Evolutionary game dynamics of combining two different aspiration-driven update rules in structured populations

In evolutionary games,most studies on finite populations have focused on a single updating mechanism.However,given the differences in individual cognition,individuals may change their strategies according to different updating mechanisms.For this reason,we consider two different aspiration-driven updating mechanisms in structured populations:satisfied-stay unsatisfied shift(SSUS)and satisfied-cooperate unsatisfied defect(SCUD).To simulate the game player’s learning process,this paper improves the particle swarm optimization algorithm,which will be used to simulate the game player’s strategy selection,i.e.,population particle swarm optimization(PPSO)algorithms.We find that in the prisoner’s dilemma,the conditions that SSUS facilitates the evolution of cooperation do not enable cooperation to emerge.In contrast,SCUD conditions that promote the evolution of cooperation enable cooperation to emerge.In addition,the invasion of SCUD individuals helps promote cooperation among SSUS individuals.Simulated by the PPSO algorithm,the theoretical approximation results are found to be consistent with the trend of change in the simulation results.

Evolutionary dynamics of tax-based strong altruistic reward andpunishment in a public goods game

In public goods games, punishments and rewards have been shown to be effective mechanisms for maintaining individualcooperation. However, punishments and rewards are costly to incentivize cooperation. Therefore, the generation ofcostly penalties and rewards has been a complex problem in promoting the development of cooperation. In real society,specialized institutions exist to punish evil people or reward good people by collecting taxes. We propose a strong altruisticpunishment or reward strategy in the public goods game through this phenomenon. Through theoretical analysis and numericalcalculation, we can get that tax-based strong altruistic punishment (reward) has more evolutionary advantages thantraditional strong altruistic punishment (reward) in maintaining cooperation and tax-based strong altruistic reward leads toa higher level of cooperation than tax-based strong altruistic punishment.

Estimating the Scarlet Fever Epidemics Using a Seasonal Autoregressive Fractionally Integrated Moving Average Model

Scarlet fever(SF)is a common infectious disease caused by group A streptococcus(GAS)[1].During the 18th and 19th centuries,SF was a significant cause of mortality in children aged 5-15 years worldwide[2].The incidence and fatality rates of SF have decreased remarkably due to the widespread use of effective antibiotics and improvements in diet and sanitation[3].However,the recent resurgence of SF has sparked significant interest in infectious diseases[1,3].Given the insufficient understanding of the triggers that cause SF outbreaks and the absence of available vaccines to prevent GAS infection to date[1],effective prevention and control programs are needed to manage the ongoing spread of SF.

Activation of endogenous neurogenesis and angiogenesis by basic fibroblast growth factor-chitosan gel in an adult rat model of ischemic stroke

Attempts have been made to use cell transplantation and biomaterials to promote cell proliferation,differentiation,migration,and survival,as well as angiogenesis,in the context of brain injury.However,whether bioactive materials can repair the damage caused by ischemic stroke by activating endogenous neurogenesis and angiogenesis is still unknown.In this study,we applied chitosan gel loaded with basic fibroblast growth factor to the stroke cavity 7 days after ischemic stroke in rats.The gel slowly released basic fibroblast growth factor,which improved the local microenvironment,activated endogenous neural stem/progenitor cells,and recruited these cells to migrate toward the penumbra and stroke cavity and subsequently differentiate into neurons,while enhancing angiogenesis in the penumbra and stroke cavity and ultimately leading to partial functional recovery.This study revealed the mechanism by which bioactive materials repair ischemic strokes,thus providing a new strategy for the clinical application of bioactive materials in the treatment of ischemic stroke.

