Model-Driven Analysis of ECG Using Reinforcement Learning

Modeling is essential to better understand the generative mechanisms responsible for experimental observations gathered from complex systems. In this work, we are using such an approach to analyze the electrocardiogram (ECG). We present a systematic framework to decompose ECG signals into sums of overlapping lognormal components. We use reinforcement learning to train a deep neural network to estimate the modeling parameters from an ECG recorded in babies from 1 to 24 months of age. We demonstrate this model-driven approach by showing how the extracted parameters vary with age. From the 751,510 PQRST complexes modeled, 82.7% provided a signal-to-noise ratio that was sufficient for further analysis (>5 dB). After correction for multiple tests, 10 of the 24 modeling parameters exhibited statistical significance below the 0.01 threshold, with absolute Kendall rank correlation coefficients in the [0.27, 0.51] range. These results confirm that this model-driven approach can capture sensitive ECG parameters. Due to its physiological interpretability, this approach can provide a window into latent variables which are important for understanding the heart-beating process and its control by the autonomous nervous system.

BRAQUE: Bayesian Reduction for Amplified Quantization in UMAP Embedding

Single-cell biology has revolutionized the way we understand biological processes. In this paper, we provide a more tailored approach to clustering and analyzing spatial single-cell data coming from immunofluorescence imaging techniques. We propose Bayesian Reduction for Amplified Quantization in UMAP Embedding (BRAQUE) as an integrative novel approach, from data preprocessing to phenotype classification. BRAQUE starts with an innovative preprocessing, named Lognormal Shrinkage, which is able to enhance input fragmentation by fitting a lognormal mixture model and shrink each component towards its median, in order to help further the clustering step in finding more separated and clear clusters. Then, BRAQUE's pipeline consists of a dimensionality reduction step performed using UMAP, and a clustering performed using HDBSCAN on UMAP embedding. In the end, clusters are assigned to a cell type by experts, using effects size measures to rank markers and identify characterizing markers (Tier 1), and possibly characterize markers (Tier 2). The number of total cell types in one lymph node detectable with these technologies is unknown and difficult to predict or estimate. Therefore, with BRAQUE, we achieved a higher granularity than other similar algorithms such as PhenoGraph, following the idea that merging similar clusters is easier than splitting unclear ones into clear subclusters.

Estimation of a Minimum Allowable Structural Strength Based on Uncertainty in Material Test Data

Three types of uncertainties exist in the estimation of the minimum fracture strength of a full-scale component or structure size. The first, to be called the "model selection uncertainty," is in selecting a statistical distribution that best fits the laboratory test data. The second, to be called the "laboratory-scale strength uncertainty," is in estimating model parameters of a specific distribution from which the minimum failure strength of a material at a certain confidence level is estimated using the laboratory test data. To extrapolate the laboratory-scale strength prediction to that of a full-scale component, a third uncertainty exists that can be called the "full-scale strength uncertainty." In this paper, we develop a three-step approach to estimating the minimum strength of a full-scale component using two metrics: One metric is based on six goodness-of-fit and parameter-estimation-method criteria, and the second metric is based on the uncertainty quantification of the so-called A-basis design allowable (99 % coverage at 95 % level of confidence) of the full-scale component. The three steps of our approach are: (1) Find the "best" model for the sample data from a list of five candidates, namely, normal, two-parameter Weibull, three-parameter Weibull, two-parameter lognormal, and three-parameter lognormal. (2) For each model, estimate (2a) the parameters of that model with uncertainty using the sample data, and (2b) the minimum strength at the laboratory scale at 95 % level of confidence. (3) Introduce the concept of "coverage" and estimate the fullscale allowable minimum strength of the component at 95 % level of confidence for two types of coverages commonly used in the aerospace industry, namely, 99 % (A-basis for critical parts) and 90 % (B-basis for less critical parts). This uncertainty-based approach is novel in all three steps: In step-1 we use a composite goodness-of-fit metric to rank and select the "best" distribution, in step-2 we introduce uncertainty quantification in estimating the parameters of each distribution, and in step-3 we introduce the concept of an uncertainty metric based on the estimates of the upper and lower tolerance limits of the so-called A-basis design allowable minimum strength. To illustrate the applicability of this uncertainty-based approach to a diverse group of data, we present results of our analysis for six sets of laboratory failure strength data from four engineering materials. A discussion of the significance and limitations of this approach and some concluding remarks are included.

