Learning black- and gray-box chemotactic PDEs/closures from agent based Monte Carlo simulation data.

We propose a machine learning framework for the data-driven discovery of macroscopic chemotactic Partial Differential Equations (PDEs)-and the closures that lead to them- from high-fidelity, individual-based stochastic simulations of Escherichia coli bacterial motility. The fine scale, chemomechanical, hybrid (continuum-Monte Carlo) simulation model embodies the underlying biophysics, and its parameters are informed from experimental observations of individual cells. Using a parsimonious set of collective observables, we learn effective, coarse-grained "Keller-Segel class" chemotactic PDEs using machine learning regressors: (a) (shallow) feedforward neural networks and (b) Gaussian Processes. The learned laws can be black-box (when no prior knowledge about the PDE law structure is assumed) or gray-box when parts of the equation (e.g. the pure diffusion part) is known and "hardwired" in the regression process. More importantly, we discuss data-driven corrections (both additive and functional), to analytically known, approximate closures.

Coarse-scale PDEs from fine-scale observations via machine learning.

Complex spatiotemporal dynamics of physicochemical processes are often modeled at a microscopic level (through, e.g., atomistic, agent-based, or lattice models) based on first principles. Some of these processes can also be successfully modeled at the macroscopic level using, e.g., partial differential equations (PDEs) describing the evolution of the right few macroscopic observables (e.g., concentration and momentum fields). Deriving good macroscopic descriptions (the so-called "closure problem") is often a time-consuming process requiring deep understanding/intuition about the system of interest. Recent developments in data science provide alternative ways to effectively extract/learn accurate macroscopic descriptions approximating the underlying microscopic observations. In this paper, we introduce a data-driven framework for the identification of unavailable coarse-scale PDEs from microscopic observations via machine-learning algorithms. Specifically, using Gaussian processes, artificial neural networks, and/or diffusion maps, the proposed framework uncovers the relation between the relevant macroscopic space fields and their time evolution (the right-hand side of the explicitly unavailable macroscopic PDE). Interestingly, several choices equally representative of the data can be discovered. The framework will be illustrated through the data-driven discovery of macroscopic, concentration-level PDEs resulting from a fine-scale, lattice Boltzmann level model of a reaction/transport process. Once the coarse evolution law is identified, it can be simulated to produce long-term macroscopic predictions. Different features (pros as well as cons) of alternative machine-learning algorithms for performing this task (Gaussian processes and artificial neural networks) are presented and discussed.

Amplitude spectrum EEG signal evidence for the dissociation of motor and perceptual spatial working memory in the human brain.

This study investigated the question whether spatial working memory related to movement plans (motor working memory) and spatial working memory related to spatial attention and perceptual processes (perceptual spatial working memory) share the same neurophysiological substrate or there is evidence for separate motor and perceptual working memory streams of processing. Towards this aim, ten healthy human subjects performed delayed responses to visual targets presented at different spatial locations. Two tasks were attained, one in which the spatial location of the target was the goal for a pointing movement and one in which the spatial location of the target was used for a perceptual (yes or no) change detection. Each task involved two conditions: a memory condition in which the target remained visible only for the first 250 ms of the delay period and a delay condition in which the target location remained visible throughout the delay period. The amplitude spectrum analysis of the EEG revealed that the alpha (8-12 Hz) band signal was smaller, while the beta (13-30 Hz) and gamma (30-45 Hz) band signals were larger in the memory compared to the non-memory condition. The alpha band signal difference was confined to the frontal midline area; the beta band signal difference extended over the right hemisphere and midline central area, and the gamma band signal difference was confined to the right occipitoparietal area. Importantly, both in beta and gamma bands, we observed a significant increase in the movement-related compared to the perceptual-related memory-specific amplitude spectrum signal in the central midline area. This result provides clear evidence for the dissociation of motor and perceptual spatial working memory.

Single-trial magnetoencephalography signals encoded as an unfolding decision process.

