feedback boundary control of linear hyperbolic systems with relaxation we consider boundary stabilization for one dimensional systems of linear hyperbolic partial differential equations with relaxation structure such equations appear in many applications by combining weighted lyapunov functions the structure is used to derive new stabilization results the result is illustrated with an application to boundary stabilization of water flows in open canals

optimal control of the free boundary in a two phase stefan problem we present an optimal control approach for the solidification process of a melt in a container the process is described by a two phase stefan problem with the free boundary interface between the two phases modelled as a graph we control the evolution of the free boundary using the temperature on the container wall the control goal consists in tracking a prescribed evolution of the free boundary we achieve this goal by minimizing a appropriate cost functional the resulting minimization problem is solved numerically by a steepest descent method with step size control where the gradient of the cost functional is expressed in terms of the adjoint variables several numerical examples are presented which illustrate the performance of the method the novelty of the approach presented consists in using a sharp interface model for the control of the free boundary this guarantees direct access to the free boundary as optimization variable in terms of its parametrization as a graph moreover at any stage of the optimization process the physical laws constituted by the mathematical model are conserved and the heat flux into the free boundary is variable and thus does not need to be specified a priori in the optimization process this guarantees more flexibility than in the optimization approaches to two phase stefan problems taken so far

extension of hereditary symmetry operators two models of candidates for hereditary symmetry operators are proposed and thus many nonlinear systems of evolution equations possessing infinitely many commuting symmetries may be generated some concrete structures of hereditary symmetry operators are carefully analysed on the basis of the resulting general conditions and several corresponding nonlinear systems are explicitly given as illustrative examples

the attractor basin portrait of a cellular automaton local space time structures such as domains and the intervening dislocations dominate a wide class of cellular automaton ca behavior for such spatially extended dynamics regular domains vicinities and attractors are introduced as organizing principles to identify the discretized analogs of attractors basins and separatrices structures used in classifying dissipative continuous state dynamical systems we describe the attractor basin portrait of nonlinear elementary ca rule 18 whose global dynamics is largely determined by a single regular attracting domain the latter s basin is analyzed in terms of subbasin and portal structures associated with particle annihilation the conclusion is that the computational complexity of such ca is more apparent than real transducer machines are constructed that automatically identify domain and dislocation structures in space time count the number of dislocations in a spatial pattern and implement an isomorphism between rule 18 and rule 90 we use a transducer to trace dislocation trajectories and confirm that in rule 18 isolated dislocation trajectories as well as a dislocation gas agree extremely well with the classical model of annihilating diffusive particles the ca efficiently transforms randomness of an initial pattern ensemble into a random walk of dislocations in space time

luenberger boundary observer synthesis for sturm liouville systems a static luenberger observer of a system with sturm liouville operator is synthesised with the aid of a boundary control formulation to this aim approximate observability detectability and stability of the system is studied and design results are worked out for a typical biochemical case study

boundary optimal lq control of coupled hyperbolic pdes and odes this contribution addresses the development of a linear quadratic lq regulator for a set of hyperbolic pdes coupled with a set of odes through the boundary the approach is based on an infinite dimensional hilbert state space description of the system and the well known operator riccati equation ore in order to solve the optimal control problem the ore is converted to a set of matrix riccati equations the feedback operator is found by solving the resulting matrix riccati equations the performance of the designed control policy is assessed by applying it to a system of interconnected continuous stirred tank reactor cstr and a plug flow reactor pfr through a numerical simulation

state and output feedback boundary control for a coupled pde ode system abstract this note is devoted to stabilizing a coupled pde ode system with interaction at the interface first a state feedback boundary controller is designed and the system is transformed into an exponentially stable pde ode cascade with an invertible integral transformation where pde backstepping is employed moreover the solution to the resulting closed loop system is derived explicitly second an observer is proposed which is proved to exhibit good performance in estimating the original coupled system and then an output feedback boundary controller is obtained for both the state and output feedback boundary controllers exponential stability analyses in the sense of the corresponding norms for the resulting closed loop systems are provided the boundary controller and observer for a scalar coupled pde ode system as well as the solutions to the closed loop systems are given explicitly

explorations of the extended nckp hierarchy a recently obtained extension xnckp of the moyal deformed kp hierarchy nckp hierarchy by a set of evolution equations in the moyal deformation parameters is further explored formulae are derived to compute these equations efficiently reductions of the xnckp hierarchy are treated in particular to the extended nckdv and ncboussinesq hierarchies furthermore a good part of the sato formalism for the kp hierarchy is carried over to the generalized framework in particular the well known bilinear identity theorem for the kp hierarchy expressed in terms of the formal baker akhiezer function extends to the xnckp hierarchy moreover it is demonstrated that n soliton solutions of the nckp equation are also solutions of the first few deformation equations this is shown to be related to the existence of certain families of algebraic identities

