modularity maximization using completely positive programming abstract community detection is one of the most prominent problems of social network analysis in this paper a novel method for modularity maximization mm for community detection is presented which exploits the alternating direction augmented lagrangian adal method for maximizing a generalized form of newman s modularity function we first transform newman s modularity function into a quadratic program and then use completely positive programming cpp to map the quadratic program to a linear program which provides the globally optimal maximum modularity partition in order to solve the proposed cpp problem a closed form solution using the adal merged with a rank minimization approach is proposed the performance of the proposed method is evaluated on several real world data sets used for benchmarks community detection simulation results shows the proposed technique provides outstanding results in terms of modularity value for crisp partitions

fuzzy communities and the concept of bridgeness in complex networks we consider the problem of fuzzy community detection in networks which complements and expands the concept of overlapping community structure our approach allows each vertex of the graph to belong to multiple communities at the same time determined by exact numerical membership degrees even in the presence of uncertainty in the data being analyzed we create an algorithm for determining the optimal membership degrees with respect to a given goal function based on the membership degrees we introduce a measure that is able to identify outlier vertices that do not belong to any of the communities bridge vertices that have significant membership in more than one single community and regular vertices that fundamentally restrict their interactions within their own community while also being able to quantify the centrality of a vertex with respect to its dominant community the method can also be used for prediction in case of uncertainty in the data set analyzed the number of communities can be given in advance or determined by the algorithm itself using a fuzzified variant of the modularity function the technique is able to discover the fuzzy community structure of different real world networks including but not limited to social networks scientific collaboration networks and cortical networks with high confidence

minimum energy filtering for attitude estimation in this work we study minimum energy filtering for attitude kinematics with vectorial measurements using mortensen s approach the exact form of a minimum energy attitude observer is derived and is shown to depend on the hessian of the value function of an associated optimal control problem a suitably chosen matrix representation of the hessian operator leads to a riccati equation that approximates a minimum energy attitude filter an extended version of the proposed approximate filter is included for a situation where there is slowly time varying bias in the gyro measurements a unit quaternion version of the proposed filter is derived and shown to outperform the multiplicative extended kalman filter mekf for situations with large initialization errors or large measurement errors

on the classification of clifford algebras and their relation to spinors in n dimensions a classification of all the clifford algebras is given in terms of kronecker products of the quaternion and dihedral groups the relationship to spinors in n dimensions is explicitly determined we show that the real clifford algebra in minkowski spacetime is distinct from both the algebra of dirac matrices and the algebra of majorana matrices and cannot be realized by the spinor framework the matrix representations of clifford algebras are discussed and are utilized to give a classification of the real forms of lie algebras we are thus able to relate clifford lie and spinor algebras in an intrinsic geometrical setting

line graphs link partitions and overlapping communities in this paper we use a partition of the links of a network in order to uncover its community structure this approach allows for communities to overlap at nodes so that nodes may be in more than one community we do this by making a node partition of the line graph of the original network in this way we show that any algorithm that produces a partition of nodes can be used to produce a partition of links we discuss the role of the degree heterogeneity and propose a weighted version of the line graph in order to account for this

a necessary and sufficient condition for the perspective observability problem abstract in this paper we derive a necessary and sufficient condition for observing the initial condition of a new class of system known as the perspective system such a system has already been applied in the field of computer vision especially in the area of motion estimation problems our result generalizes an earlier result by popov belevitch hautus on the problem of observing a linear dynamical system

structure from motion causally integrated over time we describe an algorithm for reconstructing three dimensional structure and motion causally in real time from monocular sequences of images we prove that the algorithm is minimal and stable in the sense that the estimation error remains bounded with probability one throughout a sequence of arbitrary length we discuss a scheme for handling occlusions point features appearing and disappearing and drift in the scale factor these issues are crucial for the algorithm to operate in real time on real scenes we describe in detail the implementation of the algorithm which runs on a personal computer and has been made available to the community we report the performance of our implementation on a few representative long sequences of real and synthetic images the algorithm which has been tested extensively over the course of the past few years exhibits honest performance when the scene contains at least 20 40 points with high contrast when the relative motion is slow compared to the sampling frequency of the frame grabber 30 hz and the lens aperture is large enough typically more than 30 spl deg of visual field

