Related papers: Classification of 2-node Excitatory-Inhibitory Net…
We classify connected 3-node restricted excitatory-inhibitory networks, extending our previous paper (`Classification of 2-node Excitatory-Inhibitory Networks', Mathematical Biosciences 373 (2024) 109205). We assume that there are two…
Network classification aims to group networks (or graphs) into distinct categories based on their structure. We study the connection between classification of a network and of its constituent nodes, and whether nodes from networks in…
Coupled cell systems associated with a coupled cell network are determined by (smooth) vector fields that are consistent with the network structure. Here, we follow the formalisms of Stewart, Golubitsky and Pivato (Symmetry groupoids and…
The construction of biologically plausible models of neural circuits is crucial for understanding the computational properties of the nervous system. Constructing functional networks composed of separate excitatory and inhibitory neurons…
The brain is likely the most complex organ, given the variety of functions it controls, the number of cells it comprises, and their corresponding diversity. Studying and identifying neurons, the brain's primary building blocks, is a crucial…
We propose an approach for explaining Bayesian network classifiers, which is based on compiling such classifiers into decision functions that have a tractable and symbolic form. We introduce two types of explanations for why a classifier…
While statistical analysis of a single network has received a lot of attention in recent years, with a focus on social networks, analysis of a sample of networks presents its own challenges which require a different set of analytic tools.…
In many real-world networks, nodes have class labels, attributes, or variables that affect the network's topology. If the topology of the network is known but the labels of the nodes are hidden, we would like to select a small subset of…
In the study of reaction networks and the polynomial dynamical systems that they generate, special classes of networks with important properties have been identified. These include reversible, weakly reversible}, and, more recently,…
In the classic view of cortical rhythms, the interaction between excitatory pyramidal neurons (E) and inhibitory parvalbumin neurons (I) has been shown to be sufficient to generate gamma and beta band rhythms. However, it is now clear that…
When dealing with large graphs, such as those that arise in the context of online social networks, a subset of nodes may be labeled. These labels can indicate demographic values, interest, beliefs or other characteristics of the nodes…
Network Embedding (NE) methods, which map network nodes to low-dimensional feature vectors, have wide applications in network analysis and bioinformatics. Many existing NE methods rely only on network structure, overlooking other…
We analyze a family of clustered excitatory-inhibitory neural networks and the underlying bifurcation structures that arise because of permutation symmetries in the network as the global coupling strength $g$ is varied. We primarily…
This paper extends the Transmission Neural Network model proposed by Gao and Caines in [1]-[3] to incorporate inhibitory connections and neurotransmitter populations. The extended network model contains binary neuronal states, transmission…
This article proposes a novel Bayesian classification framework for networks with labeled nodes. While literature on statistical modeling of network data typically involves analysis of a single network, the recent emergence of complex data…
We analyze the dynamics of a deterministic model of inhibitory neuronal networks proving that the discontinuities of the Poincare map produce a never empty chaotic set, while its continuity pieces produce stable orbits. We classify the…
We minimize a linear combination of the Willmore and the length functional among networks in $\mathbb{R}^d$ belonging to a given class determined by the number of curves, the order of the junctions and the angles between curves at the…
We examine two types of similarity networks each based on a distinct notion of relevance. For both types of similarity networks we present an efficient inference algorithm that works under the assumption that every event has a nonzero…
Recurrently coupled oscillators that are sufficiently heterogeneous and/or randomly coupled can show an asynchronous activity in which there are no significant correlations among the units of the network. The asynchronous state can…
Models of biochemical networks are usually presented as connected graphs where vertices indicate proteins and edges are drawn to indicate activation or inhibition relationships. These diagrams are useful for drawing qualitative conclusions…