Localization transition on complex networks via spectral statistics

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Physica A 374(2007)483–490Identification of overlapping community structure in complexnetworks using fuzzy c -means clusteringShihua Zhang a,Ã,Rui-Sheng Wang b ,Xiang-Sun Zhang aa Academy of Mathematics &Systems Science,Chinese Academy of Science,Beijing 100080,Chinab School of Information,Renmin University of China,Beijing 100872,ChinaReceived 28June 2006Available online 7August 2006AbstractIdentification of (overlapping)communities/clusters in a complex network is a general problem in data mining of network data sets.In this paper,we devise a novel algorithm to identify overlapping communities in complex networks by the combination of a new modularity function based on generalizing NG’s Q function,an approximation mapping of network nodes into Euclidean space and fuzzy c -means clustering.Experimental results indicate that the new algorithm is efficient at detecting both good clusterings and the appropriate number of clusters.r 2006Elsevier B.V.All rights reserved.Keywords:Overlapping community structure;Modular function;Spectral mapping;Fuzzy c -means clustering;Complex network1.IntroductionLarge complex networks representing relationships among set of entities have been one of the focuses of interest of scientists in many fields in the recent years.Various complex network examples include social network,worldwide web network,telecommunication network and biological network.One of the key problems in the field is ‘How to describe/explain its community structure’.Generally,a community in a network is a subgraph whose nodes are densely connected within itself but sparsely connected with the rest of the network.Many studies have verified the community/modularity structure of various complex networks such as protein-protein interaction network,worldwide web network and co-author network.Clearly,the ability to detect community structure in a network has important practical applications and can help us understand the network system.Although the notion of community structure is straightforward,construction of an efficient algorithm for identification of the community structure in a complex network is highly nontrivial.A number of algorithms for detecting the communities have been developed in various fields (for a recent review see Ref.[1]and a recent comparison paper see Ref.[2]).There are two main difficulties in detecting community structure.The first is that we don’t know how many communities there are in a given network.The usual drawback in many /locate/physa0378-4371/$-see front matter r 2006Elsevier B.V.All rights reserved.doi:10.1016/j.physa.2006.07.023ÃCorresponding author.E-mail addresses:zsh@ (S.Zhang),wrs@ (R.-S.Wang),zxs@ (X.-S.Zhang).algorithms is that they cannot give a valid criterion for measuring the community structure.Secondly,it is a common case that some nodes in a network can belong to more than one community.This means the overlapping community structure in complex networks.Overlapping nodes may play a special role in a complex network system.Most known algorithms such as divisive algorithm [3–5]cannot detect them.Only a few community-detecting methods [6,7]can uncover the overlapping community structure.Taking into account the first difficulty,Newman and Girvan [8]has developed a new approach.They introduced a modularity function Q for measuring community structure.In order to write the context properly,we refer to a similar formulation in Ref.[5].In detail,given an undirected graph/network G ðV ;E ;W Þconsisting of the node set V ,the edge set E and a symmetric weight matrix W ¼½w ij n Ân ,where w ij X 0and n is the size of the network,the modularity function Q is defined asQ ðP k Þ¼X k c ¼1L ðV c ;V c ÞL ðV ;V ÞÀL ðV c ;V ÞL ðV ;V Þ 2"#,(1)where P k is a partition of the nodes into k groups and L ðV 0;V 00Þ¼P i 2V 0;j 2V 00w ði ;j Þ.The Q function measuresthe quality of a given community structure organization of a network and can be used to automatically select the optimal number of communities k according to the maximum Q value [8,5].The measure has been used for developing new detection algorithms such as Refs.[5,9,4].White and Smyth [5]showed that optimizing the Q function can be reformulated as a spectral relaxation problem and proposed two spectral clustering algorithms that seek to maximize Q .In this study,we develop an algorithm for detecting overlapping community structure.The algorithm combines the idea of modularity function Q [8],spectral relaxation [5]and fuzzy c -means clustering method[10]which is inspired by the general concept of fuzzy geometric clustering.The fuzzy clustering methods don’t employ hard assignment,while only assign a membership degree u ij to every node v i with respect to the cluster C j .2.MethodSimulation across a wide variety of simulated and real world networks showed that large Q values are correlated with better network clusterings [8].Then maximizing the Q function can obtain final ‘optimal’community structure.It is noted that in many complex networks,some nodes may belong to more than one community.The divisive algorithms based on maximizing the Q function fail to detect such case.Fig.1shows an example of a simple network which visually suggests three clusters and classifying node 5(or node 9)intoFig.1.An example of network showing Q and e Qvalues for different number k of clusters using the same spectral mapping but different cluster methods,i.e.k -means and fuzzy c -means,respectively.For the latter,it shows every node’s soft assignment and membership of final clusters with l ¼0:15.S.Zhang et al./Physica A 374(2007)483–490484two clusters at the same time may be more appropriate intuitively.So we introduce the concept of fuzzy membership degree to the network clustering problem in the following subsection.2.1.A new modular functionIf there are k communities in total,we define a corresponding n Âk ‘soft assignment’matrix U k ¼½u 1;...;u k with 0p u ic p 1for each c ¼1;...;k and P kc ¼1u ic ¼1for each i ¼1;...;n .With this we define the membership of each community as ¯V c ¼f i j u ic 4l ;i 2V g ,where l is a threshold that can convert a soft assignment into final clustering.We define a new modularity function e Q as e Q ðU k Þ¼X k c ¼1A ð¯V c ;¯V c ÞA ðV ;V ÞÀA ð¯V c ;V ÞA ðV ;V Þ 2"#,(2)where U k is a fuzzy partition of the vertices into k groups and A ð¯V c ;¯V c Þ¼P i 2¯V c ;j 2¯V c ððu ic þu jc Þ=2Þw ði ;j Þ,A ð¯V c ;V Þ¼A ð¯V c ;¯V c ÞþP i 2¯V c ;j 2V n ¯V c ððu ic þð1Àu jc ÞÞ=2Þw ði ;j Þand A ðV ;V Þ¼P i 2V ;j 2V w ði ;j Þ.This of coursecan be thought as a generalization of the Newman’s Q function.Our objective is to compute a soft assignment matrix by maximizing the new Q function with appropriate k .How could we do?2.2.Spectral mappingWhite and Smyth [5]showed that the problem of maximizing the modularity function Q can be reformulated as an eigenvector problem and devised two spectral clustering algorithms.Their algorithms are similar in spirit to a class of spectral clustering methods which map data points into Euclidean space by eigendecomposing a related matrix and then grouping them by general clustering methods such as k -means and hierarchical clustering [5,9].Given a network and its adjacent matrix A ¼ða ij Þn Ân and a diagonal matrix D ¼ðd ii Þ,d ii ¼P k a ik ,two matrices D À1=2AD À1=2and D À1A are often used.A recent modification [11]uses the top K eigenvectors of the