Reconstructing computational system dynamics from neural data with recurrent neural networks.

Computational models in neuroscience usually take the form of systems of differential equations. The behaviour of such systems is the subject of dynamical systems theory. Dynamical systems theory provides a powerful mathematical toolbox for analysing neurobiological processes and has been a mainstay of computational neuroscience for decades. Recently, recurrent neural networks (RNNs) have become a popular machine learning tool for studying the non-linear dynamics of neural and behavioural processes by emulating an underlying system of differential equations. RNNs have been routinely trained on similar behavioural tasks to those used for animal subjects to generate hypotheses about the underlying computational mechanisms. By contrast, RNNs can also be trained on the measured physiological and behavioural data, thereby directly inheriting their temporal and geometrical properties. In this way they become a formal surrogate for the experimentally probed system that can be further analysed, perturbed and simulated. This powerful approach is called dynamical system reconstruction. In this Perspective, we focus on recent trends in artificial intelligence and machine learning in this exciting and rapidly expanding field, which may be less well known in neuroscience. We discuss formal prerequisites, different model architectures and training approaches for RNN-based dynamical system reconstructions, ways to evaluate and validate model performance, how to interpret trained models in a neuroscience context, and current challenges.

The experience sampling methodology as a digital clinical tool for more person-centered mental health care: an implementation research agenda.

This position paper by the international IMMERSE consortium reviews the evidence of a digital mental health solution based on Experience Sampling Methodology (ESM) for advancing person-centered mental health care and outlines a research agenda for implementing innovative digital mental health tools into routine clinical practice. ESM is a structured diary technique recording real-time self-report data about the current mental state using a mobile application. We will review how ESM may contribute to (1) service user engagement and empowerment, (2) self-management and recovery, (3) goal direction in clinical assessment and management of care, and (4) shared decision-making. However, despite the evidence demonstrating the value of ESM-based approaches in enhancing person-centered mental health care, it is hardly integrated into clinical practice. Therefore, we propose a global research agenda for implementing ESM in routine mental health care addressing six key challenges: (1) the motivation and ability of service users to adhere to the ESM monitoring, reporting and feedback, (2) the motivation and competence of clinicians in routine healthcare delivery settings to integrate ESM in the workflow, (3) the technical requirements and (4) governance requirements for integrating these data in the clinical workflow, (5) the financial and competence related resources related to IT-infrastructure and clinician time, and (6) implementation studies that build the evidence-base. While focused on ESM, the research agenda holds broader implications for implementing digital innovations in mental health. This paper calls for a shift in focus from developing new digital interventions to overcoming implementation barriers, essential for achieving a true transformation toward person-centered care in mental health.

Strategies, processes, outcomes, and costs of implementing experience sampling-based monitoring in routine mental health care in four European countries: study protocol for the IMMERSE effectiveness-implementation study.

BACKGROUND: Recent years have seen a growing interest in the use of digital tools for delivering person-centred mental health care. Experience Sampling Methodology (ESM), a structured diary technique for capturing moment-to-moment variation in experience and behaviour in service users' daily life, reflects a particularly promising avenue for implementing a person-centred approach. While there is evidence on the effectiveness of ESM-based monitoring, uptake in routine mental health care remains limited. The overarching aim of this hybrid effectiveness-implementation study is to investigate, in detail, reach, effectiveness, adoption, implementation, and maintenance as well as contextual factors, processes, and costs of implementing ESM-based monitoring, reporting, and feedback into routine mental health care in four European countries (i.e., Belgium, Germany, Scotland, Slovakia). METHODS: In this hybrid effectiveness-implementation study, a parallel-group, assessor-blind, multi-centre cluster randomized controlled trial (cRCT) will be conducted, combined with a process and economic evaluation. In the cRCT, 24 clinical units (as the cluster and unit of randomization) at eight sites in four European countries will be randomly allocated using an unbalanced 2:1 ratio to one of two conditions: (a) the experimental condition, in which participants receive a Digital Mobile Mental Health intervention (DMMH) and other implementation strategies in addition to treatment as usual (TAU) or (b) the control condition, in which service users are provided with TAU. Outcome data in service users and clinicians will be collected at four time points: at baseline (t0), 2-month post-baseline (t1), 6-month post-baseline (t2), and 12-month post-baseline (t3). The primary outcome will be patient-reported service engagement assessed with the service attachment questionnaire at 2-month post-baseline. The process and economic evaluation will provide in-depth insights into in-vivo context-mechanism-outcome configurations and economic costs of the DMMH and other implementation strategies in routine care, respectively. DISCUSSION: If this trial provides evidence on reach, effectiveness, adoption, implementation and maintenance of implementing ESM-based monitoring, reporting, and feedback, it will form the basis for establishing its public health impact and has significant potential to bridge the research-to-practice gap and contribute to swifter ecological translation of digital innovations to real-world delivery in routine mental health care. TRIAL REGISTRATION: ISRCTN15109760 (ISRCTN registry, date: 03/08/2022).

