skinner rusk unified formalism for optimal control systems and applications a geometric approach to time dependent optimal control problems is proposed this formulation is based on the skinner and rusk formalism for lagrangian and hamiltonian systems the corresponding unified formalism developed for optimal control systems allows us to formulate geometrically the necessary conditions given by a weak form of pontryagin s maximum principle provided that the differentiability with respect to controls is assumed and the space of controls is open furthermore our method is also valid for implicit optimal control systems and in particular for the so called descriptor systems optimal control problems including both differential and algebraic equations

interconnection and damping assignment passivity based control of port controlled hamiltonian systems passivity based control pbc is a well established technique that has shown to be very powerful to design robust controllers for physical systems described by euler lagrange el equations of motion for regulation problems of mechanical systems which can be stabilized shaping only the potential energy pbc preserves the el structure and furthermore assigns a closed loop energy function equal to the difference between the energy of the system and the energy supplied by the controller thus we say that stabilization is achieved via energy balancing unfortunately these nice properties of el pbc are lost when used in other applications which require shaping of the total energy for instance in electrical or electromechanical systems or even some underactuated mechanical devices our main objective in this paper is to develop a new pbc theory which extends to a broader class of systems the aforementioned energy balancing stabilization mechanism and the structure invariance towards this end we depart from the el description of the systems and consider instead port controlled hamiltonian models which result from the network modelling of energy conserving lumped parameter physical systems with independent storage elements and strictly contain the class of el models

active contours without edges we propose a new model for active contours to detect objects in a given image based on techniques of curve evolution mumford shah 1989 functional for segmentation and level sets our model can detect objects whose boundaries are not necessarily defined by the gradient we minimize an energy which can be seen as a particular case of the minimal partition problem in the level set formulation the problem becomes a mean curvature flow like evolving the active contour which will stop on the desired boundary however the stopping term does not depend on the gradient of the image as in the classical active contour models but is instead related to a particular segmentation of the image we give a numerical algorithm using finite differences finally we present various experimental results and in particular some examples for which the classical snakes methods based on the gradient are not applicable also the initial curve can be anywhere in the image and interior contours are automatically detected

the matching conditions of controlled lagrangians and ida passivity based control this paper discusses the matching conditions resulting from the controlled lagrangians method and the interconnection and damping assignment passivity based control ida pbc method both methods have been presented recently in the literature as means to stabilize a desired equilibrium point of an euler lagrange respectively hamiltonian system in the context of mechanical systems with symmetry the original controlled lagrangians method is reviewed and an interpretation of the matching assumptions in terms of the matching of kinetic and potential energy is given secondly both methods are applied to the general class of underactuated mechanical systems and it is shown that the controlled lagrangians method is contained in the ida pbc method the lambda method as described in recent papers for the controlled lagrangians method transforming the matching conditions a set of non linear pdes into a set of linear pdes is discussed the method is used to transform the matching conditions obtained in the ida pbc method into a set of quadratic and linear pdes finally the extra freedom obtained in the ida pbc method with respect to the controlled lagrangians method is used to discuss the integrability of the closed loop system explicit conditions are derived under which the closed loop hamiltonian system is integrable leading to the introduction of gyroscopic terms

gromov witten invariants in algebraic geometry gromov witten invariants for arbitrary non singular projective vari eties and arbitrary genus are constructed using the techniques from k behrend b fantechi the intrinsic normal cone

controlled lagrangians and the stabilization of mechanical systems ii potential shaping for pt i see ibid vol 45 p 2253 70 2000 we extend the method of controlled lagrangians cl to include potential shaping which achieves complete state space asymptotic stabilization of mechanical systems the cl method deals with mechanical systems with symmetry and provides symmetry preserving kinetic shaping and feedback controlled dissipation for state space stabilization in all but the symmetry variables potential shaping complements the kinetic shaping by breaking symmetry and stabilizing the remaining state variables the approach also extends the method of controlled lagrangians to include a class of mechanical systems without symmetry such as the inverted pendulum on a cart that travels along an incline

