Related papers: Exploring Logistic Functions as Robust Alternative…
The asymptotic dynamical correlation functions in one-dimensional spin chains are described by power-laws. The corresponding exponents characterize different bulk and boundary critical behavior. We present novel results for the logarithmic…
Although accumulation of molecular damage is suggested to be an important molecular mechanism of aging, a quantitative link between the dynamics of damage accumulation and mortality of species has so far remained elusive. To address this…
Advances of modern sensing and sequencing technologies generate a deluge of high dimensional space-temporal physiological and next-generation sequencing (NGS) data. Physiological traits are observed either as continuous random functions, or…
We develop a variational framework to understand the properties of the functions learned by neural networks fit to data. We propose and study a family of continuous-domain linear inverse problems with total variation-like regularization in…
Graph neural networks (GNNs) have achieved remarkable success in node classification. Building on this progress, heterogeneous graph neural networks (HGNNs) integrate relation types and node and edge semantics to leverage heterogeneous…
Unraveling the complexities of Gene Regulatory Networks (GRNs) is crucial for understanding cellular processes and disease mechanisms. Traditional computational methods often struggle with the dynamic nature of these networks. This study…
The following class of sum-product statistics T_n(p)=\frac{1}{k}\sum_{h=1}^p \sum_{(s_1...s_h)\in P(p,h)} \sum_{i_1=l+1}^{i_0} ... \sum_{i_h=l+1}^{i_{h-1}} i_h \prod_{i=i_1}^{i_h} \frac{(Y_{n-i+1,n}-Y_{n-i,n})^{s_i}}{s_i!} (where $l,$…
Link prediction, which consists of predicting edges based on graph features, is a fundamental task in many graph applications. As for several related problems, Graph Neural Networks (GNNs), which are based on an attribute-centric…
In this paper the study of a nonlocal second order Cahn-Hilliard-type singularly perturbed family of functions is undertaken. The kernels considered include those leading to Gagliardo fractional seminorms for gradients. Using Gamma…
Logistic regression is the most commonly used method for constructing predictive models for binary responses. One significant drawback to this approach, however, is that the asymptotes of the logistic response function are fixed at 0 and 1,…
Gene expression datasets consist of thousand of genes with relatively small samplesizes (i.e. are large-$p$-small-$n$). Moreover, dependencies of various orders co-exist in the datasets. In the Undirected probabilistic Graphical Model (UGM)…
Link prediction is a fundamental task in graph learning, inherently shaped by the topology of the graph. While traditional heuristics are grounded in graph topology, they encounter challenges in generalizing across diverse graphs. Recent…
We prove that nested canalizing functions are the minimum-sensitivity Boolean functions for any activity ratio and we determine the functional form of this boundary which has a nontrivial fractal structure. We further observe that the…
Graphs are fundamental data structures for modeling complex interactions in domains such as social networks, molecular structures, and biological systems. Graph-level tasks, which involve predicting properties or labels for entire graphs,…
An antithetical concept, adaptive symmetry, to conservative symmetry in physics is proposed to understand the deep neural networks (DNNs). It characterizes the invariance of variance, where a biotic system explores different pathways of…
Over the past decade, Graph Neural Networks (GNNs) have achieved great success on machine learning tasks with relational data. However, recent studies have found that heterophily can cause significant performance degradation of GNNs,…
We examine the latest HERA experimental measurements of the $Q^2$ logarithmic derivative of the proton structure function. We analyze the characteristics of DGLAP with and without screening, as well as a Regge type model, and compare their…
Exciting new work on the generalization bounds for neural networks (NN) given by Neyshabur et al. , Bartlett et al. closely depend on two parameter-depenedent quantities: the Lipschitz constant upper-bound and the stable rank (a softer…
This paper explores the use of a novel form of Hierarchical Graph Neurons (HGN) for in-operation behaviour selection in a swarm of robotic agents. This new HGN is called Robotic-HGN (R-HGN), as it matches robot environment observations to…
These notes are about ridge functions. Recent years have witnessed a flurry of interest in these functions. Ridge functions appear in various fields and under various guises. They appear in fields as diverse as partial differential…