The ReCoDe addiction research consortium: Losing and regaining control over drug intake-Findings and future perspectives.

Substance use disorders (SUDs) are seen as a continuum ranging from goal-directed and hedonic drug use to loss of control over drug intake with aversive consequences for mental and physical health and social functioning. The main goals of our interdisciplinary German collaborative research centre on Losing and Regaining Control over Drug Intake (ReCoDe) are (i) to study triggers (drug cues, stressors, drug priming) and modifying factors (age, gender, physical activity, cognitive functions, childhood adversity, social factors, such as loneliness and social contact/interaction) that longitudinally modulate the trajectories of losing and regaining control over drug consumption under real-life conditions. (ii) To study underlying behavioural, cognitive and neurobiological mechanisms of disease trajectories and drug-related behaviours and (iii) to provide non-invasive mechanism-based interventions. These goals are achieved by: (A) using innovative mHealth (mobile health) tools to longitudinally monitor the effects of triggers and modifying factors on drug consumption patterns in real life in a cohort of 900 patients with alcohol use disorder. This approach will be complemented by animal models of addiction with 24/7 automated behavioural monitoring across an entire disease trajectory; i.e. from a naïve state to a drug-taking state to an addiction or resilience-like state. (B) The identification and, if applicable, computational modelling of key molecular, neurobiological and psychological mechanisms (e.g., reduced cognitive flexibility) mediating the effects of such triggers and modifying factors on disease trajectories. (C) Developing and testing non-invasive interventions (e.g., Just-In-Time-Adaptive-Interventions (JITAIs), various non-invasive brain stimulations (NIBS), individualized physical activity) that specifically target the underlying mechanisms for regaining control over drug intake. Here, we will report on the most important results of the first funding period and outline our future research strategy.

Coordinated Prefrontal State Transition Leads Extinction of Reward-Seeking Behaviors.

Extinction learning suppresses conditioned reward responses and is thus fundamental to adapt to changing environmental demands and to control excessive reward seeking. The medial prefrontal cortex (mPFC) monitors and controls conditioned reward responses. Abrupt transitions in mPFC activity anticipate changes in conditioned responses to altered contingencies. It remains, however, unknown whether such transitions are driven by the extinction of old behavioral strategies or by the acquisition of new competing ones. Using in vivo multiple single-unit recordings of mPFC in male rats, we studied the relationship between single-unit and population dynamics during extinction learning, using alcohol as a positive reinforcer in an operant conditioning paradigm. To examine the fine temporal relation between neural activity and behavior, we developed a novel behavioral model that allowed us to identify the number, onset, and duration of extinction-learning episodes in the behavior of each animal. We found that single-unit responses to conditioned stimuli changed even under stable experimental conditions and behavior. However, when behavioral responses to task contingencies had to be updated, unit-specific modulations became coordinated across the whole population, pushing the network into a new stable attractor state. Thus, extinction learning is not associated with suppressed mPFC responses to conditioned stimuli, but is anticipated by single-unit coordination into population-wide transitions of the internal state of the animal.SIGNIFICANCE STATEMENT The ability to suppress conditioned behaviors when no longer beneficial is fundamental for the survival of any organism. While pharmacological and optogenetic interventions have shown a critical involvement of the mPFC in the suppression of conditioned responses, the neural dynamics underlying such a process are still largely unknown. Combining novel analysis tools to describe behavior, single-neuron response, and population activity, we found that widespread changes in neuronal firing temporally coordinate across the whole mPFC population in anticipation of behavioral extinction. This coordination leads to a global transition in the internal state of the network, driving extinction of conditioned behavior.