stabilization of a class of underactuated mechanical systems via interconnection and damping assignment we consider the application of a formulation of passivity based control pbc known as interconnection and damping assignment ida to the problem of stabilization of underactuated mechanical systems which requires the modification of both the potential and the kinetic energies our main contribution is the characterization of a class of systems for which ida pbc yields a smooth asymptotically stabilizing controller with a guaranteed domain of attraction the class is given in terms of solvability of certain partial differential equations one important feature of ida pbc stemming from its hamiltonian formulation is that it provides new degrees of freedom for the solution of these equations using this additional freedom we are able to show that the method of controlled lagrangians in its original formulation may be viewed as a special case of our approach as illustrations we design asymptotically stabilizing ida pbcs for the classical ball and beam system and a novel inertia wheel pendulum

an in depth study of graph partitioning measures for perceptual organization in recent years one of the effective engines for perceptual organization of low level image features is based on the partitioning of a graph representation that captures gestalt inspired local structures such as similarity proximity continuity parallelism and perpendicularity over the low level image features mainly motivated by computational efficiency considerations this graph partitioning process is usually implemented as a recursive bipartitioning process where at each step the graph is broken into two parts based on a partitioning measure we focus on three such measures namely the minimum average and normalized cuts the minimum cut partition seeks to minimize the total link weights cut the average cut measure is proportional to the total link weight cut normalized by the sizes of the partitions the normalized cut measure is normalized by the product of the total connectivity valencies of the nodes in each partition we provide theoretical and empirical insight into the nature of the three partitioning measures in terms of the underlying image statistics in particular we consider for what kinds of image statistics would optimizing a measure irrespective of the particular algorithm used result in correct partitioning are the quality of the groups significantly different for each cut measure are there classes of images for which grouping by partitioning does not work well also can the recursive bipartitioning strategy separate out groups corresponding to k objects from each other in the analysis we draw from probability theory and the rich body of work on stochastic ordering of random variables our major conclusion is that optimization of none of the three measures is guaranteed to result in the correct partitioning of k objects in the strict stochastic order sense for all image statistics

weak approximation for isotrivial families we study weak approximation for isotrivial families of rationally connected varieties over a smooth projective curve in the case where the family is formed by taking a quotient of a cyclic group action we find a necessary and sufficient condition for weak approximation to hold in most other cases there is also a sufficient condition we also check that this condition is satisfied for all smooth fano hypersurfaces in projective spaces

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

singular foliations with trivial canonical class this paper describes the structure of singular codimension one foliations with numerically trivial canonical bundle on complex projective manifolds

the grothendieck ring of varieties and piecewise isomorphisms let k0 var k be the grothendieck ring of algebraic varieties over a field k l et x y be two algebraic varieties over k which are piecewise isomorphic i e x and y admit finite partitions x1 xn y1 yn into locally closed subvarieties such that xi is iso morphic to yi for all i n then x y in k0 var k larsen and lunts ask whether the converse is true for characteristic zero and algebraically closedfield k we answer positively this question when dim x 1o rx is a smooth connected projective surface or if x contains only finitely many rational curves

curve evolution implementation of the mumford shah functional for image segmentation denoising interpolation and magnification we first address the problem of simultaneous image segmentation and smoothing by approaching the mumford shah 1989 paradigm from a curve evolution perspective in particular we let a set of deformable contours define the boundaries between regions in an image where we model the data via piecewise smooth functions and employ a gradient flow to evolve these contours each gradient step involves solving an optimal estimation problem for the data within each region connecting curve evolution and the mumford shah functional with the theory of boundary value stochastic processes the resulting active contour model offers a tractable implementation of the original mumford shah model i e without resorting to elliptic approximations which have traditionally been favored for greater ease in implementation to simultaneously segment and smoothly reconstruct the data within a given image in a coupled manner various implementations of this algorithm are introduced to increase its speed of convergence we also outline a hierarchical implementation of this algorithm to handle important image features such as triple points and other multiple junctions next by generalizing the data fidelity term of the original mumford shah functional to incorporate a spatially varying penalty we extend our method to problems in which data quality varies across the image and to images in which sets of pixel measurements are missing this more general model leads us to a novel pde based approach for simultaneous image magnification segmentation and smoothing thereby extending the traditional applications of the mumford shah functional which only considers simultaneous segmentation and smoothing