visually guided ranging from observations of points lines and curves via an identifier based nonlinear observer abstract in this paper we consider the problem of estimating the range information of features on an affine plane in r 3 by observing its image with the aid of a ccd camera wherein we assume that the camera is undergoing a known motion the features considered are points lines and planar curves located on planar surfaces of static objects the dynamics of the moving projections of the features on the image plane have been described as a suitable differential equation on an appropriate feature space this dynamics is used to estimate feature parameters from which the range information is readily available in this paper the proposed identification has been carried out via a newly introduced identifier based observer performance of the observer has been studied via simulation

normalized cuts and image segmentation we propose a novel approach for solving the perceptual grouping problem in vision rather than focusing on local features and their consistencies in the image data our approach aims at extracting the global impression of an image we treat image segmentation as a graph partitioning problem and propose a novel global criterion the normalized cut for segmenting the graph the normalized cut criterion measures both the total dissimilarity between the different groups as well as the total similarity within the groups we show that an efficient computational technique based on a generalized eigenvalue problem can be used to optimize this criterion we applied this approach to segmenting static images as well as motion sequences and found the results to be very encouraging

pose estimation using line based dynamic vision and inertial sensors an observer problem from a computer vision application is studied rigid body pose estimation using inertial sensors and a monocular camera is considered and it is shown how rotation estimation can be decoupled from position estimation orientation estimation is formulated as an observer problem with implicit output where the states evolve on so 3 a careful observability study reveals interesting group theoretic structures tied to the underlying system structure a locally convergent observer where the states evolve on so 3 is proposed and numerical estimates of the domain of attraction is given further it is shown that given convergent orientation estimates position estimation can be formulated as a linear implicit output problem from an applications perspective it is outlined how delayed low bandwidth visual observations and high bandwidth rate gyro measurements can provide high bandwidth estimates this is consistent with real time constraints due to the complementary characteristics of the sensors which are fused in a multirate way

robust h filtering for nonlinear systems abstract a robust or h approach to filtering for nonlinear systems is considered a bound on the estimate error as a function of the disturbance energy is obtained the corresponding dynamic programming equation is a first order pde this has computational ramifications the case where the measurements are discrete time is considered also a numerical method is discussed

unitary representations of the 4 1 de sitter group on irreducible representation spaces of the poincare group the construction of the principal continuous series of unitary representations of the simply connected covering group of the 4 1 de sitter group on unitary irreducible representation spaces of the poincare group is presented a unitary irreducible representation space of this covering group of the de sitter group is realized as the direct sum of two irreducible representation spaces of the poincare group possible physical implications are indicated in particular an interpretation of the instantaneous velocity operator in the dirac theory as the spin part of the de sitter boosts is given we obtain a simple method of computing the matrix elements of the generators of the de sitter group in an so 4 basis using the matrix elements of the generators of the four dimensional euclidean group also we obtain explicit expressions for certain matrix elements between the spinor and so 4 basis of the representation space as functions on the coset space so 4 so 3

community detection in complex networks using extremal optimization we propose a method to find the community structure in complex networks based on an extremal optimization of the value of modularity the method outperforms the optimal modularity found by the existing algorithms in the literature giving a better understanding of the community structure we present the results of the algorithm for computer simulated and real networks and compare them with other approaches the efficiency and accuracy of the method make it feasible to be used for the accurate identification of community structure in large complex networks

motion estimation via dynamic vision estimating the three dimensional motion of an object from a sequence of projections is of paramount importance in a variety of applications in control and robotics such as autonomous navigation manipulation servo tracking docking planning and surveillance although visual motion estimation is an old problem the first formulations date back to the beginning of the century only recently have tools from nonlinear systems estimation theory hinted at acceptable solutions in this paper the authors formulate the visual motion estimation problem in terms of identification of nonlinear implicit systems with parameters on a topological manifold and propose a dynamic solution either in the local coordinates or in the embedding space of the parameter manifold such a formulation has structural advantages over previous recursive schemes since the estimation of motion is decoupled from the estimation of the structure of the object being viewed and therefore it is possible to handle occlusions in a principled way

