### The refractory period matters: unifying mechanisms of macroscopic brain waves

The relationship between complex, brain oscillations and the dynamics of individual neurons is poorly understood. Here we utilize Maximum Caliber, a dynamical inference principle, to build a minimal, yet general model of the collective (mean-field) dynamics of large populations of neurons. In agreement with previous experimental observations, we describe a simple, testable mechanism, involving only a single type of neuron, by which many of these complex oscillatory patterns may emerge. Our model predicts that the refractory period of neurons, which has been previously neglected, is essential for these behaviors.

### Control for Multifunctionality: Bioinspired Control Based on Feeding in Aplysia californica

Animals exhibit remarkable feats of behavioral flexibility and multifunctional control that remain challenging for robotic systems. The neural and morphological basis of multifunctionality in animals can provide a source of bio-inspiration for robotic controllers. However, many existing approaches to modeling biological neural networks rely on computationally expensive models and tend to focus solely on the nervous system, often neglecting the biomechanics of the periphery. As a consequence, while these models are excellent tools for neuroscience, they fail to predict functional behavior in real time, which is a critical capability for robotic control. To meet the need for real-time multifunctional control, we have developed a hybrid Boolean model framework capable of modeling neural bursting activity and simple biomechanics at speeds faster than real time. Using this approach, we present a multifunctional model of Aplysia californica feeding that qualitatively reproduces three key feeding behaviors (biting, swallowing, and rejection), demonstrates behavioral switching in response to external sensory cues, and incorporates both known neural connectivity and a simple bioinspired mechanical model of the feeding apparatus. We demonstrate that the model can be used for formulating testable hypotheses and discuss the implications of this approach for robotic control and neuroscience.

### A Monte Carlo approach to model COVID-19 deaths and infections using Gompertz functions

This study describes the dynamics of COVID-19 deaths and infections via a Monte Carlo approach. The analyses include death's data from USA, Brazil, Mexico, UK, India and Russia, which comprise the four countries with the highest number of deaths/confirmed cases, as of Aug 07, 2020, according to the WHO. The Gompertz functions were fitted to the data of weekly averaged confirmed deaths per day by mapping the $\chi^2$ values. The uncertainties, variances and covariances of the model parameters were calculated by propagation. The fitted functions for the average deaths per day for USA and India have an upward trend, with the former having a higher growth rate and quite huge uncertainties. For Mexico, UK and Russia, the fits are consistent with a slope down pattern. For Brazil we found a subtle trend down, but with significant uncertainties. The USA, UK and India data shown a first peak with a higher growth rate when compared to the second one, demonstrating the benefits of non-pharmaceutical interventions of sanitary measures and social distance flattening the curve. For USA, a third peak seems quite plausible, most likely related with the recent relaxation policies. Brazil's data are satisfactorily described by two highly overlapped Gompertz functions with similar growth rates, suggesting a two-steps process for the pandemic spreading. The 95% CI for the total number of deaths ($\times 10^3$) predicted by the model for Aug 31, 2020 are 160 to 220, 110 to 130, 59 to 62, 46.6 to 47.3, 54 to 63 and 16.0 to 16.7 for USA, Brazil, Mexico, UK, India and Russia, respectively. Our estimates for the prevalences of infections are in reasonable agreement with some preliminary reports from serological studies carried out in USA and Brazil. The method represents an effective framework to estimate the line-shape of the infection curves and the uncertainties of the relevant parameters based on the actual data.

### Inferring phenomenological models of first passage processes

Biochemical processes in cells are governed by complex networks of many chemical species interacting stochastically in diverse ways and on different time scales. Constructing microscopically accurate models of such networks is often infeasible. Instead, here we propose a systematic framework for building phenomenological models of such networks from experimental data, focusing on accurately approximating the time it takes to complete the process, the First Passage (FP) time. Our phenomenological models are mixtures of Gamma distributions, which have a natural biophysical interpretation. The complexity of the models is adapted automatically to account for the amount of available data and its temporal resolution. The framework can be used for predicting the behavior of various FP systems under varying external conditions. To demonstrate the utility of the approach, we build models for the distribution of inter-spike intervals of a morphologically complex neuron, a Purkinje cell, from experimental and simulated data. We demonstrate that the developed models can not only fit the data but also make nontrivial predictions. We demonstrate that our coarse-grained models provide constraints on more mechanistically accurate models of the involved phenomena.