The model of a stochastic decision process unfolding in motor and premotor regions of the brain was encoded in single-trial magnetoencephalographic (MEG) recordings while ten healthy subjects performed a sensorimotor Reaction Time (RT) task. The duration of single-trial MEG signals preceding the motor response, recorded over the motor cortex contralateral to the responding hand, co-varied with RT across trials according to the model's prediction. Furthermore, these signals displayed the same properties of a "rising-to-a-fixed-threshold" decision process as posited by the model and observed in the activity of single neurons in the primate cortex. The present findings demonstrate that non-averaged, single-trial MEG recordings can be used to test models of cognitive processes, like decision-making, in humans.

Construction of embedded fMRI resting-state functional connectivity networks using manifold learning.

We construct embedded functional connectivity networks (FCN) from benchmark resting-state functional magnetic resonance imaging (rsfMRI) data acquired from patients with schizophrenia and healthy controls based on linear and nonlinear manifold learning algorithms, namely, Multidimensional Scaling, Isometric Feature Mapping, Diffusion Maps, Locally Linear Embedding and kernel PCA. Furthermore, based on key global graph-theoretic properties of the embedded FCN, we compare their classification potential using machine learning. We also assess the performance of two metrics that are widely used for the construction of FCN from fMRI, namely the Euclidean distance and the cross correlation metric. We show that diffusion maps with the cross correlation metric outperform the other combinations.

Varicella zoster virus transmission dynamics in Vojvodina, Serbia.

This study aimed at establishing baseline key epidemiological parameters for varicella zoster virus (VZV) infection in Vojvodina, Serbia, with the ultimate goal to quantify the VZV transmission potential in the population. Seroprevalence data generated during the first large cross-sectional VZV serosurvey were modelled, using a two-tiered modelling approach to calculate age-specific forces of infection (FOI), the basic reproduction number (R0) and herd immunity threshold (H). Seroprevalence and modelling data were compared with corresponding pre-vaccination epidemiological parameters from 11 countries participating in the European Sero-Epidemiology Network 2 (ESEN2) project. Serbia fits into the general dynamic VZV transmission patterns in Europe in the pre-vaccine era, with estimated R0 = 4.12, (95% CI: 2.69-7.07) and H = 0.76 (95% CI: 0.63-0.86). The highest VZV transmission occurs among preschool children, as evidenced by the estimation of the highest FOI (0.22, 95% CI: 0.11-0.34) in the 0.5-4 age group, with a peak FOI of 0.25 at 2.23 years. Seroprevalence was consistently lower in 5-14 year-olds, resulting in considerable shares of VZV-susceptible adolescents (7.3%), and young adults (6%), resembling the situation in a minority of European countries. The obtained key epidemiological parameters showed most intense VZV transmission in preschool children aged <4 years, justifying the consideration of universal childhood immunization in the future. National immunization strategy should consider programs for VZV serologic screening and immunization of susceptible groups, including adolescents and women of reproductive age. This work is an important milestone towards the evaluation of varicella immunization policy options in Serbia.

Correlation of Opioid Mortality with Prescriptions and Social Determinants: A Cross-sectional Study of Medicare Enrollees.

