on the complexity of finding chordless paths in bipartite graphs and some interval operators in graphs and hypergraphs in this paper we show that the problem of finding a chordless path between a vertex s and a vertex t containing a vertex v remains np complete in bipartite graphs thereby strengthening the previous results on the same problem we show a relation between this problem and two interval operators the simple path interval operator in hypergraphs and the even chorded path interval operator in graphs we show that the problem of computing the two mentioned intervals is np complete

the stable set problem and the lift and project ranks of graphs we study the lift and project procedures for solving combinatorial optimization problems as described by lovasz and schrijver in the context of the stable set problem on graphs we investigate how the procedures performances change as we apply fundamental graph operations we show that the odd subdivision of an edge and the subdivision of a star operations as well as their common generalization the stretching of a vertex operation cannot decrease the n 0 n or n rank of the graph we also provide graph classes which contain the complete graphs where these operations do not increase the n 0 or the n rank hence we obtain the ranks for these graphs and we also present some graph minor like characterizations for them despite these properties we give examples showing that in general most of these operations can increase these ranks finally we provide improved bounds for n ranks of graphs in terms of the number of nodes in the graph and prove that the subdivision of an edge or cloning a vertex can increase the n rank of a graph

correlation measure to detect time series distances whence economy globalization abstract an instantaneous time series distance is defined through the equal time correlation coefficient the idea is applied to the gross domestic product gdp yearly increments of 21 rich countries between 1950 and 2005 in order to test the process of economic globalisation some data discussion is first presented to decide what eks gk or derived gdp series should be studied distances are then calculated from the correlation coefficient values between pairs of series the role of time averaging of the distances over finite size windows is discussed three network structures are next constructed based on the hierarchy of distances it is shown that the mean distance between the most developed countries on several networks actually decreases in time which we consider as a proof of globalization an empirical law is found for the evolution after 1990 similar to that found in flux creep the optimal observation time window size is found 15 years

universal and non universal text statistics clustering coefficient for language identification abstract in this work we analyze statistical properties of 91 relatively small texts in 7 different languages spanish english french german turkish russian icelandic as well as texts with randomly inserted spaces despite the size around 11260 different words the well known universal statistical laws namely zipf and herdan heap s laws are confirmed and are in close agreement with results obtained elsewhere we also construct a word co occurrence network of each text while the degree distribution is again universal we note that the distribution of clustering coefficients which depend strongly on the local structure of networks can be used to differentiate between languages as well as to distinguish natural languages from random texts

np hard graph problems and boundary classes of graphs any graph problem which is np hard in general graphs becomes polynomial time solvable when restricted to graphs in special classes when does a difficult problem become easy to answer this question we study the notion of boundary classes in the present paper we define this notion in its most general form describe several approaches to identify boundary classes and apply them to various graph problems

least squares identification of the dynamic relation between the electromyogram and joint moment the dynamic relation between surface emg of an agonist and isometric joint moment is important in models for the prediction of dynamic joint moment from emg an efficient approach for determining the best fitting linear transfer function relating emg and isometric moment using a least squares approach is presented and illustrated for a second order model

applying lehman s theorems to packing problems a 0 1 matrixa isideal if the polyhedronq a conv x qv a x 1 x 0 v denotes the column index set ofa is integral similarly a matrix isperfect ifp a conv x qv a x 1 x 0 is integral little is known about the relationship between these two classes of matrices we consider a transformation between the two classes which enables us to apply lehman s modified theorem about deletion minimal nonideal matrices to obtain new results about packing polyhedra this results in a polyhedral description for the stable set polytopes ofnear bipartite graphs the deletion of any neighbourhood produces a bipartite graph note that this class includes the complements of line graphs to date this is the only natural class besides the perfect graphs for which such a description is known for the graphs and their complements some remarks are also made on possible approaches to describing the stable set polyhedra of quasi line graphs and more generally claw free graphs these results also yield a new class oft perfect graphs