### How can contemporary climate research help to understand epidemic dynamics? -- Ensemble approach and snapshot attractors

Standard epidemic models based on compartmental differential equations are investigated under continuous parameter change as external forcing. We show that seasonal modulation of the contact parameter superimposed a monotonic decay needs a different description than that of the standard chaotic dynamics. The concept of snapshot attractors and their natural probability distribution has been adopted from the field of the latest climate-change-research to show the importance of transient effect and ensemble interpretation of disease spread. After presenting the extended bifurcation diagram of measles, the temporal change of the phase space structure is investigated. By defining statistical measures over the ensemble, we can interpret the internal variability of the epidemic as the onset of complex dynamics even for those values of contact parameter where regular behavior is expected. We argue that anomalous outbreaks of infectious class cannot die out until transient chaos is presented for various parameters. More important, that this fact becomes visible by using of ensemble approach rather than single trajectory representation. These findings are applicable generally in nonlinear dynamical systems such as standard epidemic models regardless of parameter values.

### Assessing Intervention Strategies for Non Homogeneous Populations Using a Closed Form Formula for R0

A general stochastic model for susceptible -> infective -> recovered (SIR) epidemics in non homogeneous populations is considered. The heterogeneity is a very important aspect here since it allows more realistic but also more complex models. The basic reproduction number $R_0$, an indication of the probability of an outbreak for homogeneous populations does not indicate the probability of an outbreak for non homogeneous models anymore, because it changes with the initially infected case. Therefore, we use "individual $R_0$" that is the expected number of secondary cases for a given initially infected individual. Thus, the effectiveness of intervention strategies can be assessed by their capability to reduce individual $R_0$ values. Also an intelligent vaccination plan for fully heterogeneous populations is proposed. It is based on the recursive calculation of individual R0 values.

### Tutorial of numerical continuation and bifurcation theory for systems and synthetic biology

Mathematical modelling allows us to concisely describe fundamental principles in biology. Analysis of models can help to both explain known phenomena, and predict the existence of new, unseen behaviours. Model analysis is often a complex task, such that we have little choice but to approach the problem with computational methods. Numerical continuation is a computational method for analysing the dynamics of nonlinear models by algorithmically detecting bifurcations. Here we aim to promote the use of numerical continuation tools by providing an introduction to nonlinear dynamics and numerical bifurcation analysis. Many numerical continuation packages are available, covering a wide range of system classes; a review of these packages is provided, to help both new and experienced practitioners in choosing the appropriate software tools for their needs.

### An Ansatz for undecidable computation in RNA-world automata

In this Ansatz we consider theoretical constructions of RNA polymers into automata, a form of computational structure. The basis for transitions in our automata are plausible RNA-world enzymes that may perform ligation or cleavage. Limited to these operations, we construct RNA automata of increasing complexity; from the Finite Automaton (RNA-FA) to the Turing Machine equivalent 2-stack PDA (RNA-2PDA) and the universal RNA-UPDA. For each automaton we show how the enzymatic reactions match the logical operations of the RNA automaton, and describe how biological exploration of the corresponding evolutionary space is facilitated by the efficient arrangement of RNA polymers into a computational structure. A critical theme of the Ansatz is the self-reference in RNA automata configurations which exploits the program-data duality but results in undecidable computation. We describe how undecidable computation is exemplified in the self-referential Liar paradox that places a boundary on a logical system, and by construction, any RNA automata. We argue that an expansion of the evolutionary space for RNA-2PDA automata can be interpreted as a hierarchical resolution of the undecidable computation by a meta-system (akin to Turing's oracle), in a continual process analogous to Turing's ordinal logics and Post's extensible recursively generated logics. On this basis, we put forward the hypothesis that the resolution of undecidable configurations in RNA-world automata represents a mechanism for novelty generation in the evolutionary space, and propose avenues for future investigation of biological automata.