Why Firing Rate Distributions Are Important for Understanding Spinal Central Pattern Generators

Networks in the spinal cord, which are responsible for the generation of rhythmic movements, commonly known as central pattern generators (CPGs), have remained elusive for decades. Although it is well-known that many spinal neurons are rhythmically active, little attention has been given to the distribution of firing rates across the population. Here, we argue that firing rate distributions can provide an important clue to the organization of the CPGs. The data that can be gleaned from the sparse literature indicate a firing rate distribution, which is skewed toward zero with a long tail, akin to a normal distribution on a log-scale, i.e., a “log-normal” distribution. Importantly, such a shape is difficult to unite with the widespread assumption of modules composed of recurrently connected excitatory neurons. Spinal modules with recurrent excitation has the propensity to quickly escalate their firing rate and reach the maximum, hence equalizing the spiking activity across the population. The population distribution of firing rates hence would consist of a narrow peak near the maximum. This is incompatible with experiments, that show wide distributions and a peak close to zero. A way to resolve this puzzle is to include recurrent inhibition internally in each CPG modules. Hence, we investigate the impact of recurrent inhibition in a model and find that the firing rate distributions are closer to the experimentally observed. We therefore propose that recurrent inhibition is a crucial element in motor circuits, and suggest that future models of motor circuits should include recurrent inhibition as a mandatory element.

Treatment effect estimators for count data models

In this paper, we consider a switching regression model with count data outcomes, where the possible outcome differs across two alternate states and individuals endogenously select one of the states. We assume lognormal latent heterogeneity. Building on the switching regression model, we derive estimators of various treatment effects: the average treatment effect, the average treatment effect on the treated, the local average treatment effect, and the marginal treatment effect. We illustrate an application that examines the effects of public insurance on the number of doctor visits using the data employed by previous studies.

Lognormal Approximations of Fault Tree Uncertainty Distributions

Fault trees are used in reliability modeling to create logical models of fault combinations that can lead to undesirable events. The output of a fault tree analysis (the top event probability) is expressed in terms of the failure probabilities of basic events that are input to the model. Typically, the basic event probabilities are not known exactly, but are modeled as probability distributions: therefore, the top event probability is also represented as an uncertainty distribution. Monte Carlo methods are generally used for evaluating the uncertainty distribution, but such calculations are computationally intensive and do not readily reveal the dominant contributors to the uncertainty. In this article, a closed-form approximation for the fault tree top event uncertainty distribution is developed, which is applicable when the uncertainties in the basic events of the model are lognormally distributed. The results of the approximate method are compared with results from two sampling-based methods: namely, the Monte Carlo method and the Wilks method based on order statistics. It is shown that the closed-form expression can provide a reasonable approximation to results obtained by Monte Carlo sampling, without incurring the computational expense. The Wilks method is found to be a useful means of providing an upper bound for the percentiles of the uncertainty distribution while being computationally inexpensive compared with full Monte Carlo sampling. The lognormal approximation method and Wilks's method appear attractive, practical alternatives for the evaluation of uncertainty in the output of fault trees and similar multilinear models.

On the origin of lognormal network synchrony in CA1

The sharp wave ripple complex in rodent hippocampus is associated with a network burst in CA3 (NB) that triggers a synchronous event in the CA1 population (SE). The number of CA1 pyramidal cells participating in a SE has been observed to follow a lognormal distribution. However, the origin of this skewed and heavy-tailed distribution of population synchrony in CA1 remains unknown. Because the size of SEs is likely to originate from the size of the NBs and the underlying neural circuitry, we model the CA3-CA1 circuit to study the underlying mechanisms and their functional implications. We show analytically that if the size of a NB in CA3 is distributed according to a normal distribution, then the size of the resulting SE in CA1 follows a lognormal distribution. Our model predicts the distribution of the NB size in CA3, which remains to be tested experimentally. Moreover, we show that a putative lognormal NB size distribution leads to an extremely heavy-tailed SE size distribution in CA1, contradicting experimental evidence. In conclusion, our model provides general insight on the origin of lognormally distributed network synchrony as a consequence of synchronous synaptic transmission of normally distributed input events.

The Spinal Neurons Exhibit an ON-OFF and OFF-ON Firing Activity Around the Onset of Fictive Scratching Episodes in the Cat

In a previous report, we found neurons with ON-OFF and OFF-ON firing activity in the obex reticular formation during scratching. The aim of the present study was to examine whether the spinal neurons also exhibit this type of activity in relation to the “postural stage” of fictive scratching in the cat. We found that the extensor and intermediate scratching neurons exhibit an ON-OFF firing rate; conversely, the flexor neurons show an OFF-ON activity, relative to every scratching episode. These patterns of spiking activity are similar to those found in neurons from the obex reticular formation during scratching. Our findings provide support to the following hypotheses. First, there is a possible functional link between supraspinal and spinal, ON-OFF and OFF-ON neuronal groups. Second, the fictive goal-directed motor action to maintain the fictive “postural stage” of the hindlimb during fictive scratching is associated with the neuronal tonic activity of the OFF-ON spinal neurons, whereas the ON-OFF spinal neurons are associated with an extensor tone that occurred prior the postural stage.

