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Abstract The global outbreak of mpox in 2022 and subsequent sporadic outbreaks in 2023 highlighted the importance of nonpharmaceutical interventions such as case isolation. Individual variations in viral shedding dynamics may lead to either premature ending of isolation for infectious individuals, or unnecessarily prolonged isolation for those who are no longer infectious. Here, we developed a modeling framework to characterize heterogeneous mpox infectiousness profiles – specifically, when infected individuals cease to be infectious – based on viral load data. We examined the potential effectiveness of three different isolation rules: a symptom-based rule (the current guideline in many countries) and rules permitting individuals to stop isolating after either a fixed duration or following tests that indicate that they are no longer likely to be infectious. Our analysis suggests that the duration of viral shedding ranges from 23 to 50 days between individuals. The risk of infected individuals ending isolation too early was estimated to be 8.8% (95% CI: 6.7–10.5) after symptom clearance and 5.4% (95% CI: 4.1–6.7) after 3 weeks of isolation. While these results suggest that the current standard practice for ending isolation is effective, we found that unnecessary isolation following the infectious period could be reduced by adopting a testing-based rule.

Abstract The echo state network (ESN) is an excellent machine learning model for processing time-series data. This model, utilising the response of a recurrent neural network, called a reservoir, to input signals, achieves high training efficiency. Introducing time-history terms into the neuron model of the reservoir is known to improve the time-series prediction performance of ESN, yet the reasons for this improvement have not been quantitatively explained in terms of reservoir dynamics characteristics. Therefore, we hypothesised that the performance enhancement brought about by time-history terms could be explained by delay capacity, a recently proposed metric for assessing the memory performance of reservoirs. To test this hypothesis, we conducted comparative experiments using ESN models with time-history terms, namely leaky integrator ESNs (LI-ESN) and chaotic echo state networks (ChESN). The results suggest that compared with ESNs without time-history terms, the reservoir dynamics of LI-ESN and ChESN can maintain diversity and stability while possessing higher delay capacity, leading to their superior performance. Explaining ESN performance through dynamical metrics are crucial for evaluating the numerous ESN architectures recently proposed from a general perspective and for the development of more sophisticated architectures, and this study contributes to such efforts.

Abstract Real systems showing regime shifts, such as ecosystems, are often composed of many dynamical elements interacting on a network. Various early warning signals have been proposed for anticipating regime shifts from observed data. However, it is unclear how one should combine early warning signals from different nodes for better performance. Based on theory of stochastic differential equations, we propose a method to optimize the node set from which to construct an early warning signal. The proposed method takes into account that uncertainty as well as the magnitude of the signal affects its predictive performance, that a large magnitude or small uncertainty of the signal in one situation does not imply the signal’s high performance, and that combining early warning signals from different nodes is often but not always beneficial. The method performs well particularly when different nodes are subjected to different amounts of dynamical noise and stress.

Abstract Reservoir computing (RC) can efficiently process time-series data by mapping the input signal into a high-dimensional space via randomly connected recurrent neural networks (RNNs), which are referred to as a reservoir. The high-dimensional representation of time-series data in the reservoir simplifies subsequent learning tasks. Although this simple architecture allows fast learning and facile physical implementation, the learning performance is inferior to that of other state-of-the-art RNN models. In this study, to improve the learning ability of RC, we propose self-modulated RC (SM-RC) that extends RC by adding a self-modulation mechanism. SM-RC can perform attention tasks where input information is retained or discarded depending on the input signal. We find that a chaotic state can emerge as a result of learning in SM-RC. Furthermore, we demonstrate that SM-RC outperforms RC in NARMA and Lorenz model tasks. Because the SM-RC architecture only requires two additional gates, it is physically implementable as RC, thereby providing a direction for realizing edge artificial intelligence.

As we learned during the COVID-19 pandemic, vaccines are one of the most important tools in infectious disease control. To date, an unprecedentedly large volume of high-quality data on COVID-19 vaccinations have been accumulated. For preparedness in future pandemics beyond COVID-19, these valuable datasets should be analyzed to best shape an effective vaccination strategy. We are collecting longitudinal data from a community-based cohort in Fukushima, Japan, that consists of 2,407 individuals who underwent serum sampling two or three times after a two-dose vaccination with either BNT162b2 or mRNA-1273. Using the individually reconstructed time courses of the vaccine-elicited antibody response based on mathematical modeling, we first identified basic demographic and health information that contributed to the main features of the antibody dynamics, i.e., the peak, the duration, and the area under the curve. We showed that these three features of antibody dynamics were partially explained by underlying medical conditions, adverse reactions to vaccinations, and medications, consistent with the findings of previous studies. We then applied to these factors a recently proposed computational method to optimally fit an "antibody score", which resulted in an integer-based score that can be used as a basis for identifying individuals with higher or lower antibody titers from basic demographic and health information. The score can be easily calculated by individuals themselves or by medical practitioners. Although the sensitivity of this score is currently not very high, in the future, as more data become available, it has the potential to identify vulnerable populations and encourage them to get booster vaccinations. Our mathematical model can be extended to any kind of vaccination and therefore can form a basis for policy decisions regarding the distribution of booster vaccines to strengthen immunity in future pandemics.

Abstract The training of multilayer spiking neural networks (SNNs) using the error backpropagation algorithm has made significant progress in recent years. Among the various training schemes, the error backpropagation method that directly uses the firing time of neurons has attracted considerable attention because it can realize ideal temporal coding. This method uses time-to-first-spike (TTFS) coding, in which each neuron fires at most once, and this restriction on the number of firings enables information to be processed at a very low firing frequency. This low firing frequency increases the energy efficiency of information processing in SNNs. However, only an upper limit has been provided for TTFS-coded SNNs, and the information-processing capability of SNNs at lower firing frequencies has not been fully investigated. In this paper, we propose two spike-timing-based sparse-firing (SSR) regularization methods to further reduce the firing frequency of TTFS-coded SNNs. Both methods are characterized by the fact that they only require information about the firing timing and associated weights. The effects of these regularization methods were investigated on the MNIST, Fashion-MNIST, and CIFAR-10 datasets using multilayer perceptron networks and convolutional neural network structures.