BACKGROUND: The opioid epidemic is an escalating health crisis. We evaluated the impact of opioid prescription rates and socioeconomic determinants on opioid mortality rates, and identified potential differences in prescription patterns by categories of practitioners. METHODS: We combined the 2013 and 2014 Medicare Part D data and quantified the opioid prescription rate in a county level cross-sectional study with data from 2710 counties, 468,614 unique prescribers and 46,665,037 beneficiaries. We used the CDC WONDER database to obtain opioid-related mortality data. Socioeconomic characteristics for each county were acquired from the US Census Bureau. RESULTS: The average national opioid prescription rate was 3.86 claims per beneficiary that received a prescription for opioids (95% CI 3.86-3.86). At a county level, overall opioid prescription rates (p < 0.001, Coeff = 0.27) and especially those provided by emergency medicine (p < 0.001, Coeff = 0.21), family medicine physicians (p = 0.11, Coeff = 0.008), internal medicine (p = 0.018, Coeff = 0.1) and physician assistants (p = 0.021, Coeff = 0.08) were associated with opioid-related mortality. Demographic factors, such as proportion of white (p white < 0.001, Coeff = 0.22), black (p black < 0.001, Coeff = - 0.19) and male population (p male < 0.001, Coeff = 0.13) were associated with opioid prescription rates, while poverty (p < 0.001, Coeff = 0.41) and proportion of white population (p white < 0.001, Coeff = 0.27) were risk factors for opioid-related mortality (p model < 0.001, R 2 = 0.35). Notably, the impact of prescribers in the upper quartile was associated with opioid mortality (p < 0.001, Coeff = 0.14) and was twice that of the remaining 75% of prescribers together (p < 0.001, Coeff = 0.07) (p model = 0.03, R 2 = 0.03). CONCLUSIONS: The prescription opioid rate, and especially that by certain categories of prescribers, correlated with opioid-related mortality. Interventions should prioritize providers that have a disproportionate impact and those that care for populations with socioeconomic factors that place them at higher risk.

Reaction time as a stochastic process implemented by functional brain networks.

Many studies focus on anatomical brain connectivity in an effort to explain the effect of practice on reaction time (RT) that is observed in many cognitive tasks. In this commentary, we suggest that RT reflects a stochastic process that varies in each single repetition of any cognitive task and cannot be attributed only to anatomical properties of the underlying neuronal circuit. Based on recent evidence from Magnetoencephalographic, Electroencephalographic, and fMRI studies, we further propose that the functional properties of key brain areas and their self-organization into functional connectivity networks contribute to the RT and could also explain the effects of training on the distribution of the RT.

To infinity and some glimpses of beyond.

When mathematical and computational dynamic models reach infinity in finite time, extending analysis and numerics beyond it becomes a notorious challenge. We suggest how, upon suitable transformations, it may become possible to go beyond infinity with the solution becoming again well behaved and the computations continuing normally. In our Ordinary Differential Equation examples the crossing of infinity occurs instantaneously. For Partial Differential Equations, the crossing of infinity may persist for finite time, necessitating the introduction of buffer zones, within which an appropriate transformation is adaptively identified. Along the path of our analysis, we present a regularization process via complexification and explore its impact on the dynamics; we also discuss a set of compactification transformations and their intuitive implications. This methodology could be useful toward a systematic approach to bypassing infinity and thus going beyond it in a broader range of evolution equation models.

Reaching to virtual targets: The oblique effect reloaded in 3-D.

Perceiving and reproducing direction of visual stimuli in 2-D space produces the visual oblique effect, which manifests as increased precision in the reproduction of cardinal compared to oblique directions. A second cognitive oblique effect emerges when stimulus information is degraded (such as when reproducing stimuli from memory) and manifests as a systematic distortion where reproduced directions close to the cardinal axes deviate toward the oblique, leading to space expansion at cardinal and contraction at oblique axes. We studied the oblique effect in 3-D using a virtual reality system to present a large number of stimuli, covering the surface of an imaginary half sphere, to which subjects had to reach. We used two conditions, one with no delay (no-memory condition) and one where a three-second delay intervened between stimulus presentation and movement initiation (memory condition). A visual oblique effect was observed for the reproduction of cardinal directions compared to oblique, which did not differ with memory condition. A cognitive oblique effect also emerged, which was significantly larger in the memory compared to the no-memory condition, leading to distortion of directional space with expansion near the cardinal axes and compression near the oblique axes on the hemispherical surface. This effect provides evidence that existing models of 2-D directional space categorization could be extended in the natural 3-D space.

Children with well controlled epilepsy possess different spatio-temporal patterns of causal network connectivity during a visual working memory task.

