Related papers: The group approach to AdS space propagators: A fas…

A method is developed to construct a non-local massless scalar field theory in a flat quantised space-time generated by an operator algebra. Implicit in the operator algebra is a fundamental length scale of the space-time. The fundamental…

Quantum many-body systems in thermal equilibrium can be described by the imaginary time Green's function formalism. However, the treatment of large molecular or solid ab inito problems with a fully realistic Hamiltonian in large basis sets…

We consider the solution of linear systems with tensor product structure using a GMRES algorithm. In order to cope with the computational complexity in large dimension both in terms of floating point operations and memory requirement, our…

In this technical report, we analyze Legendre decomposition for non-negative tensor in theory and application. In theory, the properties of dual parameters and dually flat manifold in Legendre decomposition are reviewed, and the process of…

This paper deals with simultaneously fast and in-place algorithms for formulae where the result has to be linearly accumulated: some output variables are also input variables, linked by a linear dependency. Fundamental examples include the…

Random geometric graphs are a popular choice for a latent points generative model for networks. Their definition is based on a sample of $n$ points $X_1,X_2,\cdots,X_n$ on the Euclidean sphere~$\mathbb{S}^{d-1}$ which represents the latent…

This article provides next step towards solving speed bottleneck of any system that intensively uses convolutions operations (e.g. CNN). Method described in the article is applied on deformable part models (DPM) algorithm. Method described…

In this letter we suggest a natural spinor-helicity formalism for massless fields in AdS${}_4$. It is based on the standard realization of the AdS${}_4$ isometry algebra $so(3,2)$ in terms of differential operators acting on…

We calculate four-point correlation functions of two weight-2 and two weight-3 1/2-BPS operators in \mathcal{N}=4 SYM in the large N limit in supergravity approximation. By the AdS/CFT conjecture, these operators are dual to AdS…

We examine the relative performance of algorithms for the calculation of curvature in spacetime. The classical coordinate component method is compared to two distinct versions of the Newman-Penrose tetrad approach for a variety of…

Optimizing neural networks with loss that contain high-dimensional and high-order differential operators is expensive to evaluate with back-propagation due to $\mathcal{O}(d^{k})$ scaling of the derivative tensor size and the…

This paper proposes to address the issue of complexity reduction for the numerical simulation of multiscale media in a quasi-periodic setting. We consider a stationary elliptic diffusion equation defined on a domain $D$ such that…

We propose a distributed algorithm based on Alternating Direction Method of Multipliers (ADMM) to minimize the sum of locally known convex functions using communication over a network. This optimization problem emerges in many applications…

We study the quantum analogue of primary fields and their descendants on fuzzy AdS_2, proposed in hep-th/0004072. Three-point vertices are calculated and shown to exhibit the conventional 1/N expansion as well as nonperturtive effects in…

Let $k$ be a finite field extension of the function field $\bfF_p(T)$ and $\bar{k}$ its algebraic closure. We count points in projective space $\Bbb P ^{n-1}(\bar{k})$ with given height and of fixed degree $d$ over the field $k$. If…

Using the known propagator equations for 0,1 and 2 forms in AdS_{d+1}, we find the p-form field propagator equations in dimensions where the forms are Poincare dual. Since the general equation obeyed by the propagators is linear in…

We present a non-commutative algorithm for the multiplication of a 2x2-block-matrix by its transpose using 5 block products (3 recursive calls and 2 general products) over C or any finite field.We use geometric considerations on the space…

We consider one-loop scalar and tensor integrals with an arbitrary number of external legs relevant for multi-parton processes in massless theories. We present a procedure to reduce N-point scalar functions with generic 4-dimensional…

Distributed cooperative localization in wireless networks is a challenging problem since it typically requires solving a large-scale nonconvex and nonsmooth optimization problem. In this paper, we reformulate the classic cooperative…

Here we present a new approach to compute symmetries of rational second order ordinary differential equations (rational 2ODEs). This method can compute Lie symmetries (point symmetries, dynamical symmetries and non-local symmetries)…