### Network reinforcement driven drug repurposing for COVID-19 by exploiting disease-gene-drug associations

Currently, the number of patients with COVID-19 has significantly increased. Thus, there is an urgent need for developing treatments for COVID-19. Drug repurposing, which is the process of reusing already-approved drugs for new medical conditions, can be a good way to solve this problem quickly and broadly. Many clinical trials for COVID-19 patients using treatments for other diseases have already been in place or will be performed at clinical sites in the near future. Additionally, patients with comorbidities such as diabetes mellitus, obesity, liver cirrhosis, kidney diseases, hypertension, and asthma are at higher risk for severe illness from COVID-19. Thus, the relationship of comorbidity disease with COVID-19 may help to find repurposable drugs. To reduce trial and error in finding treatments for COVID-19, we propose building a network-based drug repurposing framework to prioritize repurposable drugs. First, we utilized knowledge of COVID-19 to construct a disease-gene-drug network (DGDr-Net) representing a COVID-19-centric interactome with components for diseases, genes, and drugs. DGDr-Net consisted of 592 diseases, 26,681 human genes and 2,173 drugs, and medical information for 18 common comorbidities. The DGDr-Net recommended candidate repurposable drugs for COVID-19 through network reinforcement driven scoring algorithms. The scoring algorithms determined the priority of recommendations by utilizing graph-based semi-supervised learning. From the predicted scores, we recommended 30 drugs, including dexamethasone, resveratrol, methotrexate, indomethacin, quercetin, etc., as repurposable drugs for COVID-19, and the results were verified with drugs that have been under clinical trials. The list of drugs via a data-driven computational approach could help reduce trial-and-error in finding treatment for COVID-19.

### Microstructure with Diffusion MRI: What Scale We Are Sensitive to?

Diffusion-weighted MRI is the forerunner of the rapidly developed microstructural MRI aimed at in vivo evaluation of the cellular tissue architecture. This brief review focuses on the spatiotemporal scales of the microstructure that are accessible using different diffusion MRI techniques and the need to weight the measurability against the interpretability of results. Diffusion phenomena and models are first classified in two-dimensional space (the q-t-plane) of the measurement with narrow gradient pulses. Three-dimensional parameter space of the Stejskal--Tanner diffusion weighting adds more phenomena to this collection. Modern measurement techniques with larger number of parameters are briefly discussed under the overarching idea of diffusion weighting matching the geometry of the targeted cell species.

### Large-Scale Analysis of Iliopsoas Muscle Volumes in the UK Biobank

Psoas muscle measurements are frequently used as markers of sarcopenia and predictors of health. Manually measured cross-sectional areas are most commonly used, but there is a lack of consistency regarding the position of the measurementand manual annotations are not practical for large population studies. We have developed a fully automated method to measure iliopsoas muscle volume (comprised of the psoas and iliacus muscles) using a convolutional neural network. Magnetic resonance images were obtained from the UK Biobank for 5,000 male and female participants, balanced for age, gender and BMI. Ninety manual annotations were available for model training and validation. The model showed excellent performance against out-of-sample data (dice score coefficient of 0.912 +/- 0.018). Iliopsoas muscle volumes were successfully measured in all 5,000 participants. Iliopsoas volume was greater in male compared with female subjects. There was a small but significant asymmetry between left and right iliopsoas muscle volumes. We also found that iliopsoas volume was significantly related to height, BMI and age, and that there was an acceleration in muscle volume decrease in men with age. Our method provides a robust technique for measuring iliopsoas muscle volume that can be applied to large cohorts.

### Renal Cell Carcinoma Detection and Subtyping with Minimal Point-Based Annotation in Whole-Slide Images

Obtaining a large amount of labeled data in medical imaging is laborious and time-consuming, especially for histopathology. However, it is much easier and cheaper to get unlabeled data from whole-slide images (WSIs). Semi-supervised learning (SSL) is an effective way to utilize unlabeled data and alleviate the need for labeled data. For this reason, we proposed a framework that employs an SSL method to accurately detect cancerous regions with a novel annotation method called Minimal Point-Based annotation, and then utilize the predicted results with an innovative hybrid loss to train a classification model for subtyping. The annotator only needs to mark a few points and label them are cancer or not in each WSI. Experiments on three significant subtypes of renal cell carcinoma (RCC) proved that the performance of the classifier trained with the Min-Point annotated dataset is comparable to a classifier trained with the segmentation annotated dataset for cancer region detection. And the subtyping model outperforms a model trained with only diagnostic labels by 12% in terms of f1-score for testing WSIs.

### Darwinian evolution as Brownian motion on the simplex: A geometric perspective on stochastic replicator dynamics

We prove that stochastic replicator dynamics can be interpreted as intrinsic Brownian motion on the simplex equipped the Aitchison geometry. As an immediate consequence we derive three approximation results in the spirit of Wong-Zakai approximation, Donsker's invariance principle and a JKO-scheme. Finally, using the Fokker-Planck equation and Wasserstein-contraction estimates, we study the long time behavior of the stochastic replicator equation, as an example of a non-gradient drift diffusion on the Aitchison simplex.