Internetwork and intranetwork communications during bursting dynamics: Applications to seizure prediction

We use a simple dynamical model of two interacting networks of integrate-and-fire neurons to explain a seemingly paradoxical result observed in epileptic patients indicating that the level of phase synchrony declines below normal levels during the state preceding seizures (preictal state). We model the transition from the seizure free interval (interictal state) to the seizure (ictal state) as a slow increase in the mean depolarization of neurons in a network corresponding to the epileptic focus. We show that the transition from the interictal to preictal and then to the ictal state may be divided into separate dynamical regimes: the formation of slow oscillatory activity due to resonance between the two interacting networks observed during the interictal period, structureless activity during the preictal period when the two networks have different properties, and bursting dynamics driven by the network corresponding to the epileptic focus. Based on this result, we hypothesize that the beginning of the preictal period marks the beginning of the transition of the epileptic network from normal activity toward seizing

Functional genomics and expression analysis of the Corynebacterium glutamicum fpr2-cysIXHDNYZ gene cluster involved in assimilatory sulphate reduction

Rückert C, Koch DJ, Rey DA, et al. Functional genomics and expression analysis of the Corynebacterium glutamicum fpr2-cysIXHDNYZ gene cluster involved in assimilatory sulphate reduction. BMC Genomics. 2005;6(1): 121.Background: Corynebacterium glutamicum is a high-GC Gram-positive soil bacterium of great biotechnological importance for the production of amino acids. To facilitate the rational design of sulphur amino acid-producing strains, the pathway for assimilatory sulphate reduction providing the necessary reduced sulfur moieties has to be known. Although this pathway has been well studied in Gram-negative bacteria like Escherichia coli and low-GC Gram-positives like Bacillus subtilis, little is known for the Actinomycetales and other high-GC Gram-positive bacteria. Results: The genome sequence of C. glutamicum was searched for genes involved in the assimilatory reduction of inorganic sulphur compounds. A cluster of eight candidate genes could be identified by combining sequence similarity searches with a subsequent synteny analysis between C. glutamicum and the closely related C. efficiens. Using mutational analysis, seven of the eight candidate genes, namely cysZ, cysY, cysN, cysD, cysH, cysX, and cysI, were demonstrated to be involved in the reduction of inorganic sulphur compounds. For three of the up to now unknown genes possible functions could be proposed: CysZ is likely to be the sulphate permease, while CysX and CysY are possibly involved in electron transfer and cofactor biosynthesis, respectively. Finally, the candidate gene designated fpr2 influences sulphur utilisation only weakly and might be involved in electron transport for the reduction of sulphite. Real-time RT-PCR experiments revealed that cysIXHDNYZ form an operon and that transcription of the extended cluster fpr2 cysIXHDNYZ is strongly influenced by the availability of inorganic sulphur, as well as L-cysteine. Mapping of the fpr2 and cysIXHDNYZ promoters using RACE-PCR indicated that both promoters overlap with binding-sites of the transcriptional repressor McbR, suggesting an involvement of McbR in the observed regulation. Comparative genomics revealed that large parts of the extended cluster are conserved in 11 of 17 completely sequenced members of the Actinomycetales. Conclusion: The set of C. glutamicum genes involved in assimilatory model organisms E. coli and B. subtilis is used by members of this order, providing the basis for further biochemical studies.sulphate reduction was identified and four novel genes involved in this pathway were found. The high degree of conservation of this cluster among the Actinomycetales supports the hypothesis that a different metabolic pathway for the reduction of inorganic sulphur compounds than that known from the well-studied model organisms E. coli and B. subtilis is used by members of this order, providing the basis for further biochemical studies

