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149 results on '"Doyon, Nicolas"'

1. The determining role of covariances in large networks of stochastic neurons

Author

Painchaud, Vincent, Desrosiers, Patrick, and Doyon, Nicolas

Subjects
Quantitative Biology - Neurons and Cognition, Mathematics - Dynamical Systems, Physics - Biological Physics
Abstract

Biological neural networks are notoriously hard to model due to their stochastic behavior and high dimensionality. We tackle this problem by constructing a dynamical model of both the expectations and covariances of the fractions of active and refractory neurons in the network's populations. We do so by describing the evolution of the states of individual neurons with a continuous-time Markov chain, from which we formally derive a low-dimensional dynamical system. This is done by solving a moment closure problem in a way that is compatible with the nonlinearity and boundedness of the activation function. Our dynamical system captures the behavior of the high-dimensional stochastic model even in cases where the mean-field approximation fails to do so. Taking into account the second-order moments modifies the solutions that would be obtained with the mean-field approximation, and can lead to the appearance or disappearance of fixed points and limit cycles. We moreover perform numerical experiments where the mean-field approximation leads to periodically oscillating solutions, while the solutions of the second-order model can be interpreted as an average taken over many realizations of the stochastic model. Altogether, our results highlight the importance of including higher moments when studying stochastic networks and deepen our understanding of correlated neuronal activity., Comment: 33 pages, 9 figures

Published
2022

2. Counting Involutions on Multicomplex Numbers

Author

Doyon, Nicolas, Parisé, Pierre-Olivier, and Verreault, William

Subjects
Mathematics - Rings and Algebras, Mathematics - Combinatorics, Mathematics - Complex Variables, Primary: 05Axx, Secondary: 05A05, 15A66, 13J30
Abstract

We show that there is a bijection between real-linear automorphisms of the multicomplex numbers of order $n$ and signed permutations of length $2^{n-1}$. This allows us to deduce a number of results on the multicomplex numbers, including a formula for the number of involutions on multicomplex spaces which generalizes a recent result on the bicomplex numbers and contrasts drastically with the quaternion case. We also generalize this formula to $r$-involutions and obtain a formula for the number of involutions preserving elementary imaginary units. The proofs rely on new elementary results pertaining to multicomplex numbers that are surprisingly unknown in the literature, including a count and a representation theorem for numbers squaring to $\pm 1$.

Published
2022

3. Beyond Wilson-Cowan dynamics: oscillations and chaos without inhibition

Author

Painchaud, Vincent, Doyon, Nicolas, and Desrosiers, Patrick

Subjects
Quantitative Biology - Neurons and Cognition, Physics - Biological Physics
Abstract

Fifty years ago, Wilson and Cowan developed a mathematical model to describe the activity of neural populations. In this seminal work, they divided the cells in three groups: active, sensitive and refractory, and obtained a dynamical system to describe the evolution of the average firing rates of the populations. In the present work, we investigate the impact of the often neglected refractory state and show that taking it into account can introduce new dynamics. Starting from a continuous-time Markov chain, we perform a rigorous derivation of a mean-field model that includes the refractory fractions of populations as dynamical variables. Then, we perform bifurcation analysis to explain the occurance of periodic solutions in cases where the classical Wilson-Cowan does not predict oscillations. We also show that our mean-field model is able to predict chaotic behavior in the dynamics of networks with as little as two populations., Comment: 21 pages, 15 figures

Published
2022
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6. Repetitions of multinomial coefficients and a generalization of Singmaster's conjecture

Author

de Koninck, Jean-Marie, Doyon, Nicolas, and Verreault, William

Subjects
Mathematics - Number Theory, 11B65 (Primary) 05A10 (Secondary)
Abstract

Given two integers $k\geq 2$ and $a>1$, let $N_k(a)$ stand for the number of multinomial coefficients, with $k$ terms, equal to $a$. We study the behavior of $N_k(a)$ and show that its average and normal orders are equal to $k(k-1)$. We also prove that $N_k(a)=O\left((\log a/\log\log a)^{k-1}\right)$ and make several propositions about extreme results regarding large values of $N_k(a)$., Comment: 11 pages