Abstract During the COVID-19 pandemic, human behavior change as a result of nonpharmaceutical interventions such as isolation may have induced directional selection for viral evolution. By combining previously published empirical clinical data analysis and multi-level mathematical modeling, we find that the SARS-CoV-2 variants selected for as the virus evolved from the pre-Alpha to the Delta variant had earlier and higher peak in viral load dynamics but a shorter duration of infection. Selection for increased transmissibility shapes the viral load dynamics, and the isolation measure is likely to be a driver of these evolutionary transitions. In addition, we show that a decreased incubation period and an increased proportion of asymptomatic infection are also positively selected for as SARS-CoV-2 mutated to adapt to human behavior (i.e., Omicron variants). The quantitative information and predictions we present here can guide future responses in the potential arms race between pandemic interventions and viral evolution.

Chronic infection with hepatitis B virus (HBV) is caused by the persistence of closed circular DNA (cccDNA) in the nucleus of infected hepatocytes. Despite available therapeutic anti-HBV agents, eliminating the cccDNA remains challenging. Thus, quantifying and understanding the dynamics of cccDNA are essential for developing effective treatment strategies and new drugs. However, such study requires repeated liver biopsy to measure the intrahepatic cccDNA, which is basically not accepted because liver biopsy is potentially morbid and not common during hepatitis B treatment. We here aimed to develop a noninvasive method for quantifying cccDNA in the liver using surrogate markers in peripheral blood. We constructed a multiscale mathematical model that explicitly incorporates both intracellular and intercellular HBV infection processes. The model, based on age-structured partial differential equations, integrates experimental data from in vitro and in vivo investigations. By applying this model, we roughly predicted the amount and dynamics of intrahepatic cccDNA within a certain range using specific viral markers in serum samples, including HBV DNA, HBsAg, HBeAg, and HBcrAg. Our study represents a significant step towards advancing the understanding of chronic HBV infection. The noninvasive quantification of cccDNA using our proposed method holds promise for improving clinical analyses and treatment strategies. By comprehensively describing the interactions of all components involved in HBV infection, our multiscale mathematical model provides a valuable framework for further research and the development of targeted interventions.

Transactions in financial markets are not evenly spaced but can be concentrated within a short period of time. In this study, we investigated the factors that determine the transaction frequency in financial markets. Specifically, we employed the Hawkes process model to identify exogenous and endogenous forces governing transactions of individual stocks in the Tokyo Stock Exchange during the COVID-19 pandemic. To enhance the accuracy of our analysis, we introduced a novel EM algorithm for the estimation of exogenous and endogenous factors that specifically addresses the interdependence of the values of these factors over time. We detected a substantial change in the transaction frequency in response to policy change announcements. Moreover, there is significant heterogeneity in the transaction frequency among individual stocks. We also found a tendency where stocks with high market capitalization tend to significantly respond to external news, while their excitation relationship between transactions is weak. This suggests the capability of quantifying the market state from the viewpoint of the exogenous and endogenous factors generating transactions for various stocks.

Abstract The phenomenon of partial synchronization has attracted significant interest in the field of nonlinear dynamics, largely due to observations of related phenomena in real-world situations. In particular, the coexistence of synchronized and desynchronized phases, known as a chimera state, has been the subject of intense study. In this work, we experimentally demonstrate that networks of identical photonic spiking neurons based on coupled degenerate optical parametric oscillators can exhibit various chimera states in which, depending on their local synchronization and desynchronization, different kinds of spiking dynamics can develop in a self-organized manner. Even when only a static interaction is implemented, the spiking mode of photonic neurons can be spontaneously and adaptively changed between the Class-I and Class-II modes classified by A. L. Hodgkin. This spontaneous spiking-mode shift induces a significant change in the spiking frequency despite all neurons having the same natural spiking frequency, which encourages the generation of chimera states.

There is a critical transition before a high-dimensional network system completely deteriorates. The Dynamical Network Marker (DNM) theory has been developed for the early prediction of such critical transitions by only using High-Dimension Small-Sample-Size (HDSSS) data. This article presents a model-free dominant pole placement approach for restabilizing the high-dimensional network systems towards avoidance of critical transitions by early treatment. Instead of traditional model-based pole placement, we present a model-free exact dominant pole placement method with dominant eigenvectors of the system matrix, which can be estimated from HDSSS data of system states. We further introduce two approximations of exact dominant pole placement to reduce the complexity of implementing restabilization. The first one is to approximate the right dominant eigenvector-based pole placement by reducing the number of intervened nodes. The second one is to intervene only in the diagonal part of the system matrix. We conduct theoretical analysis and numerical simulations to investigate the performance of the proposed dominant pole placement method.

Abstract Chronic myeloid leukemia (CML) is a myeloproliferative disorder caused by the BCR-ABL1 tyrosine kinase. Although ABL1-specific tyrosine kinase inhibitors (TKIs) including nilotinib have dramatically improved the prognosis of patients with CML, the TKI efficacy depends on the individual patient. In this work, we found that the patients with different nilotinib responses can be classified by using the estimated parameters of our simple dynamical model with two common laboratory findings. Furthermore, our proposed method identified patients who failed to achieve a treatment goal with high fidelity according to the data collected only at three initial time points during nilotinib therapy. Since our model relies on the general properties of TKI response, our framework would be applicable to CML patients who receive frontline nilotinib or other TKIs.