birational automorphisms of fano hypersurfaces v v y v 0 between smooth three dimensional quartics v v4 v 0 v 0 4 in p is a projective isomorphism this is the original wording of their theorem in fact the arguments of im give a much stronger result namely they actually prove that smooth quartics are birationally superrigid the concept of birational rigidity is not visual being rather technical it makes little impression it is immediate implications of the property of being birationally super rigid that are really impressive for a projective variety x smooth in codimension 1 and a linear system jdj free from xed components we de ne the threshold of canonical adjunction or brie y just threshold of the pair x d setting

birational superrigidity and k stability of fano complete intersections of index 1 we prove that every smooth fano complete intersection of index 1 and codimension r in pn r is birationally superrigid and k stable if n 10r we also propose a generalization of tian s criterion of k stability and as an application prove the k stability of the complete intersection of a quadric and a cubic in p5 in the appendix written jointly with c stibitz we prove the conditional birational superrigidity of fano complete intersections of higher index in large dimension

mathbb a 1 connected varieties of rank one over nonclosed fields in this paper we prove two results regarding the arithmetics of separably mathbb a 1 connected varieties of rank one first we prove that over a large field there is an mathbb a 1 curve through any rational point of the boundary if the boundary divisor is smooth and separably rationally connected secondly we generalize a theorem of hassett tschinkel for the zariski density of integral points over function fields of curves

an intrinsic observer for a class of lagrangian systems we propose a new design method of asymptotic observers for a class of nonlinear mechanical systems lagrangian systems with configuration position measurements our main contribution is to introduce a state position and velocity observer that is invariant under any changes of the configuration coordinates the observer dynamics equations as the euler lagrange equations are intrinsic the design method uses the riemannian structure defined by the kinetic energy on the configuration manifold the local convergence is proved by showing that the jacobian of the observer dynamics is negative definite contraction for a particular metric defined on the state space a metric derived from the kinetic energy and the observer gains from a practical point of view such intrinsic observers can be approximated when the estimated configuration is close to the true one by an explicit set of differential equations involving the riemannian curvature tensor these equations can be automatically generated via symbolic differentiations of the metric and potential up to order two numerical simulations for the ball and beam system an example where the scalar curvature is always negative show the effectiveness of such approximation when the measured positions are noisy or include high frequency neglected dynamics

edge grouping combining boundary and region information this paper introduces a new edge grouping method to detect perceptually salient structures in noisy images specifically we define a new grouping cost function in a ratio form where the numerator measures the boundary proximity of the resulting structure and the denominator measures the area of the resulting structure this area term introduces a preference towards detecting larger size structures and therefore makes the resulting edge grouping more robust to image noise to find the optimal edge grouping with the minimum grouping cost we develop a special graph model with two different kinds of edges and then reduce the grouping problem to finding a special kind of cycle in this graph with a minimum cost in ratio form this optimal cycle finding problem can be solved in polynomial time by a previously developed graph algorithm we implement this edge grouping method test it on both synthetic data and real images and compare its performance against several available edge grouping and edge linking methods furthermore we discuss several extensions of the proposed method including the incorporation of the well known grouping cues of continuity and intensity homogeneity introducing a factor to balance the contributions from the boundary and region information and the prevention of detecting self intersecting boundaries

constructive immersion and invariance stabilization for a class of underactuated mechanical systems a constructive approach to stabilize a desired equilibrium for a class of underactuated mechanical systems which obviates the solution of partial differential equations is proposed the immersion invariance methodology is adopted with the main result formulated in the port hamiltonian framework for both model and target dynamics the procedure is applicable to mechanical systems with under actuation degree larger than one extending the results recently reported by some of the authors the approach is successfully applied to two benchmark examples and some basic connections with the interconnection and damping assignment passivity based control are revealed an additional contribution of this work is the identification of a class of mechanical systems whose mechanical structure remains invariant under partial feedback linearization