Neuronal Population Activity in Spinal Motor Circuits: Greater Than the Sum of Its Parts

The core elements of stereotypical movements such as locomotion, scratching and breathing are generated by networks in the lower brainstem and the spinal cord. Ensemble activities in spinal motor networks had until recently been merely a black box, but with the emergence of ultra-thin Silicon multi-electrode technology it was possible to reveal the spiking activity of larger parts of the network. A series of experiments revealed unexpected features of spinal networks, such as multiple spiking regimes and lognormal firing rate distributions. The lognormality renders the widespread idea of a typical firing rate ± standard deviation an ill-suited description, and therefore these findings define a new arithmetic of motor networks. Focusing on the population activity behind motor pattern generation this review summarizes this advance and discusses its implications.

Pyramidal Cell-Interneuron Circuit Architecture and Dynamics in Hippocampal Networks

Excitatory control of inhibitory neurons is poorly understood due to the difficulty of studying synaptic connectivity in vivo. We inferred such connectivity through analysis of spike timing and validated this inference using juxtacellular and optogenetic control of presynaptic spikes in behaving mice. We observed that neighboring CA1 neurons had stronger connections and that superficial pyramidal cells projected more to deep interneurons. Connection probability and strength were skewed, with a minority of highly connected hubs. Divergent presynaptic connections led to synchrony between interneurons. Synchrony of convergent presynaptic inputs boosted postsynaptic drive. Presynaptic firing frequency was read out by postsynaptic neurons through short-term depression and facilitation, with individual pyramidal cells and interneurons displaying a diversity of spike transmission filters. Additionally, spike transmission was strongly modulated by prior spike timing of the postsynaptic cell. These results bridge anatomical structure with physiological function.

Comparison of Weibull and Lognormal Cure Models with Cox in the Survival Analysis Of Breast Cancer Patients in Rafsanjan

Background: Breast cancer is the most common cancer after lung cancer and the second cause of death. In this study we compared Weibull and Lognormal Cure Models with Cox regression on the survival of breast cancer.

Study design: A cohort study.

Methods: The current study retrospective cohort study was conducted on 140 patients referred to Ali Ibn Abitaleb Hospital, Rafsanjan southeastern Iran from 2001 to 2015 suffering from breast cancer. We determined and analyzed the effective survival causes by different models using STATA14.

Results: According to AIC, log-normal model was more consistent than Weibull. In the multivariable Lognormal model, the effective factors like smoking, second -hand smoking, drinking herbal tea and the last breast-feeding period were included. In addition, using Cox regression factors of significant were the disease grade, size of tumor and its metastasis (P-value<0.05). As Rafsanjan is surrounded by pistachio orchards and pesticides applied by farmers, people of this city are exposed to agricultural pesticides and its harmful consequences. The effect of the pesticide on breast cancer was studied and the results showed that the effect of pesticides on breast cancer was not in agreement with the models used in this study.

Conclusions: Based on different methods for survival analysis, researchers can decide how they can reach a better conclusion. This comparison indicates the result of semi-parametric Cox method is closer to clinical experiences evidences.

The Goldilocks zone in neural circuits

How do networks of neurons remain both stable and sensitive to new inputs?

Lognormal firing rate distribution reveals prominent fluctuation-driven regime in spinal motor networks

When spinal circuits generate rhythmic movements it is important that the neuronal activity remains within stable bounds to avoid saturation and to preserve responsiveness. Here, we simultaneously record from hundreds of neurons in lumbar spinal circuits of turtles and establish the neuronal fraction that operates within either a 'mean-driven' or a 'fluctuation-driven' regime. Fluctuation-driven neurons have a 'supralinear' input-output curve, which enhances sensitivity, whereas the mean-driven regime reduces sensitivity. We find a rich diversity of firing rates across the neuronal population as reflected in a lognormal distribution and demonstrate that half of the neurons spend at least 50 % of the time in the 'fluctuation-driven' regime regardless of behavior. Because of the disparity in input-output properties for these two regimes, this fraction may reflect a fine trade-off between stability and sensitivity in order to maintain flexibility across behaviors.

Lognormal Lorenz and normal receiver operating characteristic curves as mirror images

The Lorenz curve for assessing economic inequality depicts the relation between two cumulative distribution functions (CDFs), one for the distribution of incomes or wealth and the other for their first-moment distribution. By contrast, the receiver operating characteristic (ROC) curve for evaluating diagnostic systems depicts the relation between the complements of two CDFs, one for the distribution noise and the other for the distribution of signal plus noise. We demonstrate that the lognormal model of the Lorenz curve, which is often adopted to model the distribution of income and wealth, is a mirror image of the equal-variance normal model of the ROC curve, which is a fundamental model for evaluating diagnostic systems. The relationship between these two models extends the potential application of each. For example, the lognormal Lorenz curve can be used to evaluate diagnostic systems derived from equal-variance normal distributions.

