Animal groups exhibit various captivating movement patterns, which manifest as intricate interactions among group members. Several models have been proposed to elucidate collective behaviors in animal groups. These models achieve a certain degree of efficacy; however, inconsistent experimental findings suggest insufficient accuracy. Experiments have shown that some organisms employ a single information channel and visual lateralization to glean knowledge from other individuals in collective movements. In this study, we consider individuals' visual lateralization and a single information channel and develop a self-propelled particle model to describe the collective behavior of large groups. The results suggest that homogeneous visual lateralization gives the group a strong sense of cohesiveness, thereby enabling diverse collective behaviors. As the overlapping field grows, the cohesiveness gradually dissipates. Inconsistent visual lateralization among group members can reduce the cohesiveness of the group, and when there is a high degree of heterogeneity in visual lateralization, the group loses their cohesiveness. This study also examines the influence of visual lateralization heterogeneity on specific formations, and the results indicate that the directional migration formation is responsive to such heterogeneity. We propose an information network to portray the transmission of information within groups, which explains the cohesiveness of groups and the sensitivity of the directional migration formation.
Behavior, Animal , Animals , Behavior, Animal/physiology , Models, Biological , Functional Laterality/physiology , Social Behavior , Visual Perception/physiology , Vision, Ocular/physiology
Finding biomarker genes for complex diseases attracts persistent attention due to its application in clinics. In this paper, we propose a network-based method to obtain a set of biomarker genes. The key idea is to construct a gene co-expression network among sensitive genes and cluster the genes into different modules. For each module, we can identify its representative, i.e., the gene with the largest connectivity and the smallest average shortest path length to other genes within the module. We believe these representative genes could serve as a new set of potential biomarkers for diseases. As a typical example, we investigated Alzheimer's disease, obtaining a total of 16 potential representative genes, three of which belong to the non-transcriptome. A total of 11 out of these genes are found in literature from different perspectives and methods. The incipient groups were classified into two different subtypes using machine learning algorithms. We subjected the two subtypes to Gene Ontology analysis and Kyoto Encyclopedia of Genes and Genomes analysis with healthy groups and moderate groups, respectively. The two sub-type groups were involved in two different biological processes, demonstrating the validity of this approach. This method is disease-specific and independent; hence, it can be extended to classify other kinds of complex diseases.
In biological or physical systems, the intrinsic properties of oscillators are heterogeneous and correlated. These two characteristics have been empirically validated and have garnered attention in theoretical studies. In this paper, we propose a power-law function existed between the dynamical parameters of the coupled oscillators, which can control discontinuous phase transition switching. Unlike the special designs for the coupling terms, this generalized function within the dynamical term reveals another path for generating the first-order phase transitions. The power-law relationship between dynamic characteristics is reasonable, as observed in empirical studies, such as long-term tremor activity during volcanic eruptions and ion channel characteristics of the Xenopus expression system. Our work expands the conditions that used to be strict for the occurrence of the first-order phase transitions and deepens our understanding of the impact of correlation between intrinsic parameters on phase transitions. We explain the reason why the continuous phase transition switches to the discontinuous phase transition when the control parameter is at a critical value.
Correlations between exchange rates are valuable for illuminating the dynamics of international trade and the financial dynamics of countries. This paper explores the changing interactions of the US foreign exchange market based on detrended cross-correlation analysis. First, we propose an objective way to choose a time scale parameter appropriate for comparing different samples by maximizing the summed magnitude of all DCCA coefficients. We then build weighted signed networks under this optimized time scale, which can clearly display the complex relationships between different exchange rates. Our study shows negative cross-correlations have become pyramidally rare in the past three decades. Both the number and strength of positive cross-correlations have grown, paralleling the increase in global interconnectivity. The balanced strong triads are identified subsequently after the network centrality analysis. Generally, while the strong development links revealed by foreign exchange have begun to spread to Asia since 2010, Europe is still the center of world finance, with the euro and Danish krone consistently maintaining the closest balanced development relationship. Finally, we propose a fluctuation propagation algorithm to investigate the propagation pattern of fluctuations in the inferred exchange rate networks. The results show that, over time, fluctuation propagation patterns have become simpler and more predictable.
