on category o over triangular generalized weyl algebras abstract we analyze the bgg category o over a large class of generalized weyl algebras henceforth termed gwas given such a triangular gwa for which category o decomposes into a direct sum of subcategories we study in detail the homological properties of blocks with finitely many simples as consequences we show that the endomorphism algebra of a projective generator of such a block is quasi hereditary finite dimensional and graded koszul we also classify all tilting modules in the block as well as all submodules of all projective and tilting modules finally we present a novel connection between blocks of triangular gwas and young tableaux which provides a combinatorial interpretation of morphisms and extensions between objects of the block

distributed model predictive control of linear systems with stochastic parametric uncertainties and coupled probabilistic constraints this paper investigates the distributed stochastic model predictive control dsmpc for multiple constrained dynamically decoupled subsystems subject to stochastic uncertainties in the parameters to obtain a computationally tractable formulation for real control applications a spectral method called generalized polynomial chaos expansions gpces is utilized to propagate the stochastic parametric uncertainties through the system model by using gpces combined with the probabilistic information on the uncertainties both local probabilistic constraints and coupled probabilistic constraints are converted explicitly into deterministic convex second order cone constraints the constraints can achieve satisfaction of coupled probabilistic constraints in a distributed way by permitting a single subsystem to optimize a local cost function at each time step while freezing the plans of others the proposed gpces based dsmpc algorithm guarantees recursive feasibility with respect to both local and coupled prob

an efficient method to design robust observer based control of uncertain linear systems in this paper the robust observer based control for a class of uncertain linear systems is considered exponential stabilizability for systems is studied and the convergence rate of system is given linear matrix inequality lmi approach is used to design the feedback control the control and observer gains are given from the lmi formulations a numerical example is given to illustrate our results

finite time stabilizability and instabilizability of delayed memristive neural networks with nonlinear discontinuous controller this paper is concerned about the finite time stabilizability and instabilizability for a class of delayed memristive neural networks dmnns through the design of a new nonlinear controller algebraic criteria based on m matrix are established for the finite time stabilizability of dmnns and the upper bound of the settling time for stabilization is estimated in addition finite time instabilizability algebraic criteria are also established by choosing different parameters of the same nonlinear controller the effectiveness and the superiority of the obtained results are supported by numerical simulations

non fragile observer based sliding mode control for markovian jump systems with mixed mode dependent time delays and input nonlinearity this paper is concerned with the state estimation and the sliding mode control smc for a class of markovian jump systems with mixed mode dependent time delays and input nonlinearity a non fragile observer is designed to estimate the system states and an observer based smc is synthesized to ensure the reachability of the sliding surfaces in the state estimation space by constructing a novel mode dependent lyapunov krasovskii functional some new criteria are established for the existence and the solvability of the desired observer based sliding mode controller finally numerical examples are presented to illustrate the effectiveness and less conservativeness of the proposed theoretical results

on doubly robust estimation in a semiparametric odds ratio model we consider the doubly robust estimation of the parameters in a semiparametric conditional odds ratio model our estimators are consistent and asymptotically normal in a union model that assumes either of two variation independent baseline functions is correctly modelled but not necessarily both furthermore when either outcome has finite support our estimators are semiparametric efficient in the union model at the intersection submodel where both nuisance functions models are correct for general outcomes we obtain doubly robust estimators that are nearly efficient at the intersection submodel our methods are easy to implement as they do not require the use of the alternating conditional expectations algorithm of chen 2007

wirtinger based multiple integral inequality for stability of time delay systems abstractnote that the conservatism of the delay dependent stability criteria can be reduced by increasing the integral terms in lyapunov krasovskii functional lkf this brief revisits the stability problem for a class of linear time delay systems via multiple integral approach the novelty of this brief lies in that a wirtinger based multiple integral inequality is employed to estimate the derivative of a class of lkf with multiple integral terms based on these innovations a new delay dependent stability criterion is derived in terms of linear matrix inequalities two numerical examples are exploited to demonstrate the effectiveness and superiority of the proposed method

on the design of observer based controller of linear neutral delay differential systems in this note the observer based control problem for a class of linear delay differential systems of neutral type is investigated using the lyapunov method a criterion for asymptotic stability is derived in terms of matrix inequalities which solved by convex optimization algorithms a numerical example is given to illustrate the proposed method