Classification of amyotrophic lateral sclerosis by brain volume, connectivity, and network dynamics.

Emerging studies corroborate the importance of neuroimaging biomarkers and machine learning to improve diagnostic classification of amyotrophic lateral sclerosis (ALS). While most studies focus on structural data, recent studies assessing functional connectivity between brain regions by linear methods highlight the role of brain function. These studies have yet to be combined with brain structure and nonlinear functional features. We investigate the role of linear and nonlinear functional brain features, and the benefit of combining brain structure and function for ALS classification. ALS patients (N = 97) and healthy controls (N = 59) underwent structural and functional resting state magnetic resonance imaging. Based on key hubs of resting state networks, we defined three feature sets comprising brain volume, resting state functional connectivity (rsFC), as well as (nonlinear) resting state dynamics assessed via recurrent neural networks. Unimodal and multimodal random forest classifiers were built to classify ALS. Out-of-sample prediction errors were assessed via five-fold cross-validation. Unimodal classifiers achieved a classification accuracy of 56.35-61.66%. Multimodal classifiers outperformed unimodal classifiers achieving accuracies of 62.85-66.82%. Evaluating the ranking of individual features' importance scores across all classifiers revealed that rsFC features were most dominant in classification. While univariate analyses revealed reduced rsFC in ALS patients, functional features more generally indicated deficits in information integration across resting state brain networks in ALS. The present work undermines that combining brain structure and function provides an additional benefit to diagnostic classification, as indicated by multimodal classifiers, while emphasizing the importance of capturing both linear and nonlinear functional brain properties to identify discriminative biomarkers of ALS.

Deep neural networks in psychiatry.

Machine and deep learning methods, today's core of artificial intelligence, have been applied with increasing success and impact in many commercial and research settings. They are powerful tools for large scale data analysis, prediction and classification, especially in very data-rich environments ("big data"), and have started to find their way into medical applications. Here we will first give an overview of machine learning methods, with a focus on deep and recurrent neural networks, their relation to statistics, and the core principles behind them. We will then discuss and review directions along which (deep) neural networks can be, or already have been, applied in the context of psychiatry, and will try to delineate their future potential in this area. We will also comment on an emerging area that so far has been much less well explored: by embedding semantically interpretable computational models of brain dynamics or behavior into a statistical machine learning context, insights into dysfunction beyond mere prediction and classification may be gained. Especially this marriage of computational models with statistical inference may offer insights into neural and behavioral mechanisms that could open completely novel avenues for psychiatric treatment.

CACNA1C gene regulates behavioral strategies in operant rule learning.

Behavioral experiments are usually designed to tap into a specific cognitive function, but animals may solve a given task through a variety of different and individual behavioral strategies, some of them not foreseen by the experimenter. Animal learning may therefore be seen more as the process of selecting among, and adapting, potential behavioral policies, rather than mere strengthening of associative links. Calcium influx through high-voltage-gated Ca2+ channels is central to synaptic plasticity, and altered expression of Cav1.2 channels and the CACNA1C gene have been associated with severe learning deficits and psychiatric disorders. Given this, we were interested in how specifically a selective functional ablation of the Cacna1c gene would modulate the learning process. Using a detailed, individual-level analysis of learning on an operant cue discrimination task in terms of behavioral strategies, combined with Bayesian selection among computational models estimated from the empirical data, we show that a Cacna1c knockout does not impair learning in general but has a much more specific effect: the majority of Cacna1c knockout mice still managed to increase reward feedback across trials but did so by adapting an outcome-based strategy, while the majority of matched controls adopted the experimentally intended cue-association rule. Our results thus point to a quite specific role of a single gene in learning and highlight that much more mechanistic insight could be gained by examining response patterns in terms of a larger repertoire of potential behavioral strategies. The results may also have clinical implications for treating psychiatric disorders.