Published
2021

7. Bounds for the counting function of the Jordan-P\'olya numbers

Author

De Koninck, Jean-Marie, Doyon, Nicolas, Razafindrasoanaivolala, A. Arthur Bonkli, and Verreault, William

Subjects
Mathematics - Number Theory, 11B65 (Primary) 11A41, 11A51, 11N05 (Secondary)
Abstract

A positive integer $n$ is said to be a Jordan-P\'olya number if it can be written as a product of factorials. We obtain non-trivial lower and upper bounds for the number of Jordan-P\'olya numbers not exceeding a given number $x$., Comment: 12 pages

Published
2021

9. Spectral dimension reduction of complex dynamical networks

Author

Laurence, Edward, Doyon, Nicolas, Dubé, Louis J, and Desrosiers, Patrick

Subjects
Physics - Physics and Society
Abstract

Dynamical networks are powerful tools for modeling a broad range of complex systems, including financial markets, brains, and ecosystems. They encode how the basic elements (nodes) of these systems interact altogether (via links) and evolve (nodes' dynamics). Despite substantial progress, little is known about why some subtle changes in the network structure, at the so-called critical points, can provoke drastic shifts in its dynamics. We tackle this challenging problem by introducing a method that reduces any network to a simplified low-dimensional version. It can then be used to describe the collective dynamics of the original system. This dimension reduction method relies on spectral graph theory and, more specifically, on the dominant eigenvalues and eigenvectors of the network adjacency matrix. Contrary to previous approaches, our method is able to predict the multiple activation of modular networks as well as the critical points of random networks with arbitrary degree distributions. Our results are of both fundamental and practical interest, as they offer a novel framework to relate the structure of networks to their dynamics and to study the resilience of complex systems., Comment: 16 pages, 8 figures

Published
2018
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12. TE-TM Electromagnetic modes and states in quantum physics

Author

Tremblay, Réal, Doyon, Nicolas, and Beaudoin-Bertrand, Julien

Subjects
Quantum Physics
Abstract

We propose, as another pedagogical approach, a quantification of the e.m. field better adapted in isolated systems, a quantification of e.m. fields in finite-spacetime which does not rely explicitly on the notion of photon, nor on the general application of gauge. Being based on the development of e.m. field in TE-TM modes and states, it obeys the limit conditions of a finite-spacetime which follows from the solution of an eigenvalue equation and allows to interpret more profoundly some phenomenons, notably: the equivalence of a Pauli principle in stationary TE-TM states, the notion of non-locality in a radiation field, a modified form of the De Broglie analysis and the notion of wave-paquets in finite-spacetime., Comment: 1 figure

Published
2016

13. $\hbar$ as a Physical Constant of Classical Optics and Electrodynamics

Author

Tremblay, Real, Doyon, Nicolas, and Allen, Claudine Ni

Subjects
Physics - Optics
Abstract

The Planck constant ($\hbar$) plays a pivotal role in quantum physics. Historically, it has been proposed as postulate, part of a genius empirical relationship $E=\hbar \omega$ in order to explain the intensity spectrum of the blackbody radiation for which classical electrodynamic theory led to an unacceptable prediction: The ultraviolet catastrophe. While the usefulness of the Planck constant in various fields of physics is undisputed, its derivation (or lack of) remains unsatisfactory from a fundamental point of view. In this paper, the analysis of the blackbody problem is performed with a series expansion of the electromagnetic field in terms of TE, TM modes in a metallic cavity with small losses, that leads to developing the electromagnetic fields in a \textit{complete set of orthonormal functions}. This expansion, based on coupled power theory, maintains both space and time together enabling modeling of the blackbody's evolution toward equilibrium. Reaching equilibrium with a multimodal waveguide analysis brings into consideration the coupling between modes in addition to absorption and emission of radiation. The properties of the modes, such as spectral broadening, losses and lifetime, then progressively become independent of frequency and explains how equilibrium is allowed in good conductor metallic cavities. Based on the free electron relaxation time in gold, a value of $\hbar = 1.02 \times 10^{-34}$ J$\cdot$s for the reduced Planck constant is found and the uncertainty principle is also emerging from this \textit{a priori} classical study. The Planck constant is then obtained no longer as an ad hoc addition but as a natural consequence of the analysis taking boundary conditions into account as into optical resonators. That analysis based on finite-spacetime paradigm, also shine new light on the notion of decoherence in classical optics and electrodynamics., Comment: 26 pages, 4 figures 1 table