Spiral waves are a type of typical pattern in open reaction-diffusion systems far from thermodynamic equilibrium. The study of spiral waves has attracted great interest because of its nonlinear characteristics and extensive applications. However, the study of spiral waves has been confined to continuous-time systems, while spiral waves in discrete-time systems have been rarely reported. In recent years, discrete-time models have been widely studied in ecology because of their appropriateness to systems with nonoverlapping generations and other factors. Therefore, spiral waves in discrete-time systems need to be studied. Here, we investigated a novel type of spiral wave called a composite spiral wave in a discrete-time predator-pest model, and we revealed the formation mechanism. To explain the observed phenomena, we defined and quantified a move state effect of multiperiod states caused by the coupling of adjacent stable multiperiod orbits, which is strictly consistent with the numerical results. The other move state effect is caused by an unstable focus, which is the state of the local points at the spiral center. The combined effect of these two influences can lead to rich dynamical behaviors of spiral waves, and the specific structure of the composite spiral waves is the result of the competition of the two effects in opposite directions. Our findings shed light on the dynamics of spiral waves in discrete-time systems, and they may guide the prediction and control of pests in deciduous forests.
INTRODUCTION: Severe fever with thrombocytopenia syndrome virus (SFTSV) is an emerging tick-borne virus associated with a high rate of mortality, as well as encephalitis. We aim to develop and validate a machine learning model to early predict the potential life-threatening conditions of SFTS. METHODS: The clinical presentation, demographic information, and laboratory parameters from 327 patients with SFTS at admission in three large tertiary hospitals in Jiangsu, China between 2010 to 2022 are retrieved. We establish a reservoir computing with boosted topology (RC-BT) algorithm to obtain the models' predictions of the encephalitis and mortality of patients with SFTS. The prediction performances of encephalitis and mortality are further tested and validated. Finally, we compare our RC-BT model with the other traditional machine learning algorithms including Lightgbm, support vector machine (SVM), Xgboost, Decision Tree, and Neural Network (NN). RESULTS: For the prediction of encephalitis among patients with SFTS, nine parameters are selected with equal weight, namely calcium, cholesterol, muscle soreness, dry cough, smoking history, temperature at admission, troponin T, potassium, and thermal peak. The accuracy for the validation cohort by the RC-BT model is 0.897 [95% confidence interval (CI) 0.873-0.921]. The sensitivity and negative predictive value (NPV) of the RC-BT model are 0.855 (95% CI 0.824-0.886) and 0.904 (95% CI 0.863-0.945), respectively. Area under curve of the RC-BT model for the validation cohort is 0.899 (95% CI 0.882-0.916). For the prediction of fatality among patients with SFTS, seven parameters are selected with equal weight, namely calcium, cholesterol, history of drinking, headache, field contact, potassium, and dyspnea. The accuracy of the RC-BT model is 0.903 (95% CI 0.881-0.925). The sensitivity and NPV of the RC-BT model are 0.913 (95% CI 0.902-0.924) and 0.946 (95% CI 0.917-0.975), respectively. The area under curve is 0.917 (95% CI 0.902-0.932). Importantly, the RC-BT models outperform the other artificial intelligence-based algorithms in both prediction tasks. CONCLUSIONS: Our two RC-BT models of SFTS encephalitis and fatality demonstrate high area under curves, specificity, and NPV, with nine and seven routine clinical parameters, respectively. Our models can not only greatly improve the early prognosis accuracy of SFTS, but can also be widely applied in underdeveloped areas with limited medical resources.
Network correlation dimension governs the distribution of network distance in terms of a power-law model and profoundly impacts both structural properties and dynamical processes. We develop new maximum likelihood methods which allow us robustly and objectively to identify network correlation dimension and a bounded interval of distances over which the model faithfully represents structure. We also compare the traditional practice of estimating correlation dimension by modeling as a power law the fraction of nodes within a distance to a proposed alternative of modeling as a power law the fraction of nodes at a distance. In addition, we illustrate a likelihood ratio technique for comparing the correlation dimension and small-world descriptions of network structure. Improvements from our innovations are demonstrated on a diverse selection of synthetic and empirical networks. We show that the network correlation dimension model accurately captures empirical network structure over neighborhoods of substantial size and span and outperforms the alternative small-world network scaling model. Our improved methods tend to lead to higher estimates of network correlation dimension, implying that prior studies could have produced or utilized systematic underestimates of dimension.
