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An essay is presented which explores theoretical and experimental advancements in evolutionary and developmental biology, as well as micro-physics of brain dynamics. Overview of the features of the dissipative quantum model of the brain, which describes the collective neuronal activity and brain behavior in terms of microscopic dynamics, is provided. Discussion on the meaning of aesthetic experience and its relationship with the dissipative character of brain dynamics is offered.

A stochastic Gompertz diffusion model for tumor growth is a topic of active interest as cancer is a leading cause of death in Korea. The direct maximum likelihood estimation of stochastic differential equations would be possible based on the continuous path likelihood on condition that a continuous sample path of the process is recorded over the interval. This likelihood is useful in providing a basis for the so-called continuous record or infill likelihood function and infill asymptotic. In practice, we do not have fully continuous data except a few special cases. As a result, the exact ML method is not applicable. In this paper we proposed a method of parameter estimation of stochastic Gompertz differential equation via Markov chain Monte Carlo methods that is applicable for several data structures. We compared a Markov transition data structure with a data structure that have an initial point. [ABSTRACT FROM AUTHOR]

This paper presents the effects of spontaneous random activity on information transmission in an auditory brain stem neuron model. In computer simulations, the supra-threshold synaptic current stimuli ascending from auditory nerve fibers (ANFs) were modeled by a filtered inhomogeneous Poisson process modulated by sinusoidal functions at a frequency of 220-3520 Hz with regard to the human speech spectrum. The stochastic sodium and stochastic high- and low-threshold potassium channels were incorporated into a single compartment model of the soma in spherical bushy neurons, so as to realize threshold fluctuations or a variation of spike firing times. The results show that the information rates estimated from the entropy of inter-spike intervals of spike trains tend toward a convex function of the spontaneous rates when the intensity of sinusoidal functions decreases. Furthermore, the results show that a convex function of the spontaneous rates tends to disappear as the frequency of the sinusoidal function increases, such that the phase-locked response can be unobserved. It is concluded that this sort of stochastic resonance (SR) phenomenon, which depends on the spontaneous rates with supra-threshold stimuli, can better enhance information transmission in a smaller intensity of sinusoidal functions within the human speech spectrum, like the situation in which the regular SR can enhance weak signals. [ABSTRACT FROM AUTHOR]

We study an inverse first-hitting problem for a one-dimensional, time-homogeneous diffusion X(t) reflected between two boundaries a and b, which starts from a random position η. Let a ≤ S ≤ b be a given threshold, such that P(η ε [a, S]) = 1, and F an assigned distribution function. The problem consists of finding the distribution of η such that the first-hitting time of X to S has distribution F. This is a generalization of the analogous problem for ordinary diffusions, that is, without reflecting, previously considered by the author. [ABSTRACT FROM PUBLISHER]

When the boundary-the total number of servers- in an Erlang loss system is a function of time, customers may also be lost due to boundary variations. On condition that these customers are selected independently of their history, we solve for the hitting-time distribution and transient distribution of busy servers. We derive concise asymptotic expressions in the time domain for normal loads in the heavy-traffic limit, i.e., when the offered load $$\rho $$ is high, and the number of servers scales as $$\rho +O\left( \sqrt{\rho }\right) $$ . The solutions are computationally efficient, and simulations confirm the theoretical results. [ABSTRACT FROM AUTHOR]

Computational models offer a unique tool for understanding the network-dynamical mechanisms which mediate between physiological and biophysical properties, and behavioral function. A traditional challenge in computational neuroscience is, however, that simple neuronal models which can be studied analytically fail to reproduce the diversity of electrophysiological behaviors seen in real neurons, while detailed neuronal models which do reproduce such diversity are intractable analytically and computationally expensive. A number of intermediate models have been proposed whose aim is to capture the diversity of firing behaviors and spike times of real neurons while entailing the simplest possible mathematical description. One such model is the exponential integrate-and-fire neuron with spike rate adaptation (aEIF) which consists of two differential equations for the membrane potential (V) and an adaptation current (w). Despite its simplicity, it can reproduce a wide variety of physiologically observed spiking patterns, can be fit to physiological recordings quantitatively, and, once done so, is able to predict spike times on traces not used for model fitting. Here we compute the steady-state firing rate of aEIF in the presence of Gaussian synaptic noise, using two approaches. The first approach is based on the 2-dimensional Fokker-Planck equation that describes the (V,w)-probability distribution, which is solved using an expansion in the ratio between the time constants of the two variables. The second is based on the firing rate of the EIF model, which is averaged over the distribution of the w variable. These analytically derived closed-form expressions were tested on simulations from a large variety of model cells quantitatively fitted to in vitro electrophysiological recordings from pyramidal cells and interneurons. Theoretical predictions closely agreed with the firing rate of the simulated cells fed with in-vivo-like synaptic noise. [ABSTRACT FROM AUTHOR]

Objective: The aim of this study was to determine the diagnostic accuracy of the CC-SF, which was developed to use calf circumference (CC) instead of BMI in the MNA-SF, for elderly people living in the community and in nursing homes. It also aimed separately to determine the correlation of CC-SF and BMI-SF with the full MNA. Study Design and Methods: The study included 640 elderly people living in their community and 243 elderly people living in nursing homes. Accuracy was assessed by determining the sensitivity and selectivity of the nutritional assessments. The correlations between the MNA-SFs and the full MNA were analyzed. Results: The correlation between MNA-SFs and full MNAs was strong, significant and almost identical both in the community and in nursing homes (r=0.86-0.88; p<0.001). The observed agreement between the BMI-SF and the full MNA was 82.2% in the community and 77.8% in the nursing homes. There was a substantial agreement by kappa values in the comparison of community and nursing homes (the Kappa value of the BMI-SF was 0.63 in the community and 0.62 in the nursing homes, and the kappa value of the CC-SF was 0.62 in the community and 0.63 in the nursing homes). When compared to the full MNA the MNA-SFs tended to underestimate nutritional status. Both MNA-SFs had similarly high sensitivity and selectivity, both in the community and nursing homes. (when dichotomized as 'malnourished-at risk of malnutrition' versus 'well nourished' and 'malnourished' versus 'at risk of malnutrition-well nourished') (over 80%). Conclusion: In cases where BMI cannot be determined, the CC-SF is a good substitute for the BMI-SF. [ABSTRACT FROM AUTHOR]