principal geodesic analysis for the study of nonlinear statistics of shape a primary goal of statistical shape analysis is to describe the variability of a population of geometric objects a standard technique for computing such descriptions is principal component analysis however principal component analysis is limited in that it only works for data lying in a euclidean vector space while this is certainly sufficient for geometric models that are parameterized by a set of landmarks or a dense collection of boundary points it does not handle more complex representations of shape we have been developing representations of geometry based on the medial axis description or m rep while the medial representation provides a rich language for variability in terms of bending twisting and widening the medial parameters are not elements of a euclidean vector space they are in fact elements of a nonlinear riemannian symmetric space in this paper we develop the method of principal geodesic analysis a generalization of principal component analysis to the manifold setting we demonstrate its use in describing the variability of medially defined anatomical objects results of applying this framework on a population of hippocampi in a schizophrenia study are presented

optimal control of the classical two phase stefan problem in level set formulation optimal control motion planning of the free interface in classical two phase stefan problems is considered the evolution of the free interface is modeled by a level set function the first order optimality system is derived on a formal basis it provides gradient information based on the adjoint temperature and adjoint level set function suitable discretization schemes for the forward and adjoint systems are described numerical examples verify the correctness and flexibility of the proposed scheme

infinite dimensional luenberger like observers for a rotating body beam system the paper proposes luenberger like observers for a rotating body beam system the latter is described by a partial differential equation and its dynamic is governed a unitary group the observers proposed in the paper are able to reconstitute the dynamic evolution of the beam profile by measuring the moment force on the boundary only meanwhile we propose a reliable numerical scheme based on a finite element method in order to simulate the observation system and the observers the efficiency of our proposed scheme and the performances of the observers are illustrated with numerical simulation results

an adaptive observer design for n 1 coupled linear hyperbolic pdes based on swapping in this paper we use swapping design filters to bring systems of n 1 partial differential equations of the hyperbolic type to static form standard parameter identification laws can then be applied to estimate unknown parameters in the boundary conditions proof of boundedness of the adaptive laws are offered and the results are demonstrated in simulations

on the structure of 2 1 dimensional commutative and noncommutative integrable equations we develop the symbolic representation method to derive the hierarchies of 2 1 dimensional integrable equations from the scalar lax operators and to study their properties globally the method applies to both commutative and noncommutative cases in the sense that the dependent variable takes its values in c or a noncommutative associative algebra we prove that these hierarchies are indeed quasi local in the commutative case as conjectured by mikhailov and yamilov j phys a 31 6707 1998 we propose a ring extension in the noncommutative case based on the symbolic representation as examples we give noncommutative versions of kadomtsev petviashvili kp modified kadomtsev petviashvili mkp and boussinesq equations

universality and complexity in cellular automata abstract cellular automata are discrete dynamical systems with simple construction but complex self organizing behaviour evidence is presented that all one dimensional cellular automata fall into four distinct universality classes characterizations of the structures generated in these classes are discussed three classes exhibit behaviour analogous to limit points limit cycles and chaotic attractors the fourth class is probably capable of universal computation so that properties of its infinite time behaviour are undecidable

a universal prior for integers and estimation by minimum description length of the number of bits required to write down the observed data has been reformulated to extend the classical maximum likelihood principle the principle permits estimation of the number of the parameters in statistical models in addition to their values and even of the way the parameters appear in the models i e of the model structures the principle rests on a new way to interpret and construct a universal prior distribution for the integers which makes sense even when the parameter is an individual object truncated realvalued parameters are converted to integers by dividing them by their precision and their prior is determined from the universal prior for the integers by optimizing the precision 1 introduction in this paper we study estimation based upon the principle of minimizing the total number of binary digits required to rewrite the observed data when each observation is given with some precision instead of attempting at an absolutely shortest description which would be futile we look for the optimum relative to a class of parametrically given distributions this minimum description length mdl principle which we introduced in a less comprehensive form in 25 turns out to degenerate to the more familiar maximum likelihood ml principle in case the number of parameters in the models is fixed so that the description length of the parameters themselves can be ignored in another extreme case where the parameters determine the data it similarly degenerates to jaynes s principle of maximum entropy 14 but the main power of the new criterion is that it permits estimates of the entire model its parameters their number and even the way the parameters appear in the model i e the model structure hence there will be no need to supplement the estimated parameters with a separate hypothesis test to decide whether a model is adequately parameterized or perhaps over parameterized

with a cole hopf transformation to solutions of the noncommutative kp hierarchy in terms of wronski matrices in the case of the kp hierarchy where the dependent variable takes values in an arbitrary associative algebra it is known that there are solutions which can be expressed in terms of quasideterminants of a wronski matrix which solves the linear heat hierarchy we obtain these solutions without the help of quasideterminants in a simple way via solutions of matrix kp hierarchies over and by use of a cole hopf transformation for this class of exact solutions we work out a correspondence with weakly nonassociative algebras

lie algebraic approach to the construction of 2 1 dimensional lattice field and field integrable hamiltonian equations two different methods for the construction of 2 1 dimensional integrable lattice field and field hamiltonian dynamical systems are presented the first method is based on the so called central extension procedure applied to the lie algebra of shift operators and the lie algebra of pseudodifferential operators the second method is the so called operand formalism both methods allow a construction of some new integrable nonlinear hamiltonian lattice field and field equations in 2 1 dimensional space

physics like models of computation abstract reversible cellular automata are computer models that embody discrete analogues of the classical physics notions of space time locality and microscopic reversibility they are offered as a step towards models of computation that are closer to fundamental physics

