A Mathematical Model Reveals That Both Randomness and Periodicity Are Essential for Sustainable Fluctuations in Stock Prices

Is it true that there is an implicit understanding that Brownian motion or fractional Brownian motion is the driving force behind stock price fluctuations? An analysis of daily prices and volumes of a particular stock revealed the following findings: 1) the logarithms of the moving averages of stock prices and volumes have a strong positive correlation, even though price and volume appear to be fluctuating independently of each other, 2) price and volume fluctuations are messy, but these time series are not necessarily Brownian motion by replacing each daily value by 1 or –1 when it rises or falls compared to the previous day’s value, and 3) the difference between the volume on the previous day and that on the current day is periodic by the frequency analysis. Using these findings, we constructed differential equations for stock prices, the number of buy orders, and the number of sell orders. These equations include terms for both randomness and periodicity. It is apparent that both randomness and periodicity are essential for stock price fluctuations to be sustainable, and that stock prices show large hill-like or valley-like fluctuations stochastically without any increasing or decreasing trend, and repeat themselves over a certain range.

A Statistical Method for Characterizing CMOS Process Fluctuations in Subthreshold Current Mirrors

A novel method to characterize CMOS process fluctuations in subthreshold current mirrors （SCM） is reported. The proposed model is succinct in methodology and calculation complexity compared with previous statistical models. However,it provides favorable estimations of CMOS process fluctuations on the SCM circuit, which makes it promising for engineering applications. The model statistically abstracts physical parameters, which depend on the IC process, into random variables with certain mean values and standard deviations, while aggregating all the random impacts into a discrete martingale. The correctness of the proposed method is experimentally verified on an SCM circuit implemented in an SMIC 0.18μm CMOS 1P6M mixed signal process with a conversion factor of 100 in an input range from 100pA to lμA. The pro- posed theory successfully predicts - 10% of die-to-die fluctuation measured in the experiment, and also suggests the -lmV of threshold voltage standard deviation over a single die,which meets the process parameters suggested by the design kit from the foundry. The deviations between calculated probabilities and measured data are less than 8%. Meanwhile, pertinent suggestions concerning high fluctuation tolerance subthreshold analog circuit design are also made and discussed.

Optimization and Sizing of a Stand-Alone Photovoltaic System and Assessment of Random Load Fluctuation on Power Supply

This study presents an optimization technique and design for a stand-alone photovoltaic (PV) system to provide the required electricity for a single residential household in remote areas. From the basic solar components analysis, the irradiance on tilted surface is derived and compared to that on horizontal surface for Furu-Awa locality to infer the appropriate tilt angle (β) that maximizes the collection of solar energy. Seven optimum values of β applicable to the PV network were then derived depending of the period of the year and this simulation resulted that the panels are to be adjusted seven times a year. The optimization technique for load demand based on total apparent power of the household appliances produces an increase of 18% compared to the simple case of the PV components design using active power but leads to the optimum configuration that meets the real load demand of the household. Following the sizing of the station, reliability tests simulations were conducted for a one year corresponding period to infer the sensitivity of power supply to initial state of charge, to check the system autonomy and to evaluate the effect of random variation of the load on the smooth functioning of the PV system using a pseudo random number generator. This analysis shows that the minimum capacity of the battery for normal run of the Plan is 22.2% and that with random fluctuation of load, there will be periods of the year where the system experiences power failure depending on how important is the variation. The result of the study may imply a small increase in the cost of the entire plant but improves the stability and flexibility of such a station.

The effect of phase fluctuation and beam splitter fluctuation on two-photon quantum random walk

In the optical quantum random walk system,phase nuctuation and Deam splitter uuctuation are two unavoldable decoherence factors.These two factors degrade the performance of quantum random walk by destroying coherence,and even degrade it into a classical one.We propose a scheme for the simulation of quantum random walk using phase shifters,tunable beam splitters,and photodetectors.This proposed scheme enables us to analyze the effect of phase fluctuation and beam splitter fluctuation on two-photon quantum random walk.Furthermore,it is helpful to guide the control of phase fluctuation and beam snlitter fluctuation in the exneriment.