An application of stochastic modeling by means of diffusion processes to the forecasting of fruit size and caliber is presented in the present paper. In a first phase, a diffusion process that adequately fits the available data on the time of fruit growth is constructed and estimated. Then, a proposal is made for a procedure employing the probability transition distributions of the fitted process for the allocation of caliber to each fruit. Tables are constructed with the values that discriminate between calibers at the time of harvest, which allow us to make a prediction from each previous time instant. Finally, the mean conditional functions to predict the percentages of each size (fruit size distribution) at the time of harvest are considered. A practical application is presented to Valencia late oranges through a modified version of the Bertalanffy process. Such a process is modified by including in its trend a time-dependent function used to model the observed deviations in the data about the evolution of the diameter of oranges with respect to the trajectories of the original process. [ABSTRACT FROM AUTHOR]

This paper presents a historical perspective on the development and application of quantum physics methodology beyond physics, especially in biology and in the area of consciousness studies. Quantum physics provides a conceptual framework for the structural aspects of biological systems and processes via quantum chemistry. In recent years individual biological phenomena such as photosynthesis and bird navigation have been experimentally and theoretically analyzed using quantum methods building conceptual foundations for quantum biology. Since consciousness is attributed to human (and possibly animal) mind, quantum underpinnings of cognitive processes are a logical extension. Several proposals, especially the Orch OR hypothesis, have been put forth in an effort to introduce a scientific basis to the theory of consciousness. At the center of these approaches are microtubules as the substrate on which conscious processes in terms of quantum coherence and entanglement can be built. Additionally, Quantum Metabolism, quantum processes in ion channels and quantum effects in sensory stimulation are discussed in this connection. We discuss the challenges and merits related to quantum consciousness approaches as well as their potential extensions. [ABSTRACT FROM AUTHOR]

A theoretical framework is developed based on the premise that brains evolved into sufficiently complex adaptive systems capable of instantiating genomic consciousness through self-awareness and complex interactions that recognize qualitatively the controlling factors of biological processes. Furthermore, our hypothesis assumes that the collective interactions in neurons yield macroergic effects, which can produce sufficiently strong electric energy fields for electronic excitations to take place on the surface of endogenous structures via alpha-helical integral proteins as electro-solitons. Specifically the process of radiative relaxation of the electro-solitons allows for the transfer of energy via interactions with deoxyribonucleic acid (DNA) molecules to induce conformational changes in DNA molecules producing an ultra weak non-thermal spontaneous emission of coherent biophotons through a quantum effect. The instantiation of coherent biophotons confined in spaces of DNA molecules guides the biophoton field to be instantaneously conducted along the axonal and neuronal arbors and in-between neurons and throughout the cerebral cortex (cortico-thalamic system) and subcortical areas (e.g., midbrain and hindbrain). Thus providing an informational character of the electric coherence of the brain - referred to as quantum coherence. The biophoton field is realized as a conscious field upon the re-absorption of biophotons by exciplex states of DNA molecules. Such quantum phenomenon brings about self-awareness and enables objectivity to have access to subjectivity in the unconscious. As such, subjective experiences can be recalled to consciousness as subjective conscious experiences or qualia through co-operative interactions between exciplex states of DNA molecules and biophotons leading to metabolic activity and energy transfer across proteins as a result of protein-ligand binding during protein-protein communication. The biophoton field as a conscious field is attributable to the resultant effect of specifying qualia from the metabolic energy field that is transported in macromolecular proteins throughout specific networks of neurons that are constantly transforming into more stable associable representations as molecular solitons. The metastability of subjective experiences based on resonant dynamics occurs when bottom-up patterns of neocortical excitatory activity are matched with top-down expectations as adaptive dynamic pressures. These dynamics of on-going activity patterns influenced by the environment and selected as the preferred subjective experience in terms of a functional field through functional interactions and biological laws are realized as subjectivity and actualized through functional integration as qualia. It is concluded that interactionism and not information processing is the key in understanding how consciousness bridges the explanatory gap between subjective experiences and their neural correlates in the transcendental brain. [ABSTRACT FROM AUTHOR]

The firing activity of intracellularly stimulated neurons in cortical slices has been demonstrated to be profoundly affected by the temporal structure of the injected current (Mainen & Sejnowski, 1995). This suggests that the timing features of the neural responsemay be controlled asmuch by its own biophysical characteristics as by how a neuron iswired within a circuit. Modeling studies have shown that the interplay between internal noise and the fluctuations of the driving input controls the reliability and the precision of neuronal spiking (Cecchi et al., 2000; Tiesinga, 2002; Fellous, Rudolph, Destexhe, & Sejnowski, 2003). In order to investigate this interplay, we focus on the stochastic leaky integrate-and-fire neuron and identify the Holder exponent H of the integrated input as the key mathematical property dictating the regime of firing of a single-unit neuron. We have recently provided numerical evidence (Taillefumier & Magnasco, 2013) for the existence of a phase transition when H becomes less than the statisticalHolder exponent associated with internal gaussian white noise (H = 1/2). Here we describe the theoretical and numerical framework devised for the study of a neuron that is periodically driven by frozen noisy inputs with exponent H > 0. In doing so, we account for the existence of a transition between two regimes of firingwhenH = 1/2, and we show that spiking times have a continuous density when the Holder exponent satisfies H > 1/2. The transition at H = 1/2 formally separates rate codes, for which the neural firing probability varies smoothly, from temporal codes, for which the neuron fires at sharply defined times regardless of the intensity of internal noise. [ABSTRACT FROM AUTHOR]

