Detection of dependence patterns with delay

The Unitary Events (UE) method is a popular and efficient method used this last decade to detect dependence patterns of joint spike activity among simultaneously recorded neurons. The first introduced method is based on binned coincidence count \citep{Grun1996} and can be applied on two or more simultaneously recorded neurons. Among the improvements of the methods, a transposition to the continuous framework has recently been proposed in \citep{muino2014frequent} and fully investigated in \citep{MTGAUE} for two neurons. The goal of the present paper is to extend this study to more than two neurons. The main result is the determination of the limit distribution of the coincidence count. This leads to the construction of an independence test between $L\geq 2$ neurons. Finally we propose a multiple test procedure via a Benjamini and Hochberg approach \citep{Benjamini1995}. All the theoretical results are illustrated by a simulation study, and compared to the UE method proposed in \citep{Grun2002}. Furthermore our method is applied on real data

Can we identify non-stationary dynamics of trial-to-trial variability?"

Identifying sources of the apparent variability in non-stationary scenarios is a fundamental problem in many biological data analysis settings. For instance, neurophysiological responses to the same task often vary from each repetition of the same experiment (trial) to the next. The origin and functional role of this observed variability is one of the fundamental questions in neuroscience. The nature of such trial-to-trial dynamics however remains largely elusive to current data analysis approaches. A range of strategies have been proposed in modalities such as electro-encephalography but gaining a fundamental insight into latent sources of trial-to-trial variability in neural recordings is still a major challenge. In this paper, we present a proof-of-concept study to the analysis of trial-to-trial variability dynamics founded on non-autonomous dynamical systems. At this initial stage, we evaluate the capacity of a simple statistic based on the behaviour of trajectories in classification settings, the trajectory coherence, in order to identify trial-to-trial dynamics. First, we derive the conditions leading to observable changes in datasets generated by a compact dynamical system (the Duffing equation). This canonical system plays the role of a ubiquitous model of non-stationary supervised classification problems. Second, we estimate the coherence of class-trajectories in empirically reconstructed space of system states. We show how this analysis can discern variations attributable to non-autonomous deterministic processes from stochastic fluctuations. The analyses are benchmarked using simulated and two different real datasets which have been shown to exhibit attractor dynamics. As an illustrative example, we focused on the analysis of the rat's frontal cortex ensemble dynamics during a decision-making task. Results suggest that, in line with recent hypotheses, rather than internal noise, it is the deterministic trend which most likely underlies the observed trial-to-trial variability. Thus, the empirical tool developed within this study potentially allows us to infer the source of variability in in-vivo neural recordings

Development of statistical and computational methods to estimate functional connectivity and topology in large-scale neuronal assemblies