Using spectral Granger causality (GC) we identified distinct spatio-temporal causal connectivity (CC) patterns in groups of control and epileptic children during the execution of a one-back matching visual discrimination working memory task. Differences between control and epileptic groups were determined for both GO and NOGO conditions. The analysis was performed on a set of 19-channel EEG cortical activity signals. We show that for the GO task, the highest brain activity in terms of the density of the CC networks is observed in α band for the control group while for the epileptic group the CC network seems disrupted as reflected by the small number of connections. For the NOGO task, the denser CC network was observed in θ band for the control group while widespread differences between the control and the epileptic group were located bilaterally at the left temporal-midline and parietal areas. In order to test the discriminative power of our analysis, we performed a pattern analysis approach based on fuzzy classification techniques. The performance of the classification scheme was evaluated using permutation tests. The analysis demonstrated that, on average, 87.6 % of the subjects were correctly classified in control and epileptic. Thus, our findings may provide a helpful insight on the mechanisms pertaining to the cognitive response of children with well controlled epilepsy and could potentially serve as "functional" biomarkers for early diagnosis.

A Complex Network Theory Approach for the Spatial Distribution of Fire Breaks in Heterogeneous Forest Landscapes for the Control of Wildland Fires.

Based on complex network theory, we propose a computational methodology which addresses the spatial distribution of fuel breaks for the inhibition of the spread of wildland fires on heterogeneous landscapes. This is a two-level approach where the dynamics of fire spread are modeled as a random Markov field process on a directed network whose edge weights are determined by a Cellular Automata model that integrates detailed GIS, landscape and meteorological data. Within this framework, the spatial distribution of fuel breaks is reduced to the problem of finding network nodes (small land patches) which favour fire propagation. Here, this is accomplished by exploiting network centrality statistics. We illustrate the proposed approach through (a) an artificial forest of randomly distributed density of vegetation, and (b) a real-world case concerning the island of Rhodes in Greece whose major part of its forest was burned in 2008. Simulation results show that the proposed methodology outperforms the benchmark/conventional policy of fuel reduction as this can be realized by selective harvesting and/or prescribed burning based on the density and flammability of vegetation. Interestingly, our approach reveals that patches with sparse density of vegetation may act as hubs for the spread of the fire.

Forecasting and control policy assessment for the Ebola virus disease (EVD) epidemic in Sierra Leone using small-world networked model simulations.

OBJECTIVES: As the Ebola virus disease is still sustained in Sierra Leone, we analysed the epidemic for a recent period (21 December 2014 to 17 April 2015) using a small-world networked model and forecasted its evolution. Policy-control scenarios for the containment of the epidemic were also examined. METHODS: We developed an agent-based model with 6 million individuals (the population of Sierra Leone) interacting through a small-world social network. The model incorporates the main epidemiological factors, including the effect of burial practices to virus transmission. The effective reproductive number (Re) was evaluated directly from the agent-based simulations. Estimates of the epidemiological variables were computed on the basis of the official cases as reported by the Centers for Disease Control and Prevention (CDC). RESULTS: From 21 December 2014 to 18 February 2015 the epidemic was in recession compared with previous months, as indicated by the estimated Re of ∼ 0.77 (95% CI 0.72 to 0.82). From 18 February to 17 April 2015, the Re rose above criticality (∼ 1.98, 95% CI 1.33 to 2.22), flashing a note of caution for the situation. By projecting in time, we predicted that the epidemic would continue through July 2015. Our predictions were close to the cases reported by CDC by the end of June, verifying the criticality of the situation. In light of these developments, while revising our manuscript, we expanded our analysis to include the most recent data (until 15 August 2015). By mid-August, Re had fallen below criticality and the epidemic was expected to fade out by early December 2015. CONCLUSIONS: Our results call for the continuation of drastic control measures, which in the absence of an effective vaccine or therapy at present can only translate to isolation of the infected section of the population, to contain the epidemic.

Isolation of C. difficile Carriers Alone and as Part of a Bundle Approach for the Prevention of Clostridium difficile Infection (CDI): A Mathematical Model Based on Clinical Study Data.