risk sensitive control and dynamic games for partially observed discrete time nonlinear systems solves a finite horizon partially observed risk sensitive stochastic optimal control problem for discrete time nonlinear systems and obtains small noise and small risk limits the small noise limit is interpreted as a deterministic partially observed dynamic game and new insights into the optimal solution of such game problems are obtained both the risk sensitive stochastic control problem and the deterministic dynamic game problem are solved using information states dynamic programming and associated separated policies a certainty equivalence principle is also discussed the authors results have implications for the nonlinear robust stabilization problem the small risk limit is a standard partially observed risk neutral stochastic optimal control problem

unitary representations of the 4 1 de sitter group on unitary irreducible representation spaces of the poincare group equivalence with their realizations as induced representations in a previous work we have constructed realizations of the principal continuous series of unitary irreducible representations of the simply connected covering group of the 4 1 de sitter group on unitary irreducible representation spaces of the simply connected covering group of the poincare group in this work we demonstrate the equivalence of the representations constructed in the previous work with their realizations as induced representations

on the linearization up to multi output injection for a class of systems with implicitly defined outputs for a class of nonlinear systems we investigate the problem of under what conditions there exists a coordinate transformation that yields a state affine linear system up to output injection with implicit outputs in particular we provide necessary and sufficient conditions for time varying linearization up to multi output injection we highlight that if the conditions hold as a consequence it is possible in the new coordinates to construct an observer with linear error dynamics we propose a methodology to find the coordinate transformation several examples illustrate the proposed procedure

harmonic analysis on spannors the spannor representation of the universal covering group of the conformal group of minkowski space time is studied herein it is an example of an indecomposable representation various parallelizations for spannors are described normalized k finite basis fields for the spannors are introduced and a computation of the actions of the scale generator and other generators of the conformal group on these basis fields is given the irreducibility of all irreducible composition factors is established and it is decided which ones are infinitesimally unitary two sets of generators for maximal abelian subalgebras of the enveloping algebra of the conformal group are introduced the action of one of the sets on k finite basis fields in the spannor representation is studied this is important for understanding of the problem of degeneracy in the spannor representation since k types occur with multiplicity 2 many calculations make use of the lowest highest weight module structures of the unitarizable and positive negative energy irreducible composition factors and thus many of our results and techniques can be used to initiate a study of the quantum deformations of the associated lie algebra representations results on the poincare content of the unitarizable irreducible composition factors are stated and unitary equivalences between certain of these factors are established

revealing network communities with a nonlinear programming method the detection of network communities has attracted significant research attention lately to discover such structures a mathematical measure known as modularity is often used for optimization unfortunately the optimization is np hard and approximated solutions have to be sought for large networks in this paper we propose a nonlinear programming method for optimization that is based on the augmented lagrangian technique we further identify the inherent connection between the proposed method and positive semi definite programming and its low rank reduction which helps to justify the performance of the method compared with previously published approaches the proposed method is empirically efficient and effective at detecting underlying network communities

partially observed differential games infinite dimensional hamilton jacobi isaacs equations and nonlinear h_ infty control this paper presents new results for partially observed nonlinear differential games using the concept of information state we solve this problem in terms of an infinite dimensional partial differential equation which turns out to be the hamilton jacobi isaacs hji equation for partially observed differential games we give definitions of smooth and viscosity solutions and prove that the value function is a viscosity solution of the hji equation we prove a verification theorem which implies that the optimal controls are separated in that they depend on the observations through the information state this constitutes a separation principle for partially observed differential games we also present some new results concerning the certainty equivalence principle under certain standard assumptions our results are applied to a nonlinear output feedback h infty robust control problem

remarks on hamilton jacobi equations with measurable time dependent hamiltonians on considere les equations de hamilton jacobi de la forme suivante u t h x t u u 0 dans r n 0 t ou h x t s p est continu en x s p et mesurable en t on considere une extension de la notion de solution viscosite au cas de h mesurable dependant du temps

risk sensitive control on an infinite time horizon stochastic control problems on an infinite time horizon with exponential cost criteria are considered the donsker varadhan large deviation rate is used as a criterion to be optimized the optimum rate is characterized as the value of an associated stochastic differential game with an ergodic expected average cost per unit time cost criterion if we take a small noise limit a deterministic differential game with average cost per unit time cost criterion is obtained this differential game is related to robust control of nonlinear systems

