DMPFIT: A Tool for Atomic-Scale Metrology via Nonlinear Least-Squares Fitting of Peaks in Atomic-Resolution TEM Images

Despite the wide availability and usage of Gatan’s DigitalMicrograph software in the electron microscopy community for image recording and analysis, nonlinear least-squares fitting in DigitalMicrograph is less straightforward. This work presents a ready-to-use tool, the DMPFIT software package, written in DigitalMicrograph script and C++ language, for nonlinear least-squares fitting of the intensity distribution of atomic columns in atomic-resolution transmission electron microscopy (TEM) images with a general two-dimensional (2D) Gaussian model. Applications of the DMPFIT software are demonstrated both in atomic-resolution conventional coherent TEM (CTEM) images recorded by the negative spherical aberration imaging technique and in high angle annular dark field (HAADF) scanning TEM (STEM) images. The implemented peak-finding algorithm based on the periodicity of 2D lattices enables reliable and convenient atomic-scale metrology as well as intuitive presentation of the resolved atomic structures.

A Residual Frequency Offset Estimation Method Based on Range Migration Fitting

Recently,researchers have proposed an emitter localization method based on passive synthetic aperture.However,the unknown residual frequency offset(RFO)between the transmit-ter and the receiver causes the received Doppler signal to shift,which affects the localization accu-racy.To solve this issue,this paper proposes a RFO estimation method based on range migration fitting.Due to the high frequency modulation slope of the linear frequency modulation(LFM)-mod-ulation radar signal,it is not affected by RFO in range compression.Therefore,the azimuth time can be estimated by fitting the peak value position of the pulse compression in range direction.Then,the matched filters are designed under different RFOs.When the zero-Doppler time obtained by the matched filters is consistent with the estimated azimuth time,the given RFO is the real RFO between the transceivers.The simulation results show that the estimation error of azimuth distance does not exceed 20 m when the received signal duration is not less than 3 s,the pulse repe-tition frequency(PRF)of the transmitter radar signal is not less than 1 kHz,the range detection is not larger than 1000 km,and the signal noise ratio(SNR)is not less than-5 dB.

The Convergence of Least-Squares Progressive Iterative Approximation for Singular Least-Squares Fitting System

Data fitting is an extensively employed modeling tool in geometric design. With the advent of the big data era, the data sets to be fitted are made larger and larger, leading to more and more least-squares fitting systems with singular coefficient matrices. LSPIA (least-squares progressive iterative approximation) is an efficient iterative method for the least-squares fitting. However, the convergence of LSPIA for the singular least-squares fitting systems remains as an open problem. In this paper, the authors showed that LSPIA for the singular least-squares fitting systems is convergent. Moreover, in a special case, LSPIA converges to the Moore-Penrose (M-P) pseudo-inverse solution to the least- squares fitting result of the data set. This property makes LSPIA, an iterative method with clear geometric meanings, robust in geometric modeling applications. In addition, the authors discussed some implementation detail of LSPIA, and presented an example to validate the convergence of LSPIA for the singular least-squares fitting systems.

LEAST-SQUARES METHOD-BASED FEATURE FITTING AND EXTRACTION IN REVERSE ENGINEERING

The main purpose of reverse engineering is to convert discrete data pointsinto piecewise smooth, continuous surface models. Before carrying out model reconstruction it issignificant to extract geometric features because the quality of modeling greatly depends on therepresentation of features. Some fitting techniques of natural quadric surfaces with least-squaresmethod are described. And these techniques can be directly used to extract quadric surfaces featuresduring the process of segmentation for point cloud.

A Robust Indoor Localization Algorithm Based on Polynomial Fitting and Gaussian Mixed Model

Wireless sensor network(WSN)positioning has a good effect on indoor positioning,so it has received extensive attention in the field of positioning.Non-line-of sight(NLOS)is a primary challenge in indoor complex environment.In this paper,a robust localization algorithm based on Gaussian mixture model and fitting polynomial is proposed to solve the problem of NLOS error.Firstly,fitting polynomials are used to predict the measured values.The residuals of predicted and measured values are clustered by Gaussian mixture model(GMM).The LOS probability and NLOS probability are calculated according to the clustering centers.The measured values are filtered by Kalman filter(KF),variable parameter unscented Kalman filter(VPUKF)and variable parameter particle filter(VPPF)in turn.The distance value processed by KF and VPUKF and the distance value processed by KF,VPUKF and VPPF are combined according to probability.Finally,the maximum likelihood method is used to calculate the position coordinate estimation.Through simulation comparison,the proposed algorithm has better positioning accuracy than several comparison algorithms in this paper.And it shows strong robustness in strong NLOS environment.