analytic solutions for links and triangles distributions in finite barabasi albert networks abstract barabasi albert model describes many different natural networks often yielding sensible explanations to the subjacent dynamics however finite size effects may prevent from discerning among different underlying physical mechanisms and from determining whether a particular finite system is driven by barabasi albert dynamics here we propose master equations for the evolution of the degrees links and triangles distributions solve them both analytically and by numerical iteration and compare with numerical simulations the analytic solutions for all these distributions predict the network evolution for systems as small as 100 nodes the analytic method we developed is applicable for other classes of networks representing a powerful tool to investigate the evolution of natural networks

general random pseudofractal networks we introduce a general random pseudofractal network model by assigning fitness to each edge in this model continuous growth and attachment determined by their fitness of already existing edges are the two ingredients we obtain the analytical results that our model exhibits a power law degree distribution with exponent 2 m 1 m 1 where m and are tunable parameters we also show that a general random pseudofractal network has a large clustering coefficient and a small average distance leading to a small world effect these theoretical results agree well with numerical simulations

a comparison of the sherali adams lov 341sz schrijver and lasserre relaxations for 0 1 programming sherali and adams sa90 lov asz and schrijver ls91 and recently lasserre las01b have proposed lift and project methods for constructing hierarchies of successive linear or semidefinite relaxations of a 0 1 polytope p subseteq or n converging to p in n steps lasserre s approach uses results about representations of positive polynomials as sums of squares and the dual theory of moments we present the three methods in a common elementary framework and show that the lasserre construction provides the tightest relaxations of p as an application this gives a direct simple proof for the convergence of the lasserre s hierarchy we describe applications to the stable set polytope and to the cut polytope

ranking the spreading ability of nodes in complex networks based on local structure abstract ranking nodes by their spreading ability in complex networks is a fundamental problem which relates to wide applications local metric like degree centrality is simple but less effective global metrics such as betweenness and closeness centrality perform well in ranking nodes but are of high computational complexity recently to rank nodes effectively and efficiently a semi local centrality measure has been proposed as a tradeoff between local and global metrics however in semi local centrality only the number of the nearest and the next nearest neighbors of a node is taken into account while the topological connections among the neighbors are neglected in this paper we propose a local structural centrality measure which considers both the number and the topological connections of the neighbors of a node to evaluate the performance of our method we use the susceptible infected recovered sir model to simulate the epidemic spreading process on both artificial and real networks by measuring the rank correlation between the ranked list generated by simulation results and the ones generated by centrality measures we show that our method can rank the spreading ability of nodes more accurately than centrality measures such as degree k shell betweenness closeness and local centrality further we show that our method can better distinguish the spreading ability of nodes

on lovasz schrijver lift and project procedures on the dantzig fulkerson johnson relaxation of the tsp we study the lovasz schrijver lift and project procedure n on the linear relaxation of the dantzig fulkerson johnson formulation of the traveling salesman problem tsp a long standing conjecture states that the integrality gap of this relaxation is frac43 in the case of metric costs in this paper we show that the n rank of 2 matching inequalities relative to this relaxation can be arbitrarily high and obtain as a corollary that even after applying n to the relaxation a fixed number of times the integrality gap of the resulting relaxation is at least frac43

clustering of correlated networks we obtain the clustering coefficient the degree dependent local clustering and the mean clustering of networks with arbitrary correlations between the degrees of the nearest neighbor vertices the resulting formulas allow one to determine the nature of the clustering of a network

