Related papers: Exploring Logistic Functions as Robust Alternative…

Let $\gamma_n $ denote the length of the $n$-th zone of instability of the Hill operator $Ly= -y^{\prime \prime} - [4t\alpha \cos2x + 2 \alpha^2 \cos 4x ] y,$ where $\alpha \neq 0, $ and either both $\alpha, t $ are real, or both are pure…

Despite theoretical advantages, causal methods for Gene Regulatory Network (GRN) inference from single-cell RNA-seq data consistently fail to match or outperform correlation-based baselines in many realistic benchmarks, a persistent puzzle…

This paper presents a new Graph Neural Network (GNN) type using feature-wise linear modulation (FiLM). Many standard GNN variants propagate information along the edges of a graph by computing "messages" based only on the representation of…

Phenotypical variability in the absence of genetic variation often reflects complex energetic landscapes associated with underlying gene regulatory networks (GRNs). In this view, different phenotypes are associated with alternative states…

The main ideas behind the classical multivariate logistic regression model make sense when translated to the functional setting, where the explanatory variable $X$ is a function and the response $Y$ is binary. However, some important…

This article summarises the theory of several bounded functional calculi for unbounded operators that have recently been discovered. The extend the Hille--Phillips calculus for (negative) generators $A$ of certain bounded $C_0$-semigroups,…

In this paper, we analyze the asymptotic behavior of a system of interacting reinforced stochastic processes $({\bf Z}_n, {\bf N}_n)_n$ on a directed network of $N$ agents. The system is defined by the coupled dynamics ${\bf…

It is well known that Hermitian and non-Hermitian models exhibit distinct physics and require different theoretical tools. In this work, we propose a unified generating-function framework for both classes with generic boundary conditions…

In this paper we provide another application of the Inhomogeneous Hopf-Ole\u{\i}nik Lemma (IHOL) proved in \cite{BM-IHOL-PartI} or \cite{Boyan-2}. As a matter of fact, we also provide a new and simpler proof of a slightly weaker version…

The aim of this paper is to show certain properties of the Green's functions related to the Hill's equation coupled with different two point boundary value conditions. We will obtain the expression of the Green's function of Neumann,…

Physics-informed neural networks (PINNs) have recently emerged as effective methods for solving partial differential equations (PDEs) in various problems. Substantial research focuses on the failure modes of PINNs due to their frequent…

Previous explorations of the Asymptotic Safety scenario in Quantum Einstein Gravity (QEG) by means of the effective average action and its associated functional renormalization group (RG) equation assumed spacetime manifolds which have no…

Functional equations (FE) arise quite naturally in the analysis of stochastic systems of different kinds : queueing and telecommunication networks, random walks, enumeration of planar lattice walks, etc. Frequently, the object is to…

Hallmarks of criticality, such as power-laws and scale invariance, have been empirically found in cortical networks and it has been conjectured that operating at criticality entails functional advantages, such as optimal computational…

The competition between non-Hermitian skin effect and Anderson localization leads to various intriguing phenomena concerning spectrums and wavefunctions. Here, we study the linear response of disordered non-Hermitian systems, which is…

We investigate the action spectrum of Hill's lunar problem by observing inclusions between the Liouville domains enclosed by the regularized energy hypersurfaces of the rotating Kepler problem and Hill's lunar problem. In this paper, we…

The statistical mechanical approach to complex networks is the dominant paradigm in describing natural and societal complex systems. The study of network properties, and their implications on dynamical processes, mostly focus on locally…

Among interpretable machine learning methods, the class of Generalised Additive Neural Networks (GANNs) is referred to as Self-Explaining Neural Networks (SENN) because of the linear dependence on explicit functions of the inputs. In binary…

Gradient-based neural network training traditionally enforces symmetry between forward and backward propagation, requiring activation functions to be differentiable (or sub-differentiable) and strictly monotonic in certain regions to…

We present a physical interpretation of machine learning functions, opening up the possibility to control properties of statistical systems via the inclusion of these functions in Hamiltonians. In particular, we include the predictive…