We derive conditions for continuous differentiability of inter-spike intervals (ISIs) of spiking neurons with respect to parameters (decision variables) of an external stimulating input current that drives a recurrent network of synaptically connected neurons. The dynamical behavior of individual neurons is represented by a class of discontinuous singleneuron models. We report here that ISIs of neurons in the network are continuously differentiable with respect to decision variables if (1) a continuously differentiable trajectory of the membrane potential exists between consecutive action potentials with respect to time and decision variables and (2) the partial derivative of the membrane potential of spiking neurons with respect to time is not equal to the partial derivative of their firing threshold with respect to time at the time of action potentials. Our theoretical results are supported by showing fulfillment of these conditions for a class of known bidimensional spiking neuron models. [ABSTRACT FROM AUTHOR]

We give an explicit representation for the time-dependent moments of a Markovian queueing system with reneging. Our expressions are comparable in form to the moment expressions for the M/ M/1 queue found in Abate and Whitt (Queueing Syst. 2:41-65, ; Adv. Appl. Probab. 20:145-178, ). We also illustrate how to use these expressions to derive analogous moment expressions for a reflected Ornstein-Uhlenbeck process, with reflection at zero. [ABSTRACT FROM AUTHOR]

We study an inverse first-passage-time problem for Wiener processX(t) subject to random jumps from a boundaryc. Let be given a thresholdS > X(0); and a distribution functionFon [0, + ∞). The problem consists of finding the distribution of the jumps which occur whenX(t) hitsc, so that the first-passage time ofX(t) throughShas distributionF. [ABSTRACT FROM AUTHOR]

The attempt to employ quantum principles for modeling cognition has enabled the introduction of several new concepts in psychology, such as the uncertainty principle, incompatibility, entanglement, and superposition. For many commentators, this is an exciting opportunity to question existing formal frameworks (notably classical probability theory) and explore what is to be gained by employing these novel conceptual tools. This is not to say that major empirical challenges are not there. For example, can we definitely prove the necessity for quantum, as opposed to classical, models? Can the distinction between compatibility and incompatibility inform our understanding of differences between human and nonhuman cognition? Are quantum models less constrained than classical ones? Does incompatibility arise as a limitation, to avoid the requirements from the principle of unicity, or is it an inherent (or essential?) characteristic of intelligent thought? For everyday judgments, do quantum principles allow more accurate prediction than classical ones? Some questions can be confidently addressed within existing quantum models. A definitive resolution of others will have to anticipate further work. What is clear is that the consideration of quantum cognitive models has enabled a new focus on a range of debates about fundamental aspects of cognition. [ABSTRACT FROM PUBLISHER]

The “Orch OR” theory suggests that quantum computations in brain neuronal dendritic-somatic microtubules regulate axonal firings to control conscious behavior. Within microtubule subunit proteins, collective dipoles in arrays of contiguous amino acid electron clouds enable “quantum channels” suitable for topological dipole “qubits” able to physically represent cognitive values, for example, those portrayed by Pothos & Busemeyer (P&B) as projections in abstract Hilbert space. [ABSTRACT FROM AUTHOR]

Classical (Bayesian) probability (CP) theory has led to an influential research tradition for modeling cognitive processes. Cognitive scientists have been trained to work with CP principles for so long that it is hard even to imagine alternative ways to formalize probabilities. However, in physics, quantum probability (QP) theory has been the dominant probabilistic approach for nearly 100 years. Could QP theory provide us with any advantages in cognitive modeling as well? Note first that both CP and QP theory share the fundamental assumption that it is possible to model cognition on the basis of formal, probabilistic principles. But why consider a QP approach? The answers are that (1) there are many well-established empirical findings (e.g., from the influential Tversky, Kahneman research tradition) that are hard to reconcile with CP principles; and (2) these same findings have natural and straightforward explanations with quantum principles. In QP theory, probabilistic assessment is often strongly context- and order-dependent, individual states can be superposition states (that are impossible to associate with specific values), and composite systems can be entangled (they cannot be decomposed into their subsystems). All these characteristics appear perplexing from a classical perspective. However, our thesis is that they provide a more accurate and powerful account of certain cognitive processes. We first introduce QP theory and illustrate its application with psychological examples. We then review empirical findings that motivate the use of quantum theory in cognitive theory, but also discuss ways in which QP and CP theories converge. Finally, we consider the implications of a QP theory approach to cognition for human rationality. [ABSTRACT FROM AUTHOR]

. Parameter estimation in diffusion processes from discrete observations up to a first-passage time is clearly of practical relevance, but does not seem to have been studied so far. In neuroscience, many models for the membrane potential evolution involve the presence of an upper threshold. Data are modelled as discretely observed diffusions which are killed when the threshold is reached. Statistical inference is often based on a misspecified likelihood ignoring the presence of the threshold causing severe bias, e.g. the bias incurred in the drift parameters of the Ornstein-Uhlenbeck model for biological relevant parameters can be up to 25-100 per cent. We compute or approximate the likelihood function of the killed process. When estimating from a single trajectory, considerable bias may still be present, and the distribution of the estimates can be heavily skewed and with a huge variance. Parametric bootstrap is effective in correcting the bias. Standard asymptotic results do not apply, but consistency and asymptotic normality may be recovered when multiple trajectories are observed, if the mean first-passage time through the threshold is finite. Numerical examples illustrate the results and an experimental data set of intracellular recordings of the membrane potential of a motoneuron is analysed. [ABSTRACT FROM AUTHOR]

