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In Systems Biology there is a growing interest in the question, whether or not a given mathematical model can admit more than one steady state. As parameter values are often unknown or subject to a very high uncertainty, one is often…
This work aims to provide understandings on the remarkable success of deep convolutional neural networks (CNNs) by theoretically analyzing their generalization performance and establishing optimization guarantees for gradient descent based…
We study the distributions of the resilience of power flow models against transmission line failures via a so-called backup capacity. We consider three ensembles of random networks and in addition, the topology of the British transmission…
We study the network reconstruction problem for an epidemic reaction-diffusion. These models are an extension of deterministic, compartmental models to a graph setting, where the reactions within the nodes are coupled by a diffusion. We…
One of the most defining features of the global financial network is its inherent complex and intertwined structure. From the perspective of systemic risk it is important to understand the influence of this network structure on default…
Efficiently counting or detecting defective items is a crucial task in various fields ranging from biological testing to quality control to streaming algorithms. The \emph{group testing estimation problem} concerns estimating the number of…
Given a mixture between two populations of coins, "positive" coins that each have -- unknown and potentially different -- bias $\geq\frac{1}{2}+\Delta$ and "negative" coins with bias $\leq\frac{1}{2}-\Delta$, we consider the task of…
Zero-one biochemical reaction networks play key roles in cell signalling such as signalling pathways regulated by protein phosphorylation. Multistability of reaction networks is a crucial dynamics feature enabling decision-making in cells.…
Unrolled neural networks emerged recently as an effective model for learning inverse maps appearing in image restoration tasks. However, their generalization risk (i.e., test mean-squared-error) and its link to network design and train…
Stochastic chemical reaction networks (CRNs) are complex systems which combine the features of concurrent transformation of multiple variables in each elementary reaction event, and nonlinear relations between states and their rates of…
The methods of non-homogeneous random graphs calibration are developed for social networks simulation. The graphs are calibrated by the degree distributions of the vertices and the edges. The mathematical foundation of the methods is formed…
Anomaly detection (AD) is increasingly recognized as a key component for ensuring the resilience of future communication systems. While deep learning has shown state-of-the-art AD performance, its application in critical systems is hindered…
Neural networks predictions are unreliable when the input sample is out of the training distribution or corrupted by noise. Being able to detect such failures automatically is fundamental to integrate deep learning algorithms into robotics.…
The eigenvalues and eigenvectors of the connectivity matrix of complex networks contain information about its topology and its collective behavior. In particular, the spectral density $\rho(\lambda)$ of this matrix reveals important network…
We derive a new upper bound on the reliability function for channel coding over discrete memoryless channels. Our bounding technique relies on two main elements: (i) adding an auxiliary genie-receiver that reveals to the original receiver a…
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…
Gene covariation networks are commonly used to study biological processes. The inference of gene covariation networks from observational data can be challenging, especially considering the large number of players involved and the small…
Biological networks often encapsulate promotion/inhibition as signed edge-weights of a graph. Nodes may correspond to genes assigned expression levels (mass) of respective proteins. The promotion/inhibition nature of co-expression between…
We present conditions which guarantee a parametrization of the set of positive equilibria of a generalized mass-action system. Our main results state that (i) if the underlying generalized chemical reaction network has an effective…
We consider an inhomogeneous Erd\H{o}s-R\'enyi random graph $G_N$ with vertex set $[N] = \{1,\dots,N\}$ for which the pair of vertices $i,j \in [N]$, $i\neq j$, is connected by an edge with probability $r(\tfrac{i}{N},\tfrac{j}{N})$,…