Utilizing viral test results to determine isolation length would minimize both the risk of prematurely ending isolation of infectious patients and the unnecessary individual burden of redundant isolation of noninfectious patients. Here, the authors develop a framework to compute the population-level risk of different isolation guidelines with rapid antigen tests.

Abstract Background Multiple waves of the COVID-19 epidemic have hit most countries by the end of 2021. Most of those waves are caused by emergence and importation of new variants. To prevent importation of new variants, combination of border control and contact tracing is essential. However, the timing of infection inferred by interview is influenced by recall bias and hinders the contact tracing process. Methods We propose a novel approach to infer the timing of infection, by employing a within-host model to capture viral load dynamics after the onset of symptoms. We applied this approach to ascertain secondary transmission which can trigger outbreaks. As a demonstration, the 12 initial reported cases in Singapore, which were considered as imported because of their recent travel history to Wuhan, were analyzed to assess whether they are truly imported. Results Our approach suggested that 6 cases were infected prior to the arrival in Singapore, whereas other 6 cases might have been secondary local infection. Three among the 6 potential secondary transmission cases revealed that they had contact history to previously confirmed cases. Conclusions Contact trace combined with our approach using viral load data could be the key to mitigate the risk of importation of new variants by identifying cases as early as possible and inferring the timing of infection with high accuracy.

Abstract Background Facing a global epidemic of new infectious diseases such as COVID-19, non-pharmaceutical interventions (NPIs), which reduce transmission rates without medical actions, are being implemented around the world to mitigate spreads. One of the problems in assessing the effects of NPIs is that different NPIs have been implemented at different times based on the situation of each country; therefore, few assumptions can be shared about how the introduction of policies affects the patient population. Mathematical models can contribute to further understanding these phenomena by obtaining analytical solutions as well as numerical simulations. Methods and results In this study, an NPI was introduced into the SIR model for a conceptual study of infectious diseases under the condition that the transmission rate was reduced to a fixed value only once within a finite time duration, and its effect was analyzed numerically and theoretically. It was analytically shown that the maximum fraction of infected individuals and the final size could be larger if the intervention starts too early. The analytical results also suggested that more individuals may be infected at the peak of the second wave with a stronger intervention. Conclusions This study provides quantitative relationship between the strength of a one-shot intervention and the reduction in the number of patients with no approximation. This suggests the importance of the strength and time of NPIs, although detailed studies are necessary for the implementation of NPIs in complicated real-world environments as the model used in this study is based on various simplifications.

We present a mixed-signal spiking neural networks processor with 8-bit synaptic weight on-chip learning in 40 nm CMOS that consists of a 10k mixed-signal synapse circuit and 100 analog leaky integrate-and-fire (LIF) neuron circuits. The processor has no clock signal except in peripheral circuits for I/O, and neuron and synapse circuits can operate asynchronously in the continuous-time domain, just like biological neurons. We demonstrate the energy efficiency of 6.24–18.7 TOPS/W in a multitarget spike learning task.

Finding the ground state of a variety of complex systems can be formulated as the minimization of the total interaction energy of Ising machines, posing a challenge as computational cost increases exponentially with system size. In this paper, the authors propose an algorithm to find the ground states of Ising-type problems by destabilising non-trivial attractors in combinatorial optimisation solvers through a heuristic modulation of the target amplitude, and show that this provides an improved scaling with respect to several existing methods.

Machine learning approaches have recently been leveraged as a substitute or an aid for physical/mathematical modeling approaches to dynamical systems. To develop an efficient machine learning method dedicated to modeling and prediction of multiscale dynamics, we propose a reservoir computing (RC) model with diverse timescales by using a recurrent network of heterogeneous leaky integrator (LI) neurons. We evaluate computational performance of the proposed model in two time series prediction tasks related to four chaotic fast-slow dynamical systems. In a one-step-ahead prediction task where input data are provided only from the fast subsystem, we show that the proposed model yields better performance than the standard RC model with identical LI neurons. Our analysis reveals that the timescale required for producing each component of target multiscale dynamics is appropriately and flexibly selected from the reservoir dynamics by model training. In a long-term prediction task, we demonstrate that a closed-loop version of the proposed model can achieve longer-term predictions compared to the counterpart with identical LI neurons depending on the hyperparameter setting.

Neuromorphic devices take inspiration from spiking dynamics of neurons in the brain. Here, the authors demonstrate synchronized spiking dynamics in 240 photonic artificial neurons, each of which is implemented with a pair of antisymmetrically coupled degenerate optical parametric oscillators.

Abstract The spread of intelligent transportation systems in urban cities has caused heavy computational loads, requiring a novel architecture for managing large-scale traffic. In this study, we develop a method for globally controlling traffic signals arranged on a square lattice by means of a quantum annealing machine, namely the D-Wave quantum annealer. We first formulate a signal optimization problem that minimizes the imbalance of traffic flows in two orthogonal directions. Then we reformulate this problem as an Ising Hamiltonian, which is compatible with quantum annealers. The new control method is compared with a conventional local control method for a large 50-by-50 city, and the results exhibit the superiority of our global control method in suppressing traffic imbalance over wide parameter ranges. Furthermore, the solutions to the global control method obtained with the quantum annealing machine are better than those obtained with conventional simulated annealing. In addition, we prove analytically that the local and the global control methods converge at the limit where cars have equal probabilities for turning and going straight. These results are verified with numerical experiments.