generalized eigensystem Ax ¼tDx instead of the K eigenvectors of the two matrices mentioned above to form a matrix whose rows correspond to original data points.The authors show that after normalizing the rows using Euclidean norm,their eigenvectors are mathematically identical and emphasize that this is a numerically more stable method.Although their result is designed to cluster real-valued points[11,12],it is also appropriate for network clustering.So in this study,we compute the top k À1eigenvectors of the eigensystem to form a ðk À1Þ-dimensional embedding of the graph into Euclidean space and use ‘soft-assignment’geometric clustering on this embedding to generate a clustering U k (k is the expected number of clusters).2.3.Fuzzy c-meansHere,in order to realize our ‘soft assignment’,we introduce fuzzy c -means (FCM)clustering method [10,13]to cluster these points and maximize the e Qfunction.Fuzzy c -means is a method of clustering which allows one piece of data to belong to two or more clusters.This method (developed by Dunn in 1973[10]and improved by Bezdek in 1981[13])is frequently used in pattern recognition.It is based on minimization of the following objective functionJ m ¼Xn i ¼1X k j ¼1u m ij k x i Àc j k 2,(3)over variables u ij and c with P j u ij ¼1.m 2½1;1Þis a weight exponent controlling the degree of fuzzification.u ij is the membership degree of x i in the cluster j .x i is the i th d -dimensional measured data point.c j is the d -dimensional center of the cluster j ,and k Ãk is any norm expressing the similarity between any measured data and the center.Fuzzy partitioning is carried out through an iterative optimization of the objective function shown above,with the update of membership degree u ij and the cluster centers c j .This procedure converges to a local minimum or a saddle point of J m .S.Zhang et al./Physica A 374(2007)483–4904852.4.The flow of the algorithmGiven an upper bound K of the number of clusters and the adjacent matrix A ¼ða ij Þn Ân of a network.The detailed algorithm is stated straightforward for a given l as follows:Spectral mapping:(i)Compute the diagonal matrix D ¼ðd ii Þ,where d ii ¼P k a ik .(ii)Form the eigenvector matrix E K ¼½e 1;e 2;...;e K by computing the top K eigenvectors of thegeneralized eigensystem Ax ¼tDx .Fuzzy c -means:for each value of k ,2p k p K :(i)Form the matrix E k ¼½e 2;e 3;...;e k from the matrix E K .(ii)Normalize the rows of E k to unit length using Euclidean distance norm.(iii)Cluster the row vectors of E k using fuzzy c -means or any other fuzzy clustering method to obtain a softassignment matrix U k .Maximizing the modular function:Pick the k and the corresponding fuzzy partition U k that maximizes e QðU k Þ.In the algorithm above,we initialize FCM such that the starting centroids are chosen to be as orthogonal as possible which is suggested for k -means clustering method in Ref.[12].The initialization does not change the time complexity,and also can improve the quality of the clusterings,thus at the same time reduces the need for restarting the random initialization process.The framework of our algorithm is similar to several spectral clustering methods in previous studies[5,9,12,11].We also map data points (work nodes in our study)into Euclidean space by computing the top K eigenvectors of a generalized eigen system and then cluster the embedding using a fuzzy clustering method just as others using geometric clustering algorithm or general hierarchical clustering algorithm.Here,we emphasize two key points different from those earlier studies:We introduce a generalized modular function e Q employing fuzzy concept,which is devised for evaluating the goodness of overlapping community structure. In combination with the novel e Qfunction,we introduce fuzzy clustering method into network clustering instead of general hard clustering methods.This means that our algorithm can uncover overlapping clusters,whereas general framework:‘‘Objective function such as Q function and Normalized cut function+Spectral mapping+general geometric clustering/hierarchical clustering’’cannot achieve this.3.Experimental resultsWe have implemented the proposed algorithm by Matlab.And the fuzzy clustering toolbox [14]is used for our analysis.In order to make an intuitive comparison,we also compute the hard clustering based on the original Q -function,spectral mapping (same as we used)and k -means clustering.We illustrate the fuzzy concept and the difference of our method with traditional divisive algorithms by a simple example shown in Fig.1.Just as mentioned above,the network visually suggests three clusters.But classifying node 5(or node 9)simultaneously into two clusters may be more reasonable.We can see from Fig.1that our method did uncover the overlapping communities for this simple network,while the traditional method can only make one node belong to a single cluster.We also present the analysis of two real networks,i.e.the Zachary’s karate club network and the American college football team network for better understanding the differences between our method and traditional methods.S.Zhang et al./Physica A 374(2007)483–490486S.Zhang et al./Physica A374(2007)483–490487 3.1.Zachary’s karate clubThe famous karate club network analyzed by Zachary[15]is widely used as a test example for methods of detecting communities in complex networks[1,8,16,3,4,17,9,18,19].The network consists of34members of a karate club as nodes and78edges representing friendship between members of the club which was observed over a period of two years.Due to a disagreement between the club’s administrator and the club’s instructor, the club split into two smaller ones.The question we concern is that if we can uncover the potential behavior of the network,detect the two communities or multiple groups,and particularly identify which community a node belongs to.The network is presented in Fig.2,where the squares and the circles label the members of the two groups.The results of k-means and our analysis are illustrated in Fig.3.The k-means combined with Q function divides the network into three parts(see in Fig.3A),but we can see that some nodes in one cluster are also connected densely with another cluster such as node9and31in cluster 1densely connecting with cluster2,and node1in cluster2with cluster3.Fig.3B shows the results of our method,from which we can see that node1,9,10,31belong to two clusters at the same time.These nodes in the network link evenly with two clusters.Another thing is that the two methods both uncover three communities but not two.There is a small community included in the instructor’s faction,since the set of nodes5,6,7,11,17only connects with node1in the instructor’s faction.Note that our method also classifies node1into the small community,while k-means does not.work of American college football teamsThe second network we have investigated is the college football network which represents the game schedule of the2000season of Division I of the US college football league.The nodes in the network represent the115 teams,while the links represent613games played in the course of the year.The teams are divided into conferences of8–12teams each and generally games are more frequent between members of the same conference than between teams of different conferences.The natural community structure in the network makes it a commonly used workbench for community-detecting algorithm testing[3,5,7].Fig.4shows how the modularity Q and e Q vary with k with respect to k-means and our method,respectively. The peak for k-means is at k¼12,Q¼0:5398,while for our algorithm at k¼10,e Q¼0:4673with l¼0:10. Both methods identify ten communities which contain ten conferences almost exactly.Only teams labeled as Sunbelt are not recognized as belonging to a same community for both methods.This group is classified as well in the results of Refs.