Analyzing spatio-temporal patterns of genuine cross-correlations

In multivariate time series analysis, the equal-time cross-correlation is a classic and computationally efficient measure for quantifying linear interrelations between data channels. When the cross-correlation coefficient is estimated using a finite amount of data points, its non-random part may be strongly contaminated by a sizable random contribution, such that no reliable conclusion can be drawn about genuine mutual interdependencies. The random correlations are determined by the signals' frequency content and the amount of data points used. Here, we introduce adjusted correlation matrices that can be employed to disentangle random from non-random contributions to each matrix element independently of the signal frequencies. Extending our previous work these matrices allow analyzing spatial patterns of genuine cross-correlation in multivariate data regardless of confounding influences. The performance is illustrated by example of model systems with known interdependence patterns. Finally, we apply the methods to electroencephalographic (EEG) data with epileptic seizure activity.

Uniform approach to linear and nonlinear interrelation patterns in multivariate time series

Currently, a variety of linear and nonlinear measures is in use to investigate spatiotemporal interrelation patterns of multivariate time series. Whereas the former are by definition insensitive to nonlinear effects, the latter detect both nonlinear and linear interrelation. In the present contribution we employ a uniform surrogate-based approach, which is capable of disentangling interrelations that significantly exceed random effects and interrelations that significantly exceed linear correlation. The bivariate version of the proposed framework is explored using a simple model allowing for separate tuning of coupling and nonlinearity of interrelation. To demonstrate applicability of the approach to multivariate real-world time series we investigate resting state functional magnetic resonance imaging (rsfMRI) data of two healthy subjects as well as intracranial electroencephalograms (iEEG) of two epilepsy patients with focal onset seizures. The main findings are that for our rsfMRI data interrelations can be described by linear cross-correlation. Rejection of the null hypothesis of linear iEEG interrelation occurs predominantly for epileptogenic tissue as well as during epileptic seizures.

Multiple time scales of temporal response in pyramidal and fast spiking cortical neurons

Neural dynamic processes correlated over several time scales are found in vivo, in stimulus-evoked as well as spontaneous activity, and are thought to affect the way sensory stimulation is processed. Despite their potential computational consequences, a systematic description of the presence of multiple time scales in single cortical neurons is lacking. In this study, we injected fast spiking and pyramidal (PYR) neurons in vitro with long-lasting episodes of step-like and noisy, in-vivo-like current. Several processes shaped the time course of the instantaneous spike frequency, which could be reduced to a small number (1-4) of phenomenological mechanisms, either reducing (adapting) or increasing (facilitating) the neuron's firing rate over time. The different adaptation/facilitation processes cover a wide range of time scales, ranging from initial adaptation (<10 ms, PYR neurons only), to fast adaptation (<300 ms), early facilitation (0.5-1 s, PYR only), and slow (or late) adaptation (order of seconds). These processes are characterized by broad distributions of their magnitudes and time constants across cells, showing that multiple time scales are at play in cortical neurons, even in response to stationary stimuli and in the presence of input fluctuations. These processes might be part of a cascade of processes responsible for the power-law behavior of adaptation observed in several preparations, and may have far-reaching computational consequences that have been recently described.

The influence of a continuous rate infusion of dexmedetomidine on the nociceptive withdrawal reflex and temporal summation during isoflurane anaesthesia in dogs

Objective To examine the influence of a low dose dexmedetomidine infusion on the nociceptive withdrawal reflex and temporal summation in dogs during isoflurane anaesthesia. Study design Prospective experimental blinded cross-over study. Animals Eight healthy mixed breed dogs, body weight Mean +/- SD 26.5 +/- 8.4 kg and age 25 +/- 16 months. Methods Anaesthesia was induced with propofol and maintained with isoflurane (Fe'ISO 1.3%) delivered in oxygen and air. After stabilization, baseline recordings (time 0) were obtained, then a dexmedetomidine bolus (1 mug kg(-1) IV) followed by a continuous rate infusion (1 mug kg(-1) hour(-1) ) or saline placebo were administered. At times 10, 30 and 60 minutes after the initial bolus, electrical stimulations of increasing intensity were applied over the lateral plantar digital nerve, and administered both as single and as repeated stimuli. The resulting reflex responses were recorded using electromyography. Data were analysed using a multivariable linear regression model and a Kruskal Wallis test for single stimulation data, and repeated measures anova and paired t-test for repeated stimulation data. Results The AUC for the stimulus-response curves after single stimulation were similar for both treatments at time 0. At times 10, 30 and 60 the AUCs for the stimulus-response curves were significantly lower with dexmedetomidine treatment than with placebo. Temporal summation was evident in both treatments at times 0, 10, 30 and 60 starting from a stimulation intensity of 10 mA. The magnitude of temporal summation was smaller in dexmedetomidine than in placebo treated dogs at time 10, 30 and 60, but not at time 0. Conclusions During isoflurane anaesthesia, low dose dexmedetomidine suppresses the nociceptive reflex responses after single and repeated electrical stimulation. Clinical relevance This experimental study confirms previous reports on its peri-operative efficacy under clinical conditions, and further indicates that dexmedetomidine might reduce the risk of post-operative chronic pain development.

