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The cortex organizes sensory information to enable discrimination and generalization1-4. As systematic representations of chemical odour space have not yet been described in the olfactory cortex, it remains unclear how odour relationships are encoded to place chemically distinct but similar odours, such as lemon and orange, into perceptual categories, such as citrus5-7. Here, by combining chemoinformatics and multiphoton imaging in the mouse, we show that both the piriform cortex and its sensory inputs from the olfactory bulb represent chemical odour relationships through correlated patterns of activity. However, cortical odour codes differ from those in the bulb: cortex more strongly clusters together representations for related odours, selectively rewrites pairwise odour relationships, and better matches odour perception. The bulb-to-cortex transformation depends on the associative network originating within the piriform cortex, and can be reshaped by passive odour experience. Thus, cortex actively builds a structured representation of chemical odour space that highlights odour relationships; this representation is similar across individuals but remains plastic, suggesting a means through which the olfactory system can assign related odour cues to common and yet personalized percepts.
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Odorantes/análisis , Corteza Olfatoria/anatomía & histología , Corteza Olfatoria/fisiología , Vías Olfatorias , Compuestos Orgánicos/análisis , Compuestos Orgánicos/química , Animales , Masculino , Ratones , Bulbo Olfatorio/citología , Bulbo Olfatorio/fisiología , Corteza Olfatoria/citología , Percepción Olfatoria/fisiología , OlfatoRESUMEN
An amendment to this paper has been published and can be accessed via a link at the top of the paper.
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The causal structure of a system imposes constraints on the joint probability distribution of variables that can be generated by the system. Archetypal constraints consist of conditional independencies between variables. However, particularly in the presence of hidden variables, many causal structures are compatible with the same set of independencies inferred from the marginal distributions of observed variables. Additional constraints allow further testing for the compatibility of data with specific causal structures. An existing family of causally informative inequalities compares the information about a set of target variables contained in a collection of variables, with a sum of the information contained in different groups defined as subsets of that collection. While procedures to identify the form of these groups-decomposition inequalities have been previously derived, we substantially enlarge the applicability of the framework. We derive groups-decomposition inequalities subject to weaker independence conditions, with weaker requirements in the configuration of the groups, and additionally allowing for conditioning sets. Furthermore, we show how constraints with higher inferential power may be derived with collections that include hidden variables, and then converted into testable constraints using data processing inequalities. For this purpose, we apply the standard data processing inequality of conditional mutual information and derive an analogous property for a measure of conditional unique information recently introduced to separate redundant, synergistic, and unique contributions to the information that a set of variables has about a target.
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Understanding how different information sources together transmit information is crucial in many domains. For example, understanding the neural code requires characterizing how different neurons contribute unique, redundant, or synergistic pieces of information about sensory or behavioral variables. Williams and Beer (2010) proposed a partial information decomposition (PID) that separates the mutual information that a set of sources contains about a set of targets into nonnegative terms interpretable as these pieces. Quantifying redundancy requires assigning an identity to different information pieces, to assess when information is common across sources. Harder et al. (2013) proposed an identity axiom that imposes necessary conditions to quantify qualitatively common information. However, Bertschinger et al. (2012) showed that, in a counterexample with deterministic target-source dependencies, the identity axiom is incompatible with ensuring PID nonnegativity. Here, we study systematically the consequences of information identity criteria that assign identity based on associations between target and source variables resulting from deterministic dependencies. We show how these criteria are related to the identity axiom and to previously proposed redundancy measures, and we characterize how they lead to negative PID terms. This constitutes a further step to more explicitly address the role of information identity in the quantification of redundancy. The implications for studying neural coding are discussed.
