Genetic characterization and implications for conservation of the last autochthonous Mouflon population in Europe

Population genetic studies provide accurate information on population structure, connectivity, and hybridization. These are key elements to identify units for conservation and define wildlife management strategies aimed to maintain and restore biodiversity. The Mediterranean island of Sardinia hosts one of the last autochthonous mouflon populations, descending from the wild Neolithic ancestor. The first mouflon arrived in Sardinia ~ 7000 years ago and thrived across the island until the twentieth century, when anthropogenic factors led to population fragmentation. We analysed the three main allopatric Sardinian mouflon sub-populations, namely: the native sub-populations of Montes Forest and Mount Tonneri, and the reintroduced sub-population of Mount Lerno. We investigated the spatial genetic structure of the Sardinian mouflon based on the parallel analysis of 14 highly polymorphic microsatellite loci and mitochondrial D-loop sequences. The Montes Forest sub-population was found to harbour the ancestral haplotype in the phylogeny of European mouflon. We detected high levels of relatedness in all the sub-populations and a mitochondrial signature of hybridization between the Mount Lerno sub-population and domestic sheep. Our findings provide useful insights to protect such an invaluable genetic heritage from the risk of genetic depletion by promoting controlled inter-population exchange and drawing informed repopulation plans sourcing from genetically pure mouflon stocks.

Study on Consumer Preference for Traceable Pork With Animal Welfare Attribute

We determined consumer preferences for traceable pork attributes in 328 consumers in Wuxi City, Jiangsu Province, China, based on a traceable pork attribute system composed of traceability, animal welfare, place of origin, and price attributes. Preference was studied using a Choice Experiment and Bayesian inference analysis. Results showed that the marginal utility of health welfare was lower than that of high-level traceability information and similar to that of place of origin but was higher than that of middle-level traceability information. A complementary relationship existed between dietary animal welfare and high-level traceability information and between health welfare and non-indigenous production. A substitution relationship existed between health welfare and indigenous production and between environmental animal welfare and non-indigenous production. The marginal utilities of health welfare and dietary welfare were higher than those of all price levels, and consumers accept a higher price as a result of increased production costs due to the inclusion of animal welfare information. Due to the harsh realities of COVID-19, China has recently approved the animal welfare attribute to be integrated into traceability market systems of new animal-derived food. The government should encourage manufacturers to produce diverse traceable animal-derived food not only to protect animal welfare and promote the construction of an ecological civilization, but also to develop new animal-derived food markets to satisfy different levels of consumer demand.

Direct extraction of signal and noise correlations from two-photon calcium imaging of ensemble neuronal activity

Neuronal activity correlations are key to understanding how populations of neurons collectively encode information. While two-photon calcium imaging has created a unique opportunity to record the activity of large populations of neurons, existing methods for inferring correlations from these data face several challenges. First, the observations of spiking activity produced by two-photon imaging are temporally blurred and noisy. Secondly, even if the spiking data were perfectly recovered via deconvolution, inferring network-level features from binary spiking data is a challenging task due to the non-linear relation of neuronal spiking to endogenous and exogenous inputs. In this work, we propose a methodology to explicitly model and directly estimate signal and noise correlations from two-photon fluorescence observations, without requiring intermediate spike deconvolution. We provide theoretical guarantees on the performance of the proposed estimator and demonstrate its utility through applications to simulated and experimentally recorded data from the mouse auditory cortex.

Does It Pay Off to Explicitly Link Functional Gene Expression to Denitrification Rates in Reaction Models?

Environmental omics and molecular-biological data have been proposed to yield improved quantitative predictions of biogeochemical processes. The abundances of functional genes and transcripts relate to the number of cells and activity of microorganisms. However, whether molecular-biological data can be quantitatively linked to reaction rates remains an open question. We present an enzyme-based denitrification model that simulates concentrations of transcription factors, functional-gene transcripts, enzymes, and solutes. We calibrated the model using experimental data from a well-controlled batch experiment with the denitrifier Paracoccous denitrificans. The model accurately predicts denitrification rates and measured transcript dynamics. The relationship between simulated transcript concentrations and reaction rates exhibits strong non-linearity and hysteresis related to the faster dynamics of gene transcription and substrate consumption, relative to enzyme production and decay. Hence, assuming a unique relationship between transcript-to-gene ratios and reaction rates, as frequently suggested, may be an erroneous simplification. Comparing model results of our enzyme-based model to those of a classical Monod-type model reveals that both formulations perform equally well with respect to nitrogen species, indicating only a low benefit of integrating molecular-biological data for estimating denitrification rates. Nonetheless, the enzyme-based model is a valuable tool to improve our mechanistic understanding of the relationship between biomolecular quantities and reaction rates. Furthermore, our results highlight that both enzyme kinetics (i.e., substrate limitation and inhibition) and gene expression or enzyme dynamics are important controls on denitrification rates.