trajectory tracking control of port controlled hamiltonian systems via generalized canonical transformations this paper addresses trajectory tracking control of port controlled hamiltonian systems via generalized canonical transformations and passivity based control the main strategy adopted in this paper is to construct an error system which describes the dynamics of the tracking error by a passive port controlled hamiltonian system after obtaining the error system tracking control of the original system can be achieved by stabilizing the error system via passivity based approach first a fundamental framework is provided for constructing the error system via generalized canonical transformations then a concrete design procedure is derived for a class of electro mechanical systems furthermore the proposed method is applied to a magnetic levitation system and laboratory experiments demonstrate its effectiveness

shaping the energy of mechanical systems without solving partial differential equations control of underactuated mechanical systems via energy shaping is a well established robust design technique unfortunately its application is often stymied by the need to solve partial differential equations pdes in this technical note a new fully constructive procedure to shape the energy for a class of mechanical systems that obviates the solution of pdes is proposed the control law consists of a first stage of partial feedback linearization followed by a simple proportional plus integral controller acting on two new passive outputs the class of systems for which the procedure is applicable is identified imposing some directly verifiable conditions on the systems inertia matrix and its potential energy function it is shown that these conditions are satisfied by three benchmark examples

fast approximate energy minimization via graph cuts many tasks in computer vision involve assigning a label such as disparity to every pixel a common constraint is that the labels should vary smoothly almost everywhere while preserving sharp discontinuities that may exist e g at object boundaries these tasks are naturally stated in terms of energy minimization the authors consider a wide class of energies with various smoothness constraints global minimization of these energy functions is np hard even in the simplest discontinuity preserving case therefore our focus is on efficient approximation algorithms we present two algorithms based on graph cuts that efficiently find a local minimum with respect to two types of large moves namely expansion moves and swap moves these moves can simultaneously change the labels of arbitrarily large sets of pixels in contrast many standard algorithms including simulated annealing use small moves where only one pixel changes its label at a time our expansion algorithm finds a labeling within a known factor of the global minimum while our swap algorithm handles more general energy functions both of these algorithms allow important cases of discontinuity preserving energies we experimentally demonstrate the effectiveness of our approach for image restoration stereo and motion on real data with ground truth we achieve 98 percent accuracy

control by interconnection and standard passivity based control of port hamiltonian systems the dynamics of many physical processes can be suitably described by port hamiltonian ph models where the importance of the energy function the interconnection pattern and the dissipation of the system is underscored to regulate the behavior of ph systems it is natural to adopt a passivity based control pbc perspective where the control objectives are achieved shaping the energy function and adding dissipation in this paper we consider the pbc techniques of control by interconnection cbi and standard pbc in cbi the controller is another ph system connected to the plant through a power preserving interconnection to add up their energy functions while in standard pbc energy shaping is achieved via static state feedback in spite of the conceptual appeal of formulating the control problem as the interaction of dynamical systems the current version of cbi imposes a severe restriction on the plant dissipation structure that stymies its practical application on the other hand standard pbc which is usually derived from a uninspiring and non intuitive ldquopassive output generationrdquo viewpoint is one of the most successful controller design techniques the main objectives of this paper are 1 to extend the cbi method to make it more widely applicable in particular to overcome the aforementioned dissipation obstacle 2 to show that various popular variants of standard pbc can be derived proceeding from a unified perspective 3 to establish the connections between cbi and standard pbc proving that the latter is obtained restricting the former to a suitable subset providing a nice geometric interpretation to standard pbc and comparing the size of the set of ph plants for which they are applicable

a variational framework for multiregion pairwise similarity based image segmentation variational cost functions that are based on pairwise similarity between pixels can be minimized within level set framework resulting in a binary image segmentation in this paper we extend such cost functions and address multi region image segmentation problem by employing a multi phase level set framework for multi modal images cost functions become more complicated and relatively difficult to minimize we extend our previous work proposed for background foreground separation to the segmentation of images in more than two regions we also demonstrate an efficient implementation of the curve evolution which reduces the computational time significantly finally we validate the proposed method on the berkeley segmentation data set by comparing its performance with other segmentation techniques