Time courses and quantitative analysis of atrial fibrillation episode number and duration after circular plus linear left atrial lesions: trigger elimination or substrate modification: early or delayed cure?

OBJECTIVES We sought to analyze the time course of atrial fibrillation (AF) episodes before and after circular plus linear left atrial ablation and the percentage of patients with complete freedom from AF after ablation by using serial seven-day electrocardiograms (ECGs). BACKGROUND The curative treatment of AF targets the pathophysiological corner stones of AF (i.e., the initiating triggers and/or the perpetuation of AF). The pathophysiological complexity of both may not result in an "all-or-nothing" response but may modify number and duration of AF episodes. METHODS In patients with highly symptomatic AF, circular plus linear ablation lesions were placed around the left and right pulmonary veins, between the two circles, and from the left circle to the mitral annulus using the electroanatomic mapping system. Repetitive continuous 7-day ECGs administered before and after catheter ablation were used for rhythm follow-up. RESULTS In 100 patients with paroxysmal (n = 80) and persistent (n = 20) AF, relative duration of time spent in AF significantly decreased over time (35 +/- 37% before ablation, 26 +/- 41% directly after ablation, and 10 +/- 22% after 12 months). Freedom from AF stepwise increased in patients with paroxysmal AF and after 12 months measured at 88% or 74% depending on whether 24-h ECG or 7-day ECG was used. Complete pulmonary vein isolation was demonstrated in <20% of the circular lesions. CONCLUSIONS The results obtained in patients with AF treated with circular plus linear left atrial lesions strongly indicate that substrate modification is the main underlying pathophysiologic mechanism and that it results in a delayed cure instead of an immediate cure.

Canonical proof nets for classical logic

Proof nets provide abstract counterparts to sequent proofs modulo rule permutations; the idea being that if two proofs have the same underlying proof-net, they are in essence the same proof. Providing a convincing proof-net counterpart to proofs in the classical sequent calculus is thus an important step in understanding classical sequent calculus proofs. By convincing, we mean that (a) there should be a canonical function from sequent proofs to proof nets, (b) it should be possible to check the correctness of a net in polynomial time, (c) every correct net should be obtainable from a sequent calculus proof, and (d) there should be a cut-elimination procedure which preserves correctness. Previous attempts to give proof-net-like objects for propositional classical logic have failed at least one of the above conditions. In Richard McKinley (2010) [22], the author presented a calculus of proof nets (expansion nets) satisfying (a) and (b); the paper defined a sequent calculus corresponding to expansion nets but gave no explicit demonstration of (c). That sequent calculus, called LK∗ in this paper, is a novel one-sided sequent calculus with both additively and multiplicatively formulated disjunction rules. In this paper (a self-contained extended version of Richard McKinley (2010) [22]), we give a full proof of (c) for expansion nets with respect to LK∗, and in addition give a cut-elimination procedure internal to expansion nets – this makes expansion nets the first notion of proof-net for classical logic satisfying all four criteria.

Socioeconomic, Temporal and Regional Variation in Body Mass Index among 188,537 Swiss Male Conscripts Born between 1986 and 1992

BACKGROUND Rising levels of overweight and obesity are important public-health concerns worldwide. The purpose of this study is to elucidate their prevalence and trends in Switzerland by analyzing variations in Body Mass Index (BMI) of Swiss conscripts. METHODS The conscription records were provided by the Swiss Army. This study focussed on conscripts 18.5-20.5 years of age from the seven one-year birth cohorts spanning the period 1986-1992. BMI across professional status, area-based socioeconomic position (abSEP), urbanicity and regions was analyzed. Two piecewise quantile regression models with linear splines for three birth-cohort groups were used to examine the association of median BMI with explanatory variables and to determine the extent to which BMI has varied over time. RESULTS The study population consisted of 188,537 individuals. Median BMI was 22.51 kg/m2 (22.45-22.57 95% confidence interval (CI)). BMI was lower among conscripts of high professional status (-0.46 kg/m2; 95% CI: -0.50, -0.42, compared with low), living in areas of high abSEP (-0.11 kg/m2; 95% CI: -0.16, -0.07 compared to medium) and from urban communities (-0.07 kg/m2; 95% CI: -0.11, -0.03, compared with peri-urban). Comparing with Midland, median BMI was highest in the North-West (0.25 kg/m2; 95% CI: 0.19-0.30) and Central regions (0.11 kg/m2; 95% CI: 0.05-0.16) and lowest in the East (-0.19 kg/m2; 95% CI: -0.24, -0.14) and Lake Geneva regions (-0.15 kg/m2; 95% CI: -0.20, -0.09). Trajectories of regional BMI growth varied across birth cohorts, with median BMI remaining high in the Central and North-West regions, whereas stabilization and in some cases a decline were observed elsewhere. CONCLUSIONS BMI of Swiss conscripts is associated with individual and abSEP and urbanicity. Results show regional variation in the levels and temporal trajectories of BMI growth and signal their possible slowdown among recent birth cohorts.

