on identifiability of linear time delay systems identifiability analysis is developed for linear time delay systems with delayed states control inputs and measured outputs all with a finite number of lumped delays these systems are governed by linear functional differential equations with uncertain time invariant parameters and delays it is shown that the transfer function of such a system admits the online identification if a sufficiently nonsmooth input signal is applied to the system sufficiently nonsmooth signals are constructively defined by imposing different smoothness properties on the control input and the state of the system the required nonsmoothness property is verified independently of any underlying time delay system

invariants of 3 manifolds via link polynomials and quantum groups the aim of this paper is to construct new topological invariants of compact oriented 3 manifolds and of framed links in such manifolds our invariant of a link in a closed oriented 3 manifold is a sequence of complex numbers parametrized by complex roots of 1 for a framed link in s 3 the terms of the sequence are equale to the values of the suitably parametrized jones polynomial of the link in the corresponding roots of 1 in the case of manifolds with boundary our invariant is a sequence of finite dimensional complex linear operators this produces from each root of unity q a 3 dimensional topological quantum field theory

quantum chains of hopf algebras with quantum double cosymmetry given a finite dimensional c hopf algebra h and its dual we construct the infinite crossed product and study its superselection sectors in the framework of algebraic quantum field theory is the observable algebra of a generalized quantum spin chain with h order and disorder symmetries where by a duality transformation the role of order and disorder may also appear interchanged if is a group algebra then becomes an ordinary g spin model we classify all dhr sectors of relative to some haag dual vacuum representation and prove that their symmetry is described by the drinfeld double to achieve this we construct localized coactions and use a certain compressibility property to prove that they are universal amplimorphisms on in this way the double can be recovered from the observable algebra as a universal cosymmetry

a model compression scheme for nonlinear electromagnetic inversions abstractwe have developed a model compression scheme for improving the efficiency of the regularized gauss newton inversion algorithm for marine controlled source electromagnetic applications in this scheme the unknown model parameters the conductivity resistivity distribution are represented in terms of a basis such as fourier and wavelet haar and daubechies by applying a truncation criterion the model may then be approximated by a reduced number of basis functions which is usually much less than the number of the model parameters further because the controlled source electromagnetic measurements have low resolution it is sufficient for inversion to only keep the low spatial frequency part of the image this model compression scheme accelerates the computational time and also reduces the memory usage of the gauss newton method we are able to significantly reduce the algorithm computational complexity without compromising the quality of the inverted models

brief paper on analytic and algebraic observability of nonlinear delay systems the observability of nonlinear delay systems has previously been defined in an algebraic setting by a rank condition on modules over noncommutative rings we introduce an analytic definition of observability to ensure the local uniqueness of state and initial conditions that correspond to a given input output behaviour it is shown that an algebraically observable delay system can be reformulated as a system of ordinary differential equations analytic observability is then decided by the local uniqueness of solutions to a boundary value problem for this ode system

a low rank approximation for large scale 3d controlled source electromagnetic gauss newton inversion abstractwe have developed an approximation to the hessian for inversion of 3d controlled source electromagnetic data our approach can considerably reduce the numerical complexity in terms of the number of forward solutions as well as the size and complexity of the calculations required to compute the update direction from the gauss newton equation the approach makes use of supershots in which several source positions are combined for simultaneous source simulations the resulting hessian can be described as a low rank approximation to the gauss newton hessian the structure of the approximate hessian facilitates a matrix free direct solver for the gauss newton equation and the reduced memory complexity allows the use of a large number of unknowns we studied the crosstalk introduced in the approximation and we determined how the dissipative nature of marine electromagnetic field propagation reduces the impact of this noise inversion results from recent field data demonstrated the numerical and pra

brief analysis of nonlinear time delay systems using modules over non commutative rings the theory of non commutative rings is introduced to provide a basis for the study of nonlinear control systems with time delays the left ore ring of non commutative polynomials defined over the field of meromorphic function is suggested as the framework for such a study this approach is then generalized to a broader class of nonlinear systems with delays that are called generalized roesser systems finally the theory is applied to analyze nonlinear time delay systems a weak observability is defined and characterized generalizing the well known linear result properties of closed submodules are then developed to obtain a result on the accessibility of such systems

on observation of time delay systems with unknown inputs causal and non causal observability are discussed in this technical note for nonlinear time delay systems with unknown inputs using the theory of non commutative rings and the algebraic framework introduced by xia the nonlinear time delay system is transformed into a suitable canonical form to solve the problem a necessary and sufficient condition is given to guarantee the existence of a change of coordinates leading to such a form

