Spatio-Temporal Credit Assignment in Neuronal Population Learning

n learning from trial and error, animals need to relate behavioral decisions to environmental reinforcement even though it may be difficult to assign credit to a particular decision when outcomes are uncertain or subject to delays. When considering the biophysical basis of learning, the credit-assignment problem is compounded because the behavioral decisions themselves result from the spatio-temporal aggregation of many synaptic releases. We present a model of plasticity induction for reinforcement learning in a population of leaky integrate and fire neurons which is based on a cascade of synaptic memory traces. Each synaptic cascade correlates presynaptic input first with postsynaptic events, next with the behavioral decisions and finally with external reinforcement. For operant conditioning, learning succeeds even when reinforcement is delivered with a delay so large that temporal contiguity between decision and pertinent reward is lost due to intervening decisions which are themselves subject to delayed reinforcement. This shows that the model provides a viable mechanism for temporal credit assignment. Further, learning speeds up with increasing population size, so the plasticity cascade simultaneously addresses the spatial problem of assigning credit to synapses in different population neurons. Simulations on other tasks, such as sequential decision making, serve to contrast the performance of the proposed scheme to that of temporal difference-based learning. We argue that, due to their comparative robustness, synaptic plasticity cascades are attractive basic models of reinforcement learning in the brain.

Climate-induced interannual variability of marine primary and export production in three global coupled climate carbon cycle models

Fully coupled climate carbon cycle models are sophisticated tools that are used to predict future climate change and its impact on the land and ocean carbon cycles. These models should be able to adequately represent natural variability, requiring model validation by observations. The present study focuses on the ocean carbon cycle component, in particular the spatial and temporal variability in net primary productivity (PP) and export production (EP) of particulate organic carbon (POC). Results from three coupled climate carbon cycle models (IPSL, MPIM, NCAR) are compared with observation-based estimates derived from satellite measurements of ocean colour and results from inverse modelling (data assimilation). Satellite observations of ocean colour have shown that temporal variability of PP on the global scale is largely dominated by the permanently stratified, low-latitude ocean (Behrenfeld et al., 2006) with stronger stratification (higher sea surface temperature; SST) being associated with negative PP anomalies. Results from all three coupled models confirm the role of the low-latitude, permanently stratified ocean for anomalies in globally integrated PP, but only one model (IPSL) also reproduces the inverse relationship between stratification (SST) and PP. An adequate representation of iron and macronutrient co-limitation of phytoplankton growth in the tropical ocean has shown to be the crucial mechanism determining the capability of the models to reproduce observed interactions between climate and PP.

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.

Performance on auditory and visual temporal informationprocessing is related to psychometric intelligence

The present study investigated the relationship between psychometric intelligence and temporal resolution power (TRP) as simultaneously assessed by auditory and visual psychophysical timing tasks. In addition, three different theoretical models of the functional relationship between TRP and psychometric intelligence as assessed by means of the Adaptive Matrices Test (AMT) were developed. To test the validity of these models, structural equation modeling was applied. Empirical data supported a hierarchical model that assumed auditory and visual modality-specific temporal processing at a first level and amodal temporal processing at a second level. This second-order latent variable was substantially correlated with psychometric intelligence. Therefore, the relationship between psychometric intelligence and psychophysical timing performance can be explained best by a hierarchical model of temporal information processing.

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.

Matrix models for quantifying competitive intransitivity from species abundance data

In a network of competing species, a competitive intransitivity occurs when the ranking of competitive abilities does not follow a linear hierarchy (A > B > C but C > A). A variety of mathematical models suggests that intransitive networks can prevent or slow down competitive exclusion and maintain biodiversity by enhancing species coexistence. However, it has been difficult to assess empirically the relative importance of intransitive competition because a large number of pairwise species competition experiments are needed to construct a competition matrix that is used to parameterize existing models. Here we introduce a statistical framework for evaluating the contribution of intransitivity to community structure using species abundance matrices that are commonly generated from replicated sampling of species assemblages. We provide metrics and analytical methods for using abundance matrices to estimate species competition and patch transition matrices by using reverse-engineering and a colonization-competition model. These matrices provide complementary metrics to estimate the degree of intransitivity in the competition network of the sampled communities. Benchmark tests reveal that the proposed methods could successfully detect intransitive competition networks, even in the absence of direct measures of pairwise competitive strength. To illustrate the approach, we analyzed patterns of abundance and biomass of five species of necrophagous Diptera and eight species of their hymenopteran parasitoids that co-occur in beech forests in Germany. We found evidence for a strong competitive hierarchy within communities of flies and parasitoids. However, for parasitoids, there was a tendency towards increasing intransitivity in higher weight classes, which represented larger resource patches. These tests provide novel methods for empirically estimating the degree of intransitivity in competitive networks from observational datasets. They can be applied to experimental measures of pairwise species interactions, as well as to spatio-temporal samples of assemblages in homogenous environments or environmental gradients.

