on the existence of local observables in theories with a factorizing s matrix the scaling limit of the two dimensional ising model above the critical temperature is considered as an example for relativistic quantum theories on two dimensional minkowski space exhibiting a factorizing s matrix in this model a recently proposed criterion for the existence of local quantum field theories with a prescribed factorizing scattering matrix is verified thereby establishing a new constructive approach to two dimensional quantum field theory in a particular example the existence proof is accomplished by analysing the nuclearity properties of certain specific subsets of fermionic fock spaces and yields as a byproduct also a verification of the energy nuclearity condition of buchholz and wichmann in models of free fermions in four spacetime dimensions

on quantum fields that generate local algebras the properties of quantum fields generating local nets of von neumann algebras are discussed for fields that satisfy certain energy bounds necessary and sufficient conditions for the existence of such a net and for the existence of product states are given in terms of the vacuum expectation values

brief paper root mean square gains of switched linear systems a variational approach we consider the problem of computing the root mean square rms gain of switched linear systems we develop a new approach which is based on an attempt to characterize the worst case switching law wcsl that is the switching law that yields the maximal possible gain our main result provides a sufficient condition guaranteeing that the wcsl can be characterized explicitly using the differential riccati equations dres corresponding to the linear subsystems this condition automatically holds for first order siso systems so we obtain a complete solution to the rms gain problem in this case

translationally invariant states and the spectrum ideal in the algebra of test functions for quantum fields a class of states on borchers tensor algebra is constructed these states are invariant under the translation group and fulfill the spectrum condition this leads to a characterization of the linear span of all such states in terms of a simple continuity property

on prediction of individual sequences sequential randomized prediction of an arbitrary binary sequence isinvestigated no assumption is made on the mechanism of generating the bit sequence the goal of the predictor is to minimize its relative loss i e to make almost as few mistakes as the best expert in a fixed possibly infinite set of experts we point out a surprising connection between this prediction problem and empirical process theory first in the special case of static memoryless experts we completely characterize the minimax relative loss in terms of the maximum of an associated rademacher process then we show general upper and lower bounds on the minimaxrelative loss in terms of the geometry of the class of experts as main examples we determine the exact order of magnitude of the minimax relative loss for the class of autoregressive linear predictors and for the class of markov experts

brief paper dynamic output feedback h control of switched linear systems this paper is devoted to dynamic output feedback h control design of switched linear systems in both continuous and discrete time domains more specifically the main purpose is to jointly design a switching rule and a full order dynamic output feedback switched controller that render the associated closed loop switched linear system globally asymptotically stable and impose a pre specified upper bound to the l 2 gain an example of practical importance is presented to illustrate the validity and efficiency of the theory

brief paper output feedback sampled data polynomial controller for nonlinear systems this paper presents the stability analysis and control synthesis for a sampled data control system which consists of a nonlinear plant and an output feedback sampled data polynomial controller connected in a closed loop the output feedback sampled data polynomial controller which can be implemented by a microcontroller or a digital computer is proposed to stabilize the nonlinear plant based on the lyapunov stability theory stability conditions in terms of sum of squares are obtained to guarantee the stability and to aid the design of a polynomial controller a simulation example is given to demonstrate the effectiveness of the proposed control approach

discrete denoising with shifts we introduce s dude a new algorithm for denoising discrete memoryless channel dmc corrupted data the algorithm which generalizes the recently introduced dude discrete universal denoiser aims to compete with a genie that has access in addition to the noisy data also to the underlying clean data and that can choose to switch up to m times between sliding window denoisers in a way that minimizes the overall loss when the underlying data form an individual sequence we show that the s dude performs essentially as well as this genie provided that m is sublinear in the size of the data when the clean data are emitted by a piecewise stationary process we show that the s dude achieves the optimum distribution dependent performance provided that the same sublinearity condition is imposed on the number of switches to further substantiate the universal optimality of the s dude we show that when the number of switches is allowed to grow linearly with the size of the data any sequence of scheme s fails to compete in the above sense using dynamic programming we derive an efficient implementation of the s dude which has complexity time and memory growing linearly with the data size and the number of switches m preliminary experimental results are presented suggesting that s dude has the capacity to improve on the performance attained by the original dude in applications where the nature of the data abruptly changes in time or space as is often the case in practice