Published
2015

14. The Determining Role of Covariances in Large Networks of Stochastic Neurons.

Author

Painchaud, Vincent, Desrosiers, Patrick, and Doyon, Nicolas

Subjects
BIOLOGICAL neural networks, NEURAL circuitry, LIMIT cycles, NEURONS, DYNAMICAL systems, MARKOV processes, FUZZY neural networks
Abstract

Biological neural networks are notoriously hard to model due to their stochastic behavior and high dimensionality. We tackle this problem by constructing a dynamical model of both the expectations and covariances of the fractions of active and refractory neurons in the network's populations. We do so by describing the evolution of the states of individual neurons with a continuous-time Markov chain, from which we formally derive a low-dimensional dynamical system. This is done by solving a moment closure problem in a way that is compatible with the nonlinearity and boundedness of the activation function. Our dynamical system captures the behavior of the high-dimensional stochastic model even in cases where the mean-field approximation fails to do so. Taking into account the second-order moments modifies the solutions that would be obtained with the mean-field approximation and can lead to the appearance or disappearance of fixed points and limit cycles. We moreover perform numerical experiments where the mean-field approximation leads to periodically oscillating solutions, while the solutions of the second-order model can be interpreted as an average taken over many realizations of the stochastic model. Altogether, our results highlight the importance of including higher moments when studying stochastic networks and deepen our understanding of correlated neuronal activity. [ABSTRACT FROM AUTHOR]

Published
2024
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17. A computational model of Alzheimer's disease at the nano, micro, and macroscales.

Author

Chamberland, Éléonore, Moravveji, Seyedadel, Doyon, Nicolas, and Duchesne, Simon

Subjects
ALZHEIMER'S disease, ORDINARY differential equations, MULTISCALE modeling, EXPERIMENTAL literature, EVOLUTION equations
Abstract

Introduction: Mathematical models play a crucial role in investigating complex biological systems, enabling a comprehensive understanding of interactions among various components and facilitating in silico testing of intervention strategies. Alzheimer's disease (AD) is characterized by multifactorial causes and intricate interactions among biological entities, necessitating a personalized approach due to the lack of effective treatments. Therefore, mathematical models offer promise as indispensable tools in combating AD. However, existing models in this emerging field often suffer from limitations such as inadequate validation or a narrow focus on single proteins or pathways. Methods: In this paper, we present a multiscale mathematical model that describes the progression of AD through a system of 19 ordinary differential equations. The equations describe the evolution of proteins (nanoscale), cell populations (microscale), and organ-level structures (macroscale) over a 50-year lifespan, as they relate to amyloid and tau accumulation, inflammation, and neuronal death. Results: Distinguishing our model is a robust foundation in biological principles, ensuring improved justification for the included equations, and rigorous parameter justification derived from published experimental literature. Conclusion: This model represents an essential initial step toward constructing a predictive framework, which holds significant potential for identifying effective therapeutic targets in the fight against AD. [ABSTRACT FROM AUTHOR]

Published
2024
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18. Morphine hyperalgesia gated through microglia-mediated disruption of neuronal Cl− homeostasis

Author

Ferrini, Francesco, Trang, Tuan, Mattioli, Theresa-Alexandra M, Laffray, Sophie, Del'Guidice, Thomas, Lorenzo, Louis-Etienne, Castonguay, Annie, Doyon, Nicolas, Zhang, Wenbo, Godin, Antoine G, Mohr, Daniela, Beggs, Simon, Vandal, Karen, Beaulieu, Jean-Martin, Cahill, Catherine M, Salter, Michael W, and De Koninck, Yves

