A nanobody-based blocking enzyme-linked immunosorbent assay for detecting antibodies against pseudorabies virus glycoprotein E

Pseudorabies(PR)is an acute infectious disease of pigs caused by the PR virus(PRV)and results in great economic losses to the pig industry worldwide.PRV glycoprotein E(gE)-based enzyme-linked immunosorbent assay(ELISA)has been used to distinguish gE-deleted vaccine-immunized pigs from wild-type virus-infected pigs to eradicate PR in some countries.Nanobody has the advantages of small size and easy genetic engineering and has been a promising diagnostic reagent.However,there were few reports about developing nanobody-based ELISA for detecting anti-PRV-gE antibodies.In the present study,the recombinant PRV-gE was expressed with a bacterial system and used to immunize the Bactrian camel.Then,two nanobodies against PRV-gE were screened from the immunized camel by phage display technique.Subsequently,two nanobody-HRP fusion proteins were expressed with HEK293T cells.The PRV-gE-Nb36-HRP fusion protein was selected as the probe for developing the blocking ELISA(bELISA)to detect anti-PRV-gE antibodies.Through optimizing the conditions of bELISA,the amount of coated antigen was 200 ng per well,and dilutions of the fusion protein and tested pig sera were separately 1:320 and 1:5.The cut-off value of bELISA was 24.20%,and the sensitivity and specificity were 96.43 and 92.63%,respectively.By detecting 233 clinical pig sera with the developed bELISA and a commercial kit,the results showed that the coincidence rate of two assays was 93.99%.Additionallly,epitope mapping showed that PRV-gE-Nb36 recognized a conserved conformational epitope in different reference PRV strains.Simple,great stability and low-cost nanobody-based bELISA for detecting anti-PRV-gE antibodies were developed.The bELISA could be used for monitoring and eradicating PR.

三维动脉自旋标记成像量化脑转移瘤放疗前后灌注变化的研究

目的:应用三维动脉自旋标记(three-dimensional arterial spin labeling,3D-ASL)定量分析脑转移瘤(brain metastasis,BMs)患者放射治疗(放疗)过程中BMs肿瘤靶区、正常脑区域及瘤周水肿区的血流灌注变化。建立三者灌注变化与放疗剂量梯度的关系,为BMs患者进行个体化放疗提供参考依据。方法:收集2018年7月至2019年6月山东省肿瘤防治研究院26例BMs患者放疗前及放疗后的MR模拟定位图像(包括强化T1WI图像和3D-ASL的灌注图,由强化T1WI图像获得BMs肿瘤靶区,3D-ASL图像获得血流灌注信息)。分别定义强化T1WI中BMs高信号区、正常脑区域及瘤周水肿区为感兴趣区域(regions of interest,ROIs)。研究BMs肿瘤靶区放疗前后平均最大截面积、平均最大脑血流量(cerebral blood flow,CBF)的变化及相关性;分析不同剂量梯度下3个ROIs CBF值的变化规律。结果:BMs肿瘤靶区放疗前后平均最大截面积和CBF值分别降低26.46%和29.64%(P<0.05)。BMs肿瘤靶区在30~40、40~50 Gy和>50 Gy剂量梯度下,CBF放疗前后下降率分别为33.75%、24.61%和27.55%(P<0.05),30~40 Gy时最大。正常脑区域在0~10、10~20、20~30、30~40、40~50 Gy和>50 Gy剂量梯度下,CBF放疗前后下降率分别为7.65%、11.12%、18.42%、20.23%、19.79%和17.89%(P<0.05),30~40 Gy时最大。瘤周水肿区放疗后CBF下降率与剂量梯度增高同步。BMs肿瘤靶区放疗前后的灌注下降较正常脑区域和瘤周水肿区更为显著。结论:3D-ASL可客观反映BMs肿瘤靶区、正常脑区域及瘤周水肿区放疗中灌注变化情况。依据CBF的变化,正常脑区域的放疗剂量建议控制在30 Gy以下,而肿瘤靶区高灌注区和瘤周水肿区应给予高剂量。

