Spatial analysis of the osteoarthritis microenvironment: techniques, insights, and applications

Osteoarthritis(OA)is a debilitating degenerative disease affecting multiple joint tissues,including cartilage,bone,synovium,and adipose tissues.OA presents diverse clinical phenotypes and distinct molecular endotypes,including inflammatory,metabolic,mechanical,genetic,and synovial variants.Consequently,innovative technologies are needed to support the development of effective diagnostic and precision therapeutic approaches.Traditional analysis of bulk OA tissue extracts has limitations due to technical constraints,causing challenges in the differentiation between various physiological and pathological phenotypes in joint tissues.This issue has led to standardization difficulties and hindered the success of clinical trials.Gaining insights into the spatial variations of the cellular and molecular structures in OA tissues,encompassing DNA,RNA,metabolites,and proteins,as well as their chemical properties,elemental composition,and mechanical attributes,can contribute to a more comprehensive understanding of the disease subtypes.Spatially resolved biology enables biologists to investigate cells within the context of their tissue microenvironment,providing a more holistic view of cellular function.Recent advances in innovative spatial biology techniques now allow intact tissue sections to be examined using various-omics lenses,such as genomics,transcriptomics,proteomics,and metabolomics,with spatial data.This fusion of approaches provides researchers with critical insights into the molecular composition and functions of the cells and tissues at precise spatial coordinates.Furthermore,advanced imaging techniques,including high-resolution microscopy,hyperspectral imaging,and mass spectrometry imaging,enable the visualization and analysis of the spatial distribution of biomolecules,cells,and tissues.Linking these molecular imaging outputs to conventional tissue histology can facilitate a more comprehensive characterization of disease phenotypes.This review summarizes the recent advancements in the molecular imaging modalities and methodologies for in-depth spatial analysis.It explores their applications,challenges,and potential opportunities in the field of OA.Additionally,this review provides a perspective on the potential research directions for these contemporary approaches that can meet the requirements of clinical diagnoses and the establishment of therapeutic targets for OA.

Estimation-free spatial-domain image reconstruction of structured illumination microscopy

Structured illumination microscopy(SIM)achieves super-resolution(SR)by modulating the high-frequency information of the sample into the passband of the optical system and subsequent image reconstruction.The traditional Wiener-filtering-based reconstruction algorithm operates in the Fourier domain,it requires prior knowledge of the sinusoidal illumination patterns which makes the time-consuming procedure of parameter estimation to raw datasets necessary,besides,the parameter estimation is sensitive to noise or aberration-induced pattern distortion which leads to reconstruction artifacts.Here,we propose a spatial-domain image reconstruction method that does not require parameter estimation but calculates patterns from raw datasets,and a reconstructed image can be obtained just by calculating the spatial covariance of differential calculated patterns and differential filtered datasets(the notch filtering operation is performed to the raw datasets for attenuating and compensating the optical transfer function(OTF)).Experiments on reconstructing raw datasets including nonbiological,biological,and simulated samples demonstrate that our method has SR capability,high reconstruction speed,and high robustness to aberration and noise.

Design of Protograph LDPC-Coded MIMO-VLC Systems with Generalized Spatial Modulation

This paper investigates the bit-interleaved coded generalized spatial modulation(BICGSM) with iterative decoding(BICGSM-ID) for multiple-input multiple-output(MIMO) visible light communications(VLC). In the BICGSM-ID scheme, the information bits conveyed by the signal-domain(SiD) symbols and the spatial-domain(SpD) light emitting diode(LED)-index patterns are coded by a protograph low-density parity-check(P-LDPC) code. Specifically, we propose a signal-domain symbol expanding and re-allocating(SSER) method for constructing a type of novel generalized spatial modulation(GSM) constellations, referred to as SSERGSM constellations, so as to boost the performance of the BICGSM-ID MIMO-VLC systems.Moreover, by applying a modified PEXIT(MPEXIT) algorithm, we further design a family of rate-compatible P-LDPC codes, referred to as enhanced accumulate-repeat-accumulate(EARA) codes,which possess both excellent decoding thresholds and linear-minimum-distance-growth property. Both analysis and simulation results illustrate that the proposed SSERGSM constellations and P-LDPC codes can remarkably improve the convergence and decoding performance of MIMO-VLC systems. Therefore, the proposed P-LDPC-coded SSERGSM-mapped BICGSMID configuration is envisioned as a promising transmission solution to satisfy the high-throughput requirement of MIMO-VLC applications.

