Random Fuzzy Chance-constrained Programming Based on Adaptive Chaos Quantum Honey Bee Algorithm and Robustness Analysis

This paper proposes an adaptive chaos quantum honey bee algorithm （CQHBA） for solving chance-constrained program- ming in random fuzzy environment based on random fuzzy simulations. Random fuzzy simulation is designed to estimate the chance of a random fuzzy event and the optimistic value to a random fuzzy variable. In CQHBA, each bee carries a group of quantum bits representing a solution. Chaos optimization searches space around the selected best-so-far food source. In the marriage process, random interferential discrete quantum crossover is done between selected drones and the queen. Gaussian quantum mutation is used to keep the diversity of whole population. New methods of computing quantum rotation angles are designed based on grads. A proof of con- vergence for CQHBA is developed and a theoretical analysis of the computational overhead for the algorithm is presented. Numerical examples are presented to demonstrate its superiority in robustness and stability, efficiency of computational complexity, success rate, and accuracy of solution quality. CQHBA is manifested to be highly robust under various conditions and capable of handling most random fuzzy programmings with any parameter settings, variable initializations, system tolerance and confidence level, perturbations, and noises.

Distributionally robust optimization based chance-constrained energy management for hybrid energy powered cellular networks

Energy harvesting has been recognized as a promising technique with which to effectively reduce carbon emis-sions and electricity expenses of base stations.However,renewable energy is inherently stochastic and inter-mittent,imposing formidable challenges on reliably satisfying users'time-varying wireless traffic demands.In addition,the probability distribution of the renewable energy or users’wireless traffic demand is not always fully known in practice.In this paper,we minimize the total energy cost of a hybrid-energy-powered cellular network by jointly optimizing the energy sharing among base stations,the battery charging and discharging rates,and the energy purchased from the grid under the constraint of a limited battery size at each base station.In solving the formulated non-convex chance-constrained stochastic optimization problem,a new ambiguity set is built to characterize the uncertainties in the renewable energy and wireless traffic demands according to interval sets of the mean and covariance.Using this ambiguity set,the original optimization problem is transformed into a more tractable second-order cone programming problem by exploiting the distributionally robust optimization approach.Furthermore,a low-complexity distributionally robust chance-constrained energy management algo-rithm,which requires only interval sets of the mean and covariance of stochastic parameters,is proposed.The results of extensive simulation are presented to demonstrate that the proposed algorithm outperforms existing methods in terms of the computational complexity,energy cost,and reliability.

Chance-Constrained Approaches for Multiobjective Stochastic Linear Programming Problems

Multiple objective stochastic linear programming is a relevant topic. As a matter of fact, many practical problems ranging from portfolio selection to water resource management may be cast into this framework. Severe limitations on objectivity are encountered in this field because of the simultaneous presence of randomness and conflicting goals. In such a turbulent environment, the mainstay of rational choice cannot hold and it is virtually impossible to provide a truly scientific foundation for an optimal decision. In this paper, we resort to the bounded rationality principle to introduce satisfying solution for multiobjective stochastic linear programming problems. These solutions that are based on the chance-constrained paradigm are characterized under the assumption of normality of involved random variables. Ways for singling out such solutions are also discussed and a numerical example provided for the sake of illustration.

Reconstruction of geological surfaces using chance-constrained programming

Geological surface modeling is typically based on seismic data, well data, and models of regional geology. However, structural interpretation of these data is error-prone, especially in the absence of structural morphology information, Existing geological surface models suffer from high levels of uncertainty, which exposes oil and gas exploration and development to additional risk. In this paper, we achieve a reconstruction of the uncertainties associated with a geological surface using chance-constrained programming based on multisource data. We also quantifi ed the uncertainty of the modeling data and added a disturbance term to the objective function. Finally, we verifi ed the applicability of the method using both synthetic and real fault data. We found that the reconstructed geological models met geological rules and reduced the reconstruction uncertainty.

