Universality in Systems with Power-Law Memory and Fractional Dynamics

There are a few different ways to extend regular nonlinear dynamical systems by introducing power-law memory or considering fractional differential/difference equations instead of integer ones. This extension allows the introduction of families of nonlinear dynamical systems converging to regular systems in the case of an integer power-law memory or an integer order of derivatives/differences. The examples considered in this review include the logistic family of maps (converging in the case of the first order difference to the regular logistic map), the universal family of maps, and the standard family of maps (the latter two converging, in the case of the second difference, to the regular universal and standard maps). Correspondingly, the phenomenon of transition to chaos through a period doubling cascade of bifurcations in regular nonlinear systems, known as "universality", can be extended to fractional maps, which are maps with power-/asymptotically power-law memory. The new features of universality, including cascades of bifurcations on single trajectories, which appear in fractional (with memory) nonlinear dynamical systems are the main subject of this review.Comment: 23 pages 7 Figures, to appear Oct 28 201

Intrinsic gain modulation and adaptive neural coding

In many cases, the computation of a neural system can be reduced to a receptive field, or a set of linear filters, and a thresholding function, or gain curve, which determines the firing probability; this is known as a linear/nonlinear model. In some forms of sensory adaptation, these linear filters and gain curve adjust very rapidly to changes in the variance of a randomly varying driving input. An apparently similar but previously unrelated issue is the observation of gain control by background noise in cortical neurons: the slope of the firing rate vs current (f-I) curve changes with the variance of background random input. Here, we show a direct correspondence between these two observations by relating variance-dependent changes in the gain of f-I curves to characteristics of the changing empirical linear/nonlinear model obtained by sampling. In the case that the underlying system is fixed, we derive relationships relating the change of the gain with respect to both mean and variance with the receptive fields derived from reverse correlation on a white noise stimulus. Using two conductance-based model neurons that display distinct gain modulation properties through a simple change in parameters, we show that coding properties of both these models quantitatively satisfy the predicted relationships. Our results describe how both variance-dependent gain modulation and adaptive neural computation result from intrinsic nonlinearity.Comment: 24 pages, 4 figures, 1 supporting informatio

Distributed brain co-processor for tracking spikes, seizures and behaviour during electrical brain stimulation

Early implantable epilepsy therapy devices provided open-loop electrical stimulation without brain sensing, computing, or an interface for synchronized behavioural inputs from patients. Recent epilepsy stimulation devices provide brain sensing but have not yet developed analytics for accurately tracking and quantifying behaviour and seizures. Here we describe a distributed brain co-processor providing an intuitive bi-directional interface between patient, implanted neural stimulation and sensing device, and local and distributed computing resources. Automated analysis of continuous streaming electrophysiology is synchronized with patient reports using a handheld device and integrated with distributed cloud computing resources for quantifying seizures, interictal epileptiform spikes and patient symptoms during therapeutic electrical brain stimulation. The classification algorithms for interictal epileptiform spikes and seizures were developed and parameterized using long-term ambulatory data from nine humans and eight canines with epilepsy, and then implemented prospectively in out-of-sample testing in two pet canines and four humans with drug-resistant epilepsy living in their natural environments. Accurate seizure diaries are needed as the primary clinical outcome measure of epilepsy therapy and to guide brain-stimulation optimization. The brain co-processor system described here enables tracking interictal epileptiform spikes, seizures and correlation with patient behavioural reports. In the future, correlation of spikes and seizures with behaviour will allow more detailed investigation of the clinical impact of spikes and seizures on patients