A technology that simultaneously records membrane potential from multiple neurons in behaving animals will have a transformative effect on neuroscience research 1,2 . Genetically encoded voltage indicators are a promising tool for these purposes; however, these have so far been limited to single-cell recordings with a marginal signal-to-noise ratio in vivo 3-5 . Here we developed improved near-infrared voltage indicators, high-speed microscopes and targeted gene expression schemes that enabled simultaneous in vivo recordings of supra- and subthreshold voltage dynamics in multiple neurons in the hippocampus of behaving mice. The reporters revealed subcellular details of back-propagating action potentials and correlations in subthreshold voltage between multiple cells. In combination with stimulation using optogenetics, the reporters revealed changes in neuronal excitability that were dependent on the behavioural state, reflecting the interplay of excitatory and inhibitory synaptic inputs. These tools open the possibility for detailed explorations of network dynamics in the context of behaviour. Fig. 1 PHOTOACTIVATED QUASAR3 (PAQUASAR3) REPORTS NEURONAL ACTIVITY IN VIVO.: a, Schematic of the paQuasAr3 construct. b, Photoactivation by blue light enhanced voltage signals excited by red light in cultured neurons that expressed paQuasAr3 (representative example of n = 4 cells). c, Model of the photocycle of paQuasAr3. d, Confocal images of sparsely expressed paQuasAr3 in brain slices. Scale bars, 50 μm. Representative images, experiments were repeated in n = 3 mice. e, Simultaneous fluorescence and patch-clamp recordings from a neuron expressing paQuasAr3 in acute brain slice. Top, magnification of boxed regions. Schematic shows brain slice, patch pipette and microscope objective. f, Simultaneous fluorescence and patch-clamp recordings of inhibitory post synaptic potentials in an L2-3 neuron induced by electrical stimulation of L5-6 in acute slice. g, Normalized change in fluorescence (ΔF/F) and SNR of optically recorded post-synaptic potentials (PSPs) as a function of the amplitude of the post-synaptic potentials. The voltage sensitivity was ΔF/F = 40 ± 1.7% per 100 mV. The SNR was 0.93 ± 0.07 per 1 mV in a 1-kHz bandwidth (n = 42 post-synaptic potentials from 5 cells, data are mean ± s.d.). Schematic shows brain slice, patch pipette, field stimulation electrodes and microscope objective. h, Optical measurements of paQuasAr3 fluorescence in the CA1 region of the hippocampus (top) and glomerular layer of the olfactory bulb (bottom) of anaesthetized mice (representative traces from n = 7 CA1 cells and n = 13 olfactory bulb cells, n = 3 mice). Schematics show microscope objective and the imaged brain region. i, STA fluorescence from 88 spikes in a CA1 oriens neuron. j, Frames from the STA video showing the delay in the back-propagating action potential in the dendrites relative to the soma. k, Sub-Nyquist fitting of the action potential delay and width shows electrical compartmentalization in the dendrites. Experiments in k-m were repeated in n = 2 cells from n = 2 mice.

In this paper we study the distribution of the location, at time t, of a particle moving U time units upwards, V time units downwards, and W time units of no movement (idle). These are repeated cyclically, according to independent alternating renewals. The distributions of U, V, and W are absolutely continuous. The velocities are v = +1 upwards, v = - 1 downwards, and v = 0 during idle periods. Let Y+(t), Y-(t), and Y0(t) denote the total time in (0, t) of movements upwards, downwards, and no movements, respectively. The exact distribution of Y+(t) is derived. We also obtain the probability law of X(t) = Y+(t) - Y-(t), which describes the particle's location at time t. Explicit formulae are derived for the cases of exponential distributions with equal rates, with different rates, and with linear rates (leading to damped processes). [ABSTRACT FROM AUTHOR]

We study the stochastic FitzHugh-Nagumo equations, modelling the dynamics of neuronal action potentials in parameter regimes characterized by mixedmode oscillations. The interspike time interval is related to the random number of small-amplitude oscillations separating consecutive spikes. We prove that this number has an asymptotically geometric distribution, whose parameter is related to the principal eigenvalue of a substochastic Markov chain. We provide rigorous bounds on this eigenvalue in the small-noise regime and derive an approximation of its dependence on the system's parameters for a large range of noise intensities. This yields a precise description of the probability distribution of observed mixed-mode patterns and interspike intervals. [ABSTRACT FROM AUTHOR]

In a previous paper (Rudolph & Destexhe, 2006), we proposed various models, the gIF neuron models, of analytical integrate-and-fire (IF) neurons with conductance-based (COBA) dynamics for use in event-driven simulations. These models are based on an analytical approximation of the differential equation describing the IF neuron with exponential synaptic conductance's and were successfully tested with respect to their response to random and oscillating inputs. Because they are analytical and mathematically simple, the gIF models are best suited for fast event-driven simulation strategies. However, the drawback of such models is they rely on a nonrealistic postsynaptic potential (PSP) time course, consisting of a discontinuous jump followed by a decay governed by the membrane time constant. Here, we address this limitation by conceiving an analytical approximation of the COBA IF neuron model with the full PSP time course. The subthreshold and suprathreshold response of this gIF4 model reproduces remarkably well the postsynaptic responses of the numerically solved passive membrane equation subject to conductance noise, while gaining at least two orders of magnitude in computational performance. Although the analytical structure of the gIF4 model is more complex than that of its predecessors due to the necessity of calculating future spike times, a simple and fast algorithmic implementation for use in large-scale neural network simulations is proposed. [ABSTRACT FROM AUTHOR]