Identifying nonlinear dynamical systems via generative recurrent neural networks with applications to fMRI.

A major tenet in theoretical neuroscience is that cognitive and behavioral processes are ultimately implemented in terms of the neural system dynamics. Accordingly, a major aim for the analysis of neurophysiological measurements should lie in the identification of the computational dynamics underlying task processing. Here we advance a state space model (SSM) based on generative piecewise-linear recurrent neural networks (PLRNN) to assess dynamics from neuroimaging data. In contrast to many other nonlinear time series models which have been proposed for reconstructing latent dynamics, our model is easily interpretable in neural terms, amenable to systematic dynamical systems analysis of the resulting set of equations, and can straightforwardly be transformed into an equivalent continuous-time dynamical system. The major contributions of this paper are the introduction of a new observation model suitable for functional magnetic resonance imaging (fMRI) coupled to the latent PLRNN, an efficient stepwise training procedure that forces the latent model to capture the 'true' underlying dynamics rather than just fitting (or predicting) the observations, and of an empirical measure based on the Kullback-Leibler divergence to evaluate from empirical time series how well this goal of approximating the underlying dynamics has been achieved. We validate and illustrate the power of our approach on simulated 'ground-truth' dynamical systems as well as on experimental fMRI time series, and demonstrate that the learnt dynamics harbors task-related nonlinear structure that a linear dynamical model fails to capture. Given that fMRI is one of the most common techniques for measuring brain activity non-invasively in human subjects, this approach may provide a novel step toward analyzing aberrant (nonlinear) dynamics for clinical assessment or neuroscientific research.

Addiction Research Consortium: Losing and regaining control over drug intake (ReCoDe)-From trajectories to mechanisms and interventions.

One of the major risk factors for global death and disability is alcohol, tobacco, and illicit drug use. While there is increasing knowledge with respect to individual factors promoting the initiation and maintenance of substance use disorders (SUDs), disease trajectories involved in losing and regaining control over drug intake (ReCoDe) are still not well described. Our newly formed German Collaborative Research Centre (CRC) on ReCoDe has an interdisciplinary approach funded by the German Research Foundation (DFG) with a 12-year perspective. The main goals of our research consortium are (i) to identify triggers and modifying factors that longitudinally modulate the trajectories of losing and regaining control over drug consumption in real life, (ii) to study underlying behavioral, cognitive, and neurobiological mechanisms, and (iii) to implicate mechanism-based interventions. These goals will be achieved by: (i) using mobile health (m-health) tools to longitudinally monitor the effects of triggers (drug cues, stressors, and priming doses) and modify factors (eg, age, gender, physical activity, and cognitive control) on drug consumption patterns in real-life conditions and in animal models of addiction; (ii) the identification and computational modeling of key mechanisms mediating the effects of such triggers and modifying factors on goal-directed, habitual, and compulsive aspects of behavior from human studies and animal models; and (iii) developing and testing interventions that specifically target the underlying mechanisms for regaining control over drug intake.

A state space approach for piecewise-linear recurrent neural networks for identifying computational dynamics from neural measurements.