Abstract Reservoir computing (RC) is a machine learning algorithm that can learn complex time series from data very rapidly based on the use of high-dimensional dynamical systems, such as random networks of neurons, called “reservoirs.” To implement RC in edge computing, it is highly important to reduce the amount of computational resources that RC requires. In this study, we propose methods that reduce the size of the reservoir by inputting the past or drifting states of the reservoir to the output layer at the current time step. To elucidate the mechanism of model-size reduction, the proposed methods are analyzed based on information processing capacity proposed by Dambre et al. (Sci Rep 2:514, 2012). In addition, we evaluate the effectiveness of the proposed methods on time-series prediction tasks: the generalized Hénon-map and NARMA. On these tasks, we found that the proposed methods were able to reduce the size of the reservoir up to one tenth without a substantial increase in regression error.

Predicting future values of a short time series remains a challenge. Here, the authors propose an auto-reservoir computing framework, which achieved accurate and robust multistep ahead prediction by transforming high-dimensional data into temporal dynamics.

It is crucial yet challenging to identify cause-consequence relation in complex dynamical systems where direct causal links can mix with indirect ones. Leng et al. propose a data-driven model-independent method to distinguish direct from indirect causality and test its applicability to real-world data.

BackgroundDevelopment of an effective antiviral drug for Coronavirus Disease 2019 (COVID-19) is a global health priority. Although several candidate drugs have been identified through in vitro and in vivo models, consistent and compelling evidence from clinical studies is limited. The lack of evidence from clinical trials may stem in part from the imperfect design of the trials. We investigated how clinical trials for antivirals need to be designed, especially focusing on the sample size in randomized controlled trials.Methods and findingsA modeling study was conducted to help understand the reasons behind inconsistent clinical trial findings and to design better clinical trials. We first analyzed longitudinal viral load data for Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) without antiviral treatment by use of a within-host virus dynamics model. The fitted viral load was categorized into 3 different groups by a clustering approach. Comparison of the estimated parameters showed that the 3 distinct groups were characterized by different virus decay rates (p-value < 0.001). The mean decay rates were 1.17 d-1 (95% CI: 1.06 to 1.27 d-1), 0.777 d-1 (0.716 to 0.838 d-1), and 0.450 d-1 (0.378 to 0.522 d-1) for the 3 groups, respectively. Such heterogeneity in virus dynamics could be a confounding variable if it is associated with treatment allocation in compassionate use programs (i.e., observational studies). Subsequently, we mimicked randomized controlled trials of antivirals by simulation. An antiviral effect causing a 95% to 99% reduction in viral replication was added to the model. To be realistic, we assumed that randomization and treatment are initiated with some time lag after symptom onset. Using the duration of virus shedding as an outcome, the sample size to detect a statistically significant mean difference between the treatment and placebo groups (1:1 allocation) was 13,603 and 11,670 (when the antiviral effect was 95% and 99%, respectively) per group if all patients are enrolled regardless of timing of randomization. The sample size was reduced to 584 and 458 (when the antiviral effect was 95% and 99%, respectively) if only patients who are treated within 1 day of symptom onset are enrolled. We confirmed the sample size was similarly reduced when using cumulative viral load in log scale as an outcome. We used a conventional virus dynamics model, which may not fully reflect the detailed mechanisms of viral dynamics of SARS-CoV-2. The model needs to be calibrated in terms of both parameter settings and model structure, which would yield more reliable sample size calculation.ConclusionsIn this study, we found that estimated association in observational studies can be biased due to large heterogeneity in viral dynamics among infected individuals, and statistically significant effect in randomized controlled trials may be difficult to be detected due to small sample size. The sample size can be dramatically reduced by recruiting patients immediately after developing symptoms. We believe this is the first study investigated the study design of clinical trials for antiviral treatment using the viral dynamics model.

Since the start of the COVID-19 pandemic, two mainstream guidelines for defining when to end the isolation of SARS-CoV-2-infected individuals have been in use: the one-size-fits-all approach (i.e. patients are isolated for a fixed number of days) and the personalized approach (i.e. based on repeated testing of isolated patients). We use a mathematical framework to model within-host viral dynamics and test different criteria for ending isolation. By considering a fixed time of 10 days since symptom onset as the criterion for ending isolation, we estimated that the risk of releasing an individual who is still infectious is low (0–6.6%). However, this policy entails lengthy unnecessary isolations (4.8–8.3 days). In contrast, by using a personalized strategy, similar low risks can be reached with shorter prolonged isolations. The obtained findings provide a scientific rationale for policies on ending the isolation of SARS-CoV-2-infected individuals.

The incubation period, or the time from infection to symptom onset, of COVID-19 has usually been estimated by using data collected through interviews with cases and their contacts. However, this estimation is influenced by uncertainty in the cases’ recall of exposure time. We propose a novel method that uses viral load data collected over time since hospitalization, hindcasting the timing of infection with a mathematical model for viral dynamics. As an example, we used reported data on viral load for 30 hospitalized patients from multiple countries (Singapore, China, Germany, and Korea) and estimated the incubation period. The median, 2.5, and 97.5 percentiles of the incubation period were 5.85 days (95 % CI: 5.05, 6.77), 2.65 days (2.04, 3.41), and 12.99 days (9.98, 16.79), respectively, which are comparable to the values estimated in previous studies. Using viral load to estimate the incubation period might be a useful approach, especially when it is impractical to directly observe the infection event.

Summary: Antiviral treatments targeting the coronavirus disease 2019 are urgently required. We screened a panel of already approved drugs in a cell culture model of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) and identified two new agents having higher antiviral potentials than the drug candidates such as remdesivir and chroloquine in VeroE6/TMPRSS2 cells: the anti-inflammatory drug cepharanthine and human immunodeficiency virus protease inhibitor nelfinavir. Cepharanthine inhibited SARS-CoV-2 entry through the blocking of viral binding to target cells, while nelfinavir suppressed viral replication partly by protease inhibition. Consistent with their different modes of action, synergistic effect of this combined treatment to limit SARS-CoV-2 proliferation was highlighted. Mathematical modeling in vitro antiviral activity coupled with the calculated total drug concentrations in the lung predicts that nelfinavir will shorten the period until viral clearance by 4.9 days and the combining cepharanthine/nelfinavir enhanced their predicted efficacy. These results warrant further evaluation of the potential anti-SARS-CoV-2 activity of cepharanthine and nelfinavir.