We derive the first-passage-time statistics of a Brownian motion driven by an exponential time-dependent drift up to a threshold. This process corresponds to the signal integration in a simple neuronal model supplemented with an adaptation-like current and reaching the threshold for the first time represents the condition for declaring a spike. Based on the backward Fokker-Planck formulation, we consider the survival probability of this process in a domain restricted by an absorbent boundary. The solution is given as an expansion in terms of the intensity of the time-dependent drift, which results in an infinite set of recurrence equations. We explicitly obtain the complete solution by solving each term in the expansion in a recursive scheme. From the survival probability, we evaluate the first-passage-time statistics, which itself preserves the series structure. We then compare theoretical results with data extracted from numerical simulations of the associated dynamical system, and show that the analytical description is appropriate whenever the series is truncated in an adequate order. [ABSTRACT FROM AUTHOR]

Every computational unit in the brain monitors incoming signals, instant by instant, for meaningful changes in the face of stochastic fluctuation. Recent studies have suggested that even a single neuron can detect changes in noisy signals. In this paper, we demonstrate that a single leaky integrate-and-fire neuron can achieve change-point detection close to that of theoretical optimal, for uniform-rate process, functions even better than a Bayes-optimal algorithm when the underlying rate deviates from a presumed uniform rate process. Given a reasonable number of synaptic connections (order 10) and the rate of the input spike train, the values of the membrane time constant and the threshold found for optimizing change-point detection are close to those seen in biological neurons. These findings imply that biological neurons could act as sophisticated change-point detectors. [ABSTRACT FROM AUTHOR]

In this paper, a stochastic queuing model for a catastrophic-cum-restorative queuing system with correlated batch arrivals and general service time distribution has been developed. The transient analysis of the queuing model has been performed. The Laplace Transform of the probability generating function of the system size has been obtained. Finally, some particular cases of the model have been derived and discussed. [ABSTRACT FROM AUTHOR]

The set of firing rates of the presynaptic excitatory and inhibitory neurons constitutes the input signal to the postsynaptic neuron. Estimation of the time-varying input rates from intracellularly recorded membrane potential is investigated here. For that purpose, the membrane potential dynamics must be specified. We consider the Ornstein-Uhlenbeck stochastic process, one of the most common single-neuron models, with time-dependent mean and variance. Assuming the slow variation of these two moments, it is possible to formulate the estimation problem by using a state-space model. We develop an algorithm that estimates the paths of the mean and variance of the input current by using the empirical Bayes approach. Then the input firing rates are directly available from the moments. The proposed method is applied to three simulated data examples: constant signal, sinusoidally modulated signal, and constant signal with a jump. For the constant signal, the estimation performance of the method is comparable to that of the traditionally applied maximum likelihood method. Further, the proposed method accurately estimates both continuous and discontinuous time-variable signals. In the case of the signal with a jump, which does not satisfy the assumption of slow variability, the robustness of the method is verified. It can be concluded that the method provides reliable estimates of the total input firing rates, which are not experimentally measurable. [ABSTRACT FROM AUTHOR]

Stochastic leaky integrate-and-fire models are popular due to their simplicity and statistical tractability. They have been widely applied to gain understanding of the underlying mechanisms for spike timing in neurons, and have served as building blocks for more elaborate models. Especially the Ornstein-Uhlenbeck process is popular to describe the stochastic fluctuations in the membrane potential of a neuron, but also other models like the square-root model or models with a non-linear drift are sometimes applied. Data that can be described by such models have to be stationary and thus, the simple models can only be applied over short time windows. However, experimental data show varying time constants, state dependent noise, a graded firing threshold and time-inhomogeneous input. In the present study we build a jump diffusion model that incorporates these features, and introduce a firing mechanism with a state dependent intensity. In addition, we suggest statistical methods to estimate all unknown quantities and apply these to analyze turtle motoneuron membrane potentials. Finally, simulated and real data are compared and discussed. We find that a square-root diffusion describes the data much better than an Ornstein-Uhlenbeck process with constant diffusion coefficient. Further, the membrane time constant decreases with increasing depolarization, as expected from the increase in synaptic conductance. The network activity, which the neuron is exposed to, can be reasonably estimated to be a threshold version of the nerve output from the network. Moreover, the spiking characteristics are well described by a Poisson spike train with an intensity depending exponentially on the membrane potential. [ABSTRACT FROM AUTHOR]

When a neuronal spike train is observed, what can we deduce from it about the properties of the neuron that generated it? A natural way to answer this question is to make an assumption about the type of neuron, select an appropriate model for this type, and then choose the model parameters as those that are most likely to generate the observed spike train. This is the maximum likelihood method. If the neuron obeys simple integrate-and-fire dynamics, Paninski, Pillow, and Simoncelli (2004) showed that its negative log-likelihood function is convex and that, at least in principle, its unique global minimum can thus be found by gradient descent techniques. Many biological neurons are, however, known to generate a richer repertoire of spiking behaviors than can be explained in a simple integrate-and-fire model. For instance, such a model retains only an implicit (through spike-induced currents), not an explicit, memory of its input; an example of a physiological situation that cannot be explained is the absence of firing if the input current is increased very slowly. Therefore, we use an expanded model (Mihalas & Niebur, 2009), which is capable of generating a large number of complex firing patterns while still being linear. Linearity is important because it maintains the distribution of the random variables and still allows maximum likelihood methods to be used. In this study, we show that although convexity of the negative log-likelihood function is not guaranteed for this model, the minimum of this function yields a good estimate for the model parameters, in particular if the noise level is treated as a free parameter. Furthermore, we show that a nonlinear function minimization method (r-algorithm with space dilation) usually reaches the global minimum. [ABSTRACT FROM AUTHOR]

