2013
DOI: 10.1088/1751-8113/46/41/415003
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Immune networks: multitasking capabilities near saturation

Abstract: Abstract. Pattern-diluted associative networks were introduced recently as models for the immune system, with nodes representing T-lymphocytes and stored patterns representing signalling protocols between T-and B-lymphocytes. It was shown earlier that in the regime of extreme pattern dilution, a system with N T Tlymphocytes can manage a number N B = O(N δ T ) of B-lymphocytes simultaneously, with δ < 1. Here we study this model in the extensive load regime N B = αN T , with also a high degree of pattern diluti… Show more

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Cited by 64 publications
(125 citation statements)
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“…2) provided that nonlinear Φ (ReLU) and appropriate threshold values θ are considered. The presence of the fields g i acting on the visible units (absent in the v i = ±1 model of [17][18][19]), is also crucial for the existence of our compositional phase as explained above.It would be interesting to extend our work to more than one layers of hidden units, or to other types of nonlinear Φ. While numerical studies of RBMs with Bernoulli hidden units show no qualitative change compared to ReLU, choosing Φ(h) growing asymptotically faster than h could affect the nature of the extracted features [23].…”
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confidence: 94%
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“…2) provided that nonlinear Φ (ReLU) and appropriate threshold values θ are considered. The presence of the fields g i acting on the visible units (absent in the v i = ±1 model of [17][18][19]), is also crucial for the existence of our compositional phase as explained above.It would be interesting to extend our work to more than one layers of hidden units, or to other types of nonlinear Φ. While numerical studies of RBMs with Bernoulli hidden units show no qualitative change compared to ReLU, choosing Φ(h) growing asymptotically faster than h could affect the nature of the extracted features [23].…”
mentioning
confidence: 94%
“…In this framework magnetized hidden units identify retrieved patterns, and α corresponds to the capacity of the autoassociative memory. Tsodyks and Feigel'man showed how the critical capacity (for single pattern retrieval) could be dramatically increased with sparse weights (p 1) and appropriate tuning of the fields g i [21]; however this effect could be achieved only with vanishingly low activities q. Agliari and collaborators showed in a series of papers [17,18] that multiple sparse patterns could be simultaneously retrieved in the case of linear Φ and vanishing capacity α = 0 (finite M ). Finite capacity α ∼ c −2 could be achieved at zero 5 temperature in the limit of extreme sparsity, p = c/N , only [19]; for MNIST p 0.1 and N = 784 would give α ∼ 2.10 −4 .…”
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confidence: 99%
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“…From the theoretical counterpart, models coming from mathematics or theoretical physics, such as maximum entropy principle4, disordered statistical mechanics56, complex optimization7, graph theory8, stochastic processes9 and dynamical systems10 are being adapted to biological systems, allowing a more complete picture of cellular behavior from advanced imaging studies. In parallel, the development of methods aimed at considering the system as a whole, hence with all its constituents mutually interacting, have become a major topic, involved as a necessary step beyond reductionism limitations6111213.…”
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confidence: 99%
“…In parallel, the development of methods aimed at considering the system as a whole, hence with all its constituents mutually interacting, have become a major topic, involved as a necessary step beyond reductionism limitations6111213. For example, cancer progression involves multiple events and is the result of the interactions with cells of the immune system within the tumor micro-environment1415161718192021.…”
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confidence: 99%