The computational and cognitive properties of neural systems are often thought to be implemented in terms of their (stochastic) network dynamics. Hence, recovering the system dynamics from experimentally observed neuronal time series, like multiple single-unit recordings or neuroimaging data, is an important step toward understanding its computations. Ideally, one would not only seek a (lower-dimensional) state space representation of the dynamics, but would wish to have access to its statistical properties and their generative equations for in-depth analysis. Recurrent neural networks (RNNs) are a computationally powerful and dynamically universal formal framework which has been extensively studied from both the computational and the dynamical systems perspective. Here we develop a semi-analytical maximum-likelihood estimation scheme for piecewise-linear RNNs (PLRNNs) within the statistical framework of state space models, which accounts for noise in both the underlying latent dynamics and the observation process. The Expectation-Maximization algorithm is used to infer the latent state distribution, through a global Laplace approximation, and the PLRNN parameters iteratively. After validating the procedure on toy examples, and using inference through particle filters for comparison, the approach is applied to multiple single-unit recordings from the rodent anterior cingulate cortex (ACC) obtained during performance of a classical working memory task, delayed alternation. Models estimated from kernel-smoothed spike time data were able to capture the essential computational dynamics underlying task performance, including stimulus-selective delay activity. The estimated models were rarely multi-stable, however, but rather were tuned to exhibit slow dynamics in the vicinity of a bifurcation point. In summary, the present work advances a semi-analytical (thus reasonably fast) maximum-likelihood estimation framework for PLRNNs that may enable to recover relevant aspects of the nonlinear dynamics underlying observed neuronal time series, and directly link these to computational properties.

A Quantitative Analysis of Context-Dependent Remapping of Medial Frontal Cortex Neurons and Ensembles.

UNLABELLED: The frontal cortex has been implicated in a number of cognitive and motivational processes, but understanding how individual neurons contribute to these processes is particularly challenging as they respond to a broad array of events (multiplexing) in a manner that can be dynamically modulated by the task context, i.e., adaptive coding (Duncan, 2001). Fundamental questions remain, such as how the flexibility gained through these mechanisms is balanced by the need for consistency and how the ensembles of neurons are coherently shaped by task demands. In the present study, ensembles of medial frontal cortex neurons were recorded from rats trained to perform three different operant actions either in two different sequences or two different physical environments. Single neurons exhibited diverse mixtures of responsivity to each of the three actions and these mixtures were abruptly altered by context/sequence switches. Remarkably, the overall responsivity of the population remained highly consistent both within and between context/sequences because the gains versus losses were tightly balanced across neurons and across the three actions. These data are consistent with a reallocation mixture model in which individual neurons express unique mixtures of selectivity for different actions that become reallocated as task conditions change. However, because the allocations and reallocations are so well balanced across neurons, the population maintains a low but highly consistent response to all actions. The frontal cortex may therefore balance consistency with flexibility by having ensembles respond in a fixed way to task-relevant actions while abruptly reconfiguring single neurons to encode "actions in context." SIGNIFICANCE STATEMENT: Flexible modes of behavior involve performance of similar actions in contextually relevant ways. The present study quantified the changes in how rat medial frontal cortex neurons respond to the same actions when performed in different task contexts (sequences or environments). Most neurons altered the mixture of actions they were responsive to in different contexts or sequences. Nevertheless, the responsivity profile of the ensemble remained fixed as did the ability of the ensemble to differentiate between the three actions. These mechanisms may help to contextualize the manner in which common events are represented across different situations.

A Detailed Data-Driven Network Model of Prefrontal Cortex Reproduces Key Features of In Vivo Activity.

The prefrontal cortex is centrally involved in a wide range of cognitive functions and their impairment in psychiatric disorders. Yet, the computational principles that govern the dynamics of prefrontal neural networks, and link their physiological, biochemical and anatomical properties to cognitive functions, are not well understood. Computational models can help to bridge the gap between these different levels of description, provided they are sufficiently constrained by experimental data and capable of predicting key properties of the intact cortex. Here, we present a detailed network model of the prefrontal cortex, based on a simple computationally efficient single neuron model (simpAdEx), with all parameters derived from in vitro electrophysiological and anatomical data. Without additional tuning, this model could be shown to quantitatively reproduce a wide range of measures from in vivo electrophysiological recordings, to a degree where simulated and experimentally observed activities were statistically indistinguishable. These measures include spike train statistics, membrane potential fluctuations, local field potentials, and the transmission of transient stimulus information across layers. We further demonstrate that model predictions are robust against moderate changes in key parameters, and that synaptic heterogeneity is a crucial ingredient to the quantitative reproduction of in vivo-like electrophysiological behavior. Thus, we have produced a physiologically highly valid, in a quantitative sense, yet computationally efficient PFC network model, which helped to identify key properties underlying spike time dynamics as observed in vivo, and can be harvested for in-depth investigation of the links between physiology and cognition.