identifiability analysis of an epidemiological model in a structured population we investigate the parameter identifiability problem for a system of nonlinear integro partial differential equations of transport type representing the spread of a disease with a long infectious but undetectable period in an individual population after obtaining the expression of the model input output relationships we give sufficient conditions on the initial and boundary conditions of the system that guarantee the parameter identifiability on a finite time horizon we finally illustrate our findings with numerical simulations

a compressed implicit jacobian scheme for 3d electromagnetic data inversion we developed a compressed implicit jacobian scheme for the regularized gauss newton inversion algorithm for reconstructing 3d conductivity distributions from electromagnetic data in this algorithm the jacobian matrix whose storage usually requires a large amount of memory is decomposed in terms of electric fields excited by sources located and oriented identically to the physical sources and receivers as a result the memory usage for the jacobian matrix reduces from o nfnsnrnp to o nf ns nr np where nf is the number of frequencies ns is the number of sources nr is the number of receivers and np is the number of conductivity cells to be inverted when solving the gauss newton linear system of equations using iterative solvers the multiplication of the jacobian matrix with a vector is converted to matrix vector operations between the matrices of the electric fields and the vector in order to mitigate the additional computational overhead of this scheme these fields are further compressed us

brief paper a sufficient condition to test identifiability of nonlinear delayed differential models with constant delays and multi inputs in this paper an original result in terms of a sufficient condition to test the identifiability of nonlinear delayed differential models with constant delays and multi inputs is given the identifiability is studied for the linearized system and a criterion for linear systems with constant delays is provided from which the identifiability of the original nonlinear system can be proved this result is obtained by combining a classical identifiability result for nonlinear ordinary differential systems due to grewal and glover 1976 with the identifiability of linear delayed differential models developed by orlov belkoura richard and dambrine 2002 this paper is a generalization of denis vidal jauberthie and joly blanchard 2006 which deals with the specific case of nonlinear delayed differential models with two delays and a single input

efficient sampling of electromagnetic fields via the adaptive cross approximation the adaptive cross approximation method is applied to the problem of efficiently sampling an electromagnetic field across two dimensions the algorithm uses previously collected samples to determine which field samples to take next and reduces the number of samples required to accurately represent the field in this way the field may be sampled faster than it would have been if it had been raster scanned this is achieved without significant changes to the sensor hardware

observer design for nonlinear systems under unknown time varying delays the design of observers for nonlinear systems with unknown time varying bounded delays on both state and input still constitutes an open problem in this technical note we show how to solve it for a class of nonlinear systems by combining the high gain observer approach with a lyapunov krasovskii functional suitable choice sufficient conditions are provided to prove the practical stability of the observer it is shown that the observation error is bounded and depends on the size of two parameters the known upper bound delay of the unknown time varying function delay and the instantaneous state dynamic variation furthermore for the particular case of constant known time delay the convergence of the proposed observer becomes exponential the feasibility of the proposed strategy is illustrated by a numerical example

vertex operators from a toy model to lattice algebras within the framework of the discrete wess zumino novikov witten theory we analyze the structure of vertex operators on a lattice in particular the lattice analogues of operator product expansions and braid relations are discussed as the main physical application a rigorous construction for the discrete counterpart g n of the group valued field g x is provided we study several automorphisms of the lattice algebras including discretizations of the evolution in the wznw model our analysis is based on the theory of modular hopf algebras and its formulation in terms of universal elements algebras of vertex operators and their structure constants are obtained for the deformed universal enveloping algebras throughout the whole paper the abelian wznw model is used as a simple example to illustrate the steps of our construction

joint state estimation and delay identification for nonlinear systems with delayed measurements the problem of state estimation for nonlinear systems with unknown state or measurement delays is still an open problem in this paper we consider the case of measurement delay and propose an approach that combines a delay identifier with a suitable high gain observer in order to achieve simultaneous estimation of state and delay we provide sufficient conditions that guarantee the exponential convergence to zero of the errors globally with respect to the system variables and locally with respect to the delay estimation we validate the method through an example concerning population models

application of the multiplicative regularized gauss newton algorithm for three dimensional microwave imaging we apply the so called multiplicative regularized gauss newton inversion algorithm for solving three dimensional electromagnetic microwave inverse problems this inversion algorithm automatically adjusts the regularization parameter and when combined with the total variation type regularization function it can provide inversion results with excellent edge preserving characteristics in addition in order to deal with an extensive memory requirement for the gauss newton method we employ an implicit jacobian calculation scheme by using this scheme we do not have to explicitly store the jacobian matrix hence we are able to significantly reduce the memory requirement of the gauss newton method albeit at an additional computational overhead furthermore in order to be able to handle a large scale computational problem both the forward and the inversion algorithms are parallelized using the mpi library where we obtain a nearly linear speedup factor we demonstrate efficiency and robustness of this algorithm by inverting synthetic data fresnel experimental data and biomedical experimental data

