Related papers: On positive definite thresholding of correlation m…
Material scientists and condensed matter physicists have long been divided on the issue of choosing the conceptual framework for explaining why open-shell transition-metal oxides tend to be insulators, whereas otherwise successful theories…
We propose a Cholesky factor parameterization of correlation matrices that facilitates a priori restrictions on the correlation matrix. It is a smooth and differentiable transform that allows additional boundary constraints on the…
We consider, within the algebraic formalism, the time dependence of fidelity for qubits encoded into an open physical system. We relate the decay of fidelity to the evolution of correlation functions and, in the particular case of a…
We develop methods to study the scalar sector of multi-Higgs models with large discrete symmetry groups that are softly broken. While in the exact symmetry limit, the model has very few parameters and can be studied analytically,…
The paper addresses the problem of learning a regression model parameterized by a fixed-rank positive semidefinite matrix. The focus is on the nonlinear nature of the search space and on scalability to high-dimensional problems. The…
In a nutshell, we intend to extend Schoenberg's classical theorem connecting conditionally positive semidefinite functions $F\colon \mathbb{R}^n \to \mathbb{C}$, $n \in \mathbb{N}$, and their positive semidefinite exponentials $\exp(tF)$,…
We use nearly parallel pure states to characterize positive linear functionals $\phi$ on $\mathbb{M}_n$ as positive multiples of the trace if and only if $\phi(A \natural B) \leq \sqrt{\phi(A) \phi(B)}$ for all positive definite matrices…
We investigate linear maps between matrix algebras that remain positive under tensor powers, i.e., under tensoring with $n$ copies of themselves. Completely positive and completely co-positive maps are trivial examples of this kind. We show…
Due to common architecture designs, symmetries exist extensively in contemporary neural networks. In this work, we unveil the importance of the loss function symmetries in affecting, if not deciding, the learning behavior of machine…
A new approach to solving random matrix models directly in the large $N$ limit is developed. First, a set of numerical values for some low-pt correlation functions is guessed. The large $N$ loop equations are then used to generate values of…
How to understand the set of correlations admissible in nature is one outstanding open problem in the core of the foundations of quantum theory. Here we take a complementary viewpoint to the device-independent approach, and explore the…
Symmetry plays a fundamental role in quantum many-body physics, and a central concept is spontaneous symmetry breaking, which imposes crucial constraints on the possible quantum phases and their transitions. Recent developments have…
We show that the correlation functions of any single-field cosmological model with constant growing-modes are constrained by an infinite number of novel consistency relations, which relate (N+1)-point correlation functions with a…
In large part, the future utility of modern numerical conformal bootstrap depends on its ability to accurately predict the existence of hitherto unknown non-trivial conformal field theories (CFTs). Here we investigate the extent to which…
Positive semidefinite Hermitian matrices that are not fully specified can be completed provided their underlying graph is chordal. If the matrix is positive definite the completion can be uniquely characterized as the matrix that maximizes…
Conformal symmetry is broken in physical QCD; nevertheless, one can use conformal symmetry as a template, systematically correcting for its nonzero $\beta$ function as well as higher-twist effects. For example, commensurate scale relations…
Using the formalism of soft-collinear effective theory, a complete separation of short- and long-distance contributions to heavy-to-light transition form factors at large recoil is performed. The universal functions $\zeta_M(E)$…
Symmetries as well as other special conditions can cause anomalous slowing down of fidelity decay. These situations will be characterized, and a family of random matrix models to emulate them generically presented. An analytic solution…
Recently, interesting empirical phenomena known as Neural Collapse have been observed during the final phase of training deep neural networks for classification tasks. We examine this issue when the feature dimension d is equal to the…
Isotropic positive definite functions on spheres play important roles in spatial statistics, where they occur as the correlation functions of homogeneous random fields and star-shaped random particles. In approximation theory, strictly…