[3,19].This happens because the Sunbelt teams played nearly as many games against Western Athletic teams as they played in their own conference,and they also played quite a number of gamesagainst Mid-American team.Our method identified11nodes(teams)which belong to at least twoFig.2.Zachary’s karate club network.Square nodes and circle nodes represent the instructor’s faction and the administrator’s faction, respectively.Thisfigure is from Newman and Girvan[8].communities (see Fig.5,11red nodes).These nodes generally connect evenly with more than one community,so we cannot classify them into one specific community correctly.These nodes represent ‘fuzzy’points which cannot be classified correctly by employing current link information.Maybe such points play a ‘bridge’role in two or more communities in complex network of other types.4.Conclusion and discussionIn this paper,we present a new method to identify the community structure in complex networks with a fuzzy concept.The method combines a generalized modularity function,spectral mapping,and fuzzy clustering technique.The nodes of the network are projected into d -dimensional Euclidean space which is obtained by computing the top d nontrivial eigenvectors of the generalized eigensystem Ax ¼tDx .Then the fuzzy c -means clustering method is introduced into the d -dimensional space based on general Euclidean distance to cluster the data points.By maximizing the generalized modular function e QðU d Þfor varying d ,we obtain the appropriate number of clusters.The final soft assignment matrix determines the final clusters’membership with a designated threshold l .Fig.3.The results of both k -means and our method applied to karate club network.A:The different colors represent three different communities obtained by k -means and the right table shows values of NG’Q versus different k .B:Four red nodes represent the overlap of two adjacent communities obtained by our method and the right table shows values of new Q versus different k with l ¼0:25.3.t y 0510152000.10.20.30.40.50.6k-meansK N G ' Q 0510152000.10.20.30.40.5fuzzy c-means K N e w Q Fig.4.Q and e Qvalues versus k with respect to k -means and fuzzy c -means clustering methods for the network of American college football team.S.Zhang et al./Physica A 374(2007)483–490488Although spectral mapping has been comprehensively used before to detect communities in complex networks (even in clustering the real-valued points),we believe that our method represents a step forward in this field.A fuzzy method is introduced naturally with the generalized modular function and fuzzy c -means clustering technique.As our tests have suggested,it is very natural that some nodes should belong to more than one community.These nodes may play a special role in a complex network system.For example,in a biological network such as protein interaction network,one node (protein or gene)belonging to two functional modules may act as a bridge between them which transfers biological information or acts as multiple functional units [6].One thing should be noted is that when this method is applied to large complex networks,computational complexity is a key problem.Fortunately,some fast techniques for solving eigensystem have been developed[20]and several methods of FCM acceleration can also be found in the literature [21].For instance,if we adopt the implicitly restarted Lanczos method (IRLM)[20]to compute the K À1eigenvectors and the efficient implementation of the FCM algorithm in Ref.[21],we can have the worse-case complexity of O ðmKh þnK 2h þK 3h Þand O ðnK 2Þ,respectively,where m is the number of edges in the network and h is the number of iteration required until convergence.For large sparse networks where m $n ,and K 5n ,the algorithms will scale roughly linearly as a function of the number of nodes n .Nonetheless,the eigenvector computation is still the most computationally expensive step of the method.We expect that this new method will be employed with promising results in the detection of communities in complex networks.AcknowledgmentsThis work is partly supported by Important Research Direction Project of CAS ‘‘Some Important Problem in Bioinformatics’’,National Natural Science Foundation of China under Grant No.10471141.The authors thank Professor M.E.J.Newman for providing the data of karate club network and the college football team network.Fig.5.Fuzzy communities of American college football team network (k ¼10and e Q¼0:4673)with given l ¼0:10(best viewed in color).S.Zhang et al./Physica A 374(2007)483–490489References[1]M.E.J.Newman,Detecting community structure in networks,Eur.Phys.J.B 38(2004)321–330.[2]L.Danon,J.Duch,A.Diaz-Guilera,A.Arenas,Comparing community structure identification,J.Stat.Mech.P09008(2005).[3]M.Girvan,M.E.J.Newman,Community structure in social and biological networks,A 99(12)(2002)7821–7826.[4]J.Duch,A.Arenas,Community detection in complex networks using extremal optimization,Phys.Rev.E 72(2005)027104.[5]S.White,P.Smyth,A spectral clustering approach to finding communities in graphs,SIAM International Conference on DataMining,2005.[6]G.Palla,I.Derenyi,I.Farkas,T.Vicsek,Uncovering the overlapping community structure of complex networks in nature and society,Nature 435(2005)814–818.[7]J.Reichardt,S.Bornholdt,Detecting fuzzy community structures in complex networks with a Potts model,Phys.Rev.Lett.93(2004)218701.[8]M.E.J.Newman,M.Girvan,Finding and evaluating community structure in networks,Phys.Rev.E 69(2004)026113.[9]L.Donetti,M.A.Mun oz,Detecting network communities:a new systematic and efficient algorithm,J.Stat.Mech.P10012(2004).[10]J.C.Dunn,A fuzzy relative of the ISODATA process and its use in detecting compact well-separated clusters,J.Cybernet.3(1973)32–57.[11]D.Verma,M.Meila,A comparison of spectral clustering algorithms.Technical Report,2003,UW CSE Technical Report 03-05-01.[12]A.Ng,M.Jordan,Y.Weiss,On spectral clustering:analysis and an algorithm,Adv.Neural Inf.Process.Systems 14(2002)849–856.[13]J.C.Bezdek,Pattern Recognition with Fuzzy Objective Function Algorithms,Plenum Press,New York,1981.[14]Fuzzy Clustering Toolbox-h http://www.fmt.vein.hu/softcomp/fclusttoolbox/i .[15]W.W.Zachary,An information flow model for conflict and fission in small groups,J.Anthropol.Res.33(1977)452–473.[16]M.E.J.Newman,Fast algorithm for detecting community structure in networks,Phys.Rev.E 69(2004)066133.[17]F.Radicchi,C.Castellano,F.Cecconi,V.Loreto,D.Parisi,Defining and identifying communities in networks,Proc.Natl.Acad.A 101(9)(2004)2658–2663.[18]F.Wu,B.A.Huberman,Finding communities in linear time:a physics approach,Eur.Phys.J.B 38(2004)331–338.[19]S.Fortunato,tora,M.Marchiori,A method to find community structures based on information centrality,Phys.Rev.E 70(2004)056104.[20]Z.Bai,J.Demmel,J.Dongarra,A.Ruhe,H.Vorst (Eds.),Templates for the Solution of Algebraic Eigenvalue Problems:A PracticalGuide,SIAM,Philadelphia,PA,2000.[21]J.F.Kelen,T.Hutcheson,Reducing the time complexity of the fuzzy c -means algorithm,IEEE Trans.Fuzzy Systems 10(2)(2002)263–267.S.Zhang et al./Physica A 374(2007)483–490490。