Theoretical and experimental study of a bi-stable piezoelectric energy harvester under hybrid galloping and band-limited random excitations

In the practical environment,it is very common for the simultaneous occurrence of base excitation and crosswind.Scavenging the combined energy of vibration and wind with a single energy harvesting structure is fascinating.For this purpose,the effects of the wind speed and random excitation level are investigated with the stochastic averaging method(SAM)based on the energy envelope.The results of the analytical prediction are verified with the Monte-Carlo method(MCM).The numerical simulation shows that the introduction of wind can reduce the critical excitation level for triggering an inter-well jump and make a bi-stable energy harvester(BEH)realize the performance enhancement for a weak base excitation.However,as the strength of the wind increases to a particular level,the influence of the random base excitation on the dynamic responses is weakened,and the system exhibits a periodic galloping response.A comparison between a BEH and a linear energy harvester(LEH)indicates that the BEH demonstrates inferior performance for high-speed wind.Relevant experiments are conducted to investigate the validity of the theoretical prediction and numerical simulation.The experimental findings also show that strong random excitation is favorable for the BEH in the range of low wind speeds.However,as the speed of the incoming wind is up to a particular level,the disadvantage of the BEH becomes clear and evident.

Chance-constrained programming (CCP)abatement of SO_2 emission for acid deposition control in Liuzhou City

A deterministic linear programming model which optimizes the abatement of each SO2 emission source, is extended into a CCP form by introducing equations of probabilistic constrained through the incorporation of uncertainty in the source-receptor-specific transfer coefficients. Based on the calculation of SO2 and sulfate average residence time for Liuzhou City, a sulfur deposition model has been developed and the distribution of transfer coefficients have been found to be approximately log-normal. Sulfur removal minimization of the model shows that the abatement of emission sources in the city is more effective, while control cost optimization provides the lowest cost programmes for source abatement at each allowable deposition limit under varied environmental risk levels. Finally a practicable programme is recommended.

A real-time intelligent lithology identification method based on a dynamic felling strategy weighted random forest algorithm

Real-time intelligent lithology identification while drilling is vital to realizing downhole closed-loop drilling. The complex and changeable geological environment in the drilling makes lithology identification face many challenges. This paper studies the problems of difficult feature information extraction,low precision of thin-layer identification and limited applicability of the model in intelligent lithologic identification. The author tries to improve the comprehensive performance of the lithology identification model from three aspects: data feature extraction, class balance, and model design. A new real-time intelligent lithology identification model of dynamic felling strategy weighted random forest algorithm(DFW-RF) is proposed. According to the feature selection results, gamma ray and 2 MHz phase resistivity are the logging while drilling(LWD) parameters that significantly influence lithology identification. The comprehensive performance of the DFW-RF lithology identification model has been verified in the application of 3 wells in different areas. By comparing the prediction results of five typical lithology identification algorithms, the DFW-RF model has a higher lithology identification accuracy rate and F1 score. This model improves the identification accuracy of thin-layer lithology and is effective and feasible in different geological environments. The DFW-RF model plays a truly efficient role in the realtime intelligent identification of lithologic information in closed-loop drilling and has greater applicability, which is worthy of being widely used in logging interpretation.

Enhancing the resolution of sparse rock property measurements using machine learning and random field theory

The travel time of rock compressional waves is an essential parameter used for estimating important rock properties,such as porosity,permeability,and lithology.Current methods,like wireline logging tests,provide broad measurements but lack finer resolution.Laboratory-based rock core measurements offer higher resolution but are resource-intensive.Conventionally,wireline logging and rock core measurements have been used independently.This study introduces a novel approach that integrates both data sources.The method leverages the detailed features from limited core data to enhance the resolution of wireline logging data.By combining machine learning with random field theory,the method allows for probabilistic predictions in regions with sparse data sampling.In this framework,12 parameters from wireline tests are used to predict trends in rock core data.The residuals are modeled using random field theory.The outcomes are high-resolution predictions that combine both the predicted trend and the probabilistic realizations of the residual.By utilizing unconditional and conditional random field theories,this method enables unconditional and conditional simulations of the underlying high-resolution rock compressional wave travel time profile and provides uncertainty estimates.This integrated approach optimizes the use of existing core and logging data.Its applicability is confirmed in an oil project in West China.