stability analysis for neural networks with time varying delay based on quadratic convex combination in this paper a novel method is developed for the stability problem of a class of neural networks with time varying delay new delay dependent stability criteria in terms of linear matrix inequalities for recurrent neural networks with time varying delay are derived by the newly proposed augmented simple lyapunov krasovski functional different from previous results by using the first order convex combination property our derivation applies the idea of second order convex combination and the property of quadratic convex function which is given in the form of a lemma without resorting to jensen s inequality a numerical example is provided to verify the effectiveness and superiority of the presented results

a robust state observer scheme this note proposes a new approach to robust state observer construction the scheme is derived by including an extra term and adopting the lyapunov stability theorem and requires the solution of an algebraic riccati equation the scheme is implemented in a gas fired furnace system example satisfactory results have been obtained though in general special attention need be paid to some numerical issues in implementing the scheme

new approach to delay dependent stability analysis and stabilization for continuous time fuzzy systems with time varying delay this paper is concerned with delay dependent stability analysis and stabilization problems for continuous time takagi and sugeno t s fuzzy systems with a time varying delay a new method for the delay dependent stability analysis and stabilization is suggested which is less conservative than other existing ones first based on a fuzzy lyapunov krasovskii functional lkf a delay dependent stability criterion is derived for the open loop fuzzy systems in the derivation process some free fuzzy weighting matrices are introduced to express the relationships among the terms of the system equation and among the terms in the leibniz newton formula then a delay dependent stabilization condition based on the so called parallel distributed compensation pdc scheme is worked out for the closed loop fuzzy systems the proposed stability criterion and stabilization condition are represented in terms of linear matrix inequalities lmis and compared with the existing ones via two examples finally application to control of a truck trailer is also given to illustrate the effectiveness of the proposed design method

global exponential periodicity and stability of a class of memristor based recurrent neural networks with multiple delays the paper presents theoretical results on the global exponential periodicity and stability of a class of memristor based recurrent neural networks with multiple delays the dynamic analysis in the paper employs the theory of differential equations with discontinuous right hand side as introduced by filippov by using the inequality techniques and a useful lyapunov functional some new testable algebraic criteria are obtained for ensuring the existence and global exponential stability of periodic solution of the system the model based on the memristor widens the application scope for the design of neural networks and the new effective results also enrich the toolbox for the qualitative analysis of neural networks

lmi approach to robust h filtering for neutral delay differential systems in this paper we investigate the problems of stability and h filtering for a class of linear neutral delay differential systems a linear matrix inequality approach is proposed to design a robust h filter such that the filtering system remains asymptotically stable and the bound of h norm is minimized the lyapunov stability theory is used for analysis of the system a numerical example illustrate the theoretical results

delay range dependent observer based control of nonlinear systems under input and output time delays observer based control of nonlinear systems under input output delays is studied time varying nature of delays is incorporated for the controller design delay range dependent observer based control is reported decoupling technique is applied to compute controller and observer gains the control scheme is tested to control a one link flexible joint robotic arm the problem of designing observer based controller for a class of nonlinear time delay systems subjected to input and output time varying delays is addressed in this paper more incisively a delay range dependent criterion incorporating variation of delays between known lower and upper bounds is established for control of nonlinear time delay systems the proposed methodology ensures asymptotic stability of the closed loop system s state and the estimation error between states of the system and observer by application of a lyapunov krasovskii functional jensen s inequality standard matrix inequality procedures luenberger type observer delay interval bounds and delay derivative limits observer based controller synthesis approach using nonlinear matrix inequalities for the nonlinear time delay systems is provided further a decoupling approach is employed to render a simpler condition for the observer and the controller synthesis a novel observer based control scheme for the linear time delay systems with interval time varying input as well as output lags is derived from the proposed control strategy the traditional delay dependent controller design incorporating zero lower bound of the delay for the time delay systems is a particular scenario of the projected delay range dependent approach the proposed decoupled observer based controller synthesis condition is cast into linear matrix inequalities by means of the cone complementary linearization approach finally a numerical simulation example of control of one link flexible joint robotic arm is provided to verify the proposed design methodology

stability for neural networks with time varying delays via some new approaches this paper considers the problem of delay dependent stability criteria for neural networks with time varying delays first by constructing a newly augmented lyapunov krasovskii functional a less conservative stability criterion is established in terms of linear matrix inequalities second by proposing novel activation function conditions which have not been proposed so far further improved stability criteria are proposed finally three numerical examples used in the literature are given to show the improvements over the existing criteria and the effectiveness of the proposed idea