DYPTOP: a cost-efficient TOPMODEL implementation to simulate sub-grid spatio-temporal dynamics of global wetlands and peatlands

Simulating the spatio-temporal dynamics of inundation is key to understanding the role of wetlands under past and future climate change. Earlier modelling studies have mostly relied on fixed prescribed peatland maps and inundation time series of limited temporal coverage. Here, we describe and assess the the Dynamical Peatland Model Based on TOPMODEL (DYPTOP), which predicts the extent of inundation based on a computationally efficient TOPMODEL implementation. This approach rests on an empirical, grid-cell-specific relationship between the mean soil water balance and the flooded area. DYPTOP combines the simulated inundation extent and its temporal persistency with criteria for the ecosystem water balance and the modelled peatland-specific soil carbon balance to predict the global distribution of peatlands. We apply DYPTOP in combination with the LPX-Bern DGVM and benchmark the global-scale distribution, extent, and seasonality of inundation against satellite data. DYPTOP successfully predicts the spatial distribution and extent of wetlands and major boreal and tropical peatland complexes and reveals the governing limitations to peatland occurrence across the globe. Peatlands covering large boreal lowlands are reproduced only when accounting for a positive feedback induced by the enhanced mean soil water holding capacity in peatland-dominated regions. DYPTOP is designed to minimize input data requirements, optimizes computational efficiency and allows for a modular adoption in Earth system models.

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.

Achieving a more realistic assessment of rockfall hazards by coupling three-dimensional process models and field-based tree-ring data

Sound knowledge of the spatial and temporal patterns of rockfalls is fundamental for the management of this very common hazard in mountain environments. Process-based, three-dimensional simulation models are nowadays capable of reproducing the spatial distribution of rockfall occurrences with reasonable accuracy through the simulation of numerous individual trajectories on highly-resolved digital terrain models. At the same time, however, simulation models typically fail to quantify the ‘real’ frequency of rockfalls (in terms of return intervals). The analysis of impact scars on trees, in contrast, yields real rockfall frequencies, but trees may not be present at the location of interest and rare trajectories may not necessarily be captured due to the limited age of forest stands. In this article, we demonstrate that the coupling of modeling with tree-ring techniques may overcome the limitations inherent to both approaches. Based on the analysis of 64 cells (40 m × 40 m) of a rockfall slope located above a 1631-m long road section in the Swiss Alps, we illustrate results from 488 rockfalls detected in 1260 trees. We illustrate that tree impact data cannot only be used (i) to reconstruct the real frequency of rockfalls for individual cells, but that they also serve (ii) the calibration of the rockfall model Rockyfor3D, as well as (iii) the transformation of simulated trajectories into real frequencies. Calibrated simulation results are in good agreement with real rockfall frequencies and exhibit significant differences in rockfall activity between the cells (zones) along the road section. Real frequencies, expressed as rock passages per meter road section, also enable quantification and direct comparison of the hazard potential between the zones. The contribution provides an approach for hazard zoning procedures that complements traditional methods with a quantification of rockfall frequencies in terms of return intervals through a systematic inclusion of impact records in trees.

Sample size considerations using mathematical models: an example with Chlamydia trachomatis infection and its sequelae pelvic inflammatory disease.

BACKGROUND The success of an intervention to prevent the complications of an infection is influenced by the natural history of the infection. Assumptions about the temporal relationship between infection and the development of sequelae can affect the predicted effect size of an intervention and the sample size calculation. This study investigates how a mathematical model can be used to inform sample size calculations for a randomised controlled trial (RCT) using the example of Chlamydia trachomatis infection and pelvic inflammatory disease (PID). METHODS We used a compartmental model to imitate the structure of a published RCT. We considered three different processes for the timing of PID development, in relation to the initial C. trachomatis infection: immediate, constant throughout, or at the end of the infectious period. For each process we assumed that, of all women infected, the same fraction would develop PID in the absence of an intervention. We examined two sets of assumptions used to calculate the sample size in a published RCT that investigated the effect of chlamydia screening on PID incidence. We also investigated the influence of the natural history parameters of chlamydia on the required sample size. RESULTS The assumed event rates and effect sizes used for the sample size calculation implicitly determined the temporal relationship between chlamydia infection and PID in the model. Even small changes in the assumed PID incidence and relative risk (RR) led to considerable differences in the hypothesised mechanism of PID development. The RR and the sample size needed per group also depend on the natural history parameters of chlamydia. CONCLUSIONS Mathematical modelling helps to understand the temporal relationship between an infection and its sequelae and can show how uncertainties about natural history parameters affect sample size calculations when planning a RCT.