Experimental investigation of the fluctuations in nonchaotic scattering in microwave billiards

We report on the experimental investigation of the properties of the eigenvalues and wavefunctions and the fluctuation properties of the scattering matrix of closed and open billiards, respectively, of which the classical dynamics undergoes a transition from integrable via almost integrable to fully chaotic. To realize such a system, we chose a billiard with a 60° sector shape of which the classical dynamics is integrable, and introduced circular scatterers of varying number, size,and position. The spectral properties of generic quantum systems of which the classical counterpart is either integrable or chaotic are universal and well understood. If, however, the classical dynamics is pseudo-integrable or almost-integrable,they exhibit a non-universal intermediate statistics, for which analytical results are known only in a few cases, e.g., if it corresponds to semi-Poisson statistics. Since the latter is, above all, clearly distinguishable from those of integrable and chaotic systems, our aim was to design a billiard with these features which indeed is achievable by adding just one scatterer of appropriate size and position to the sector billiard. We demonstrated that, while the spectral properties of almostintegrable billiards are sensitive to the classical dynamics, this is not the case for the distribution of the wavefunction components, which was analyzed in terms of the strength distribution, and the fluctuation properties of the scattering matrix which coincide with those of typical, fully chaotic systems.

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.

Temperature Fluctuations in a Rectangular Nanochannel

We consider an incompressible fluid in a rectangular nanochannel. We solve numerically the three dimensional Fourier heat equation to get the steady solution for the temperature. Then we set and solve the Langevin equation for the temperature. We have developed equations in order to determine relaxation time of the temperature fluctuations, τT = 4.62 × 10-10s. We have performed a spectral analysis of the thermal fluctuations, with the result that temporal correlations are in the one-digit ps range, and the thermal noise excites the thermal modes in the two-digit GHz range. Also we observe long-range spatial correlation up to more than half the size of the cell, 600 nm;the wave number, q, is in the 106 m-1 range. We have also determined two thermal relaxation lengths in the z direction: l1 = 1.18 nm and l2 = 9.86 nm.

Prediction of NFT Sale Price Fluctuations on OpenSea Using Machine Learning Approaches

The rapid expansion of the non-fungible token(NFT)market has attracted many investors.However,studies on the NFT price fluctuations have been relatively limited.To date,the machine learning approach has not been used to demonstrate a specific error in NFT sale price fluctuation prediction.The aim of this study was to develop a prediction model for NFT price fluctuations using the NFT trading information obtained from OpenSea,the world’s largest NFT marketplace.We used Python programs to collect data and summarized them as:NFT information,collection information,and related account information.AdaBoost and Random Forest(RF)algorithms were employed to predict the sale price and price fluctuation of NFTs using regression and classification models,respectively.We found that the NFT related account information,especially the number of favorites and activity status of creators,confer a good predictive power to both the models.AdaBoost in the regression model had more accurate predictions,the root mean square error(RMSE)in predicting NFT sale price was 0.047.In predicting NFT sale price fluctuations,RF performed better,which the area under the curve(AUC)reached 0.956.We suggest that investors should pay more attention to the information of NFT creators.We anticipate that these prediction models will reduce the number of investment failures for the investors.

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.

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。

Random vortex induced vibration response of suspended flexible cable to fluctuating wind

A popular dynamical model for the vortex induced vibration(VIV)of a suspended flexible cable consists of two coupled equations.The first equation is a partial differential equation governing the cable vibration.The second equation is a wake oscillator that models the lift coefficient acting on the cable.The incoming wind acting on the cable is usually assumed as the uniform wind with a constant velocity,which makes the VIV model be a deterministic one.In the real world,however,the wind velocity is randomly fluctuant and makes the VIV of a suspended flexible cable be treated as a random vibration.In the present paper,the deterministic VIV model of a suspended flexible cable is modified to a random one by introducing the fluctuating wind.Using the normal mode approach,the random VIV system is transformed into an infinite-dimensional modal vibration system.Depending on whether a modal frequency is close to the aeolian frequency or not,the corresponding modal vibration is characterized as a resonant vibration or a non-resonant vibration.By applying the stochastic averaging method of quasi Hamiltonian systems,the response of modal vibrations in the case of resonance or non-resonance can be analytically predicted.Then,the random VIV response of the whole cable can be approximately calculated by superimposing the response of the most influential modal vibrations.Some numerical simulation results confirm the obtained analytical results.It is found that the intensity of the resonant modal vibration is much higher than that of the non-resonant modal vibration.Thus,the analytical results of the resonant modal vibration can be used as a rough estimation for the whole response of a cable.

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).