The scientific community is focused on developing antiviral therapies to mitigate the impacts of the ongoing novel coronavirus disease 2019 (COVID-19) outbreak. This will be facilitated by improved understanding of viral dynamics within infected hosts. Here, using a mathematical model in combination with published viral load data, we compare within-host viral dynamics of SARS-CoV-2 with analogous dynamics of MERS-CoV and SARS-CoV. Our quantitative analyses using a mathematical model revealed that the within-host reproduction number at symptom onset of SARS-CoV-2 was statistically significantly larger than that of MERS-CoV and similar to that of SARS-CoV. In addition, the time from symptom onset to the viral load peak for SARS-CoV-2 infection was shorter than those of MERS-CoV and SARS-CoV. These findings suggest the difficulty of controlling SARS-CoV-2 infection by antivirals. We further used the viral dynamics model to predict the efficacy of potential antiviral drugs that have different modes of action. The efficacy was measured by the reduction in the viral load area under the curve (AUC). Our results indicate that therapies that block de novo infection or virus production are likely to be effective if and only if initiated before the viral load peak (which appears 2-3 days after symptom onset), but therapies that promote cytotoxicity of infected cells are likely to have effects with less sensitivity to the timing of treatment initiation. Furthermore, combining a therapy that promotes cytotoxicity and one that blocks de novo infection or virus production synergistically reduces the AUC with early treatment. Our unique modeling approach provides insights into the pathogenesis of SARS-CoV-2 and may be useful for development of antiviral therapies.

We previously proposed, on theoretical grounds, that the cerebellum must regulate the dimensionality of its neuronal activity during motor learning and control to cope with the low firing frequency of inferior olive neurons, which form one of two major inputs to the cerebellar cortex. Such dimensionality regulation is possible via modulation of electrical coupling through the gap junctions between inferior olive neurons by inhibitory GABAergic synapses. In addition, we previously showed in simulations that intermediate coupling strengths induce chaotic firing of inferior olive neurons and increase their information carrying capacity. However, there is no in vivo experimental data supporting these two theoretical predictions. Here, we computed the levels of synchrony, dimensionality, and chaos of the inferior olive code by analyzing in vivo recordings of Purkinje cell complex spike activity in three different coupling conditions: carbenoxolone (gap junctions blocker), control, and picrotoxin (GABA-A receptor antagonist). To examine the effect of electrical coupling on dimensionality and chaotic dynamics, we first determined the physiological range of effective coupling strengths between inferior olive neurons in the three conditions using a combination of a biophysical network model of the inferior olive and a novel Bayesian model averaging approach. We found that effective coupling co-varied with synchrony and was inversely related to the dimensionality of inferior olive firing dynamics, as measured via a principal component analysis of the spike trains in each condition. Furthermore, for both the model and the data, we found an inverted U-shaped relationship between coupling strengths and complexity entropy, a measure of chaos for spiking neural data. These results are consistent with our hypothesis according to which electrical coupling regulates the dimensionality and the complexity in the inferior olive neurons in order to optimize both motor learning and control of high dimensional motor systems by the cerebellum.

During the 2012-13 rubella outbreak in Japan, local governments implemented subsidy programs for catch-up vaccination to mitigate the rubella outbreak and prevent congenital rubella syndrome (CRS). In most local governments, to prevent CRS, eligible persons of the subsidy program were women who were planning to have a child and men who were partners of pregnant women. On the other hand, in Kawasaki City, unimmunized men aged 23-39 years were additionally included in the eligible persons, because they were included in an unimmunized men group resulting from the historical transition of the national routine vaccination in Japan. The number of rubella cases in the city decreased earlier than that in the whole Japan. First, in order to estimate the effect of the catch-up vaccination campaign in Kawasaki City on the epidemic outcome, we performed numerical simulations with a Susceptible-Vaccinated-Exposed-Infectious-Recovered (SVEIR) model incorporating real data. The result indicated that the catch-up vaccination campaign showed a beneficial impact on the early decay of the rubella cases. Second, we numerically compared several different implementation strategies of catch-up vaccinations under a fixed amount of total vaccinations. As a result, we found that early and intensive vaccinations are vital for significant reduction in the number of rubella cases and CRS occurrences. Our study suggests that mathematical models with epidemiological and social data can contribute to identifying the most effective vaccination strategy.

Modeling cell differentiation from omics data is an essential problem in systems biology research. Although many algorithms have been established to analyze scRNA-seq data, approaches to infer the pseudo-time of cells or quantify their potency have not yet been satisfactorily solved. Here, we propose the Landscape of Differentiation Dynamics (LDD) method, which calculates cell potentials and constructs their differentiation landscape by a continuous birth-death process from scRNA-seq data. From the viewpoint of stochastic dynamics, we exploited the features of the differentiation process and quantified the differentiation landscape based on the source-sink diffusion process. In comparison with other scRNA-seq methods in seven benchmark datasets, we found that LDD could accurately and efficiently build the evolution tree of cells with pseudo-time, in particular quantifying their differentiation landscape in terms of potency. This study provides not only a computational tool to quantify cell potency or the Waddington potential landscape based on scRNA-seq data, but also novel insights to understand the cell differentiation process from a dynamic perspective.