a flexible terminal approach to stochastic stability and stabilization of continuous time semi markovian jump systems with time varying delay abstract this paper addresses the stochastic stability and stabilization problems for a class of semi markovian jump systems smjss with time varying delay where the time varying delay t is assumed to satisfy 1 t 2 based on the flexible terminal approach the time varying delay t is first transformed such that 1 t t 2 t by utilizing a novel semi markovian lyapunov krasoviskii functional smlkf and an improved reciprocally convex inequality rci sufficient conditions are established to guarantee a feasible solution two illustrated examples are shown the effectiveness of the main results

dirac cohomology for graded affine hecke algebras we define an analogue of the casimir element for a graded affine hecke algebra mathbb h and then introduce an approximate square root called the dirac element using it we define the dirac cohomology hd x of an mathbb h module x and show that hd x carries a representation of a canonical double cover of the weyl group widetilde w our main result shows that the widetilde w structure on the dirac cohomology of an irreducible mathbb h module x determines the central character of x in a precise way this can be interpreted as p adic analogue of a conjecture of vogan for harish chandra modules we also apply our results to the study of unitary representations of mathbb h

non fragile asynchronous h control for uncertain stochastic memory systems with bernoulli distribution abstract this study constructs and investigates the non fragile asynchronous h control for uncertain stochastic memory systems with bernoulli distribution the system not only contains the randomly occurring uncertainties of all parameters rouaps and stochastic disturbances in the system model but also includes randomly gain perturbations in the controller by introducing the stochastic variables a new model structure is built obeying bernoulli distribution to describe the system and the controller moreover a modified lyapunov krasovskii function lkf is constructed combining ito s differential formula and free weighting matrix method less conservative results are presented in terms of the linear matrix inequality lmi furthermore an observer based non fragile asynchronous h controller is designed without any limits on the system parameters finally three numerical examples are provided to demonstrate the effectiveness and feasibility of the proposed results

non fragile robust h control for uncertain spacecraft rendezvous system with pole and input constraints this article investigates the robust h control problem for a class of spacecraft rendezvous systems with parameter uncertainties and subject to input constraint pole constraint and external and controller perturbations based on the lyapunov theory a sufficient condition for the existence of the non fragile robust state feedback controller is given in terms of linear matrix inequalities lmis then proper non fragile controller design can be cast as a convex optimisation problem subject to lmi constraints with the obtained controller the spacecraft rendezvous mission can be accomplished an illustrative example is provided to show the effectiveness of the proposed control design method

non fragile positive real control for uncertain linear neutral delay systems this paper is concerned with the problem of non fragile positive real control for uncertain neutral delay systems with time invariant norm bounded parameter uncertainty time delays are assumed to appear in both the state and the controlled output equations the state feedback gains are with norm bounded controller uncertainties for both the cases with additive and multiplicative controller uncertainties we address the problem of designing memoryless state feedback controllers such that for all admissible uncertainties the resulting closed loop system is stable and the closed loop transfer function is extended strictly positive real sufficient conditions for the existence of desired controllers are given in terms of linear matrix inequalities lmis when these lmis are feasible the expected memoryless state feedback controller can be easily constructed via convex optimization an illustrative example is given to demonstrate the validity and applicability of the proposed approach

new unified h dynamic observer design for linear systems with unknown inputs in this paper a unified h dynamic observer uo is proposed for a class of linear systems in the presence of unknown inputs and disturbances it generalizes the existing results on the proportional observer po the proportional integral observer pio and the dynamic observer do the design approach of the uo is derived from the solution of the linear matrix inequality lmi based on the new dynamic observer formulation and the solution of the algebraic constraints obtained from the unbiased estimation error a numerical example is provided to show the applicability and the performance of our results

stability analysis of reaction diffusion uncertain memristive neural networks with time varying delays and leakage term in this paper the stability problem is investigated for a class of reaction diffusion uncertain memristive neural networks with time varying delays and leakage term to investigate the dynamic behavior of the memristive system we turn to the qualitative analysis of a relevant differential inclusion under the framework of filippov s solution which is easier to handle by using lyapunov stability theory jensen integral inequality schur complement lemma free weighting matrix approach together with the linear matrix inequality lmi approach the sufficient conditions are derived to ensure the stability of the considered systems the easy to test stability criteria established in this paper depend on the leakage delay as well as the reaction diffusion terms which is more reasonable moreover the existing stability criteria can be treated as a special case of this paper finally two numerical examples are exploited to show the effectiveness of the derived lmi based stability conditions