SARS-CoV-2 has produced various variants during its ongoing evolution. The competitive behavior driven by the co-transmission of these variants has influenced the pandemic transmission dynamics. Therefore, studying the impact of competition between SARS-CoV-2 variants on pandemic transmission dynamics is of considerable practical importance. In order to formalize the mechanism of competition between SARS-CoV-2 variants, we propose an epidemic model that takes into account the co-transmission of competing variants. The model focuses on how cross-immunity influences the transmission dynamics of SARS-CoV-2 through competitive mechanisms between strains. We found that inter-strain competition affects not only both the final size and the replacement time of the variants, but also the invasive behavior of new variants in the future. Due to the limited extent of cross-immunity in previous populations, we predict that the new strain may infect the largest number of individuals in China without control interventions. Moreover, we also observed the possibility of periodic outbreaks in the same lineage and the possibility of the resurgence of previous lineages. Without the invasion of a new variant, the previous variant (Delta variant) is projected to resurgence as early as 2023. However, its resurgence may be prevented by a new variant with a greater competitive advantage.
INTRODUCTION: Balancing the benefits and risks of antimicrobials in health care requires an understanding of their effects on antimicrobial resistance at the population scale. Therefore, we aimed to investigate the association between the population antibiotics use and resistance rates and further identify their critical thresholds. METHODS: Data for monthly consumption of six antibiotics (daily defined doses [DDDs]/1000 inpatient-days) and the number of cases caused by five common drug-resistant bacteria (occupied bed days [OBDs]/10,000 inpatient-days) from inpatients during 2009-2020 were retrieved from the electronic prescription system at Nanjing Drum Tower Hospital, a tertiary hospital in Jiangsu Province, China. Then, a nonlinear time series analysis method, named generalized additive models (GAM), was applied to analyze the pairwise relationships and thresholds of these antibiotic consumption and resistance. RESULTS: The incidence densities of carbapenem-resistant Acinetobacter baumannii (CRAB), carbapenem-resistant Klebsiella pneumoniae (CRKP), and aminoglycoside-resistant Pseudomonas aeruginosa were all strongly synchronized with recent hospital use of carbapenems and glycopeptides. Besides, the prevalence of carbapenem-resistant Escherichia coli was also highly connected the consumption of carbapenems and fluoroquinolones. To lessen resistance, we determined a threshold for carbapenem and glycopeptide usage, where the maximum consumption should not exceed 31.042 and 25.152 DDDs per 1000 OBDs, respectively; however, the thresholds of fluoroquinolones, third-generation cephalosporin, aminoglycosides, and ß-lactams have not been identified. CONCLUSIONS: The inappropriate usage of carbapenems and glycopeptides was proved to drive the incidence of common drug-resistant bacteria in hospitals. Nonlinear time series analysis provided an efficient and simple way to determine the thresholds of these antibiotics, which could provide population-specific quantitative targets for antibiotic stewardship.
Circadian rhythms of physiological and behavioral activities are regulated by a central clock. This clock is located in the bilaterally symmetrical suprachiasmatic nucleus (SCN) of mammals. Each nucleus contains a light-sensitive group of neurons, named the ventrolateral (VL) part, with the rest of the neurons being insensitive to light, named the dorsomedial (DM) group. While the coupling between the VL and DM subgroups have been investigated quite well, the communication among the four subgroups across the nuclei did not get a lot of attention. In this article, we theoretically analyzed seven motiflike connection patterns to investigate the network of the two nuclei of the SCN as a whole in relation to the function of the SCN. We investigated the entrainment ability of the SCN and found that the entrainment range is larger in the motifs containing a link between the two VL parts across the nuclei, but it is smaller in the motifs that contain a link between the two DM parts across the nuclei. The SCN may strengthen or weaken connections between the left and right nucleus to accomodate changes in external conditions, such as resynchronization after a jet lag, adjustment to photoperiod or for the aging SCN.