Immune cell signatures and causal association with irritable bowel syndrome:A mendelian randomization study

BACKGROUND The mucosal barrier's immune-brain interactions,pivotal for neural development and function,are increasingly recognized for their potential causal and therapeutic relevance to irritable bowel syndrome(IBS).Prior studies linking immune inflammation with IBS have been inconsistent.To further elucidate this relationship,we conducted a Mendelian randomization(MR)analysis of 731 immune cell markers to dissect the influence of various immune phenotypes on IBS.Our goal was to deepen our understanding of the disrupted brain-gut axis in IBS and to identify novel therapeutic targets.AIM To leverage publicly available data to perform MR analysis on 731 immune cell markers and explore their impact on IBS.We aimed to uncover immunophenotypic associations with IBS that could inform future drug development and therapeutic strategies.METHODS We performed a comprehensive two-sample MR analysis to evaluate the causal relationship between immune cell markers and IBS.By utilizing genetic data from public databases,we examined the causal associations between 731 immune cell markers,encompassing median fluorescence intensity,relative cell abundance,absolute cell count,and morphological parameters,with IBS susceptibility.Sensitivity analyses were conducted to validate our findings and address potential heterogeneity and pleiotropy.RESULTS Bidirectional false discovery rate correction indicated no significant influence of IBS on immunophenotypes.However,our analysis revealed a causal impact of IBS on 30 out of 731 immune phenotypes(P<0.05).Nine immune phenotypes demonstrated a protective effect against IBS[inverse variance weighting(IVW)<0.05,odd ratio(OR)<1],while 21 others were associated with an increased risk of IBS onset(IVW≥0.05,OR≥1).CONCLUSION Our findings underscore a substantial genetic correlation between immune cell phenotypes and IBS,providing valuable insights into the pathophysiology of the condition.These results pave the way for the development of more precise biomarkers and targeted therapies for IBS.Furthermore,this research enriches our comprehension of immune cell roles in IBS pathogenesis,offering a foundation for more effective,personalized treatment approaches.These advancements hold promise for improving IBS patient quality of life and reducing the disease burden on individuals and their families.

An Optimized System of Random Forest Model by Global Harmony Search with Generalized Opposition-Based Learning for Forecasting TBM Advance Rate

As massive underground projects have become popular in dense urban cities,a problem has arisen:which model predicts the best for Tunnel Boring Machine(TBM)performance in these tunneling projects?However,performance level of TBMs in complex geological conditions is still a great challenge for practitioners and researchers.On the other hand,a reliable and accurate prediction of TBM performance is essential to planning an applicable tunnel construction schedule.The performance of TBM is very difficult to estimate due to various geotechnical and geological factors and machine specifications.The previously-proposed intelligent techniques in this field are mostly based on a single or base model with a low level of accuracy.Hence,this study aims to introduce a hybrid randomforest(RF)technique optimized by global harmony search with generalized oppositionbased learning(GOGHS)for forecasting TBM advance rate(AR).Optimizing the RF hyper-parameters in terms of,e.g.,tree number and maximum tree depth is the main objective of using the GOGHS-RF model.In the modelling of this study,a comprehensive databasewith themost influential parameters onTBMtogetherwithTBM AR were used as input and output variables,respectively.To examine the capability and power of the GOGHSRF model,three more hybrid models of particle swarm optimization-RF,genetic algorithm-RF and artificial bee colony-RF were also constructed to forecast TBM AR.Evaluation of the developed models was performed by calculating several performance indices,including determination coefficient(R2),root-mean-square-error(RMSE),and mean-absolute-percentage-error(MAPE).The results showed that theGOGHS-RF is a more accurate technique for estimatingTBMAR compared to the other applied models.The newly-developedGOGHS-RFmodel enjoyed R2=0.9937 and 0.9844,respectively,for train and test stages,which are higher than a pre-developed RF.Also,the importance of the input parameters was interpreted through the SHapley Additive exPlanations(SHAP)method,and it was found that thrust force per cutter is the most important variable on TBMAR.The GOGHS-RF model can be used in mechanized tunnel projects for predicting and checking performance.

Causal associations between gastroesophageal reflux disease and essential hypertension: A bidirectional Mendelian randomization study