string localized quantum fields and modular localization we study free covariant quantum bose fields that are associated with irreducible representations of the poincare group and localized in semi infinite strings extending to spacelike infinity among these are fields that generate the irreducible representations of mass zero and infinite spin that are known to be incompatible with point like localized fields for the massive representations and the massless representations of finite helicity all string localized free fields can be written as an integral along the string of point localized tensor or spinor fields as a special case we discuss the string localized vector fields associated with the point like electromagnetic field and their relation to the axial gauge condition in the usual setting

string and brane localized causal fields in a strongly nonlocal model we study a weakly local but nonlocal model in spacetime dimension d 2 and prove that it is maximally nonlocal in a certain specific quantitative sense nevertheless depending on the number of dimensions d it has string localized or brane localized operators which commute at spatial distances in two spacetime dimensions the model even comprises a covariant and local subnet of operators localized in bounded subsets of minkowski space which has a nontrivial scattering matrix the model thus exemplifies the algebraic construction of local operators from algebras associated with nonlocal fields

universal prediction this paper consists of an overview on universal prediction from an information theoretic perspective special attention is given to the notion of probability assignment under the self information loss function which is directly related to the theory of universal data compression both the probabilistic setting and the deterministic setting of the universal prediction problem are described with emphasis on the analogy and the differences between results in the two settings

sliding mode control of discrete time switched systems with repeated scalar nonlinearities this note studies the design of sliding mode control smc for discrete time hybrid stochastic switched systems with repeated scalar nonlinearities the weighed mathcal h infty gain performance is considered for the system dynamics to optimize its transient state performance first sufficient conditions are given to guarantee the corresponding system is exponentially stable while achieving a desired weighed mathcal h infty performance a new switching surface function is constructed by the average dwell time technique and the positive diagonally dominant lyapunov functional method to further reduce the conservativeness induced by the repeated scalar nonlinearity then the corresponding sliding mode dynamics are obtained and the solvability condition for the desired switching surface function is derived furthermore the synthesis of the proposed smc law is proposed to force the resulting closed loop system trajectories onto the pre specified sliding mode region with a desired level of accuracy finally the feasibility and the effectiveness of the presented new design techniques are illustrated by examples and simulations

on the connection between quantum fields and von neumann algebras of local operators the relationship between a standard local quantum field and a net of local von neumann algebras is discussed two natural possibilities for such an association are identified and conditions for these to obtain are found it is shown that the local net can naturally be so chosen that it satisfies the special condition of duality the notion of an intrinsically local field operator is introduced and it is shown that such an operator defines a local net with which the field is locally associated a regularity condition on the field is formulated and it is shown that if this condition holds then there exists a unique local net with which the field is locally associated if and only if the field algebra contains at least one intrinsically local operator conditions under which a field and other fields in its borchers class are associated with the same local net are found in terms of the regularity condition mentioned

universal filtering via prediction we consider the filtering problem where a finite alphabet individual sequence is corrupted by a discrete memoryless channel and the goal is to causally estimate each sequence component based on the past and present noisy observations we establish a correspondence between the filtering problem and the problem of prediction of individual sequences which leads to the following result given an arbitrary finite set of filters there exists a filter which performs with high probability essentially as well as the best in the set regardless of the underlying noiseless individual sequence we use this relationship between the problems to derive a filter guaranteed of attaining the finite state filterability of any individual sequence by leveraging results from the prediction problem

further enhancement on robust h_ infty control design for discrete time singular systems this note deals with the robust h control design for uncertain discrete time singular systems necessary and sufficient conditions for the admissibility for these systems are formulated in strict linear matrix inequalities lmis formulation then both state feedback and static output feedback controllers are studied and robust necessary and sufficient design conditions are expressed in terms of strict bilinear matrix inequalities bmis robust h controllers are designed for uncertain singular systems including uncertainties on matrix e lmi design conditions are also proposed an illustrative example is provided to show the effectiveness of the proposed approach