Cauchy, infinitesimals and ghosts of departed quantifiers

Procedures relying on infinitesimals in Leibniz, Euler and Cauchy have been interpreted in both a Weierstrassian and Robinson's frameworks. The latter provides closer proxies for the procedures of the classical masters. Thus, Leibniz's distinction between assignable and inassignable numbers finds a proxy in the distinction between standard and nonstandard numbers in Robinson's framework, while Leibniz's law of homogeneity with the implied notion of equality up to negligible terms finds a mathematical formalisation in terms of standard part. It is hard to provide parallel formalisations in a Weierstrassian framework but scholars since Ishiguro have engaged in a quest for ghosts of departed quantifiers to provide a Weierstrassian account for Leibniz's infinitesimals. Euler similarly had notions of equality up to negligible terms, of which he distinguished two types: geometric and arithmetic. Euler routinely used product decompositions into a specific infinite number of factors, and used the binomial formula with an infinite exponent. Such procedures have immediate hyperfinite analogues in Robinson's framework, while in a Weierstrassian framework they can only be reinterpreted by means of paraphrases departing significantly from Euler's own presentation. Cauchy gives lucid definitions of continuity in terms of infinitesimals that find ready formalisations in Robinson's framework but scholars working in a Weierstrassian framework bend over backwards either to claim that Cauchy was vague or to engage in a quest for ghosts of departed quantifiers in his work. Cauchy's procedures in the context of his 1853 sum theorem (for series of continuous functions) are more readily understood from the viewpoint of Robinson's framework, where one can exploit tools such as the pointwise definition of the concept of uniform convergence. Keywords: historiography; infinitesimal; Latin model; butterfly modelComment: 45 pages, published in Mat. Stu

Asymmetrical competition and patterns of abundance of Aedes albopictus and Culex pipiens (Diptera : Culicidae)

We tested for competitive advantage among larvae of Aedes albopictus (Skuse) and Culex pipiens L. in a laboratory experiment and determined the frequency and spatial and temporal patterns of co-occurrence in the field in East St. Louis, IL. In a laboratory competition experiment at multiple combined densities of Ae. albopictus and Cx. pipiens larvae, Ae. albopictus survivorship, and developmental times were significantly affected by conspecific densities but not by Cx. pipiens densities. In contrast, Cx. pipiens survivorship, and developmental times were significantly affected by both conspecific and Ae. albopictus densities. Per capita rate of increase (r\u27) for Ae. albopictus cohorts declined significantly due to density of conspecifics, but not density of Cx. pipiens. Interspecific competition between Ae. albopictus and Cx. pipiens under these laboratory conditions was strong and asymmetrical, with the effect of Ae. albopictus on Cx. pipiens much stronger than the reverse. In monthly samples from tire sites in East St. Louis, Ae. albopictus was highly seasonal, occurring in relatively low abundance from early May to July and increasing in abundance in August and September. Co-occurrence corresponded to the seasonality of Ae. albopictus, with Cx. pipiens encountering Ae. albopictus in more tires and at higher numbers within a tire, in August and September. Abundance of both species was high in residential areas and was unrelated to overstory cover, total nitrogen, and total phosphorus. Abundance of Ae. albopictus, but not of Cx. pipiens, was positively associated with conductivity. We expect Cx. pipiens to suffer from the effects of interspecific competition in tires in which it encounters Ae. albopictus. Interspecific competition between these species may be of both ecological and medical importance

Identifying phase synchronization clusters in spatially extended dynamical systems

We investigate two recently proposed multivariate time series analysis techniques that aim at detecting phase synchronization clusters in spatially extended, nonstationary systems with regard to field applications. The starting point of both techniques is a matrix whose entries are the mean phase coherence values measured between pairs of time series. The first method is a mean field approach which allows to define the strength of participation of a subsystem in a single synchronization cluster. The second method is based on an eigenvalue decomposition from which a participation index is derived that characterizes the degree of involvement of a subsystem within multiple synchronization clusters. Simulating multiple clusters within a lattice of coupled Lorenz oscillators we explore the limitations and pitfalls of both methods and demonstrate (a) that the mean field approach is relatively robust even in configurations where the single cluster assumption is not entirely fulfilled, and (b) that the eigenvalue decomposition approach correctly identifies the simulated clusters even for low coupling strengths. Using the eigenvalue decomposition approach we studied spatiotemporal synchronization clusters in long-lasting multichannel EEG recordings from epilepsy patients and obtained results that fully confirm findings from well established neurophysiological examination techniques. Multivariate time series analysis methods such as synchronization cluster analysis that account for nonlinearities in the data are expected to provide complementary information which allows to gain deeper insights into the collective dynamics of spatially extended complex systems

Analysis of cross-correlations in electroencephalogram signals as an approach to proactive diagnosis of schizophrenia