颅骨及脑组织CT MR显示差异对脑肿瘤放疗剂量学影响的研究

目的:研究颅骨及脑组织CT/MR显示差异对脑瘤放疗剂量学的影响。方法:选取60例接受放疗的脑转移瘤(brain metastases,BM)患者,每例患者均行CT和MR模拟定位,将CT图像和MR图像刚性配准,在CT/MR融合图像上勾画肿瘤靶区、危及器官、颅骨(分别命名为Skull-CT、Skull-MR)、脑组织(分别命名为Brain-CT、不包含脑膜的Brain-MR-1、包含脑膜的Brain-MR-2)等组织和器官。基于CT图像制定三维适形放射治疗(3D-CRT)或调强放射治疗(IMRT)计划为Plan1;复制CT图像,基于CT/MR图像确定的颅骨(Skull)显示的差异区域Skull-sub赋予CT值20 HU,得到CT2图像,再将Plan1复制到CT2图像上进行放疗剂量的再次计算,获得Plan2。评估两组计划的靶区及组织器官的剂量学变化。结果:Skull-MR较Skull-CT体积平均减少约46%,Brain-CT的体积较不包含脑膜的Brain-MR-1与包含脑膜的Brain-MR-2平均减少约0.8%和6.7%,差异均具有统计学意义(均P<0.05)。相比Plan1,Plan2的颅骨剂量变化率平均<3.5%;计划靶区(planning target volcome,PTV)剂量指标的变化率除了靶区剂量均匀性(HI)平均减少约6.8%,其他指标平均变化均<1.1%;危及器官的剂量平均变化率均<2%。此外,全脑放疗患者的PTV_(Brain-MR-1)及PTV_(Brain-MR-2)剂量指标较PTV_(Brain-CT),除了HI平均变化约11%和2.4%,其他指标的平均变化率均<2.2%。结论:颅骨及脑组织在CT/MR上的显示差异显著,虽然未对正常器官与肿瘤靶区的放疗剂量带来显著性变化,但对HI的影响仍不可忽视。

Estimation of extreme wind speed in SCS and NWP by a non-stationary model

In offshore engineering design, it is considerably significant to have an adequately accurate estimation of marine environmental parameters, in particular, the extreme wind speed of tropical cyclone （TC） with different return periods to guarantee the safety in projected operating life period. Based on the 71-year （1945-2015） TC data in the Northwest Pacific （NWP） by the Joint Typhoon Warning Center （JTWC） of US, a notable growth of the TC intensity is observed in the context of climate change. The fact implies that the traditional stationary model might be incapable of predicting parameters in the extreme events. Therefore, a non-stationary model is proposed in this study to estimate extreme wind speed in the South China Sea （SCS） and NWP. We find that the extreme wind speeds of different return periods exhibit an evident enhancement trend, for instance, the extreme wind speeds with different return periods by non- stationary model are 4.1%-4.4% higher than stationary ones in SCS. Also, the spatial distribution of extreme wind speed in NWP has been examined with the same methodology by dividing the west sea areas of the NWP 0°-45°N, 105°E-130°E into 45 subareas of 5° × 5°, where oil and gas resources are abundant. Similarly, remarkable spacial in-homogeneity in the extreme wind speed is seen in this area： the extreme wind speed with 50-year return period in the subarea （15°N-20°N, 115°E-120°E） of Zhongsha and Dongsha Islands is 73.8 m/s, while that in the subarea of Yellow Sea （30°N-35°N, 120°E-125°E） is only 47.1 m/s. As a result, the present study demonstrates that non-stationary and in-homogeneous effects should be taken into consideration in the estimation of extreme wind speed.

