相关论文: Blobbed topological recursion for correlation func…

We present explicit recursive relations for the four-point superconformal block functions that are essentially particular contributions of the given conformal class to the four-point correlation function. The approach is based on the…

We consider the problem of correlation functions in the stationary states of one-dimensional stochastic models having conformal invariance. If one considers the space dependence of the correlators, the novel aspect is that although one…

Coupled tensor decomposition reveals the joint data structure by incorporating priori knowledge that come from the latent coupled factors. The tensor ring (TR) decomposition is invariant under the permutation of tensors with different mode…

We study the estimation of a planted signal hidden in a recently introduced nested matrix-tensor model, which is an extension of the classical spiked rank-one tensor model, motivated by multi-view clustering. Prior work has theoretically…

We build upon previous analytical treatments of scalar perturbations in curved inflationary universes to obtain analytical templates for the primordial tensor power spectrum in models with non-zero primordial spatial curvature. These…

Characterising intractable high-dimensional random variables is one of the fundamental challenges in stochastic computation. The recent surge of transport maps offers a mathematical foundation and new insights for tackling this challenge by…

Real-world signals typically span across multiple dimensions, that is, they naturally reside on multi-way data structures referred to as tensors. In contrast to standard ``flat-view'' multivariate matrix models which are agnostic to data…

Topologically ordered systems are characterized by topological invariants that are often calculated from the momentum space integration of a certain function that represents the curvature of the many-body state. The curvature function may…

In this paper we study the double scaling limit of the multi-orientable tensor model. We prove that, contrary to the case of matrix models but similarly to the case of invariant tensor models, the double scaling series are convergent. We…

Modular graph functions arise in the calculation of the low-energy expansion of closed-string scattering amplitudes. For toroidal world-sheets, they are ${\rm SL}(2,\mathbb{Z})$-invariant functions of the torus complex structure that have…

We consider a pivotal monoidal functor whose domain is a modular tensor category (MTC). We show that the trace of such a functor naturally extends to a representation of the corresponding tube category. As irreducible representations of the…

We present a braided circuit topology framework for investigating topology and structural phase transitions in aggregates of semiflexible polymers. In the conventional approach to circuit topology, which specifically applies to single…

Deep neural networks are composed of layers of parametrised linear operations intertwined with non linear activations. In basic models, such as the multi-layer perceptron, a linear layer operates on a simple input vector embedding of the…

The full set of cosmological observables coming from linear scalar and tensor perturbations of loop quantum cosmology is computed in the presence of inverse-volume corrections. Background inflationary solutions are found at linear order in…

We prove rigorously that the symmetric traceless and the antisymmetric tensor models in rank three with tetrahedral interaction admit a $1/N$ expansion, and that at leading order they are dominated by melon diagrams. This proves the recent…

We study the global and local topological properties of multi-lepton patterns reconstructed at the detectors. We investigate the sensitivity of Forman Ricci curvature distributions and persistent homology features to kinematic cuts,…

Persistence has proved to be a valuable tool to analyze real world data robustly. Several approaches to persistence have been attempted over time, some topological in flavor, based on the vector space-valued homology functor, other…

We consider the $O(N)^3$ tensor model of Klebanov and Tarnopolsky \cite{Klebanov:2016xxf} in $d<4$ with a free covariance modified to fit the infrared conformal scaling. We study the renormalization group flow of the model using a Wilsonian…

We show that the large N expansion in the multi-trace 1 formal hermitian matrix model is governed by the topological recursion of [Eynard and Orantin, 2007] with initial conditions. In terms of a 1d gas of eigenvalues, this model includes -…

The cluster expansion formalism used in materials science is reconstructed on an axiomatic basis with the aims of clarifying underlying concepts and improving computational procedures, and without using conventional cluster functions.…