Mixed-effect Bayesian network reveals personal effects of nutrition

Nutrition experts know by their experience that people can react very differently to the same nutrition. If we could systematically quantify these differences, it would enable more personal dietary understanding and guidance. This work proposes a mixed-effect Bayesian network as a method for modeling the multivariate system of nutrition effects. Estimation of this network reveals a system of both population-wide and personal correlations between nutrients and their biological responses. Fully Bayesian estimation in the method allows managing the uncertainty in parameters and incorporating the existing nutritional knowledge into the model. The method is evaluated by modeling data from a dietary intervention study, called Sysdimet, which contains personal observations from food records and the corresponding fasting concentrations of blood cholesterol, glucose, and insulin. The model's usefulness in nutritional guidance is evaluated by predicting personally if a given diet increases or decreases future levels of concentrations. The proposed method is shown to be comparable with the well-performing Extreme Gradient Boosting (XGBoost) decision tree method in classifying the directions of concentration increases and decreases. In addition to classification, we can also predict the precise concentration level and use the biologically interpretable model parameters to understand what personal effects contribute to the concentration. We found considerable personal differences in the contributing nutrients, and while these nutritional effects are previously known at a population level, recognizing their personal differences would result in more accurate estimates and more effective nutritional guidance.

Bayesian Random Tomography of Particle Systems

Random tomography is a common problem in imaging science and refers to the task of reconstructing a three-dimensional volume from two-dimensional projection images acquired in unknown random directions. We present a Bayesian approach to random tomography. At the center of our approach is a meshless representation of the unknown volume as a mixture of spherical Gaussians. Each Gaussian can be interpreted as a particle such that the unknown volume is represented by a particle cloud. The particle representation allows us to speed up the computation of projection images and to represent a large variety of structures accurately and efficiently. We develop Markov chain Monte Carlo algorithms to infer the particle positions as well as the unknown orientations. Posterior sampling is challenging due to the high dimensionality and multimodality of the posterior distribution. We tackle these challenges by using Hamiltonian Monte Carlo and a global rotational sampling strategy. We test the approach on various simulated and real datasets.

Tracking the time course of reproduction number and lockdown's effect on human behaviour during SARS-CoV-2 epidemic: nonparametric estimation

Understanding the SARS-CoV-2 dynamics has been subject of intense research in the last months. In particular, accurate modeling of lockdown effects on human behaviour and epidemic evolution is a key issue in order e.g. to inform health-care decisions on emergency management. In this regard, the compartmental and spatial models so far proposed use parametric descriptions of the contact rate, often assuming a time-invariant effect of the lockdown. In this paper we show that these assumptions may lead to erroneous evaluations on the ongoing pandemic. Thus, we develop a new class of nonparametric compartmental models able to describe how the impact of the lockdown varies in time. Our estimation strategy does not require significant Bayes prior information and exploits regularization theory. Hospitalized data are mapped into an infinite-dimensional space, hence obtaining a function which takes into account also how social distancing measures and people's growing awareness of infection's risk evolves as time progresses. This also permits to reconstruct a continuous-time profile of SARS-CoV-2 reproduction number with a resolution never reached before in the literature. When applied to data collected in Lombardy, the most affected Italian region, our model illustrates how people behaviour changed during the restrictions and its importance to contain the epidemic. Results also indicate that, at the end of the lockdown, around [Formula: see text] of people in Lombardy and [Formula: see text] in Italy was affected by SARS-CoV-2, with the fatality rate being 1.14%. Then, we discuss how the situation evolved after the end of the lockdown showing that the reproduction number dangerously increased in the summer, due to holiday relax, reaching values larger than one on August 1, 2020. Finally, we also document how Italy faced the second wave of infection in the last part of 2020. Since several countries still observe a growing epidemic and others could be subject to other waves, the proposed reproduction number tracking methodology can be of great help to health care authorities to prevent SARS-CoV-2 diffusion or to assess the impact of lockdown restrictions on human behaviour to contain the spread.