sensory contributions to stabilization of trunk posture in the sagittal plane trunk stabilization is required to control posture and movement during daily activities various sensory modalities such as muscle spindles golgi tendon organs and the vestibular system might contribute to trunk stabilization and our aim was to assess the contribution of these modalities to trunk stabilization in 35 healthy subjects upper body sway was evoked by continuous unpredictable force controlled perturbations to the trunk in the anterior direction subjects were instructed to either maximally resist the perturbation or to relax but remain upright with eyes closed frequency response functions frfs of admittance the amount of movement per unit of force applied and reflexes the modulation of trunk extensor activity per unit of trunk displacement were obtained to these frfs we fitted physiological models to estimate intrinsic trunk stiffness and damping as well as feedback gains and delays the different model versions were compared to assess which feedback loops contribute to trunk stabilization intrinsic stiffness and damping and muscle spindle short delay feedback alone were sufficient to accurately describe trunk stabilization but only with unrealistically low reflex delays addition of muscle spindle acceleration feedback or inhibitory golgi tendon organ feedback yielded realistic delays and improved the model fit with a significantly better model fit with acceleration feedback addition of vestibular feedback did not improve the model fit in conclusion muscle spindle feedback and intrinsic mechanical properties are sufficient to describe trunk stabilization in the sagittal plane under small mechanical perturbations provided that muscle spindles encode acceleration in addition to velocity and position information

a lift and project cutting plane algorithm for mixed 0 1 programs we propose a cutting plane algorithm for mixed 0 1 programs based on a family of polyhedra which strengthen the usual lp relaxation we show how to generate a facet of a polyhedron in this family which is most violated by the current fractional point this cut is found through the solution of a linear program that has about twice the size of the usual lp relaxation a lifting step is used to reduce the size of the lp s needed to generate the cuts an additional strengthening step suggested by balas and jeroslow is then applied we report our computational experience with a preliminary version of the algorithm this approach is related to the work of balas on disjunctive programming the matrix cone relaxations of lovasz and schrijver and the hierarchy of relaxations of sherali and adams

when does the positive semidefiniteness constraint help in lifting procedures we study the lift and project procedures of lovaisz and schrijver for 0 1 integer programming problems we prove that the procedure using the positive semidefiniteness constraint is not better than the one without it in the worst case various examples are considered we also provide geometric conditions characterizing when the positive semidefiniteness constraint does not help

near perfect matrices a 0 1 matrixa isnear perfect if the integer hull of the polyhedron x 0 ax bar 1 can be obtained by adding one extra rank constraint we show that in general such matrices arise as the cliquenode incidence matrices of graphs we give a colouring like characterization of the corresponding class of near perfect graphs which shows that one need only check integrality of a certain linear program for each 0 1 2 valued objective function this in contrast with perfect matrices where it is sufficient to check 0 1 valued objective functions we also make the following conjecture a graph is near perfect if and only if sequentially lifting any rank inequality associated with a minimally imperfect graph results in the rank inequality for the whole graph we show that the conjecture is implied by the strong perfect graph conjecture it is also shown to hold for graphs with no stable set of size eleven our results are used to strengthen and give a new proof of a theorem of padberg this results in a new characterization of minimally imperfect graphs a graph is minimally imperfect if and only if both the graph and its complement are near perfect

the strong perfect graph theorem a graph g is perfect if for every induced subgraph h the chromatic number of h equals the size of the largest complete subgraph of h and g is berge if no induced subgraph of g is an odd cycle of length at least five or the complement of one the strong perfect graph conjecture berge 1961 asserts that a graph is perfect if and only if it is berge a stronger conjecture was made recently by conforti cornu ejols and vuiskovi c that every berge graph either falls into one of a few basic classes or admits one of a few kinds of separation designed so that a minimum counterexample to berge s conjecture cannot have either of these properties in this paper we prove both of these conjectures

cones of matrices and set functions and 0 1 optimization it has been recognized recently that to represent a polyhedron as the projection of a higher dimensional but simpler polyhedron is a powerful tool in polyhedral combinatorics a general method is developed to construct higher dimensional polyhedra or in some cases convex sets whose projection approximates the convex hull of 0 1 valued solutions of a system of linear inequalities an important feature of these approximations is that one can optimize any linear objective function over them in polynomial time in the special case of the vertex packing polytope a sequence of systems of inequalities is obtained such that the first system already includes clique odd hole odd antihole wheel and orthogonality constraints in particular for perfect and many other graphs this first system gives the vertex packing polytope for various classes of graphs including t perfect graphs it follows that the stable set polytope is the projection of a polytope with a polynomial number of facets an extension o