event triggered sampling control for stability and stabilization of memristive neural networks with communication delays this paper investigates the global asymptotic stability and stabilization of memristive neural networks mnns with communication delays via event triggered sampling control first based on the novel approach in lemma 1 the concerned mnns are converted into traditional neural networks with uncertain parameters next a discrete event triggered sampling control scheme which only needs supervision of the system state at discrete instants is designed for mnns for the first time thanks to this controller the number of control updates could greatly reduce then by getting utmost out of the usable information on the actual sampling pattern a newly augmented lyapunov krasovskii functional lkf is constructed to formulate stability and stabilization criteria it should be mentioned that the lkf is positive definite only at endpoints of each subinterval of the holding intervals but not necessarily positive definite inside the holding intervals finally the feasibility and effectiveness of the proposed results are tested by two numerical examples

hochschild cohomology and graded hecke algebras we develop and collect techniques for determining hochschild cohomology of skew group algebras s v g and apply our results to graded hecke algebras we discuss the explicit computation of certain types of invariants under centralizer subgroups focusing on the infinite family of complex reflection groups g r p n to illustrate our ideas resulting formulas for hochschild two cocycles give information about deformations of s v g and in particular about graded hecke algebras we expand the definition of a graded hecke algebra to allow a nonfaithful action of g on v and we show that there exist nontrivial graded hecke algebras for g r 1 n in contrast to the case of the natural reflection representation we prove that one of these graded hecke algebras is equivalent to an algebra that has appeared before in a different form

robust stabilization for a class of discrete time non linear systems via output feedback the unified lmi approach this paper discusses a robust stabilization problem for a class of multi input and multi output mimo discrete time non linear systems with both state and control inputs containing non linear perturbations the problem is solved via static output feedback and dynamic output feedback respectively a unified approach is used to cast the problem into a convex optimization involving linear matrix inequalities lmi all the controllers can robustly stabilize the systems and maximize the bound on the non linear perturbations this paper also extends the output feedback centralized design approach to a class of discrete time mimo non linear decentralized systems both robust static and dynamic output feedback controllers are obtained

direct adaptive fuzzy control for nonlinear systems with time varying delays this paper focuses on the problem of direct adaptive fuzzy control for nonlinear strict feedback systems with time varying delays based on the razumikhin function approach a novel adaptive fuzzy controller is designed the proposed controller guarantees that the system output converges to a small neighborhood of the reference signal and all the signals in the closed loop system remain bounded different from the existing adaptive fuzzy control methodology the fuzzy logic systems are used to model the desired but unknown control signals rather than the unknown nonlinear functions in the systems as a result the proposed adaptive controller has a simpler form and requires fewer adaptation parameters

stability of a stochastic two dimensional non hamiltonian system we study the top lyapunov exponent of the response of a two dimensional non hamiltonian system driven by additive white noise the origin is not a fixed point for the system however there is an invariant measure for the one point motion of the system in this paper we consider the stability of the two point motion by khasminskii s method of linearization along trajectories the specific system we consider is the third order truncated normal form of the unfolding of a hopf bifurcation we show that in the small noise limit the top lyapunov exponent always approaches zero from below and is thus negative for noise sufficiently small we also show that there exist open sets of parameters for which the top lyapunov exponent is positive thus the two point motion can be either stable or unstable while the stationary density that describes the one point motion always exists

nonfragile control with guaranteed cost of t s fuzzy singular systems based on parallel distributed compensation this paper investigates the nonfragile guaranteed cost control problem for a class of uncertain nonlinear singular state delayed systems that is described by takagi sugeno models the upper bound of state delay is assumed to be available a linear quadratic cost function is specified as the performance index of the closed loop system attention is focused on the fuzzy state feedback controller design via parallel distributed compensation scheme which not only guarantees the regular impulse free and asymptotically stable of the closed loop fuzzy singular delay system but also provides an optimized upper bound of the guaranteed cost function for the possibility of feedback gain variation and all admissible uncertainties all derived sufficient conditions are given in terms of linear matrix inequalities some numerical examples are provided to illustrate the effectiveness of the proposed design scheme