construction of quantum field theories with factorizing s matrices the subject of this thesis is a novel construction method for interacting relativistic quantum field theories on two dimensional minkowski space employing the algebraic framework of quantum field theory it is shown under which conditions an algebra of observables localized in a wedge shaped region of spacetime can be used to construct model theories a crucial input in this context is the modular nuclearity condition for wedge algebras which implies the existence of local observables as an application of the new method a rigorous construction of a large family of models with factorizing s matrices is obtained in an inverse scattering approach a given factorizing scattering operator is used to define certain semi localized wightman fields associated to it with the help of these fields a wedge algebra can be defined which determines the local observable content of a well defined quantum field theory in this approach the modular nuclearity condition translates to certain analyticity and boundedness conditions on the formfactors of wedge local observables these conditions are shown to hold for a large class of underlying s matrices including the scattering operators of the sinh gordon model and the scaling ising model as special examples the so constructed models are investigated with respect to their scattering properties they are shown to solve the inverse scattering problem for the underlying s matrices and a proof of asymptotic completeness for these models is given

bounds of the induced norm and model reduction errors for systems with repeated scalar nonlinearities the class of nonlinear systems described by a discrete time state equation containing a repeated scalar nonlinearity as in recurrent neural networks is considered sufficient conditions are derived for the stability and induced norm of such systems using positive definite diagonally dominant lyapunov functions or storage functions satisfying appropriate linear matrix inequalities results are also presented for model reduction errors for such systems

positivity of wightman functionals and the existence of local nets the paper is concerned with the existence of a local net of von neumann algebras associated with a given wightman field for fields satisfying a generalizedh bound the existence of such a net is shown to be equivalent to a certain positivity property of the wightman distributions

on designing of sliding mode control for stochastic jump systems in this note we consider the problems of stochastic stability and sliding mode control for a class of linear continuous time systems with stochastic jumps in which the jumping parameters are modeled as a continuous time discrete state homogeneous markov process with right continuous trajectories taking values in a finite set by using linear matrix inequalities lmis approach sufficient conditions are proposed to guarantee the stochastic stability of the underlying system then a reaching motion controller is designed such that the resulting closed loop system can be driven onto the desired sliding surface in a limited time it has been shown that the sliding mode control problem for the markovian jump systems is solvable if a set of coupled lmis have solutions a numerical example is given to show the potential of the proposed techniques

dissipativity based sliding mode control of switched stochastic systems this technical brief is concerned with dissipativity analysis and dissipativity based sliding mode control smc of continuous time switched stochastic systems firstly a sufficient condition is proposed to guarantee the mean square exponential stability and strict dissipativity for the switched stochastic system then an integral type sliding surface function is designed for establishing a sliding mode dynamics which can be formulated by a switched stochastic system with an external disturbance uncertainty dissipativity analysis and synthesis are both investigated for the sliding mode dynamics and consequently sufficient conditions are derived which pave the way for solving the dissipativity analysis and control problems moreover a smc law is synthesized to drive the system trajectories onto the predefined sliding surface in a finite time finally the efficiency of the theoretical findings is demonstrated by an illustrative example

nice reachability for planar bilinear control systems with applications to planar linear switched systems corrected we consider planar bilinear control systems with measurable controls we show that any point in the reachable set can be reached by a ldquonicerdquo control specifically a control that is a concatenation of a bang arc with either 1 a bang bang control that is periodic after the third switch or 2 a piecewise constant control with no more than two discontinuities under the additional assumption that the bilinear system is positive or invariant for any proper cone we show that the reachable set is spanned by a concatenation of a bang arc with either 1 a bang bang control with no more than two discontinuities or 2 a piecewise constant control with no more than two discontinuities in particular any point in the reachable set can be reached using a piecewise constant control with no more than three discontinuities several known results on the stability of planar linear switched systems under arbitrary switching follow as corollaries of our result we demonstrate this with an example