Evaluation of COVID-19 Cases and Vaccinations in the State of Georgia, United States: A Spatial Perspective

This study evaluates the distribution of COVID-19 cases and mass vaccination campaigns from January 2020 to April 2023. There are over 235,000 COVID-19 cases and over 733,000 vaccinations across the 159 counties in the state of Georgia. Data on COVID-19 was acquired from usafact.org while the vaccination records were obtained from COVID-19 vaccination tracker. The spatial patterns across the counties were analyzed using spatial statistical techniques which include both global and local spatial autocorrelation. The study further evaluates the effect of vaccination and selected socio-economic predictors on COVID-19 cases across the study area. The result of hotspot analysis reveals that the epicenters of COVID-19 are distributed across Cobb, Fulton, Gwinnett, and DeKalb counties. It was also affirmed that the vaccination records followed the same pattern as COVID-19 cases’ epicenters. The result of the spatial error model performed well and accounted for a considerable percentage of the regression with an adjusted R squared of 0.68, Akaike Information Criterion (AIC) 387.682 and Breusch-Pagan of 9.8091. ESDA was employed to select the main explanatory variables. The selected variables include vaccination, population density, percentage of people that do not have health insurance, black race, Hispanic and these variables accounted for 68% of the number of COVID-19 cases in the state of Georgia during the study period. The study concludes that both COVID-19 cases and vaccinated individuals have spatial peculiarities across counties in Georgia state. Lastly, socio-economic variables and vaccination are very important to reduce the vulnerability of individuals to COVID-19 disease.

Spatial evolution and spatial production of traditional villages from "backward poverty villages" to "ecologically well-off villages": Experiences from the hinterland of national nature reserves in China

With the rapid urbanization process,the space of traditional villages in China is undergoing significant changes.Studying the spatial evolution of traditional villages is significant in promoting rural spatial transformation and realizing rural revitalization and sustainable rural development.Based on the traceability analysis of spatial production theory,this paper constructed an analytical framework for the spatial production evolution of traditional villages,analyzed the spatial evolution process and characteristics of traditional villages by using buffer analysis,spatial syntax,and other research methods,and revealed the characteristics of the spatial production evolution of traditional villages and the driving mechanism.The results show that:(1)The village spatial formation and development follow the village life cycle theory and usually develop from embryonic villages to diversified and integrated villages;(2)The evolution of village spatial production is characterized by the diversity of material space,the sublimation of daily life space,and the integration of social system space and generalization of emotional space;(3)The evolution of village spatial production from backward and poor village to ecologically well-off village is influenced by a combination of factors;(4)The village has formed a spatial structure of"people-land-scape-culture-industry",realized comprehensive reconstruction and spatial reproduction.The study results reflect the spatial evolution characteristics of traditional villages in mountainous areas in a more comprehensive way,which helps to promote the protection and development of traditional villages in mountainous areas and,to a certain extent,provides a reference for the development of rural revitalization.

Spatial transcriptomics:recent developments and insights in respiratory research

The respiratory system's complex cellular heterogeneity presents unique challenges to researchers in this field.Although bulk RNA sequencing and single-cell RNA sequencing(scRNA-seq)have provided insights into cell types and heterogeneity in the respiratory system,the relevant specific spatial localization and cellular interactions have not been clearly elucidated.Spatial transcriptomics(ST)has filled this gap and has been widely used in respiratory studies.This review focuses on the latest iterative technology of ST in recent years,summarizing how ST can be applied to the physiological and pathological processes of the respiratory system,with emphasis on the lungs.Finally,the current challenges and potential development directions are proposed,including high-throughput full-length transcriptome,integration of multi-omics,temporal and spatial omics,bioinformatics analysis,etc.These viewpoints are expected to advance the study of systematic mechanisms,including respiratory studies.