The mitochondrial genome of Stereolepis doederleini (Pempheriformes: Polyprionidae) and mitogenomic phylogeny of Pempheriformes

The complete mitochondrial (mt) genome of Stereolepis doederleini was sequenced from a specimen collected in a commercial aquarium in Jeju Island. The sequence was 16,513 base pairs in length and, similar to other vertebrate mt genomes, included 37 mt genes and a noncoding control region; the gene order was identical to that of typical vertebrate mt genome. Mitochondrial genome sequences of 17 species from 12 families were used to reconstruct phylogenetic relationships within the order Pempheriformes. The phylogenetic trees were constructed with three methods (neighbor joining [NJ], maximum likelihood [ML], and Bayesian method) using 12 protein coding genes, but not ND6. In all phylogenetic trees, Pempheriformes were clustered into three strongly supported clades. Two Acropomatidae species (Synagrops japonicus in clade-Ⅰ and Doederleinia berycoides in clade-Ⅲ) were polyphyletic; S. japonicus was close to Lateolabracidae and was the sister of Glaucosomatidae + (Pempheridae/(Percophidae+Creediidae)), and D. berycoides was sister to Howellidae + Epigonidae. All phylogenetic trees supported a sister relationship between Creediidae and Percophidae in clade-Ⅰ. Glaucosomatidae formed a sister clade with Pempheridae. The relationships within clade-Ⅱ, which was composed of four families (Pentacerotidae, Polyprionidae, Banjosidae, and Bathyclupeidae), slightly differed between NJ/ML and BI tree topologies. In clade-Ⅲ, the relationships among Howellidae, Epigonidae, and Acropomatidae were strongly supported.

Low Complexity Robust Data Demodulation for GNSS

In this article, we provide closed-form approximations of log-likelihood ratio (LLR) values for direct sequence spread spectrum (DS-SS) systems over three particular scenarios, which are commonly found in the Global Navigation Satellite System (GNSS) environment. Those scenarios are the open sky with smooth variation of the signal-to-noise ratio (SNR), the additive Gaussian interference, and pulsed jamming. In most of the current communications systems, block-wise estimators are considered. However, for some applications such as GNSSs, symbol-wise estimators are available due to the low data rate. Usually, the noise variance is considered either perfectly known or available through symbol-wise estimators, leading to possible mismatched demodulation, which could induce errors in the decoding process. In this contribution, we first derive two closed-form expressions for LLRs in additive white Gaussian and Laplacian noise channels, under noise uncertainty, based on conjugate priors. Then, assuming those cases where the statistical knowledge about the estimation error is characterized by a noise variance following an inverse log-normal distribution, we derive the corresponding closed-form LLR approximations. The relevance of the proposed expressions is investigated in the context of the GPS L1C signal where the clock and ephemeris data (CED) are encoded with low-density parity-check (LDPC) codes. Then, the CED is iteratively decoded based on the belief propagation (BP) algorithm. Simulation results show significant frame error rate (FER) improvement compared to classical approaches not accounting for such uncertainty.

Estimating Similarity of Dose-Response Relationships in Phase I Clinical Trials-Case Study in Bridging Data Package

Bridging studies are designed to fill the gap between two populations in terms of clinical trial data, such as toxicity, efficacy, comorbidities and doses. According to ICH-E5 guidelines, clinical data can be extrapolated from one region to another if dose–reponse curves are similar between two populations. For instance, in Japan, Phase I clinical trials are often repeated due to this physiological/metabolic paradigm: the maximum tolerated dose (MTD) for Japanese patients is assumed to be lower than that for Caucasian patients, but not necessarily for all molecules. Therefore, proposing a statistical tool evaluating the similarity between two populations dose–response curves is of most interest. The aim of our work is to propose several indicators to evaluate the distance and the similarity of dose–toxicity curves and MTD distributions at the end of some of the Phase I trials, conducted on two populations or regions. For this purpose, we extended and adapted the commensurability criterion, initially proposed by Ollier et al. (2019), in the setting of completed phase I clinical trials. We evaluated their performance using three synthetic sets, built as examples, and six case studies found in the literature. Visualization plots and guidelines on the way to interpret the results are proposed.