Proceedings of the New3SC International Conference: to be published in Physica CInhomogeneous Charge State in HTSC Cuprates and CMR Manganites T. EgamiDepartment of Materials Science and Engineering and Laboratory for Research on the Structure of Matter, University of Pennsylvania, Philadelphia, PA 19104(Received: Jan. 15, 2001, revised: Feb. 14, 2001)Abstract: Recent measurements of neutron elastic and inelastic scattering suggest that the charge states are spatially inhomogeneous at two lengthscales, atomic and nanometer scales, in both the high-temperature superconducting (HTSC) cuprates and colossal mag-netoresistive (CMR) manganites. We suggest that the two-phonon mechanism that con-trols the charge localization in CMR manganites is also at work in HTSC cuprates, and may hold a key to understanding the mechanism of superconductivity.Key words: neutron scattering, charge inhomogeneity, phonons, CMR manganitese-mail: egami@1. IntroductionGenerally local lattice distortion and charge inhomogeneity are considered to be harmful to superconductivity, including high-temperature superconductivity (HTSC). Thus in spite of numerous reports of local lattice distortions in cuprates [1] the majority view has been that they are unimportant to the mechanism of superconductivity, and are merely the consequences of strong interactions and short coherence length. However, the perception appears to be changing due to the observation of the spin-charge stripes in non-superconducting cuprates with 1/8 charge density and the conjecture that dynamic stripes might be present in the superconducting state [2]. In this paper we discuss recent results by neutron inelastic scattering that indicate the presence of charge inhomogemei-ties at two lengthscales, atomic and nanometer scales, which are in many ways similar to those in the manganites that show colossal magnetoresistance (CMR). We suggest that the two-phonon mechanism of charge localization in CMR manganites must be in opera-tion also in cuprates, and such phonon involvement may be an integral part of the HTSC phenomenon.2. Inelastic Neutron ScatteringWe have made a series of inelastic neutron scattering measurements on the high-energy LO phonons in cuprates, La1.85Sr0.15CuO4 [3] and YBa2Cu3O6+x [4,5]. The pho-non branch we studied was the Cu-O bond-stretching mode as shown in Fig. 1. It mainly involves oxygen motion, and at the zone-center, q = 0, it is the ferroelectric mode, while at the zone-edge, q = (π, 0, 0) in the unit of 1/a (a is the Cu-Cu distance), it is a half-breathing mode. This mode induces the hybridization between the Cu-d and O-p orbitals to change and results in charge transfer. For this reason it is expected to interact strongly with charge carriers [6,7]. Indeed this is the only mode that shows strong softening near the zone-edge upon doping [8], and the kink in the electron dispersion determined by photoemission is likely due to this phonon mode [9]. The neutron results revealed a rather anomalous nature of this branch:1. At low temperatures the branch splits into two, a high-energy branch and a low en-ergy-branch, both of which show little dispersion.2. The splitting of the phonon dispersion becomes weak at higher temperatures. InYBa2Cu3O6.95 the temperature dependence of the change in the dispersion agrees with the superconducting order parameter.3. As the doped charge density is increased in YBCO, one would expect the LO phonondispersion to soften gradually near the zone-edge. Surprisingly the energy at the zone-edge does not change much with doping and the phonon dispersion is always split into two. But the intensity is transferred from the high energy-branch to the low-energy branch with increased doping.The point 1 is best explained by doubling of the unit cell that halves the Brillouin zone, such as the charge pattern shown in Fig. 2 that has the periodicity of 2a [3]. The usual stripe pattern with the periodicity of 4a fails to account for the dispersion. The 2a perio-dicity appears to reflect the underlying Peierls instability, and may give rise to the cou-pled ladder state [10]. As point 2 shows this charge pattern is temperature dependent. The point 3 is best interpreted in terms of an inhomogeneous structure; microscopic seg-regation into charge-rich and charge-poor regions. The high-energy branch must be as-sociated with charge-poor regions, since it agrees with the dispersion in the undoped sample [8], and the low-energy branch with charge-rich regions, since its intensity grows with doping. The lengthscale for the segregation must be a nanometer at most; otherwise the q dependence of the phonon structure factors for the two branches must be similar. This micro-phase segregation was seen also by a neutron scattering PDF study [11]. Thus the results suggest that the charge state of cuprates is inhomogeneous at two lengthscales, atomic and nanometer scales.3. Polaron stability in CMR manganitesIn manganites charges can become localized forming polarons, depending on tem-perature and composition [12,13]. Nanometer-scale charge inhomogeneity is also seen, even in the metallic state just above the insulator-to-metal transition, suggesting the charge segregation tendency [14,15]. There is a striking parallelism between polaron formation in manganites (0-d) and stripe formation in cuprates (1-d) as the mechanism of charge localization, and the presence of nanometer charge inhomogeneity in both. It is well understood that, in manganites, charge localization is controlled by the balance be-tween the localization forces (electron-lattice coupling and antiferromagnetic or orbital ordering) and the delocalizaton forces (kinetic energy and elastic energy) [12,13]. These forces can be affected by the ionic size of the A-site ions in the perovskite, <r A> [16].While the standard explanation is that the ionic size modulates the bandwidth, this has been questioned by a number of results [15]. Our alternate interpretation is based upon the local structure of polarons [15,17]. In the case of simple lattice polarons the spatial extensions of the charge and the lattice distortion are about the same. However, in man-ganites and cuprates spins play a large role in confining the charge, so that a hole can be localized on a single Mn site, while the elastic field that a polaron generates is long-range. This long-range stress field increases the polaron self-energy by a factor of about 2, according to the continuum elasticity theory [18,19]. But if the value of <r A> is small enough the Mn-O-Mn bonds are buckled. Then, when the local Jahn-Teller distortion is removed within the polaron and the long Mn-O bond locally becomes short, this change can be accommodated by unbuckling the bond (Fig. 3) [17]. In other words this unbuck-ling screens the local polaronic strain, and