Subpopulations of regulatory T cells are associated with subclinical atherosclerotic plaques,levels of LDL,and cardiorespiratory fitness in the elderly

Background:Atherosclerosis forms the pathological basis for the development of cardiovascular disease.Since pathological processes initially develop without clinically relevant symptoms,the identification of early markers in the subclinical stage plays an important role for initiating early interventions.There is evidence that regulatory T cells(Tregs)are involved in the development of atherosclerosis.Therefore,the present study aimed to identify and investigate associations with Tregs and their subsets in a cohort of healthy elderly individuals with and without subclinical atherosclerotic plaques(SAP).In addition,various lifestyle and risk factors,such as cardiorespiratory fitness,were investigated as associated signatures.Methods:A cross-sectional study was performed in 79 participants(male:n=50;age=63.6±3.7 years;body mass index=24.9±3.1 kg/m2;mean±SD)who had no previous diagnosis of chronic disease and were not taking medication.Ultrasound of the carotids to identify SAP,cardiovascular function measurement for vascular assessment and a cardiorespiratory fitness test to determine peak oxygen uptake were performed.Additionally,tests were conducted to assess blood lipids and determine glucose levels.Immunophenotyping of Tregs and their subtypes(resting(rTregs)and effector/memory(mTregs))was performed by 8-chanel flow cytometry.Participants were categorized according to atherosclerotic plaque status.Linear and logistic regression models were used to analyze associations between parameters.Results:SAP was detected in a total of 29 participants.The participants with plaque were older(64.8±3.6 years vs.62.9±3.5 years)and had higher peripheral systolic blood pressure(133.8±14.7 mmHg vs.125.8±10.9 mmHg).The participants with SAP were characterized by a lower percentage of rTregs(28.8%±10.7%vs.34.6%±10.7%)and a higher percentage of mTregs(40.3%±14.7%vs.30.0%±11.9%).Multiple logistic regression identified age(odds ratio(OR)=1.20(95%confidence interval(95%CI):1.011.42))and mTregs(OR=1.05(95%CI:1.021.10))as independent risk factors for SAP.Stepwise linear regression could reveal an association of peak oxygen uptake(β=0.441),low-density lipoprotein(LDL)(β=0.096),and SAP(β=6.733)with mTregs and LDL(β=0.104)with rTregs.Conclusion:While at an early stage of SAP,the total proportion of Tregs gives no indication of vascular changes,this is indicated by a shift in the Treg subgroups.Factors such as serum LDL or cardiopulmonary fitness may be associated with this shift and may also be additional diagnostic indicators.This could be used to initiate lifestyle-based preventive measures at an early stage,which may have a protective effect against disease progression.

Least-squares reverse time migration in visco-acoustic media based on symplectic stereo-modeling method

The authors proposed a symplectic stereo-modeling method(SSM)in the Birkhoffian dynam-ics and apply it to the visco-acoustic least-squares reverse time migration(LSRTM).The SSM adopts ste-reo-modeling operator in space and symplectic Runge-Kutta scheme in time,resulting in great ability in suppressing numerical dispersion and long-time computing.These advantages are further confirmed by numerical dispersion analysis,long-time computation test and computational efficiency comparison.After these theoretical analyses and experiments,acoustic and visco-acoustic LSRTM are tested and compared between SSM method and the conventional symplectic method(CSM)using the fault and marmousi models.Meanwhile,dynamic source encoding and exponential decay moving average gradients method are adopted to reduce the computation cost and improve the convergence rate.The imaging results show that LSRTM based on visco-acoustic wave equations effectively takes into account the influence of viscosity can therefore compensate for the amplitude attenuation.Besides,SSM method not only has high numerical accuracy and computational efficiency,but also performs effectively in LSRTM.