Assessing the Spatial Equality of COVID Testing Sites Maintaining Zero COVID Policy

Rapid and timely testing is essential to minimize the COVID-19 spread. Decision makers and policy planners need to determine the equal distribution and accessibility of testing sites. This study mainly examines the spatial equality of COVID-19 testing sites that maintain a zero COVID policy in Guangzhou City. The study has identified the spatial disparities of COVID testing sites, characteristics of testing locations, and accessibility. The study has obtained information on COVID testing sites in Guangzhou City and population data. Point pattern analyses, Euclidian distance and allocation, and network analyses are the main methods used to achieve the research objectives, and 1183 total COVID testing sites can be recognized in Guangzhou City. Results revealed that spatial disparities could be noticed over the study area. Testing locations of Guangzhou City are highly clustered. The most significant testing sites are located in Haizhu District, which has the third largest population. The highest population density can be identified in Yuexiu District. However, only 94 testing sites are located there. According to all the results, higher disparities can be identified, and a lack of testing sites is located in the north part of the study area. Some people in the northern part have to travel more than 10 km to reach a testing site. Finally, this paper suggests increasing the number of testing sites in the north and south parts of the study area and keeping the same distribution, considering the area, total population, and population density. This kind of research will be helpful to decision-makers in making proper decisions to maintain a zero COVID policy.

Dynamics of Advantageous Mutant Spread in Spatial Death-Birth and Birth-Death Moran Models

The spread of an advantageous mutation through a population is of fundamental interest in population genetics. While the classical Moran model is formulated for a well-mixed population, it has long been recognized that in real-world applications, the population usually has an explicit spatial structure which can significantly influence the dynamics. In the context of cancer initiation in epithelial tissue, several recent works have analyzed the dynamics of advantageous mutant spread on integer lattices, using the biased voter model from particle systems theory. In this spatial version of the Moran model, individuals first reproduce according to their fitness and then replace a neighboring individual. From a biological standpoint, the opposite dynamics, where individuals first die and are then replaced by a neighboring individual according to its fitness, are equally relevant. Here, we investigate this death-birth analogue of the biased voter model. We construct the process mathematically, derive the associated dual process, establish bounds on the survival probability of a single mutant, and prove that the process has an asymptotic shape. We also briefly discuss alternative birth-death and death-birth dynamics, depending on how the mutant fitness advantage affects the dynamics. We show that birth-death and death-birth formulations of the biased voter model are equivalent when fitness affects the former event of each update of the model, whereas the birth-death model is fundamentally different from the death-birth model when fitness affects the latter event.

Analysis of spatial distribution characteristics and driving factors of ethnicminority villages in China using geospatial technology and statistical models

This study aims to reveal the spatial structural characteristics of 1,652 Ethnic-Minority Villages(EMV)in China and to analyze the mechanisms driving their spatial heterogeneity.EMV are a special type of settlement space that preserve a large number of historical traces of the ethnic culture of ancient China.They are important carriers of China’s excellent traditional culture and are key to the implementation of rural revitalization strategies.In this study,1652 EMV in China were selected as the research subjects.The Nearest Neighbor Index,kernel density,and spatial autocorrelation index were employed to reveal the spatial structural characteristics of minority villages.Neural network models,spatial lag models,and geographical detectors were used to analyze the formation mechanism of spatial heterogeneity in EMV.The results indicate that:(1)EMV exhibit significant spatial differentiation characterized by“single-core with multiple surrounding sub-centers,”“polarization between east and west,”“decreasing quantity from southwest to east coast to northeast to northwest,”and“large dispersion with small agglomeration.”(2)EMV are mainly distributed in areas rich in intangible cultural heritage,with high vegetation coverage and low altitude,far from central cities,and having limited arable land and an underdeveloped economy and transportation,particularly in shaded or riverbank areas.(3)Distance from the nearest river(X3),distance from central cities(X8),national intangible cultural heritage(X9),and NDVI(X10)were the main driving factors affecting the spatial distribution of EMV,whereas elevation(X1)and GDP(X5)had the weakest influence.As EMV are a relatively unique territorial spatial unit,the identification of their spatial heterogeneity characteristics not only deepens the research content of settlement geography,but also involves the assessment,protection,and development of Minority Villages,which is of great significance for the inheritance and utilization of excellent ethnic cultures in the era.

Enhancing transboundary natural tourism resources governance:unveiling the spatial pattern and its influencing factors