Neural membrane potential data are necessarily conditional on observation being prior to a firing time. In a stochastic leaky integrate-and-fire model, this corresponds to conditioning the process on not crossing a boundary. In the literature, simulation and estimation have almost always been done using unconditioned processes. In this letter, we determine the stochastic differential equations of a diffusion process conditioned to stay below a level S up to a fixed time t1 and of a diffusion process conditioned to cross the boundary for the first time at t1.This allows simulation of sample paths and identification of the corresponding mean process. Differences between the mean of free and conditioned processes are illustrated, as well as the role of noise in increasing these differences. [ABSTRACT FROM AUTHOR]

We prove that the first passage time density ρ(t) for an Ornstein--Uhlenbeck process X(t) obeying dX = -β X dt + σ dW to reach a fixed threshold θ from a suprathreshold initial condition x0 > θ > 0 has a lower bound of the form ρ (t) > k exp[-pe6βt] for positive constants k and p for times t exceeding some positive value u. We obtain explicit expressions for k, p, and u in terms of β, σ, x0, and θ, and discuss the application of the results to the synchronization of periodically forced stochastic leaky integrate-and-fire model neurons. [ABSTRACT FROM AUTHOR]

We investigate the optimal control of neuronal spiking activity for classical Stein's model, Stein's model with reversal potentials with continuous random inputs, characterized by a positive parameter α and Stein's model with Poisson inputs. We solve the optimal control problems and obtain optimal rates λ(t) for different kinds of models. The numerical simulations on variable parameters show that it is possible to make the interval of spikes the same as our expected time in the range of the values of parameters. [ABSTRACT FROM AUTHOR]

The leaky integrate-and-fire neuronal model proposed in Stevens and Zador (1998), in which time constant and resting potential are postulated to be time dependent, is revisited within a stochastic framework in which the membrane potential is mathematically described as a gaussdiffusion process. The first-passage-time probability density, miming in such a context the firing probability density, is evaluated by either the Volterra integral equation of Buonocore, Nobile, and Ricciardi (1987) or, when possible, by the asymptotics of Giorno, Nobile, and Ricciardi (1990). The model examined here represents an extension of the classic leaky integrate-and-fire one based on the Ornstein-Uhlenbeck process in that it is in principle compatible with the inclusion of some other physiological characteristics such as relative refractoriness. It also allows finer tuning possibilities in view of its accounting for certain qualitative as well as quantitative features, such as the behavior of the time course of the membrane potential prior to firings and the computation of experimentally measurable statistical descriptors of the firing time: mean, median, coefficient of variation, and skewness. Finally, implementations of this model are provided in connection with certain experimental evidence discussed in the literature. [ABSTRACT FROM AUTHOR]

Delivery of neurotransmitter produces on a synapse a current that flows through the membrane and gets transmitted into the soma of the neuron, where it is integrated. The decay time of the current depends on the synaptic receptor's type and ranges from a few (e.g., AMPA receptors) to a few hundred milliseconds (e.g., NMDA receptors). The role of the variety of synaptic timescales, several of them coexisting in the same neuron, is at present not understood. A prime question to answer is which is the effect of temporal filtering at different timescales of the incoming spike trains on the neuron's response. Here, based on our previous work on linear synaptic filtering, we build a general theory for the stationary firing response of integrate-and-fire (IF) neurons receiving stochastic inputs filtered by one, two, or multiple synaptic channels, each characterized by an arbitrary timescale. The formalism applies to arbitrary IF model neurons and arbitrary forms of input noise (i.e., not required to be gaussian or to have small amplitude), as well as to any form of synaptic filtering (linear or nonlinear). The theory determines with exact analytical expressions the firing rate of an IF neuron for long synaptic time constants using the adiabatic approach. The correlated spiking (cross-correlations function) of two neurons receiving common as well as independent sources of noise is also described. The theory is illustrated using leaky, quadratic, and noise-thresholded IF neurons. Although the adiabatic approach is exact when at least one of the synaptic timescales is long, it provides a good prediction of the firing rate even when the timescales of the synapses are comparable to that of the leak of the neuron; it is not required that the synaptic time constants are longer than the mean interspike intervals or that the noise has small variance. The distribution of the potential for general IF neurons is also characterized. Our results provide powerful analytical tools that can allow a quantitative description of the dynamics of neuronal networks with realistic synaptic dynamics. [ABSTRACT FROM AUTHOR]

We study the subthreshold voltage fluctuations of a conductance-based passive point neuron stimulated by filtered Poissonian shot noise. We give exact analytical expressions in terms of quadratures for the first two time-dependent moments and the autocorrelation function of the membrane voltage. We also derive simplified expressions for the moments in terms of elementary functions that hold true in the limit case of short filter time, small spike amplitude, and a single synaptic reversal potential. By means of these expressions, we show that for an ensemble of equilibrated conductances but sharp initial voltage (corresponding to a short voltage clamp at the initial time), the mean and the standard deviation can display nonmonotonic time courses. In particular, transient changes in the standard deviation disagree strongly with the predictions of the commonly used effective time constant approximation over a large parameter range. We also study the dependence of the correlation time of the voltage on the synaptic spike amplitude and the synaptic input rate. All results are confirmed by extensive stochastic simulations. [ABSTRACT FROM AUTHOR]

Stochastic leaky integrate-and-fire (LIF) neuronal models are common theoretical tools for studying properties of real neuronal systems. Experimental data of frequently sampled membrane potential measurements between spikes show that the assumption of constant parameter values is not realistic and that some (random) fluctuations are occurring. In this letter, we extend the stochastic LIF model, allowing a noise source determining slow fluctuations in the signal. This is achieved by adding a random variable to one of the parameters characterizing the neuronal input, considering each interspike interval (ISI) as an independent experimental unit with a different realization of this random variable. In this way, the variation of the neuronal input is split into fast (within-interval) and slow (between-intervals) components. A parameter estimationmethod is proposed, allowing the parameters to be estimated simultaneously over the entire data set. This increases the statistical power, and the average estimate over all ISIs will be improved in the sense of decreased variance of the estimator compared to previous approaches,where the estimation has been conducted separately on each individual ISI. The results obtained on real data show good agreement with classical regression methods. [ABSTRACT FROM AUTHOR]