the long-range field will not be generated. Thus the renormalization of the polaron energy due to the long-range field does not hap-pen, reducing the polaron energy by a factor of 2 compared to the previous case. In man-ganites this change in the polaron self-energy apparently is sufficient to stabilize polaron when <r A> is small, and destabilize when <r A> is large. At the crossover polarons are marginally stable, giving rise to the CMR phenomenon.4. Electron-phonon coupling in cupratesIn our view an exact parallel should be observed for cuprates [20]. An increase in the local hole density will cause the Cu-O bond to be reduced in length, or in the phonon language, excite the in-plane LO phonons. If the Cu-O-Cu bond is buckled, the in-plane LO phonons couple to the c-axis oxygen mode, as in Fig. 3. The coupling is proportional to the deviation of the Cu-O-Cu bond angle from π. This coupling will soften the in-plane mode, by the screening mechanism described above. There are two possibilities of the in-plane modes that are softened by this coupling. The first obvious choice is the stripe mode (q = π/2), since when the buckling is strong charges will be localized into the stripe state, driving the system insulating. This is consistent with the effect of the CuO6 tilting [21], and the need of Nd in (La,Nd)1.875Sr0.125CuO4 to produce the stripe structure [2], since Nd3+ is smaller than La3+ (1.27 vs. 1.36 Å [22]). The second possibility is the Peierls mode (q = π). Our neutron results strongly suggest that this mode is present, per-haps competing against the stripe mode and consequently not developing into the stable state. This could produce a local spin-singlet state, suppress the antiferromagnetic order, and promote superconductivity [10]. At the same time the two-phonon mixing could produce multi-band HTSC [23,24]. While this scenario is highly speculative at this mo-ment, it explains quite well the anomaly in the pulsed neutron PDF at T C involving the out-of-plane oxygen motion [25], and the dependence of T C on the “micro-strain” pro-posed recently by Bianconi et al. [26]. Indeed a remarkable similarity between the phase diagram in Fig. 6 of Ref. 26 and that for manganites (Fig. 4) [15,17] suggests that similar mechanisms must be at work. In Ref. 26, however, the stripe mode itself is considered to generate HTSC. In the present scenario the stripe mode merely terminates HTSC by CDW formation, while the competition between the Peierls state and the stripe state plays a crucial role in HTSC. Further experimental works are being conducted to examine these scenarios.5. ConclusionsIn CMR manganites the stability of polarons is determined by the local structure, i.e. screening of the local in-plane LO phonons by the c-axis oxygen phonons. An exact par-allel should hold in cuprates where the coupling between LO phonons and c-axis phonons could play a crucial role in determining the stability of the stripe structure, and possibly superconductivity.Acknowledgments: The author is grateful to the collaborators of the phonon and CMR projects, R. J. McQueeney, M. Yethiraj, D. Louca, Y. Petrov, M. Arai, J. F. Mitchell, H.A. Mook, G. Shirane and Y. Endoh. He is also thankful to A. Bianconi, S. J. L. Billinge, A. R. Bishop, A. Bussmann-Holder, J.B. Goodenough, L. P. Gor’kov, V. Kresin, A. Lanzara, K. A. Müller, J.C. Phillips, S. Sachdev, Z.-X. Shen, S. R. Shenoy, and M. Tachiki for useful discussions. Research at the University of Pennsylvania was supported by the National Science Foundation through DMR96-28136.References:1. T. Egami and S. J. L. Billinge, in Physical Properties of High Temperature Super-conductors V, ed. D. Ginsberg (Singapore, World Scientific, 1996) p. 265.2. J. M. Tranquada et al., Nature375, 561 (1995).3. R. J. McQueeney, Y. Petrov, T. Egami, M. Yethiraj, G. Shirane and Y. Endoh, Phys.Rev. Lett. 82, 628 (1999).4. T. Egami, R. J. McQueeney, Y. Petrov, M. Yethiraj, G. Shirane, and Y. Endoh, AIPConf. Proc. 483, 231 (1999).5. Y. Petrov, T. Egami, R. J. McQueeney, M. Yethiraj, H. A. Mook, and F. Dogan,cond-mat/0003414.6. S. Ishihara, T. Egami and M. Tachiki, Phys. Rev. B55, 3163 (1997).7. Y. Petrov and T. Egami, Phys. Rev. B58, 9485 (1998).8. L. Pintschovius, et al., Physica C185-189, 156 (1991).9. A. Lanzara, et al., cond-mat/0102227.10. S. Sachdev, Science288, 475 (2000); S. Sachdev and N. Read, Int. J. Mod. Phys. B5, 219 (1991).11. E. S. Bozin, G. H. Kwei, H. Takagi and S. J. L. Billinge, Phys. Rev. Lett. 84, 5856(2000).12. A. J. Mills, P. B. Littlewood, and B. I. Shraiman, Phys. Rev. Lett. 74, 5144 (1995).13. H. Röder, J. Zang and A. R. Bishop, Phys. Rev. Lett., 76, 1356 (1996).14. D. Louca, T. Egami, E. L. Brosha, H. Röder, and A. R. Bishop, Phys. Rev. B56,R8475 (1997).15. T. Egami and D. Louca, J. Superconductivity13, 247 (2000).16. H. Y. Hwang, S.-W. Cheong, P. G. Radaelli, M. Marezio, B. Batlogg, Phys. Rev.Lett.75, 914 (1995).17. T. Egami and D. Louca, J. Superconductivity12, 23 (1999).18. J. D. Eshelby, Proc. Roy. Soc. A241, 376 (1957).19. T. Egami and D. Louca, unpublished.20. T. Egami, AIP Conf. Proc., in press.21. B. Büchner, et al., Phys. Rev. Lett.73, 1841 (1994).22. R. Shannon, Acta Cryst. A32, 751 (1976).23. S. R. Shenoy, V. Subrahmanyam and A. R. Bishop, Phys. Rev. Lett.79, 4657 (1997).24. A. Bussmann-Holder, K. A. Müller, R. Micnas, H. Büttner, A. Simon, A. R. Bishopand T. Egami, submitted.25. B. H. Toby, T. Egami, J. D. Jorgensen and M. A. Subramanian, Phys. Rev. Lett. 64,2414 (1990).26. A. Bianconi, G. Bianconi, S. Caprara, D. Di Castro, H. Oyanagi and N. L. Saini, J.Phys.: Condens. Matter12, 10655 (2000).Figure captions:Figure 1. (a) High-energy LO phonons at the zone-center, and (b) at the zone-edge, (π, 0, 0).Figure 2. A possible charge pattern with the 2a periodicity [3]. Large circles denote oxygen, with different charge densities indicated by grades of lightness. For clarity we show the pattern with a long-range order, but in reality the pattern should be dynamic and short-range, with the correlation length about 20 × 8 Å.Figure 3. Accommodation of the reduction in the local Mn-O distance due to the presence of a hole on Mn, (a) when the Mn-O-Mn bond is straight this causes the neighboring Mn-O bonds to stretch, (b) when the Mn-O-Mn bond is buckled, unbuckling will locally accommodate the change in the Mn-O distance, without producing a long-range stress field [13,15].Figure 4. Phase diagram for the CMR phenomenon in A1-x A’x MnO3, plotted for the ionic radius (9-coordinated), <r A>, against the charge density, x [13,15]. When <r A> is greater than 1.24 Å polarons are not stable, resulting in the metallic state. When <r A> is less than 1.18 Å polarons are stable, making the system insulating. The CMR phenome-non is observed in the crossover region.(b)Fig. 1Fig. 2(a) (b) Fig. 3Fig. 4。