The classical Turing mechanism containing a long-range inhibition and a short-range self-enhancement provides a type of explanation for the formation of patterns on body surfaces of some vertebrates, e.g., zebras, giraffes, and cheetahs. For other type of patterns (irregular spots) on body surfaces of some vertebrates, e.g., loaches, finless eels, and dalmatian dogs, the classical Turing mechanism no longer applies. Here, we propose a mechanism, i.e., the supercritical pitchfork bifurcation, which may explain the formation of this type of irregular spots, and present a method to quantify the similarity of such patterns. We assume that, under certain conditions, the only stable state of "morphogen" loses its stability and transitions to two newly generated stable states with the influence of external noise, thus producing such ruleless piebald patterns in space. The difference between the competitiveness of these two states may affect the resulting pattern. Moreover, we propose a mathematical model based on this conjecture and obtain this type of irregular patterns by numerical simulation. Furthermore, we also study the influence of parameters in the model on pattern structures and obtain the corresponding pattern structures of some vertebrates in nature, which verifies our conjecture.
Models, Biological , Vertebrates , Animals , Computer Simulation , Dogs , Models, Theoretical
Dimension governs dynamical processes on networks. The social and technological networks which we encounter in everyday life span a wide range of dimensions, but studies of spreading on finite-dimensional networks are usually restricted to one or two dimensions. To facilitate investigation of the impact of dimension on spreading processes, we define a flexible higher-dimensional small world network model and characterize the dependence of its structural properties on dimension. Subsequently, we derive mean field, pair approximation, intertwined continuous Markov chain and probabilistic discrete Markov chain models of a COVID-19-inspired susceptible-exposed-infected-removed (SEIR) epidemic process with quarantine and isolation strategies, and for each model identify the basic reproduction number R 0 , which determines whether an introduced infinitesimal level of infection in an initially susceptible population will shrink or grow. We apply these four continuous state models, together with discrete state Monte Carlo simulations, to analyse how spreading varies with model parameters. Both network properties and the outcome of Monte Carlo simulations vary substantially with dimension or rewiring rate, but predictions of continuous state models change only slightly. A different trend appears for epidemic model parameters: as these vary, the outcomes of Monte Carlo change less than those of continuous state methods. Furthermore, under a wide range of conditions, the four continuous state approximations present similar deviations from the outcome of Monte Carlo simulations. This bias is usually least when using the pair approximation model, varies only slightly with network size, and decreases with dimension or rewiring rate. Finally, we characterize the discrepancies between Monte Carlo and continuous state models by simultaneously considering network efficiency and network size.
A master clock located in the suprachiasmatic nucleus (SCN) regulates the circadian rhythm of physiological and behavioral activities in mammals. The SCN has two main functions in the regulation: an endogenous clock produces the endogenous rhythmic signal in body rhythms, and a calibrator synchronizes the body rhythms to the external light-dark cycle. These two functions have been determined to depend on either the dynamic behaviors of individual neurons or the whole SCN neuronal network. In this review, we first introduce possible network structures for the SCN, as revealed by time series analysis from real experimental data. It was found that the SCN network is heterogeneous and sparse, that is, the average shortest path length is very short, some nodes are hubs with large node degrees but most nodes have small node degrees, and the average node degree of the network is small. Secondly, the effects of the SCN network structure on the SCN function are reviewed based on mathematical models of the SCN network. It was found that robust rhythms with large amplitudes, a high synchronization between SCN neurons and a large entrainment ability exists mainly in small-world and scale-free type networks, but not other types. We conclude that the SCN most probably is an efficient small-world type or scale-free type network, which drives SCN function.