the geometrically invariant form of evolution equations we study the evolution of geometric invariants for equations such as the davey stewartson and novikov veselov equations

resonance and web structure in discrete soliton systems the two dimensional toda lattice and its fully discrete and ultra discrete analogues we present a class of solutions of the two dimensional toda lattice equation its fully discrete analogue and its ultra discrete limit these solutions demonstrate the existence of soliton resonance and web like structure in discrete integrable systems such as differential difference equations difference equations and cellular automata ultra discrete equations

hamiltonian theory over noncommutative rings and integrability in multidimensions a generalization of the adler gel fand dikii scheme is used to generate bi hamiltonian structures in two spatial dimensions in order to implement this scheme a hamiltonian theory is built over a noncommutative ring namely the ring of formal pseudodifferential operators bi hamiltonian structures generated in this way can be used for the kadomtsev petviashvili equation as well as other integrable equations in 2 1

nijenhuis g manifolds and lenard bicomplexes a new approach to kp systems we suggest a method to extend the theory of recursion operators to integrable hamiltonian systems in two space dimensions like kp systems the approach aims to stress the conceptual unity of the theories in one and two space dimensions a sound explanation of the appearance of bilocal operators is also given

control of continuum models of production systems a production system which produces a large number of items in many steps can be modelled as a continuous flow problem the resulting hyperbolic partial differential equation pde typically is nonlinear and nonlocal modeling a factory whose cycle time depends nonlinearly on the work in progress one of the few ways to influence the output of such a factory is by adjusting the start rate in a time dependent manner we study two prototypical control problems for this case i demand tracking where we determine the start rate that generates an output rate which optimally tracks a given time dependent demand rate and ii backlog tracking which optimally tracks the cumulative demand the method is based on the formal adjoint method for constrained optimization incorporating the hyperbolic pde as a constraint of a nonlinear optimization problem we show numerical results on optimal start rate profiles for steps in the demand rate and for periodically varying demand rates and discuss the influence of the nonlinearity of the cycle time on the limits of the reactivity of the production system differences between perishable and non perishable demand demand versus backlog tracking are highlighted

an inversion formula for recursion operator of kp hierarchy an inversion formula is established for the recursion operator of the kp hierarchy the formula explains in part how operators y i are cancelled each other in certain combination of i y j that is essential for generating the kp hierarchy

recursion operators and conservation laws for discrete lax equations in this paper a method for constructing recursion operator of discrete lax equations is proposed to illustrate the method recursion operators for discrete boussinesq equation and discrete kdv equation are obtained then the recursion operators of continuous boussinesq equation and kdv equation are successfully recovered by the discrete ones infinitely many conservation laws of discrete boussinesq equation are constructed by the discrete residue formula and the first three conserved quantities are given explicitly and verified numerically existence of recursion operators and infinite number of conservation laws proves the integrability of the discrete lax equations

the hamiltonian structure of the 2 1 dimensional ablowitz kaup newell segur hierarchy by considering hamiltonian theory over a suitable noncommutative ring the nonlinear evolution equations of the ablowitz kaup newell segur 2 1 hierarchy are incorporated into a hamiltonian framework and a modified lenard scheme

poisson and hamiltonian superpairs over polarized associative algebras a poisson superpair is a pair of poisson superalgebra structures on a supercommutative associative algebra whose any linear combination is also a poisson superalgebra structure in this paper we first construct certain linear and quadratic poisson superpairs over a semi finitely filtered polarized 2 graded associative algebra then we give a construction of certain hamiltonian superpairs in the formal variational calculus over any finite dimensional 2 graded associative algebra with a supersymmetric nondegenerate associative bilinear form our constructions are based on the adler mapping in a general sense our results in this paper can be viewed as noncommutative generalizations of the adler gel fand dikii hamiltonian pair

on construction of recursion operators from lax representation in this work we develop a general procedure for constructing the recursion operators for nonlinear integrable equations admitting lax representation several new examples are given in particular we find the recursion operators for some kdv type systems of integrable equations

on the theory of recursion operator the general structure and properties of recursion operators for hamiltonian systems with a finite number and with a continuum of degrees of freedom are considered weak and strong recursion operators are introduced the conditions which determine weak and strong recursion operators are found

multiscale medial loci and their properties blum s medial axes have great strengths in principle in intuitively describing object shape in terms of a quasi hierarchy of figures but it is well known that derived from a boundary they are damagingly sensitive to detail in that boundary the development of notions of spatial scale has led to some definitions of multiscale medial axes different from the blum medial axis that considerably overcame the weakness three major multiscale medial axes have been proposed iteratively pruned trees of voronoi edges ogniewicz 1993 szekely 1996 naf 1996 shock loci of reaction diffusion equations kimia et al 1995 siddiqi and kimia 1996 and height ridges of medialness cores fritsch et al 1994 morse et al 1993 pizer et al 1998 these are different from the blum medial axis and each has different mathematical properties of generic branching and ending properties singular transitions and geometry of implied boundary and they have different strengths and weaknesses for computing object descriptions from images or from object boundaries these mathematical properties and computational abilities are laid out and compared and contrasted in this paper