Tourism resources that span provincial boundaries in China play a pivotal role in regional development,yet effective governance poses persistent challenges.This study addresses this issue by constructing a comprehensive database of transboundary natural tourism resources(TNTR)through amalgamation of diverse data sources.Utilizing the Getis-Ord Gi^(*),kernel density estimation,and geographical detectors,we scrutinize the spatial patterns of TNTR,focusing on both named and unnamed entities,while exploring the influencing factors.Our findings reveal 7883 identified TNTR in China,with mountain tourism resources emerging as the predominant type.Among provinces,Hunan boasts the highest count,while Shanghai exhibits the lowest.Southern China demonstrates a pronounced clustering trend in TNTR distribution,with the spatial arrangement of biological landscapes appearing more random compared to geological and water landscapes.Western China,characterized by intricate terrain,exhibits fewer TNTR,concurrently unveiling a significant presence of unnamed natural tourism resources.Crucially,administrative segmentation influences TNTR development,generating disparities in regional goals,developmental stages and intensities,and management approaches.In response to these variations,we advocate for strengthening the naming of the unnamed transboundary tourism resources,constructing a geographic database of TNTR for government and establishing a collaborative management mechanism based on TNTR database.Our research contributes to elucidating the intricate landscape of TNTR,offering insights for tailored governance strategies in the realm of cross-provincial tourism resource management.

Manipulating the Spatial Structure of Second-Order Quantum Coherence Using Entangled Photons

High-order quantum coherence reveals the statistical correlation of quantum particles. Manipulation of quantum coherence of light in the temporal domain enables the production of the single-photon source, which has become one of the most important quantum resources. High-order quantum coherence in the spatial domain plays a crucial role in a variety of applications, such as quantum imaging, holography, and microscopy. However, the active control of second-order spatial quantum coherence remains a challenging task. Here we predict theoretically and demonstrate experimentally the first active manipulation of second-order spatial quantum coherence,which exhibits the capability of switching between bunching and anti-bunching, by mapping the entanglement of spatially structured photons. We also show that signal processing based on quantum coherence exhibits robust resistance to intensity disturbance. Our findings not only enhance existing applications but also pave the way for broader utilization of higher-order spatial quantum coherence.

Spatial and temporal evolution of electromagnetic pulses from solid target irradiated with multi-hundred-terawatt laser pulse inside target chamber

Giant electromagnetic pulses(EMPs) induced by high-power laser irradiating solid targets interfere with various experimental diagnoses and even damage equipment,so unveiling the evolution of EMPs inside the laser chamber is crucial for designing effective EMP shielding.In this work,the transmission characteristics of EMPs as a function of distances from the target chamber center(TCC) are studied using B-dot probes.The mean EMP amplitude generated by picosecond laser-target interaction reaches 561 kV m^(-1),357 kV m^(-1),395 kV m^(-1),and 341 kV m^(-1)at 0.32 m,0.53 m,0.76 m,and 1 m from TCC,which decreases dramatically from 0.32 m to 0.53 m.However,it shows a fluctuation from 0.53 m to 1 m.The temporal features of EMPs indicate that time-domain EMP signals near the target chamber wall have a wider full width at half maximum compared to that close to TCC,mainly due to the echo oscillation of electromagnetic waves inside the target chamber based on simulation and experimentation.The conclusions of this study will provide a new approach to mitigate strong electromagnetic pulses by decreasing the echo oscillation of electromagnetic waves inside the target chamber during laser coupling with targets.

Spatially resolved transcriptomic profiling of placental development in dairy cow

The placenta plays a crucial role in successful mammalian reproduction.Ruminant animals possess a semi-invasive placenta characterized by a highly vascularized structure formed by maternal endometrial caruncles and fetal placental cotyledons,essential for full-term fetal development.The cow placenta harbors at least two trophoblast cell populations:uninucleate(UNC)and binucleate(BNC)cells.However,the limited capacity to elucidate the transcriptomic dynamics of the placental natural environment has resulted in a poor understanding of both the molecular and cellular interactions between trophoblast cells and niches,and the molecular mechanisms governing trophoblast differentiation and functionalization.To fill this knowledge gap,we employed Stereo-seq to map spatial gene expression patterns at near single-cell resolution in the cow placenta at 90 and 130 days of gestation,attaining high-resolution,spatially resolved gene expression profiles.Based on clustering and cell marker gene expression analyses,key transcription factors,including YBX1 and NPAS2,were shown to regulate the heterogeneity of trophoblast cell subpopulations.Cell communication and trajectory analysis provided a framework for understanding cell-cell interactions and the differentiation of trophoblasts into BNCs in the placental microenvironment.Differential analysis of cell trajectories identified a set of genes involved in regulation of trophoblast differentiation.Additionally,spatial modules and co-variant genes that help shape specific tissue structures were identified.Together,these findings provide foundational insights into important biological pathways critical to the placental development and function in cows.