robust estimation for neural networks with randomly occurring distributed delays and markovian jump coupling this paper studies the issue of robust state estimation for coupled neural networks with parameter uncertainty and randomly occurring distributed delays where the polytopic model is employed to describe the parameter uncertainty a set of bernoulli processes with different stochastic properties are introduced to model the randomly occurrences of the distributed delays novel state estimators based on the local coupling structure are proposed to make full use of the coupling information the augmented estimation error system is obtained based on the kronecker product a new lyapunov function which depends both on the polytopic uncertainty and the coupling information is introduced to reduce the conservatism sufficient conditions which guarantee the stochastic stability and the l 2 l infty performance of the augmented estimation error system are established then the estimator gains are further obtained on the basis of these conditions finally a numerical example is used to prove the effectiveness of the results

stability criteria for recurrent neural networks with time varying delay based on secondary delay partitioning method a secondary delay partitioning method is proposed to study the stability problem for a class of recurrent neural networks rnns with time varying delay the total interval of the time varying delay is first divided into two parts and then each part is further divided into several subintervals to deal with the state variables associated with these subintervals an extended reciprocal convex combination approach and a double integral term with variable upper and lower limits of integral as a lyapunov functional are proposed which help to obtain the stability criterion the main feature of the proposed result is more effective for the rnns with fast time varying delay a numerical example is used to show the effectiveness of the proposed stability result

periodic attractor for reactiondiffusion high order hopfield neural networks with time varying delays this paper is concerned with a class of reactiondiffusion high order hopfield neural networks with time varying delays subject to the dirichlet boundary condition in a bounded domain easily verifiable delay independent criteria are established to ensure the existence of periodic mild solutions and the global exponential stability of the periodic mild solutions is also discussed by using the exponential dissipation property of semigroup of operators the obtained results are easy to check and they effectually complement previously known results a numerical example is given to show the effectiveness of theoretical results

exponential stability of complex valued memristive recurrent neural networks in this brief we establish a novel complex valued memristive recurrent neural network cvmrnn to study its stability as a generalization of real valued memristive neural networks cvmrnn can be separated into real and imaginary parts by means of m matrix and lyapunov function the existence uniqueness and exponential stability of the equilibrium point for cvmrnns are investigated and sufficient conditions are presented finally the effectiveness of obtained results is illustrated by two numerical examples

dirac cohomology unitary representations and a proof of a conjecture of vogan u radu je dokazana slutnja d vogana koja odredjuje infinitesimalni karakter ireducibilnog g k modula koji ima diracovu kohomologiju razlicitu od nula infinitesimalni karakter je dan kao rho translat najvece tezine k tipa u diracovoj kohomologiji diracova kohomologija se definira kao ker d im d cap ker d gdje d oznacava diracov operator na zadanom g k modulu tenzoriranom sa spin modulom

dissipativity analysis for stochastic memristive neural networks with time varying delays a discrete time case in this paper the dissipativity problem of discrete time memristive neural networks dmnns with time varying delays and stochastic perturbation is investigated a class of logical switched functions are put forward to reflect the memristor based switched property of connection weights and the dmnns are then recast into a tractable model based on the tractable model the robust analysis method and refined jensen based inequalities are applied to establish some sufficient conditions that ensure the mathcal q mathcal s mathcal r gamma text disspativity of dmnns two numerical examples are presented to illustrate the effectiveness of the obtained results

estimation of a semiparametric natural direct effect model incorporating baseline covariates establishing cause effect relationships is a standard goal of empirical science once the presence of a causal relationship is established the precise causal mechanism involved becomes a topic of interest a particularly popular type of mechanism analysis concerns questions of mediation that is to what extent an effect is direct and to what extent it is mediated by a third variable a semiparametric theory has recently been proposed which allows multiply robust estimation of direct and mediated marginal effect functionals in observational studies tchetgen tchetgen shpitser 2012 in this paper we extend the new theory to handle parametric models of natural direct and indirect effects within levels of pre exposure variables with an identity or log link function where the model for the observed data likelihood is otherwise unrestricted we show that estimation is generally not feasible in this model because of the curse of dimensionality associated with the required estimation of auxiliary conditional densities or expectations given high dimensional covariates thus we consider multiply robust estimation and propose a more general model which assumes that a subset but not all of several working models holds

pbw deformations of braided products abstract we present new examples of deformations of smash product algebras that arise from hopf algebra actions on pairs of module algebras these examples involve module algebras that are koszul in which case a pbw theorem we established previously applies our construction generalizes several double constructions appearing in the literature including weyl algebras and some types of cherednik algebras and it complements the braided double construction of bazlov and berenstein many suggestions of further directions are provided at the end of the work