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UNLABELLED: Top-down attention increases coding abilities by altering firing rates and rate variability. In the frontal eye field (FEF), a key area enabling top-down attention, attention induced firing rate changes are profound, but its effect on different cell types is unknown. Moreover, FEF is the only cortical area investigated in which attention does not affect rate variability, as assessed by the Fano factor, suggesting that task engagement affects cortical state nonuniformly. We show that putative interneurons in FEF of Macaca mulatta show stronger attentional rate modulation than putative pyramidal cells. Partitioning rate variability reveals that both cell types reduce rate variability with attention, but more strongly so in narrow-spiking cells. The effects are captured by a model in which attention stabilizes neuronal excitability, thereby reducing the expansive nonlinearity that links firing rate and variance. These results show that the effect of attention on different cell classes and different coding properties are consistent across the cortical hierarchy, acting through increased and stabilized neuronal excitability. SIGNIFICANCE STATEMENT: Cortical processing is critically modulated by attention. A key feature of this influence is a modulation of "cortical state," resulting in increased neuronal excitability and resilience of the network against perturbations, lower rate variability, and an increased signal-to-noise ratio. In the frontal eye field (FEF), an area assumed to control spatial attention in human and nonhuman primates, firing rate changes with attention occur, but rate variability, quantified by the Fano factor, appears to be unaffected by attention. Using recently developed analysis tools and models to quantify attention effects on narrow- and broad-spiking cell activity, we show that attention alters cortical state strongly in the FEF, demonstrating that its effect on the neuronal network is consistent across the cortical hierarchy.
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Potenciales de Acción/fisiología , Atención/fisiología , Mapeo Encefálico , Neuronas/fisiología , Corteza Visual/citología , Campos Visuales/fisiología , Análisis de Varianza , Animales , Señales (Psicología) , Fijación Ocular , Análisis de Fourier , Macaca mulatta , Neuronas/citología , Estimulación LuminosaRESUMEN
Adaptive behaviors are built on the arbitrary linkage of sensory inputs to actions and goals. Although the sensorimotor and associative frontostriatal circuits are known to mediate arbitrary visuomotor mappings, the underlying corticocortico dynamics remain elusive. Here, we take a novel approach exploiting gamma-band neural activity to study the human cortical networks and corticocortical functional connectivity mediating arbitrary visuomotor mapping. Single-trial gamma-power time courses were estimated for all Brodmann areas by combing magnetoencephalographic and MRI data with spectral analysis and beam-forming techniques. Linear correlation and Granger causality analyses were performed to investigate functional connectivity between cortical regions. The performance of visuomotor associations was characterized by an increase in gamma-power and functional connectivity over the sensorimotor and frontoparietal network, in addition to medial prefrontal areas. The superior parietal area played a driving role in the network, exerting Granger causality on the dorsal premotor area. Premotor areas acted as relay from parietal to medial prefrontal cortices, which played a receiving role in the network. Link community analysis further revealed that visuomotor mappings reflect the coordination of multiple subnetworks with strong overlap over motor and frontoparietal areas. We put forward an associative account of the underlying cognitive processes and corticocortical functional connectivity. Overall, our approach and results provide novel perspectives toward a better understanding of how distributed brain activity coordinates adaptive behaviors. SIGNIFICANCE STATEMENT: In everyday life, most of our behaviors are based on the arbitrary linkage of sensory information to actions and goals, such as stopping at a red traffic light. Despite their automaticity, such behaviors rely on the activity of a large brain network and elusive interareal functional connectivity. We take a novel approach exploiting noninvasive recordings of human brain activity to reveal the cortical networks and corticocortical functional connectivity mediating visuomotor mappings. Parietal areas were found to play a driving role in the network, whereas premotor areas acted as relays from parietal to medial prefrontal cortices, which played a receiving role. Overall, our approach and results provide novel perspectives toward a better understanding of how distributed brain activity coordinates adaptive behaviors.
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Corteza Cerebral/fisiología , Modelos Neurológicos , Movimiento/fisiología , Red Nerviosa/fisiología , Estimulación Luminosa , Desempeño Psicomotor/fisiología , Conducta Espacial/fisiología , Adulto , Mapeo Encefálico/métodos , Corteza Cerebral/ultraestructura , Femenino , Dedos/fisiología , Ritmo Gamma/fisiología , Objetivos , Humanos , Imagen por Resonancia Magnética/métodos , Magnetoencefalografía/métodos , Masculino , Red Nerviosa/ultraestructura , Neuronas/fisiología , Tiempo de Reacción/fisiología , Adulto JovenRESUMEN
The role of correlations between neuronal responses is crucial to understanding the neural code. A framework used to study this role comprises a breakdown of the mutual information between stimuli and responses into terms that aim to account for different coding modalities and the distinction between different notions of independence. Here we complete the list of types of independence and distinguish activity independence (related to total correlations), conditional independence (related to noise correlations), signal independence (related to signal correlations), coding independence (related to information transmission), and information independence (related to redundancy). For each type, we identify the probabilistic criterion that defines it, indicate the information-theoretic measure used as statistic to test for it, and provide a graphical criterion to recognize the causal configurations of stimuli and responses that lead to its existence. Using this causal analysis, we first provide sufficiency conditions relating these types. Second, we differentiate the use of the measures as statistics to test for the existence of independence from their use for quantification. We indicate that signal and noise correlation cannot be quantified separately. Third, we explicitly define alternative system configurations used to construct the measures, in which noise correlations or noise and signal correlations are eliminated. Accordingly, we examine which measures are meaningful only as a comparison across configurations and which ones provide a characterization of the actually observed responses without resorting to other configurations. Fourth, we compare the commonly used nonparametric approach to eliminate noise correlations with a functional (model-based) approach, showing that the former approach does not remove those effects of noise correlations captured by the tuning properties of the individual neurons, and implies nonlocal causal structure manipulations. These results improve the interpretation of the measures on the framework and help in understanding how to apply it to analyze the role of correlations.