One of the most fundamental features of a neural circuit is its connectivity since the single neuron activity is not due only to its intrinsic properties but especially to the direct or indirect influence of other neurons1. It is fundamental to elaborate research strategies aimed at a comprehensive structural description of neuronal interconnections as well as the networks\u2019 elements forming the human connectome. The connectome will significantly increase our understanding of how functional brain states emerge from their underlying structural substrate, and will provide new mechanistic insights into how brain function is affected if this structural substrate is disrupted. The connectome is characterized by three different types of connectivity: structural, functional and effective connectivity. It is evident that the final goal of a connectivity analysis is the reconstruction of the human connectome, thus, the application of statistical measures to the in vivo model in both physiological and pathological states. Since the system under study (i.e. brain areas, cell assemblies) is highly complex, to achieve the purpose described above, it is useful to adopt a reductionist approach. During my PhD work, I focused on a reduced and simplified model, represented by neural networks chronically coupled to Micro Electrodes Arrays (MEAs). Large networks of cortical neurons developing in vitro and chronically coupled to MEAs2 represent a well-established experimental model for studying the neuronal dynamics at the network level3, and for understanding the basic principles of information coding4 learning and memory5. Thus, during my PhD work, I developed and optimized statistical methods to infer functional connectivity from spike train data. In particular, I worked on correlation-based methods: cross-correlation and partial correlation, and information-theory based methods: Transfer Entropy (TE) and Joint Entropy (JE). More in detail, my PhD\u2019s aim has been applying functional connectivity methods to neural networks coupled to high density resolution system, like the 3Brain active pixel sensor array with 4096 electrodes6. To fulfill such an aim, I re-adapted the computational logic operations of the aforementioned connectivity methods. Moreover, I worked on a new method based on the cross-correlogram, able to detect both inhibitory and excitatory links. I called such an algorithm Filtered Normalized Cross-Correlation Histogram (FNCCH). The FNCCH shows a very high precision in detecting both inhibitory and excitatory functional links when applied to our developed in silico model. I worked also on a temporal and pattern extension of the TE algorithm. In this way, I developed a Delayed TE (DTE) and a Delayed High Order TE (DHOTE) version of the TE algorithm. These two extension of the TE algorithm are able to consider different temporal bins at different temporal delays for the pattern recognition with respect to the basic TE. I worked also on algorithm for the JE computation. Starting from the mathematical definition in7, I developed a customized version of JE capable to detect the delay associated to a functional link, together with a dedicated shuffling based thresholding approach. Finally, I embedded all of these connectivity methods into a user-friendly open source software named SPICODYN8. SPICODYN allows the user to perform a complete analysis on data acquired from any acquisition system. I used a standard format for the input data, providing the user with the possibility to perform a complete set of operations on the input data, including: raw data viewing, spike and burst detection and analysis, functional connectivity analysis, graph theory and topological analysis. SPICODYN inherits the backbone structure from TOOLCONNECT, a previously published software that allowed to perform a functional connectivity analysis on spike trains dat

Neuronal dynamics and connectivity analysis of neuronal cultures on multi electrode arrays

Despite a number of attempts over the past two decades, research into reliable, controlled induction of long term evoked responses, mimicking low level learning and memory in dissociated cell cultures remains challenging. In addition, a full understanding of the stimulus-response relationships that underlie synaptic plasticity has not yet been achieved, and many of the underlying principles remain largely unknown. Plasticity studies have been predominantly limited to low density Multi/Micro Electrode Arrays (MEAs). With the advent of complementary metal-oxide-semiconductor (CMOS) based High-Density (HD) MEAs, unprecedented spatial and temporal resolution is now possible. In this thesis, an attempt to bridge the gap between studies of neural plasticity and the use of CMOS based HD-MEAs with thousands of electrodes, is reported. Additionally, since such HD-MEAs generate a large volume of data and require advanced analytics to efficiently process and analyse recordings, computational tools and novel algorithms to infer connectivity during plasticity have been developed. The study showed that the responsiveness, stability and initial firing rate of neuronal cultures are the deciding factors to reliably induce evoked responses. With multi-site stimulation, sustained long term potentiation was achieved, which was validated both by evoked response plots and overall firing rates measured at five different time points - before and after repeated stimulation, and at a three day time points. In contrast, while depression responses were observed, it was found that the effects were not sustained over many days. The findings of the study suggest that appropriate selection of neuronal cultures is crucial for inducing desired evoked responses and criteria for this have been developed. Furthermore, it is concluded that the initial responses to test stimuli can be used to determine whether potentiated or depressed responses are to be expected. To analyse the recordings, pipeline of computational tools was developed. Firstly, neuronal synchrony metrics were adapted for the first time for large HD-MEA recordings and shown to correspond effectively to the firing dynamics. To analyse functional connectivity, an information theoretic approach, Transfer Entropy(TE), was utilised. The method showed accurate estimation of functional connectivity with mid 80th percentile accuracy on simulated data. A superimposition method was proposed to enhance confidence in the connectivity estimation. To statistically evaluate connectivity estimation, a new surrogate method, based on ISI distribution approach, was proposed and validated with a simulated Izhikevich network. The method achieved improved accuracy, compared to the existing ISI shuffling method. This newly developed method was later utilised to infer connectivity and refine connections during the learning process of real neuronal cultures over many days of stimulation. The connectivity inference corresponded accurately to both the spontaneous and stimulated networks during evoked responses and the proposed method permitted observation of the evolution of connections for the potentiated network

Uncovering representations of sleep-associated hippocampal ensemble spike activity

