27 papers · ranked by Valyu relevance
Leo Kozachkov, Mikael Lundqvist, Jean-Jacques Slotine, Earl K. Miller
The brain consists of many interconnected networks with time-varying activity. There are multiple sources of noise and variation yet activity has to eventually converge to a stable state for its computations to make sense. We approached this from a control-theory perspective by applying contraction analysis to…
Leo Kozachkov, Mikael Lundqvist, Jean-Jacques Slotine, Earl K. Miller
The brain consists of many interconnected networks with time-varying, partially autonomous activity. There are multiple sources of noise and variation yet activity has to eventually converge to a stable, reproducible state (or sequence of states) for its computations to make sense. We approached this problem from a…
Leo Kozachkov, Mikael Lundqvist, Jean-Jacques Slotine, Earl K. Miller + 1 more
'Earl K. Miller' 'Adrian M Haith'] The brain consists of many interconnected networks with time-varying, partially autonomous activity. There are multiple sources of noise and variation yet activity has to eventually converge to a stable, reproducible state (or sequence of states) for its computations to make sense. We…
Milan Korda
This work makes several contributions on stability and performance verification of nonlinear dynamical systems controlled by neural networks. First, we show that the stability and performance of a polynomial dynamical system controlled by a neural network with semialgebraically representable activation functions (e.g.…
Daniel Harnack, Miha Pelko, Antoine Chaillet, Yacine Chitour + 2 more
'Mark C.W. van Rossum' 'Boris S. Gutkin'] Neurons are equipped with homeostatic mechanisms that counteract long-term perturbations of their average activity and thereby keep neurons in a healthy and information-rich operating regime. While homeostasis is believed to be crucial for neural function, a systematic analysis…
Axel Hutt, Scott Rich, Taufik A Valiante, Jérémie Lefebvre
Heterogeneity is the norm in biology. The brain is no different: neuronal cell-types are myriad, reflected through their cellular morphology, type, excitability, connectivity motifs and ion channel distributions. While this biophysical diversity enriches neural systems’ dynamical repertoire, it remains challenging to…
Faming Guo, Ricai Luo, Xiaolan Qin, Yunfei Yi
In this paper, we study the problem of exponential stability for the Hopfield neural network with time-varying delays. Different from the existing results, we establish new stability criteria by employing the method of variation of constants and Gronwall's integral inequality. Finally, we give several examples to show…
Divyansh Mittal, Rishikesh Narayanan
Grid cells in the medial entorhinal cortex manifest multiple firing fields, patterned to tessellate external space with triangles. Although two-dimensional continuous attractor network (CAN) models have offered remarkable insights about grid-patterned activity generation, their functional stability in the presence of…
Julián Barreiro-Gomez, Salah Eddine Choutri, Boualem Djehiche
— In this paper, we present an approach to neural network mean-field-type control and its stochastic stability analysis by means of adversarial inputs (aka adversarial attacks). This is a class of data-driven mean-field-type control where the distribution of the variables such as the system states and control inputs…
Michaela Ennis, Leo Kozachkov, Jean-Jacques Slotine
Recurrent neural networks (RNNs) are widely used throughout neuroscience as models of local neural activity. Many properties of single RNNs are well characterized theoretically, but experimental neuroscience has moved in the direction of studying multiple interacting areas, and RNN theory needs to be likewise extended.…
Daniel Ehrens, Duluxan Sritharan, Sridevi V. Sarma
It has recently been proposed that the epileptic cortex is fragile in the sense that seizures manifest through small perturbations in the synaptic connections that render the entire cortical network unstable. Closed-loop therapy could therefore entail detecting when the network goes unstable, and then stimulating with…
Xiang Zou, Lie Yao, Donghua Zhao, Liang Chen + 1 more
Brain is a fantastic organ that helps creature adapting to the environment. If we dissect functions from brain, there are at least three kinds of modules: receptor, effector and median integrated network. Receptor and effector is the most fundamental functions for a brain, even for a single neuron. In the advanced…
Rakesh Sengupta, Anindya Pattanayak, Raju Surampudi Bapi
The stability analysis of dynamical neural network systems generally follows the route of finding a suitable Liapunov function after the fashion Hopfield’s famous paper on content addressable memory network or by finding conditions that make divergent solutions impossible. For the current work we focused on biological…
Plamen Dimitrov