passivity and passification of memristor based recurrent neural networks with additive time varying delays this paper presents a new design scheme for the passivity and passification of a class of memristor based recurrent neural networks mrnns with additive time varying delays the predictable assumptions on the boundedness and lipschitz continuity of activation functions are formulated the systems considered here are based on a different time delay model suggested recently which includes additive time varying delay components in the state the connection between the time varying delay and its upper bound is considered when estimating the upper bound of the derivative of lyapunov functional it is recognized that the passivity condition can be expressed in a linear matrix inequality lmi format and by using characteristic function method for state feedback passification it is verified that it is apathetic to use immediate or delayed state feedback by constructing a lyapunov krasovskii functional and employing jensen s inequality and reciprocal convex combination technique together with a tighter estimation of the upper bound of the cross product terms derived from the derivatives of the lyapunov functional less conventional delay dependent passivity criteria are established in terms of lmis moreover second order reciprocally convex approach is employed for deriving the upper bound for terms with inverses of squared convex parameters the model based on the memristor with additive time varying delays widens the application scope for the design of neural networks finally pertinent examples are given to show the advantages of the derived passivity criteria and the significant improvement of the theoretical approaches

global stabilizability of uncertain systems with time varying delays via dynamic observer based output feedback in this paper the dynamic observer based output feedback control for uncertain time delay systems with time varying delays is investigated a delay independent dynamic observer based output feedback control is proposed such that the feedback controlled system with time varying delays is globally asymptotically stable if some mild conditions are met an upper bound of arbitrary time varying delays without destroying stability is also given such that the asymptotic stability is preserved a numerical example is given to illustrate the use of our main results

global exponential stability in continuous time and discrete time delayed bidirectional neural networks convergence dynamics of continuous time bidirectional neural networks with constant transmission delays are studied without assuming the symmetry of synaptic connection weights and the monotonicity and differentiability of activation functions lyapunov functionals and halanay type inequalities are constructed and employed to derive delay independent sufficient conditions under which the continuous time networks converge exponentially to the equilibria associated with temporally uniform external inputs to the networks discrete time analogues of the continuous time networks are formulated and we study their dynamical characteristics it is shown that the convergence dynamics of the continuous time networks are preserved by the discrete time analogues without any restriction on the discretization step size several examples are given to illustrate the advantages of the discrete time analogues in numerically simulating the continuous time networks

reciprocally convex approach to stability of systems with time varying delays whereas the upper bound lemma for matrix cross product introduced by park 1999 and modified by moon park kwon and lee 2001 plays a key role in guiding various delay dependent criteria for delayed systems the jensen inequality has become an alternative as a way of reducing the number of decision variables it directly relaxes the integral term of quadratic quantities into the quadratic term of the integral quantities resulting in a linear combination of positive functions weighted by the inverses of convex parameters this paper suggests the lower bound lemma for such a combination which achieves performance behavior identical to approaches based on the integral inequality lemma but with much less decision variables comparable to those based on the jensen inequality lemma

robust observer based control of systems with state perturbations via lmi approach in this note the observer based control for a class of uncertain linear systems is considered exponential stabilizability for the systems is studied and the convergence rate of the system is estimated a linear matrix inequality lmi approach is used to design the observer based control the control and observer gains are given from lmi feasible solution a numerical example is given to illustrate our results

inverse odds ratio weighted estimation for causal mediation analysis an important scientific goal of studies in the health and social sciences is increasingly to determine to what extent the total effect of a point exposure is mediated by an intermediate variable on the causal pathway between the exposure and the outcome a causal framework has recently been proposed for mediation analysis which gives rise to new definitions formal identification results and novel estimators of direct and indirect effects in the present paper the author describes a new inverse odds ratio weighted iorw approach to estimate so called natural direct and indirect effects the approach which uses as a weight the inverse of an estimate of the odds ratio function relating the exposure and the mediator is universal in that it can be used to decompose total effects in a number of regression models commonly used in practice specifically the approach may be used for effect decomposition in generalized linear models with a nonlinear link function and in a number of other commonly used models such as the cox proportional hazards regression for a survival outcome the approach is simple and can be implemented in standard software provided a weight can be specified for each observation an additional advantage of the method is that it easily incorporates multiple mediators of a categorical discrete or continuous nature