Pyramidal neurons in the rodent hippocampus exhibit spatial tuning during spatial navigation, and they are reactivated in specific temporal order during sharp-wave ripples observed in quiet wakefulness or slow wave sleep. However, analyzing representations of sleep-associated hippocampal ensemble spike activity remains a great challenge. In contrast to wake, during sleep there is a complete absence of animal behavior, and the ensemble spike activity is sparse (low occurrence) and fragmental in time. To examine important issues encountered in sleep data analysis, we constructed synthetic sleep-like hippocampal spike data (short epochs, sparse and sporadic firing, compressed timescale) for detailed investigations. Based upon two Bayesian population-decoding methods (one receptive field-based, and the other not), we systematically investigated their representation power and detection reliability. Notably, the receptive-field-free decoding method was found to be well-tuned for hippocampal ensemble spike data in slow wave sleep (SWS), even in the absence of prior behavioral measure or ground truth. Our results showed that in addition to the sample length, bin size, and firing rate, number of active hippocampal pyramidal neurons are critical for reliable representation of the space as well as for detection of spatiotemporal reactivated patterns in SWS or quiet wakefulness.Collaborative Research in Computational Neuroscience (Award IIS-1307645)United States. Office of Naval Research. Multidisciplinary University Research Initiative (Grant N00014-10-1-0936)National Institutes of Health (U.S.) (Grant TR01-GM10498

Spatial encoding in primate hippocampus during free navigation.

The hippocampus comprises two neural signals-place cells and θ oscillations-that contribute to facets of spatial navigation. Although their complementary relationship has been well established in rodents, their respective contributions in the primate brain during free navigation remains unclear. Here, we recorded neural activity in the hippocampus of freely moving marmosets as they naturally explored a spatial environment to more explicitly investigate this issue. We report place cells in marmoset hippocampus during free navigation that exhibit remarkable parallels to analogous neurons in other mammalian species. Although θ oscillations were prevalent in the marmoset hippocampus, the patterns of activity were notably different than in other taxa. This local field potential oscillation occurred in short bouts (approximately .4 s)-rather than continuously-and was neither significantly modulated by locomotion nor consistently coupled to place-cell activity. These findings suggest that the relationship between place-cell activity and θ oscillations in primate hippocampus during free navigation differs substantially from rodents and paint an intriguing comparative picture regarding the neural basis of spatial navigation across mammals

Hippocampal reactivation of random trajectories resembling Brownian Diffusion

Hippocampal activity patterns representing movement trajectories are reactivated in immobility and sleep periods, a process associated with memory recall, consolidation, and decision making. It is thought that only fixed, behaviorally relevant patterns can be reactivated, which are stored across hippocampal synaptic connections. To test whether some generalized rules govern reactivation, we examined trajectory reactivation following non-stereotypical exploration of familiar open-field environments. We found that random trajectories of varying lengths and timescales were reactivated, resembling that of Brownian motion of particles. The animals’ behavioral trajectory did not follow Brownian diffusion demonstrating that the exact behavioral experience is not reactivated. Therefore, hippocampal circuits are able to generate random trajectories of any recently active map by following diffusion dynamics. This ability of hippocampal circuits to generate representations of all behavioral outcome combinations, experienced or not, may underlie a wide variety of hippocampal-dependent cognitive functions such as learning, generalization, and planning

Modeling operating system crash behavior through multifractal analysis, long range dependence and mining of memory usage patterns

Software Aging is a phenomenon where the state of the operating systems degrades over a period of time due to transient errors. These transient errors can result in resource exhaustion and operating system hangups or crashes.;Three different techniques from fractal geometry are studied using the same datasets for operating system crash modeling and prediction. Holder Exponent is an indicator of how chaotic a signal is. M5 Prime is a nominal classification algorithm that allows prediction of a numerical quantity such as time to crash based on current and previous data. Hurst exponent measures the self similarity and long range dependence or memory of a process or data set and has been used to predict river flows and network usage.;For each of these techniques, a thorough investigation was conducted using crash, hangup and nominal operating system monitoring data. All three approaches demonstrated a promising ability to identify software aging and predict upcoming operating system crashes. This thesis describes the experiments, reports the best candidate techniques and identifies the topics for further investigation