BACKGROUND Clinical studies have reported that patients with gastroesophageal reflux disease(GERD)have a higher prevalence of hypertension.AIM To performed a bidirectional Mendelian randomization(MR)analysis to investi-gate the causal link between GERD and essential hypertension.METHODS Eligible single nucleotide polymorphisms(SNPs)were selected,and weighted median,inverse variance weighted(IVW)as well as MR egger(MR-Egger)re-gression were used to examine the potential causal association between GERD and hypertension.The MR-Pleiotropy RESidual Sum and Outlier analysis was used to detect and attempt to reduce horizontal pleiotropy by removing outliers SNPs.The MR-Egger intercept test,Cochran’s Q test and“leave-one-out”sen-sitivity analysis were performed to evaluate the horizontal pleiotropy,heterogen-eities,and stability of single instrumental variable.RESULTS IVW analysis exhibited an increased risk of hypertension(OR=1.46,95%CI:1.33-1.59,P=2.14E-16)in GERD patients.And the same result was obtained in replication practice(OR=1.002,95%CI:1.0008-1.003,P=0.000498).Meanwhile,the IVW analysis showed an increased risk of systolic blood pressure(β=0.78,95%CI:0.11-1.44,P=0.021)and hypertensive heart disease(OR=1.68,95%CI:1.36-2.08,P=0.0000016)in GERD patients.Moreover,we found an decreased risk of Barrett's esophagus(OR=0.91,95%CI:0.83-0.99,P=0.043)in essential hypertension patients.CONCLUSION We found that GERD would increase the risk of essential hypertension,which provided a novel prevent and therapeutic perspectives of essential hypertension.

Exploring the role of interleukin-6 receptor blockade in epilepsy and associated neuropsychiatric conditions through a mendelian randomization study

BACKGROUND The interplay between inflammation,immune dysregulation,and the onset of neurological disorders,including epilepsy,has become increasingly recognized.Interleukin(IL)-6,a pro-inflammatory cytokine,is suspected to not only mediate traditional inflammatory pathways but also contribute to neuroinflammatory responses that could underpin neuropsychiatric symptoms and broader psychiatric disorders in epilepsy patients.The role of IL-6 receptor(IL6R)blockade presents an intriguing target for therapeutic intervention due to its potential to attenuate these processes.neuropsychiatric conditions due to neuroinflammation.METHODS Mendelian randomization(MR)analysis employing single nucleotide poly-morphisms(SNPs)in the vicinity of the IL6R gene(total individuals=408225)was used to evaluate the putative causal relationship between IL6R blockade and epilepsy(total cases/controls=12891/312803),focal epilepsy(cases/controls=7526/399290),and generalized epilepsy(cases/controls=1413/399287).SNP weights were determined by their effect on C-reactive protein(CRP)levels and integrated using inverse variance-weighted meta-analysis as surrogates for IL6R effects.To address potential outlier and pleiotropic influences,sensitivity analyses were conducted employing a variety of MR methods under different modeling assumptions.RESULTS The genetic simulation targeting IL6R blockade revealed a modest but significant reduction in overall epilepsy risk[inverse variance weighting:Odds ratio(OR):0.827;95%confidence interval(CI):0.685-1.000;P=0.05].Subtype analysis showed variability,with no significant effect observed in generalized,focal,or specific childhood and juvenile epilepsy forms.Beyond the primary inflammatory marker CRP,the findings also suggested potential non-inflammatory pathways mediated by IL-6 signaling contributing to the neurobiological landscape of epilepsy,hinting at possible links to neuroinflammation,psychiatric symptoms,and associated mental disorders.CONCLUSION The investigation underscored a tentative causal relationship between IL6R blockade and decreased epilepsy incidence,likely mediated via complex neuroinflammatory pathways.These results encouraged further in-depth studies involving larger cohorts and multifaceted psychiatric assessments to corroborate these findings and more thoroughly delineate the neuro-psychiatric implications of IL-6 signaling in epilepsy.The exploration of IL6R blockade could herald a novel therapeutic avenue not just for seizure management but also for addressing the broader psychiatric and cognitive disturbances often associated with epilepsy.

Genetically predicted fatty liver disease and risk of psychiatric disorders: A mendelian randomization study