uniqueness for viscosity solutions of nonstationary hamilton jacobi bellman equations under some a priori conditions with applications this paper extends the uniqueness results for viscosity solutions of nonstationary hamilton jacobi bellman equations the conditions for uniqueness which are obtained can involve a trade off between the growth of the solution and the growth of the hamiltonian in particular the result is valid for solutions which grow quadratically in the space variable and are associated with hamiltonians which also grow quadratically this particular class arises in the robust control limit of risk sensitive stochastic control problems

a perspective theory for motion and shape estimation in machine vision in this paper we consider the problem of motion and shape estimation of a moving body with the aid of a monocular camera we show that the estimation problem reduces to a specific parameter estimation of a perspective dynamical system surprisingly the above reduction is independent of whether the data measured is the brightness pattern which the object produces on the image plane or whether the data observed are points lines or curves on the image plane produced as a result of discontinuities in the brightness pattern many cases of the perspective parameter estimation problem have been analyzed in this paper these cases include a fairly complete analysis of a planar textured surface undergoing a rigid flow and an affine flow these two cases have been analyzed for orthographic pseudo orthographic and image centered projections the basic procedure introduced for parameter estimation is to subdivide the problem into two modules one for spatial averaging and the other for time averaging the estimation procedure is carried out with the aid of a new realization theory for perspective systems introduced for systems described in discrete time and in continuous time finally much of our analysis has been substantiated by computer simulation of specific algorithms developed in order to explicitly compute the parameters detailed simulation that would answer the perspective realizability question is a subject of future research

an embedding of the poincare lie algebra into an extension of the lie field of so0 1 4 the isomorphism between algebraic extensions of the lie fields of so0 1 4 and the poincare group are considered herein it is shown that the principal series of unitary ray representations of so0 1 4 are associated via the isomorphism with real mass positive and negative energy representations of the poincare lie algebra with arbitrary spin results on the most degenerate exceptional series of so0 1 4 representations are also given

an efficient community detection method based on rank centrality abstract community detection is a very important problem in social network analysis classical clustering approach k means has been shown to be very efficient to detect communities in networks however k means is quite sensitive to the initial centroids or seeds especially when it is used to detect communities to solve this problem in this study we propose an efficient algorithm k rank which selects the top k nodes with the highest rank centrality as the initial seeds and updates these seeds by using an iterative technique like k means then we extend k rank to partition directed weighted networks and to detect overlapping communities the empirical study on synthetic and real networks show that k rank is robust and better than the state of the art algorithms including k means bgll lpa infomap and oslom

minimum energy state estimation for systems with perspective outputs this paper addresses the state estimation of systems with perspective outputs we derive a minimum energy estimator which produces an estimate of the state that is most compatible with the dynamics in the sense that it requires the least amount of noise energy to explain the measured outputs under suitable observability assumptions the estimate converges globally asymptotically to the true value of the state in the absence of noise and disturbance in the presence of noise the estimate converges to a neighborhood of the true value of the state these results are also extended to solve the estimation problem when the measured outputs are transmitted through a network in that case we assume that the measurements arrive at discrete time instants are time delayed noisy and may not be complete we show that the redesigned minimum energy estimator preserves the same convergence properties we apply these results to the estimation of position and orientation for a mobile robot that uses a monocular charged coupled device ccd camera mounted on board to observe the apparent motion of stationary points in the context of our application the estimator can deal directly with the usual problems associated with vision systems such as noise latency and intermittency of observations experimental results are presented and discussed

generalized viscosity solutions for hamilton jacobi equations with time measurable hamiltonians the objective of this paper is to extend the idea of viscosity solution for nonlinear first order hamilton jacobi equations u h t x d u 0 with time continuous h to time measurable hamiltonians we are primarily motivated by the fact that control problems for which the value function is the viscosity solution of a hamilton jacobi equation should not be restric ted to continuity in time in barron and jensen 1 we were confronted with a linear hamilton jacobi equation arising in the proof of the pon tryagin which had time measurable coeflicients the existing theory of viscosity solutions did not apply to even this case moreover important models of controlled first order hamiltonjacobi equations require time measurable controls for example models of controlled traffic flow or queueing processes might be of this type we are about then to extend the definition of viscosity solution to generalized viscosity solution applying to time measurable hamiltonians in this paper we give the definition and derive the corresponding uni queness result with an implicit domain of dependence consequent the fun damental technique used in the proof is the so called blow up method which has also been used elsewhere s although not in the generality discussed here this method effectively freezes the point to x0 under consideration and essentially removes it from the problem of course t is

