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The integer quantum Hall transition (IQHT) is one of the most mysterious members of the family of Anderson transitions. Since the 1980s, the scaling behavior near the IQHT has been vigorously studied in experiments and numerical…
As integrated circuit scale grows and design complexity rises, effective circuit representation helps support logic synthesis, formal verification, and other automated processes in electronic design automation. And-Inverter Graphs (AIGs),…
In two dimensional conformal field theories the limit of large central charge plays the role of a semi-classical limit. Certain universal observables, such as conformal blocks involving the exchange of the identity operator, can be expanded…
Despite the success of Heterogeneous Graph Neural Networks (HGNNs) in modeling real-world Heterogeneous Information Networks (HINs), challenges such as expressiveness limitations and over-smoothing have prompted researchers to explore Graph…
We develop a linear theory of very weak solutions for nonlocal eigenvalue problems $\mathcal L u = \lambda u + f$ involving integro-differential operators posed in bounded domains with homogeneous Dirichlet exterior condition, with and…
The small x behaviour of the non-singlet structure function is studied within the double logarithmic approximation (DLA) of perturbative QCD. Since there is neither $k_T$ nor $\theta$ ordering in the ladder Feynman graphs, the predicted…
A chain of connected genes with activation-repression links is analysed. It is shown that for various promoter activity functions (parametrised by Hill coefficient) the equations describing the concentrations of transcription factors, are…
We study the problem of estimating the derivatives of a regression function, which has a wide range of applications as a key nonparametric functional of unknown functions. Standard analysis may be tailored to specific derivative orders, and…
Green's functions are fundamental quantities that determine the linear responses of physical systems. The recent developments of non-Hermitian systems, therefore, call for Green's function formulas of non-Hermitian bands. This task is…
Nilsystems are a natural generalization of rotations and arise in various contexts, including in the study of multiple ergodic averages in ergodic theory, in the structural analysis of topological dynamical systems, and in asymptotics for…
The Hill coefficient is often used as a direct measure of the cooperativity of binding processes. It is an essential tool for probing properties of reactions in many biochemical systems. Here we analyze existing experimental data and…
Scalable and symmetry-consistent force-field models are essential for extending quantum-accurate simulations to large spatiotemporal scales. While descriptor-based neural networks can incorporate lattice symmetries through carefully…
Heterogeneous information networks (HINs) can be used to model various real-world systems. As HINs consist of multiple types of nodes, edges, and node features, it is nontrivial to directly apply graph neural network (GNN) techniques in…
We show examples of total Boolean functions that depend on $n$ variables and have spectral sensitivity $\Theta(\sqrt{\log n})$, which is asymptotically minimal. Our main new function combines the Hamming code with the Boolean address…
The center of interest in this work are variational problems with integral functionals depending on special nonlocal gradients. The latter correspond to truncated versions of the Riesz fractional gradient, as introduced in [Bellido, Cueto &…
Griffiths phases (GPs), generated by the heterogeneities on modular networks, have recently been suggested to provide a mechanism, rid of fine parameter tuning, to explain the critical behavior of complex systems. One conjectured…
Fully inhomogeneous spin Hall-Littlewood symmetric rational functions $F_\lambda$ arise as partition functions of certain path configurations in the $\mathfrak{sl}_2$ higher spin six vertex models. They are multiparameter generalizations of…
Gene regulatory networks, i.e. DNA segments in a cell which interact with each other indirectly through their RNA and protein products, lie at the heart of many important intracellular signal transduction processes. In this paper we analyse…
Genetic algorithms have played an important role in engineering optimization. Traditional GAs treat each gene separately. However, biophysical studies of gene regulatory networks revealed direct associations between different genes. It…
Intrinsic interpretability of graph neural networks (GNNs) is to find a small subset of the input graph's features -- rationale -- which guides the model prediction. Unfortunately, the leading rationalization models often rely on data…