This work presents the current collection of mathematical models related to neural networks and proposes a new family of such with extended structure and dynamics in order to attain a selection of cognitive capabilities. It starts by providing a basic background to the morphology and physiology of the biological and…
Yue Kris Wu, Friedemann Zenke, Timothy O'Leary, Ronald L Calabrese
To rapidly process information, neural circuits have to amplify specific activity patterns transiently. How the brain performs this nonlinear operation remains elusive. Hebbian assemblies are one possibility whereby strong recurrent excitatory connections boost neuronal activity. However, such Hebbian amplification is…
Ueli Rutishauser, Jean-Jacques Slotine, Rodney Douglas, Olaf Sporns
Previous explanations of computations performed by recurrent networks have focused on symmetrically connected saturating neurons and their convergence toward attractors. Here we analyze the behavior of asymmetrical connected networks of linear threshold neurons, whose positive response is unbounded. We show that, for a…
YaJun Li, Zhaowen Huang
The passivity problem for a class of stochastic neural networks systems (SNNs) with varying delay and leakage delay has been further studied in this paper. By constructing a more effective Lyapunov functional, employing the free-weighting matrix approach, and combining with integral inequality technic and stochastic…
Stephen Lynch, Jon Borresen
This paper presents a stability analysis of simple neuromodules displaying fold bifurcations (leading to hysteresis), flip bifurcations (period doubling and undoubling to and from chaos) and Neimark-Sacker bifurcations (quasiperiodic and periodic bifurcations). For the first time, bifurcation diagrams are plotted using…
Carlo Michaelis, Andrew B. Lehr, Christian Tetzlaff
Neuromorphic hardware has several promising advantages compared to von Neumann architectures and is highly interesting for robot control. However, despite the high speed and energy efficiency of neuromorphic computing, algorithms utilizing this hardware in control scenarios are still rare. One problem is the transition…
Georgios Detorakis, Antoine Chaillet, Nicolas P. Rougier
We provide theoretical conditions guaranteeing that a self-organizing map efficiently develops representations of the input space. The study relies on a neural field model of spatiotemporal activity in area 3b of the primary somatosensory cortex. We rely on Lyapunov’s theory for neural fields to derive theoretical…
Veerupaksh Singla, Qiyuan Zhao, Brett Savoie
The absence of computational methods to predict stressor-specific degradation susceptibilities represents a significant and costly challenge to the introduction of new materials into applications. Here, a machine-learning framework is developed that predicts stressor-specific stability scores from computationally…
Sara Tkaczyk, Johannes Karwounopoulos, Andreas Schöller, H. Lee Woodcock + 3 more
- 1. Faculty of Chemistry, Institute of Computational Biological Chemistry, Währingerstrasse 17, University of Vienna, Vienna, Austria - 2. Department of Pharmaceutical Sciences, Pharmaceutical Chemistry Division, Josef-Holaubek-Platz 2, University of Vienna, 1090 Vienna, Austria - 3. Doctoral School of Pharmaceutical…
James Swift, Matthew Arran Turner, James Christopher Reynolds
A rapid headspace analysis method for the authenticity testing of whiskies of different brands and years was developed for a low cost, deployable atmospheric pressure ionisation mass spectrometer, which required minimal sample preparation. Principal component analysis was applied to the time-averaged mass spectra, the…
Hannes Stagge, Theresa Kunz, Sina Ramsayer, Robert Güttel
The calculation of chemical equilibria in detailed reactor simulations frequently requires elaborate numerical solution of the governing equations in an iterative way, which is often computationally expensive and can significantly increase the overall computation time. In order to reduce these computational costs, we…
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Electrospray ionization (ESI) mass spectrometry is an essential technique for chemical analysis in a range of fields. In ESI, analytes can produce multiple charge states, which must be correctly assigned for identification. Existing approaches to charge state assignment can suffer from limited accuracy and/or poor…
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Artificial intelligence (AI) is reshaping chemical engineering. Still, its role in safety-critical operations is limited because we rarely see tools that link physical models with data-driven methods. This study brings together three elements: physics-constrained neural networks, uncertainty quantification, and a…
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Finding microkinetic parameters for heterogeneously catalyzed processes with conventional methods is a challenging task. Recently, the use of artificial neural networks has been described as a promising and flexible tool for kinetic parameter estimation. In this work, an extension to the methodology of chemical reaction…