Abstract  Recent works on the response of barrel neurons to periodic deflections of the rat vibrissae have shown that the stimulus velocity is encoded in the corti cal spike rate (Pinto et al., Journal of Neurophysiology, 83(3), 1158–1166, 2000; Arabzadeh et al., Journal of Neuroscience, 23(27), 9146–9154, 2003). Other studies have reported that repetitive pulse stimulation produces band-pass filtering of the barrel response rate centered around 7–10 Hz (Garabedian et al., Journal of Neurophysiology, 90, 1379–1391, 2003) whereas sinusoidal stimulation gives an increasing rate up to 350 Hz (Arabzadeh et al., Journal of Neuroscience, 23(27), 9146–9154, 2003). To explore the mechanisms underlying these results we propose a simple computational model consisting in an ensemble of cells in the ventro-posterior medial thalamic nucleus (VPm) encoding the stimulus velocity in the temporal profile of their response, connected to a single barrel cell through synapses showing short-term depression. With sinusoidal stimulation, encoding the velocity in VPm facilitates the response as the stimulus frequency increases and it causes the velocity to be encoded in the cortical rate in the frequency range 20–100 Hz. Synaptic depression does not suppress the response with sinusoidal stimulation but it produces a band-pass behavior using repetitive pulses. We also found that the passive properties of the cell membrane eventually suppress the response to sinusoidal stimulation at high frequencies, something not observed experimentally. We argue that network effects not included here must be important in sustaining the response at those frequencies. [ABSTRACT FROM AUTHOR]

Spike correlations between neurons are ubiquitous in the cortex, but their role is not understood. Here we describe the firing response of a leaky integrate-and-fire neuron (LIF) when it receives a temporarily correlated input generated by presynaptic correlated neuronal populations. Input correlations are characterized in terms of the firing rates, Fano factors, correlation coefficients, and correlation timescale of the neurons driving the target neuron. We show that the sum of the presynaptic spike trains cannot be well described by a Poisson process. In fact, the total input current has a nontrivial two-point correlation function described by two main parameters: the correlation timescale (how precise the input correlations are in time) and the correlation magnitude (how strong they are). Therefore, the total current generated by the input spike trains is not well described by a white noise gaussian process. Instead, we model the total current as a colored gaussian process with the same mean and two-point correlation function, leading to the formulation of the problem in terms of a Fokker-Planck equation. Solutions of the output firing rate are found in the limit of short and long correlation timescales. The solutions described here expand and improve on our previous results (Moreno, de la Rocha, Renart, & Parga, 2002) by presenting new analytical expressions for the output firing rate for general IF neurons, extending the validity of the results for arbitrarily large correlation magnitude, and by describing the differential effect of correlations on the mean-driven or noise-dominated firing regimes. Also the details of this novel formalism are given here for the first time. We employ numerical simulations to confirm the analytical solutions and study the firing response to sudden changes in the input correlations. We expect this formalism to be useful for the study of correlations in neuronal networks and their role in neural processing and information transmission. [ABSTRACT FROM AUTHOR]

We study the discrimination capability of spike time sequences using the Chernoff distance as a metric. We assume that spike sequences are generated by renewal processes and study how the Chernoff distance depends on the shape of interspike interval (ISI) distribution. First, we consider a lower bound to the Chernoff distance because it has a simple closed form. Then we consider specific models of ISI distributions such as the gamma, inverse gaussian (IG), exponential with refractory period (ER), and that of the leaky integrate-and-fire (LIF) neuron. We found that the discrimination capability of spike times strongly depends on highorder moments of ISI and that it is higher when the spike time sequence has a larger skewness and a smaller kurtosis. High variability in terms of coefficient of variation (CV) does not necessarily mean that the spike times have less discrimination capability. Spike sequences generated by the gamma distribution have the minimum discrimination capability for a given mean and variance of ISI. We used series expansions to calculate the mean and variance of ISIs for LIF neurons as a function of the mean input level and the input noise variance. Spike sequences from an LIF neuron are more capable of discrimination than those of IG and gamma distributions when the stationary voltage level is close to the neuron's threshold value of the neuron. [ABSTRACT FROM AUTHOR]

Abstract  The Ornstein-Uhlenbeck process has been proposed as a model for the spontaneous activity of a neuron. In this model, the firing of the neuron corresponds to the first passage of the process to a constant boundary, or threshold. While the Laplace transform of the first-passage time distribution is available, the probability distribution function has not been obtained in any tractable form. We address the problem of estimating the parameters of the process when the only available data from a neuron are the interspike intervals, or the times between firings. In particular, we give an algorithm for computing maximum likelihood estimates and their corresponding confidence regions for the three identifiable (of the five model) parameters by numerically inverting the Laplace transform. A comparison of the two-parameter algorithm (where the time constant τ is known a priori) to the three-parameter algorithm shows that significantly more data is required in the latter case to achieve comparable parameter resolution as measured by 95% confidence intervals widths. The computational methods described here are a efficient alternative to other well known estimation techniques for leaky integrate-and-fire models. Moreover, it could serve as a template for performing parameter inference on more complex integrate-and-fire neuronal models. [ABSTRACT FROM AUTHOR]