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Modelos Neurológicos , Red Nerviosa/fisiología , Neuronas/fisiología , Estadística como Asunto , Potenciales de Acción , Animales , Humanos , Transmisión SinápticaRESUMEN
Recently, the SPIKE-distance has been proposed as a parameter-free and timescale-independent measure of spike train synchrony. This measure is time resolved since it relies on instantaneous estimates of spike train dissimilarity. However, its original definition led to spuriously high instantaneous values for eventlike firing patterns. Here we present a substantial improvement of this measure that eliminates this shortcoming. The reliability gained allows us to track changes in instantaneous clustering, i.e., time-localized patterns of (dis)similarity among multiple spike trains. Additional new features include selective and triggered temporal averaging as well as the instantaneous comparison of spike train groups. In a second step, a causal SPIKE-distance is defined such that the instantaneous values of dissimilarity rely on past information only so that time-resolved spike train synchrony can be estimated in real time. We demonstrate that these methods are capable of extracting valuable information from field data by monitoring the synchrony between neuronal spike trains during an epileptic seizure. Finally, the applicability of both the regular and the real-time SPIKE-distance to continuous data is illustrated on model electroencephalographic (EEG) recordings.
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Sincronización de Fase en Electroencefalografía , Potenciales de Acción/fisiología , Animales , Encéfalo/fisiopatología , Electrofisiología/métodos , Epilepsia/fisiopatología , Humanos , Convulsiones/fisiopatología , Factores de TiempoRESUMEN
Encapsulation is a well-known impact factor on the durability of Photovoltaics (PV) modules. Currently there is a lack of understanding on the relationship between lamination process and module durability. In this paper, the effects of different lamination parameters on the encapsulant stability due to stress testing have been investigated from both on-site production quality and long-term stability viewpoints. Rather than focusing on single stability factors, this paper evaluates lamination stability using a number of indicators including EVA (ethylene-vinyl acetate copolymer) curing level, voids generation, chemical stability, optical stability, and adhesion strength. The influences of EVA curing level on the stability of other properties are also discussed. It is shown that laminates stability increases with increasing curing level to an upper limit, beyond which leading to the formation of voids, reduced transmittance stability, discoloration, and unstable interfaces. A minimum gel content is identified but an upper limit should not be surpassed. The best range of gel content for the materials tested here is 84-90%. Samples with gel content below 70% show low chemical and optical stability, weak adhesion strength, and EVA flowing. Laminates with gel content over 92% are more likely to become yellow and are less stable in adhesion.
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Quantifying the amount, content and direction of communication between brain regions is key to understanding brain function. Traditional methods to analyze brain activity based on the Wiener-Granger causality principle quantify the overall information propagated by neural activity between simultaneously recorded brain regions, but do not reveal the information flow about specific features of interest (such as sensory stimuli). Here, we develop a new information theoretic measure termed Feature-specific Information Transfer (FIT), quantifying how much information about a specific feature flows between two regions. FIT merges the Wiener-Granger causality principle with information-content specificity. We first derive FIT and prove analytically its key properties. We then illustrate and test them with simulations of neural activity, demonstrating that FIT identifies, within the total information flowing between regions, the information that is transmitted about specific features. We then analyze three neural datasets obtained with different recording methods, magneto- and electro-encephalography, and spiking activity, to demonstrate the ability of FIT to uncover the content and direction of information flow between brain regions beyond what can be discerned with traditional anaytical methods. FIT can improve our understanding of how brain regions communicate by uncovering previously hidden feature-specific information flow.