Effects of a school-based karate intervention on academic achievement,psychosocial functioning,and physical fitness:A multi-country cluster randomized controlled trial

Purpose:To examine the effects of a school-based karate intervention on academic achievement,psychosocial functioning,and physical fitness in children aged 7-8 years.Methods:Twenty schools in 5 different European countries(2 second-grade classrooms per school)participated in a cluster randomized controlled trial(Sport at School trial).Participants were assigned to either a control group,which continued with their habitual physical education lessons,or to an intervention group,which replaced these lessons with a 1-year karate intervention(Karate Mind and Movement program).A total of 721 children(344 girls and 377 boys,7.4±0.5 years old,mean±SD)completed the study,of which 333 and 388 were assigned to the control group and intervention group,respectively.Outcomes included academic performance(average grade),psychosocial functioning(Strengths and Difficulties Questionnaire for parents),and different markers of physical fitness(cardiorespiratory fitness,balance,and flexibility).Results:The intervention provided small but significant benefits compared to the control group for academic achievement(d=0.16;p=0.003),conduct problems(d=-0.28;p=0.003),cardiorespiratory fitness(d=0.36;p<0.001),and balance(d=0.24;p=0.015).There was a trend towards significant benefits for flexibility(d=0.24;p=0.056).No significant benefits were observed for other variables,including psychosocial difficulties,emotional symptoms,hyperactivity/inattention,peer problems,or prosocial behaviour(all p>0.05).Conclusion:A 1-year school-based karate intervention was effective in improving academic achievement,conduct problems,and physical fitness in primary school children.The results support the inclusion of karate during physical education lessons.

Comparative Analysis of Equal and Unequal Grounding Grid Configurations by Compression Ratio and Least Square Curve Fitting Techniques

The primary aim of the power system grounding is to safeguard the person and satisfying the performance of the power systemtomaintain reliable operation.With equal conductor spacing grounding grid design,the distribution of the current in the grid is not uniform.Hence,unequal grid conductor span in which grid conductors are concentrated more at the periphery is safer to practice than equal spacing.This paper presents the comparative analysis of two novel techniques that create unequal spacing among the grid conductors:the least-square curve fitting technique and the compression ratio techniquewith equal grid configuration for both square and rectangular grids.Particle Swarm Optimization(PSO)is adopted for finding out one optimal feasible solution among many feasible solutions of equal grid configuration for both square and rectangular grids.Comparative analysis is also carried out between square and rectangular grids using the least square curve fitting technique as it results in only one unequal grid configuration.Simulation results are obtained by theMATLAB software developed.Percentage of improvement in ground potential rise,step voltage,touch voltage,and grid resistancewith variation in compression ratios are plotted.

Associations between health-related fitness and patient-reported symptoms in newly diagnosed breast cancer patients

Background:Newly diagnosed breast cancer patients experience symptoms that may affect their quality of life,treatment outcomes,and survival.Preventing and managing breast cancer-related symptoms soon after diagnosis is essential.The purpose of this study was to investigate the associations between health-related fitness(HRF)and patient-reported symptoms in newly diagnosed breast cancer patients.Methods:This study utilized baseline data from the Alberta Moving Beyond Breast Cancer Cohort Study that were collected within 90 days of diagnosis.HRF measures included peak cardiopulmonary fitness(peak volume of oxygen consumption(VO_(2peak))),maximal muscular strength and endurance,flexibility,and body composition.Symptom measures included depression,sleep quality,and fatigue.Adjusted multivariable logistic regression was performed for analyses.Results:Of 1458 participants,51.5%reported poor sleep quality,26.5%reported significant fatigue,and 10.4%reported moderate depression.In multivariable-adjusted models,lower relative VO_(2peak)was independently associated with a greater likelihood of all symptom measures,including moderate depression(p<0.001),poor sleep quality(p=0.009),significant fatigue(p=0.008),any symptom(p<0.001),and multiple symptoms(p<0.001).VO_(2peak)demonstrated threshold associations with all symptom measures such that all 3 lower quartiles exhibited similar elevated risk compared to the highest quartile.The strength of the threshold associations varied by the symptom measure with odds ratios ranging from-1.5 for poor sleep quality to-3.0 for moderate depression and multiple symptoms.Moreover,lower relative upper body muscular endurance was also independently associated with fatigue in a dose-response manner(p=0.001),and higher body weight was independently associated with poor sleep quality in an inverted U pattern(p=0.021).Conclusion:Relative VO_(2peak)appears to be a critical HRF component associated with multiple patient-reported symptoms in newly diagnosed breast cancer patients.Other HRF parameters may also be important for specific symptoms.Exercise interventions targeting different HRF components may help newly diagnosed breast cancer patients manage specific symptoms and improve outcomes.