Understanding the educational inequalities in suicide attempts and their mediators:a Mendelian randomisation study

Background Educational inequalities in suicide have become increasingly prominent over the past decade.Elucidating modifiable risk factors that serve as intermediaries in the impact of low educational attainment on suicide has the potential to reduce health disparities.Aims To examine the risk factors that mediate the relationship between educational attainment and suicide attempts and quantify their contributions to the mediation effect.Methods We conducted a two-sample Mendelian randomisation(MR)analysis to estimate the causal effect of educational attainment on suicide attempts,utilising genome-wide association study summary statistics from the Integrative Psychiatric Research(iPSYCH;6024 cases and 44240 controls)and FinnGen(8978 cases and 368299 controls).We systematically evaluated 42 putative mediators within the causal pathway connecting reduced educational attainment to suicide attempts and employed two-step and multivariable MR to quantify the proportion of the mediated effect.Results In the combined analysis of iPSYCH and FinnGen,each standard deviation(SD)decrease in genetically predicted educational attainment(equating to 3.4 years of education)was associated with a 105%higher risk of suicide attempts(odds ratio(OR):2.05;95%confidence interval(Cl):1.81 to 2.31).0f the 42 risk factors analysed,the two-step MR identified five factors that mediated the association between educational attainment and suicide attempts.The respective proportions of mediation were 47%(95%Cl:29%to 66%)for smoking behaviour,36%(95%Cl:0%to 84%)for chronic pain,49%(95%Cl:36%to 61%)for depression,35%(95%Cl:12%to 59%)for anxiety and 26%(95%Cl:18%to 34%)for insomnia.Multivariable MR implicated these five mediators collectively,accounting for 68%(95%Cl:40%to 96%)of the total effect.Conclusions This study identified smoking,chronic pain and mental disorders as primary intervention targets for attenuating suicide risk attributable to lower educational levels in the European population.

Plant-based dietary patterns and risk of esophageal cancer:A prospective cohort study spanning 17 years

Objective: Plant-based diets have multiple health benefits for cancers;however, little is known about the association between plant-based dietary patterns and esophageal cancer(EC).This study presents an investigation of the prospective associations among three predefined indices of plant-based dietary patterns and the risk of EC.Methods: We performed endoscopic screening for 15,709 participants aged 40-69 years from two high-risk areas of China from January 2005 to December 2009 and followed the cohort until December 31, 2022. The overall plant-based diet index(PDI), healthful plant-based diet index(h PDI), and unhealthful plant-based diet index(u PDI), were calculated using survey responses to assess dietary patterns. We applied Cox proportional hazard regression to estimate the multivariable hazard ratios(HRs) and 95% confidence intervals(95% CIs) of EC across 3plant-based diet indices and further stratified the analysis by subgroups.Results: The final study sample included 15,184 participants in the cohort. During a follow-up of 219,365person-years, 176 patients with EC were identified. When the highest quartile was compared with the lowest quartile, the pooled multivariable-adjusted HR of EC was 0.50(95% CI, 0.32-0.77) for h PDI. In addition, the HR per 10-point increase in the h PDI score was 0.42(95% CI, 0.27-0.66) for ECs. Conversely, u PDI was positively associated with the risk of EC, and the HR was 1.80(95% CI, 1.16-2.82). The HR per 10-point increase in the u PDI score was 1.90(95% CI, 1.26-2.88) for ECs. The associations between these scores and the risk of EC were consistent in most subgroups. These results remained robust in sensitivity analyses.Conclusions: A healthy plant-based dietary pattern was associated with a reduced risk of EC. Emphasizing the healthiness and quality of plant-based diets may be important for preventing the development of EC.

Changes in the Non-targeted Metabolomic Profile of Three-year-old Toddlers with Elevated Exposure to Polycyclic Aromatic Hydrocarbons

Objective To investigate changes in the urinary metabolite profiles of children exposed to polycyclic aromatic hydrocarbons(PAHs)during critical brain development and explore their potential link with the intestinal microbiota.Methods Liquid chromatography-tandem mass spectrometry was used to determine ten hydroxyl metabolites of PAHs(OH-PAHs)in 36-month-old children.Subsequently,37 children were categorized into low-and high-exposure groups based on the sum of the ten OH-PAHs.Ultra-high-performance liquid chromatography coupled with quadrupole time-of-flight mass spectrometry was used to identify non-targeted metabolites in the urine samples.Furthermore,fecal flora abundance was assessed by 16S rRNA gene sequencing using Illumina MiSeq.Results The concentrations of 21 metabolites were significantly higher in the high exposure group than in the low exposure group(variable importance for projection>1,P<0.05).Most of these metabolites were positively correlated with the hydroxyl metabolites of naphthalene,fluorine,and phenanthrene(r=0.336–0.531).The identified differential metabolites primarily belonged to pathways associated with inflammation or proinflammatory states,including amino acid,lipid,and nucleotide metabolism.Additionally,these distinct metabolites were significantly associated with specific intestinal flora abundances(r=0.34–0.55),which were mainly involved in neurodevelopment.Conclusion Higher PAH exposure in young children affected metabolic homeostasis,particularly that of certain gut microbiota-derived metabolites.Further investigation is needed to explore the potential influence of PAHs on the gut microbiota and their possible association with neurodevelopmental outcomes.