on a representation of the matching polytope via semidefinite liftings we consider the relaxation of the matching polytope defined by the non negativity and degree constraints we prove that given an undirected graph on n nodes and the corresponding relaxation of the matching polytope n 2 iterations of the lovasz schrijver semidefinite lifting procedure are needed to obtain the matching polytope in the worst case we show that n 2 iterations of the procedure always suffice

characterizing and bounding the imperfection ratio for some classes of graphs perfect graphs constitute a well studied graph class with a rich structure which is reflected by many characterizations with respect to different concepts perfect graphs are for instance precisely those graphs g where the stable set polytope stab g equals the fractional stable set polytope qstab g the dilation ratio rm min t rm qstab g subseteq t rm stab g of the two polytopes yields the imperfection ratio of g it is np hard to compute and for most graph classes it is even unknown whether it is bounded for graphs g such that all facets of stab g are rank constraints associated with antiwebs we characterize the imperfection ratio and bound it by 3 2 outgoing from this result we characterize and bound the imperfection ratio for several graph classes including near bipartite graphs and their complements namely quasi line graphs by means of induced antiwebs and webs respectively

mean field theory for clustering coefficients in barabasi albert networks we applied a mean field approach to study clustering coefficients in barabasi albert ba networks we found that the local clustering in ba networks depends on the node degree analytic results have been compared to extensive numerical simulations finding a very good agreement for nodes with low degrees clustering coefficient of a whole network calculated from our approach perfectly fits numerical data

approximation of the stability number of a graph via copositive programming lovasz and schrijver siam j optim 1 1991 pp 166 190 showed how to formulate increasingly tight approximations of the stable set polytope of a graph by solving semidefinite programs sdps of increasing size lift and project method in this paper we present a similar idea we show how the stability number can be computed as the solution of a conic linear program lp over the cone of copositive matrices subsequently we show how to approximate the copositive cone ever more closely via a hierarchy of linear or semidefinite programs of increasing size liftings the latter idea is based on recent work by parrilo structured semidefinite programs and semi algebraic geometry methods in robustness and optimization ph d thesis california institute of technology pasadena ca 2000 in this way we can compute the stability number alpha g of any graph g v e after at most alpha g 2 successive liftings for the lp based approximations one can compare this to the n alpha g 1 bound for the lp based lift and project scheme of lovasz and schrijver our approach therefore requires fewer liftings for families of graphs where alpha g o sqrt n we show that the first sdp based approximation for alpha g in our series of increasingly tight approximations coincides with the vartheta function of schrijver ieee trans inform theory 25 1979 pp 425 429 we further show that the second approximation is tight for complements of triangle free graphs and for odd cycles

myoelectric activity detection during a sit to stand movement using threshold methods myoelectric signals recorded via surface electrodes contain rich muscle activity information that is beneficial for both clinical diagnosis and biomedical research when synchronized with the kinematic data these signals provide investigators an insight into muscle activation sequence onset levels and periods a primary difficulty with the analysis and interpretation of electromyography emg signals lies in the inherent stochastic nature of the emg process which arises from its biological variability as well as noise added during the collection process various techniques for muscle onset and activity detection from the myoelectric signal have been proposed in the literature our focus in this study is myoelectric activity detection from emg signals collected during sit to stand sts and stand to sit stst movements we explore a previously established double threshold detection method and compare its results with a novel detection scheme based on the energy of the signal accordingly emg signals from four lower extremity muscles and synchronized kinematic data were collected for 180 trials of sts and stst movements performed in the laboratory detection thresholds above baseline in the case of both algorithms were computed and analyzed using a 2 detectors x 4 activity thresholds repeated measures analysis of variance our statistical analysis revealed that the energy detection method performed similarly to the double threshold method while both methods required a considerably higher threshold above baseline for detection

