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Lattice Hamiltonian systems underpin models across condensed matter, nonlinear optics, and biophysics, yet learning their dynamics from data is obstructed by two unknowns: the interaction topology and whether node dynamics are homogeneous.…
Functional Hamilton-Jacobi (HJ) equation, the central equation of the holographic renormalization group (HRG), functional Schr\"{o}dinger equation, and generalized Wilson-Polchinski (WP) equation, the central equation of the functional…
Random feature ridge regression is often analyzed in the high-dimensional regime under the homogeneous sampling model $x_i=\Sigma^{1/2}x_i'$, where the vectors $x_i'$ have iid entries and the same covariance matrix $\Sigma$ is shared by all…
Despite the recent success of graph neural networks (GNN), common architectures often exhibit significant limitations, including sensitivity to oversmoothing, long-range dependencies, and spurious edges, e.g., as can occur as a result of…
Efficiently solving the Job Shop Scheduling Problem in real-world industrial applications requires policies that are both computationally lean and topologically robust. While Reinforcement Learning has shown potential in automating…
Among gauged dynamics motivated by string theory, we find many with gapless asymptotic directions. Although the natural boundary condition for ground states is $L^2$, one often turns on chemical potentials or supersymmetric mass terms to…
Inferring the structure of gene regulatory networks (GRN) from gene expression data has many applications, from the elucidation of complex biological processes to the identification of potential drug targets. It is however a notoriously…
$1$-parameter persistent homology, a cornerstone in Topological Data Analysis (TDA), studies the evolution of topological features such as connected components and cycles hidden in data. It has been applied to enhance the representation…
Bistability plays a central role in the gene regulatory networks (GRNs) controlling many essential biological functions, including cellular differentiation and cell cycle control. However, establishing the network topologies that can…
In traditional logistic regression models, the link function is often assumed to be linear and continuous in predictors. Here, we consider a threshold model that all continuous features are discretized into ordinal levels, which further…
The integration of Graph Neural Networks (GNNs) and Neural Ordinary and Partial Differential Equations has been extensively studied in recent years. GNN architectures powered by neural differential equations allow us to reason about their…
The Gene Regulatory Network (GRN) of biological cells governs a number of key functionalities that enables them to adapt and survive through different environmental conditions. Close observation of the GRN shows that the structure and…
A lattice version of the widely used Functional Renormalization Group (FRG) for the Legendre effective action is solved - in principle exactly - in terms of graph rules for the linked cluster expansion. Conversely, the FRG induces nonlinear…
We use the homological perturbation lemma to produce explicit formulas computing the class in the twisted de Rham complex represented by an arbitrary polynomial. This is a non-asymptotic version of the method of Feynman diagrams. In…
Genes communicate with each other through different regulatory effects, which lead to the emergence of complex structures in cells, and such structures are expected to be different for normal and cancerous cells. To study breast cancer…
We examine several higher spin modes of the Poincar\'e gauge theory (PGT) of gravity using the Hamiltonian analysis. The appearance of certain undesirable effects due to non-linear constraints in the Hamiltonian analysis are used as a test.…
Log-periodic oscillations have been found to decorate the usual power law behavior found to describe the approach to a critical point, when the continuous scale-invariance symmetry is partially broken into a discrete-scale invariance (DSI)…
Understanding how gene regulatory networks (GRNs) give rise to stable and dynamic cellular states remains a central challenge in theoretical biology, particularly when slow epigenetic feedback reshapes the underlying regulatory landscape.…
Gene regulatory network (GRN)-based morphogenetic models have recently gained an increasing attention. However, the relationship between microscopic properties of intracellular GRNs and macroscopic properties of morphogenetic systems has…
The vast majority of biological sequences encode unknown functions and bear little resemblance to experimentally characterized proteins, limiting both our understanding of biology and our ability to harness functional potential for the…