Subjects
Chronic Pain, Neurosciences, Substance Misuse, Drug Abuse (NIDA only), Pain Research, Neurological, Animals, Biophysical Phenomena, Brain-Derived Neurotrophic Factor, CD11b Antigen, Chlorides, Down-Regulation, Gene Expression Regulation, Homeostasis, Hot Temperature, Hyperalgesia, Ion Channel Gating, Male, Membrane Potentials, Mice, Mice, Inbred C57BL, Mice, Transgenic, Microglia, Morphine, Motor Activity, Naloxone, Narcotic Antagonists, Narcotics, Neurons, Pain Threshold, Patch-Clamp Techniques, Protein Synthesis Inhibitors, Rats, Rats, Sprague-Dawley, Receptors, Purinergic P2X4, Ribosome Inactivating Proteins, Type 1, Rotarod Performance Test, Saporins, Signal Transduction, Spinal Cord, Symporters, Time Factors, Touch, Vocalization, Animal, Psychology, Cognitive Sciences, Neurology & Neurosurgery
Abstract

A major unresolved issue in treating pain is the paradoxical hyperalgesia produced by the gold-standard analgesic morphine and other opiates. We found that hyperalgesia-inducing treatment with morphine resulted in downregulation of the K(+)-Cl(-) co-transporter KCC2, impairing Cl(-) homeostasis in rat spinal lamina l neurons. Restoring the anion equilibrium potential reversed the morphine-induced hyperalgesia without affecting tolerance. The hyperalgesia was also reversed by ablating spinal microglia. Morphine hyperalgesia, but not tolerance, required μ opioid receptor-dependent expression of P2X4 receptors (P2X4Rs) in microglia and μ-independent gating of the release of brain-derived neurotrophic factor (BDNF) by P2X4Rs. Blocking BDNF-TrkB signaling preserved Cl(-) homeostasis and reversed the hyperalgesia. Gene-targeted mice in which Bdnf was deleted from microglia did not develop hyperalgesia to morphine. However, neither morphine antinociception nor tolerance was affected in these mice. Our findings dissociate morphine-induced hyperalgesia from tolerance and suggest the microglia-to-neuron P2X4-BDNF-KCC2 pathway as a therapeutic target for preventing hyperalgesia without affecting morphine analgesia.

Published
2013

29. The convergence of doubly stochastic Markov chains

Author

Bouthat, Ludovick, Doyon, Nicolas, Mashreghi, Javad, Morneau-Guérin, Frédéric, Bouthat, Ludovick, Doyon, Nicolas, Mashreghi, Javad, and Morneau-Guérin, Frédéric

Abstract

In recent years, some interest has been devoted to studying doubly stochastic Markov chains. These chains appears naturally in many real-life applications such as quantum measurements. In this note, we proceed to characterize the asymptotic behavior of an homogeneous doubly stochastic Markov chains. In particular, we characterize the doubly stochastic matrices whose associated Markov chain (1) describes a cycle; (2) converges to a given matrix; and (3) diverges. We also provide a new sufficient condition for the infinite product of doubly stochastic matrices

Published
2022

31. Computational modeling of trans-synaptic nanocolumns, a modulator of synaptic transmission.

Author

Xiaoting Li, Hémond, Gabriel, Godin, Antoine G., and Doyon, Nicolas

Subjects
NEURAL transmission, NEUROTRANSMITTER receptors, PRESYNAPTIC receptors, COMPUTER simulation
Abstract

Understanding synaptic transmission is of crucial importance in neuroscience. The spatial organization of receptors, vesicle release properties and neurotransmittermolecule diffusion can strongly influence features of synaptic currents. Newly discovered structures coined trans-synaptic nanocolumns were shown to align presynaptic vesicles release sites and postsynaptic receptors. However, how these structures, spanning a few tens of nanometers, shape synaptic signaling remains little understood. Given the difficulty to probe submicroscopic structures experimentally, computer modeling is a useful approach to investigate the possible functional impacts and role of nanocolumns. In our in silico model, as has been experimentally observed, a nanocolumn is characterized by a tight distribution of postsynaptic receptors aligned with the presynaptic vesicle release site and by the presence of trans-synaptic molecules which can modulate neurotransmitter molecule diffusion. In this work, we found that nanocolumns can play an important role in reinforcing synaptic current mostly when the presynaptic vesicle contains a small number of neurotransmitter molecules. Our work proposes a new methodology to investigate in silico how the existence of trans-synaptic nanocolumns, the nanometric organization of the synapse and the lateral diffusion of receptors shape the features of the synaptic current such as its amplitude and kinetics. [ABSTRACT FROM AUTHOR]

Published
2022
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34. Spectral dimension reduction of complex dynamical networks