第 22卷第 10期2023年 10月Vol.22 No.10Oct.2023软件导刊Software Guide一种基于物体追踪的改进语义SLAM算法杜小双，施展，华云松（上海理工大学光电信息与计算机工程学院，上海 200093）摘要：在视觉同步定位与建图（SLAM）算法中，使用语义分割和目标检测以剔除异常点的方法成为主流，但使用中无法对物体语义信息进行充分追踪。

为此，提出一种基于物体追踪的改进语义SLAM算法，通过YOLACT++网络分割物体掩码，提取物体特征点后，利用帧间匹配实现物体追踪。

该方法对匹配特征点进行深度、重投影误差和极线约束三重检测后判断物体动静态，实现物体追踪并判断运动状态。

通过对TUM RGB-D数据集测试，实验表明该方法可有效追踪物体，且轨迹估计精度优于其他SLAM算法，具有较好实用价值。

关键词：视觉SLAM；语义分割；物体追踪；动态场景；几何约束DOI：10.11907/rjdk.222298开放科学（资源服务）标识码（OSID）：中图分类号：TP301 文献标识码：A文章编号：1672-7800（2023）010-0205-06 An Improved Semantic SLAM Algorithm Based on Object TrackingDU Xiaoshuang， SHI Zhan， HUA Yunsong（School of Optical-Electrical and Computer Engineering，University of Shanghai for Science and Technology，Shanghai 200093，China）Abstract：In the visual SLAM （simultaneous localization and mapping）， the method of using semantic segmentation and object detection to detect dynamic objects and remove outliers has become the mainstream， but its disadvantage is that it is unable to fully track the semantic in⁃formation of objects. Therefore， this paper proposes an improved semantic SLAM algorithm based on object tracking， which uses YOLACT++ network to segment object mask， extract object feature points， and use inter frame matching to achieve object tracking. The method detects the depth， reprojection error and epipolar constraint of the matched feature points， and then judges the dynamic and static state of the object to achieve object tracking and judge the motion state. After testing the TUM RGB-D dataset， the experiment shows that the method can effective⁃ly track objects， and the trajectory estimation accuracy is better than other SLAM algorithms， which has practical value.Key Words：visual SLAM； semantic segmentation； object tracking； dynamic environment； geometric constraint0 引言随着机器人技术、无人驾驶、增强现实等领域的发展与普及，视觉SLAM作为其应用的基础技术之一［1］，得到了学者们的广泛关注与研究，并成为机器人定位与建图研究领域的一个热点［2］。

§5 超导体的电磁性质1本节主要内容： 1. 超导体特性之一：零电阻 2. 超导体特性之二：完全抗磁性(Meissner 迈斯纳效应) 3. 超导体的电动力学性质 4. 超导环的磁通俘获和磁通量子化现象2气体液化与低温环境的获得 1892年，发明了杜瓦瓶（中间抽真空，内胆涂有银 的双层玻璃瓶）  1899年，杜瓦（James Dewar）在伦敦皇家研究所成 立100周年庆典上，展示氢气（H2）的液化实验3水银超导体的发现Heike Kamerlingh Onnes (1853-1926) Dutch Physicist、  1882年，进入Leiden大学,研 究低温气体；  1908年,将液体的温度降低到 大约1K，成功将氦气液化；  1911年，开始研究金属在极 低温下的性质；  1912年，发现了水银的超导 电性，  1913年，获Nobel奖4The discovery of superconductivityNotebook 56, 8 April, 1911 Notebook 57, 26 October, 1911“Mercury[‘s resistance] practically zero [at 3 K] ……repeated with gold…”2014/11/5The historic plot. Superconducting transition at 4.2k in mercury5Meissner effectFritz Walther Meissner (1882-1974) 1933 Robert Ochsenfeld (1901-1993)German physicists2014/11/5Perfect diamagnetism below Tc6Londons’ theoryHeinz Fritz Wolfgang London London (1907-1970) (1900-1954) Londons’ Equation: (1935)Ampère's law:German Physicists2014/11/5 7Ginzburg-Landu theoryLev Landau (1908-1968) Vitaly Ginzburg (1916-2009) 1950 The free energy density:Complex order parameterU(1) gauge symmetry broken Soviet physicists2014/11/5其它几种超导体 元素 Al（铝） In（铟） Sn（锡） Pb（铅） Nb（铌） 1911 超导转变温度 1.2 K 3.4 K 3.7 K 7.2 K 9.2 K 198691986年，Muller和Bednorz发现：陶瓷氧化物 LaBaCuO的转变温度可达到35K。

cell theory细胞学说：一切生物从单细胞到高等动、植物都是由细胞组成；细胞是生物形态结构和功能活动的基本单位。

cytology细胞学：是研究细胞生命现象的科学。

其研究范围包括：细胞的形态结构和功能、分裂和分化、遗传和变异以及衰老和病变等。

cell biology细胞生物学：应用现代物理、化学、实验生物学及分子生物学技术和方法, 从细胞整体层次、亚细胞层次和分子层次三个层面、并将其有机地结合起来去研究探索细胞结构及其基本生命活动。

Ribozyme核酶：具有催化功能的RNA分子。

它具有高度专一内切核酸酶的活性。

miRNA小RNA：是广泛存在于真核生物中的一组短小的、不编码蛋白质的RNA家族，它们是由21-25个核苷酸组成的单链RNA。

unit membrane单位膜：电镜下，膜有三层结构组成，两层深色带，中间隔有一层疏松的浅色带，此三层结构作为一种单位，称为单位膜。

amphipathic molecule兼性分子或双亲媒性分子：即含有亲水的头又含有疏水的尾. 其头部具有亲水性，尾部疏水且寻求与其他疏水分子相聚.Fluid mosaic model液态镶嵌模型：生物膜是球形蛋白质和脂类分子呈二维状态排列的液态体,不是静止状态,而是具有流动性特点的结构. 脂类双分子层既具有液态分子的流动性、又具有固体分子排列的有序性,即流动的脂类双分子层构成的连续性膜性结构,各种球状蛋白质镶嵌于脂类双分子层中. 蛋白质分子的非极性部分嵌入脂类双分子层的疏水区；极性部分露于膜表面,似一群岛屿一样,无规则地分散在脂类的海洋中.Lipid Rafts Model 脂筏模型：即在生物膜的脂双分子层的外层有很多胆固醇和鞘磷脂富集而成的有序的、脂相的微结构域，它是一种动态结构,位于质膜的外层. 这些区域结构致密,介于无序液体与液晶之间(称为有序液体),是鞘磷脂与胆固醇的动态集合,如同“脂筏”一样,不同脂筏载有特定的蛋白,脂筏可根据胞内外不同刺激而改变自身大小和组成,以利于与另一特定蛋白相互作用,激活相应信号开关.脂筏间可彼此合并,使信号放大,脂筏就像蛋白质的停泊平台,与膜的信号转导、蛋白质分选均有密切的关系。