Time-Series Panel Analysis (TSPA): Multivariate Modeling of Temporal Associations in Psychotherapy Process.

Objective: Processes occurring in the course of psychotherapy are characterized by the simple fact that they unfold in time and that the multiple factors engaged in change processes vary highly between individuals (idiographic phenomena). Previous research, however, has neglected the temporal perspective by its traditional focus on static phenomena, which were mainly assessed at the group level (nomothetic phenomena). To support a temporal approach, the authors introduce time-series panel analysis (TSPA), a statistical methodology explicitly focusing on the quantification of temporal, session-to-session aspects of change in psychotherapy. TSPA-models are initially built at the level of individuals and are subsequently aggregated at the group level, thus allowing the exploration of prototypical models. Method: TSPA is based on vector auto-regression (VAR), an extension of univariate auto-regression models to multivariate time-series data. The application of TSPA is demonstrated in a sample of 87 outpatient psychotherapy patients who were monitored by postsession questionnaires. Prototypical mechanisms of change were derived from the aggregation of individual multivariate models of psychotherapy process. In a 2nd step, the associations between mechanisms of change (TSPA) and pre- to postsymptom change were explored. Results: TSPA allowed a prototypical process pattern to be identified, where patient's alliance and self-efficacy were linked by a temporal feedback-loop. Furthermore, therapist's stability over time in both mastery and clarification interventions was positively associated with better outcomes. Conclusions: TSPA is a statistical tool that sheds new light on temporal mechanisms of change. Through this approach, clinicians may gain insight into prototypical patterns of change in psychotherapy.

Dynamic directed interictal connectivity in left and right temporal lobe epilepsy.

OBJECTIVE There is increasing evidence that epileptic activity involves widespread brain networks rather than single sources and that these networks contribute to interictal brain dysfunction. We investigated the fast-varying behavior of epileptic networks during interictal spikes in right and left temporal lobe epilepsy (RTLE and LTLE) at a whole-brain scale using directed connectivity. METHODS In 16 patients, 8 with LTLE and 8 with RTLE, we estimated the electrical source activity in 82 cortical regions of interest (ROIs) using high-density electroencephalography (EEG), individual head models, and a distributed linear inverse solution. A multivariate, time-varying, and frequency-resolved Granger-causal modeling (weighted Partial Directed Coherence) was applied to the source signal of all ROIs. A nonparametric statistical test assessed differences between spike and baseline epochs. Connectivity results between RTLE and LTLE were compared between RTLE and LTLE and with neuropsychological impairments. RESULTS Ipsilateral anterior temporal structures were identified as key drivers for both groups, concordant with the epileptogenic zone estimated invasively. We observed an increase in outflow from the key driver already before the spike. There were also important temporal and extratemporal ipsilateral drivers in both conditions, and contralateral only in RTLE. A different network pattern between LTLE and RTLE was found: in RTLE there was a much more prominent ipsilateral to contralateral pattern than in LTLE. Half of the RTLE patients but none of the LTLE patients had neuropsychological deficits consistent with contralateral temporal lobe dysfunction, suggesting a relationship between connectivity changes and cognitive deficits. SIGNIFICANCE The different patterns of time-varying connectivity in LTLE and RTLE suggest that they are not symmetrical entities, in line with our neuropsychological results. The highest outflow region was concordant with invasive validation of the epileptogenic zone. This enhanced characterization of dynamic connectivity patterns could better explain cognitive deficits and help the management of epilepsy surgery candidates.

Temporal association between childhood leukaemia and population growth in Swiss municipalities.

The population mixing hypothesis proposes that childhood leukaemia (CL) might be a rare complication of a yet unidentified subclinical infection. Large population influxes into previously isolated rural areas may foster localised epidemics of the postulated infection causing a subsequent increase of CL. While marked population growth after a period of stability was central to the formulation of the hypothesis and to the early studies on population mixing, there is a lack of objective criteria to define such growth patterns. We aimed to determine whether periods of marked population growth coincided with increases in the risk of CL in Swiss municipalities. We identified incident cases of CL aged 0-15 years for the period 1985-2010 from the Swiss Childhood Cancer Registry. Annual data on population counts in Swiss municipalities were obtained for 1980-2010. As exposures, we defined (1) cumulative population growth during a 5-year moving time window centred on each year (1985-2010) and (2) periods of 'take-off growth' identified by segmented linear regression. We compared CL incidence across exposure categories using Poisson regression and tested for effect modification by degree of urbanisation. Our study included 1500 incident cases and 2561 municipalities. The incident rate ratio (IRR) comparing the highest to the lowest quintile of 5-year population growth was 1.18 (95 % CI 0.96, 1.46) in all municipalities and 1.33 (95 % CI 0.93, 1.92) in rural municipalities (p value interaction 0.36). In municipalities with take-off growth, the IRR comparing the take-off period (>6 % annual population growth) with the initial period of low or negative growth (<2 %) was 2.07 (95 % CI 0.95, 4.51) overall and 2.99 (1.11, 8.05) in rural areas (p interaction 0.52). Our study provides further support for the population mixing hypothesis and underlines the need to distinguish take-off growth from other growth patterns in future research.