219 research outputs found

    Automatic Network Fingerprinting through Single-Node Motifs

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    Complex networks have been characterised by their specific connectivity patterns (network motifs), but their building blocks can also be identified and described by node-motifs---a combination of local network features. One technique to identify single node-motifs has been presented by Costa et al. (L. D. F. Costa, F. A. Rodrigues, C. C. Hilgetag, and M. Kaiser, Europhys. Lett., 87, 1, 2009). Here, we first suggest improvements to the method including how its parameters can be determined automatically. Such automatic routines make high-throughput studies of many networks feasible. Second, the new routines are validated in different network-series. Third, we provide an example of how the method can be used to analyse network time-series. In conclusion, we provide a robust method for systematically discovering and classifying characteristic nodes of a network. In contrast to classical motif analysis, our approach can identify individual components (here: nodes) that are specific to a network. Such special nodes, as hubs before, might be found to play critical roles in real-world networks.Comment: 16 pages (4 figures) plus supporting information 8 pages (5 figures

    Distribution of the daily Sunspot Number variation for the last 14 solar cycles

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    The difference between consecutive daily Sunspot Numbers was analysed. Its distribution was approximated on a large time scale with an exponential law. In order to verify this approximation a Maximum Entropy distribution was generated by a modified version of the Simulated Annealing algorithm. The exponential approximation holds for the generated distribution too. The exponential law is characteristic for time scales covering whole cycles and it is mostly a characteristic of the Sunspot Number fluctuations and not of its average variation.Comment: Accepted for publication in Solar Physic

    Large-Scale Cortical Dynamics of Sleep Slow Waves

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    Slow waves constitute the main signature of sleep in the electroencephalogram (EEG). They reflect alternating periods of neuronal hyperpolarization and depolarization in cortical networks. While recent findings have demonstrated their functional role in shaping and strengthening neuronal networks, a large-scale characterization of these two processes remains elusive in the human brain. In this study, by using simultaneous scalp EEG and intracranial recordings in 10 epileptic subjects, we examined the dynamics of hyperpolarization and depolarization waves over a large extent of the human cortex. We report that both hyperpolarization and depolarization processes can occur with two different characteristic time durations which are consistent across all subjects. For both hyperpolarization and depolarization waves, their average speed over the cortex was estimated to be approximately 1 m/s. Finally, we characterized their propagation pathways by studying the preferential trajectories between most involved intracranial contacts. For both waves, although single events could begin in almost all investigated sites across the entire cortex, we found that the majority of the preferential starting locations were located in frontal regions of the brain while they had a tendency to end in posterior and temporal regions

    Kernel bandwidth optimization in spike rate estimation

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    Kernel smoother and a time-histogram are classical tools for estimating an instantaneous rate of spike occurrences. We recently established a method for selecting the bin width of the time-histogram, based on the principle of minimizing the mean integrated square error (MISE) between the estimated rate and unknown underlying rate. Here we apply the same optimization principle to the kernel density estimation in selecting the width or “bandwidth” of the kernel, and further extend the algorithm to allow a variable bandwidth, in conformity with data. The variable kernel has the potential to accurately grasp non-stationary phenomena, such as abrupt changes in the firing rate, which we often encounter in neuroscience. In order to avoid possible overfitting that may take place due to excessive freedom, we introduced a stiffness constant for bandwidth variability. Our method automatically adjusts the stiffness constant, thereby adapting to the entire set of spike data. It is revealed that the classical kernel smoother may exhibit goodness-of-fit comparable to, or even better than, that of modern sophisticated rate estimation methods, provided that the bandwidth is selected properly for a given set of spike data, according to the optimization methods presented here

    Probabilistic change detection and visualization methods for the assessment of temporal stability in biomedical data quality

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    The final publication is available at Springer via http://dx.doi.org/DOI 10.1007/s10618-014-0378-6. Published online.Knowledge discovery on biomedical data can be based on on-line, data-stream analyses, or using retrospective, timestamped, off-line datasets. In both cases, changes in the processes that generate data or in their quality features through time may hinder either the knowledge discovery process or the generalization of past knowledge. These problems can be seen as a lack of data temporal stability. This work establishes the temporal stability as a data quality dimension and proposes new methods for its assessment based on a probabilistic framework. Concretely, methods are proposed for (1) monitoring changes, and (2) characterizing changes, trends and detecting temporal subgroups. First, a probabilistic change detection algorithm is proposed based on the Statistical Process Control of the posterior Beta distribution of the Jensen–Shannon distance, with a memoryless forgetting mechanism. This algorithm (PDF-SPC) classifies the degree of current change in three states: In-Control, Warning, and Out-of-Control. Second, a novel method is proposed to visualize and characterize the temporal changes of data based on the projection of a non-parametric information-geometric statistical manifold of time windows. This projection facilitates the exploration of temporal trends using the proposed IGT-plot and, by means of unsupervised learning methods, discovering conceptually-related temporal subgroups. Methods are evaluated using real and simulated data based on the National Hospital Discharge Survey (NHDS) dataset.The work by C Saez has been supported by an Erasmus Lifelong Learning Programme 2013 Grant. This work has been supported by own IBIME funds. 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    A Unifying Framework for Mutual Information Methods for Use in Non-linear Optimisation

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    Many variants of MI exist in the literature. These vary primarily in how the joint histogram is populated. This paper places the four main variants of MI: Standard sampling, Partial Volume Estimation (PVE), In-Parzen Windowing and Post-Parzen Windowing into a single mathematical framework. Jacobians and Hessians are derived in each case. A particular contribution is that the non-linearities implicit to standard sampling and post-Parzen windowing are explicitly dealt with. These non-linearities are a barrier to their use in optimisation. Side-by-side comparison of the MI variants is made using eight diverse data-sets, considering computational expense and convergence. In the experiments, PVE was generally the best performer, although standard sampling often performed nearly as well (if a higher sample rate was used). The widely used sum of squared differences metric performed as well as MI unless large occlusions and non-linear intensity relationships occurred. The binaries and scripts used for testing are available online

    PAC learning using Nadaraya-Watson estimator based on orthonormal systems

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    Regression or function classes of Euclidean type with compact support and certain smoothness properties are shown to be PAC learnable by the Nadaraya-Watson estimator based on complete orthonormal systems. While requiring more smoothness properties than typical PAC formulations, this estimator is computationally efficient, easy to implement, and known to perform well in a number of practical applications. The sample sizes necessary for PAC learning of regressions or functions under sup norm cost are derived for a general orthonormal system. The result covers the widely used estimators based on Haar wavelets, trignometric functions, and Daubechies wavelets
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