Avalanche risk assessment - a multi-temporal approach, results from Galtür, Austria

Snow avalanches pose a threat to settlements and infrastructure in alpine environments. Due to the catastrophic events in recent years, the public is more aware of this phenomenon. Alpine settlements have always been confronted with natural hazards, but changes in land use and in dealing with avalanche hazards lead to an altering perception of this threat. In this study, a multi-temporal risk assessment is presented for three avalanche tracks in the municipality of Galtür, Austria. Changes in avalanche risk as well as changes in the risk-influencing factors (process behaviour, values at risk (buildings) and vulnerability) between 1950 and 2000 are quantified. An additional focus is put on the interconnection between these factors and their influence on the resulting risk. The avalanche processes were calculated using different simulation models (SAMOS as well as ELBA+). For each avalanche track, different scenarios were calculated according to the development of mitigation measures. The focus of the study was on a multi-temporal risk assessment; consequently the used models could be replaced with other snow avalanche models providing the same functionalities. The monetary values of buildings were estimated using the volume of the buildings and average prices per cubic meter. The changing size of the buildings over time was inferred from construction plans. The vulnerability of the buildings is understood as a degree of loss to a given element within the area affected by natural hazards. A vulnerability function for different construction types of buildings that depends on avalanche pressure was used to assess the degree of loss. No general risk trend could be determined for the studied avalanche tracks. Due to the high complexity of the variations in risk, small changes of one of several influencing factors can cause considerable differences in the resulting risk. This multi-temporal approach leads to better understanding of the today's risk by identifying the main changes and the underlying processes. Furthermore, this knowledge can be implemented in strategies for sustainable development in Alpine settlements.

A regional climate palaeosimulation for Europe in the period 1500–1990 – Part 2: Shortcomings and strengths of models and reconstructions

This study compares gridded European seasonal series of surface air temperature (SAT) and precipitation (PRE) reconstructions with a regional climate simulation over the period 1500–1990. The area is analysed separately for nine subareas that represent the majority of the climate diversity in the European sector. In their spatial structure, an overall good agreement is found between the reconstructed and simulated climate features across Europe, supporting consistency in both products. Systematic biases between both data sets can be explained by a priori known deficiencies in the simulation. Simulations and reconstructions, however, largely differ in the temporal evolution of past climate for European subregions. In particular, the simulated anomalies during the Maunder and Dalton minima show stronger response to changes in the external forcings than recorded in the reconstructions. Although this disagreement is to some extent expected given the prominent role of internal variability in the evolution of regional temperature and precipitation, a certain degree of agreement is a priori expected in variables directly affected by external forcings. In this sense, the inability of the model to reproduce a warm period similar to that recorded for the winters during the first decades of the 18th century in the reconstructions is indicative of fundamental limitations in the simulation that preclude reproducing exceptionally anomalous conditions. Despite these limitations, the simulated climate is a physically consistent data set, which can be used as a benchmark to analyse the consistency and limitations of gridded reconstructions of different variables. A comparison of the leading modes of SAT and PRE variability indicates that reconstructions are too simplistic, especially for precipitation, which is associated with the linear statistical techniques used to generate the reconstructions. The analysis of the co-variability between sea level pressure (SLP) and SAT and PRE in the simulation yields a result which resembles the canonical co-variability recorded in the observations for the 20th century. However, the same analysis for reconstructions exhibits anomalously low correlations, which points towards a lack of dynamical consistency between independent reconstructions.

Chow–Liu trees are sufficient predictive models for reproducing key features of functional networks of periictal EEG time-series

Seizure freedom in patients suffering from pharmacoresistant epilepsies is still not achieved in 20–30% of all cases. Hence, current therapies need to be improved, based on a more complete understanding of ictogenesis. In this respect, the analysis of functional networks derived from intracranial electroencephalographic (iEEG) data has recently become a standard tool. Functional networks however are purely descriptive models and thus are conceptually unable to predict fundamental features of iEEG time-series, e.g., in the context of therapeutical brain stimulation. In this paper we present some first steps towards overcoming the limitations of functional network analysis, by showing that its results are implied by a simple predictive model of time-sliced iEEG time-series. More specifically, we learn distinct graphical models (so called Chow–Liu (CL) trees) as models for the spatial dependencies between iEEG signals. Bayesian inference is then applied to the CL trees, allowing for an analytic derivation/prediction of functional networks, based on thresholding of the absolute value Pearson correlation coefficient (CC) matrix. Using various measures, the thus obtained networks are then compared to those which were derived in the classical way from the empirical CC-matrix. In the high threshold limit we find (a) an excellent agreement between the two networks and (b) key features of periictal networks as they have previously been reported in the literature. Apart from functional networks, both matrices are also compared element-wise, showing that the CL approach leads to a sparse representation, by setting small correlations to values close to zero while preserving the larger ones. Overall, this paper shows the validity of CL-trees as simple, spatially predictive models for periictal iEEG data. Moreover, we suggest straightforward generalizations of the CL-approach for modeling also the temporal features of iEEG signals.