region competition unifying snakes region growing and bayes mdl for multiband image segmentation we present a novel statistical and variational approach to image segmentation based on a new algorithm named region competition this algorithm is derived by minimizing a generalized bayes minimum description length mdl criterion using the variational principle the algorithm is guaranteed to converge to a local minimum and combines aspects of snakes balloons and region growing the classic snakes balloons and region growing algorithms can be directly derived from our approach we provide theoretical analysis of region competition including accuracy of boundary location criteria for initial conditions and the relationship to edge detection using filters it is straightforward to generalize the algorithm to multiband segmentation and we demonstrate it on gray level images color images and texture images the novel color model allows us to eliminate intensity gradients and shadows thereby obtaining segmentation based on the albedos of objects it also helps detect highlight regions

an optimal graph theoretic approach to data clustering theory and its application to image segmentation a novel graph theoretic approach for data clustering is presented and its application to the image segmentation problem is demonstrated the data to be clustered are represented by an undirected adjacency graph g with arc capacities assigned to reflect the similarity between the linked vertices clustering is achieved by removing arcs of g to form mutually exclusive subgraphs such that the largest inter subgraph maximum flow is minimized for graphs of moderate size approximately 2000 vertices the optimal solution is obtained through partitioning a flow and cut equivalent tree of g which can be efficiently constructed using the gomory hu algorithm 1961 however for larger graphs this approach is impractical new theorems for subgraph condensation are derived and are then used to develop a fast algorithm which hierarchically constructs and partitions a partially equivalent tree of much reduced size this algorithm results in an optimal solution equivalent to that obtained by partitioning the complete equivalent tree and is able to handle very large graphs with several hundred thousand vertices the new clustering algorithm is applied to the image segmentation problem the segmentation is achieved by effectively searching for closed contours of edge elements equivalent to minimum cuts in g which consist mostly of strong edges while rejecting contours containing isolated strong edges this method is able to accurately locate region boundaries and at the same time guarantees the formation of closed edge contours

potentially non klt locus and its applications we introduce the notion of potentially klt pairs for normal projective varieties with pseudoeffective anticanonical divisor the potentially non klt locus is a subset of x which is birationally transformed precisely into the non klt locus on a k x minimal model of x we prove basic properties of potentially non klt locus in comparison with those of classical non klt locus as applications we give a new characterization of varieties of fano type and we also improve results on the rational connectedness of uniruled varieties with pseudoeffective anticanonical divisor

total energy shaping control of mechanical systems simplifying the matching equations via coordinate changes total energy shaping is a controller design methodology that achieves asymptotic stabilization of mechanical systems endowing the closed loop system with a lagrangian or hamiltonian structure with a desired energy function that qualifies as lyapunov function for the desired equilibrium the success of the method relies on the possibility of solving two pdes which identify the kinetic and potential energy functions that can be assigned to the closed loop particularly troublesome is the partial differential equation pde associated to the kinetic energy which is nonlinear and inhomogeneous and the solution that defines the desired inertia matrix must be positive definite in this note we prove that we can eliminate or simplify the forcing term in this pde by modifying the target dynamics and introducing a change of coordinates in the original system furthermore it is shown that in the particular case of transformation to the lagrangian coordinates the possibility of simplifying the pdes is determined by the interaction between the coriolis and centrifugal forces and the actuation structure the examples of pendulum on a cart and furuta s pendulum are used to illustrate the results

image segmentation with ratio cut this paper proposes a new cost function cut ratio for segmenting images using graph based methods the cut ratio is defined as the ratio of the corresponding sums of two different weights of edges along the cut boundary and models the mean affinity between the segments separated by the boundary per unit boundary length this new cost function allows the image perimeter to be segmented guarantees that the segments produced by bipartitioning are connected and does not introduce a size shape smoothness or boundary length bias the latter allows it to produce segmentations where boundaries are aligned with image edges furthermore the cut ratio cost function allows efficient iterated region based segmentation as well as pixel based segmentation these properties may be useful for some image segmentation applications while the problem of finding a minimum ratio cut in an arbitrary graph is np hard one can find a minimum ratio cut in the connected planar graphs that arise during image segmentation in polynomial time while the cut ratio alone is not sufficient as a baseline method for image segmentation it forms a good basis for an extended method of image segmentation when combined with a small number of standard techniques we present an implemented algorithm for finding a minimum ratio cut prove its correctness discuss its application to image segmentation and present the results of segmenting a number of medical and natural images using our techniques