Amphetamine Exerts Dose-Dependent Changes in Prefrontal Cortex Attractor Dynamics during Working Memory.

Modulation of neural activity by monoamine neurotransmitters is thought to play an essential role in shaping computational neurodynamics in the neocortex, especially in prefrontal regions. Computational theories propose that monoamines may exert bidirectional (concentration-dependent) effects on cognition by altering prefrontal cortical attractor dynamics according to an inverted U-shaped function. To date, this hypothesis has not been addressed directly, in part because of the absence of appropriate statistical methods required to assess attractor-like behavior in vivo. The present study used a combination of advanced multivariate statistical, time series analysis, and machine learning methods to assess dynamic changes in network activity from multiple single-unit recordings from the medial prefrontal cortex (mPFC) of rats while the animals performed a foraging task guided by working memory after pretreatment with different doses of d-amphetamine (AMPH), which increases monoamine efflux in the mPFC. A dose-dependent, bidirectional effect of AMPH on neural dynamics in the mPFC was observed. Specifically, a 1.0 mg/kg dose of AMPH accentuated separation between task-epoch-specific population states and convergence toward these states. In contrast, a 3.3 mg/kg dose diminished separation and convergence toward task-epoch-specific population states, which was paralleled by deficits in cognitive performance. These results support the computationally derived hypothesis that moderate increases in monoamine efflux would enhance attractor stability, whereas high frontal monoamine levels would severely diminish it. Furthermore, they are consistent with the proposed inverted U-shaped and concentration-dependent modulation of cortical efficiency by monoamines.

Contextual encoding by ensembles of medial prefrontal cortex neurons.

Contextual representations serve to guide many aspects of behavior and influence the way stimuli or actions are encoded and interpreted. The medial prefrontal cortex (mPFC), including the anterior cingulate subregion, has been implicated in contextual encoding, yet the nature of contextual representations formed by the mPFC is unclear. Using multiple single-unit tetrode recordings in rats, we found that different activity patterns emerged in mPFC ensembles when animals moved between different environmental contexts. These differences in activity patterns were significantly larger than those observed for hippocampal ensembles. Whereas ≈11% of mPFC cells consistently preferred one environment over the other across multiple exposures to the same environments, optimal decoding (prediction) of the environmental setting occurred when the activity of up to ≈50% of all mPFC neurons was taken into account. On the other hand, population activity patterns were not identical upon repeated exposures to the very same environment. This was partly because the state of mPFC ensembles seemed to systematically shift with time, such that we could sometimes predict the change in ensemble state upon later reentry into one environment according to linear extrapolation from the time-dependent shifts observed during the first exposure. We also observed that many strongly action-selective mPFC neurons exhibited a significant degree of context-dependent modulation. These results highlight potential differences in contextual encoding schemes by the mPFC and hippocampus and suggest that the mPFC forms rich contextual representations that take into account not only sensory cues but also actions and time.

Neurocomputational models of time perception.

Mathematical modeling is a useful tool for understanding the neurodynamical and computational mechanisms of cognitive abilities like time perception, and for linking neurophysiology to psychology. In this chapter, we discuss several biophysical models of time perception and how they can be tested against experimental evidence. After a brief overview on the history of computational timing models, we list a number of central psychological and physiological findings that such a model should be able to account for, with a focus on the scaling of the variability of duration estimates with the length of the interval that needs to be estimated. The functional form of this scaling turns out to be predictive of the underlying computational mechanism for time perception. We then present four basic classes of timing models (ramping activity, sequential activation of neuron populations, state space trajectories and neural oscillators) and discuss two specific examples in more detail. Finally, we review to what extent existing theories of time perception adhere to the experimental constraints.