To understand the effect of attention on neuronal dynamics, we propose a multi-module network, with each module consisting of fully interconnected groups of excitatory and inhibitory neurons. This network shows transitive dynamics among quasi-attractors as its typical dynamics. When the release of acetylcholine onto the network is simulated by attention, the transitive dynamics change into stable dynamics in which the system converges to an attractor. We found that this network can reproduce three experimentally observed properties of attention-dependent response modulation, namely an increase in the firing rate, a decrease in the Fano factor of the firing rate, and a decrease in the correlation coefficients between the firing rates of pairs of neurons. Moreover, we also showed theoretically that the release of acetylcholine increases the sensitivity to bottom-up inputs by changing the response function.

Dynamic network biomarkers (DNB) can identify the critical state or tipping point of a disease, thereby predicting rather than diagnosing the disease. However, it is difficult to apply the DNB theory to clinical practice because evaluating DNB at the critical state required the data of multiple samples on each individual, which are generally not available, and thus limit the applicability of DNB. In this study, we developed a novel method, i.e., single-sample DNB (sDNB), to detect early-warning signals or critical states of diseases in individual patients with only a single sample for each patient, thus opening a new way to predict diseases in a personalized way. In contrast to the information of differential expressions used in traditional biomarkers to "diagnose disease", sDNB is based on the information of differential associations, thereby having the ability to "predict disease" or "diagnose near-future disease". Applying this method to datasets for influenza virus infection and cancer metastasis led to accurate identification of the critical states or correct prediction of the immediate diseases based on individual samples. We successfully identified the critical states or tipping points just before the appearance of disease symptoms for influenza virus infection and the onset of distant metastasis for individual patients with cancer, thereby demonstrating the effectiveness and efficiency of our method for quantifying critical states at the single-sample level.

The capacity for flexible sensory-action association in animals has been related to context-dependent attractor dynamics outside the sensory cortices. Here, we report a line of evidence that flexibly modulated attractor dynamics during task switching are already present in the higher visual cortex in macaque monkeys. With a nonlinear decoding approach, we can extract the particular aspect of the neural population response that reflects the task-induced emergence of bistable attractor dynamics in a neural population, which could be obscured by standard unsupervised dimensionality reductions such as PCA. The dynamical modulation selectively increases the information relevant to task demands, indicating that such modulation is beneficial for perceptual decisions. A computational model that features nonlinear recurrent interaction among neurons with a task-dependent background input replicates the key properties observed in the experimental data. These results suggest that the context-dependent attractor dynamics involving the sensory cortex can underlie flexible perceptual abilities.

Autism spectrum disorder (ASD) is a developmental disorder that involves developmental delays. It has been hypothesized that aberrant neural connectivity in ASD may cause atypical brain network development. Brain graphs not only describe the differences in brain networks between clinical and control groups, but also provide information about network development within each group. In the present study, graph indices of brain networks were estimated in children with ASD and in typically developing (TD) children using magnetoencephalography performed while the children viewed a cartoon video. We examined brain graphs from a developmental point of view, and compared the networks between children with ASD and TD children. Network development patterns (NDPs) were assessed by examining the association between the graph indices and the raw scores on the achievement scale or the age of the children. The ASD and TD groups exhibited different NDPs at both network and nodal levels. In the left frontal areas, the nodal degree and efficiency of the ASD group were negatively correlated with the achievement scores. Reduced network connections were observed in the temporal and posterior areas of TD children. These results suggested that the atypical network developmental trajectory in children with ASD is associated with the development score rather than age.

In recent years, serious infectious diseases tend to transcend national borders and widely spread in a global scale. The incidence and prevalence of epidemics are highly influenced not only by pathogen-dependent disease characteristics such as the force of infection, the latent period, and the infectious period, but also by human mobility and contact patterns. However, the effect of heterogeneous mobility of individuals on epidemic outcomes is not fully understood. Here, we aim to elucidate how spatial mobility of individuals contributes to the final epidemic size in a spatial susceptible-exposed-infectious-recovered (SEIR) model with mobile individuals in a square lattice. After illustrating the interplay between the mobility parameters and the other parameters on the spatial epidemic spreading, we propose an index as a function of system parameters, which largely governs the final epidemic size. The main contribution of this study is to show that the proposed index is useful for estimating how parameter scaling affects the final epidemic size. To demonstrate the effectiveness of the proposed index, we show that there is a positive correlation between the proposed index computed with the real data of human airline travels and the actual number of positive incident cases of influenza B in the entire world, implying that the growing incidence of influenza B is attributed to increased human mobility.

Identifying causal relations from time series is the first step to understanding the behavior of complex systems. Although many methods have been proposed, few papers have applied multiple methods together to detect causal relations based on time series generated from coupled nonlinear systems with some unobserved parts. Here we propose the combined use of three methods and a majority vote to infer causality under such circumstances. Two of these methods are proposed here for the first time, and all of the three methods can be applied even if the underlying dynamics is nonlinear and there are hidden common causes. We test our methods with coupled logistic maps, coupled Rössler models, and coupled Lorenz models. In addition, we show from ice core data how the causal relations among the temperature, the CH4 level, and the CO2 level in the atmosphere changed in the last 800,000 years, a conclusion also supported by irregularly sampled data analysis. Moreover, these methods show how three regions of the brain interact with each other during the visually cued, two-choice arm reaching task. Especially, we demonstrate that this is due to bottom up influences at the beginning of the task, while there exist mutual influences between the posterior medial prefrontal cortex and the presupplementary motor area. Based on our results, we conclude that identifying causality with an appropriate ensemble of multiple methods ensures the validity of the obtained results more firmly.

