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High-density carbon nanotube networks (CNNs) continue to attract interest as active elements in nanoelectronic devices, nanoelectromechanical systems (NEMS) and multifunctional nanocomposites. The interplay between the network nanostructure…

According to the chemical reaction network theory, the topology of a certain class of chemical reaction networks, regardless of the kinetic details, sets a limit on the dynamical properties that a particular network can potentially admit;…

Signal transduction within biological cells is governed by networks of interacting proteins. Communication between these proteins is mediated by signaling molecules which bind to receptors and induce stochastic transitions between different…

We propose a novel sensitivity analysis to unobserved confounding in observational studies using copulas and normalizing flows. Using the idea of interventional equivalence of structural causal models, we develop $\rho$-GNF…

Boolean networks are a valuable class of discrete dynamical systems models, but they remain fundamentally limited by their inability to capture multi-way interactions in their components. To remedy this limitation, we propose a model of…

A random boolean cellular automaton is a network of boolean gates where the inputs, the boolean function, and the initial state of each gate are chosen randomly. In this article, each gate has two inputs. Let $a$ (respectively $c$) be the…

Convolutional neural networks (CNNs) often perform well, but their stability is poorly understood. To address this problem, we consider the simple prototypical problem of signal denoising, where classical approaches such as nonlinear…

The sensitivity of a Boolean function f is the maximum over all inputs x, of the number of sensitive coordinates of x. The well-known sensitivity conjecture of Nisan (see also Nisan and Szegedy) states that every sensitivity-s Boolean…

Attention-based neural networks have achieved state-of-the-art results on a wide range of tasks. Most such models use deterministic attention while stochastic attention is less explored due to the optimization difficulties or complicated…

Deep convolutional neural networks (CNNs) are becoming increasingly popular models to predict neural responses in visual cortex. However, contextual effects, which are prevalent in neural processing and in perception, are not explicitly…

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…

Boolean functions can be represented in many ways including logical forms, truth tables, and polynomials. Additionally, Boolean functions have different canonical representations such as minimal disjunctive normal forms. Other canonical…

CNNs exhibit many behaviors different from humans, one of which is the capability of employing high-frequency components. This paper discusses the frequency bias phenomenon in image classification tasks: the high-frequency components are…

Recently the study of noise sensitivity and noise stability of Boolean functions has received considerable attention. The purpose of this paper is to extend these notions in a natural way to a different class of perturbations, namely those…

Probabilistic Boolean Networks (PBNs) have been previously proposed so as to gain insights into complex dy- namical systems. However, identification of large networks and of the underlying discrete Markov Chain which describes their…

We define a measure for the complexity of Boolean functions related to their implementation in neural networks, and in particular close related to the generalization ability that could be obtained through the learning process. The measure…

Network Function Virtualization (NFV) prescribes the instantiation of network functions on general-purpose network devices, such as servers and switches. While yielding a more flexible and cost-effective network architecture, NFV is…

Data-agnostic quasi-imperceptible perturbations on inputs are known to degrade recognition accuracy of deep convolutional networks severely. This phenomenon is considered to be a potential security issue. Moreover, some results on…

We consider the influence of local noise on a generalized network of populations having positive and negative feedbacks. The population dynamics at the nodes is nonlinear, typically chaotic, and allows cessation of activity if the…

This paper presents conservative probabilistic bounds for the spectrum of the admittance matrix and classical linear power flow models under uncertain network parameters; for example, probabilistic line contingencies. Our proposed approach…