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We characterize the connectivity structure of feed-forward, deep neural networks (DNNs) using network motif theory. To address whether a particular motif distribution is characteristic of the training task, or function of the DNN, we…

Machine Learning · Computer Science 2024-03-05 Olivia T. Zahn , Thomas L. Daniel , J. Nathan Kutz

The ability to compare complex systems can provide new insight into the fundamental nature of the processes captured in ways that are otherwise inaccessible to observation. Here, we introduce the $n$-tangle method to directly compare two…

Physics and Society · Physics 2014-11-27 Lazaros K. Gallos , Nina H. Fefferman

The task of the brain is to look for structure in the external input. We study a network of integrate-and-fire neurons with several types of recurrent connections that learns the structure of its time-varying feedforward input by attempting…

Neurons and Cognition · Quantitative Biology 2020-10-13 Lyudmila Kushnir , Sophie Denève

Motion perception is a critical capability determining a variety of aspects of insects' life, including avoiding predators, foraging and so forth. A good number of motion detectors have been identified in the insects' visual pathways.…

Computer Vision and Pattern Recognition · Computer Science 2019-04-04 Qinbing Fu , Hongxin Wang , Cheng Hu , Shigang Yue

Motifs are the fundamental components of complex systems. The topological structure of networks representing complex systems and the frequency and distribution of motifs in these networks are intertwined. The complexities associated with…

Social and Information Networks · Computer Science 2020-05-21 Ali Jazayeri , Christopher C. Yang

Many biological, technological, and social systems can be effectively described as networks of interacting subsystems. Typically, these networks are not isolated objects, but interact with their environment through both signals and…

Systems and Control · Electrical Eng. & Systems 2026-01-06 Amirhossein Nazerian , Malbor Asllani , Melvyn Tyloo , Wai Lim Ku , Francesco Sorrentino

Olfaction, the sense of smell, has received scant attention from a signal processing perspective in comparison to audition and vision. In this paper, we develop a signal processing paradigm for olfactory signals based on new scientific…

Information Theory · Computer Science 2015-09-16 Kush R. Varshney , Lav R. Varshney

We develop a biophysical model of neuro-sensory integration in the model organism Caenorhabditis elegans. Building on recent experimental findings of the neuron conductances and their resolved connectome, we posit the first full dynamic…

Neurons and Cognition · Quantitative Biology 2015-06-17 James Kunert , Eli Shlizerman , J. Nathan Kutz

We study the global dynamics of integrate and fire neural networks composed of an arbitrary number of identical neurons interacting by inhibition and excitation. We prove that if the interactions are strong enough, then the support of the…

Dynamical Systems · Mathematics 2013-09-10 E. Catsigeras , P. Guiraud

Recently, low-dimensional models of neuronal activity have been exactly derived for large networks of deterministic, Quadratic Integrate-and-Fire (QIF) neurons. Such firing rate models (FRM) describe the emergence of fast collective…

Neurons and Cognition · Quantitative Biology 2024-02-02 Pau Clusella , Ernest Montbrió

Network inference has been extensively studied in several fields, such as systems biology and social sciences. Learning network topology and internal dynamics is essential to understand mechanisms of complex systems. In particular, sparse…

Machine Learning · Statistics 2022-06-13 Yasen Wang , Junyang Jin , Jorge Goncalves

Nonlinear phenomena including multiple equilibria and spontaneous oscillations are common in fluid networks containing either multiple phases or constituent flows. In many systems, such behavior might be attributed to the complicated…

Dynamical Systems · Mathematics 2013-06-26 Nathaniel J. Karst , Brian D. Storey , John B. Geddes

Machine learning (ML) classifiers always benefit from more informative input features. We seek to auto-generate stronger feature sets in order to address the difficulty that ML methods often experience given limited training data. A wide…

Emerging Technologies · Computer Science 2020-09-15 Charles B Delahunt , J Nathan Kutz

Network models are widely used as structural summaries of biochemical systems. Statistical estimation of networks is usually based on linear or discrete models. However, the dynamics of these systems are generally nonlinear, suggesting that…

Applications · Statistics 2014-06-03 C. J. Oates , F. Dondelinger , N. Bayani , J. Korola , J. W. Gray , S. Mukherjee

It is widely perceived that leveraging the success of modern machine learning techniques to mobile devices and wireless networks has the potential of enabling important new services. This, however, poses significant challenges, essentially…

Machine Learning · Computer Science 2023-04-13 Matei Moldoveanu , Abdellatif Zaidi

We investigate the organization of traffic flow on preexisting uni- and bidirectional ant trails. Our investigations comprise a theoretical as well as an empirical part. We propose minimal models of uni- and bi-directional traffic flow…

An inverse procedure is proposed and tested which aims at recovering the a priori unknown functional and structural information from global signals of living brains activity. To this end we consider a Leaky-Integrate and Fire (LIF) model…

The time elapsed model describes the firing activity of an homogeneous assembly of neurons thanks to the distribution of times elapsed since the last discharge. It gives a mathematical description of the probability density of neurons…

Analysis of PDEs · Mathematics 2011-09-16 Khashayar Pakdaman , Benoît Perthame , Delphine Salort

Recurrent neural network architectures can have useful computational properties, with complex temporal dynamics and input-sensitive attractor states. However, evaluation of recurrent dynamic architectures requires solution of systems of…

Neural and Evolutionary Computing · Computer Science 2019-11-18 Dylan Richard Muir

Insect swarms are common phenomena in nature and therefore have been actively pursued in computer animation. Realistic insect swarm simulation is difficult due to two challenges: high-fidelity behaviors and large scales, which make the…

Graphics · Computer Science 2020-07-23 Wei Xiang , Xinran Yao , He Wang , Xiaogang Jin