Related papers: Inversion and Integral Identities in dCFTs
In this paper, we study convergence and superconvergence theory of integer and fractional derivatives of the one-point and the two-point Hermite interpolations. When considering the integer-order derivative, exponential decay of the error…
The Quaternion Fourier transform (QFT) is one of the key tools in studying color image processing. Indeed, a deep understanding of the QFT has created the color images to be transformed as whole, rather than as color separated component. In…
State-of-the-art face recognition systems are based on deep (convolutional) neural networks. Therefore, it is imperative to determine to what extent face templates derived from deep networks can be inverted to obtain the original face…
Conformal field theory (CFT) is an extremely powerful tool for explicitly computing critical exponents and correlation functions of statistical mechanics systems at a second order phase transition, or of condensed matter systems at a…
Computation of the spherical harmonic rotation coefficients or elements of Wigner's d-matrix is important in a number of quantum mechanics and mathematical physics applications. Particularly, this is important for the Fast Multipole Methods…
Iterative Fast Fourier Transform methods are useful for calculating the fields in composite materials and their macroscopic response. By iterating back and forth until convergence, the differential constraints are satisfied in Fourier…
We show that the four-point functions in conformal field theory are defined as distributions on the boundary of the region of convergence of the conformal block expansion. The conformal block expansion converges in the sense of…
Deep convolutional neural networks (DCNNs) are an influential tool for solving various problems in the machine learning and computer vision fields. In this paper, we introduce a new deep learning model called an Inception- Recurrent…
We develop new methods for constructing confidence sets and intervals in linear instrumental variables (IV) models based on tests that remain valid under weak identification and under heteroskedastic, autocorrelated, or clustered errors. In…
For a map (function) $F(x):\ftwo^n\rightarrow\ftwo^n$ and a given $y$ in the image of $F$ the problem of \emph{local inversion} of $F$ is to find all inverse images $x$ in $\ftwo^n$ such that $y=F(x)$. In Cryptology, such a problem arises…
We investigate two aspects of conformal field theories. In the first part, we study the general 4-point correlator of identical scalars around the fully crossing symmetric point $u=v=1$, where $u,v$ are conformally invariant cross ratios.…
The renormalization of composite operators is a fundamental aspect of quantum field theory, relevant for the description of phase transitions and high energy phenomenology. We calculate the anomalous dimensions of a large set of operators…
Various observables in compact CFTs are required to obey positivity, discreteness, and integrality. Positivity forms the crux of the conformal bootstrap, but understanding of the abstract implications of discreteness and integrality for the…
We calculate CFT data for the Gross-Neveu model in $2<d<4$ dimensions at the next-to-leading order in the $1/N$ expansion. In particular, we make use of the background field method to derive various conformal triangles involving the…
We review the emergence of hypergeometric structures (of $F_4$ Appell functions) from the conformal Ward identities (CWIs) in conformal field theories (CFTs) in dimensions $d > 2$. We illustrate the case of scalar 3- and 4-point functions.…
We analyze the convergence properties of operator product expansions (OPE) for Lorentzian CFT four-point functions of scalar operators. We give a complete classification of Lorentzian four-point configurations. All configurations in each…
We present a real-space formulation and higher-order finite-difference implementation of periodic Orbital-free Density Functional Theory (OF-DFT). Specifically, utilizing a local reformulation of the electrostatic and kernel terms, we…
This paper analyzes the convergence of fixed-point iterations of the form u = f(u) and the properties of the inverse of the related pentadiagonal matrices, associated with the fourth-order nonlinear beam equation. This nonlinear problem is…
In this note we consider the problem of extracting the corrections to CFT data induced by the exchange of a primary operator and its descendents in the crossed channel. We show how those corrections which are analytic in spin can be…
Interferometric closure invariants, constructed from triangular loops of mixed Fourier components, capture calibration-independent information on source morphology. While a complete set of closure invariants is directly obtainable from…