families of rationally connected varieties recall that a proper variety x is said to be rationally connected if two general points p q x are contained in the image of a map g p x this is clearly a birationally invariant property when x is smooth this turns out to be equivalent to the a priori weaker condition that two general points can be joined by a chain of rational curves and also to the a priori stronger condition that for any finite subset x there is a map g p x whose image contains and such that gtx is an ample bundle

controlled lagrangians and the stabilization of mechanical systems i the first matching theorem we develop a method for the stabilization of mechanical systems with symmetry based on the technique of controlled lagrangians the procedure involves making structured modifications to the lagrangian for the uncontrolled system thereby constructing the controlled lagrangian the euler lagrange equations derived from the controlled lagrangian describe the closed loop system where new terms in these equations are identified with control forces since the controlled system is lagrangian by construction energy methods can be used to find control gains that yield closed loop stability we use kinetic shaping to preserve symmetry and only stabilize systems module the symmetry group the procedure is demonstrated for several underactuated balance problems including the stabilization of an inverted planar pendulum on a cart moving on a line and an inverted spherical pendulum on a cart moving in the plane

geometric flow approach for region based image segmentation geometric flows have been successfully used for surface modeling and designing largely because they are inherently good at controlling geometric shape evolution variational image segmentation approaches on the other hand detect objects of interest by deforming certain given shapes this motivates us to revisit the minimal partition problem for segmentation of images and propose a new geometric flow based formulation and solution to it our model intends to derive a mapping that will evolve given contours or piecewise constant regions toward objects in the image the mapping is approximated by b spline basis functions and the positions of the control points are to be determined starting with the energy functional based on intensity averaging we derive a euler lagrange equation and then a geometric evolution equation the linearized system of equations is efficiently solved via a special matrix vector multiplication technique furthermore we extend the piecewise constant model to a piecewise smooth model which effectively handles images with intensity inhomogeneity

globally optimal regions and boundaries as minimum ratio weight cycles we describe a new form of energy functional for the modeling and identification of regions in images the energy is defined on the space of boundaries in the image domain and can incorporate very general combinations of modeling information both from the boundary intensity gradients etc and from the interior of the region texture homogeneity etc we describe two polynomial time digraph algorithms for finding the global minima of this energy one of the algorithms is completely general minimizing the functional for any choice of modeling information it runs in a few seconds on a 256 spl times 256 image the other algorithm applies to a subclass of functionals but has the advantage of being extremely parallelizable neither algorithm requires initialization

multi region active contours with a single level set function segmenting an image into an arbitrary number of coherent regions is at the core of image understanding many formulations of the segmentation problem have been suggested over the past years these formulations include among others axiomatic functionals which are hard to implement and analyze and graph based alternatives which impose a non geometric metric on the problem we propose a novel method for segmenting an image into an arbitrary number of regions using an axiomatic variational approach the proposed method allows to incorporate various generic region appearance models while avoiding metrication errors in the suggested framework the segmentation is performed by level set evolution yet contrarily to most existing methods here multiple regions are represented by a single non negative level set function the level set function evolution is efficiently executed through the voronoi implicit interface method for multi phase interface evolution the proposed approach is shown to obtain accurate segmentation results for various natural 2d and 3d images comparable to state of the art image segmentation algorithms

an lmi approach to stabilization of linear port controlled hamiltonian systems in this paper it is shown that controllers for stabilizing linear port controlled hamiltonian pch systems via interconnection and damping assignment can be obtained by solving a set of linear matrix inequalities lmis two sets of almost equivalent lmis are proposed in the first set the interconnection and damping matrices do not appear explicitly which makes it more difficult to directly manipulate those matrices by requiring the system to have no uncontrollable pole at s 0 the second set of lmis explicitly containing the interconnection and damping matrices can be obtained taking into account the physical properties of the system some prespecified structures can be imposed directly on those matrices

