Stimulus-Response Reliability of Biological Networks

Lin, Kevin K.

doi:10.1007/978-3-319-03080-7_4

Cited by 6 publications

(10 citation statements)

References 41 publications

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“…To see that this should be the case, imagine a cloud of initial conditions evolving according to the same stimulus. The state-space expansion associated with positive exponents tends to “stretch” this cloud, leading to the formation of smooth Λ + -dimensional surfaces, where Λ + is the number of positive exponents (see, e.g., [44] for a general, non-technical introduction and [56, 57] for more details). If all exponents are negative, for example, then the attractor is just a (time-dependent) point, whereas the presence of a single positive exponent suggests that the attractor is curve-like, etc.…”

Section: Resultsmentioning

confidence: 99%

“…As such, those ensembles cannot be used to model the type of discrimination task we are interested in here. In more probabilistic language, equating “ensembles” with stochastic processes, our response ensembles are precisely the conditional probability distributions obtained by conditioning a MF-type statistical ensemble by a particular stimulus history I ( t ); see, e.g., [44] for a more detailed discussion of response ensembles.…”

Section: Methodsmentioning

confidence: 99%

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Encoding in Balanced Networks: Revisiting Spike Patterns and Chaos in Stimulus-Driven Systems

et al. 2016

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Highly connected recurrent neural networks often produce chaotic dynamics, meaning their precise activity is sensitive to small perturbations. What are the consequences of chaos for how such networks encode streams of temporal stimuli? On the one hand, chaos is a strong source of randomness, suggesting that small changes in stimuli will be obscured by intrinsically generated variability. On the other hand, recent work shows that the type of chaos that occurs in spiking networks can have a surprisingly low-dimensional structure, suggesting that there may be room for fine stimulus features to be precisely resolved. Here we show that strongly chaotic networks produce patterned spikes that reliably encode time-dependent stimuli: using a decoder sensitive to spike times on timescales of 10’s of ms, one can easily distinguish responses to very similar inputs. Moreover, recurrence serves to distribute signals throughout chaotic networks so that small groups of cells can encode substantial information about signals arriving elsewhere. A conclusion is that the presence of strong chaos in recurrent networks need not exclude precise encoding of temporal stimuli via spike patterns.

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Section: Resultsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Encoding in Balanced Networks: Revisiting Spike Patterns and Chaos in Stimulus-Driven Systems

et al. 2016

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“…It has a mathematical setup that is rather different from the theory of Markov processes, and the literature is somewhat inaccessible to a nonspecialist. RDS approach has found interesting applications in studies of synchronization, a concept inherited from the theory of non-autonomous ODEs, of neural firing in recent years [26]; it will have wide applications in studying cellular automata [51] within a fluctuating environment as well as many other complex dynamics, such as in finance [46]. With a fixed environment, a cellular automaton is a discrete-state discrete-time deterministic dynamical system which has an unambiguously defined response follows an unambiguous stimulus [49].…”

Section: Felix X-f Ye Yue Wang and Hong Qianmentioning

confidence: 99%

“…Furthermore, the most probable deterministic transition matrix corresponds to the deterministic transformation that maps to the state with the largest probability given the current state, i.e, its deterministic matrix has entry one in the position that is maximum in each row of the transition matrix M. It is a very insightful result since this is the most reasonable "deterministic counterpart" for a given MC with transition probability matrix M. [2]. Synchronization is a well-developed concept in the theory of nonautonomous ODEs [26]. Through studying synchronization in an RDS, one appreciates the fact that RDS formulation is a more refined model of stochastic dynamics than an MC.…”

Section: 3mentioning

confidence: 99%

Stochastic dynamics: Markov chains and random transformations

Ye¹,

Wang²,

Qian³

2016

DCDS-B

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This article outlines an attempt to lay the groundwork for understanding stochastic dynamical descriptions of biological processes in terms of a discrete-state space, discrete-time random dynamical system (RDS), or random transformation approach. Such mathematics is not new for continuous systems, but the discrete state space formulation significantly reduces the technical requirements for its introduction to a much broader audiences. In particular, we establish some elementary contradistinctions between Markov chain (MC) and RDS descriptions of a stochastic dynamics. It is shown that a given MC is compatible with many possible RDS, and we study in particular the corresponding RDS with maximum metric entropy. Specifically, we show an emergent behavior of an MC with a unique absorbing and aperiodic communicating class, after all the trajectories of the RDS synchronizes. In biological modeling, it is now widely acknowledged that stochastic dynamics is a more complete description of biological reality than deterministic equations; here we further suggest that the RDS description could be a more refined description of stochastic dynamics than a Markov process. Possible applications of discretestate RDS are systems with fluctuating law of motion, or environment, rather than inherent stochastic movements of individuals.

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“…However, not every finite RDS have such properties and the sufficient condition is the RDS is monotone and ergodic [33]. Except for sampling, synchronization in RDS has also been widely discovered in applied science [23,40].…”

mentioning

confidence: 99%

Stochastic dynamics Ⅱ: Finite random dynamical systems, linear representation, and entropy production

Ye¹,

Qian²

2019

Discrete &Amp; Continuous Dynamical Systems - B

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We study finite state random dynamical systems (RDS) and their induced Markov chains (MC) as stochastic models for complex dynamics. The linear representation of deterministic maps in RDS is a matrix-valued random variable whose expectation corresponds to the transition matrix of the MC. The instantaneous Gibbs entropy, Shannon-Khinchin entropy of a step, and the entropy production rate of the MC are discussed. These three concepts, as key anchoring points in applications of stochastic dynamics, characterize respectively the uncertainties of a system at instant time t, the randomness generated in a step in the dynamics, and the dynamical asymmetry with respect to time reversal. The stationary entropy production rate, expressed in terms of the cycle distributions, has found an expression in terms of the probability of the deterministic maps with single attractor in the maximum entropy RDS. For finite RDS with invertible transformations, the non-negative entropy production rate of its MC is bounded above by the Kullback-Leibler divergence of the probability of the deterministic maps with respect to its time-reversal dual probability.

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Stimulus-Response Reliability of Biological Networks

Cited by 6 publications

References 41 publications

Encoding in Balanced Networks: Revisiting Spike Patterns and Chaos in Stimulus-Driven Systems

Encoding in Balanced Networks: Revisiting Spike Patterns and Chaos in Stimulus-Driven Systems

Stochastic dynamics: Markov chains and random transformations

Stochastic dynamics Ⅱ: Finite random dynamical systems, linear representation, and entropy production

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