Sample Size Requirements for Calibrated Approximate Credible Intervals for Proportions in Clinical Trials

In Bayesian analysis of clinical trials data, credible intervals are widely used for inference on unknown parameters of interest, such as treatment effects or differences in treatments effects. Highest Posterior Density (HPD) sets are often used because they guarantee the shortest length. In most of standard problems, closed-form expressions for exact HPD intervals do not exist, but they are available for intervals based on the normal approximation of the posterior distribution. For small sample sizes, approximate intervals may be not calibrated in terms of posterior probability, but for increasing sample sizes their posterior probability tends to the correct credible level and they become closer and closer to exact sets. The article proposes a predictive analysis to select appropriate sample sizes needed to have approximate intervals calibrated at a pre-specified level. Examples are given for interval estimation of proportions and log-odds.

Bayesian Learning of Shifted-Scaled Dirichlet Mixture Models and Its Application to Early COVID-19 Detection in Chest X-ray Images

Early diagnosis and assessment of fatal diseases and acute infections on chest X-ray (CXR) imaging may have important therapeutic implications and reduce mortality. In fact, many respiratory diseases have a serious impact on the health and lives of people. However, certain types of infections may include high variations in terms of contrast, size and shape which impose a real challenge on classification process. This paper introduces a new statistical framework to discriminate patients who are either negative or positive for certain kinds of virus and pneumonia. We tackle the current problem via a fully Bayesian approach based on a flexible statistical model named shifted-scaled Dirichlet mixture models (SSDMM). This mixture model is encouraged by its effectiveness and robustness recently obtained in various image processing applications. Unlike frequentist learning methods, our developed Bayesian framework has the advantage of taking into account the uncertainty to accurately estimate the model parameters as well as the ability to solve the problem of overfitting. We investigate here a Markov Chain Monte Carlo (MCMC) estimator, which is a computer–driven sampling method, for learning the developed model. The current work shows excellent results when dealing with the challenging problem of biomedical image classification. Indeed, extensive experiments have been carried out on real datasets and the results prove the merits of our Bayesian framework.

Predicting Rice Heading Date Using an Integrated Approach Combining a Machine Learning Method and a Crop Growth Model

Accurate prediction of heading date under various environmental conditions is expected to facilitate the decision-making process in cultivation management and the breeding process of new cultivars adaptable to the environment. Days to heading (DTH) is a complex trait known to be controlled by multiple genes and genotype-by-environment interactions. Crop growth models (CGMs) have been widely used to predict the phenological development of a plant in an environment; however, they usually require substantial experimental data to calibrate the parameters of the model. The parameters are mostly genotype-specific and are thus usually estimated separately for each cultivar. We propose an integrated approach that links genotype marker data with the developmental genotype-specific parameters of CGMs with a machine learning model, and allows heading date prediction of a new genotype in a new environment. To estimate the parameters, we implemented a Bayesian approach with the advanced Markov chain Monte-Carlo algorithm called the differential evolution adaptive metropolis and conducted the estimation using a large amount of data on heading date and environmental variables. The data comprised sowing and heading dates of 112 cultivars/lines tested at 7 locations for 14 years and the corresponding environmental variables (day length and daily temperature). We compared the predictive accuracy of DTH between the proposed approach, a CGM, and a single machine learning model. The results showed that the extreme learning machine (one of the implemented machine learning models) was superior to the CGM for the prediction of a tested genotype in a tested location. The proposed approach outperformed the machine learning method in the prediction of an untested genotype in an untested location. We also evaluated the potential of the proposed approach in the prediction of the distribution of DTH in 103 F₂ segregation populations derived from crosses between a common parent, Koshihikari, and 103 cultivars/lines. The results showed a high correlation coefficient (ca. 0.8) of the 10, 50, and 90th percentiles of the observed and predicted distribution of DTH. In this study, the integration of a machine learning model and a CGM was better able to predict the heading date of a new rice cultivar in an untested potential environment.

