Related papers: Local Immunodeficiency: Minimal Networks and Stabi…

We present Locally Orderless Networks (LON) and its theoretic foundation which links it to Convolutional Neural Networks (CNN), to Scale-space histograms, and measurement theory. The key elements are a regular sampling of the bias and the…

We investigate the loss surface of neural networks. We prove that even for one-hidden-layer networks with "slightest" nonlinearity, the empirical risks have spurious local minima in most cases. Our results thus indicate that in general "no…

A mechanism for self-organization of the degree of connectivity in model neural networks is studied. Network connectivity is regulated locally on the basis of an order parameter of the global dynamics which is estimated from an observable…

Populations are seldom completely isolated from their environment. Individuals in a particular geographic or social region may be considered a distinct network due to strong local ties, but will also interact with individuals in other…

Bistability plays a central role in the gene regulatory networks (GRNs) controlling many essential biological functions, including cellular differentiation and cell cycle control. However, establishing the network topologies that can…

We show that subsets of interacting oscillators may synchronize in different ways within a single network. This diversity of synchronization patterns is promoted by increasing the heterogeneous distribution of coupling weights and/or…

Recovering and reconstructing networks by accurately identifying missing and unreliable links is a vital task in the domain of network analysis and mining. In this article, by studying a specific local structure, namely a degree block…

We discuss quantum network Bell nonlocality in a setting where the network structure is not fully known. More concretely, an honest user may trust their local network topology, but not the structure of the rest of the network, involving…

We present a detailed analytical and numerical study for the spreading of infections in complex population networks with acquired immunity. We show that the large connectivity fluctuations usually found in these networks strengthen…

Resilience of cyber-physical networks to unexpected failures is a critical need widely recognized across domains. For instance, power grids, telecommunication networks, transportation infrastructures and water treatment systems have all…

The widespread use of Multi-layer perceptrons (MLPs) often relies on a fixed activation function (e.g., ReLU, Sigmoid, Tanh) for all nodes within the hidden layers. While effective in many scenarios, this uniformity may limit the networks…

Many complex systems, such as communication networks, display a surprising degree of robustness: while key components regularly malfunction, local failures rarely lead to the loss of the global information-carrying ability of the network.…

Interconnected networks describe the dynamics of important systems in a wide range such as biological systems and electrical power grids. Some important features of these systems were successfully studied and understood through simplified…

We study the robustness of the steady states of a class of systems of autonomous ordinary differential equations (ODEs), having as a central example those arising from (bio)chemical reaction networks. More precisely, we study under what…

Biochemical models that exhibit bistability are of interest to biologists and mathematicians alike. Chemical reaction network theory can provide sufficient conditions for the existence of bistability, and on the other hand can rule out the…

Understanding the spread of diseases through complex networks is of great interest where realistic, heterogeneous contact patterns play a crucial role in the spread. Most works have focused on mean-field behavior -- quantifying how contact…

It is well-known that biological and social interaction networks have a varying degree of redundancy, though a consensus of the precise cause of this is so far lacking. In this paper, we introduce a topological redundancy measure for…

Can three-dimensional, microvasculature networks still ensure blood supply if individual links fail? We address this question in the sinusoidal network, a plexus-like microvasculature network, which transports nutrient-rich blood to every…

Heterogeneous wireless networks (HetNets) provide a means to increase network capacity by introducing small cells and adopting a layered architecture. HetNets allocate resources flexibly through time sharing and cell range…

We consider self-tolerance and its failure -autoimmunity- in a minimal mathematical model of the idiotypic network. A node in the network represents a clone of B-lymphocytes and its antibodies of the same idiotype which is encoded by a…