exponential state estimation for stochastically disturbed discrete time memristive neural networks multiobjective approach the state estimation of the discrete time memristive model is studied in this article by applying the stochastic analysis technique sufficient formulas are established to ensure the exponentially mean square stability of the error model moreover the derived control gain matrix can be calculated via the linear matrix inequality lmi it should be mentioned that by extending the derived conclusion to a multiobjective optimization problem the maximum bound of the active function and the minimum bound of the disturbance attenuation are derived the corresponding simulation figures are provided in the end

delay dependent robust stabilization of uncertain state delayed systems this paper concerns a problem of robust stabilization of uncertain state delayed systems a new delay dependent stabilization condition using a memoryless controller is formulated in terms of matrix inequalities an algorithm involving convex optimization is proposed to design a controller guaranteeing a suboptimal maximal delay such that the system can be stabilized for all admissible uncertainties

lmi based approach for global asymptotic stability analysis of recurrent neural networks with various delays and structures global asymptotic stability problem is studied for a class of recurrent neural networks with distributed delays satisfying lebesgue stieljies measures on the basis of linear matrix inequality the concerned network model includes many neural network models with various delays and structures as its special cases such as the delays covering the discrete delays and distributed delays and the network structures containing the neutral type networks and high order networks therefore many new stability criteria for the above neural network models have also been derived from the present stability analysis method all the obtained stability results have similar matrix inequality structures and can be easily checked three numerical examples are used to show the effectiveness of the obtained results

attractivity analysis of memristor based cellular neural networks with time varying delays this paper presents new theoretical results on the invariance and attractivity of memristor based cellular neural networks mcnns with time varying delays first sufficient conditions to assure the boundedness and global attractivity of the networks are derived using state space decomposition and some analytic techniques it is shown that the number of equilibria located in the saturation regions of the piecewise linear activation functions of an n neuron mcnn with time varying delays increases significantly from 2n to 22n2 n 22n2 times compared with that without a memristor in addition sufficient conditions for the invariance and local or global attractivity of equilibria or attractive sets in any designated region are derived finally two illustrative examples are given to elaborate the characteristics of the results in detail

poincare birkhoff witt theorem for quadratic algebras of koszul type abstract in this paper we prove a general poincare birkhoff witt theorem for quadratic koszul algebras the result is similar to that obtained by polischuk and positselsky but the proof is entirely different and uses algebraic deformation theory in particular we obtain a new proof of the classical pbw theorem for lie algebras based on deformation theory

stability and stabilization of discrete time t s fuzzy systems with stochastic perturbation and time varying delay this paper is concerned with the problems of stability analysis and stabilization for a class of discrete time takagi sugeno t s fuzzy systems with stochastic perturbation and time varying state delay by means of the delay partitioning method and slack variables a novel fuzzy lyapunov krasovskii function is constructed to reduce the conservatism of stability conditions those conditions are converted to finite linear matrix inequalities which can be readily solved by standard numerical software then the delay dependent stabilization approach which is based on a nonparallel distributed compensation scheme is introduced for the closed loop fuzzy systems finally illustrative examples are provided to illustrate the feasibility and effectiveness of the proposed methods

design of state estimator for bidirectional associative memory neural networks with leakage delays this paper considers the issue of state estimation for a class of bidirectional associative memory bam neural networks more precisely the bam model is considered with mixed delays which includes a constant delay in the leakage term time varying discrete delay and constant distributed delay by constructing a novel lyapunov krasovskii functional lkf together with free weighting matrix technique a new delay dependent sufficient condition is derived to estimate the neuron states through available output measurements such that for all admissible delay bounds the resulting estimation error system is globally asymptotically stable also it is assumed that the derivative of time delay is not necessarily zero or less than one further the derived conditions are formulated in terms of a set of linear matrix inequalities lmis which can be easily solved by using some standard numerical packages finally a numerical example with simulation result is presented to show the effectiveness of the proposed theory the result reveals that the leakage delays have a destabilizing influence on the system and they cannot be ignored

finite time stability analysis for markovian jump memristive neural networks with partly unknown transition probabilities this paper is concerned with the finite time stochastically stability ftss analysis of markovian jump memristive neural networks with partly unknown transition probabilities in the neural networks there exist a group of modes determined by markov chain and thus the markovian jump was taken into consideration and the concept of ftss is first introduced for the memristive model by introducing a markov switching lyapunov functional and stochastic analysis theory an ftss test procedure is proposed from which we can conclude that the settling time function is a stochastic variable and its expectation is finite the system under consideration is quite general since it contains completely known and completely unknown transition probabilities as two special cases more importantly a nonlinear measure method was introduced to verify the uniqueness of the equilibrium point compared with the fixed point theorem that has been widely used in the existing results this method is more easy to implement besides the delay interval was divided into four subintervals which make full use of the information of the subsystems upper bounds of the time varying delays finally the effectiveness and superiority of the proposed method is demonstrated by two simulation examples