an algebraic construction of boundary quantum field theory we build up local time translation covariant boundary quantum field theory nets of von neumann algebras mathcal a v on the minkowski half plane m starting with a local conformal net mathcal a of von neumann algebras on mathbb r and an element v of a unitary semigroup mathcal e mathcal a associated with mathcal a the case v 1 reduces to the net mathcal a considered by rehren and one of the authors if the vacuum character of mathcal a is summable mathcal a v is locally isomorphic to mathcal a we discuss the structure of the semigroup mathcal e mathcal a by using a one particle version of borchers theorem and standard subspace analysis we provide an abstract analog of the beurling lax theorem that allows us to describe in particular all unitaries on the one particle hilbert space whose second quantization promotion belongs to mathcal e mathcal a 0 with mathcal a 0 the u 1 current net each such unitary is attached to a scattering function or more generally to a symmetric inner function we then obtain families of models via any buchholz mack todorov extension of mathcal a 0 a further family of models comes from the ising model

model approximation for fuzzy switched systems with stochastic perturbation in this paper the model approximation problem is investigated for a takagi sugeno fuzzy switched system with stochastic disturbance for a high order considered system our attention is focused on the construction of a reduced order model which not only approximates the original system well with a hankel norm performance but translates it into a lower dimensional fuzzy switched system as well by using the average dwell time approach and the piecewise lyapunov function technique a sufficient condition is first proposed to guarantee the mean square exponential stability with a hankel norm error performance for the error system the model approximation is then converted into a convex optimization problem by using a linearization procedure finally simulations are provided to illustrate the effectiveness of the proposed theory

stabilization and performance synthesis for systems with repeated scalar nonlinearities the class of nonlinear systems described by a discrete time state equation containing a repeated scalar nonlinearity as in recurrent neural networks is considered given a plant of this form sufficient conditions are derived for 1 the parametrization of all controllers of the same form such that the closed loop is stable in the sense of a diagonally dominant lyapunov function and 2 the synthesis of a controller of the same form so that the induced norm of the closed loop is under a prescribed level several of these conditions can be written into linear matrix inequalities

induced l sub 2 and generalized h sub 2 filtering for systems with repeated scalar nonlinearities this paper provides complete results on the filtering problem for a class of nonlinear systems described by a discrete time state equation containing a repeated scalar nonlinearity as in recurrent neural networks both induced l sub 2 and generalized h sub 2 indexes are introduced to evaluate the filtering performance for a given stable discrete time systems with repeated scalar nonlinearities our purpose is to design a stable full order or reduced order filter with the same repeated scalar nonlinearities such that the filtering error system is asymptotically stable and has a guaranteed induced l sub 2 or generalized h sub 2 performance sufficient conditions are obtained for the existence of admissible filters since these conditions involve matrix equalities the cone complementarity linearization procedure is employed to cast the nonconvex feasibility problem into a sequential minimization problem subject to linear matrix inequalities which can be readily solved by using standard numerical software if these conditions are feasible a desired filter can be easily constructed these filtering results are further extended to discrete time systems with both state delay and repeated scalar nonlinearities the techniques used in this paper are very different from those used for previous controller synthesis problems which enable us to circumvent the difficulty of dilating a positive diagonally dominant matrix a numerical example is provided to show the applicability of the proposed theories

deformations of quantum field theories and integrable models deformations of quantum field theories which preserve poincare covariance and localization in wedges are a novel tool in the analysis and construction of model theories here a general scenario for such deformations is discussed and an infinite class of explicit examples is constructed on the borchers uhlmann algebra underlying wightman quantum field theory these deformations exist independently of the space time dimension and contain the recently studied warped convolution deformation as a special case in the special case of two dimensional minkowski space they can be used to deform free field theories to integrable models with non trivial s matrix