rigid body attitude estimation based on the lagrange d alembert principle estimation of rigid body attitude and angular velocity without any knowledge of the attitude dynamics model is treated using the lagrange d alembert principle from variational mechanics it is shown that wahba s cost function for attitude determination from two or more non collinear vector measurements can be generalized and represented as a morse function of the attitude estimation error on the lie group of rigid body rotations with body fixed sensor measurements of direction vectors and angular velocity a lagrangian is obtained as the difference between a kinetic energy like term that is quadratic in the angular velocity estimation error and an artificial potential obtained from wahba s function an additional dissipation term that depends on the angular velocity estimation error is introduced and the lagrange d alembert principle is applied to the lagrangian with this dissipation a lyapunov analysis shows that the state estimation scheme so obtained provides stable asymptotic convergence of state estimates to actual states in the absence of measurement noise with an almost global domain of attraction these estimation schemes are discretized for computer implementation using discrete variational mechanics a first order lie group variational integrator is obtained as a discrete time implementation in the presence of bounded measurement noise numerical simulations show that the estimated states converge to a bounded neighborhood of the actual states

some group theoretical aspects of the so0 1 4 invariant theory some properties of unitary representations of the de sitter group so0 1 4 are considered in the case of spin zero and positivity of the mass operator these representations involve a decomposition which ensures the fulfilment of the cluster separability condition and allows for the conventional interpretation of the de sitter analogues of momentum and boost operators the decomposition of the tensor product of representations belonging to the principal series contains the representations of the principal series with all masses under natural assumptions concerning the interaction operators there are no bound states in the theory which is due to the universal de sitter antigravity

the problem of interactions in de sitter invariant theories the structure of representations describing systems of free particles in the theory with the invariance group is investigated the property of the particles to be free means as usual that the representation describing a many particle system is the tensor product of the corresponding single particle representations i e no interaction is introduced it is shown that the mass operator contains only continuous spectrum in the interval and such representations are unitarily equivalent to ones describing interactions gravitational electromagnetic etc this means that there are no bound states in the theory and the hilbert space of the many particle system contains a subspace of states with the following property the action of free representation operators on these states is manifested in the form of different interactions possible consequences of the results are discussed

strong duality for semidefinite programming it is well known that the duality theory for linear programming lp is powerful and elegant and lies behind algorithms such as simplex and interior point methods however the standard lagrangian for nonlinear programs requires constraint qualifications to avoid duality gaps semidefinite linear programming sdp is a generalization of lp where the nonnegativity constraints are replaced by a semidefiniteness constraint on the matrix variables there are many applications e g in systems and control theory and combinatorial optimization however the lagrangian dual for sdp can have a duality gap we discuss the relationships among various duals and give a unified treatment for strong duality in semidefinite programming these duals guarantee strong duality i e a zero duality gap and dual attainment this paper is motivated by the recent paper by ramana where one of these duals is introduced

riccati observers for the nonstationary pnp problem this paper revisits the problem of estimating the pose position and orientation of a body in 3 d space with respect to w r t an inertial frame by using 1 the knowledge of source points positions in the inertial frame 2 the measurements of the body angular velocity expressed in the body s frame 3 the measurements of the body translational velocity either in the body frame or in the inertial frame and 4 source points bearing measurements performed in the body frame an important difference with the much studied static perspective n point problem addressed with iterative algorithms is that body motion is not only allowed but also used as a source of information that improves the estimation possibilities with respect to the probabilistic framework commonly used in other studies that develop extended kalman filter solutions the deterministic approach here adopted is better suited to point out the observability conditions that involve the number and disposition of the source points in combination with body motion characteristics under which the proposed observers ensure robust estimation of the body pose these observers are here named riccati observers because of the instrumental role played by the continuous riccati equation in the design of the observers and in the lyapunov stability and convergence analysis that we develop independently of the well known complementary either deterministic or probabilistic optimality properties associated with kalman filtering the set of these observers also encompasses extended kalman filter solutions another contribution of this study is to show the importance of using body motion to improve the observers performance and when this is possible of measuring the body translational velocity in the inertial frame rather than in the body frame to allow for the body pose estimation from a single source point taken as the origin of the inertial frame this latter possibility finds a natural extension in the simultaneous localisation and mapping slam problem in robotics