Author

Laurence, Edward, Dubé, Louis J., Doyon, Nicolas, Desrosiers, Patrick, Laurence, Edward, Dubé, Louis J., Doyon, Nicolas, and Desrosiers, Patrick

Abstract

Dynamical networks are powerful tools for modeling a broad range of complex systems, including financial markets, brains, and ecosystems. They encode how the basic elements (nodes) of these systems interact altogether (via links) and evolve (nodes’ dynamics). Despite substantial progress, little is known about why some subtle changes in the network structure, at the so-called critical points, can provoke drastic shifts in its dynamics. We tackle this challenging problem by introducing a method that reduces any network to a simplified low-dimensional version. It can then be used to describe the collective dynamics of the original system. This dimension reduction method relies on spectral graph theory and, more specifically, on the dominant eigenvalues and eigenvectors of the network adjacency matrix. Contrary to previous approaches, our method is able to predict the multiple activation of modular networks as well as the critical points of random networks with arbitrary degree distributions. Our results are of both fundamental and practical interest, as they offer a novel framework to relate the structure of networks to their dynamics and to study the resilience of complex systems.

Published
2020

35. Counting hidden neural networks

Author

Young, Richard A., Hardy, Simon, Doyon, Nicolas, Desrosiers, Patrick, Young, Richard A., Hardy, Simon, Doyon, Nicolas, and Desrosiers, Patrick

Abstract

We apply combinatorial tools, including P´olya’s theorem, to enumerate all possible networks for which (1) the network contains distinguishable input and output nodes as well as partially distinguishable intermediate nodes; (2) all connections are directed and for each pair of nodes, there are at most two connections, that is, at most one connection per direction; (3) input nodes send connections but don’t receive any, while output nodes receive connections but don’t send any; (4) every intermediate node receives a path from an input node and sends a path to at least one output node; and (5) input nodes don’t send direct connections to output nodes. We first obtain the generating function for the number of such networks, and then use it to obtain precise estimates for the number of networks. Finally, we develop a computer algorithm that allows us to generate these networks. This work could become useful in the field of neuroscience, in which the problem of deciphering the structure of hidden networks is of the utmost importance, since there are several instances in which the activity of input and output neurons can be directly measured, while no direct access to the intermediate network is possible. Our results can also be used to count the number of finite automata in which each cell plays a relevant role.

Published
2020

42. Spectral dimension reduction of complex dynamical networks

Author

Laurence, Edward, Doyon, Nicolas, Dubé, Louis J., Desrosiers, Patrick, Laurence, Edward, Doyon, Nicolas, Dubé, Louis J., and Desrosiers, Patrick

Abstract

Dynamical networks are powerful tools for modeling a broad range of complex systems, including financial markets, brains, and ecosystems. They encode how the basic elements (nodes) of these systems interact altogether (via links) and evolve (nodes’ dynamics). Despite substantial progress, little is known about why some subtle changes in the network structure, at the so-called critical points, can provoke drastic shifts in its dynamics. We tackle this challenging problem by introducing a method that reduces any network to a simplified low-dimensional version. It can then be used to describe the collective dynamics of the original system. This dimension reduction method relies on spectral graph theory and, more specifically, on the dominant eigenvalues and eigenvectors of the network adjacency matrix. Contrary to previous approaches, our method is able to predict the multiple activation of modular networks as well as the critical points of random networks with arbitrary degree distributions. Our results are of both fundamental and practical interest, as they offer a novel framework to relate the structure of networks to their dynamics and to study the resilience of complex systems.

Published
2019

46. TE-TM Electromagnetic modes and states in quantum physics

Author

Tremblay, R��al, Doyon, Nicolas, and Beaudoin-Bertrand, Julien

Subjects
Quantum Physics, FOS: Physical sciences, Quantum Physics (quant-ph)
Abstract

We propose, as another pedagogical approach, a quantification of the e.m. field better adapted in isolated systems, a quantification of e.m. fields in finite-spacetime which does not rely explicitly on the notion of photon, nor on the general application of gauge. Being based on the development of e.m. field in TE-TM modes and states, it obeys the limit conditions of a finite-spacetime which follows from the solution of an eigenvalue equation and allows to interpret more profoundly some phenomenons, notably: the equivalence of a Pauli principle in stationary TE-TM states, the notion of non-locality in a radiation field, a modified form of the De Broglie analysis and the notion of wave-paquets in finite-spacetime., 1 figure