We apply flicker-noise spectroscopy (FNS), a time series analysis method operating on structure functions and power spectrum estimates, to study the clinical electroencephalogram (EEG) signals recorded in children/adolescents (11 to 14 years of age) with diagnosed schizophrenia-spectrum symptoms at the National Center for Psychiatric Health (NCPH) of the Russian Academy of Medical Sciences. The EEG signals for these subjects were compared with the signals for a control sample of chronically depressed children/adolescents. The purpose of the study is to look for diagnostic signs of subjects' susceptibility to schizophrenia in the FNS parameters for specific electrodes and cross-correlations between the signals simultaneously measured at different points on the scalp. Our analysis of EEG signals from scalp-mounted electrodes at locations F3 and F4, which are symmetrically positioned in the left and right frontal areas of cerebral cortex, respectively, demonstrates an essential role of frequency-phase synchronization, a phenomenon representing specific correlations between the characteristic frequencies and phases of excitations in the brain. We introduce quantitative measures of frequency-phase synchronization and systematize the values of FNS parameters for the EEG data. The comparison of our results with the medical diagnoses for 84 subjects performed at NCPH makes it possible to group the EEG signals into 4 categories corresponding to different risk levels of subjects' susceptibility to schizophrenia. We suggest that the introduced quantitative characteristics and classification of cross-correlations may be used for the diagnosis of schizophrenia at the early stages of its development.Comment: 36 pages, 6 figures, 2 tables; to be published in "Physica A

Theory of Concepts

UID/FIL/00183/2013authorsversionpublishe

Toward a Theory of the Pragmatic A Priori: From Carnap to Lewis and Beyond

The aim of this paper is make a contribution to the ongoing search for an adequate concept of the a priori element in scientific knowledge. The point of departure is C.I. Lewis’s account of a pragmatic a priori put forward in his "Mind and the World Order" (1929). Recently, Hasok Chang in "Contingent Transcendental Arguments for Metaphysical Principles" (2008) reconsidered Lewis’s pragmatic a priori and proposed to conceive it as the basic ingredient of the dynamics of an embodied scientific reason. The present paper intends to further elaborate Chang’s account by relating it with some conceptual tools from cognitive semantics and certain ideas that first emerged in the context of the category-theoretical foundations of mathematics

Scaling Effects and Spatio-Temporal Multilevel Dynamics in Epileptic Seizures

Epileptic seizures are one of the most well-known dysfunctions of the nervous system. During a seizure, a highly synchronized behavior of neural activity is observed that can cause symptoms ranging from mild sensual malfunctions to the complete loss of body control. In this paper, we aim to contribute towards a better understanding of the dynamical systems phenomena that cause seizures. Based on data analysis and modelling, seizure dynamics can be identified to possess multiple spatial scales and on each spatial scale also multiple time scales. At each scale, we reach several novel insights. On the smallest spatial scale we consider single model neurons and investigate early-warning signs of spiking. This introduces the theory of critical transitions to excitable systems. For clusters of neurons (or neuronal regions) we use patient data and find oscillatory behavior and new scaling laws near the seizure onset. These scalings lead to substantiate the conjecture obtained from mean-field models that a Hopf bifurcation could be involved near seizure onset. On the largest spatial scale we introduce a measure based on phase-locking intervals and wavelets into seizure modelling. It is used to resolve synchronization between different regions in the brain and identifies time-shifted scaling laws at different wavelet scales. We also compare our wavelet-based multiscale approach with maximum linear cross-correlation and mean-phase coherence measures

‘Functional Connectivity’ Is a Sensitive Predictor of Epilepsy Diagnosis after the First Seizure

Background: Although epilepsy affects almost 1 % of the world population, diagnosis of this debilitating disease is still difficult. The EEG is an important tool for epilepsy diagnosis and classification, but the sensitivity of interictal epileptiform discharges (IEDs) on the first EEG is only 30–50%. Here we investigate whether using ‘functional connectivity ’ can improve the diagnostic sensitivity of the first interictal EEG in the diagnosis of epilepsy. Methodology/Principal Findings: Patients were selected from a database with 390 standard EEGs of patients after a first suspected seizure. Patients who were later diagnosed with epilepsy (i.e. $two seizures) were compared to matched nonepilepsy patients (with a minimum follow-up of one year). The synchronization likelihood (SL) was used as an index of functional connectivity of the EEG, and average SL per patient was calculated in seven frequency bands. In total, 114 patients were selected. Fifty-seven patients were diagnosed with epilepsy (20 had IEDs on their EEG) and 57 matched patients had other diagnoses. Epilepsy patients had significantly higher SL in the theta band than non-epilepsy patients. Furthermore, theta band SL proved to be a significant predictor of a diagnosis of epilepsy. When only those epilepsy patients without IEDs were considered (n = 74), theta band SL could predict diagnosis with specificity of 76 % and sensitivity of 62%. Conclusion/Significance: Theta band functional connectivity may be a useful diagnostic tool in diagnosing epilepsy