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Understanding perceptual decision-making requires linking sensory neural responses to behavioral choices. In two-choice tasks, activity-choice covariations are commonly quantified with a single measure of choice probability (CP), without characterizing their changes across stimulus levels. We provide theoretical conditions for stimulus dependencies of activity-choice covariations. Assuming a general decision-threshold model, which comprises both feedforward and feedback processing and allows for a stimulus-modulated neural population covariance, we analytically predict a very general and previously unreported stimulus dependence of CPs. We develop new tools, including refined analyses of CPs and generalized linear models with stimulus-choice interactions, which accurately assess the stimulus- or choice-driven signals of each neuron, characterizing stimulus-dependent patterns of choice-related signals. With these tools, we analyze CPs of macaque MT neurons during a motion discrimination task. Our analysis provides preliminary empirical evidence for the promise of studying stimulus dependencies of choice-related signals, encouraging further assessment in wider data sets.
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Conducta Animal , Encéfalo/fisiología , Conducta de Elección , Células Receptoras Sensoriales/fisiología , Potenciales de Acción , Animales , Retroalimentación Psicológica , Macaca , Modelos Animales , Modelos Neurológicos , Estimulación Luminosa , Detección de Señal Psicológica , Vías Visuales/fisiología , Percepción VisualRESUMEN
To detect directional couplings from time series various measures based on distances in reconstructed state spaces were introduced. These measures can, however, be biased by asymmetries in the dynamics' structure, noise color, or noise level, which are ubiquitous in experimental signals. Using theoretical reasoning and results from model systems we identify the various sources of bias and show that most of them can be eliminated by an appropriate normalization. We furthermore diminish the remaining biases by introducing a measure based on ranks of distances. This rank-based measure outperforms existing distance-based measures concerning both sensitivity and specificity for directional couplings. Therefore, our findings are relevant for a reliable detection of directional couplings from experimental signals.
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Perceptual learning, the improvement in perceptual abilities with training, is thought to be mediated by an alteration of neuronal tuning. It remains poorly understood how tuning properties change as training progresses, whether improved stimulus tuning directly links to increased behavioural readout of sensory information, or how population coding mechanisms change with training. Here, we recorded continuously from multiple neuronal clusters in area V4 while macaque monkeys learned a fine contrast categorization task. Training increased neuronal coding abilities by shifting the steepest point of contrast response functions towards the categorization boundary. Population coding accuracy of difficult discriminations resulted largely from an increased information coding of individual channels, particularly for those channels that in early learning had larger ability for easy discriminations, but comparatively small encoding abilities for difficult discriminations. Population coding was also enhanced by specific changes in correlations. Neuronal activity became more indicative of upcoming choices with training.
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Neuronas/citología , Neuronas/fisiología , Corteza Visual/citología , Corteza Visual/fisiología , Percepción Visual/fisiología , Animales , Electrofisiología , Aprendizaje/fisiología , Macaca mulatta , Masculino , Plasticidad Neuronal/genética , Plasticidad Neuronal/fisiología , Percepción Visual/genéticaRESUMEN
In recent years, powerful general algorithms of causal inference have been developed. In particular, in the framework of Pearl's causality, algorithms of inductive causation (IC and IC(*)) provide a procedure to determine which causal connections among nodes in a network can be inferred from empirical observations even in the presence of latent variables, indicating the limits of what can be learned without active manipulation of the system. These algorithms can in principle become important complements to established techniques such as Granger causality and Dynamic Causal Modeling (DCM) to analyze causal influences (effective connectivity) among brain regions. However, their application to dynamic processes has not been yet examined. Here we study how to apply these algorithms to time-varying signals such as electrophysiological or neuroimaging signals. We propose a new algorithm which combines the basic principles of the previous algorithms with Granger causality to obtain a representation of the causal relations suited to dynamic processes. Furthermore, we use graphical criteria to predict dynamic statistical dependencies between the signals from the causal structure. We show how some problems for causal inference from neural signals (e.g., measurement noise, hemodynamic responses, and time aggregation) can be understood in a general graphical approach. Focusing on the effect of spatial aggregation, we show that when causal inference is performed at a coarser scale than the one at which the neural sources interact, results strongly depend on the degree of integration of the neural sources aggregated in the signals, and thus characterize more the intra-areal properties than the interactions among regions. We finally discuss how the explicit consideration of latent processes contributes to understand Granger causality and DCM as well as to distinguish functional and effective connectivity.