Genetic Variations and Nonalcoholic Fatty Liver Disease:Field Synopsis,Systematic Meta-Analysis,and Epidemiological Evidence

Objective To systematically summarize the published literature on the genetic variants associated with nonalcoholic fatty liver disease(NAFLD).Methods Literature from Web of Science,PubMed,and Embase between January 1980 and September 2022 was systematically searched.Meta-analyses of the genetic variants were conducted using at least five data sources.The epidemiologic credibility of the significant associations was graded using the Venice criteria.Results Based on literature screening,399 eligible studies were included,comprising 381 candidate gene association,16 genome-wide association,and 2 whole-exome sequencing studies.We identified 465 genetic variants in 173 genes in candidate gene association studies,and 25 genetic variants in 17 genes were included in the meta-analysis.The meta-analysis identified 11 variants in 10 genes that were significantly associated with NAFLD,with cumulative epidemiological evidence of an association graded as strong for two variants in two genes(HFE,TNF),moderate for four variants in three genes(TM6SF2,GCKR,and ADIPOQ),and weak for five variants in five genes(MBOAT7,PEMT,PNPLA3,LEPR,and MTHFR).Conclusion This study identified six variants in five genes that had moderate to strong evidence of an association with NAFLD,which may help understand the genetic architecture of NAFLD risk.

Low Level of Cystic Fibrosis Transmembrane Conductance Regulator Is Associated with Human Sperm Autophagy and Vitality

Low sperm motility is one of the main causes of male infertility. Cystic fibrosis transmembrane conductance regulator (CFTR, an anion channel protein) is related to the progressive motility of sperm. CFTR disruptor CFTRinh-172 or forskolin (FSK) in this study were used to treat human sperm separately, and the rates of sperm autophagy and progressive motility, mitochondrial membrane potential (MMP) and ATP concentration, and the expression levels of related factors were detected to explore their relationship. It was showed that sperms treated with CFTRinh-172 or FSK reduced the levels of cAMP, CFTR and PKA, but increased sperm autophagy rate, expression levels of AMPK and LC3B. However, reactive oxygen species content had no significant difference. It was indicated that low level of CFTR performed with cAMP and its downstream effectors such as PKA and AMPK to regulate mitochondrial structure and function, leading to increased autophagy rate and reduced vitality of sperm.

Development of diabetic complications and influencing factors among 32653 type 2 diabetes patients:retrospective cohort study using a multi-state Markov

Background:Patients with type 2 diabetes are at high risk for developing multiple chronic complications.However,there is a lack of studies of the cumulative number of diabetic complications in China.Methods:A retrospective cohort study was performed from 2009 to 2021.Type 2 diabetes patients who were first diagnosed after the age of 35 years between January 1,2009,and December 31,2017,were included.Five states were defined according to the number of chronic complications:no(S0),one(S1),two(S2),three(S3),and four or more complications(S4).A multi-state Markov model was constructed to estimate transition probability,transition intensity,mean sojourn time,and the possible factors for each state.Results:The study included 32653 type 2 diabetes patients(mean age,59.59 years;15929(48.8%)male),and mean follow-up time of 7.75 years.In all,4375 transitions were observed.The 12-year transition probability of from state S0 to S1 was the lowest at 16.4%,while that from S2 to S3 was the highest,at 45.6%.Higher fasting blood glucose,lower high-density lipoprotein cholesterol,higher total cholesterol,and an unhealthy diet were associated with higher risk of progression from S0 to S1.Being female,less than 60 years old,weekly physical activity,and vegetarian diet decreased this risk.Being female and less than 60 years old reduced the likelihood of transition from S1 to S2,whereas lower high-density lipoprotein cholesterol increased this likelihood.Conclusions:Following the occurrence of two complications in type 2 diabetes patients,the risk for accumulating a third complication within a short time is significantly increased.It is important to take advantage of the stable window period when patients have fewer than two complications,strengthen the monitoring of blood glucose and blood lipids,and encourage patients to maintain good living habits to prevent further deterioration.

