Related papers: Finite-$N$ Bootstrap Constraints in Matrix and Ten…

We study constraints coming from the modular invariance of the partition function of two-dimensional conformal field theories. We constrain the spectrum of CFTs in the presence of holomorphic and anti-holomorphic currents using the…

We conjecture that the $O(N)$-symmetric non-linear sigma model in the semi-infinite $(1+1)$-dimensional space is ``integrable'' with respect to the ``free'' and the ``fixed'' boundary conditions. We then derive, for both cases, the boundary…

We consider diagonal matrix elements of local operators between multi-soliton states in finite volume in the sine-Gordon model, and formulate a conjecture regarding their finite size dependence which is valid up to corrections exponential…

The double scaling limit of a new class of the multi-matrix models proposed in \cite{MMM91}, which possess the $W$-symmetry at the discrete level, is investigated in details. These models are demonstrated to fall into the same universality…

A well studied problem in algebraic complexity theory is the determination of the complexity of problems relying on evaluations of bilinear maps. One measure of the complexity of a bilinear map (or 3-tensor) is the optimal number of…

Dynamic nonlinear systems exhibit distortions arising from coupled static and dynamic effects. Their intertwined nature poses major challenges for data-driven modeling. This paper presents a theoretical framework grounded in structured…

Matrix models with continuous symmetry are powerful tools for studying quantum gravity and holography. Tensor models have also found applications in holographic quantum gravity. Matrix models with discrete permutation symmetry have been…

Ordinary tensor models of rank $D\geq 3$ are dominated at large $N$ by tree-like graphs, known as melonic triangulations. We here show that non-melonic contributions can be enhanced consistently, leading to different types of large $N$…

The representation theory of tensor functions is a powerful mathematical tool for constitutive modeling of anisotropic materials. A major limitation of the traditional theory is that many point groups require fourth- or sixth-order…

The attempt of extending to higher dimensions the matrix model formulation of two-dimensional quantum gravity leads to the consideration of higher rank tensor models. We discuss how these models relate to four dimensional quantum gravity…

We focus on \emph{row sampling} based approximations for matrix algorithms, in particular matrix multipication, sparse matrix reconstruction, and \math{\ell_2} regression. For \math{\matA\in\R^{m\times d}} (\math{m} points in \math{d\ll m}…

We consider matrices $\boldsymbol{A}(\boldsymbol\theta)\in\mathbb{R}^{m\times m}$ that depend, possibly nonlinearly, on a parameter $\boldsymbol\theta$ from a compact parameter space $\Theta$. We present a Monte Carlo estimator for…

S-matrix bootstrap and positivity bounds are usually viewed as constraints on low-energy theories imposed by the requirement of a standard UV completion. By considering graviton--photon scattering in the Standard Model, we argue that the…

We study the geometrical meaning of higher-order terms in matrix models of Yang-Mills type in the semi-classical limit, generalizing recent results arXiv:1003.4132 to the case of 4-dimensional space-time geometries with general Poisson…

We introduce a non-perturbative framework for computing structure constants of single-trace operators in the N=4 SYM theory at large N. Our approach features new vertices, with hexagonal shape, that can be patched together into three- and…

Deep learning models have proven to be exceptionally useful in performing many machine learning tasks. However, for each new dataset, choosing an effective size and structure of the model can be a time-consuming process of trial and error.…

The black-box nature of neural networks limits the ability to encode or impose specific structural relationships between inputs and outputs. While various studies have introduced architectures that ensure the network's output adheres to a…

We study the mixed system of correlation functions involving a scalar field charged under a global $U(1)$ symmetry and the associated conserved spin-1 current $J_\mu$. Using numerical bootstrap techniques we obtain bounds on new observables…

We derive bounds on Wilson coefficients in gravitational effective field theories using fully crossing symmetric dispersion relations. These sum rules naturally isolate finite subsets of low-energy couplings without relying on the forward…

Bottom-Up Hidden Tree Markov Model is a highly expressive model for tree-structured data. Unfortunately, it cannot be used in practice due to the intractable size of its state-transition matrix. We propose a new approximation which lies on…