link space formalism for network analysis we introduce the link space formalism for analyzing network models with degree degree correlations the formalism is based on a statistical description of the fraction of links l i j connecting nodes of degrees i and j to demonstrate its use we apply the framework to some pedagogical network models namely random attachment barab asi albert preferential attachment and the classical erd ifmmode mbox h o else h o fi s and r enyi random graph for these three models the link space matrix can be solved analytically we apply the formalism to a simple one parameter growing network model whose numerical solution exemplifies the effect of degree degree correlations for the resulting degree distribution we also employ the formalism to derive the degree distributions of two very simple network decay models more specifically that of random link deletion and random node deletion the formalism allows detailed analysis of the correlations within networks and we also employ it to derive the form of a perfectly nonassortative network for arbitrary degree distribution

identifying intrinsic and reflexive contributions to low back stabilization motor control deficits have been suggested as potential cause and or effect of a specific chronic low back pain and its recurrent behavior therefore the goal of this study is to identify motor control in low back stabilization by simultaneously quantifying the intrinsic and reflexive contributions upper body sway was evoked using continuous force perturbations at the trunk while subjects performed a resist or relax task frequency response functions frfs and coherences of the admittance kinematics and reflexes semg were obtained in comparison with the relax task the resist task resulted in a 61 decrease in admittance and a 73 increase in reflex gain below 1 1 hz intrinsic and reflexive contributions were captured by a physiologically based neuromuscular model including proprioceptive feedback from muscle spindles position and velocity and golgi tendon organs force this model described on average 90 of the variance in kinematics and 39 of the variance in semg while resulting parameter values were consistent over subjects

parameterized complexity of vertex deletion into perfect graph classes vertex deletion problems are at the heart of parameterized complexity for a graph class f the f deletion problem takes as input a graph g and an integer k the question is whether it is possible to delete at most k vertices from g such that the resulting graph belongs to f whether perfect deletion is fixed parameter tractable and whether chordal deletion admits a polynomial kernel when parameterized by k have been stated as open questions in previous work we show that perfect deletion and weakly chordal deletion are w 2 hard when parameterized by k in search of positive results we study a restricted variant of the f deletion problem in this restricted variant the deleted vertices must be taken from a specified set x and we parameterize by x we show that for perfect deletion and weakly chordal deletion although this restriction immediately ensures fixed parameter tractability it is not enough to yield polynomial kernels unless np conp poly on the positive side for chordal deletion the restriction enables us to obtain a kernel with o x 4 vertices

identification of dynamic myoelectric signal to force models during isometric lumbar muscle contractions a 14 muscle myoelectric signal mes driven muscle force prediction model of the l3 l4 cross section is developed which includes a dynamic mes force relationship and allows for cocontraction model parameters are estimated from mes and moments data recorded during rapid exertions in trunk flexion extension lateral bending and axial twist nine young healthy males participated in the experimental testing the model used in the parameter estimation is of the output error type consistent and physically feasible parameter estimates were obtained by normalizing the rms mes to maximum exertion levels and using nonlinear constrained optimization to minimize a cost function consisting of the trace of the output error covariance matrix model performance was evaluated by comparing measured and mes predicted moments over a series of slow and rapid exertions moment prediction errors were on the order of 25 30 and 40 during attempted trunk flexion extensions lateral bends and axial twists respectively the model and parameter estimation methods developed provide a means to estimate lumbar muscle and spine loads as well as to empirically investigate the use and effects of cocontraction during physical task performances

the ba model with finite precision preferential attachment abstract preferential attachment is an indispensable ingredient of the ba model and its variants in this paper we modify the ba model by considering the effect of finite precision preferential attachment which exists in many real networks finite precision preferential attachment refers to existing nodes with preferential probability varying within a certain interval which is determined by the value of a given precision being considered to have an equal chance of capturing a new link the new model reveals a transition from exponential scaling to a power law distribution along with the increase of the precision epidemic dynamics and immunization on the new network are investigated and it is found that the finite precision effect should be considered in tasks such as infection rate prediction or immunization policy making