Published
2016

47. 26th Annual Computational Neuroscience Meeting (CNS*2017): Part 2

Author

Rubchinsky, Leonid L., primary, Ahn, Sungwoo, additional, Klijn, Wouter, additional, Cumming, Ben, additional, Yates, Stuart, additional, Karakasis, Vasileios, additional, Peyser, Alexander, additional, Woodman, Marmaduke, additional, Diaz-Pier, Sandra, additional, Deraeve, James, additional, Vassena, Eliana, additional, Alexander, William, additional, Beeman, David, additional, Kudela, Pawel, additional, Boatman-Reich, Dana, additional, Anderson, William S., additional, Luque, Niceto R., additional, Naveros, Francisco, additional, Carrillo, Richard R., additional, Ros, Eduardo, additional, Arleo, Angelo, additional, Huth, Jacob, additional, Ichinose, Koki, additional, Park, Jihoon, additional, Kawai, Yuji, additional, Suzuki, Junichi, additional, Mori, Hiroki, additional, Asada, Minoru, additional, Oprisan, Sorinel A., additional, Dave, Austin I., additional, Babaie, Tahereh, additional, Robinson, Peter, additional, Tabas, Alejandro, additional, Andermann, Martin, additional, Rupp, André, additional, Balaguer-Ballester, Emili, additional, Lindén, Henrik, additional, Christensen, Rasmus K., additional, Nakamura, Mari, additional, Barkat, Tania R., additional, Tosi, Zach, additional, Beggs, John, additional, Lonardoni, Davide, additional, Boi, Fabio, additional, Di Marco, Stefano, additional, Maccione, Alessandro, additional, Berdondini, Luca, additional, Jędrzejewska-Szmek, Joanna, additional, Dorman, Daniel B., additional, Blackwell, Kim T., additional, Bauermeister, Christoph, additional, Keren, Hanna, additional, Braun, Jochen, additional, Dornas, João V., additional, Mavritsaki, Eirini, additional, Aldrovandi, Silvio, additional, Bridger, Emma, additional, Lim, Sukbin, additional, Brunel, Nicolas, additional, Buchin, Anatoly, additional, Kerr, Clifford Charles, additional, Chizhov, Anton, additional, Huberfeld, Gilles, additional, Miles, Richard, additional, Gutkin, Boris, additional, Spencer, Martin J., additional, Meffin, Hamish, additional, Grayden, David B., additional, Burkitt, Anthony N., additional, Davey, Catherine E., additional, Tao, Liangyu, additional, Tiruvadi, Vineet, additional, Ali, Rehman, additional, Mayberg, Helen, additional, Butera, Robert, additional, Gunay, Cengiz, additional, Lamb, Damon, additional, Calabrese, Ronald L., additional, Doloc-Mihu, Anca, additional, López-Madrona, Víctor J., additional, Matias, Fernanda S., additional, Pereda, Ernesto, additional, Mirasso, Claudio R., additional, Canals, Santiago, additional, Geminiani, Alice, additional, Pedrocchi, Alessandra, additional, D’Angelo, Egidio, additional, Casellato, Claudia, additional, Chauhan, Ankur, additional, Soman, Karthik, additional, Srinivasa Chakravarthy, V., additional, Muddapu, Vignayanandam R., additional, Chuang, Chao-Chun, additional, Chen, Nan-yow, additional, Bayati, Mehdi, additional, Melchior, Jan, additional, Wiskott, Laurenz, additional, Azizi, Amir Hossein, additional, Diba, Kamran, additional, Cheng, Sen, additional, Smirnova, Elena Y., additional, Yakimova, Elena G., additional, Chizhov, Anton V., additional, Chen, Nan-Yow, additional, Shih, Chi-Tin, additional, Florescu, Dorian, additional, Coca, Daniel, additional, Courtiol, Julie, additional, Jirsa, Viktor K., additional, Covolan, Roberto J. M., additional, Teleńczuk, Bartosz, additional, Kempter, Richard, additional, Curio, Gabriel, additional, Destexhe, Alain, additional, Parker, Jessica, additional, Klishko, Alexander N., additional, Prilutsky, Boris I., additional, Cymbalyuk, Gennady, additional, Franke, Felix, additional, Hierlemann, Andreas, additional, da Silveira, Rava Azeredo, additional, Casali, Stefano, additional, Masoli, Stefano, additional, Rizza, Martina, additional, Rizza, Martina