Mechano-Sensing by Endothelial Primary Cilium

Introduction Primary cilium is a non-motile microstructure,protruding from cell surface of most mammalian cells.It was previously thought to be vestigial.However,recent studies indicate that it may serve as one of the most vital mechanosensors for many types of cells such as epithelial and endothelial cells and osteocytes.Protruding from the apical membrane,the primary cilium can directly sense subtle variation of mechanical forces exerted on the cell and then transduce the mechanical cues into biochemical signals into the cell,although the mechanism remain elusive.Vascular endothelial cells(ECs)lining the inner wall of our blood vessels are continuously exposed to the blood flow.In order to maintain proper functions for the cardiovascular system,ECs should have a variety of mechano-sensors and transducers to sense the blood flow change and adjust the vessel size and transport across the vessel wall accordingly.Among more than a dozen recognized EC mechano-sensors,the primary cilium has drawn more and more attention recently.Primary cilium on endothelial cells is essential for the homeostasis of vessels.It is reported to be prevalent in areas of disturbed flow where atherosclerosis and intracranial aneurysm usually occur.Deficiencies of primary cilia may promote atherosclerosis,endothelial-to-mesenchymal transition(EndoMT)and loss of direction orientation,to name a few.Therefore understanding why the primary cilia are necessary to maintain the homeostasis of blood vessels and how will help us develop better treatment strategies for the common cardiovascular diseases.Dimension and structure of primary cilium Primary cilium is reported to be shorter than 8 in length and about 0.2 in diameter.The length of primary cilium varies in different cell types and under different conditions.The major structural components of the primary cilium include basal body,ciliary axoneme(consisting of nine doublet microtubules),ciliary membrane,transition zone,basal feet,and striated rootlets.Each part of the primary cilium is essential and has specific function.Current methods investigating the EC primary cilium as a mechano-sensor:Immunostaining and imaging techniques have been used to investigate the molecular mechanisms by which EC primary cilium serves as a mechano-sensor and transducer.It has been found that various proteins locate on the primary cilium,working together to maintain the function of primary cilium.Some proteins function as ion-channels,mediating Ca2+entry into the primary cilium.Some are involved in the cascade signal pathway.Others are related to the assembly and maintenance of primary cilium.Briefly,the flow induces the deflection of the EC primary cilium,which triggers calcium increase via opening of the PC2 cation channel that is responsible for calcium ion influx.This PC2 cation channel is localized to the primary cilium and is assumed to be stretch-activated.The resulting change in the intracellular calcium concentration then regulates numerous molecular activities inside the cell that contribute to vessel homeostasis.In addition to triggering calcium release,another mechanism has also been found in blood-pressure maintenance in the vasculature,where the vessel diameter is regulated by endothelial primary cilia through adjusting nitric oxide production.So far,little is known about the mechanical mechanism behind this deflection-triggered o-pening of signaling pathways.For example,what is the flow induced bending behavior and force distribution? What is the threshold value of stretch/defection for activating a corresponding signaling pathway? These all remain to be answered.In combination of image data and experiments,several computational models have been established to answer these questions.However,the current models are not able to include the complex structure of primary cilium and the model predictions are limited.Future studies With the development of super high resolution optical microscopy,more detailed images for the structural(molecular)components of EC primary cilia will be revealed,especially when the ECs are alive and the forces are known.Combining these experimental observations with more sophisticated mathematical models will elucidate the mechano-sensing mechanism of EC primary cilia,as the force and stress distribution on cilium along with other mechanical properties are still beyond the capability of experimental approaches due to the scales of the quantities involved.By using numerical approaches,much more detailed dynamic information can be obtained.

基于MR超长期延迟强化量化分析鼻咽癌放疗GTV退缩规律的研究

目的:探讨基于MR超长期延迟强化扫描对鼻咽癌(nasopharyngeal carcinoma,NPC)肿瘤靶区及淋巴结不同区域差异性退缩规律的研究。方法:选取2019年12月至2020年8月山东省肿瘤医院53例接受放疗的NPC患者,获得放疗前、中及后MR(T2WI、15s强化及>10 min超长期延迟强化的T1WI像)。在T2WI上确定大体肿瘤靶区(GTVp)和淋巴结(GTVn)。根据15 s强化与>10 min强化T1WI的剪影图像确定造影剂清除比较快的区域(GTVp_(快)、GTVn_(快)),清除慢的区域(GTVp_(慢)、GTVn_(慢)),分析不同亚靶区放疗后的退缩差异性。结果:1)GTVp在接受50 Gy及放疗结束的退缩率分别为57.37%、18.61%,低于GTVp_(快)的64.52%、29.66%,而显著高于GTVp_(慢)的25.21%、7.55%(P<0.05),GTVn、GTVn_(快)、GTVn_(慢)的退缩也具有相似变化趋势;2)放疗前、后GTVp_(快)与GTVp、GTVn_(快)与GTVn体积变化均具有相关性(r=0.872、0.998,P<0.05)。而GTVp_(慢)与GTVp、GTVn_(慢)与GTVn体积变化差异无统计学意义(P<0.05);3)放疗后GTVp_(慢)与接受50 Gy放疗时相比体积增加了7.55%,而GTVp与GTVp_(快)、GTVp_(慢)的退缩均小于淋巴结。结论:MR超长期延迟强化扫描可以将NPC及阳性淋巴结分为造影剂清除快、慢的亚区域,不同亚区域及整体靶区退缩显著不同步;在以体积为标准进行NPC放疗疗效评估时,不同亚区域应行个体化分析。

Mechano-Sensing and shear stress-shielding by endothelial primary cilia:structure,composition,and function