BACKGROUND Non-alcoholic fatty liver disease(NAFLD)and alcohol-related liver disease(Ar-LD)constitute the primary forms of chronic liver disease,and their incidence is progressively increasing with changes in lifestyle habits.Earlier studies have do-cumented a correlation between the occurrence and development of prevalent mental disorders and fatty liver.AIM To investigate the correlation between fatty liver and mental disorders,thus ne-cessitating the implementation of a mendelian randomization(MR)study to elu-cidate this association.METHODS Data on NAFLD and ArLD were retrieved from the genome-wide association studies catalog,while information on mental disorders,including Alzheimer's disease,schizophrenia,anxiety disorder,attention deficit hyperactivity disorder(ADHD),bipolar disorder,major depressive disorder,multiple personality dis-order,obsessive-compulsive disorder(OCD),post-traumatic stress disorder(PTSD),and schizophrenia was acquired from the psychiatric genomics consor-tium.A two-sample MR method was applied to investigate mediators in signifi-cant associations.RESULTS After excluding weak instrumental variables,a causal relationship was identified between fatty liver disease and the occurrence and development of some psychia-tric disorders.Specifically,the findings indicated that ArLD was associated with a significantly elevated risk of developing ADHD(OR:5.81,95%CI:5.59-6.03,P<0.01),bipolar disorder(OR:5.73,95%CI:5.42-6.05,P=0.03),OCD(OR:6.42,95%CI:5.60-7.36,P<0.01),and PTSD(OR:5.66,95%CI:5.33-6.01,P<0.01).Meanwhile,NAFLD significantly increased the risk of developing bipolar disorder(OR:55.08,95%CI:3.59-845.51,P<0.01),OCD(OR:61.50,95%CI:6.69-565.45,P<0.01),and PTSD(OR:52.09,95%CI:4.24-639.32,P<0.01).CONCLUSION Associations were found between genetic predisposition to fatty liver disease and an increased risk of a broad range of psychiatric disorders,namely bipolar disorder,OCD,and PTSD,highlighting the significance of preven-tive measures against psychiatric disorders in patients with fatty liver disease.

一种基于KMeans与Random Forest的异常温升捕捉方法

针对线路老化、线路过载的火灾频发问题,分析了线路老化、线路过载与异常温升之间的关联性,以电流值、线缆温度作为输入,利用KMeans聚类算法划分可能存在异常温升的区间,通过Random Forest算法识别线路过载问题,可以提前通知用户整改线路,预防火灾的发生。

Exploring the Impact of Alcohol Consumption and Smoking on Primary Open Angle Glaucoma: A Mendelian Randomization Study

Objective: Utilizing Mendelian Randomization, this study employs Single Nucleotide Polymorphisms (SNPs) as instrumental variables to explore the causal relationships between bibulosity, smoking, and Primary Open Angle Glaucoma (POAG). Methods: GWAS data for bibulosity, smoking, and POAG were obtained from the Social Science Genetic Association Consortium website and the IEU OpenGWAS Project website, respectively. Using a P-value threshold of −8, a linkage disequilibrium coefficient (r2) of 0.001, and a linkage disequilibrium region width of 10,000 kb, the data were aggregated, resulting in 6 SNPs for bibulosity and 253 SNPs for smoking. Three regression models, MR-Egger, Weighted Median Estimator (WME), and Random-Effects Inverse-Variance Weighted (IVW) were applied to analyze the causal impact of bibulosity and smoking on POAG. Results: The GWAS data for alcohol consumption and smoking were derived from European populations, while the GWAS data for Primary Open-Angle Glaucoma (POAG) were sourced from East Asian populations, with no gender restrictions. Analysis using three different regression models revealed that neither excessive alcohol consumption nor smoking significantly increased the risk of developing POAG. Specifically, the odds ratios with 95% confidence intervals for the alcohol consumption group were 0.854 (0.597 - 1.221) in MR-Egger regression, 0.922 (0.691 - 1.231) in WME regression, and 0.944 (0.711 - 1.252) in IVW regression. For the smoking group, the odds ratios were 1.146 (0.546 - 2.406) in MR-Egger regression, 0.850 (0.653 - 1.111) in WME regression, and 0.939 (0.780 - 1.131) in IVW regression. Given the significant heterogeneity in the SNPs associated with smoking, the focus was primarily on the results from the IVW regression model. Conclusion: Alcohol consumption and smoking are not significant risk factors for the development of POAG.

Python语言random库经典案例教学

Python是一种计算生态语言,也是开源的语言,具有丰富和强大的类库,语法简洁、清晰明了。随着物联网、大数据、人工智能等技术的兴起,Python位于PYPL全球编程语言排行榜的榜首,成为受人们欢迎的编程语言。主要阐述利用Python的random库解决一些实际问题,既提高学习者的兴趣和积极性,又能提高学习者利用所学知识分析和处理实际问题的能力。

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.