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The analysis of dynamic dependencies in complex systems such as the brain helps to understand how emerging properties arise from interactions. Here we propose an information-theoretic framework to analyze the dynamic dependencies in multivariate time-evolving systems. This framework constitutes a fully multivariate extension and unification of previous approaches based on bivariate or conditional mutual information and Granger causality or transfer entropy. We define multi-information measures that allow us to study the global statistical structure of the system as a whole, the total dependence between subsystems, and the temporal statistical structure of each subsystem. We develop a stationary and a nonstationary formulation of the framework. We then examine different decompositions of these multi-information measures. The transfer entropy naturally appears as a term in some of these decompositions. This allows us to examine its properties not as an isolated measure of interdependence but in the context of the complete framework. More generally we use causal graphs to study the specificity and sensitivity of all the measures appearing in these decompositions to different sources of statistical dependence arising from the causal connections between the subsystems. We illustrate that there is no straightforward relation between the strength of specific connections and specific terms in the decompositions. Furthermore, causal and noncausal statistical dependencies are not separable. In particular, the transfer entropy can be nonmonotonic in dependence on the connectivity strength between subsystems and is also sensitive to internal changes of the subsystems, so it should not be interpreted as a measure of connectivity strength. Altogether, in comparison to an analysis based on single isolated measures of interdependence, this framework is more powerful to analyze emergent properties in multivariate systems and to characterize functionally relevant changes in the dynamics.
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Biofisica/métodos , Algoritmos , Encéfalo/patología , Simulación por Computador , Entropía , Humanos , Cadenas de Markov , Modelos Neurológicos , Modelos Estadísticos , Modelos Teóricos , Neuronas/patología , Distribución Normal , Procesos Estocásticos , Factores de TiempoRESUMEN
Biological systems often consist of multiple interacting subsystems, the brain being a prominent example. To understand the functions of such systems it is important to analyze if and how the subsystems interact and to describe the effect of these interactions. In this work we investigate the extent to which the cause-and-effect framework is applicable to such interacting subsystems. We base our work on a standard notion of causal effects and define a new concept called natural causal effect. This new concept takes into account that when studying interactions in biological systems, one is often not interested in the effect of perturbations that alter the dynamics. The interest is instead in how the causal connections participate in the generation of the observed natural dynamics. We identify the constraints on the structure of the causal connections that determine the existence of natural causal effects. In particular, we show that the influence of the causal connections on the natural dynamics of the system often cannot be analyzed in terms of the causal effect of one subsystem on another. Only when the causing subsystem is autonomous with respect to the rest can this interpretation be made. We note that subsystems in the brain are often bidirectionally connected, which means that interactions rarely should be quantified in terms of cause-and-effect. We furthermore introduce a framework for how natural causal effects can be characterized when they exist. Our work also has important consequences for the interpretation of other approaches commonly applied to study causality in the brain. Specifically, we discuss how the notion of natural causal effects can be combined with Granger causality and Dynamic Causal Modeling (DCM). Our results are generic and the concept of natural causal effects is relevant in all areas where the effects of interactions between subsystems are of interest.
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Encéfalo/fisiología , Modelos Neurológicos , Animales , Causalidad , Humanos , Red Nerviosa/fisiología , Biología de SistemasRESUMEN
A wide variety of approaches to estimate the degree of synchrony between two or more spike trains have been proposed. One of the most recent methods is the ISI-distance which extracts information from the interspike intervals (ISIs) by evaluating the ratio of the instantaneous firing rates. In contrast to most previously proposed measures it is parameter free and time-scale independent. However, it is not well suited to track changes in synchrony that are based on spike coincidences. Here we propose the SPIKE-distance, a complementary measure which is sensitive to spike coincidences but still shares the fundamental advantages of the ISI-distance. In particular, it is easy to visualize in a time-resolved manner and can be extended to a method that is also applicable to larger sets of spike trains. We show the merit of the SPIKE-distance using both simulated and real data.