Correlation between postoperative chemotherapy regimen and survival in patients with resectable gastric adenocarcinoma accompanied with vascular cancer thrombus

BACKGROUND Patients with resectable gastric adenocarcinoma accompanied by vascular cancer thrombus(RGAVCT)have a poor prognosis,with a 5-year survival rate ranging from 18.42%-53.57%.These patients need a reasonable postoperative treatment plan to improve their prognosis.AIM To determine the most effective postoperative chemotherapy regimen for patients with RGAVCT.METHODS We retrospectively collected the clinicopathological data of 530 patients who un-derwent radical resection for gastric cancer between January 2017 and January 2022 and who were pathologically diagnosed with gastric adenocarcinoma with a choroidal cancer embolus.Fur-thermore,we identified the high-risk variables that can influence the prognosis of patients with RGAVCT by asse-ssing the clinical and pathological features of the patients who met the inclusion criteria.We also assessed the significance of survival outcomes using Mantel-Cox univariate and multivariate analyses.The subgroups of pa-tients with stages Ⅰ,Ⅱ,and Ⅲ disease who received single-,dual-,or triple-drug regimens following surgery were analyzed using SPSS 25.0 and the ggplot2 package in R 4.3.0.RESULTS In all,530 eligible individuals with RGAVCT were enrolled in this study.The median overall survival(OS)of patients with RGAVCT was 24 months,and the survival rates were 80.2%,62.5%,and 42.3%at 12,24,and 59 months,respectively.Preoperative complications,tumor size,T stage,and postoperative chemotherapy were identified as independent factors that influenced OS in patients with RGAVCT according to the Cox multivariate analysis model.A Kaplan-Meier analysis revealed that chemotherapy had no effect on OS of patients with stage Ⅰ or Ⅱ RGAVCT;however,chemotherapy did have an effect on OS of stage Ⅲ patients.Stage Ⅲ patients who were treated with chemotherapy consisting of dual-or triple-agent regimens had better survival than those treated with single-agent regimens,and no significant difference was observed in the survival of patients treated with chemo-therapy consisting of dual-or triple-agent regimens.CONCLUSION For patients with stage Ⅲ RGAVCT,a dual-agent regimen of postoperative chemotherapy should be recom-mended rather than a triple-agent treatment,as the latter is associated with increased frequency of adverse events.

Optimization of Douchi Fibrinolytic Enzyme Production by Statistical Experimental Methods

Thrombus disease, one of the common cardiovascular diseases, has attracted worldwide at- tention for its rising mortality and morbidity. Due to the distinct shortages of current fibrinolytic drugs, new fibrinolytic agents warrant investigation. In this study, 8 fibrinolytic enzyme-producing strains were isolated from Douchi--a traditional Chinese food, and strain XY-1 which produced the largest amount of the enzyme was chosen for the following experiments. The enzyme produced by strain XY-1 was named Douchi fibrinolytic enzyme （DFE）. We optimized the liquid culture medium of strain XY-1 for enzyme production using Plackett-Burman and Box-Behnken design. The predicted maximal DFE yield was 19.78 FU/mL with 11.4 g/L peptone, 0.5 g/L magnesium sulfate and 1 g/L sodium chloride. How- ever, we acquired maximal production of 21.33 FU/mL in actual experiments, equal to 107.84% of the theoretical value, and the yield had been increased by 79.55% as compared to the yield of un-optimized culture. It was demonstrated that the combined use of Plackett-Burman design and response surface methodology in fermentation optimization can effectively and rapidly increase DFE production.