algebraic structure of the gradient holonomic algorithm for lax integrable nonlinear dynamical systems i the algebraic structure of the gradient holonomic algorithm for lax integrable dynamical systems is discussed a generalization of the r structure approach for the case of operator valued affine lie algebras is used to prove the bi hamiltonian formulation of nonlinear integrable dynamical systems in multidimensions the monodromy transfer matrix is constructed to describe the operator manifold in relation to canonical lie poisson bracket on initial affine lie algebra with gauge central extension as an illustration the two dimensional operator benney kaup integrable hierarchy is considered and their bi hamiltonicity is proved

hierarchic voronoi skeletons abstract robust and time efficient skeletonization of a planar shape which is connectivity preserving and based on euclidean metrics can be achieved by first regularizing the voronoi diagram vd of a shape s boundary points i e by removal of noise sensitive parts of the tessellation and then by establishing a hierarchic organization of skeleton constituents each component of the vd is attributed with a measure of prominence which exhibits the expected invariance under geometric transformations and noise the second processing step a hierarchic clustering of skeleton branches leads to a multiresolution representation of the skeleton termed skeleton pyramid

soliton cellular automata abstract we study the evolution of an arbitrary initial configuration of a certain filter cellular automaton introduced by park steiglitz and thurston any given state can be thought of as a collection of particles we find that a the interaction properties of these particles are richer than the usual solitons in particular periodic particles may interact solitonically or they may recombine to form new periodic configurations even if two particles interact solitonically they may interact several times before they get separated with the faster particle moving to the left of the slower one b arbitrary initial data will decompose as t into a number of periodic particles and into a number of certain new periodic coherent structures which we call breathers the particles and the breathers are ordered according to their speed c we formulate the above cellular automaton as a difference equation this formulation implies that the coherent structures found here are a manifestation of the coupling between the linear part and the nonlinear part of the difference equation

feedback stabilization for the mass balance equations of an extrusion process in this article we study the stabilization problem for an extrusion process in the isothermal case the model expresses the mass conservation in the extruder chamber and consists of a hyperbolic partial differential equation pde and a nonlinear ordinary differential equation ode whose dynamics describes the evolution of a moving interface by using a lyapunov approach we obtain the exponential stabilization for the closed loop system under natural feedback controls through indirect measurements numerical simulations are also provided with a comparison between the proposed approach and linear pi feedback controller

untangling the blum medial axis transform for over 30 years blum s medial axis transform mat has proven to be an intriguing tool for analyzing and computing with form but it is one that is notoriously difficult to apply in a robust and stable way it is well documented how a tiny change to an object s boundary can cause a large change in its mat there has also been great difficulty in using the mat to decompose an object into a hierarchy of parts reflecting the natural parts hierarchy that we perceive this paper argues that the underlying cause of these problems is that medial representations embody both the substance of each part of an object and the connections between adjacent parts a small change in an object s boundary corresponds to a small change in its substance but may involve a large change in its connection information the problems with blum s mat are generated because it does not explicitly represent this dichotomy of information to use the blum mat to it s full potential this paper presents a method for separating the substance and connection information of an object this provides a natural parts hierarchy while eliminating instabilities due to small boundary changes the method also allows for graded fuzzy classifications of object parts to match the ambiguity in human perception of many objects

symmetries and reductions on the noncommutative kadomtsev petviashvili and gelfand dickey hierarchies in this paper we construct the additional flows of the noncommutative kadomtsev petviashvili kp hierarchy and the additional symmetry flows constitute an infinite dimensional lie algebra w1 in addition the generating function of the additional symmetries can also be proved to have a nice form in terms of wave functions and this generating symmetry is used to construct the noncommutative kp hierarchy with self consistent sources and the constrained noncommutative kp hierarchy the above results will be further generalized to the noncommutative gelfand dickey hierarchies which contain many interesting noncommutative integrable systems such as the noncommutative kdv hierarchy and noncommutative boussinesq hierarchy meanwhile we construct two new noncommutative systems including odd noncommutative c type gelfand dickey and even noncommutative c type gelfand dickey hierarchies also using the symmetry we can construct a new noncommutative gelfand dickey hierarchy with self consistent sources based on the natural differential lax operator of the noncommutative gelfand dickey hierarchy the string equations of the noncommutative gelfand dickey hierarchy are also derived in this paper we construct the additional flows of the noncommutative kadomtsev petviashvili kp hierarchy and the additional symmetry flows constitute an infinite dimensional lie algebra w1 in addition the generating function of the additional symmetries can also be proved to have a nice form in terms of wave functions and this generating symmetry is used to construct the noncommutative kp hierarchy with self consistent sources and the constrained noncommutative kp hierarchy the above results will be further generalized to the noncommutative gelfand dickey hierarchies which contain many interesting noncommutative integrable systems such as the noncommutative kdv hierarchy and noncommutative boussinesq hierarchy meanwhile we construct two new noncommutative systems including odd noncommutative c type gelfand dickey and even noncommutative c type gelfand dickey hierarchies also using the symmetry we can construct a new noncommutative gelfand dickey hierarchy with self consistent sources based o