Francesca, additional, Sun, Yinming, additional, Wong, Willy, additional, Farzan, Faranak, additional, Blumberger, Daniel M., additional, Daskalakis, Zafiris J., additional, Popovych, Svitlana, additional, Viswanathan, Shivakumar, additional, Rosjat, Nils, additional, Grefkes, Christian, additional, Daun, Silvia, additional, Gentiletti, Damiano, additional, Suffczynski, Piotr, additional, Gnatkovski, Vadym, additional, De Curtis, Marco, additional, Lee, Hyeonsu, additional, Paik, Se-Bum, additional, Choi, Woochul, additional, Jang, Jaeson, additional, Park, Youngjin, additional, Song, Jun Ho, additional, Song, Min, additional, Pallarés, Vicente, additional, Gilson, Matthieu, additional, Kühn, Simone, additional, Insabato, Andrea, additional, Deco, Gustavo, additional, Glomb, Katharina, additional, Ponce-Alvarez, Adrián, additional, Ritter, Petra, additional, Campo, Adria Tauste, additional, Thiele, Alexander, additional, Deeba, Farah, additional, Robinson, P. A., additional, van Albada, Sacha J., additional, Rowley, Andrew, additional, Hopkins, Michael, additional, Schmidt, Maximilian, additional, Stokes, Alan B., additional, Lester, David R., additional, Furber, Steve, additional, Diesmann, Markus, additional, Barri, Alessandro, additional, Wiechert, Martin T., additional, DiGregorio, David A., additional, Dimitrov, Alexander G., additional, Vich, Catalina, additional, Berg, Rune W., additional, Guillamon, Antoni, additional, Ditlevsen, Susanne, additional, Cazé, Romain D., additional, Girard, Benoît, additional, Doncieux, Stéphane, additional, Doyon, Nicolas, additional, Boahen, Frank, additional, Desrosiers, Patrick, additional, Laurence, Edward, additional, Dubé, Louis J., additional, Eleonora, Russo, additional, Durstewitz, Daniel, additional, Schmidt, Dominik, additional, Mäki-Marttunen, Tuomo, additional, Krull, Florian, additional, Bettella, Francesco, additional, Metzner, Christoph, additional, Devor, Anna, additional, Djurovic, Srdjan, additional, Dale, Anders M., additional, Andreassen, Ole A., additional, Einevoll, Gaute T., additional, Næss, Solveig, additional, Ness, Torbjørn V., additional, Halnes, Geir, additional, Halgren, Eric, additional, Pettersen, Klas H., additional, Sætra, Marte J., additional, Hagen, Espen, additional, Schiffer, Alina, additional, Grzymisch, Axel, additional, Persike, Malte, additional, Ernst, Udo, additional, Harnack, Daniel, additional, Ernst, Udo A., additional, Tomen, Nergis, additional, Zucca, Stefano, additional, Pasquale, Valentina, additional, Pica, Giuseppe, additional, Molano-Mazón, Manuel, additional, Chiappalone, Michela, additional, Panzeri, Stefano, additional, Fellin, Tommaso, additional, Oie, Kelvin S., additional, Boothe, David L., additional, Crone, Joshua C., additional, Yu, Alfred B., additional, Felton, Melvin A., additional, Zulfiqar, Isma, additional, Moerel, Michelle, additional, De Weerd, Peter, additional, Formisano, Elia, additional, Oie, Kelvin, additional, Franaszczuk, Piotr, additional, Diggelmann, Roland, additional, Fiscella, Michele, additional, Guarino, Domenico, additional, Antolík, Jan, additional, Davison, Andrew P., additional, Frègnac, Yves, additional, Etienne, Benjamin Xavier, additional, Frohlich, Flavio, additional, Lefebvre, Jérémie, additional, Marcos, Encarni, additional, Mattia, Maurizio, additional, Genovesio, Aldo, additional, Fedorov, Leonid A., additional, Dijkstra, Tjeerd M.H., additional, Sting, Louisa, additional, Hock, Howard, additional, Giese, Martin A., additional, Buhry, Laure, additional, Langlet, Clément, additional, Giovannini, Francesco, additional, Verbist, Christophe, additional, Salvadé, Stefano, additional, Giugliano, Michele, additional, Henderson, James