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Potenciales de Acción/fisiología , Modelos Neurológicos , Conducción Nerviosa/fisiología , Células Ganglionares de la Retina/fisiología , Animales , Humanos , TiempoRESUMEN
Time scale parametric spike train distances like the Victor and the van Rossum distances are often applied to study the neural code based on neural stimuli discrimination. Different neural coding hypotheses, such as rate or coincidence coding, can be assessed by combining a time scale parametric spike train distance with a classifier in order to obtain the optimal discrimination performance. The time scale for which the responses to different stimuli are distinguished best is assumed to be the discriminative precision of the neural code. The relevance of temporal coding is evaluated by comparing the optimal discrimination performance with the one achieved when assuming a rate code. We here characterize the measures quantifying the discrimination performance, the discriminative precision, and the relevance of temporal coding. Furthermore, we evaluate the information these quantities provide about the neural code. We show that the discriminative precision is too unspecific to be interpreted in terms of the time scales relevant for encoding. Accordingly, the time scale parametric nature of the distances is mainly an advantage because it allows maximizing the discrimination performance across a whole set of measures with different sensitivities determined by the time scale parameter, but not due to the possibility to examine the temporal properties of the neural code.
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Potenciales de Acción/fisiología , Vías Aferentes/fisiología , Algoritmos , Simulación por Computador , Análisis Discriminante , Humanos , Modelos Neurológicos , Distribución de Poisson , Tiempo de Reacción , Células Receptoras Sensoriales/fisiología , Factores de TiempoRESUMEN
OBJECTIVE: To test whether epileptic seizure prediction algorithms have true predictive power, their performance must be compared with the one expected under well-defined null hypotheses. For this purpose, analytical performance estimates and seizure predictor surrogates were introduced. We here extend the Monte Carlo framework of seizure predictor surrogates by introducing alarm times surrogates. METHODS: We construct artificial seizure time sequences and artificial seizure predictors to be consistent or inconsistent with various null hypotheses to determine the frequency of null hypothesis rejections obtained from analytical performance estimates and alarm times surrogates under controlled conditions. RESULTS: Compared to analytical performance estimates, alarm times surrogates are more flexible with regard to the testable null hypotheses. Both approaches have similar, high statistical power to indicate true predictive power. For Poisson predictors that fulfill the null hypothesis of analytical performance estimates, the frequency of false positive null hypothesis rejections can exceed the significance level for long mean inter-alarm intervals, revealing an intrinsic bias of these analytical estimates. CONCLUSIONS: Alarm times surrogates offer important advantages over analytical performance estimates. SIGNIFICANCE: The key question in the field of seizure prediction is whether seizures can in principle be predicted or whether algorithms which have been presumed to perform better than chance actually are unable to predict seizures and simply have not yet been tested against the appropriate null hypotheses. Alarm times surrogates can help to answer this question.
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Cadenas de Markov , Convulsiones/diagnóstico , Electroencefalografía , Estudios de Evaluación como Asunto , Humanos , Modelos Biológicos , Modelos Estadísticos , Dinámicas no Lineales , Valor Predictivo de las Pruebas , Sensibilidad y Especificidad , Procesamiento de Señales Asistido por Computador , Factores de TiempoRESUMEN
Measures of multiple spike train synchrony are essential in order to study issues such as spike timing reliability, network synchronization, and neuronal coding. These measures can broadly be divided in multivariate measures and averages over bivariate measures. One of the most recent bivariate approaches, the ISI-distance, employs the ratio of instantaneous interspike intervals (ISIs). In this study we propose two extensions of the ISI-distance, the straightforward averaged bivariate ISI-distance and the multivariate ISI-diversity based on the coefficient of variation. Like the original measure these extensions combine many properties desirable in applications to real data. In particular, they are parameter-free, time scale independent, and easy to visualize in a time-resolved manner, as we illustrate with in vitro recordings from a cortical neuron. Using a simulated network of Hindemarsh-Rose neurons as a controlled configuration we compare the performance of our methods in distinguishing different levels of multi-neuron spike train synchrony to the performance of six other previously published measures. We show and explain why the averaged bivariate measures perform better than the multivariate ones and why the multivariate ISI-diversity is the best performer among the multivariate methods. Finally, in a comparison against standard methods that rely on moving window estimates, we use single-unit monkey data to demonstrate the advantages of the instantaneous nature of our methods.