Corrigendum: A Probabilistic Framework for Decoding Behavior From in vivo Calcium Imaging Data

[This corrects the article DOI: 10.3389/fncir.2020.00019.].

Bayesian inference for biophysical neuron models enables stimulus optimization for retinal neuroprosthetics

While multicompartment models have long been used to study the biophysics of neurons, it is still challenging to infer the parameters of such models from data including uncertainty estimates. Here, we performed Bayesian inference for the parameters of detailed neuron models of a photoreceptor and an OFF- and an ON-cone bipolar cell from the mouse retina based on two-photon imaging data. We obtained multivariate posterior distributions specifying plausible parameter ranges consistent with the data and allowing to identify parameters poorly constrained by the data. To demonstrate the potential of such mechanistic data-driven neuron models, we created a simulation environment for external electrical stimulation of the retina and optimized stimulus waveforms to target OFF- and ON-cone bipolar cells, a current major problem of retinal neuroprosthetics.

A machine learning Automated Recommendation Tool for synthetic biology

Synthetic biology allows us to bioengineer cells to synthesize novel valuable molecules such as renewable biofuels or anticancer drugs. However, traditional synthetic biology approaches involve ad-hoc engineering practices, which lead to long development times. Here, we present the Automated Recommendation Tool (ART), a tool that leverages machine learning and probabilistic modeling techniques to guide synthetic biology in a systematic fashion, without the need for a full mechanistic understanding of the biological system. Using sampling-based optimization, ART provides a set of recommended strains to be built in the next engineering cycle, alongside probabilistic predictions of their production levels. We demonstrate the capabilities of ART on simulated data sets, as well as experimental data from real metabolic engineering projects producing renewable biofuels, hoppy flavored beer without hops, fatty acids, and tryptophan. Finally, we discuss the limitations of this approach, and the practical consequences of the underlying assumptions failing.

Training deep neural density estimators to identify mechanistic models of neural dynamics

Mechanistic modeling in neuroscience aims to explain observed phenomena in terms of underlying causes. However, determining which model parameters agree with complex and stochastic neural data presents a significant challenge. We address this challenge with a machine learning tool which uses deep neural density estimators-trained using model simulations-to carry out Bayesian inference and retrieve the full space of parameters compatible with raw data or selected data features. Our method is scalable in parameters and data features and can rapidly analyze new data after initial training. We demonstrate the power and flexibility of our approach on receptive fields, ion channels, and Hodgkin-Huxley models. We also characterize the space of circuit configurations giving rise to rhythmic activity in the crustacean stomatogastric ganglion, and use these results to derive hypotheses for underlying compensation mechanisms. Our approach will help close the gap between data-driven and theory-driven models of neural dynamics.

Visualizing the invisible: The effect of asymptomatic transmission on the outbreak dynamics of COVID-19

Understanding the outbreak dynamics of the COVID-19 pandemic has important implications for successful containment and mitigation strategies. Recent studies suggest that the population prevalence of SARS-CoV-2 antibodies, a proxy for the number of asymptomatic cases, could be an order of magnitude larger than expected from the number of reported symptomatic cases. Knowing the precise prevalence and contagiousness of asymptomatic transmission is critical to estimate the overall dimension and pandemic potential of COVID-19. However, at this stage, the effect of the asymptomatic population, its size, and its outbreak dynamics remain largely unknown. Here we use reported symptomatic case data in conjunction with antibody seroprevalence studies, a mathematical epidemiology model, and a Bayesian framework to infer the epidemiological characteristics of COVID-19. Our model computes, in real time, the time-varying contact rate of the outbreak, and projects the temporal evolution and credible intervals of the effective reproduction number and the symptomatic, asymptomatic, and recovered populations. Our study quantifies the sensitivity of the outbreak dynamics of COVID-19 to three parameters: the effective reproduction number, the ratio between the symptomatic and asymptomatic populations, and the infectious periods of both groups For nine distinct locations, our model estimates the fraction of the population that has been infected and recovered by Jun 15, 2020 to 24.15% (95% CI: 20.48%-28.14%) for Heinsberg (NRW, Germany), 2.40% (95% CI: 2.09%-2.76%) for Ada County (ID, USA), 46.19% (95% CI: 45.81%-46.60%) for New York City (NY, USA), 11.26% (95% CI: 7.21%-16.03%) for Santa Clara County (CA, USA), 3.09% (95% CI: 2.27%-4.03%) for Denmark, 12.35% (95% CI: 10.03%-15.18%) for Geneva Canton (Switzerland), 5.24% (95% CI: 4.84%-5.70%) for the Netherlands, 1.53% (95% CI: 0.76%-2.62%) for Rio Grande do Sul (Brazil), and 5.32% (95% CI: 4.77%-5.93%) for Belgium. Our method traces the initial outbreak date in Santa Clara County back to January 20, 2020 (95% CI: December 29, 2019 - February 13, 2020). Our results could significantly change our understanding and management of the COVID-19 pandemic: A large asymptomatic population will make isolation, containment, and tracing of individual cases challenging. Instead, managing community transmission through increasing population awareness, promoting physical distancing, and encouraging behavioral changes could become more relevant.

