相关论文: Tap Complexity, the Cavity Method and Supersymmetr…

In this paper, we consider the problem of quantifying parametric uncertainty in classical empirical interatomic potentials (IPs) using both Bayesian (Markov Chain Monte Carlo) and frequentist (profile likelihood) methods. We interface these…

We extend \cite{chen2025srkbp} by analyzing the complexity of the $k$-block-positivity testing algorithm that stems from the optimization problem in Definition \ref{definition:SDP-k-block-positivity}. In this paper, we investigate a…

We compute the 1-loop chiral corrections to the bag parameters which are needed for the discussion of the SUSY K-Kbar mixing problem in both finite and infinite volume. We then show how the bag parameters can be combined among themselves…

We analyse the matrix factorization problem. Given a noisy measurement of a product of two matrices, the problem is to estimate back the original matrices. It arises in many applications such as dictionary learning, blind matrix…

A quantum Parisi formula for the transverse field Sherrington-Kirkpatrick (SK) model is proven with an elementary mathematical method. First, a self-overlap corrected quantum model of the transverse field SK model is represented in terms of…

We prove a theorem justifying the regularity conditions which are needed for Path Sampling in Factor Models. We then show that the remaining ingredient, namely, MCMC for calculating the integrand at each point in the path, may be seriously…

The general features and characteristics of Kapteyn series, which are a special type of series involving Bessel function, are investigated. For many applications to physics, astrophysics, and mathematics, it is crucial to have closed-form…

Within a Kuhn-Tucker cavity method introduced in a former paper, we study optimal stability learning for situations, where in the replica formalism the replica symmetry may be broken, namely (i) the case of a simple perceptron above the…

We study globally supersymmetric 3d gauge theories on curved manifolds by describing the coupling of 3d topological gauge theories, with both Yang-Mills and Chern-Simons terms in the action, to background topological gravity. In our…

SHAP explanations are a popular feature-attribution mechanism for explainable AI. They use game-theoretic notions to measure the influence of individual features on the prediction of a machine learning model. Despite a lot of recent…

Symmetry Adapted Perturbation Theory (SAPT) has become an important tool when predicting and analyzing intermolecular interactions. Unfortunately, DFT-SAPT, which uses Density Functional Theory (DFT) for the underlying monomers, has some…

In Batalin-Vilkovisky formalism a classical mechanical system is specified by means of a solution to the {\sl classical master equation}. Geometrically such a solution can be considered as a $QP$-manifold, i.e. a super\m equipped with an…

Quantum Hamiltonian complexity studies computational complexity aspects of local Hamiltonians and ground states; these questions can be viewed as generalizations of classical computational complexity problems related to local constraint…

The mathematical software \texttt{GAP} (Groups, Algorithms, Programming) offers a powerful set of tools to investigate computationally group theory. Using this software package we investigate a variation of a well-known problem in…

This paper addresses the sparse representation (SR) problem within a general Bayesian framework. We show that the Lagrangian formulation of the standard SR problem, i.e., $\mathbf{x}^\star=\arg\min_\mathbf{x} \lbrace \|…

Let $p$ be a branched covering of a Riemann surface to the Riemann sphere $\mathbb{P}^1$, with branching set $B \subset \mathbb{P}^1$. We define the complexity of $p$ as infinity, if $\mathbb{P}^1 \setminus B$ does not admit a hyperbolic…

We give the first quasipolynomial upper bound $\phi n^{\text{polylog}(n)}$ for the smoothed complexity of the SWAP algorithm for local Graph Partitioning (also known as Bisection Width), where $n$ is the number of nodes in the graph and…

New two-dimensional quantum model - the generalization of the Scarf II - is completely solved analytically for the integer values of parameter. This model being not amenable to conventional procedure of separation of variables is solved by…

The BRST cohomology of free chiral SUSY has a wealth of Extraordinary Invariants. When one adds a superpotential to the free theory, the extention of the Extraordinary Invariants leads to some constraints on that superpotential. A…

The performance of space-time adaptive processing (STAP) is often degraded by factors such as limited sample size and moving targets. Traditional clutter covariance matrix (CCM) estimation relies on Euclidean metrics, which fail to capture…