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In open, driven systems where parity-time symmetry is preserved, phenomena that defy conventional wisdom emerge near exceptional points, promising advances in photonics. While most studies focus on two-level systems of a conventional…

We study the critical behavior of the 2D $N$-color Ashkin-Teller model in the presence of random bond disorder whose correlations decays with the distance $r$ as a power-law $r^{-a}$. We consider the case when the spins of different colors…

We study Clustered Planarity with Linear Saturators, which is the problem of augmenting an $n$-vertex planar graph whose vertices are partitioned into independent sets (called clusters) with paths - one for each cluster - that connect all…

We study how the topology of feature embedding space changes as it passes through the layers of a well-trained deep neural network (DNN) through Betti numbers. Motivated by existing studies using simplicial complexes on shallow fully…

Additive models can be used for interpretable machine learning for their clarity and simplicity. However, In the classical models for high-order data, the vectorization operation disrupts the data structure, which may lead to degenerated…

Pathway enrichment analysis has become a key tool for biomedical researchers to gain insight into the underlying biology of differentially expressed genes, proteins and metabolites. It reduces complexity and provides a system-level view of…

Recent studies of disorder or non-Hermiticity induced topological insulators inject new ingredients for engineering topological matter. Here we consider the effect of purely non-Hermitian disorders, a combination of these two ingredients,…

We develop the idea of an effective conformal theory describing the low-lying spectrum of the dilatation operator in a CFT. Such an effective theory is useful when the spectrum contains a hierarchy in the dimension of operators, and a small…

A simple yet paradigmatic model for the interplay of strong electronic correlations and geometric frustration is the triangular lattice Hubbard model. Recently it was proposed that moir\'e structures of transition metal dichalcogenides can…

We use the Riemann-Hilbert approach, together with string and Toda equations, to study the topological expansion in the quartic random matrix model. The coefficients of the topological expansion are generating functions for the numbers…

We propose an optimistic estimate to evaluate the best possible fitting performance of nonlinear models. It yields an optimistic sample size that quantifies the smallest possible sample size to fit/recover a target function using a…

We apply Density Matrix Renormalization Group methods to study the phase diagram of the quantum ANNNI model in the region of low frustration where the ferromagnetic coupling is larger than the next-nearest-neighbor antiferromagnetic one. By…

We consider a framework for the construction of iterative schemes for operator equations that combine low-rank approximation in tensor formats and adaptive approximation in a basis. Under fairly general assumptions, we obtain a rigorous…

Biological signals of interest in high-dimensional data are often masked by dominant variation shared across conditions. This variation, arising from baseline biological structure or technical effects, can prevent standard dimensionality…

In this paper we study systems of $N$ uniformly expanding coupled maps when $N$ is finite but large. We introduce self-consistent transfer operators that approximate the evolution of measures under the dynamics, and quantify this…

We propose a simple, exactly solvable, model of interface growth in a random medium that is a variant of the zero-temperature random-field Ising model on the Cayley tree. This model is shown to have a phase diagram (critical depinning field…

In recent years there has been a great interest in topological materials and in their fascinating properties. Topological band theory was initially developed for condensed matter systems, but it can be readily applied to arbitrary wave…

We consider a new class of perturbation expansions, which incorporate in a systematic way the available information about the divergent character of the perturbation series in QCD. The new expansion functions, which replace the powers of…

Traditional analytical reflectance models, while compact and interpretable, lack the capacity to accurately represent physical measurements. Recent neural models, which closely fit input data, are less generalizable and often more expensive…

Asymptotic analysis on some statistical properties of the random binary-tree model is developed. We quantify a hierarchical structure of branching patterns based on the Horton-Strahler analysis. We introduce a transformation of a binary…