the intrinsic normal cone let x be an algebraic stack in the sense of deligne mumford we construct a purely 0 dimensional algebraic stack over x in the sense of artin the intrinsic normal cone frak c x the notion of perfect obstruction theory for x is introduced and it is shown how to construct given a perfect obstruction theory for x a pure dimensional virtual fundamental class in the chow group of x we then prove some properties of such classes both in the absolute and in the relative context via a deformation theory interpretation of obstruction theories we prove that several kinds of moduli spaces carry a natural obstruction theory and sometimes a perfect one

on the matching equations of energy shaping controllers for mechanical systems total energy shaping is a controller design methodology that achieves asymptotic stabilisation of mechanical systems endowing the closed loop system with a lagrangian or hamiltonian structure with a desired energy function the success of the method relies on the possibility of solving two partial differential equations pdes which identify the kinetic and potential energy functions that can be assigned to the closed loop particularly troublesome is the pde associated to the kinetic energy ke which is quasi linear and non homogeneous and the solution that defines the desired inertia matrix must be positive definite this task is simplified by the inclusion of gyroscopic forces in the target dynamics which translates into the presence of a free skew symmetric matrix in the ke matching equation that reduces the number of pdes to be solved recently it has been claimed that considering a more general form for the target dynamic forces that relax the skew symmetry condition further reduces the number

brief matching linear systems and the ball and beam a recent approach to the control of underactuated systems is to look for control laws which will induce some specified structure on the closed loop system in this paper we describe one matching condition and an approach for finding all control laws that fit the condition after an analysis of the resulting control laws for linear systems we present the results from an experiment on a nonlinear ball and beam system

winding number constrained contour detection salient contour detection can benefit from the integration of both contour cues and region cues however this task is difficult due to different nature of region representations and contour representations to solve this problem this paper proposes an energy minimization framework based on winding number constraints in this framework both region cues such as color texture homogeneity and contour cues such as local contrast and continuity are represented in a joint objective function which has both region and contour labels the key problem is how to design constraints that ensure the topological consistency of the two kinds of labels our technique is based on the topological concept of winding number using a fast method for winding number computation a small number of linear constraints are derived to ensure label consistency our method is instantiated by ratio based energy functions by successfully integrating both region and contour cues our method shows advantages over competitive methods our method is extended to incorporate user interaction which leads to further improvements

birational geometry of fano hypersurfaces of index two we prove that every non trivial structure of a rationally connected fibre space on a generic in the sense of zariski topology hypersurface v of degree m in the m 1 dimensional projective space for m ge 16 is given by a pencil of hyperplane sections in particular the variety v is non rational and its group of birational self maps coincides with the group of biregular automorphisms and for that reason is trivial the proof is based on the techniques of the method of maximal singularities and inversion of adjunction

on feedback equivalence to port controlled hamiltonian systems in the last few years port controlled hamiltonian pch systems have emerged as an interesting class of nonlinear models suitable for a large number of physical applications in this paper we study the question of feedback equivalence of nonlinear systems to pch systems more precisely we give conditions under which a general nonlinear system can be transformed into a pch system via static state feedback we consider the two extreme cases where the target pch system is completely a priori fixed or completely free as well as the case where it is only partially predetermined when the energy function is free a set of partial differential equations needs to be solved on the other hand if it is fixed we have to deal with a set of algebraic equations in the former case we give some verifiable necessary and sufficient conditions for solvability as a by product of our analysis we obtain some stabilization results for nonlinear systems

bloch s conjecture for catanese and barlow surfaces catanese surfaces are regular surfaces of general type with pg 0 they specialize to double covers of barlow surfaces we prove that the ch0 group of a catanese surface is equal to z which implies the same result for the barlow surfaces

control of nonlinear underactuated systems in this paper we introduce a new method to design control laws for nonlinear underactuated systems our method produces an infinite dimensional family of control laws whereas most control techniques only produce a finite dimensional family these control laws each come with a natural lyapunov function the inverted pendulum cart is used as an example in addition we construct an abstract system that is open loop unstable and cannot be stabilized using any linear control law and demonstrate that our method produces a stabilizing control law 2000 john wiley sons inc