observer design for a class of nonlinear ode pde cascade systems abstract the problem of state observation is addressed for nonlinear systems that can be modeled by an ode pde series association the ode subsystem assumes a triangular structure while the pde element is of heat diffusion type the aim is to accurately estimate online the state vector of the ode subsystem and the distributed state of the pde element one major difficulty is that the state observation must only rely on the global system output i e the pde state at the terminal boundary in particular the connection point between the ode and the pde blocks is not accessible to measurements the observation problem is dealt with by designing a high gain type observer sufficient conditions involving the pde domain length are formally established that ensure the observer exponential convergence

control of homodirectional and general heterodirectional linear coupled hyperbolic pdes research on stabilization of coupled hyperbolic pdes has been dominated by the focus on pairs of counter convecting heterodirectional transport pdes with distributed local coupling and with controls at one or both boundaries a recent extension allows stabilization using only one control for a system containing an arbitrary number of coupled transport pdes that convect at different speeds against the direction of the pde whose boundary is actuated in this paper we present a solution to the fully general case in which the number of pdes in either direction is arbitrary and where actuation is applied on only one boundary to all the pdes that convect downstream from that boundary to solve this general problem we solve as a special case the problem of control of coupled homodirectional hyperbolic linear pdes where multiple transport pdes convect in the same direction with arbitrary local coupling our approach is based on pde backstepping and yields solutions to stabilization by both full state and observer based output feedback and trajectory tracking problems

soliton turbulence in one dimensional cellular automata abstract statistical properties of cellular automata which support simple solitary waves are numerically studied under these rules spatio temporal patterns are sensitively dependent on the collision processes of solitons and other elementary excitations such as breathers kinks and nuclei patterns typically become randomized as collisions proceed turbulent states are realized after many collisions the resulting global patterns can be classified by the types of elementary excitations they contain in many turbulent states the spectra reveal a long range order with a k v anomaly for k 1 the irreversible process leading to turbulent equilibrium is characterized by the transient spectrum together with the allan variance the mean free motion of a soliton in the turbulent states is measured by the mutual information flow and the information loss is shown to obey an inverse power law the transient time to reach an attractor grows exponentially with system size which suggests that in the thermodynamic limit soliton turbulence is not an attractor but rather a transient state

dissipation inequalities for the analysis of a class of pdes in this paper we develop dissipation inequalities for a class of well posed systems described by partial differential equations pdes we study passivity reachability induced input output norm boundedness and input to state stability iss we consider both cases of in domain and boundary inputs and outputs we study the interconnection of pde pde systems and formulate small gain conditions for stability for pdes polynomial in dependent and independent variables we demonstrate that sum of squares sos programming can be used to compute certificates for each property therefore the solution to the proposed dissipation inequalities can be obtained via semi definite programming the results are illustrated with examples

state and observer based feedback control of normal flow equations abstract we investigate wellposedness and stability of normal flow equations with two different control schemes the first one considers the velocity field as a control action and relies on a proportional regulator that is proved to be stable in the second one control acts on the source term and is based on an observer providing an estimate of the gradient of the normal flow solution convergence properties are demonstrated in this case numerical results are presented to show the effectiveness of the proposed approaches

medial based deformable models in nonconvex shape spaces for medical image segmentation we explore the application of genetic algorithms ga to deformable models through the proposition of a novel method for medical image segmentation that combines ga with nonconvex localized medial based shape statistics we replace the more typical gradient descent optimizer used in deformable models with ga and the convex implicit global shape statistics with nonconvex explicit localized ones specifically we propose ga to reduce typical deformable model weaknesses pertaining to model initialization pose estimation and local minima through the simultaneous evolution of a large number of models furthermore we constrain the evolution and thus reduce the size of the search space by using statistically based deformable models whose deformations are intuitive stretch bulge bend and are driven in terms of localized principal modes of variation instead of modes of variation across the entire shape that often fail to capture localized shape changes although ga are not guaranteed to achieve the global optima our method compares favorably to the prevalent optimization techniques convex nonconvex gradient based optimizers and to globally optimal graph theoretic combinatorial optimization techniques when applied to the task of corpus callosum segmentation in 50 mid sagittal brain magnetic resonance images

on parameter estimation using level sets consider the problem of selecting the member of a parametrized family of curves that best matches a given curve this is a key step in determining proper values for adjustable parameters in low order plasma etching and deposition models level set methods offer several attractive features for treating such problems this paper presents a parameter estimation scheme that exploits the level set formulation the method is completely geometric there is no need to introduce an arbitrary coordinate system for the curves analytic results necessary for the application of gradient descent algorithms are derived and some preliminary numerical results are presented

backstepping forwarding control and observation for hyperbolic pdes with fredholm integrals an integral transform is introduced which allows the construction of boundary controllers and observers for a class of first order hyperbolic pides with fredholm integrals these systems do not have a strict feedback structure and thus the standard backstepping approach cannot be applied sufficient conditions for the existence of the backstepping forwarding transform are given in terms of spectral properties of some integral operators and more conservatively but easily verifiable in terms of the norms of the coefficients in the equations an explicit transform is given for particular coefficient structures in the case of strict feedback systems the procedure detailed in this paper reduces to the well known backstepping design the results are illustrated with numerical simulations