representations of the poincare lie algebra from unitary representations of so 1 4 an algebraic isomorphism of an extension of the lie field of so 1 4 and an extension of the poincare lie field was given in havlicek and moylan j math phys 34 5320 1993 here we use the isomorphism described in that paper in order to obtain matrix elements of the poincare lie algebra generators in a normalizable basis for an arbitrary unitary spherical principal series representation of so0 1 4

a soft modularity function for detecting fuzzy communities in social networks we discuss a new formulation of a fuzzy validity index that generalizes the newman girvan ng modularity function the ng function serves as a cluster validity functional in community detection studies the input data is an undirected weighted graph that represents e g a social network clusters correspond to socially similar substructures in the network we compare our fuzzy modularity with two existing modularity functions using the well studied karate club and american college football datasets

second order optimal minimum energy filters on lie groups systems on lie groups naturally appear as models for physical systems with full symmetry we consider the state estimation problem for such systems where both input and output measurements are corrupted by unknown disturbances we provide an explicit formula for the second order optimal nonlinear filter on a general lie group where optimality is with respect to a deterministic cost measuring the cumulative energy in the unknown system disturbances minimum energy filtering the resulting filter depends on the choice of affine connection which encodes the nonlinear geometry of the state space as an example we look at attitude estimation where we are given a second order mechanical system on the tangent bundle of the special orthogonal group so 3 namely the rigid body kinematics together with the euler equation when we choose the symmetric cartan schouten 0 connection the resulting filter has the familiar form of a gradient observer combined with a perturbed matrix riccati differential equation that updates the filter gain this example demonstrates how to construct a matrix representation of the abstract general filter formula

near optimal deterministic filtering on the rotation group this technical note considers the problem of obtaining minimum energy state estimates for a system defined on the rotation group the signals of the system are modeled as purely deterministic signals we derive a nonlinear observer filter posed directly on that respects the geometry of the group and achieves a performance that is close to optimal in the sense of minimizing an integral cost that is measuring the state energy the performance of the proposed filter is demonstrated in simulations involving large initialization process and measurement errors where the results are compared against a quaternion implementation of an extended kalman filter our results indicate that the proposed filter achieves better robustness against a range of noise levels and initialization errors

linearly and nonlinearly transforming fields on homogeneous spaces of the 4 1 de sitter group scalar functions on the homogeneous spaces hr of the de sitter group g so 4 1 are studied where the spaces hr are of the form g k with k being a subgroup of the lorentz group h so 3 1 contained in so 4 1 the spaces hr can be regarded as fiber bundles er er g h h k with the base v 4 g h being a space of constant negative curvature characterized by a fundamental length parameter r 4 1 de sitter space and the fiber s h k being a homogeneous space of the lorentz group the action of g on the spaces er is a linear action on v4 and a nonlinear action on s where the latter action is defined by a generalized wigner rotation a gauge theory based on the 4 1 de sitter group is investigated with matter represented in terms of a generalized wave function x y with x u4 riemann cartan space time v 4 and y s which is defined as a map from a cross section on the bundle e e u4 f er g so 4 1 over space time u4 with fiber f er g k and structural group g so 4 1 into the complex numbers th

on the integrability of certain symmetric representations of the lie algebra of so0 4 1 a proof of the existence of an essentially self adjoint extension of a symmetric so0 4 1 nelson operator which is constructed out of the generators of a positive mass arbitrary spin unitary irreducible representation of the poincare group is presented our analysis of so0 4 1 and its lie algebra provides us with an example of an observation of harish chandra there exist subspaces of the space of differentiable vectors of a representation of a noncompact group which are invariant under the lie algebra but the closures of the subspaces are not invariant under the group the chief results of this paper should hold true for so0 n 1 in particular we should have a realization of an arbitrary principal series irreducible unitary representation of so0 n 1 on the direct sum of two identical unitary irreducible representation spaces of the motion group in an n dimensional minkowski space which has one timelike dimension