Resistance development,cross-resistance,and fitness costs associated with Aphis gossypii resistance towards sulfoxaflor and acetamiprid in different geographical regions

Aphis gossypii has become increasingly difficult to manage due to its strong insecticide resistance.In the laboratory,we established sulfoxaflor-resistant and acetamiprid-resistant strains in two A.gossypii populations with different basal insecticide resistance levels,and evaluated the effects of basal insecticide resistance on the resistance development and cross-resistance,as well as differences in fitness.Under the same selection pressure,Yarkant A.gossypii(with low basal insecticide resistance)evolved resistance to sulfoxaflor and acetamiprid more quickly than Jinghe A.gossypii(with high basal insecticide resistance),and the evolution of A.gossypii resistance to sulfoxaflor developed faster than acetamiprid in both Yarkant and Jinghe,Xingjiang,China.The sulfoxaflor-resistant strains selected from Yarkant and Jinghe developed significant cross-resistance to acetamiprid,imidacloprid,thiamethoxam and pymetrozine;while the acetamiprid-resistant strains developed significant cross-resistance to sulfoxaflor,imidacloprid,thiamethoxam,pymetrozine,and chlorpyrifos.The relative fitness of A.gossypii decreased as the resistance to sulfoxaflor and acetamiprid developed.The relative fitness levels of the sulfoxaflor-resistant strains(Yarkant-SulR and Jinghe-SulR)were lower than those of the acetamipridresistant strains(Yarkant-AceR and Jinghe-AceR).In addition,the relative fitness levels of sulfoxaflor-and acetamiprid-resistant strains were lower in Jinghe than in Yarkant.In summary,basal insecticide resistance of A.gossypii and insecticide type affected the evolution of resistance to insecticides in A.gossypii,as well as cross-resistance to other insecticides.The sulfoxaflor-and acetamiprid-resistant A.gossypii strains had obvious fitness costs.The results of this work will contribute to the insecticide resistance management and integrated management of A.gossypii.

Genetic benefits of female from extra-pair paternity are context dependent within the socially monogamous Tree Sparrow

Females actively seek extra-pair paternity(EPP)to acquire a fitness advantage for their offspring.The“contextdependence hypothesis”posits that female extra-pair mate choice has plasticity in response to environmental conditions,and therefore magnitude of female genetic benefits from EPP depends on the environmental variation.Furthermore,chronic heavy metal pollution can cause adverse effects on fitness-related traits of wild birds.However,few studies were available on the interactions between heavy metal pollution and EPP.We selected an area that was contaminated by heavy metals for more than 60 years(Baiyin,BY),a relatively unpolluted area(Liujiaxia,LJX),and Tree Sparrows(Passer montanus)as study species to explore the response of female extrapair mate choice and genetic benefits from EPP to heavy metal pollution in socially monogamous birds.The relatedness between social mates and extra-pair mates was investigated.Additionally,we compared the body size and heterozygosity of extra-pair offspring(EPO),within-pair offspring(WPO),social males and extra-pair males from the two Tree Sparrow populations.We found that at BY,female Tree Sparrows tended to choose extra-pair males with larger body size and lower genetic similarity,thereby producing higher heterozygosity and larger body size of EPO compared with those of WPO.However,no similar phenomenon was observed in the Tree Sparrow population from LJX.In addition,there was a significant interaction between population and paternity in the analyses of the fitness-related traits,suggesting that environmental variation could affect female genetic benefits from EPP.This study confirmed the existence of presumed interactions between environmental pollution and EPP within the natural population of socially monogamous Tree Sparrows.Our findings shed lights on the possible effects of long-term environmental stress on mating system in wild birds.

The Impact and Intervention of Handheld Tai Chi Water-Resistance Fitness Ball on Middle-Aged and Elderly Patients with Parkinson’s Disease

Through the use of a survey and statistical methods, this study explores the effects and interventions of handheld Tai Chi water resistance fitness balls on the elderly with Parkinson’s disease. Firstly, a questionnaire on exercise compliance for patients with Parkinson’s disease was developed, and its reliability and validity were tested. Then, a survey was conducted to investigate the current status of exercise compliance among Parkinson’s disease patients, including general information, scoring status, and single and multiple factor analyses of influencing factors [1]. The results of the study show that through qualitative research, the dimensions and item pools of the questionnaire were initially constructed, and the reliability analysis of the questionnaire was conducted through Delphi expert consultation, with favorable results in terms of its reliability and validity [2]. Regarding the current status of exercise compliance among Parkinson’s disease patients, the study found that the level of exercise compliance needs improvement, and there are significant differences in exercise compliance levels among patients under different circumstances. Finally, the research results were discussed and conclusions were drawn. The innovation of this study lies in the development of a questionnaire on exercise compliance for patients with Parkinson’s disease and the preliminary qualitative research and Delphi expert consultation conducted on it, providing new ideas and methods for the study of exercise compliance. However, the study also has limitations as it did not examine the effects of other interventions on Parkinson’s disease, so further research should be conducted [3].