when retarded nonlinear time delay systems admit an input output representation of neutral type the paper shows that nonlinear retarded time delay systems can admit an input output representation of neutral type this behaviour represents a strictly nonlinear phenomenon for it cannot happen in the linear time delay case where retarded systems always admit an input output representation of retarded type a necessary and sufficient condition for a nonlinear system to exhibit this behaviour is given and a strategy for finding an input output representation of retarded type is outlined some open problems that arise consequently are discussed as well all the systems considered in this work are time invariant and have commensurable delays

representation theory of lattice current algebras lattice current algebras were introduced as a regularization of the left and right moving degrees of freedom in the wznw model they provide examples of lattice theories with a local quantum symmetry their representation theory is studied in detail in particular we construct all irreducible representations along with a lattice analogue of the fusion product for representations of the lattice current algebra it is shown that for an arbitrary number of lattice sites the representation categories of the lattice current algebras agree with their continuum counterparts

parameter identifiability of nonlinear systems with time delay in this note various parameter identifiability concepts for nonlinear systems with time delay are defined complete characterizations of these concepts as well as easily checkable criteria are provided it is proved that geometric identifiability is equivalent to identifiability with known initial conditions algebraic identifiability implies geometric identifiability as for identifiability with partially known initial conditions an easy characterization is also provided

approximation of boundary element matrices this article considers the problem of approximating a general asymptotically smooth function in two variables typically arising in integral formulations of boundary value problems by a sum of products of two functions in one variable from these results an iterative algorithm for the low rank approximation of blocks of large unstructured matrices generated by asymptotically smooth functions is developed this algorithm uses only few entries from the original block and since it has a natural stopping criterion the approximative rank is not needed in advance

a three dimensional model based inversion algorithm using radial basis functions for microwave data we present a three dimensional 3d model based inversion algorithm for inverting electromagnetic data in our approach the models are described by points in the 3d space and the so called radial basis functions are used as the interpolation functions for connecting these points the use of the radial basis functions renders the surface of the target intrinsically smooth the l2 norm and weighted l2 norm regularization schemes are employed to constrain the curvature and to further smooth the surface of the target we tested this inversion algorithm using both synthetic and experimental data sets the inversion results demonstrate that both the shapes and material properties of the target are well reconstructed as a complementary algorithm to the pixel based tomographic inversion algorithms the model based inversion algorithm has fewer parameters to invert hence it has a higher computational efficiency the model based inversion algorithm also gives the users the freedom to construct an initial model based on their knowledge and other related information it helps to reduce the non uniqueness in the data interpretation

brief paper state elimination and identifiability of the delay parameter for nonlinear time delay systems the identifiability of the delay parameter for nonlinear systems with a single constant time delay is analyzed we show the existence of input output equations and relate the identifiability of the delay parameter to their form explicit criteria based on rank calculations are formulated the identifiability of the delay parameter is shown not to be directly related to the well characterized identifiability observability of the other system parameters states

unbraiding the braided tensor product we show that the braided tensor product algebra a1 a2 of two module algebras a1 a2 of a quasitriangular hopf algebra h is isomorphic to the ordinary tensor product a1 a2 provided there exists a realization of h within a1 in other words under this assumption we construct a transformation of generators which decouples a1 a2 i e makes them commuting we apply the theorem to the braided tensor product algebras of two or more quantum group covariant quantum spaces deformed heisenberg algebras and q deformed fuzzy spheres

delay identification for a class of nonlinear systems abstractthe problem of state estimation for nonlinear systems with unknown state delays is still an open problem in this paper we propose to add a delay identifier to suitable high gain observers in order to achieve simultaneous estimation of state and delay in the case of one constant delay in the state we provide sufficient conditions to guarantee the exponential convergence to zero of the errors globally with respect to the initial choice of the system state variables and locally with respect to the initial delay estimation we validate the method through an example concerning chaotic oscillators

an invariance theorem with applications to adaptive control a generalized invariance principle is developed to prove that model reference adaptive control does stabilize a given linear system the results address a scalar adaptive control problem and an nth order adaptive control problem in order to demonstrate the wide applicability of the results a class of scalar direct indirect adaptive control problems considered previously is also discussed