asymptotic behaviour of contraction non autonomous semi flows in a banach space the asymptotic behaviour is studied for a class of non autonomous infinite dimensional non linear dissipative systems this is achieved by using the concept of contraction semi flow which is a generalization of contraction non linear semigroup conditions are presented under which the solution of the abstract differential equation converges to the omega limit set the equilibrium profile respectively the general development is applied to semi linear systems with time varying non linearity asymptotic behaviour and stability criteria are established on the basis of the conditions given in the early portion of the paper the theoretical results are applied to a general class of first order hyperbolic time varying semi linear pdes

extraction of the euclidean skeleton based on a connectivity criterion abstract the skeleton is essential for general shape representation the commonly required properties of a skeletonization algorithm are that the extracted skeleton should be accurate robust to noise position and rotation able to reconstruct the original object and able to produce a connected skeleton in order to preserve its topological and hierarchical properties however the use of a discrete image presents a lot of problems that may influence the extraction of the skeleton moreover most of the methods are memory intensive and computationally intensive and require a complex data structure in this paper we propose a fast efficient and accurate skeletonization method for the extraction of a well connected euclidean skeleton based on a signed sequential euclidean distance map a connectivity criterion is proposed which can be used to determine whether a given pixel is a skeleton point independently the criterion is based on a set of point pairs along the object boundary which are the nearest contour points to the pixel under consideration and its 8 neighbors our proposed method generates a connected euclidean skeleton with a single pixel width without requiring a linking algorithm or iteration process experiments show that the runtime of our algorithm is faster than the distance transformation and is linearly proportional to the number of pixels of an image

hamiltonian structure of dubrovin s equation of associativity in 2 d topological field theory a third order monge ampere type equation of associativity that dubrovin has obtained in 2 d topological field theory is formulated in terms of a variational principle subject to second class constraints using dirac s theory of constraints this degenerate lagrangian system is cast into hamiltonian form and the hamiltonian operator is obtained from the dirac bracket there is a new type of kac moody algebra that corresponds to this hamiltonian operator in particular it is not a w algebra

alternative bi hamiltonian structures for wdvv equations of associativity the wdvv equations of associativity in two dimensional topological field theory are completely integrable third order monge ampere equations which admit bi hamiltonian structure the time variable plays a distinguished role in the discussion of hamiltonian structure whereas in the theory of wdvv equations none of the independent variables merits such a distinction wdvv equations admit very different alternative hamiltonian structures under different possible choices of the time variable but all these various hamiltonian formulations can be brought together in the framework of the covariant theory of symplectic structure they can be identified as different components of the covariant witten zuckerman symplectic 2 form current density where a variational formulation of the wdvv equation that leads to the hamiltonian operator through the dirac bracket is available

algebraic structure of the gradient holonomic algorithm for lax integrable nonlinear dynamical systems ii the reduction via dirac and canonical quantization procedure the generalized theory of the r structure on affine operator lie algebras is used to construct a complete theory of lax integrable nonlinear dynamical systems in multidimensions the operator bi hamiltonian structures and their functional reductions are discussed in great detail in the examples of operator korteweg de vries and benney kaup dynamical systems as an important by product of the developed algebraic theory the dirac canonical quantization problem is solved almost completely for the neumann bogoliubov type oscillatory dynamical system on spheres associated via moser with the spectral moment map on an affine associative metrized lie coalgebra with a one parameter gauge two cocycle some remarks are given on the problem of extending the developed algebraic theory to the case of lax integrable dynamical systems on discrete manifolds

the groupwise medial axis transform for fuzzy skeletonization and pruning medial representations of shapes are useful due to their use of an object centered coordinate system that directly captures intuitive notions of shape such as thickness bending and elongation however it is well known that an object s medial axis transform mat is unstable with respect to small perturbations of its boundary this instability results in additional unwanted branches in the skeletons which must be pruned in order to recover the portions of the skeletons arising purely from the uncorrupted shape information almost all approaches to skeleton pruning compute a significance measure for each branch according to some heuristic criteria and then prune the least significant branches first current approaches to branch significance computation can be classified as either local solely using information from a neighborhood surrounding each branch or global using information about the shape as a whole in this paper we propose a third groupwise approach to branch significance computation we develop a groupwise skeletonization framework that yields a fuzzy significance measure for each branch derived from information provided by the group of shapes we call this framework the groupwise medial axis transform g mat we propose and evaluate four groupwise methods for computing branch significance and report superior performance compared to a recent leading method we measure the performance of each pruning algorithm using denoising classification and within class skeleton similarity measures this research has several applications including object retrieval and shape analysis

infinite dimensional and reduced order observers for burgers equation obtaining a representative model in feedback control system design problems is a key step and is generally a challenge for spatially continuous systems it becomes more difficult as the dynamics is infinite dimensional and the well known techniques of systems and control engineering are difficult to apply directly in this paper observer design is reported for one dimensional burgers equation which is a non linear partial differential equation an infinite dimensional form of the observer is demonstrated to converge asymptotically to the target dynamics and proper orthogonal decomposition is used to obtain the reduced order observer when this is done the corresponding observer is shown to be successful under certain circumstances the paper unfolds the connections between target dynamics observer and their finite dimensional counterparts a set of simulation results has been presented to justify the theoretical claims of the paper