基于多靶点粪便FIT-DNA联合检测技术的结直肠癌早筛应用研究

目的评价多靶点粪便FIT-DNA联合检测技术在结直肠癌早期筛查中的效果并进一步分析其应用前景。方法选取内蒙古医科大学附属医院就诊人群,每位受试者分别行血清肿瘤标志物检测、多靶点粪便FIT-DNA联合检测、肠镜检查,以接受多靶点粪便FIT-DNA联合检测人群为实验组,以接受肠镜检查及血清肿瘤标志物检测人群为对照组,以病理结果为金标准,评价新型粪便分子检测技术对于结直肠癌筛查的效果,对筛出的阳性人群给予及时干预。结果共分析了115例患者。血清肿瘤标志物检测敏感度63.2%(43/68),特异度74.5%(35/47);肠镜检查敏感度97.1%(66/68),特异度80.7%(38/47);而多靶点粪便FIT-DNA联合检测敏感度89.7%(61/68),特异度87.2%(41/47)。多靶点粪便FIT-DNA联合检测敏感度、特异度等均优于血清肿瘤标志物检测,敏感度虽低于肠镜检查,但相较肠镜检查操作简单,可居家自测。

Weighted Least-Squares for a Nearly Perfect Min-Max Fit

In this note, we experimentally demonstrate, on a variety of analytic and nonanalytic functions, the novel observation that if the least squares polynomial approximation is repeated as weight in a second, now weighted, least squares approximation, then this new, second, approximation is nearly perfect in the uniform sense, barely needing any further, say, Remez correction.

Is economic fitness helpful in achieving environmental sustainability in BRICS economies?A risk exposure perspective

A country’s ability to create complex goods and diversify its lines of products is essential for addressing all types of vulnerabilities.Quantifying a country’s vulnerability to extreme climatic events,such as droughts,superstorms,and other natural disasters,and its capacity for successful adaption,is an essential global need that has been ignored.This study examines the role of economic fitness(EF)in addressing climate change risk ex‐posure in BRICS countries in the context of the environmental Kuznets curve using panel data from 1995 to 2015.Panel threshold methodology is employed to ascertain the nonlinear relationship between EF and climate change risk exposure(i.e.,Notre Dame Global Adaptation Initiative Country Index(ND-GAIN)).In addition,empirical associations were estimated using panel-corrected standard errors,Driscoll-Kraay standard errors,and feasible generalized least squares estimation techniques.These findings demonstrated an inverted N shaped link between EF and ND-GAIN.Moreover,even after controlling for significant ND-GAIN influencing variables such as gross domestic product per capita,financial development,and urbanization,our robustness checks revealed significant and consistent findings.

Yr5-virulent races of Puccinia striiformis f.sp.tritici possess relative parasitic fitness higher than current main predominant races and potential risk

Wheat stripe rust,caused by Puccinia striiformis f.sp.tritici(Pst),is one of the most destructive fungal diseases of wheat,and seriously threatens safe production of the crop worldwide.In China,new races historically appeared and rapidly developed to be predominant races and have resulted in ineffectiveness and replacement of wheat resistance cultivars as well as massive reduction in yield.In the present study,the relative parasitic fitness of the two newlyemerged Yr5-virulent races(TSA-6 and TSA-9)were compared with those of four currently predominant Chinese races(CYR31,CYR32,CYR33,and CYR34)based on evaluation on 10 Chinese wheat cultivars.As a result,there were significant differences in the relative parasitic fitness parameters among overall tested races based on multiple comparison(LSD)analysis(P<0.05).The principal component analysis(PCA)of overall parasitic fitness parameters indicated that the sporulation ability,infection and spore survivability,expansion capacity,and potential pathogenicity were the most important parasitic fitness attributes of the tested races.Based on the establishment of extracted three principal components and a comprehensive factor score mathematical models,evaluations of the parasitic fitness attributes of tested races showed that the level of relative parasitic fitness of the tested six races was:CYR32(1.15)>TSA-9(0.95)>TSA-6(0.92)>CYR34(0.29)>CYR31(–1.54)>CYR33(–1.77).The results indicated that two Yr5-virulent races TSA-9 and TSA-6 possessed relative parasitic fitness higher than races CYR34,CYR31,and CYR33,but lower than race CYR32,and have potential risks in developing to be predominant races.Therefore,continual monitoring of both Yr5-virulent races,and their variants is needed.The use of wheat cultivars(lines)with Yr5 resistance gene singly in wheat breeding is essential for being avoided,and is suggested to combine with other effective stripe rust resistance genes.