Statistical Analysis and Evaluation of Macroeconomic Policies: A Selective Review

In this paper,we highlight some recent developments of a new route to evaluate macroeconomic policy effects,which are investigated under the framework with potential outcomes.First,this paper begins with a brief introduction of the basic model setup in modern econometric analysis of program evaluation.Secondly,primary attention goes to the focus on causal effect estimation of macroeconomic policy with single time series data together with some extensions to multiple time series data.Furthermore,we examine the connection of this new approach to traditional macroeconomic models for policy analysis and evaluation.Finally,we conclude by addressing some possible future research directions in statistics and econometrics.

Short-term Impact of Cognition-Motivation-Emotional IntelligenceResistance Skills Program on Drug Use Prevention for School Students in Wuhan,China

Drug abuse continues to be a serious public health threat worldwide.Most drug abuse prevention research has been conducted with predominantly American or European adolescent populations.Little is known about approaches that work best to prevent the initiation of Chinese adolescent drug use.For targeting risk factors of drug initiation in Chinese adolescents,a school-based health intervention program named "Cognition-Motivation-Emotional IntelligenceResistance Skills" (CMER) was developed to enhance cognition upon drug use,to decrease motivation of drug use and to improve emotional adjusting and drug resistance skills in this study.A total of 798 students from 3 senior high schools in Wuhan,a city in central China,were assigned randomly to intervention and control groups.The intervention group received the CMER program in which knowledge,development of positive attitude and motivation towards drugs and training of peer resistance skills were basic elements.The immediate impact was compared by measuring the above mentioned elements prior to and three-month after the training session.Students from both groups were asked to complete a self-administered questionnaire.The questionnaire included demographic items,self-reported drug use behavior,cognition,attitude,and motivation associated with the initiation of drug use and resistance skills.Three months after the intervention,significant effects were found on "illegal substance use at least once" (P【0.05) between the intervention and control groups.Immediate effects of the intervention were also found on knowledge,motivation and peer resistance skills (P【0.05),but there was no clear evidence for any effects on attitude towards substance use (P】0.05).It was concluded that the CMER program,which significantly increased the knowledge of drugs and peer resistance skills,was effective in the drug abuse prevention in a sample of school students in Wuhan,China.

Relationship between Migration and HIV Risky Behavior: a Comparative Study of Returning Migrants and Non Migrants Based on Rural Out-of-school Youth in Jilin, China

Objective To estimate the relationship between migration and HIV risky behavior when controlling for gender, age, and educational levels and to evaluate the gender differences in migration, HIV knowledge, and HIV risky behaviors among rural youth in China. Methods A cross-sectional, anonymous, investigative questionnaire for 1710 unmarried, out-of-school rural youth, aged between 15 and 24 years, was handed out in Gongzhuling county of Jilin province, China. Results 58.5% of participants had a history of migration, irrespective of gender. There were gender differences observed in other factors such as drug abuse（4.3% for males and 5.5% for females, P〈0.01）, multiple sexual partners（24.1% for males and 44.1% for females, P〈0.01）, and HIV knowledge rate（35.2% for males and 25.5% for females, P〈0.001）. While controlling for gender, age, and educational levels, the relationships between migration and drug abuse, selling sex, and non usage of condoms during last instance of sexual activity were found to be significant. The cases of premarital sex and multiple sexual partners were both not found to be related to migration. Conclusion Among rural youth, the HIV risky behavior such as drug abuse, selling sex, and lack of condom use, is significantly related to migration, while premarital sex and multiple sexual partners seem unrelated to migration.

Comparison of two statistical models in predicting the outcome of female systemic lupus erythematosus patients in China

Objectives: Comparing two different statistical models to predict female SLE patients’ outcome and analyze some related factors. Methods: 1072 female SLE patients were from the Provincial Hospital of Anhui Province and The First Ancillary Hospital of Anhui Medical University from 1990 to 2000. Two types of statistical models including loglinear and Cox proportional hazard model were performed according to this data. Results: Marriage situation, family place, admission situation, whether coming from a different division, nosocomial infection, first occurrent or not and number of drug types had significant effects on LOS after fitting of a loglinear model. Related factors from Cox proportional hazard model were little more than those selected from loglinear model. Based on the former model, a female SLE patient could be predicted that how long she would stay in hospital. But from the latter model, we could predict the ratio of the probability of improvement between different groups of female SLE patients with different individual or clinical characteristics. Conclusions: Factors affecting the length of stay of female SLE patients could be selected from either loglinear model or Cox model. But these two models would be used to do different predictions.