A., additional, Wernecke, Hendrik, additional, Sándor, Bulcsú, additional, Gros, Claudius, additional, Voges, Nicole, additional, Dabrovska, Paulina, additional, Riehle, Alexa, additional, Brochier, Thomas, additional, Grün, Sonja, additional, Gu, Yifan, additional, Gong, Pulin, additional, Dumont, Grégory, additional, Novikov, Nikita A., additional, Gutkin, Boris S., additional, Tewatia, Parul, additional, Eriksson, Olivia, additional, Kramer, Andrei, additional, Santos, Joao, additional, Jauhiainen, Alexandra, additional, Kotaleski, Jeanette H., additional, Belić, Jovana J., additional, Kumar, Arvind, additional, Kotaleski, Jeanette Hellgren, additional, Shimono, Masanori, additional, Hatano, Naomichi, additional, Ahmad, Subutai, additional, Cui, Yuwei, additional, Hawkins, Jeff, additional, Senk, Johanna, additional, Korvasová, Karolína, additional, Tetzlaff, Tom, additional, Helias, Moritz, additional, Kühn, Tobias, additional, Denker, Michael, additional, Mana, PierGianLuca, additional, Dahmen, David, additional, Schuecker, Jannis, additional, Goedeke, Sven, additional, Keup, Christian, additional, Heuer, Katja, additional, Bakker, Rembrandt, additional, Tiesinga, Paul, additional, Toro, Roberto, additional, Qin, Wei, additional, Hadjinicolaou, Alex, additional, Ibbotson, Michael R., additional, Kameneva, Tatiana, additional, Lytton, William W., additional, Mulugeta, Lealem, additional, Drach, Andrew, additional, Myers, Jerry G., additional, Horner, Marc, additional, Vadigepalli, Rajanikanth, additional, Morrison, Tina, additional, Walton, Marlei, additional, Steele, Martin, additional, Anthony Hunt, C., additional, Tam, Nicoladie, additional, Amaducci, Rodrigo, additional, Muñiz, Carlos, additional, Reyes-Sánchez, Manuel, additional, Rodríguez, Francisco B., additional, Varona, Pablo, additional, Cronin, Joseph T., additional, Hennig, Matthias H., additional, Iavarone, Elisabetta, additional, Yi, Jane, additional, Shi, Ying, additional, Zandt, Bas-Jan, additional, Van Geit, Werner, additional, Rössert, Christian, additional, Markram, Henry, additional, Hill, Sean, additional, O’Reilly, Christian, additional, Perin, Rodrigo, additional, Lu, Huanxiang, additional, Bryson, Alexander, 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Published
2017
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48. Counting hidden neural networks

Author

Richard, Anthony, Desrosiers, Patrick, Hardy, Simon, Doyon, Nicolas, Richard, Anthony, Desrosiers, Patrick, Hardy, Simon, and Doyon, Nicolas

Abstract

We apply combinatorial tools, including P´olya’s theorem, to enumerate all possible networks for which (1) the network contains distinguishable input and output nodes as well as partially distinguishable intermediate nodes; (2) all connections are directed and for each pair of nodes, there are at most two connections, that is, at most one connection per direction; (3) input nodes send connections but don’t receive any, while output nodes receive connections but don’t send any; (4) every intermediate node receives a path from an input node and sends a path to at least one output node; and (5) input nodes don’t send direct connections to output nodes. We first obtain the generating function for the number of such networks, and then use it to obtain precise estimates for the number of networks. Finally, we develop a computer algorithm that allows us to generate these networks. This work could become useful in the field of neuroscience, in which the problem of deciphering the structure of hidden networks is of the utmost importance, since there are several instances in which the activity of input and output neurons can be directly measured, while no direct access to the intermediate network is possible. Our results can also be used to count the number of finite automata in which each cell plays a relevant role.

Published
2016

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