Populations of neurons in the retina, olfactory system, visual and somatosensory thalamus, and several cortical regions show temporal correlation between the discharge times of their action potentials (spike trains). Correlated firing has been linked to stimulus encoding, attention, stimulus discrimination, and motor behaviour. Nevertheless, the mechanisms underlying correlated spiking are poorly understood, and its coding implications are still debated. It is not clear, for instance, whether correlations between the discharges of two neurons are determined solely by the correlation between their afferent currents, or whether they also depend on the mean and variance of the input. We addressed this question by computing the spike train correlation coefficient of unconnected pairs of in vitro cortical neurons receiving correlated inputs. Notably, even when the input correlation remained fixed, the spike train output correlation increased with the firing rate, but was largely independent of spike train variability. With a combination of analytical techniques and numerical simulations using ‘integrate-and-fire’ neuron models we show that this relationship between output correlation and firing rate is robust to input heterogeneities. Finally, this overlooked relationship is replicated by a standard threshold-linear model, demonstrating the universality of the result. This connection between the rate and correlation of spiking activity links two fundamental features of the neural code. [ABSTRACT FROM AUTHOR]

Spike trains from cortical neurons show a high degree of irregularity, with coefficients of variation (CV) of their interspike interval (ISI) distribution close to or higher than one. It has been suggested that this irregularity might be a reflection of a particular dynamical state of the local cortical circuit in which excitation and inhibition balance each other. In this "balanced" state, themean current to the neurons is below threshold, and firing is driven by current fluctuations, resulting in irregular Poisson-like spike trains. Recent data show that the degree of irregularity in neuronal spike trains recorded during the delay period of working memory experiments is the same for both low-activity states of a few Hz and for elevated, persistent activity states of a few tens of Hz. Since the difference between these persistent activity states cannot be due to external factors coming from sensory inputs, this suggests that the underlying network dynamics might support coexisting balanced states at different firing rates.We use mean field techniques to study the possible existence of multiple balanced steady states in recurrent networks of current-based leaky integrate-and-fire (LIF) neurons. To assess the degree of balance of a steady state, we extend existing mean-field theories so that not only the firing rate, but also the coefficient of variation of the interspike interval distribution of the neurons, are determined self-consistently. Depending on the connectivity parameters of the network,we find bistable solutions of different types. If the local recurrent connectivity is mainly excitatory, the two stable steady states differ mainly in the mean current to the neurons. In this case, the mean drive in the elevated persistent activity state is suprathreshold and typically characterized by low spiking irregularity. If the local recurrent excitatory and inhibitory drives are both large and nearly balanced, or even dominated by inhibition, two stable states coexist, both with subthreshold current drive. In this case, the spiking variability in both the resting state and the mnemonic persistent state is large, but the balance condition implies parameter fine-tuning. Since the degree of required fine-tuning increases with network size and, on the other hand, the size of the fluctuations in the afferent current to the cells increases for small networks, overall we find that fluctuation-driven persistent activity in the very simplified type of models we analyze is not a robust phenomenon. Possible implications of considering more realistic models are discussed. [ABSTRACT FROM AUTHOR]

Event-driven simulation strategies were proposed recently to simulate integrate-and-fire (IF) type neuronal models. These strategies can lead to computationally efficient algorithms for simulating large-scale networks of neurons; most important, such approaches are more precise than traditional clock-driven numerical integration approaches because the timing of spikes is treated exactly. The drawback of such event-driven methods is that in order to be efficient, the membrane equations must be solvable analytically, or at least provide simple analytic approximations for the state variables describing the system. This requirement prevents, in general, the use of conductance-based synaptic interactions within the framework of event-driven simulations and, thus, the investigation of network paradigms where synaptic conductances are important. We propose here a number of extensions of the classical leaky IF neuron model involving approximations of the membrane equation with conductance-based synaptic current, which lead to simple analytic expressions for the membrane state, and therefore can be used in the event-driven framework. These conductance-based IF (gIF) models are compared to commonly used models, such as the leaky IF model or biophysical models in which conductances are explicitly integrated. All models are compared with respect to various spiking response properties in the presence of synaptic activity, such as the spontaneous discharge statistics, the temporal precision in resolving synaptic inputs, and gain modulation under in vivo-like synaptic bombardment. Being based on the passive membrane equation with fixed-threshold spike generation, the proposed gIF models are situated in between leaky IF and biophysical models but are much closer to the latter with respect to their dynamic behavior and response characteristics, while still being nearly as computationally efficient as simple IF neuron models. gIF models should therefore provide a useful tool for efficient and precise simulation of large-scale neuronal networks with realistic, conductance-based synaptic interactions. [ABSTRACT FROM AUTHOR]

We prove the existence of C0 semigroups related to some birth-and-death type infinite systems of ODEs with possibly unbounded coefficients, in the scale of spaces lp, $1\leq p<\infty.$ For some particular cases we also provide a characterization of the spectra of their generators. For the proof of the generation theorem in the case p > 1 we extend the Chernoff perturbation result ([9]) on relatively bounded perturbations of generators. The results presented here have been used in [5] and they play important role for analysing chaoticity of dynamical systems considered there. As a by-product of our approach we obtain a result related to the classical Shubin theorem [20]. We show that this theorem, saying that for a class of bounded infinite matrices the spectrum of the corresponding maximal operator in lp is independent on $p\in [1,\infty),$ cannot be extended to unbounded matrices. [ABSTRACT FROM AUTHOR]

In this article we propose a methodology for building a lognormal diffusion process with polynomial exogenous factors in order to fit data that present an exponential trend and show deviations with respect to an exponential curve in the observed time interval. We show that such a process approaches a nonhomogeneous lognormal diffusion and proves that it is specially useful in the case when external information (exogenous factors) about the process is not available even though the existence of these influences is clear. An application to the global man-made emissions of methane is provided. [ABSTRACT FROM AUTHOR]