The Effect of the Family’s Socioeconomic Factors on Nutrition of Elementary School Children

Introduction: Anthropometric indices are used for assessing the nutrition status of people and societies. The indices determine the growth of the child’s nutrition status, his socioeconomic status and his quality of life. This research aims to study the anthropometric indices of elementary school children in the Iranian city of Piranshahr using the Body Mass Index (BMI) and waist circumference in the first six months of 2011. Methods: In this descriptive-analytical cross-sectional study, 1803 students aged between 7 and 11 in Piranshahr were studied. Multi-stage cluster sampling was used. The research setting was an elementary school in Piranshahr. Demographic data were collected through interviews and record in questionnaires. A Secca stadiometer was used to measure the height of each student standing without shoes (accuracy of 0.1 centimeter). The weight was measured using a spring scale with an accuracy of 0.1 kilogram with the least possible clothes on. The weight was divided by the square of height (square meter) to calculate BMI. To determine overweight and obesity, BMI percentiles of Center for Disease Control (CDC) were used. In order to use appropriate tests, the normality and equality of variances were measured by Leven and K-S tests, respectively. Results: The study found that 231 children (12.8%) were at risk of overweight and 96 children (5.3%) were overweight. Conclusion: There was a meaningful difference between boys and girls in terms of nutrition status of BMI, father’s higher education level, shortness, abdominal obesity and family history of obesity, and father’s jobs

Cognitive and Behavioral Effects of Participatory Sex Education on the Dual Prevention of STI/HIV/AIDS and Unwanted Pregnancies among Adolescents in Kinshasa High Schools, DR Congo

Context: With the view to reorient both STI/HIV/AIDS prevention and adolescents pregnancies, this research study aims at evaluating cognitive and behavioral acquisitions, as well as the process of interactive sex education participatory approach among adolescents in Kinshasa high schools. Methods: Based on a “pre and post” virtually experimental design, two crosswise surveys were conducted in Kinshasa, for six months in 2011-2012 on 484 high school students (pre-survey) and on 441 high school students (post-survey), whose age range from 14 - 19 years including both sexes. Two participatory educational talks (PET) “A” and “B”, covered weekly in two different schools, were compared to a control group school. The PET “A” consisted of interactive interpersonal communication sessions given by an external expert as a substitute for the life education course in one school. The PET “B” carried out in another school, included more educational talk sessions, led by the external expert and supplemented by a close follow-up of teenagers divided into small groups of 10 participants. The subjects’ assessment was based on their knowledge, attitudes and practices relating to STI/HIV/AIDS dual prevention as well as to unwanted pregnancies. Results: The subjects involved in the PET “B” displayed a better/higher performance based on their knowledge, attitudes and practices related to STI/HIV/AIDS dual prevention and unwanted pregnancies. Broadly speaking, knowledge has been improved 6 times with the PET “B” (OR = 6, 10, IC 95%) (3.24 - 11.9), and 3 times with the PET “A” (OR = 3, 45, IC 95%) (1.79 - 6.81), compared to control school. Similarly, findings on subjects’ attitudes show an improvement rated 12 times with the PET”B” (OR = 11, 99, IC 95%) (5.67 - 27.38) and 5 times for the PET “A” (OR = 5.51, IC 95%) (2.54 - 12.87). As far as the subjects’ practices are concerned, an improvement of 6 more times of protected sexual intercourses with the PET “B” compared with the control school group (OR = 6, 52, IC 95%) (3.60 - 12.0). The process assessment records a spontaneous involvement of schools enhanced by the positive contribution of Life Education and Biology teachers;add a massive participation of adolescents who requested permanent PET program. Conclusion: The results of this study suggest that school sexual education programs can be improved to increase the quality of apprenticeship. The use of interactive methods and the consideration of the adolescents’ specific needs that take into account the gender approach may bring about beneficial advantages on both educational outcomes and reproductive health of adolescents.