Application of Flipped Classroom Teaching Model Based on Micro-Course in Practical Training Teaching of Contact Lens Fitting Technology

Objective:This paper aims to study the application of flipped classroom teaching model based on micro-course in the practical training teaching of contact lens fitting technology.Methods:From September 21 to July 23,120 students majoring in ophthalmology and optometry were selected and randomly divided into groups.The control group adopted the traditional teaching mode,and the study group adopted the flipped classroom teaching mode based on micro-course.Teaching scores and the skills,observation and judgment,adaptability,and communication skills were compared between the groups.Results:Statistical comparison of teaching scores under different management methods showed that the clinical thinking score and practice work quality in the study group were higher than those of the control group,and the effect of the study group was better(P<0.05).The overall scores of skills,observation and judgment,adaptability,and communication skills of the study group were better than those in the control group,and the comprehensive ability scores in the two groups were significantly different(P<0.05).Conclusion:In practical training teaching of contact lens fitting technology,the application of flipped classroom teaching based on micro-course can improve the skill scores of personnel,and the overall effect is good.This can lay the foundation for advanced ophthalmology and optometry talents with profound theoretical knowledge and professional skills.

Visceral adiposity index,cardiorespiratory fitness,and fasting plasma glucose associations in adolescents

BACKGROUND The global rise in the prevalence of type 2 diabetes mellitus(T2DM)in children and adolescents is partly linked to the increasing rates of childhood obesity and physical inactivity.AIM To explore the independent relationships of visceral adiposity index(VAI)and cardiorespiratory fitness(CRF)with fasting plasma glucose(FPG)in adolescents.METHODS This descriptive cross-sectional study included 403 adolescents(202 boys and 201 girls)aged 11-19 years.Participants were evaluated for VAI,CRF,and FPG.Regression models,adjusted for age and maturity status,were used to assess the associations between VAI,CRF,and FPG.RESULTS The prevalence of T2DM risk was 15.3%(girls=7.4%;boys=7.9%).In boys,high VAI was positively associated with FPG(β=0.190,P=0.009),while low CRF was negatively associated with FPG(β=-0.206,P=0.010).These associations persisted even after adjusting for CRF and VAI.However,no significant associations between VAI,CRF,and FPG were observed in girls(P>0.05).Adolescents with high VAI and low fitness levels demonstrated poorer glycemic profiles.CONCLUSION Among boys,both VAI and CRF were independently associated with T2DM risk,with CRF showing a stronger association.These associations were not observed in girls.Promoting regular aerobic exercise and healthy diets may serve as essential public health promotion strategies in preventing and managing T2DM risk in adolescents.

Path-dependent speciation in dynamic fitness landscapes

Species is a fundamental concept in evolutionary biology and biodiversity.However,existing species definitions are often influenced by artificial factors or are challenging in practical application,leading to confusion in species classification.Due to uncertain environmental changes and random genetic drift,the fitness expectations of a population may shift,causing species to evolve to a new evolutionary state based on their current instantaneous fitness within a dynamic fitness landscape.This contrasts with the classic static fitness landscape,where fitness expectations are constant.In a dynamic fitness landscape,speciation may exhibit path dependence,where the evolution of traits follows a probabilistic path,creating feedback that shapes evolutionary trajectories.The path-dependent evolutionary mechanism suggests that species survival within an ecosystem is not directly determined by their fitness but by the probability of their evolutionary pathways.This model also indicates that species can coexist with varying probabilities under limited environmental pressures.Consequently,new species,cryptic species,or sympatric species may emerge via path-dependent evolutionary processes.Within this framework,we developed a mathematical species concept,which may guide future species classification methodologies.