Cell-to-cell viral infection, in which viruses spread through contact of infected cell with surrounding uninfected cells, has been considered as a critical mode of virus infection. However, since it is technically difficult to experimentally discriminate the two modes of viral infection, namely cell-free infection and cell-to-cell infection, the quantitative information that underlies cell-to-cell infection has yet to be elucidated, and its impact on virus spread remains unclear. To address this fundamental question in virology, we quantitatively analyzed the dynamics of cell-to-cell and cell-free human immunodeficiency virus type 1 (HIV-1) infections through experimental-mathematical investigation. Our analyses demonstrated that the cell-to-cell infection mode accounts for approximately 60% of viral infection, and this infection mode shortens the generation time of viruses by 0.9 times and increases the viral fitness by 3.9 times. Our results suggest that even a complete block of the cell-free infection would provide only a limited impact on HIV-1 spread.

The classical information-theoretic measures such as the entropy and the mutual information (MI) are widely applicable to many areas in science and engineering. Csiszar generalized the entropy and the MI by using the convex functions. Recently, we proposed the grid occupancy (GO) and the quasientropy (QE) as measures of independence. The QE explicitly includes a convex function in its definition, while the expectation of GO is a subclass of QE. In this paper, we study the effect of different convex functions on GO, QE, and Csiszar’s generalized mutual information (GMI). A quality factor (QF) is proposed to quantify the sharpness of their minima. Using the QF, it is shown that these measures can have sharper minima than the classical MI. Besides, a recursive algorithm for computing GMI, which is a generalization of Fraser and Swinney’s algorithm for computing MI, is proposed. Moreover, we apply GO, QE, and GMI to chaotic time series analysis. It is shown that these measures are good criteria for determining the optimum delay in strange attractor reconstruction.

When a physician decides on a treatment and its schedule for a specific patient, information gained from prior patients and experience in the past is taken into account. A more objective way to make such treatment decisions based on actual data would be useful to the clinician. Although there are many mathematical models proposed for various diseases, so far there is no mathematical method that accomplishes optimization of the treatment schedule using the information gained from past patients or "rapid learning" technology. In an attempt to use this approach, we integrate the information gained from patients previously treated with intermittent androgen suppression (IAS) with that from a current patient by first fitting the time courses of clinical data observed from the previously treated patients, then constructing the prior information of the parameter values of the mathematical model, and finally, maximizing the posterior probability for the parameters of the current patient using the prior information. Although we used data from prostate cancer patients, the proposed method is general, and thus can be applied to other diseases once an appropriate mathematical model is established for that disease.

Understanding network robustness against failures of network units is useful for preventing large-scale breakdowns and damages in real-world networked systems. The tolerance of networked systems whose functions are maintained by collective dynamical behavior of the network units has recently been analyzed in the framework called dynamical robustness of complex networks. The effect of network structure on the dynamical robustness has been examined with various types of network topology, but the role of network assortativity, or degree-degree correlations, is still unclear. Here we study the dynamical robustness of correlated (assortative and disassortative) networks consisting of diffusively coupled oscillators. Numerical analyses for the correlated networks with Poisson and power-law degree distributions show that network assortativity enhances the dynamical robustness of the oscillator networks but the impact of network disassortativity depends on the detailed network connectivity. Furthermore, we theoretically analyze the dynamical robustness of correlated bimodal networks with two-peak degree distributions and show the positive impact of the network assortativity.

Several APOBEC3 proteins, particularly APOBEC3D, APOBEC3F, and APOBEC3G, induce G-to-A hypermutations in HIV-1 genome, and abrogate viral replication in experimental systems, but their relative contributions to controlling viral replication and viral genetic variation in vivo have not been elucidated. On the other hand, an HIV-1-encoded protein, Vif, can degrade these APOBEC3 proteins via a ubiquitin/proteasome pathway. Although APOBEC3 proteins have been widely considered as potent restriction factors against HIV-1, it remains unclear which endogenous APOBEC3 protein(s) affect HIV-1 propagation in vivo. Here we use a humanized mouse model and HIV-1 with mutations in Vif motifs that are responsible for specific APOBEC3 interactions, DRMR/AAAA (4A) or YRHHY/AAAAA (5A), and demonstrate that endogenous APOBEC3D/F and APOBEC3G exert strong anti-HIV-1 activity in vivo. We also show that the growth kinetics of 4A HIV-1 negatively correlated with the expression level of APOBEC3F. Moreover, single genome sequencing analyses of viral RNA in plasma of infected mice reveal that 4A HIV-1 is specifically and significantly diversified. Furthermore, a mutated virus that is capable of using both CCR5 and CXCR4 as entry coreceptor is specifically detected in 4A HIV-1-infected mice. Taken together, our results demonstrate that APOBEC3D/F and APOBEC3G fundamentally work as restriction factors against HIV-1 in vivo, but at the same time, that APOBEC3D and APOBEC3F are capable of promoting viral diversification and evolution in vivo.

A structure-based lead optimization procedure is an essential step to finding appropriate ligand molecules binding to a target protein structure in order to identify drug candidates. This procedure takes a known structure of a protein-ligand complex as input, and structurally similar compounds with the query ligand are designed in consideration with all possible combinations of atomic species. This task is, however, computationally hard since such combinatorial optimization problems belong to the non-deterministic nonpolynomial-time hard (NP-hard) class. In this paper, we propose the structure-based lead generation and optimization procedures by a degenerate optical parametric oscillator (DOPO) network. Results of numerical simulation demonstrate that the DOPO network efficiently identifies a set of appropriate ligand molecules according to the Boltzmann sampling law.

