, these correlations often exhibit a high-dimensional and strongly nonlinear…
We discuss various aspect of the holographic correspondence between 5-d gravity and 4-d field theory. First of all, we describe deformations of N=4 Super Yang-Mills (SYM) theories in terms of 5-d gauged supergravity. In particular, we…
In a regression setting we propose algorithms that reduce the dimensionality of the features while simultaneously maximizing a statistical measure of dependence known as distance correlation between the low-dimensional features and a…
An example of the holographic correspondence between 2d, N=2 quantum field theories and classical 4d, N=2 supergravity theories is found. The constraints on the target space geometry of the 4d, N=2 non-linear sigma-models in N=2…
We calculate holographically three-point functions of scalar operators with large dimensions at finite density and finite temperature. To achieve this, we construct new solutions that involve two isometries of the deformed internal space.…
We construct a new type of holographic correspondence between non-relativistic string theory in String Newton-Cartan AdS$_5\times$S$^5$ and Galilean Yang-Mills supplemented with 5 adjoint interacting scalar fields living on the 3+1…
We compare two definitions of connected correlation functions in fluctuating geometries. We show results of the MC simulations for 4D dynamical triangulation in the elongated phase and compare them with the exact calculations of correlation…
As is well known, in mathematics, any function could be approximated by the Pad\'e approximant. The Pad\'e approximant is the best approximation of a function by a rational function of given order. In fact, the Pad\'e approximant often…
Based on the uniqueness and universality of gravity, it is clear that theories with different dynamical exponents are related in the holographic approach. Concretely, we construct an M-theory background from pure QCD dual and show that a…
Correlation clustering is a widely-used approach for clustering large data sets based only on pairwise similarity information. In recent years, there has been a steady stream of better and better classical algorithms for approximating this…
We discuss the geometrical connection between 2D conformal field theories, random walks on hyperbolic Riemann surfaces and knot theory. For the wide class of CFTs with monodromies being the discrete subgroups of SL(2,R), the determination…
We describe recent nonlinear analytic approximation tools in the classical setting of Hardy spaces in the upper half plane and show how to transfer them to the higher dimensional real setting of harmonic functions in upper half spaces. It…
The evaluation of robustness and reliability of realistic structures in the presence of uncertainty involves costly numerical simulations with a very high number of evaluations. This motivates model order reduction techniques like the…
We compute holographically correlation functions for giant gravitons in $\mathcal{N}=4$ SYM in the presence of monodromy defects through probe branes. The computation boils down to the study of charged geodesics in certain five-dimensional…
In this paper we consider the fundamental operations dilation and erosion of mathematical morphology. Many powerful image filtering operations are based on their combinations. We establish homomorphism between max-plus semi-ring of integers…
We consider here the percolation problem in thin films, both in the direction normal to the film and in the direction parallel to the film. We thereby describe here the cross-over between 2D and 3D percolation, which we do on cubic and…
We study one and two point functions of conformal field theories on spaces of maximal symmetry with and without boundaries and investigate their spectral representations. Integral transforms are found, relating the spectral decomposition to…