Impact of the Mid-Pleistocene Revolution and Anthropogenic Factors on the Dispersion of Asian Black-Spined Toads (Duttaphrynus melanostictus)

Divergence-time estimation critically improves the understanding of biogeography processes underlying the distribution of species, especially when fossil data is not available. We hypothesise that the Asian black-spined toad, Duttaphrynus melanostictus, expanded into the Eastern Indomalaya following the Quaternary glaciations with the subsequent colonisation of new landscapes during the Last Glacial Maximum. Divergence dating inferred from 364 sequences of mitochondrial tRNAGly ND3 supported the emergence of a common ancestor to the three D. melanostictus clades around 1.85 (±0.77) Ma, matching with the Lower to Mid-Pleistocene transition. Duttaphrynus melanostictus then dispersed into Southeast Asia from the central Indo-Pacific and became isolated in the Southern Sundaic and Wallacea regions 1.43 (±0.10) Ma through vicariance as a result of sea level oscillations. The clade on the Southeast Asian mainland then colonised the peninsula from Myanmar to Vietnam and expanded towards Southeastern China at the end of the Mid-Pleistocene Revolution 0.84 (±0.32) Ma. Population dynamics further highlight an expansion of the Southeast Asian mainland population towards Taiwan, the Northeastern edge of the species' range after the last interglacial, and during the emergence of the Holocene human settlements around 7000 BP. Thus, the current divergence of D. melanostictus into three segregated clades was mostly shaped by Quaternary glaciations, followed by natural dispersion events over land bridges and accelerated by anthropogenic activities.

Estimating the Size of a COVID-19 Epidemic from Surveillance Systems

Public health policy makers in countries with Coronavirus Disease 2019 (COVID-19) outbreaks face the decision of when to switch from measures that seek to contain and eliminate the outbreak to those designed to mitigate its effects. Estimates of epidemic size are complicated by surveillance systems that cannot capture all cases, and by the need for timely estimates as the epidemic is ongoing. This article provides a Bayesian methodology to estimate outbreak size from one or more surveillance systems such as virologic testing of pneumonia cases or samples from a network of general practitioners.

Hippocampal remapping as hidden state inference

Cells in the hippocampus tuned to spatial location (place cells) typically change their tuning when an animal changes context, a phenomenon known as remapping. A fundamental challenge to understanding remapping is the fact that what counts as a ‘‘context change’’ has never been precisely defined. Furthermore, different remapping phenomena have been classified on the basis of how much the tuning changes after different types and degrees of context change, but the relationship between these variables is not clear. We address these ambiguities by formalizing remapping in terms of hidden state inference. According to this view, remapping does not directly reflect objective, observable properties of the environment, but rather subjective beliefs about the hidden state of the environment. We show how the hidden state framework can resolve a number of puzzles about the nature of remapping.