strong lift and project cutting planes for the stable set problem a great deal of research has been focusing since the early seventies on finding strong relaxations for the stable set problem polyhedral combinatorics techniques have been at first developed to strengthen the natural linear formulation afterward strong semidefinite programming relaxations have been deeply investigated nevertheless the resulting integer programming ip algorithms cannot be regarded as being quite successful in practice as most of the relaxations give rise to one out of two extreme situations either provide weak bounds at low computational cost or give good bounds sometimes excellent but too demanding to compute in this paper we present a method to bridge such a gap in particular a new lift and project relaxation is obtained by a problem specific variant of the lifting operator m k k by lovasz and schrijver combined with benders decomposition this yields strong cutting planes generated by solving a cut generating linear program an extensive computational experience shows that embedding these cuts in a branch and cut framework significantly reduces the size of the enumeration trees as well as the cpu times with respect to state of the art ip algorithms

progress on perfect graphs a graph is perfect if for every induced subgraph the chromatic number is equal to the maximum size of a complete subgraph the class of perfect graphs is important for several reasons for instance many problems of interest in practice but intractable in general can be solved efficiently when restricted to the class of perfect graphs also the question of when a certain class of linear programs always have an integer solution can be answered in terms of perfection of an associated graph

tighter linear and semidefinite relaxations for max cut based on the lovasz schrijver lift and project procedure we study how the lift and project method introduced by lovasz and schrijver siam j optim 1 1991 pp 166 190 applies to the cut polytope we show that the cut polytope of a graph can be found in k iterations if there exist k edges whose contraction produces a graph with no k5 minor therefore for a graph g with n ge 4 nodes with stability number alpha g n 4 iterations suffice instead of the m number of edges iterations required in general and under some assumption n alpha g 3 iterations suffice the exact number of needed iterations is determined for small n le 7 by a detailed analysis of the new relaxations if positive semidefiniteness is added to the construction then one finds in one iteration a relaxation of the cut polytope which is tighter than its basic semidefinite relaxation and than another one introduced recently by anjos and wolkowicz discrete appl math to appear we also show how the lovasz schrijver relaxations for the stable set polytope of g can be strengthened using the corresponding relaxations for the cut polytope of the graph g nabla obtained from g by adding a node adjacent to all nodes of g

perfectness is an elusive graph property a graph property is called elusive or evasive if every algorithm for testing this property has to read in the worst case n choose 2 entries of the adjacency matrix of the given graph several graph properties have been shown to be elusive e g planarity or k colorability a famous conjecture of karp says that every nontrivial monotone graph property is elusive we prove that a nonmonotone but hereditary graph property is elusive perfectness

clustering coefficients of growing networks abstract in this paper we develop a general analytical method to compute clustering coefficients of growing networks this method can be applied to any network as long as we can construct and solve the dynamic equation for the degree of any node we also verify the accuracy of the method through simulation

on the matrix cut rank of polyhedra lovasz and schrijver 1991 described a semidefinite operator for generating strong valid inequalities for the 0 1 vectors in a prescribed polyhedron among their results they showed that n iterations of the operator are sufficient to generate the convex hull of 0 1 vectors contained in a polyhedron in n space we give a simple example having chvatal rank 1 that meets this worst case bound of n we describe another example requiring n iterations even when combining the semidefinite and gomory chvatal operators this second example is used to show that the standard linear programming relaxation of a k city traveling salesman problem requires at least k 8 iterations of the combined operator this bound is best possible up to a constant factor as k 1 iterations suffice