Visualization of Discontinuous Vector Field Topology.

This paper extends the concept and the visualization of vector field topology to vector fields with discontinuities. We address the non-uniqueness of flow in such fields by introduction of a time-reversible concept of equivalence. This concept generalizes streamlines to streamsets and thus vector field topology to discontinuous vector fields in terms of invariant streamsets. We identify respective novel critical structures as well as their manifolds, investigate their interplay with traditional vector field topology, and detail the application and interpretation of our approach using specifically designed synthetic cases and a simulated case from physics.

Quantifying brain-functional dynamics using deep dynamical systems: Technical considerations.

Both mental health and mental illness unfold in complex and unpredictable ways. Novel artificial intelligence approaches from the area of dynamical systems reconstruction can characterize such dynamics and help understand the underlying brain mechanisms, which can also be used as potential biomarkers. However, applying deep learning to model dynamical systems at the individual level must overcome numerous computational challenges to be reproducible and clinically useful. In this study, we performed an extensive analysis of these challenges using generative modeling of brain dynamics from fMRI data as an example and demonstrated their impact on classifying patients with schizophrenia and major depression. This study highlights the tendency of deep learning models to identify functionally unique solutions during parameter optimization, which severely impacts the reproducibility of downstream predictions. We hope this study guides the future development of individual-level generative models and similar machine learning approaches aimed at identifying reproducible biomarkers of mental illness.

Method for stationarity-segmentation of spike train data with application to the Pearson cross-correlation.

Correlations among neurons are supposed to play an important role in computation and information coding in the nervous system. Empirically, functional interactions between neurons are most commonly assessed by cross-correlation functions. Recent studies have suggested that pairwise correlations may indeed be sufficient to capture most of the information present in neural interactions. Many applications of correlation functions, however, implicitly tend to assume that the underlying processes are stationary. This assumption will usually fail for real neurons recorded in vivo since their activity during behavioral tasks is heavily influenced by stimulus-, movement-, or cognition-related processes as well as by more general processes like slow oscillations or changes in state of alertness. To address the problem of nonstationarity, we introduce a method for assessing stationarity empirically and then "slicing" spike trains into stationary segments according to the statistical definition of weak-sense stationarity. We examine pairwise Pearson cross-correlations (PCCs) under both stationary and nonstationary conditions and identify another source of covariance that can be differentiated from the covariance of the spike times and emerges as a consequence of residual nonstationarities after the slicing process: the covariance of the firing rates defined on each segment. Based on this, a correction of the PCC is introduced that accounts for the effect of segmentation. We probe these methods both on simulated data sets and on in vivo recordings from the prefrontal cortex of behaving rats. Rather than for removing nonstationarities, the present method may also be used for detecting significant events in spike trains.

A systems medicine research approach for studying alcohol addiction.

According to the World Health Organization, about 2 billion people drink alcohol. Excessive alcohol consumption can result in alcohol addiction, which is one of the most prevalent neuropsychiatric diseases afflicting our society today. Prevention and intervention of alcohol binging in adolescents and treatment of alcoholism are major unmet challenges affecting our health-care system and society alike. Our newly formed German SysMedAlcoholism consortium is using a new systems medicine approach and intends (1) to define individual neurobehavioral risk profiles in adolescents that are predictive of alcohol use disorders later in life and (2) to identify new pharmacological targets and molecules for the treatment of alcoholism. To achieve these goals, we will use omics-information from epigenomics, genetics transcriptomics, neurodynamics, global neurochemical connectomes and neuroimaging (IMAGEN; Schumann et al. ) to feed mathematical prediction modules provided by two Bernstein Centers for Computational Neurosciences (Berlin and Heidelberg/Mannheim), the results of which will subsequently be functionally validated in independent clinical samples and appropriate animal models. This approach will lead to new early intervention strategies and identify innovative molecules for relapse prevention that will be tested in experimental human studies. This research program will ultimately help in consolidating addiction research clusters in Germany that can effectively conduct large clinical trials, implement early intervention strategies and impact political and healthcare decision makers.