Related papers: Numerical Conformal bootstrap with Analytic Functi…
Recently an efficient numerical method has been developed to implement the constraints of crossing symmetry and unitarity on the operator dimensions and OPE coefficients of conformal field theories (CFT) in diverse space-time dimensions. It…
We propose a novel test statistic for testing exogeneity in the functional linear regression model. In contrast to Hausman-type tests in finite dimensional linear regression setups, a direct extension to the functional linear regression…
We study multiscalar theories with $\text{O}(N) \times \text{O}(2)$ symmetry. These models have a stable fixed point in $d$ dimensions if $N$ is greater than some critical value $N_c(d)$. Previous estimates of this critical value from…
Predicting missing segments in partially observed functions is challenging due to infinite-dimensionality, complex dependence within and across observations, and irregular noise. These challenges are further exacerbated by the existence of…
We define the two-dimensional $O(n)$ conformal field theory as a theory that includes the critical dilute and dense $O(n)$ models as special cases, and depends analytically on the central charge. For generic values of $n\in\mathbb{C}$, we…
We consider the problem of Gaussian multiplier bootstrap procedures for the $k$th largest statistics and functions of the top $k$ order statistics, which are commonly encountered in high-dimensional statistical inference. Such a problem has…
The magnetic line defect in the $O(N)$ model gives rise to a non-trivial one-dimensional defect conformal field theory of theoretical and experimental value. This model is considered here in $d=4-\varepsilon$ and the full spectrum of defect…
In this paper, we consider a finite-dimensional optimization problem minimizing a continuous objective on a compact domain subject to a multi-dimensional constraint function. For the latter, we assume the availability of a global Lipschitz…
The smooth bootstrap for estimating copula functionals in small samples is investigated. It can be used both to gauge the distribution of the estimator in question and to augment the data. Issues arising from kernel density and distribution…
Spectral polynomial approximation of smooth functions allows real-time manipulation of and computation with them, as in the Chebfun system. Extension of the technique to two-dimensional and three-dimensional functions on hyperrectangles has…
We initiate a numerical conformal bootstrap study of CFTs with $S_n \ltimes (S_Q)^n$ global symmetry. These include CFTs that can be obtained as coupled replicas of two-dimensional critical Potts models. Particular attention is paid to the…
Polynomial approximations of functions are widely used in scientific computing. In certain applications, it is often desired to require the polynomial approximation to be non-negative (resp. non-positive), or bounded within a given range,…
Molecular dynamics is often considered as a numerical experiment. The error bars on the results are therefore mandatory, but sometimes difficult to determine and computationally demanding. As a low-cost approach, we describe the application…
This paper introduces a framework for uncertainty quantification in regression models defined in metric spaces. Leveraging a newly defined notion of homoscedasticity, we develop a conformal prediction algorithm that offers finite-sample…
In this thesis we study the momentum space approach to the solution of the CWI's of CFT's in higher dimensions. Our work's goal is to illustrate the essential steps needed to build tensor correlators starting from the scalar solutions, for…
Logarithmic conformal field theories have a vast range of applications, from critical percolation to systems with quenched disorder. In this paper we thoroughly examine the structure of these theories based on their symmetry properties. Our…
This work is focused on the application of functional-type a posteriori error estimates and corresponding indicators to a class of time-dependent problems. We consider the algorithmic part of their derivation and implementation and also…
We propose conformal hyperrectangular prediction regions for multi-target regression. We propose split conformal prediction algorithms for both point and quantile regression to form hyperrectangular prediction regions, which allow for easy…
In this letter we study how the exact non-perturbative integrability methods in 4D N=4 Super-Yang-Mills can work efficiently together with the numerical conformal bootstrap techniques to go beyond the spectral observables and access…
Roughly speaking, functional analysis is the study of vector spaces of arbitrary dimension over the field of real or complex numbers, and the continuous linear mappings between such spaces. Naturally, the notion of continuity requires a…