Effective connectivity reveals strategy differences in an expert calculator

Mathematical reasoning is a core component of cognition and the study of experts defines the upper limits of human cognitive abilities, which is why we are fascinated by peak performers, such as chess masters and mental calculators. Here, we investigated the neural bases of calendrical skills, i.e. the ability to rapidly identify the weekday of a particular date, in a gifted mental calculator who does not fall in the autistic spectrum, using functional MRI. Graph-based mapping of effective connectivity, but not univariate analysis, revealed distinct anatomical location of “cortical hubs” supporting the processing of well-practiced close dates and less-practiced remote dates: the former engaged predominantly occipital and medial temporal areas, whereas the latter were associated mainly with prefrontal, orbitofrontal and anterior cingulate connectivity. These results point to the effect of extensive practice on the development of expertise and long term working memory, and demonstrate the role of frontal networks in supporting performance on less practiced calculations, which incur additional processing demands. Through the example of calendrical skills, our results demonstrate that the ability to perform complex calculations is initially supported by extensive attentional and strategic resources, which, as expertise develops, are gradually replaced by access to long term working memory for familiar material

Decreased cerebral blood flow in the limbic and prefrontal cortex using SPECT imaging in a cohort of completed suicides

Suicide has a high comorbidity with impulsivity and depression, and finding imaging biomarkers indicative of patients at high risk for suicidal behavior is invaluable to the clinician. Using single-photon emission computed tomography (SPECT) imaging, we have previously reported regional cerebral blood flow (rCBF) decreases in the medial prefrontal cortex, ventral tegmental area and subgenual cingulate cortex (Brodmann area 25 (BA 25)), a region found to be hypoperfused with treatment-resistant depression. From 2007 to 2010, we have extended our analysis to include nine additional completed suicides. In all, 27 healthy, age- and gender-matched subjects from a previously acquired healthy brain study served as controls to our 21 completed suicides. All 21 suicides had been previously diagnosed with depression according to Diagnostic and Statistical Manual of Mental Disorder-IV criterion. Voxel-by-voxel analyses were performed using statistical parametric mapping to compare the differences in technetium-99m hexamethylpropylene amine oxime brain uptake between the groups. Factor analysis of the data identified the top 10 regions of hypoperfusion in the suicidal group, including the bilateral superior frontal lobes, the right precuneus, the rolandic operculum, postcentral gyrus, left caudate and insular cortex. We also demonstrate more focal decreases in rCBF in the subgenual cingulate cortex (BA 25) in 18 subjects, supporting our previous hypothesis that hypoperfusion of BA 25 may be a risk factor for suicide in depressed patients. This work suggests that SPECT might be useful in predicting risk for suicide completion in subjects with depression or treatment-resistant depression. Further investigation of this work is necessary to better understand the predictive value of this finding

Network adaptation improves temporal representation of naturalistic stimuli in drosophila eye: II Mechanisms

Retinal networks must adapt constantly to best present the ever changing visual world to the brain. Here we test the hypothesis that adaptation is a result of different mechanisms at several synaptic connections within the network. In a companion paper (Part I), we showed that adaptation in the photoreceptors (R1-R6) and large monopolar cells (LMC) of the Drosophila eye improves sensitivity to under-represented signals in seconds by enhancing both the amplitude and frequency distribution of LMCs' voltage responses to repeated naturalistic contrast series. In this paper, we show that such adaptation needs both the light-mediated conductance and feedback-mediated synaptic conductance. A faulty feedforward pathway in histamine receptor mutant flies speeds up the LMC output, mimicking extreme light adaptation. A faulty feedback pathway from L2 LMCs to photoreceptors slows down the LMC output, mimicking dark adaptation. These results underline the importance of network adaptation for efficient coding, and as a mechanism for selectively regulating the size and speed of signals in neurons. We suggest that concert action of many different mechanisms and neural connections are responsible for adaptation to visual stimuli. Further, our results demonstrate the need for detailed circuit reconstructions like that of the Drosophila lamina, to understand how networks process information

The location of the axon initial segment affects the bandwidth of spike initiation dynamics