The output signals of neurons that are exposed to external stimuli are of great importance for brain functionality. Traditional time-series analysis methods have provided encouraging results; however, the associated patterns and their correlations in the output signals of neurons are masked by statistical procedures. Here, graphlets are employed to extract the local temporal patterns and the transitions between them from the output signals when neurons are exposed to external stimuli with selected stimulating periods. A transition network is defined where the node is the graphlet and the direct link is the transition between two successive graphlets. The transition-network structure is affected by the simulating periods. When the stimulating period moves close to an integer multiple of the neuronal intrinsic period, only the backbone or core survives, while the other linkages disappear. Interestingly, the size of the backbone (number of nodes) equals the multiple. The transition-network structure is conservative within each stimulating region, which is defined as the range between two successive integer multiples. Nevertheless, the backbone or detailed structure is significantly altered between different stimulating regions. This alternation is induced primarily from a total of 12 active linkages. Hence, the transition network shows the structure of cross correlations in the output time-series for a single neuron.
Neurons
Lymphoma is the most complicated cancer that can be divided into several tens of subtypes. It may occur in any part of body that has lymphocytes, and is closely correlated with diverse environmental factors such as the ionizing radiation, chemocarcinogenesis, and virus infection. All the environmental factors affect the lymphoma through genes. Identifying pathogenic genes for lymphoma is consequently an essential task to understand its complexity in a unified framework. In this paper, we propose a new method to expose high-confident edges in gene regulatory networks (GRNs) for a total of 32 organs, called Filtered GRNs (f-GRNs), comparison of which gives us a proper reference for the Lymphoma, i.e. the B-lymphocytes cells, whose f-GRN is closest with that for the Lymphoma. By using the Gene Ontology and Biological Process analysis we display the differences of the two networks' hubs in biological functions. Matching with the Genecards shows that most of the hubs take part in the genetic information transmission and expression, except a specific gene of Retinoic Acid Receptor Alpha (RARA) that encodes the retinoic acid receptor. In the lymphoma, the genes in the RARA ego-network are involved in two cancer pathways, and the RARA is present only in these cancer pathways. For the lymphoid B cells, however, the genes in the RARA ego-network do not participate in cancer-related pathways.
Gene Regulatory Networks , Lymphoma/genetics , B-Lymphocytes/physiology , Computational Biology/methods , Gene Expression Regulation, Neoplastic , Gene Ontology , Humans , Lymphoma/pathology , Retinoic Acid Receptor alpha/genetics
Significant advances have recently been made in modeling chaotic systems with the reservoir computing approach, especially for prediction. We find that although state prediction of the trained reservoir computer will gradually deviate from the actual trajectory of the original system, the associated geometric features remain invariant. Specifically, we show that the typical geometric metrics including the correlation dimension, the multiscale entropy, and the memory effect are nearly identical between the trained reservoir computer and its learned chaotic systems. We further demonstrate this fact on a broad range of chaotic systems ranging from discrete and continuous chaotic systems to hyperchaotic systems. Our findings suggest that the successfully reservoir computer may be topologically conjugate to an observed dynamical system.
Previous studies claim that the dynamic behaviors of spiral waves are uniquely determined by the nature of the medium, which can be determined by control parameters. In this article, the authors break from the previous view and present an alternate stable state of spiral waves, named the excited state. The authors find that two states of the spiral wave switch to each other after a one-off pulse is applied to the medium. The dynamic behaviors of the two states are quite different, specifically, the spiral tip trajectory of the original spiral, which is named the ground-state spiral as observed in the previous studies, is a point, while the spiral tip trajectory of the excited-state spiral is a circle. Moreover, the authors study the trajectories of the spiral tip of spiral waves in both states after the pulse is applied and find two types of trajectories, a spiral trajectory and a spiral-inward-petal trajectory. The frequency of the spiral wave in the excited state is less than that in the ground state. The findings enrich the dynamics of pattern formation.