The precise role of viral protein R (Vpr), an HIV-1-encoded protein, during HIV-1 infection and its contribution to the development of AIDS remain unclear. Previous reports have shown that Vpr has the ability to cause G2 cell cycle arrest and apoptosis in HIV-1-infected cells in vitro. In addition, vpr is highly conserved in transmitted/founder HIV-1s and in all primate lentiviruses, which are evolutionarily related to HIV-1. Although these findings suggest an important role of Vpr in HIV-1 pathogenesis, its direct evidence in vivo has not been shown. Here, by using a human hematopoietic stem cell-transplanted humanized mouse model, we demonstrated that Vpr causes G2 cell cycle arrest and apoptosis predominantly in proliferating CCR5(+) CD4(+) T cells, which mainly consist of regulatory CD4(+) T cells (Tregs), resulting in Treg depletion and enhanced virus production during acute infection. The Vpr-dependent enhancement of virus replication and Treg depletion is observed in CCR5-tropic but not CXCR4-tropic HIV-1-infected mice, suggesting that these effects are dependent on the coreceptor usage by HIV-1. Immune activation was observed in CCR5-tropic wild-type but not in vpr-deficient HIV-1-infected humanized mice. When humanized mice were treated with denileukin diftitox (DD), to deplete Tregs, DD-treated humanized mice showed massive activation/proliferation of memory T cells compared to the untreated group. This activation/proliferation enhanced CCR5 expression in memory CD4(+) T cells and rendered them more susceptible to CCR5-tropic wild-type HIV-1 infection than to vpr-deficient virus. Taken together, these results suggest that Vpr takes advantage of proliferating CCR5(+) CD4(+) T cells for enhancing viremia of CCR5-tropic HIV-1. Because Tregs exist in a higher cycling state than other T cell subsets, Tregs appear to be more vulnerable to exploitation by Vpr during acute HIV-1 infection.

Corticopetal acetylcholine (ACh) is released transiently from the nucleus basalis of Meynert (NBM) into the cortical layers and is associated with top-down attention. Recent experimental data suggest that this release of ACh disinhibits layer 2/3 pyramidal neurons (PYRs) via muscarinic presynaptic effects on inhibitory synapses. Together with other possible presynaptic cholinergic effects on excitatory synapses, this may result in dynamic and temporal modifications of synapses associated with top-down attention. However, the system-level consequences and cognitive relevance of such disinhibitions are poorly understood. Herein, we propose a theoretical possibility that such transient modifications of connectivity associated with ACh release, in addition to top-down glutamatergic input, may provide a neural mechanism for the temporal reactivation of attractors as neural correlates of memories. With baseline levels of ACh, the brain returns to quasi-attractor states, exhibiting transitive dynamics between several intrinsic internal states. This suggests that top-down attention may cause the attention-induced deformations between two types of attractor landscapes: the quasi-attractor landscape (Q-landscape, present under low-ACh, non-attentional conditions) and the attractor landscape (A-landscape, present under high-ACh, top-down attentional conditions). We present a conceptual computational model based on experimental knowledge of the structure of PYRs and interneurons (INs) in cortical layers 1 and 2/3 and discuss the possible physiological implications of our results.

BACKGROUND: The way we formulate a mathematical model of an infectious disease to capture symptomatic and asymptomatic transmission can greatly influence the likely effectiveness of vaccination in the presence of vaccine effect for preventing clinical illness. The present study aims to assess the impact of model building strategy on the epidemic threshold under vaccination. METHODOLOGY/PRINCIPAL FINDINGS: We consider two different types of mathematical models, one based on observable variables including symptom onset and recovery from clinical illness (hereafter, the "observable model") and the other based on unobservable information of infection event and infectiousness (the "unobservable model"). By imposing a number of modifying assumptions to the observable model, we let it mimic the unobservable model, identifying that the two models are fully consistent only when the incubation period is identical to the latent period and when there is no pre-symptomatic transmission. We also computed the reproduction numbers with and without vaccination, demonstrating that the data generating process of vaccine-induced reduction in symptomatic illness is consistent with the observable model only and examining how the effective reproduction number is differently calculated by two models. CONCLUSIONS: To explicitly incorporate the vaccine effect in reducing the risk of symptomatic illness into the model, it is fruitful to employ a model that directly accounts for disease progression. More modeling studies based on observable epidemiological information are called for.

Since the allocation of vaccines is often constrained by limited resources, designing an economical vaccination strategy is a fundamental goal of the epidemiological modelling. In this study, with the objective of reducing costs, we determine the optimal allocation of vaccines for a general class of infectious diseases that spread mainly via contact. We use an optimization routine to identify the roles of nodes with distinct degrees as depending on the cost of treatment to that of vaccination (relative cost of treatment). The optimal allocation drives vaccination priority to medium-degree nodes at a low relative cost of treatment or to high-degree nodes at a high relative cost of treatment. According to the presented results, we may adjust the vaccination priority in the face of an endemic situation.

Online social media are increasingly facilitating our social interactions, thereby making available a massive "digital fossil" of human behavior. Discovering and quantifying distinct patterns using these data is important for studying social behavior, although the rapid time-variant nature and large volumes of these data make this task difficult and challenging. In this study, we focused on the emergence of "collective attention" on Twitter, a popular social networking service. We propose a simple method for detecting and measuring the collective attention evoked by various types of events. This method exploits the fact that tweeting activity exhibits a burst-like increase and an irregular oscillation when a particular real-world event occurs; otherwise, it follows regular circadian rhythms. The difference between regular and irregular states in the tweet stream was measured using the Jensen-Shannon divergence, which corresponds to the intensity of collective attention. We then associated irregular incidents with their corresponding events that attracted the attention and elicited responses from large numbers of people, based on the popularity and the enhancement of key terms in posted messages or "tweets." Next, we demonstrate the effectiveness of this method using a large dataset that contained approximately 490 million Japanese tweets by over 400,000 users, in which we identified 60 cases of collective attentions, including one related to the Tohoku-oki earthquake. "Retweet" networks were also investigated to understand collective attention in terms of social interactions. This simple method provides a retrospective summary of collective attention, thereby contributing to the fundamental understanding of social behavior in the digital era.