Probabilistic time series forecasting with deep non-linear state space models

Probabilistic time series forecasting aims at estimating future probabilistic distributions based on given time series observations.It is a widespread challenge in various tasks,such as risk management and decision making.To investigate temporal patterns in time series data and predict subsequent probabilities,the state space model(SSM)provides a general framework.Variants of SSM achieve considerable success in many fields,such as engineering and statistics.However,since underlying processes in real-world scenarios are usually unknown and complicated,actual time series observations are always irregular and noisy.Therefore,it is very difficult to determinate an SSM for classical statistical approaches.In this paper,a general time series forecasting framework,called Deep Nonlinear State Space Model(DNLSSM),is proposed to predict the probabilistic distribution based on estimated underlying unknown processes from historical time series data.We fuse deep neural networks and statistical methods to iteratively estimate states and network parameters and thus exploit intricate temporal patterns of time series data.In particular,the unscented Kalman filter(UKF)is adopted to calculate marginal likelihoods and update distributions recursively for non-linear functions.After that,a non-linear Joseph form covariance update is developed to ensure that calculated covariance matrices in UKF updates are symmetric and positive definitive.Therefore,the authors enhance the tolerance of UKF to round-off errors and manage to combine UKF and deep neural networks.In this manner,the DNLSSM effectively models non-linear correlations between observed time series data and underlying dynamic processes.Experiments in both synthetic and real-world datasets demonstrate that the DNLSSM consistently improves the accuracy of probability forecasts compared to the baseline methods.

Time series analysis-based seasonal autoregressive fractionally integrated moving average to estimate hepatitis B and C epidemics in China

BACKGROUND Hepatitis B(HB)and hepatitis C(HC)place the largest burden in China,and a goal of eliminating them as a major public health threat by 2030 has been set.Making more informed and accurate forecasts of their spread is essential for developing effective strategies,heightening the requirement for early warning to deal with such a major public health threat.AIM To monitor HB and HC epidemics by the design of a paradigmatic seasonal autoregressive fractionally integrated moving average(SARFIMA)for projections into 2030,and to compare the effectiveness with the seasonal autoregressive integrated moving average(SARIMA).METHODS Monthly HB and HC incidence cases in China were obtained from January 2004 to June 2023.Descriptive analysis and the Hodrick-Prescott method were employed to identify trends and seasonality.Two periods(from January 2004 to June 2022 and from January 2004 to December 2015,respectively)were used as the training sets to develop both models,while the remaining periods served as the test sets to evaluate the forecasting accuracy.RESULTS There were incidents of 23400874 HB cases and 3590867 HC cases from January 2004 to June 2023.Overall,HB remained steady[average annual percentage change(AAPC)=0.44,95%confidence interval(95%CI):-0.94-1.84]while HC was increasing(AAPC=8.91,95%CI:6.98-10.88),and both had a peak in March and a trough in February.In the 12-step-ahead HB forecast,the mean absolute deviation(15211.94),root mean square error(18762.94),mean absolute percentage error(0.17),mean error rate(0.15),and root mean square percentage error(0.25)under the best SARFIMA(3,0,0)(0,0.449,2)12 were smaller than those under the best SARIMA(3,0,0)(0,1,2)12(16867.71,20775.12,0.19,0.17,and 0.27,respectively).Similar results were also observed for the 90-step-ahead HB,12-step-ahead HC,and 90-step-ahead HC forecasts.The predicted HB incidents totaled 9865400(95%CI:7508093-12222709)cases and HC totaled 1659485(95%CI:856681-2462290)cases during 2023-2030.CONCLUSION Under current interventions,China faces enormous challenges to eliminate HB and HC epidemics by 2030,and effective strategies must be reinforced.The integration of SARFIMA into public health for the management of HB and HC epidemics can potentially result in more informed and efficient interventions,surpassing the capabilities of SARIMA.