Primary cilium is an antenna-like and non-motile structure protruding from the apical surface of most mammalian cells including endothelial cells lining the inner side of all the blood vessels in our body.Although it has been over a century since primary cilia were discovered,the investigation about their mechano-sensing and other roles in maintaining normal functions of cardiovascular system has just started in recent years.This focused review aims to give an update about the current literature for the role of endothelial primary cilia in blood flow mechanosensing and shear stress-shielding.To do this,we first summarized the characteristic features of endothelial primary cilia in terms of structure,dimension,molecular composition,and mechanical properties(e.g.,bending rigidity),which are the dominant factors for their functions in mechano-sensing and transduction,as well as vascular protection from the blood flow-induced wall shear stress.We also described the experimental techniques and mathematical models for determining the dimension and mechanical properties of the primary cilium.Then we reviewed the molecular mechanisms underlying mechano-sensing and transduction by endothelial primary cilia and the mathematical model prediction for their roles in redistribution and reduction of wall shear stresses.Finally,we briefly discussed the common cardiovascular diseases,e.g.,atherosclerosis,hypertension,and aneurysm,due to defects and malfunction of endothelial primary cilia and suggested potential targets for therapeutic treatments.

Angiogenesis and proliferation of endothelial cells in hypertrophic and nodular port-wine stain

Background:Port-wine stain(PWS)has been classified not as the hyperplasia of cells,but rather,as an expansion of malformed vessels.However,previous studies have reported upregulated expression of proangiogenic factors in PWS.Several studies have indicated that the pathology exhibits proliferation of numerous endothelial cells in hypertrophic/nodular PWS.This study aimed to determine the expression of vascular epithelial growth factor(VEGF),matrix metalloproteinase-9(MMP-9),angiopoietin-2(ANG-2),and basic fibroblast growth factor(bFGF)in hypertrophic PWS.Methods:Immunohistochemistry was used to analyze skin samples from 33 patients with hypertrophic PWS.Expression levels of VEGF,MMP-9,ANG-2,and bFGF in hypertrophic PWS were determined by multiplying the intensity by the percentage of immunoreactive cells.Immunoreactivity scores were classified as follows:negative(0),low(1),moderate(2,3,and 4),or high(6).Results:Based on pathological characteristics,hypertrophic PWS was divided into vascular malformation and pyogenic granuloma(PG)types.VEGF,MMP-9,ANG-2,and bFGF were significantly activated in the blood vessels of PG-type PWS samples compared with their counterparts in blood vessels of vascular malformation-type PWS samples and controls.PG-type hypertrophic PWS,which exhibited proliferation of endothelial cells,showed the strongest activation.Conclusion:The exuberant proliferation of endothelial cells in PG-type hypertrophic PWS may be associated with the regulation of proangiogenic factors during development.These proangiogenic factors that function in the angiogenesis and proliferation of endothelial cells may play an important role in the pathogenesis and progression of PWS.Furthermore,these factors may be dynamic and behave differently in various types of hypertrophic PWS.

Effect of mechanical stresses on degradation behavior of high-purity magnesium in bone environments

High-purity(HP)magnesium(Mg)has emerged as a promising biomaterial for supporting functional bone tissue.Our previous study found that mechanical stresses and the surrounding fibrotic tissue(subcuta-neous)both play crucial roles in the degradation of HP Mg.However,due to challenges in the degradation and regeneration process in vivo,it remains unclear how stress affects HP Mg degradation in bone en-vironments,limiting its further application.In this study,novel loading devices were designed and the effects of tensile and compressive stresses on HP Mg degradation in vivo and in vitro bone environments were quantitatively analyzed.In addition,bone osteointegration around HP Mg was explored preliminar-ily.Tensile stress increases the degradation rate of HP Mg in vivo and in vitro.HP Mg degradation in vivo is more sensitive to stress factors than in vitro,but the sensitivity decreases with corrosion time.The volume loss rate of HP Mg is multilinear with the applied stress and degradation time.The volume of bone tissue surrounding HP Mg is larger in the no-stress group compared to the stressed groups,which is more pronounced with increasing implantation time.These results provide valuable insights for optimiz-ing the design of HP Mg-based implants considering load conditions.This will help to achieve a balance between the degradation rate of the implant and the regeneration rate of the surrounding bone.