Interactions dominate the dynamics of visual cognition

Many cognitive theories have described behavior as the summation of independent contributions from separate components. Contrasting views have emphasized the importance of multiplicative interactions and emergent structure. We describe a statistical approach to distinguishing additive and multiplicative processes and apply it to the dynamics of eye movements during classic visual cognitive tasks. The results reveal interaction-dominant dynamics in eye movements in each of the three tasks, and that fine-grained eye movements are modulated by task constraints. These findings reveal the interactive nature of cognitive processing and are consistent with theories that view cognition as an emergent property of processes that are broadly distributed over many scales of space and time rather than a componential assembly line.

Characterizing pulmonary blood flow distribution measured using arterial spin labeling

The arterial spin labeling (ASL) method provides images in which, ideally, the signal intensity of each image voxel is proportional to the local perfusion. For studies of pulmonary perfusion, the relative dispersion (RD, standard deviation/mean) of the ASL signal across a lung section is used as a reliable measure of flow heterogeneity. However, the RD of the ASL signals within the lung may systematically differ from the true RD of perfusion because the ASL image also includes signals from larger vessels, which can reflect the blood volume rather than blood flow if the vessels are filled with tagged blood during the imaging time. Theoretical studies suggest that the pulmonary vasculature exhibits a lognormal distribution for blood flow and thus an appropriate measure of heterogeneity is the geometric standard deviation (GSD). To test whether the ASL signal exhibits a lognormal distribution for pulmonary blood flow, determine whether larger vessels play an important role in the distribution, and extract physiologically relevant measures of heterogeneity from the ASL signal, we quantified the ASL signal before and after an intervention (head-down tilt) in six subjects. The distribution of ASL signal was better characterized by a lognormal distribution than a normal distribution, reducing the mean squared error by 72% (p < 0.005). Head-down tilt significantly reduced the lognormal scale parameter (p = 0.01) but not the shape parameter or GSD. The RD increased post-tilt and remained significantly elevated (by 17%, p < 0.05). Test case results and mathematical simulations suggest that RD is more sensitive than the GSD to ASL signal from tagged blood in larger vessels, a probable explanation of the change in RD without a statistically significant change in GSD. This suggests that the GSD is a useful measure of pulmonary blood flow heterogeneity with the advantage of being less affected by the ASL signal from tagged blood in larger vessels.

Prevalence, Incidence, and Severity of Sorghum Diseases in Western Kenya

To assess the prevalence and severity of sorghum diseases in western Kenya, a 2-year survey was conducted (July 1995 and 1996), in 91 and 109 farmers' fields, respectively. Fields were generally <0.5 ha and production environment ranged from warm-humid to warm-semi-arid. Fourteen foliar and six panicle diseases were observed, with limited variation in disease prevalence and severity between the 2 years. The most common foliar diseases observed were (in decreasing order of prevalence) oval leaf spot (Ramulispora sorghicola), rust (Puccinia purpurea), ladder leaf spot (Cercospora fusimaculans), zonate leaf spot (Gloeocercospora sorghi), gray leaf spot (Cercospora sorghi), leaf blight (Exserohilum turcicum), and anthracnose (Colletotrichum sublineolum); with prevalence ranging from 95 to 97% of fields for oval leaf spot, and 44 to 65% of fields for anthracnose. Head smut (Sporisorium reilianum), was observed in 73 to 75% of fields, covered kernel smut (S. sorghi) 42 to 43% of fields, and loose smut (S. cruenta) 14 to 24% of fields. Head smut incidence was >25% in 3% of fields surveyed. Grain yield reduction from smut diseases alone was estimated to be 5%. Out of eight probability distribution functions compared, the double Gaussian model best described the frequency of disease severity levels for most diseases. Based on the best-fitting model, the proportion of fields with disease severity level thought to cause yield loss (severity rating >5 on a 1 to 9 scale, where 1 = no disease) was calculated as 26.6% for oval leaf spot, 15.3% for rust, 14.8% for anthracnose, 4.8% for ladder leaf spot, and 1.5% for leaf blight. The production environment influenced the prevalence of disease severity. Severe anthracnose, leaf blight, and ladder leaf spot were confined to fields in the humid LM1 and LM2 agro-ecological zones, rust was ubiquitous, and severe gray leaf spot was more prevalent in the dryer LM4 zone.