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ophthalmodiastimeter ophthalmograph ophthalmography ophthalmologicophthalmologic examination ophthalmologyophthalmometer ophthalmophantom ophthalmoreaction ophthalmoscope ophthalmoscopy ophthalmostasisophthalmostat ophthalmotonometer ophthalmotrope ophthalmotropometer ophthalmotropometryopiateopiate receptoropinionopinion leaderopinion pollopinion pollingopinion surveyopinion testopinionableopinionaireopinionalopinionateopinionationOpinionation Scaleopinionativeopinionatoropiomaniaopiomaniacopisthencephalonopisthoporeiaopisthotonosopiumopium denopligationOppel Kundt figureOppel's illusionopponent color theoryopponent process theoryopponents theory of color vision opportune confabulationopportune moment for interrogation opportunityopportunity classopportunity factoropportunity to performopposites test opposites viewpoint oppositionopsialgia opsigenesopsinopsiometer opsomaniaopsonic action optesthesia opthalmusopticoptic angleoptic aphasiaoptic apraxiaoptic atrophyoptic axisoptic canaloptic celloptic centreoptic chiasmaoptic cupoptic discoptic glandoptic grooveoptic lobeoptic nerveoptic nerve fiber optic nystagmus optic papillaoptic radiationoptic segmentoptic stalkoptic thalamusoptic tractoptic typeoptic zoneoptica axisopticaloptical aberrationoptical activityoptical aidoptical alexiaoptical allachesthesiaoptical antimeroptical artoptical axisoptical centeroptical character recognition optical communicationoptical computeroptical correctionoptical dispersionoptical frequencyoptical illusionoptical imageoptical instrumentoptical isomerismoptical landing systemoptical lanternoptical measurementoptical mechanical systemoptical microscopeoptical parallaxoptical phenomenaoptical rangeoptical rangefinderoptical readeroptical revolving power optical rotationoptical systemoptically activeopticociliaryopticokineticopticokinetic reflex opticokineticsoptimaloptimal allocationoptimal arousal level optimal arousal level theory optimal choiceoptimal coloroptimal conditionoptimal controloptimal control model optimal decisionoptimal decodingoptimal functioningoptimal groupingoptimal illuminationoptimal movementoptimal performanceoptimal personality traits, optimal propertyoptimal proportionoptimal ratiooptimal samplingoptimal sampling plan optimal scalingoptimal seeking method optimal sequence trainer optimal state of performance optimal stimulationoptimal strategyoptimal work spaceoptimeteroptimismoptimizationoptimizeoptimizing modeloptimumoptimum cd ratiooptimum conditionoptimum controloptimum decision making optimum degreeoptimum estimateoptimum loadoptimum rangeoptimum selectionoptimum speedoptimum stateoptimum state of performance optimum strategyoptimum temperatureoption experimentoptionaloptional altruistic suicide optional routeoptional variantoptionsoptoblastoptogramoptogravit illusion optogyral illusion optokinetic response optomeninxoptometeroptometryoptomotoroptomyometeroptophoneORoraora serrataoracyoral aggressionoral anxietyoral arithmeticoral behaviororal cavityoral characteroral communicationoral complexoral contraceptive oral dependence oral driveoral erotismoral examination oral fixationoral incorporation oral languageoral literature oral methodoral optimismoral orientation oral personality oral pessimismoral phaseoral primacyoral readingoral reportoral sadismoral sensationoral sensory stage oral stageoral temperature oral testoralismorality orangoutang orangutanorbOrbeli phenomenonOrbison illusionorbitaorbitofrontal cortex orderorder codeorder disorder transition order effectorder of birthorder of dominanceorder of meritorder of merit method order of merit scale order statisticsordered alternative ordered change theory ordered metric scale ordered recallorderingordering relation orderlinessordinal dispersionordinal interaction ordinal measureordinal positionordinal scaleordinal variableordinaryordinateorectic processesOrestes complex oreximaniaorexisorganorgan inferiority organ languageorgan neurosisorgan of Cortiorgan of equilibration organ of language organ of locomotion organ of special sense organ of speechorgan of surveyorgan of tasteorgan of visionorgan sensationorgan sensuumorgan specificity organ transplantation organaorganicorganic amnesia organic anxiety organic brain damage organic brain disorder organic brain syndrome organic deafness organic dementia organic disorder organic factororganic feeling organic imitationorganic melancholiaorganic memoryorganic modelorganic psychosisorganic repressionorganic rulesorganic selectionorganic sensationorganic theory of organization organic theory of societyorganic therapyorganic traitorganic variableorganicismorganismorganismal theoryorganismic ageorganismic experienceorganismic psychologyorganismic theoryorganismic variableorganizationorganization behaviororganization chartsorganization cultureorganization developmentorganization development intervention organization effectorganization manorganization of animal society organization of dataorganization structureorganization theoryorganizational behaviorOrganizational Behavior and Human Decision Processes organizational changeorganizational climateorganizational commitmentOrganizational Commitment Scaleorganizational communicationorganizational crisisorganizational cultureorganizational departmentalizationorganizational designorganizational developmentorganizational diagnosisorganizational effectorganizational effectivenessorganizational factororganizational goalorganizational identificationorganizational maintenanceorganizational matrixorganizational mergerorganizational objectiveorganizational planningorganizational politicsorganizational processorganizational productivityorganizational psychologyorganizational reformorganizational shape organizational span of control organizational stress organizational structure organized criminal gang organized fermentorganized playorganized supplementary play organized wholeorganizerorganizingorganogenesisorganogenicorganolepticorganoleptic research organologyorganonorganon auditusorganon gustusorganon olfactusorganon visusorganonomyorganopathyorganotherapyorganphysiologyorganuleorganum gustatoriusorganum olfactoriumorganum sensuumorgasmorgasmic dysfunctionorgasmphaseorgyorientating reflexorientationorientation disturbanceorientation motion detector orientation of consuming requirement orientation of motor learning orientation of purchasing power orientation perceptionorientation reactionorientation reflexorientation responseorientation trainingorientational trainingorienting reflexorienting responseorienting response in animal orienting taskoriginorigin of consciousnessorigin of infants imaginationorigin of infants self consciousness origin of internal speechorigin of languageorigin of lifeorigin of mindorigin of neonatal attentionorigin of neonatal memoryorigin of speciesorigin of speechorigin of thinkingorigin of volitional movementoriginaloriginal civilizationoriginal dataoriginal descriptionoriginal groundoriginal