Related papers: Parametric dependence of irregular conformal block

Conformal prediction provides a distribution-free framework for uncertainty quantification via prediction sets with exact finite-sample coverage. In low dimensions these sets are easy to interpret, but in high-dimensional or structured…

We study the relation of irregular conformal blocks with the Painlev\'e III$_3$ equation. The functional representation for the quasiclassical irregular block is shown to be consistent with the BPZ equations of conformal field theory and…

We study the momentum-space 4-point correlation function of identical scalar operators in conformal field theory. Working specifically with null momenta, we show that its imaginary part admits an expansion in conformal blocks. The blocks…

In many practical applications, spatial data are often collected at areal levels (i.e., block data) and the inferences and predictions about the variable at points or blocks different from those at which it has been observed typically…

Conformal blocks are the central ingredient of the conformal bootstrap programme. We elaborate on our recent observation that uncovered a relation with wave functions of an integrable Calogero-Sutherland Hamiltonian in order to develop a…

Conformal prediction is a statistical tool for producing prediction regions for machine learning models that are valid with high probability. A key component of conformal prediction algorithms is a \emph{non-conformity score function} that…

Parameter estimation-based observer (PEBO) is a recently developed constructive tool to design state observers for nonlinear systems. It reformulates the state estimation problem as one of online parameter identification, effectively…

We examine the symmetry-breaking effect of fixed constellations of particles on the surface-directed spinodal decomposition of binary blends in the presence of particles whose surfaces have a preferential affinity for one of the components.…

A deformed differential calculus is developed based on an associative star-product. In two dimensions the Hamiltonian vector fields model the algebra of pseudo-differential operator, as used in the theory of integrable systems. Thus one…

Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…

We investigate how invariant subspaces corresponding to a single eigenvalue will change when a matrix is perturbed. We focus on the invariant subspaces corresponding to an eigenvalue associated with the Jordan blocks that have the same…

We use numerical simulations to show how noninteracting hard particles binding to a deformable elastic shell may self-assemble into a variety of linear patterns. This is a result of the nontrivial elastic response to deformations of shells.…

Nonlinear independent component analysis (ICA) aims to recover the underlying independent latent sources from their observable nonlinear mixtures. How to make the nonlinear ICA model identifiable up to certain trivial indeterminacies is a…

We consider the challenging problem of statistical inference for exponential-family random graph models based on a single observation of a random graph with complex dependence. To facilitate statistical inference, we consider random graphs…

Given a non-contracting trajectory of a nonlinear system, we consider the question of designing an input perturbation that makes the perturbed trajectory contracting. This paper stresses the analogy of this question with the classical…

We study numerical conformal mapping of multiply connected planar domains with boundaries consisting of unions of finitely many circular arcs, so called polycircular domains. We compute the conformal capacities of condensers defined by…

We consider conformal field theories around points of large twist degeneracy. Examples of this are theories with weakly broken higher spin symmetry and perturbations around generalised free fields. At the degenerate point we introduce twist…

In this paper, we present a new matrix approach for the analysis of subdivision schemes whose non-stationarity is due to linear dependency on parameters whose values vary in a compact set. Indeed, we show how to check the convergence in…

It is shown how to obtain conformal blocks from embedding space with the help of the operator product expansion. The minimal conformal block originates from scalar exchange in a four-point correlation functions of four scalars. All…

As anticipated in [1], elaborated in [2-4], and explicitly formulated in [5], the Dotsenko-Fateev integral discriminant coincides with conformal blocks, thus providing an elegant approach to the AGT conjecture, without any reference to an…