reconfiguration of colorable sets in classes of perfect graphs abstract a set of vertices in a graph is c colorable if the subgraph induced by the set has a proper c coloring in this paper we study the problem of finding a step by step transformation called a reconfiguration sequence between two c colorable sets in the same graph this problem generalizes the well studied independent set reconfiguration problem as the first step toward a systematic understanding of the complexity of this general problem we study the problem on classes of perfect graphs we first focus on interval graphs and give a combinatorial characterization of the distance between two c colorable sets this gives a linear time algorithm for finding an actual shortest reconfiguration sequence for interval graphs since interval graphs are exactly the graphs that are simultaneously chordal and co comparability we then complement the positive result by showing that even deciding reachability is pspace complete for chordal graphs and for co comparability graphs the hardness for chordal graphs holds even for split graphs we also consider the case where c is a fixed constant and show that in such a case the reachability problem is polynomial time solvable for split graphs but still pspace complete for co comparability graphs the complexity of this case for chordal graphs remains unsettled as by products our positive results give the first polynomial time solvable cases split graphs and interval graphs for feedback vertex set reconfiguration

subgraph centrality and clustering in complex hyper networks abstract the representation of complex systems as networks is inappropriate for the study of certain problems we show several examples of social biological ecological and technological systems where the use of complex networks gives very limited information about the structure of the system consequently we extend the concepts of subgraph centrality and clustering for complex networks represented by hypergraphs complex hyper networks the first parameter characterizes the node participation in different sub hypergraphs and the second one characterizes the transitivity in the hyper network through the proportion of hyper triangles to paths of length two another measure characterizing the formation of triples of mutually adjacent groups in the hyper network is also introduced all of these characteristics are studied in three different hyper networks a scientific collaboration hyper network an ecological competition hyper network and the hyper network formed by the american corporate elite in 1999

statistical analysis of 22 public transport networks in poland public transport systems in 22 polish cities have been analyzed the sizes of these networks range from n 152 to 2881 depending on the assumed definition of network topology the degree distribution can follow a power law or can be described by an exponential function distributions of path lengths in all considered networks are given by asymmetric unimodal functions clustering assortativity and betweenness are studied all considered networks exhibit small world behavior and are hierarchically organized a transition between dissortative small networks n approximately or 500 is observed

predictions of knee and ankle moments of force in walking from emg and kinematic data abstract a deterministic model was developed and validated to calculate instantaneous ankle and knee moments during walking using processed emg from representative muscles instantaneous joint angle as a correlate of muscle length and angular velocity as a correlate of muscle velocity and having available total instantaneous joint moments for derivation of certain model parameters a linear regression of the moment on specifically processed emg recorded while each subject performed cycled isometric calibration contractions yielded the constants for a basic moment emg relationship using the resultant moment for optimization the predicted moment was proportionally augmented for longer muscle lengths and reduced for shorter lengths similarly the predicted moment was reduced for shortening velocities and increased if the muscle was lengthening the plots of moments predicted using the full model and those calculated from link segment mechanics followed each other quite closely the range of root mean square errors were 3 2 9 5 nm for the ankle and 4 7 13 0 nm for the knee

computing the stability number of a graph via linear and semidefinite programming we study certain linear and semidefinite programming lifting approximation schemes for computing the stability number of a graph our work is based on and refines de klerk and pasechnik s approach to approximating the stability number via copositive programming siam j optim 12 2002 pp 875 892 we provide a closed form expression for the values computed by the linear programming approximations we also show that the exact value of the stability number alpha g is attained by the semidefinite approximation of order alpha g 1 as long as alpha g leq 6 our results reveal some sharp differences between the linear and the semidefinite approximations for instance the value of the linear programming approximation of any order is strictly larger than alpha g whenever alpha g 1

lovasz schrijver sdp operator near perfect graphs and near bipartite graphs we study the lovasz schrijver lift and project operator mathrm text ls ls based on the cone of symmetric positive semidefinite matrices applied to the fractional stable set polytope of graphs the problem of obtaining a combinatorial characterization of graphs for which the mathrm text ls ls operator generates the stable set polytope in one step has been open since 1990 we call these graphs mathrm text ls ls perfect in the current contribution we pursue a full combinatorial characterization of mathrm text ls ls perfect graphs and make progress towards such a characterization by establishing a new close relationship among mathrm text ls ls perfect graphs near bipartite graphs and a newly introduced concept of full support perfect graphs