Q-homotopy analysis method for time-fractional Newell–Whitehead equation and time-fractional generalized Hirota–Satsuma coupled KdV system

In this paper,two types of fractional nonlinear equations in Caputo sense,time-fractional Newell–Whitehead equation(FNWE)and time-fractional generalized Hirota–Satsuma coupled KdV system(HS-cKdVS),are investigated by means of the q-homotopy analysis method(q-HAM).The approximate solutions of the proposed equations are constructed in the form of a convergent series and are compared with the corresponding exact solutions.Due to the presence of the auxiliary parameter h in this method,just a few terms of the series solution are required in order to obtain better approximation.For the sake of visualization,the numerical results obtained in this paper are graphically displayed with the help of Maple.

基于模糊密度峰值聚类的区域同位模式并行挖掘算法

区域同位模式挖掘(RCPM,regional co-location pattern mining)是为了发掘某个局部区域内存在的同位(co-location)模式,以发现在全局中无法发现的信息.传统的区域挖掘大多会采用明确界限的几何体框定同位模式产生的区域.但是现实中的各类区域可能是无明确边界的.另外,数据的分布情况作为区域的重要特征之一,也应该成为区域选择的因素.基于上述思考,本文引入密度峰值聚类(DPC,density peak-based clustering),提出新的密度度量函数,并结合模糊集理论与k近邻距离,设计了一个行之有效的并行区域同位模式挖掘算法.实验结果表明,利用本文方法挖掘到的结果更具有现实意义,并且并行化极大地提升了挖掘算法的效率.在真实数据上,2线程下的加速比达到了1.89.

Effects of Geometrical Characteristics of Suture on Fracture Resistance of Walnut Shell

Nut shells have good impact and fracture resistance,but many kinds of nut shells have suture structures with low bonding strength.Therefore,the mechanism of impact and fracture resistance of nut shells as a whole is important to study,particularly given that sutures maintain low bonding strength.In this study,we investigated the effect of the geometrical characteristics of sutures(morphology,thickness,and number)on the overall fracture resistance of walnuts,based on mechanical tests of C-ring samples,microstructure analysis after cracking,quantitative analysis of suture geometric model,and numerical simulations.We found that the cracking of walnuts was mainly caused by tensile stress,and the bonding strength was approximately 2.48±0.64 MPa.We discovered that the thickness of the suture was 1.55±0.32 times thicker than the shell,which improved the fracture resistance ability by more than 28.4%.The undulating and inclined morphology of the walnut suture also increased the fracture force.Additionally,an appropriate suture number reduced the cracking of walnuts.In conclusion,our study sheds light on the physiological function of walnut sutures from a biomechanical perspective and provides useful references for designing fracture resistance measures in thin shell structures.

Dose-dependent tandem responses of osteoblasts during osteogenesis

Irisin,a myokine mainly secreted from contracted skeleton muscle,plays a profound role in bone formation and remodeling.Although irisin has been revealed to elevate bone mass in vivo,details whether there is a dosedependent relationship between irisin and bone formation remain unclear.In this study,we explored the dosedependent effects of irisin on osteoblast proliferation and differentiation.Our results first demonstrated a remarkable increase in cell proliferation rate and viability in response to elevated concentrations of r-irisin,which was further enhanced over time.Notably,this increase was subject to complex dose-response relationships as the proliferation-enhancing effects of r-irisin may have a saturation point between 10 ng/ml and 100 ng/ml.Furthermore,we determined that 1,10,and 100 ng/ml r-irisin were able to upregulate the expression of osteogenic transcription factors(Runx2,Osx,and Atf4),as well as osteogenic markers(Alp,Col1a1 and Spp1),albeit without significant difference among these 3 concentrations.Interestingly,nutrient-depleted osteoblasts and those with standard culture showed distinct responses to higher doses of irisin regarding osteogenic differentiation.Further investigation is required to uncover the molecular mechanisms underlying the observed tandem effects of irisin on osteogenesis.

The Regulatory Effect of Braided Silk Fiber Skeletons with Differential Porosities on In Vivo Vascular Tissue Regeneration and Long-Term Patency

The development of small-diameter vascular grafts that can meet the long-term patency required for implementation in clinical practice presents a key challenge to the research field.Although techniques such as the braiding of scaffolds can offer a tunable platform for fabricating vascular grafts,the effects of braided silk fiber skeletons on the porosity,remodeling,and patency in vivo have not been thoroughly investigated.