In mammals, an endogenous clock located in the suprachiasmatic nucleus (SCN) of the brain regulates the circadian rhythms of physiological and behavioral activities. The SCN is composed of about 20,000 neurons that are autonomous oscillators with nonidentical intrinsic periods ranging from 22 h to 28 h. These neurons are coupled through neurotransmitters and synchronized to form a network, which produces a robust circadian rhythm of a uniform period. The neurons, which are the nodes in the network, are known to be heterogeneous in their characteristics, which is reflected in different phenotypes and different functionality. This heterogeneous nature of the nodes of the network leads to the question as to whether the structure of the SCN network is assortative or disassortative. Thus far, the disassortativity of the SCN network has not been assessed and neither have its effects on the collective behaviors of the SCN neurons. In the present study, we build a directed SCN network composed of hundreds of neurons for a single slice using the method of transfer entropy, based on the experimental data. Then, we measured the synchronization degree as well as the disassortativity coefficient of the network structure (calculated by either the out-degrees or the in-degrees of the nodes) and found that the network of the SCN is a disassortative network. Furthermore, a positive relationship is observed between the synchronization degree and disassortativity of the network, which is confirmed by simulations of our modeling. Our finding suggests that the disassortativity of the network structure plays a role in the synchronization between SCN neurons; that is, the synchronization degree increases with the increase of the disassortativity, which implies that a more heterogeneous coupling in the network of the SCN is important for proper function of the SCN.
Biological Clocks , Circadian Rhythm , Nerve Net/physiology , Neurons/physiology , Suprachiasmatic Nucleus/physiology , Algorithms , Animals , Computer Simulation , Entropy , In Vitro Techniques , Mice , Models, Theoretical , Nerve Net/drug effects , Neurons/drug effects , Suprachiasmatic Nucleus/cytology , Suprachiasmatic Nucleus/drug effects , Tetrodotoxin/pharmacology
Recent advances have demonstrated the effectiveness of a machine-learning approach known as "reservoir computing" for model-free prediction of chaotic systems. We find that a well-trained reservoir computer can synchronize with its learned chaotic systems by linking them with a common signal. A necessary condition for achieving this synchronization is the negative values of the sub-Lyapunov exponents. Remarkably, we show that by sending just a scalar signal, one can achieve synchronism in trained reservoir computers and a cascading synchronization among chaotic systems and their fitted reservoir computers. Moreover, we demonstrate that this synchronization is maintained even in the presence of a parameter mismatch. Our findings possibly provide a path for accurate production of all expected signals in unknown chaotic systems using just one observational measure.
Recent years have witnessed special attention on complex network based time series analysis. To extract evolutionary behaviors of a complex system, an interesting strategy is to separate the time series into successive segments, map them further to graphlets as representatives of states, and extract from the state (graphlet) chain transition properties, called graphlet based time series analysis. Generally speaking, properties of time series depend on the time scale. In reality, a time series consists of records that are sampled usually with a specific frequency. A natural question is how the evolutionary behaviors obtained with the graphlet approach depend on the sampling frequency? In the present paper, a new concept called the sampling frequency dependent visibility graphlet is proposed to answer this problem. The key idea is to extract a new set of series in which the successive elements have a specified delay and obtain the state transition network with the graphlet based approach. The dependence of the state transition network on the sampling period (delay) can show us the characteristics of the time series at different time scales. Detailed calculations are conducted with time series produced by the fractional Brownian motion, logistic map and Rössler system, and the empirical sentence length series for the famous Chinese novel entitled A Story of the Stone. It is found that the transition networks for fractional Brownian motions with different Hurst exponents all share a backbone pattern. The linkage strengths in the backbones for the motions with different Hurst exponents have small but distinguishable differences in quantity. The pattern also occurs in the sentence length series; however, the linkage strengths in the pattern have significant differences with that for the fractional Brownian motions. For the period-eight trajectory generated with the logistic map, there appear three different patterns corresponding to the conditions of the sampling period being odd/even-fold of eight or not both. For the chaotic trajectory of the logistic map, the backbone pattern of the transition network for sampling 1 saturates rapidly to a new structure when the sampling period is larger than 2. For the chaotic trajectory of the Rössler system, the backbone structure of the transition network is initially formed with two self-loops, the linkage strengths of which decrease monotonically with the increase of the sampling period. When the sampling period reaches 9, a new large loop appears. The pattern saturates to a complex structure when the sampling period is larger than 11. Hence, the new concept can tell us new information on the trajectories. It can be extended to analyze other series produced by brains, stock markets, and so on.