Different effects of 24 dietary intakes on gastroesophageal reflux disease: A mendelian randomization

BACKGROUND In observational studies,dietary intakes are associated with gastroesophageal re-flux disease(GERD).AIM To conduct a two-sample mendelian randomization(MR)analysis to determine whether those associations are causal.METHODS To explore the relationship between dietary intake and the risk of GERD,we extracted appropriate single nucleotide polymorphisms from genome-wide asso-ciation study data on 24 dietary intakes.Three methods were adopted for data analysis:Inverse variance weighting,weighted median methods,and MR-Egger's method.The odds ratio(OR)and 95%confidence interval(CI)were used to eva-luate the causal association between dietary intake and GERD.RESULTS Our univariate Mendelian randomization(UVMR)results showed significant evidence that pork intake(OR,2.83;95%CI:1.76-4.55;P=1.84×10–5),beer intake(OR,2.70,95%CI:2.00-3.64;P=6.54×10–11),non-oily fish intake(OR,2.41;95%CI:1.49-3.91;P=3.59×10–4)have a protective effect on GERD.In addition,dried fruit intake(OR,0.37;95%CI:0.27-0.50;6.27×10–11),red wine intake(OR,0.34;95%CI:0.25-0.47;P=1.90×10-11),cheese intake(OR,0.46;95%CI:0.39-0.55;P=3.73×10-19),bread intake(OR,0.72;95%CI:0.56-0.92;P=0.0009)and cereal intake(OR,0.45;95%CI:0.36-0.57;P=2.07×10-11)were negatively associated with the risk of GERD.There was a suggestive asso-ciation for genetically predicted coffee intake(OR per one SD increase,1.22,95%CI:1.03-1.44;P=0.019).Multi-variate Mendelian randomization further confirmed that dried fruit intake,red wine intake,cheese intake,and cereal intake directly affected GERD.In contrast,the impact of pork intake,beer intake,non-oily fish intake,and bread intake on GERD was partly driven by the common risk factors for GERD.However,after adjusting for all four elements,there was no longer a suggestive association between coffee intake and GERD.CONCLUSION This study provides MR evidence to support the causal relationship between a broad range of dietary intake and GERD,providing new insights for the treatment and prevention of GERD.

Dissecting the association between gut microbiota,body mass index and specific depressive symptoms:a mediation Mendelian randomisation study

Background Observational studies highlight the association between gut microbiota(GM)composition and depression;however,evidence for the causal relationship between GM and specific depressive symptoms remains lacking.Aims We aimed to evaluate the causal relationship between GM and specific depressive symptoms as well as the mediating role of body mass index(BMI).Methods We performed a two-sample Mendelian randomisation(MR)analysis using genetic variants associated with GM and specific depressive symptoms from genome-wide association studies.The mediating role of BMI was subsequently explored using mediation analysis via two-step MR.Results MR evidence suggested the Bifidobacterium genus(β=0.03;95%CI-0.05 to-0.02;p<0.001 andβ=0.03;95%CI-0.05 to-0.02;p<0.001)and Actinobacteria phylum(β=-0.04;95%CI-0.06 to-0.02;p<0.001 andβ=-0.03;95%CI-0.05 to-0.03;p=0.001)had protective effects on both anhedonia and depressed mood.The Actinobacteria phylum also had protective effects on appetite changes(β=-0.04;95%CI-0.06 to-0.01;p=0.005),while the FamilyⅪhad an antiprotective effect(β=0.03;95%CI 0.01 to 0.04;p<0.001).The Bifidobacteriaceae family(β=-0.01;95%CI-0.02 to-0.01;p=0.001)and Actinobacteria phylum(β=-0.02;95%CI-0.03 to-0.01;p=0.001)showed protective effects against suicidality.The two-step MR analysis revealed that BMl also acted as a mediating moderator between the Actinobacteria phylum and appetite changes(mediated proportion,34.42%)and that BMI partially mediated the effect of the Bifidobacterium genus(14.14%and 8.05%)and Actinobacteria phylum(13.10%and 8.31%)on both anhedonia and depressed mood.Conclusions These findings suggest a potential therapeutic effect of Actinobacteria and Bifidobacterium on both depression and obesity.Further studies are required to translate these findings into clinical practice.

Strong invariance principle for a counterbalanced random walk

We study a counterbalanced random walkS_(n)=X_(1)+…+X_(n),which is a discrete time non-Markovian process andX_(n) are given recursively as follows.For n≥2,X_(n) is a new independent sample from some fixed law̸=0 with a fixed probability p,andX_(n)=−X_(v(n))with probability 1−p,where v(n)is a uniform random variable on{1;…;n−1}.We apply martingale method to obtain a strong invariance principle forS_(n).