The dynamics and the sharp onset of action potential (AP) generation have recently been the subject of intense experimental and theoretical investigations. According to the resistive coupling theory, an electrotonic interplay between the site of AP initiation in the axon and the somato-dendritic load determines the AP waveform. This phenomenon not only alters the shape of AP recorded at the soma, but also determines the dynamics of excitability across a variety of time scales. Supporting this statement, here we generalize a previous numerical study and extend it to the quantification of the input-output gain of the neuronal dynamical response. We consider three classes of multicompartmental mathematical models, ranging from ball-and-stick simplified descriptions of neuronal excitability to 3D-reconstructed biophysical models of excitatory neurons of rodent and human cortical tissue. For each model, we demonstrate that increasing the distance between the axonal site of AP initiation and the soma markedly increases the bandwidth of neuronal response properties. We finally consider the Liquid State Machine paradigm, exploring the impact of altering the site of AP initiation at the level of a neuronal population, and demonstrate that an optimal distance exists to boost the computational performance of the network in a simple classification task. Copyright

Re-imagining the future:repetition decreases hippocampal involvement in future simulation

Imagining or simulating future events has been shown to activate the anterior right hippocampus (RHC) more than remembering past events does. One fundamental difference between simulation and memory is that imagining future scenarios requires a more extensive constructive process than remembering past experiences does. Indeed, studies in which this constructive element is reduced or eliminated by “pre-imagining” events in a prior session do not report differential RHC activity during simulation. In this fMRI study, we examined the effects of repeatedly simulating an event on neural activity. During scanning, participants imagined 60 future events; each event was simulated three times. Activation in the RHC showed a significant linear decrease across repetitions, as did other neural regions typically associated with simulation. Importantly, such decreases in activation could not be explained by non-specific linear time-dependent effects, with no reductions in activity evident for the control task across similar time intervals. Moreover, the anterior RHC exhibited significant functional connectivity with the whole-brain network during the first, but not second and third simulations of future events. There was also evidence of a linear increase in activity across repetitions in right ventral precuneus, right posterior cingulate and left anterior prefrontal cortex, which may reflect source recognition and retrieval of internally generated contextual details. Overall, our findings demonstrate that repeatedly imagining future events has a decremental effect on activation of the hippocampus and many other regions engaged by the initial construction of the simulation, possibly reflecting the decreasing novelty of simulations across repetitions, and therefore is an important consideration in the design of future studies examining simulation

Ion Channel Density Regulates Switches between Regular and Fast Spiking in Soma but Not in Axons

The threshold firing frequency of a neuron is a characterizing feature of its dynamical behaviour, in turn determining its role in the oscillatory activity of the brain. Two main types of dynamics have been identified in brain neurons. Type 1 dynamics (regular spiking) shows a continuous relationship between frequency and stimulation current (f-Istim) and, thus, an arbitrarily low frequency at threshold current; Type 2 (fast spiking) shows a discontinuous f-Istim relationship and a minimum threshold frequency. In a previous study of a hippocampal neuron model, we demonstrated that its dynamics could be of both Type 1 and Type 2, depending on ion channel density. In the present study we analyse the effect of varying channel density on threshold firing frequency on two well-studied axon membranes, namely the frog myelinated axon and the squid giant axon. Moreover, we analyse the hippocampal neuron model in more detail. The models are all based on voltage-clamp studies, thus comprising experimentally measurable parameters. The choice of analysing effects of channel density modifications is due to their physiological and pharmacological relevance. We show, using bifurcation analysis, that both axon models display exclusively Type 2 dynamics, independently of ion channel density. Nevertheless, both models have a region in the channel-density plane characterized by an N-shaped steady-state current-voltage relationship (a prerequisite for Type 1 dynamics and associated with this type of dynamics in the hippocampal model). In summary, our results suggest that the hippocampal soma and the two axon membranes represent two distinct kinds of membranes; membranes with a channel-density dependent switching between Type 1 and 2 dynamics, and membranes with a channel-density independent dynamics. The difference between the two membrane types suggests functional differences, compatible with a more flexible role of the soma membrane than that of the axon membrane