Statistical analysis of mechanical properties of biological soft tissue under quasi-static mechanical loading

The mechanical properties of biological soft tissues are inextricably linked to the field of health care,and their mechanical properties can be important indicators for diagnosing and detecting diseases;they can also be used to analyze the causes of organ diseases from a pathological point of view and thus guide the deployment of medical solutions.As an effective method to characterize the mechanical properties of materials,mechanical loading experiments have been successfully applied to the mechanical properties of materials,including tension,compression,pure shear,and so on.Under quasi-static loading,when the material is a biological soft tissue material between a solid and an ideal fluid,its viscoelastic properties strongly respond to the force stimulus,and the stress-strain-time in the elastic phase will have obvious disturbance characteristics.Therefore,the existing statistical methods are often difficult to quantitatively describe the mechanical properties of materials.Therefore,this study proposes an Interval Capture Point based on the principle of integration.The experimental data based on this method can characterize its nonlinear mechanical properties well,especially when the loading speed is extremely low and the soft materials show strong disturbance characteristics.The proposed method can still accurately characterize the hyperelastic and viscoelastic properties of the mechanical properties of biological soft tissues under quasi-static loading.

一种基于列计算的空间并置模式挖掘方法

空间并置(co-location)模式挖掘旨在发现空间特征间的关联关系.一个并置模式是空间特征集合的子集,它们的实例在空间中频繁并置出现.传统的并置模式挖掘方法大多基于表实例计算模式的并置程度,但表实例的生成和存储将导致巨大的时间、空间消耗.针对这一问题,本文提出了一种基于列计算的空间并置模式挖掘方法,不再生成表实例,只需要搜索模式的参与实例.为了加速参与实例搜索,设计了实例搜索空间剪枝、候选参与实例验证、频繁性提前感知等优化策略.在此基础上,提出了CPM-Col算法,讨论了算法的复杂度、正确性和完备性.在真实和模拟数据集上进行了大量实验,实验结果表明,本文提出的算法比其他7个baseline算法具有更好的性能和可扩展性,特别地,CPM-Col算法的效率提升达到数倍至数个量级.此外,实验验证了本文提出的优化策略的有效性.

Diagonal-symmetrical and Midline-symmetrical Unit Cells with Same Porosity for Bone Implant: Mechanical Properties Evaluation

In this study, mechanical properties of bionic porous structures with diagonal-symmetrical and midline-symmetrical unit cells were studied when the porosities were same. Three typical unit cells (Diamond (DO), Rhombic Dodecahedron (RD), and Octet Truss (OT)) were selected, in which DO has diagonal-symmetrical shape, while RD and OT share midline-symmetrical structure. Based on the same porosity, corresponding models were designed, and Ti6Al4V samples were manufactured by electron beam melting. Then, using Mechanical Properties Testing (MPT) and Finite Element Analysis (FEA) methodologies, mechanical properties and transmissions of different porous structures were evaluated. Besides, composition and details before and after printing were analyzed with Energy Dispersive Spectrometer (EDS), X-ray diffraction (XRD) and Scanning Electron Microscope (SEM). MPT results showed that midline-symmetrical shape would have superior compressive performance than diagonal-symmetrical shape, but opposite trend for the torsion performance, which were in line with FEA prediction. Furthermore, effective modulus of DO, RD and OT were 2.59 GPa, 4.89 GPa, and 1.77 GPa, approximating the mechanical properties of human bones. Additionally, manufacturing defects and discrepancies between FEA and MPT were found. This study would provide great helps for unit cell selection and initial mechanical properties matching for optimum bone implants.

Top-k probabilistic prevalent co-location mining in spatially uncertain data sets

A co-location pattern is a set of spatial features whose instances frequently appear in a spatial neighborhood. This paper efficiently mines the top-k probabilistic prevalent co-locations over spatially uncertain data sets and makes the following contributions： 1） the concept of the top-k prob- abilistic prevalent co-locations based on a possible world model is defined; 2） a framework for discovering the top- k probabilistic prevalent co-locations is set up; 3） a matrix method is proposed to improve the computation of the preva- lence probability of a top-k candidate, and two pruning rules of the matrix block are given to accelerate the search for ex- act solutions; 4） a polynomial matrix is developed to further speed up the top-k candidate refinement process; 5） an ap- proximate algorithm with compensation factor is introduced so that relatively large quantity of data can be processed quickly. The efficiency of our proposed algorithms as well as the accuracy of the approximation algorithms is evaluated with an extensive set of experiments using both synthetic and real uncertain data sets.