Spatial Analysis of the Aging Population and Socio-economic Factors of China:Global and Local Perspectives

Population aging has become an inevitable trend and exerted profound influences on socio-economic development in China.In this study,we utilized data from national population census and statistical yearbooks in 2010 and 2020 to explore spatio-temporal patterns of aging population and its coupling correlations with socio-economic factors from both global and local perspectives.The results from Local Indicators of Spatial Association(LISA)uncover notable spatial disparities in aging population rates,with higher rates concentrated in the eastern regions and lower rates in the western areas of the Chinese mainland.The results from the global correlation analysis with the changes in aging population rates show significant positive correlations with government interventions and industrial structures,but negatively correlated with economic development,social consumption,and medical facilities.From a local perspective,a Geographically Weighted(GW)correlation analysis is employed to uncover local correlations between aging trends and socio-economic factors.The insights gained from this technique not only underscore the complexity and diversity of economic implications stemming from population aging,but also provide invaluable guidance for crafting region-specific economic policies tailored to various stages of population aging.

Spatial Dynamics of Chickenpox Outbreaks in Rapidly Developing Regions:Implications for Global Public Health

Objective The occurrence of chickenpox in rapidly developing areas poses substantial seasonal risk to children.However,certain factors influencing local chickenpox outbreaks have not been studied.Here,we examined the relationship between spatial clustering,heterogeneity of chickenpox outbreaks,and socioeconomic factors in Southern China.Methods We assessed chickenpox outbreak data from Southern China between 2006 and 2021,comprising both relatively fast-growing parts and slower sub-regions,and provides a representative sample of many developing regions.We analyzed the spatial clustering attributes associated with chickenpox outbreaks using Moran’s I and local indicators of spatial association and quantified their socioeconomic determinants using Geodetector q statistics.Results There were significant spatial heterogeneity in the risk of chickenpox outbreaks,with strong correlations between chickenpox risk and various factors,particularly demographics and living environment.Furthermore,interactive effects among specific are factors,such as population density and per capita residential building area,percentage of households with toilets,percentage of rental housing,exhibited q statistics of 0.28,0.25,and 0.24,respectively.Conclusion This study provides valuable insights into the spatial dynamics of chickenpox outbreaks in rapidly developing regions,revealing the socioeconomic factors affecting disease transmission.These implications extend the formulation of effective public health strategies and interventions to prevent and control chickenpox outbreaks in similar global contexts.

Temporal and Spatial Dynamics of Vaccine-Derived Poliovirus (VDPV) in Democratic Republic of Congo from 2018 to 2023

Background: The Democratic Republic of Congo (DRC) has been facing outbreaks of VDPV since 2017. These wild poliovirus variants are responsible for poliomyelitis, which is in the process of eradication.. In the following lines, we try to show the evolution of VDPV cases across the country in order to understand their chronological dynamics and seasonal influence. Methods: We conducted a cross-sectional study of of VDPV notified in the DRC from 2018 to 2023. Maps of the spatial dynamics of VDPV cases were produced from attack rates with QGIS® (3.22.8). As for temporal dynamics, time series were decomposed and presented in the form of graphs showing the chronological evolution of VDPV cases and their seasonal trend, using R.4.0 software package. Results: A total of 1196 Cases of VDPV types 1, 2 and 3 were recorded in the biological confirmation databases of the INRB and the Expanded Program of Immunization during the study period across25 provinces. The eastern part of the country reporting the most cases. The general trend is upwards, with a peak in 2022 of 527 cases, whereas in 2021 there was a notable drop of 31 cases. Analysis of the temporal breakdown suggests a seasonal pattern, with peaks between the months of September and December, considered being rainy periods in some provinces. Conclusion: During the 6 years of our study (2018 - 2023) almost all the Health Zones were hit by VDPV epidemics. The eastern part was the most impacted. The seasonal component is well marked suggesting a rise in detection in the rainy season and during pivotal periods of climate change.

PARE:Privacy-Preserving Data Reliability Evaluation for Spatial Crowdsourcing in Internet of Things

The proliferation of intelligent,connected Internet of Things(IoT)devices facilitates data collection.However,task workers may be reluctant to participate in data collection due to privacy concerns,and task requesters may be concerned about the validity of the collected data.Hence,it is vital to evaluate the quality of the data collected by the task workers while protecting privacy in spatial crowdsourcing(SC)data collection tasks with IoT.To this end,this paper proposes a privacy-preserving data reliability evaluation for SC in IoT,named PARE.First,we design a data uploading format using blockchain and Paillier homomorphic cryptosystem,providing unchangeable and traceable data while overcoming privacy concerns.Secondly,based on the uploaded data,we propose a method to determine the approximate correct value region without knowing the exact value.Finally,we offer a data filtering mechanism based on the Paillier cryptosystem using this value region.The evaluation and analysis results show that PARE outperforms the existing solution in terms of performance and privacy protection.