Clostridium difficile infection is the most common hospital-acquired infection. Besides infected patients, carriers have emerged as a key player in C. difficile epidemiology. In this study, we evaluated the impact of identifying and isolating carriers upon hospital admission on the incidence of CDI incidence and hospital-acquired C. difficile colonization, as a single policy and as part of bundle approaches. We simulated C. difficile transmission using a stochastic mathematical approach, considering the contribution of carriers based on published literature. In the baseline scenario, CDI incidence was 6.18/1,000 admissions (95% CI, 5.72-6.65), simulating reported estimates from U.S. hospital discharges. The acquisition rate of C. difficile carriage was 9.72/1,000 admissions (95% CI, 9.15-10.31). Screening and isolation of colonized patients on admission to the hospital decreased CDI incidence to 4.99/1,000 admissions (95% CI, 4.59-5.42; relative reduction (RR) = 19.1%) and led to 36.2% reduction in the rate of hospital-acquired colonization. Simulating an antimicrobial stewardship program reduced CDI rate to 2.35/1,000 admissions (95% CI, 2.07-2.65). In sensitivity analysis, CDI incidence was less than 2.32/1,000 admissions (RR = 62.4%) in 95% of 1,000 simulations. The combined bundle, focusing on reducing C. difficile transmission from colonized patients and the individual risk of these patients to develop CDI, decreased significantly the incidence of both CDI and hospital-acquired colonization. Implementation of this bundle to current practice is expected to have an important impact in containing CDI.

Granger causality analysis reveals distinct spatio-temporal connectivity patterns in motor and perceptual visuo-spatial working memory.

We employed spectral Granger causality analysis on a full set of 56 electroencephalographic recordings acquired during the execution of either a 2D movement pointing or a perceptual (yes/no) change detection task with memory and non-memory conditions. On the basis of network characteristics across frequency bands, we provide evidence for the full dissociation of the corresponding cognitive processes. Movement-memory trial types exhibited higher degree nodes during the first 2 s of the delay period, mainly at central, left frontal and right-parietal areas. Change detection-memory trial types resulted in a three-peak temporal pattern of the total degree with higher degree nodes emerging mainly at central, right frontal, and occipital areas. Functional connectivity networks resulting from non-memory trial types were characterized by more sparse structures for both tasks. The movement-memory trial types encompassed an apparent coarse flow from frontal to parietal areas while the opposite flow from occipital, parietal to central and frontal areas was evident for the change detection-memory trial types. The differences among tasks and conditions were more profound in α (8-12 Hz) and ß (12-30 Hz) and less in γ (30-45 Hz) band. Our results favor the hypothesis which considers spatial working memory as a by-product of specific mental processes that engages common brain areas under different network organizations.

Mathematical modeling of infectious disease dynamics.

Over the last years, an intensive worldwide effort is speeding up the developments in the establishment of a global surveillance network for combating pandemics of emergent and re-emergent infectious diseases. Scientists from different fields extending from medicine and molecular biology to computer science and applied mathematics have teamed up for rapid assessment of potentially urgent situations. Toward this aim mathematical modeling plays an important role in efforts that focus on predicting, assessing, and controlling potential outbreaks. To better understand and model the contagious dynamics the impact of numerous variables ranging from the micro host-pathogen level to host-to-host interactions, as well as prevailing ecological, social, economic, and demographic factors across the globe have to be analyzed and thoroughly studied. Here, we present and discuss the main approaches that are used for the surveillance and modeling of infectious disease dynamics. We present the basic concepts underpinning their implementation and practice and for each category we give an annotated list of representative works.

On the effect of the path length of small-world networks on epidemic dynamics.

We show how one can trace in a systematic way the coarse-grained solutions of individual-based stochastic epidemic models evolving on heterogeneous complex networks with respect to their topological characteristics. In particular, we illustrate the "distinct" impact of the average path length (with respect to the degree and clustering distributions) on the emergent behavior of detailed epidemic models; to achieve this we have developed an algorithm that allows its tuning at will. The framework could be used to shed more light on the influence of weak social links on epidemic spread within small-world network structures, and ultimately to provide novel systematic computational modeling and exploration of better contagion control strategies.