learningoriginal natureoriginal qualityoriginal recordoriginal surveyoriginalityoriginality of thinkingoriginateoriginationoriginatorOrleans Hanna Algebra Prognosis Test Orleans Hanna Geometry Prognosis Test ornithineornithine decarboxylaseornithophobiaorphanorphanageorphanhoodorthergasiaortho raterortho sleeporthobiosisorthocephalyorthochoreaorthodoxorthodox psychoanalysis orthodoxsleeporthodromicorthodromic conduction orthogenesisorthogenicsorthogonal arrayorthogonal comparison orthogonal component orthogonal contrast orthogonal factororthogonal factor model orthogonal polynomial orthogonal rotation orthogonalityorthographic deep hypothesis orthographyorthomolecular psychiatry orthomutationorthophonyorthophoriaorthophreniaorthopsychiatryorthosisorthostatism orthosympatheticorthotonosorthropsiaoscillationoscillogramoscillographoscillometeroscillometryoscitancyOseretsky Tests of Motor 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theoryoutgroupoutingoutline making in composition outlookoutlook on lifeoutnessoutputoutput of learningoutrageoutward manifestation outward senseoutward thing outwardnessoval windowovarian obesity ovariumovaryover adaptationover anxious reaction over arousalover compensationover constancyover developmentover exerciseover fatigueover learningover self confidence over the counter drugs overachievement overachieveroveractoverageoverall rating method overall reaction overcautionovercome overcompensation overconfidence overconfident overconstancy overcontrolled overcorrectionovercredulityovercredulousovercriticalovercrowovercrowdoverdeterminationoverdeterminedoverdevelopoverdoseoveremphasizeoverestimationoverexcitationoverexcitementoverextensionoverfatigueoverfeedingoverflow activityovergeneralizationovergrowthoverheard communicationoverinclusionoverinclusive thinkingoverindulgenceoverinhibitionoverjoyedoverjustificationoverjustification effectoverlapoverlappingoverlapping control of eating and drinking overlearningoverlearning reversal effect overloadoverload imitationoverload modelovermanovermanyovermasterovermaximalovermotivationoverpersuadeoverpopulationoverproductionoverproductivityoverprotectionoverrateoverreactionoverregulationoverresponseovershadowingoverstimulationoverstocking of commodities overstrainoverstrain of excitatory process overstrain of inhibitory process overstrain of nervous process overtovert behaviorovert crimeovert cultureovert homosexualityovert intrusionovert needovert responseovertimeovertoneovertrainingovertraining reversal effect overweightoverwrokoverwroughtoverzealousovigenesisovulationovumownownerownerlessownershipownguardownnessOxford indexoxidative enzymeoxyacoiaoxyblepsiaoxycodoneoxyecoiaoxyesthesiaoxygenoxygen consumptionoxygen debtoxygen deficitoxygen demandoxygen deprivation oxygen intake oxygen intake rate oxygen lack oxygen toxicity oxygeusia oxyhemograph oxylalia oxymorphone 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ambivalent quotient positive negative conflictpositive phasepositive phototaxispositive punishmentpositive reactionpositive recollectionpositive reference grouppositive regardpositive regencypositive reinforcementpositive reinforcerpositive reinforcing stimuluspositive rewardpositive sanctionpositive self feelingpositive skewnesspositive stimuluspositive symptompositive time errorpositive transferpositive transferencepositive valencepositivismpositivistic philosophypositivity biaspositron emission tomography posodynicspossessivenesspossibilitypossible errorpossible judgmentpossible outcomepost adaptationpost columnpost conventional level post enumeration survey post formation theorypost hoc fallacypost hoc testpost hornpost hypnotic amnesiapost hypnotic behaviorpost hypnotic suggestion post industrialized society post infections psychosis post partus bluespost surveypost term infantpost testpost traumatic amnesiapost traumatic delirium post traumatic dementia post voluntary attention 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methodpotentiometryPoter's generic competitive strategies potomaniapoundpourpouring in process in instruction poverty of movementpoverty of thoughtpowderpower coercive strategypower curvepower dependence theorypower distancepower driverpower efficiencypower factorpower functionpower function lawpower motivepower needpower of imagerypower of influencepower of intellectpower of soulpower of statistical test power of testpower relationpower spectrumpower structurepower strugglepower tacticspower testpowerlessnessPPSpractical activitypractical agopractical experiencepractical frameworkpractical intelligence practical knowledgepractical levelpractical philosophypractical problempractical psychologypractical purposepractical reasoningpractical situation practicalnesspractice curvepractice curve of action practice curve of performance practice effectpractice errorpractice limitpractice periodpractice supervisionpractice teachingpractice theorypractice theory of playpradictionpraecoxpraecox 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variablepredictor variablepredilectionpredispositionpredominancepredominatepredormitiumpredreampreferencepreference methodpreference scalepreference testpreferential learning preferred colorpreferred orientation preferred orientation column preferred rewardprefoetal period preformationpreformation theory preformationismprefrontalprefrontal areaprefrontal cortexprefrontal leucotomy prefrontal lobeprefrontal lobotomy preganglionic fibre pregenital phasepregenital stage pregenitalitypregnancepregnancyprehensionprehension program prehension testpreinductionprejudgmentprejudicepreliminary analysispreliminary datapreliminary forecastingpreliminary investigation preliminary measurespreliminary mentorpreliminary observationPreliminary Scholastic Aptitude Test preliminary studypreliminary surveypreliminarytrialprelinguistic behaviorprelinguistic developmentprelogical thinking prelumirhodopisinPremack principlepremarital counselingprematurationprematurepremature childpremature ejaculationpremature infantpremature repeningprematuritypremeditated crimepremenstrual syndromepremenstrual tensionpremisepremiumpremorbidpremotor areaprenatalprenatal behaviorprenatal development prenatal development stage prenatal diagnosis prenatal environment prenatal influence prenatal periodprenatal training prenubilepreoccupationpreographpreogurative culture preoperation period preoperation thought preoperational stage preoptic areapreoptic regionpreorganic evolution preorganizerpreparationpreparation theory of play preparative period preparative stage preparatory interval preparatory measure preparatory response preparatory set preperception preponderance preponderantprepossessionprepotencyprepotentprepotent reflex prepotent response prepotent stimulus prepotential reflexes prepsychoticprepuberal stage prepuberty prepubescence prerecognition hypothesis prerecordprerelease prerepresentation prereproductive prerequisitepreretired education 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