Related papers: Symmetry Properties of Nested Canalyzing Functions
We construct a class of nonlinear coherent states (NLCSs) by introducing a more general nonlinear function and study their non-classical properties, specifically the second-order correlation function $g^{(2)}(0)$, Mandel parameter $Q$,…
A system of soft ellipsoid molecules confined between two planar walls is studied using classical Density Functional Theory (DFT). Both the isotropic and nematic phases are considered. The excess free energy is evaluated using two different…
The richly developed theory of complex manifolds plays important roles in our understanding of holomorphic functions in several complex variables. It is natural to consider manifolds that will play similar roles in the theory of holomorphic…
We introduce a jet tagger based on a neural network analyzing the Minkowski Functionals (MFs) of pixellated jet images. The MFs are geometric measures of binary images, and they can be regarded as a generalization of the particle…
We present static and dynamic properties of molecular correlation functions S_{lmn,l'm'n'}(q,t) in a simulated supercooled liquid of water molecules, as a preliminary effort in the direction of solving the molecular mode coupling theory…
Let \bar{M}_{0,n} be the moduli space of pointed, genus 0 curves. Let L_i denote the line bundle on \bar{M}_{0,n} associated to the i-th marked point (the fiber of L_i is the cotangent space of the pointed curve at the i-th point).…
Boolean networks are a popular modeling framework in computational biology to capture the dynamics of molecular networks, such as gene regulatory networks. It has been observed that many published models of such networks are defined by…
The statistical-mechanical study of the equilibrium properties of fluids, starting from the knowledge of the interparticle interaction potential, is essential to understand the role that microscopic interaction between individual particles…
Synchronization is an emergent and fundamental phenomenon in nature and engineered systems. Understanding the stability of a synchronized phenomenon is crucial for ensuring functionality in various complex systems. The stability of the…
As the core of recommender system, collaborative filtering (CF) models the affinity between a user and an item from historical user-item interactions, such as clicks, purchases, and so on. Benefited from the strong representation power,…
We consider Convolutional Neural Networks (CNNs) with 2D structured features that are symmetric in the spatial dimensions. Such networks arise in modeling pairwise relationships for a sequential recommendation problem, as well as secondary…
This work provides an additional step in the theoretical understanding of neural networks. We consider neural networks with one hidden layer and show that when learning symmetric functions, one can choose initial conditions so that standard…
Incorporating symmetry as an inductive bias into neural network architecture has led to improvements in generalization, data efficiency, and physical consistency in dynamics modeling. Methods such as CNNs or equivariant neural networks use…
Recent results of Bucciarelli show that the semilattice of degrees of parallelism of first-order boolean functions in PCF has both infinite chains and infinite antichains. By considering a simple subclass of Sieber's sequentiality…
Inequalities among symmetric functions are fundamental in various branches of mathematics, thus motivating a systematic study of their structure. Majorization has been shown to characterize inequalities among commonly used symmetric…
We introduce weighted atom-centered symmetry functions (wACSFs) as descriptors of a chemical system's geometry for use in the prediction of chemical properties such as enthalpies or potential energies via machine learning. The wACSFs are…
A free-energy functional for a crystal that contains both the symmetry conserved and symmetry broken parts of the direct pair correlation function is developed. The free-energy functional is used to investigate the crystallization of fluids…
Given a small random sample of $n$-bit strings labeled by an unknown Boolean function, which properties of this function can be tested computationally efficiently? We show an equivalence between properties that are efficiently testable from…
Cross-frequency coupling (CFC) has been proposed to coordinate neural dynamics across spatial and temporal scales. Despite its potential relevance for understanding healthy and pathological brain function, the standard CFC analysis and…
The extent of ion pairing in solution is an important phenomenon to rationalise transport and thermodynamic properties of electrolytes. A fundamental measure of this pairing is the potential of mean force (PMF) between solvated ions. The…