delay estimation via sliding mode for nonlinear time delay systems this paper deals with delay identifiability and delay estimation for a class of nonlinear time delay systems the theory of non commutative rings is used to analyze the identifiability in order to estimate the delay a sliding mode technique and a classical newton method are combined to show the possibility to have a local or global delay estimation for periodic or aperiodic delay signals

identification of the delay parameter for nonlinear time delay systems with unknown inputs using the theory of non commutative rings this paper studies the delay identification of nonlinear time delay systems with unknown inputs a sufficient condition is given in order to deduce an output delay equation from the studied system then necessary and sufficient conditions are proposed to judge whether the deduced output delay equation can be used to identify delay involved in this equation two different cases are discussed for the dependent and independent outputs respectively the presented result is applied to identify delay in a biological system

variational bayesian inversion of synthetic 3d controlled source electromagnetic geophysical data abstractinversion of controlled source electromagnetic data is dealt with for a geophysical application the goal is to retrieve a map of conductivity of an unknown body embedded in a layered underground from measurements of the scattered electric field that results from its interaction with a known interrogating wave this constitutes an inverse scattering problem whose associated forward problem is described by means of electric field domain integral equations the inverse problem is solved in a bayesian framework in which prior information is introduced via a gauss markov potts model this model describes the body as being composed of a finite number of different materials distributed into compact homogeneous regions the posterior distribution of the unknowns is approached by means of the variational bayesian approximation as a separable distribution that minimizes the kullback leibler divergence with respect to the posterior law thus we get a parametric model for the distributions of the induced cu

doubles of quasi quantum groups in dr1 drinfeld showed that any finite dimensional hopf algebra extends to a quasitriangular hopf algebra the quantum double of based on the construction of a so called diagonal crossed product developed by the authors in hn we generalize this result to the case of quasi hopf algebras as for ordinary hopf algebras as a vector space the quasi quantum double is isomorphic to where denotes the dual of we give explicit formulas for the product the coproduct the r matrix and the antipode on and prove that they fulfill drinfeld s axioms of a quasitriangular quasi hopf algebra in particular becomes an associative algebra containing as a quasi hopf subalgebra on the other hand is not a subalgebra of unless the coproduct on is strictly coassociative it is shown that the category of finite dimensional representations of coincides with what has been called the double category of modules by s majid m2 thus our construction gives a concrete realization of majid s abstract definition of quasi quantum doubles in terms of a tannaka krein like reconstruction procedure the whole construction is shown to generalize to weak quasi hopf algebras with now being linearly isomorphic to a subspace of

2 5d forward and inverse modeling for interpreting low frequency electromagnetic measurements we present 2 5d fast and rigorous forward and inversion algorithms for deep electromagnetic em applications that include crosswell and controlled source em measurements the forward algorithm is based on a finite difference approach in which a multifrontal lu decomposition algorithm simulates multisource experiments at nearly the cost of simulating one single source experiment for each frequency of operation when the size of the linear system of equations is large the use of this noniterative solver is impractical hence we use the optimal grid technique to limit the number of unknowns in the forward problem the inversion algorithm employs a regularized gauss newton minimization approach with a multiplicative cost function by using this multiplicative cost function we do not need a priori data to determine the so called regularization parameter in the optimization process making the algorithm fully automated the algorithm is equipped with two regularization cost functions that allow us to reconstruct either a smooth or a sharp conductivity image to increase the robustness of the algorithm we also constrain the minimization and use a line search approach to guarantee the reduction of the cost function after each iteration to demonstrate the pros and cons of the algorithm we present synthetic and field data inversion results for crosswell and controlled source em measurements

the disturbance decoupling problem for time delay nonlinear systems in this paper the disturbance decoupling problem ddp for a class of siso nonlinear systems with multiple delays in the input and the state is studied a pioneering mathematical approach is introduced for this class of systems and is claimed to be the cornerstone of the problem necessary and sufficient conditions are given for the existence of a bicausal feedback that solves the ddp sufficient conditions for the existence of a solution within other classes of compensators are included as well

gramian based uniform convergent observer for stable ltv systems with delayed measurements in this work an observer for a linear time varying system with delayed measurements is developed the delay is assumed to be unknown bounded and it can be time varying with no restriction on its rate of change the observer uses auxiliary signals related to the constructibility gramian of the system and it contains nonlin earities that provide a uniform fixed time convergence to a bounded region in the estimation error coordinates this means that the convergence time can be bounded by a positive constant which is independent from the initial conditions and the initial time this property is new for the addressed class of systems the ultimate bound of the estimation error depends on the maximum difference between the nominal output and the delayed one and not directly on the delay size or its time derivative these properties are illustrated in a numerical simulation