soliton like behavior in automata abstract we propose a new kind of automaton that uses newly computed site values as soon as they are available we call them filter automata fa they are analogous to infinite impulse response iir digital filters whereas the usual cellular automata ca correspond to finite impulse response fir digital filters it is shown that as a class the fa s are equivalent to ca s in the sense that the same array of space generation values can be produced they must be generated in a different order however a particular class of irreversible totalistic fa s are described that support a profusion of persistent structures that move at different speeds and these particle like patterns collide in nondestructive ways they often pass through one another with nothing more than a phase jump much like the solitons that arise in the solution of certain nonlinear differential equations histograms of speed displacement and period are given for neighborhood radii from 2 to 6 and particles with generators up to 16 bits wide we then present statistics for neighborhood radii 2 to 9 which show that collisions which preserve the identity of particles are very common

disturbance rejection in 2 x 2 linear hyperbolic systems many interesting problems in the oil and gas industry face the challenge of responding to disturbances from afar typically the disturbance occurs at the inlet of a pipeline or the bottom of an oil well while sensing and actuation equipment is installed at the outlet only kilometers away from the disturbance the present paper develops an output feedback control law for such cases based on modelling the transport phenomenon as a 2 times 2 linear partial differential equation pde of hyperbolic type and the disturbance as a finite dimensional linear system affecting the left boundary of the pde sensing and actuation are co located at the right boundary of the pde the design provides a separation principle allowing a disturbance attenuating full state feedback control law to be combined with an observer the results are applied to a relevant problem from the oil and gas industry and demonstrated in simulations

improving skeletal shape abstraction using multiple optimal solutions shape abstraction is an important problem faced by researchers in many fields such as pattern recognition computer vision and industrial design a recently developed previous shape abstraction framework demirci et al 20 generates an abstracted shape based on the correspondences between the features of the input shapes where the correspondences are obtained using the first optimal solution of a well known transportation problem as the size of the feature space grows the possibility of having more than one optimal solution for the same problem increases considering the case where multiple optimal solutions exist for the same transportation problem we first rank all optimal solutions based on how much they preserve the local neighborhood relations in this paper instead of creating the abstracted shape using the first optimal solution as done by the previous work we create the abstracted shape using the highest ranked optimal solution with this new property more effective abstracted shapes are generated experimental evaluation of the framework demonstrates that the proposed approach compares favorably with the previous technique in a set of shape retrieval experiments for different datasets highlightsskeletal shape abstraction is reformulated as the transportation problem a distortion free graph embedding is used for a better representation all optimal solutions for the transportation problem are considered the optimal solution which most resembles the neighborhood relations is used experiments demonstrate the improved performance

recursion operators and bi hamiltonian structures in multidimensions ii the algebraic properties of exactly solvable evolution equations in one spatial and one temporal dimensions have been well studied in particular the factorization of certain operators called recursion operators establishes the bi hamiltonian nature of all these equations recently we have presented the recursion operator and the bi hamiltonian formulation of the kadomtsev petviashvili equation a two spatial dimensional analogue of the korteweg devries equation here we present the general theory associated with recursion operators for bi hamiltonian equations in two spatial and one temporal dimensions as an application we show that general classes of equations which include the kadomtsev petviashvili and the davey stewartson equations possess infinitely many commuting symmetries and infinitely many constants of motion in involution under two distinct poisson brackets furthermore we show that the relevant recursion operators naturally follow from the underlying isospectral eigenvalue problems

backstepping observer based output feedback control for a class of coupled parabolic pdes with different diffusions abstract this paper aims to design a backstepping observer based output feedback controller for a class of coupled parabolic partial differential equations pdes with different diffusions the considered system is endowed with a sensor at the left boundary and an actuation at the right boundary firstly a backstepping observer is designed secondly compared to the existing literature a weaker condition is deduced to guarantee the stability of the plant system by means of a controller thirdly using the separation principle an observer based output feedback controller is set up based on the designed observer and controller finally the efficiency of the proposed method is shown by taking a simplified model of chemical tubular reactor

skeleton pruning by contour partitioning with discrete curve evolution in this paper we introduce a new skeleton pruning method based on contour partitioning any contour partition can be used but the partitions obtained by discrete curve evolution dce yield excellent results the theoretical properties and the experiments presented demonstrate that obtained skeletons are in accord with human visual perception and stable even in the presence of significant noise and shape variations and have the same topology as the original skeletons in particular we have proven that the proposed approach never produces spurious branches which are common when using the known skeleton pruning methods moreover the proposed pruning method does not displace the skeleton points consequently all skeleton points are centers of maximal disks again many existing methods displace skeleton points in order to produces pruned skeletons