A Probabilistic Framework for Decoding Behavior From in vivo Calcium Imaging Data

Understanding the role of neuronal activity in cognition and behavior is a key question in neuroscience. Previously, in vivo studies have typically inferred behavior from electrophysiological data using probabilistic approaches including Bayesian decoding. While providing useful information on the role of neuronal subcircuits, electrophysiological approaches are often limited in the maximum number of recorded neurons as well as their ability to reliably identify neurons over time. This can be particularly problematic when trying to decode behaviors that rely on large neuronal assemblies or rely on temporal mechanisms, such as a learning task over the course of several days. Calcium imaging of genetically encoded calcium indicators has overcome these two issues. Unfortunately, because calcium transients only indirectly reflect spiking activity and calcium imaging is often performed at lower sampling frequencies, this approach suffers from uncertainty in exact spike timing and thus activity frequency, making rate-based decoding approaches used in electrophysiological recordings difficult to apply to calcium imaging data. Here we describe a probabilistic framework that can be used to robustly infer behavior from calcium imaging recordings and relies on a simplified implementation of a naive Baysian classifier. Our method discriminates between periods of activity and periods of inactivity to compute probability density functions (likelihood and posterior), significance and confidence interval, as well as mutual information. We next devise a simple method to decode behavior using these probability density functions and propose metrics to quantify decoding accuracy. Finally, we show that neuronal activity can be predicted from behavior, and that the accuracy of such reconstructions can guide the understanding of relationships that may exist between behavioral states and neuronal activity.

Robust Empirical Bayesian Reconstruction of Distributed Sources for Electromagnetic Brain Imaging

Electromagnetic brain imaging is the reconstruction of brain activity from non-invasive recordings of the magnetic fields and electric potentials. An enduring challenge in this imaging modality is estimating the number, location, and time course of sources, especially for the reconstruction of distributed brain sources with complex spatial extent. Here, we introduce a novel robust empirical Bayesian algorithm that enables better reconstruction of distributed brain source activity with two key ideas: kernel smoothing and hyperparameter tiling. Since the proposed algorithm builds upon many of the performance features of the sparse source reconstruction algorithm - Champagne and we refer to this algorithm as Smooth Champagne. Smooth Champagne is robust to the effects of high levels of noise, interference, and highly correlated brain source activity. Simulations demonstrate excellent performance of Smooth Champagne when compared to benchmark algorithms in accurately determining the spatial extent of distributed source activity. Smooth Champagne also accurately reconstructs real MEG and EEG data.

Retrospective Inference as a Form of Bounded Rationality, and Its Beneficial Influence on Learning

Probabilistic models of cognition typically assume that agents make inferences about current states by combining new sensory information with fixed beliefs about the past, an approach known as Bayesian filtering. This is computationally parsimonious, but, in general, leads to suboptimal beliefs about past states, since it ignores the fact that new observations typically contain information about the past as well as the present. This is disadvantageous both because knowledge of past states may be intrinsically valuable, and because it impairs learning about fixed or slowly changing parameters of the environment. For these reasons, in offline data analysis it is usual to infer on every set of states using the entire time series of observations, an approach known as (fixed-interval) Bayesian smoothing. Unfortunately, however, this is impractical for real agents, since it requires the maintenance and updating of beliefs about an ever-growing set of states. We propose an intermediate approach, finite retrospective inference (FRI), in which agents perform update beliefs about a limited number of past states (Formally, this represents online fixed-lag smoothing with a sliding window). This can be seen as a form of bounded rationality in which agents seek to optimize the accuracy of their beliefs subject to computational and other resource costs. We show through simulation that this approach has the capacity to significantly increase the accuracy of both inference and learning, using a simple variational scheme applied to both randomly generated Hidden Markov models (HMMs), and a specific application of the HMM, in the form of the widely used probabilistic reversal task. Our proposal thus constitutes a theoretical contribution to normative accounts of bounded rationality, which makes testable empirical predictions that can be explored in future work.

Noninvasive Reconstruction of Transmural Transmembrane Potential With Simultaneous Estimation of Prior Model Error

To reconstruct electrical activity in the heart from body-surface electrocardiograms (ECGs) is an ill-posed inverse problem. Electrophysiological models have been found effective in regularizing these inverse problems by incorporating a priori knowledge about how the electrical potential in the heart propagates over time. However, these models suffer from model errors arising from, for example, parameters associated with tissue properties and the earliest sites of excitation. We present a Bayesian approach to simultaneously estimate transmembrane potential (TMP) signals and prior model errors, exploiting sparsity of the error in the gradient domain in the form of a novel sparse prior based on variational lower bound of the generalized Gaussian distribution. In synthetic and real-data experiments, we demonstrate the improvement of accuracy in TMP reconstruction brought by simultaneous model error estimation. We further provide theoretical and empirical justifications for the change of performances in the presented method at the presence of different model errors.