Salinity fronts shape spatial patterns in zooplankton distribution in Hangzhou Bay

Ocean fronts play important roles in nutrient transport and in the shaping ecological patterns.Frontal zones in small bays are typically small in scale,have a complex structure,and they are spatially and temporally variable,but there are limited data on how biological communities respond to this variation.Hangzhou Bay,a mediumsized estuary in China,is an ideal place in which to study the response of plankton to small-scale ocean fronts,because three water masses(Qiantang River Diluted Water,Changjiang River Diluted Water,and the East China Sea current) converge here and form dynamic salinity fronts throughout the year.We investigate zooplankton communities,and temperature,salinity and chlorophyll a(Chl a) in Hangzhou Bay in June(wet perio d) and December(dry period) of 2022 and examine the dominant environmental factors that affect zooplankton community spatial variability.We then match the spatial distributions of zooplankton communities with those of salinity fronts.S alinity is the most important explanatory variable to affect zooplankton community spatial variability during both wet and dry periods,in that it contributes>60% of the variability in community structure.Furthermore,the spatial distributions of zooplankton match well with salinity fronts.During December,with weaker Qiantang River Diluted Water and a stronger secondary Changjiang River Plume,zooplankton communities occur in moderate salinity(MS,salinity range 15.6±2.2) and high salinity(HS,22.4±1.7) regions,and their ecological boundaries closely match the Qiantang River Diluted Water front.In June,different zooplankton communities occur in low salinity(LS,3.9±1.0),MS(11.7±3.6) and HS(21.3±1.9) regions.Although the LS region occurs abnormally in the central bay rather than its apex because of the anomalous influence of rising and falling tides during the sampling perio d,the ecological boundaries still match salinity interfaces.Low-salinity or brackish-water zooplankter taxa are relatively more abundant in LS or MS regions,and the biomass and abundance of zooplankton is higher in the MS region.

Single-cell and spatial omics:exploring hypothalamic heterogeneity

Elucidating the complex dynamic cellular organization in the hypothalamus is critical for understanding its role in coordinating fundamental body functions. Over the past decade, single-cell and spatial omics technologies have significantly evolved, overcoming initial technical challenges in capturing and analyzing individual cells. These high-throughput omics technologies now offer a remarkable opportunity to comprehend the complex spatiotemporal patterns of transcriptional diversity and cell-type characteristics across the entire hypothalamus. Current single-cell and single-nucleus RNA sequencing methods comprehensively quantify gene expression by exploring distinct phenotypes across various subregions of the hypothalamus. However, single-cell/single-nucleus RNA sequencing requires isolating the cell/nuclei from the tissue, potentially resulting in the loss of spatial information concerning neuronal networks. Spatial transcriptomics methods, by bypassing the cell dissociation, can elucidate the intricate spatial organization of neural networks through their imaging and sequencing technologies. In this review, we highlight the applicative value of single-cell and spatial transcriptomics in exploring the complex molecular-genetic diversity of hypothalamic cell types, driven by recent high-throughput achievements.

Adaptive interaction driven by the learning effect in the spatial prisoner's dilemma

We propose a computing model in which individuals can automatically adjust their interaction intensity with their mentor according to the learning effect.This model is designed to investigate the cooperative dynamics of the spatial prisoner's dilemma.More specifically,when the cumulative payoff of a learner is more than his reference earning,he will strengthen his interaction with his mentor;otherwise,he will reduce it.The experimental results indicate that this mechanism can improve the emergence of cooperation in a networked population and that the driving coefficient of interaction intensity plays an important role in promoting cooperation.Interestingly,under a certain social dilemma condition,there exists a minimal driving coefficient that leads to optimal cooperation.This occurs due to a positive feedback effect between the individual's satisfaction frequency and the number of effective neighbors.Moreover,we find that the experimental results are in accord with theoretical predictions obtained from an extension of the classical pair-approximation method.Our conclusions obtained by considering relationships with mentors can provide a new perspective for future investigations into the dynamics of evolutionary games within structured populations.