reduction of controlled lagrangian and hamiltonian systems with symmetry we develop reduction theory for controlled lagrangian and controlled hamiltonian systems with symmetry reduction theory for these systems is needed in a variety of examples such as a spacecraft with rotors a heavy top with rotors and underwater vehicle dynamics one of our main results shows the equivalence of the method of reduced controlled lagrangian systems and that of reduced controlled hamiltonian systems in the case of simple mechanical systems with symmetry

control via interconnection and damping assignment of linear time invariant systems a tutorial interconnection and damping assignment is a controller design methodology that regulates the behaviour of dynamical systems assigning a desired port hamiltonian structure to the closed loop a key step for the application of the method is the solution of the so called matching equation that in the case of nonlinear systems is a partial differential equation it has recently been shown that for linear systems the problem boils down to the solution of a linear matrix inequality that moreover is feasible if and only if the system is stabilisable making the method universally applicable it has also been shown that if we narrow the class of assignable structures e g to mechanical instead of the larger port hamiltonian the problem is still translated to a linear matrix inequality but now stabilisability is not sufficient to ensure its feasibility it is additionally required that the uncontrolled modes are simple and lie on the j axis which is consistent with the considered scenario of mechanical

stabilization of systems with one degree of underactuation with energy shaping a geometric approach a geometric formulation for stabilization of systems with one degree of underactuation which fully solves the energy shaping problem for these system is given the results show that any linearly controllable simple mechanical system with one degree of underactuation is stabilizable by energy shaping even in the absence of gyroscopic force via a closed loop metric which is not necessarily positive definite an example of a system with one degree of underactuation is provided for which the stabilization by energy shaping method is not achievable in the absence of gyroscopic forces using a positive definite closed loop metric

log fano varieties over function fields of curves consider a smooth log fano variety over the function field of a curve suppose that the boundary has positive normal bundle choose an integral model over the curve then integral points are zariski dense after removing an explicit finite set of points on the base curve

power balancing for a new class of non linear systems and stabilization of rlc circuits in this paper the method of power shaping as recently introduced for the stabilization of non linear rlc circuits is generalized to a larger class of systems showing similarities and important differences with the class of port controlled hamiltonian systems other than for port controlled hamiltonian systems the stabilization of these new systems is not stymied by a dissipation obstacle and in fact every power shaping controller is power balancing as well it is shown that the power shaping controller can be realized as a port controlled hamiltonian system connected by means of a gyrator to the plant the theoretical results are applied to the class of non linear rlc circuits described by brayton moser s equations and a physical implementation of the controllers in terms of standard electrical circuit elements is given

graph partitioning active contours gpac for image segmentation in this paper we introduce new types of variational segmentation cost functions and associated active contour methods that are based on pairwise similarities or dissimilarities of the pixels as a solution to a minimization problem we introduce a new curve evolution framework the graph partitioning active contours gpac using global features our curve evolution is able to produce results close to the ideal minimization of such cost functions new and efficient implementation techniques are also introduced in this paper our experiments show that gpac solution is effective on natural images and computationally efficient experiments on gray scale color and texture images show promising segmentation results

controller design for mechanical systems with underactuation degree one based on controlled lagrangians method this article extends controller design based on the controlled lagrangians method from two to n degrees of freedom dof mechanical systems with underactuation degree one importantly a new kinetic energy equation k equation is found from which the gyroscopic forces are separated due to the use of their property further along with them chosen as an explicit solution the other k equations are satisfied for any regular controlled kinetic energy as our main contribution a sufficient matching condition is obtained which comprises the new k equation and one p equation potential energy equation cascaded the regular condition and the explicit gyroscopic forces accordingly the matching condition has an advantage for the fewest partial differential equations pdes to be solved and the explicit gyroscopic forces with all unknown functions of the controlled kinetic energy the new k equation can be simplified further under some choices on these functions and or assumptions on specific original systems