almost all webs are not rank perfect graphs with circular symmetry called webs are crucial for describing the stable set polytopes of two larger graph classes quasi line graphs 8 12 and claw free graphs 7 8 providing a complete linear description of the stable set polytopes of claw free graphs is a long standing problem 9 ben rebea conjectured a description for quasi line graphs see 12 chudnovsky and seymour 2 verified this conjecture recently for quasi line graphs not belonging to the subclass of fuzzy circular interval graphs and showed that rank facets are required in this case only fuzzy circular interval graphs contain all webs and even the problem of finding all facets of their stable set polytopes is open so far it is only known that stable set polytopes of webs with clique number 3 have rank facets only 5 17 while there are examples with clique number 4 having non rank facets 10 12 15

a new deterministic complex network model with hierarchical structure abstract we introduce a new simple pseudo tree like network model deterministic complex network dcn the proposed dcn model may simulate the hierarchical structure nature of real networks appropriately and have the unique property of skipping the levels which is ubiquitous in social networks our results indicate that the dcn model has a rather small average path length and large clustering coefficient leading to the small world effect strikingly our dcn model obeys a discrete power law degree distribution p k k with exponent approaching 1 0 we also discover that the relationship between the clustering coefficient and degree follows the scaling law c k k 1 which quantitatively determines the dcn s hierarchical structure

features and heterogeneities in growing network models many complex networks from the world wide web to biological networks grow taking into account the heterogeneous features of the nodes the feature of a node might be a discrete quantity such as a classification of a url document such as personal page thematic website news blog search engine social network etc or the classification of a gene in a functional module moreover the feature of a node can be a continuous variable such as the position of a node in the embedding space in order to account for these properties in this paper we provide a generalization of growing network models with preferential attachment that includes the effect of heterogeneous features of the nodes the main effect of heterogeneity is the emergence of an effective fitness for each class of nodes determining the rate at which nodes acquire new links the degree distribution exhibits a multiscaling behavior analogous to the the fitness model this property is robust with respect to variations in the model as long as links are assigned through effective preferential attachment beyond the degree distribution in this paper we give a full characterization of the other relevant properties of the model we evaluate the clustering coefficient and show that it disappears for large network size a property shared with the barabasi albert model negative degree correlations are also present in this class of models along with nontrivial mixing patterns among features we therefore conclude that both small clustering coefficients and disassortative mixing are outcomes of the preferential attachment mechanism in general growing networks

an application of the lovasz schrijver m k k operator to the stable set problem although the lift and project operators of lovasz and schrijver have been the subject of intense study their m k k operator has received little attention we consider an application of this operator to the stable set problem we begin with an initial linear programming lp relaxation consisting of clique and non negativity inequalities and then apply the operator to obtain a stronger extended lp relaxation we discuss theoretical properties of the resulting relaxation describe the issues that must be overcome to obtain an effective practical implementation and give extensive computational results remarkably the upper bounds obtained are sometimes stronger than those obtained with semidefinite programming techniques

permanents pfaffian orientations and even directed circuits given a 0 1 square matrix a when can some of the 1 s be changed toi1 s in such a way that the permanent of a equals the determinant of the modifled matrix when does a real square matrix have the property that every real matrix with the same sign pattern that is the corresponding entries either have the same sign or are both zero is nonsingular when is a hypergraph with n vertices and n hyperedges minimally nonbipartite when does a bipartite graph have a pfa an orientation given a digraph does it have no directed circuit of even length given a digraph does it have a subdivision with no even directed circuit it is known that all of the above problems are equivalent we prove a structural characterization of the feasible instances which implies a polynomial time algorithm to solve all of the above problems the structural characterization says roughly speaking that a bipartite graph has a pfa an orientation if and only if it can be obtained by piecing together in a specifled way planar bipartite graphs and one sporadic nonplanar bipartite graph