how to filter an individual sequence with feedback we consider causally estimating filtering the components of a noise corrupted sequence relative to a reference class of filters the noiseless sequence to be filtered is designed by a ldquowell informed antagonist rdquo meaning it may evolve according to an arbitrary law unknown to the filter based on past noiseless and noisy sequence components we show that this setting is more challenging than that of an individual noiseless sequence a k a the ldquosemi stochasticrdquo setting in the sense that any deterministic filter even one guaranteed to do well on every noiseless individual sequence fails under some well informed antagonist on the other hand we constructively establish the existence of a randomized filter which successfully competes with an arbitrary given finite reference class of filters under every antagonist thus unlike in the semi stochastic setting randomization is crucial in the antagonist framework our noise model allows for channels whose noisy output depends on the l past channel outputs in addition to the noiseless channel input symbol memoryless channels are obtained as a special case of our model by taking i 0 in this case our scheme coincides with one that was recently shown to compete with an arbitrary reference class when the underlying noiseless sequence is an individual sequence hence our results show that the latter scheme is universal not only for the semi stochastic setting in which it was originally proposed but also under the well informed antagonist

how to use expert advice we analyze algorithms that predict a binary value by combining the predictions of several prediction strategies called experts our analysis is for worst case situations i e we make no assumptions about the way the sequence of bits to be predicted is generated we measure the performance of the algorithm by the difference between the expected number of mistakes it makes on the bit sequence and the expected number of mistakes made by the best expert on this sequence where the expectation is taken with respect to the randomization in the predictins we show that the minimum achievable difference is on the order of the square root of the number of mistakes of the best expert and we give efficient algorithms that achieve this our upper and lower bounds have matching leading constants in most cases we then show how this leads to certain kinds of pattern recognition learning algorithms with performance bounds that improve on the best results currently know in this context we also compare our analysis to the case in which log loss is used instead of the expected number of mistakes

universal minimax discrete denoising under channel uncertainty the goal of a denoising algorithm is to recover a signal from its noise corrupted observations perfect recovery is seldom possible and performance is measured under a given single letter fidelity criterion for discrete signals corrupted by a known discrete memoryless channel dmc the discrete universal denoiser dude was recently shown to perform this task asymptotically optimally without knowledge of the statistical properties of the source in the present work we address the scenario where in addition to the lack of knowledge of the source statistics there is also uncertainty in the channel characteristics we propose a family of discrete denoisers and establish their asymptotic optimality under a minimax performance criterion which we argue is appropriate for this setting as we show elsewhere the proposed schemes can also be implemented computationally efficiently

the capacity of finite state markov channels with feedback we consider a class of finite state markov channels with feedback we first introduce a simplified equivalent channel model and then construct the optimal stationary and nonstationary input processes that maximize the long term directed mutual information furthermore we give a sufficient condition under which the channel s shannon capacity can be achieved by a stationary input process the corresponding converse coding theorem and direct coding theorem are proved

robust sliding mode control for uncertain time delay systems an lmi approach this note is devoted to robust sliding mode control for time delay systems with mismatched parametric uncertainties a delay independent sufficient condition for the existence of linear sliding surfaces is given in terms of linear matrix inequalities based on which the corresponding reaching motion controller is also developed the results are illustrated by an example

brief paper weighted h model reduction for linear switched systems with time varying delay this paper is concerned with model reduction for continuous time linear switched systems with time varying delay for a given stable switched system our attention is focused on construction of a reduced order model such that the error system is exponentially stable with a prescribed weighted performance by applying the average dwell time approach and the piecewise lyapunov function technique delay dependent deley independent sufficient conditions are proposed in terms of linear matrix inequality lmi to guarantee the exponential stability and the weighted performance for the error system the model reduction problem is solved by using the projection approach which casts the model reduction problem into a sequential minimization problem subject to lmi constraints by employing the cone complementary linearization algorithm a numerical example is provided to illustrate the effectiveness of the proposed theory

on the causal structure of minkowski spacetime the causal structure of minkowski spacetime m is discussed in terms of the notions of causal complementation and causal completion these geometric notions are relevant for quantum field theory and the theory of the klein gordon equation particular attention is given to closed convex causally complete subsets of m and the properties of such sets are discussed the study of such sets is motivated by potential applications to the theory of local nets of von neumann algebras the notion of the envelope of uniqueness of a subset of m familiar from the theory of the wave equation is discussed and some results about the relation of this envelope to the causal completion of the set are presented