finite time output regulation for linear 2 2 hyperbolic systems using backstepping this contribution presents the backstepping design of output feedback regulators for boundary controlled linear 2 2 hyperbolic systems that achieve regulation in finite time it is assumed that the disturbances can act in domain at both boundaries and at the output to be controlled the latter need not be available for measurement and consists of in domain pointwise distributed or boundary outputs firstly a solution of the finite time state feedback regulator problem is given on the basis of the regulator equations they are formulated in backstepping coordinates so that a solution is attainable in closed form this leads to a very straightforward regulator design for 2 2 hyperbolic systems with a general class of outputs then a finite dimensional reference observer that converges in finite time is introduced which consists of two observers and a delay this result is extended to the backstepping design of finite time disturbance observers for 2 2 hyperbolic systems with a collocated measurement in particular two backstepping disturbance observers are determined so that after introducing a delay the disturbance model and plant states can be estimated in finite time hence by combining the state feedback regulator with these observers a finite time output feedback regulator is obtained for the state feedback regulator and the disturbance observer existence conditions are derived in terms of the plant transfer behaviour a simple example with an in domain pointwise and distributed output illustrates the theoretical results

hamiltonian structure of real monge ampere equations the variational principle for the real homogeneous monge ampere equation in two dimensions is shown to contain three arbitrary functions of four variables there exist two different specializations of this variational principle where the lagrangian is degenerate and furthermore contains an arbitrary function of two variables the hamiltonian formulation of these degenerate lagrangian systems requires the use of dirac s theory of constraints as in the case of most completely integrable systems the constraints are second class and dirac brackets directly yield the hamiltonian operators thus the real homogeneous monge ampere equation in two dimensions admits two classes of infinitely many hamiltonian operators namely a family of local as well as another family non local hamiltonian operators and symplectic 2 forms which depend on arbitrary functions of two variables the simplest non local hamiltonian operator corresponds to the kac moody algebra of vector fields and functions on the unit circle hamiltonian operators that belong to either class are compatible with each other but between classes there is only one compatible pair in the case of real monge ampere equations with constant right hand side this compatible pair is the only pair of hamiltonian operators that survives then the complete integrability of all these real monge ampere equations follows by magri s theorem some of the remarkable properties we have obtained for the hamiltonian structure of the real homogeneous monge ampere equation in two dimensions turn out to be generic to the real homogeneous monge ampere equation and the geodesic flow for the complex homogeneous monge ampere equation in arbitrary number of dimensions hence among all integrable nonlinear evolution equations in one space and one time dimension the real homogeneous monge ampere equation is distinguished as one that retains its character as an integrable system in multiple dimensions

automatic and robust computation of 3d medial models incorporating object variability this paper presents a novel processing scheme for the automatic and robust computation of a medial shape model which represents an object population with shape variability the sensitivity of medial descriptions to object variations and small boundary perturbations are fundamental problems of any skeletonization technique these problems are approached with the computation of a model with common medial branching topology and grid sampling this model is then used for a medial shape description of individual objects via a constrained model fit the process starts from parametric 3d boundary representations with existing point to point homology between objects the voronoi skeleton of each sampled object boundary is partitioned into non branching medial sheets and simplified by a novel pruning algorithm using a volumetric contribution criterion using the surface homology medial sheets are combined to form a common medial branching topology finally the medial sheets are sampled and represented as meshes of medial primitives results on populations of up to 184 biological objects clearly demonstrate that the common medial branching topology can be described by a small number of medial sheets and that even a coarse sampling leads to a close approximation of individual objects

backstepping observers for a class of parabolic pdes in this paper we design exponentially convergent observers for a class of parabolic partial integro differential equations p i des with only boundary sensing available the problem is posed as a problem of designing an invertible coordinate transformation of the observer error system into an exponentially stable target system observer gain output injection function is shown to satisfy a well posed hyperbolic pde that is closely related to the hyperbolic pde governing backstepping control gain for the state feedback problem for several physically relevant problems the observer gains are obtained in closed form the observer gains are then used for an output feedback design in both collocated and anti collocated setting of sensor and actuator the order of the resulting compensator can be substantially lowered without affecting stability explicit solutions of a closed loop system are found in particular cases

multi dimensional fast rule filter automata abstract group valued multi dimensional filter automata fulfilling a set of neighborhood axioms are considered and a corresponding extended fast rule theorem frt is derived these automata comprise the well known reversible and irreversible parity rule filter automata with solitonic behavior in one dimension the extended fast rule gives rise to a scanning algorithm with inherent parallel structure pipelining parallelism those automata which suffice the extended fast rule theorem are completely characterized in terms of local configuration functions in contrast to the one dimensional case in several dimensions the frt does not generally imply solitonic behavior therefore examples of solitonic and non solitonic collisions for particles in two dimensional automata are given

embedding computation in one dimensional automata by phase coding solitons it is shown that some kind of meaningful computation can be embedded in very simple microscopically homogeneous one dimensional automata and in particular filter automata with a parity next state rule a systematic procedure is given for generating moving periodic structures particles these particles exhibit soliton like properties that is they often pass through one another with phase shifts ways to encode information in the phase of these particles are discussed the search for useful logical operations is reduced to a search for paths in certain graphs as a demonstration of principle the details of implementing a carry ripple adder are given

double poisson vertex algebras and non commutative hamiltonian equations we develop the formalism of double poisson vertex algebras local and non local aimed at the study of non commutative hamiltonian pdes this is a generalization of the theory of double poisson algebras developed by van den bergh which is used in the study of hamiltonian odes we apply our theory of double poisson vertex algebras to non commutative kp and gelfand dickey hierarchies we also construct the related non commutative de rham and variational complexes