new delay dependent non fragile h observer based control for continuous time delay systems the problem of the delay dependent non fragile h observer based control for a class of continuous time delay systems is investigated in this paper the additive gain variations under consideration are contained in both the controller gain and obhsiunserver gain delay dependent criteria are derived to guarantee the stability of the non fragile h observer based control system using the lyapunov functional approach the controller and observer gains are given from the lmi feasible solutions based on the result of this paper the constraint of matrix equality is not necessary for designing the non fragile h observer based controls computer software matlab can be applied to solve all the proposed results finally a numerical example is illustrated to show the improvement of this paper

estimation of controlled direct effects when regression models adjust for mediators on the causal path from exposure to outcome the regression coefficient of exposure is commonly viewed as a measure of the direct exposure effect this interpretation can be misleading even with a randomly assigned exposure this is because adjustment for post exposure measurements introduces bias whenever their association with the outcome is confounded by more than just the exposure by the same token adjustment for such confounders stays problematic when these are themselves affected by the exposure robins accommodated this by introducing linear structural nested direct effect models with direct effect parameters that can be estimated by using inverse probability weighting by a conditional distribution of the mediator the resulting estimators are consistent but inefficient and can be extremely unstable when the mediator is absolutely continuous we develop direct effect estimators which are not only more efficient but also consistent under a less demanding model for a conditional expectation of the outcome we find that the one estimator which avoids inverse probability weighting altogether performs best this estimator is intuitive computationally straightforward and as demonstrated by simulation competes extremely well with ordinary least squares estimators in settings where standard regression is valid

exponential stability and stabilization of delayed memristive neural networks based on quadratic convex combination method this paper is concerned with the exponential stability and stabilization of memristive neural networks mnns with delays first we present some generalized double integral inequalities which include some existing inequalities as their special cases second combining with quadratic convex combination method these double integral inequalities are employed to formulate a delay dependent stability condition for mnns with delays third a state dependent switching control law is obtained for mnns with delays based on the proposed stability conditions the desired feedback gain matrices are accomplished by solving a set of linear matrix inequalities finally the feasibility and effectiveness of the proposed results are tested by two numerical examples

symplectic reflection algebras calogero moser space and deformed harish chandra homomorphism to any finite group sp v of automorphisms of a symplectic vector space v we associate a new multi parameter deformation h of the algebra v smash product of with the polynomial algebra on v the parameter runs over points of r where r number of conjugacy classes of symplectic reflections in the algebra h called a symplectic reflection algebra is related to the coordinate ring of a poisson deformation of the quotient singularity v this leads to a symplectic analogue of mckay correspondence which is most complete in case of wreath products if is the weyl group of a root system in a vector space and v then the algebras h are certain rational degenerations of the double affine hecke algebra introduced earlier by cherednik

two step estimation in ratio of mediator probability weighted causal mediation analysis this study investigates appropriate estimation of estimator variability in the context of causal mediation analysis that employs propensity score based weighting such an analysis decomposes the total effect of a treatment on the outcome into an indirect effect transmitted through a focal mediator and a direct effect bypassing the mediator ratio of mediator probability weighting estimates these causal effects by adjusting for the confounding impact of a large number of pretreatment covariates through propensity score based weighting in step 1 a propensity score model is estimated in step 2 the causal effects of interest are estimated using weights derived from the prior step s regression coefficient estimates statistical inferences obtained from this 2 step estimation procedure are potentially problematic if the estimated standard errors of the causal effect estimates do not reflect the sampling uncertainty in the estimation of the weights this study extends to ratio of mediator probability weighting analysis a solution to the 2 step estimation problem by stacking the score functions from both steps we derive the asymptotic variance covariance matrix for the indirect effect and direct effect 2 step estimators provide simulation results and illustrate with an application study our simulation results indicate that the sampling uncertainty in the estimated weights should not be ignored the standard error estimation using the stacking procedure offers a viable alternative to bootstrap standard error estimation we discuss broad implications of this approach for causal analysis involving propensity score based weighting

on stabilization of stochastic cohen grossberg neural networks with mode dependent mixed time delays and markovian switching the globally exponential stabilization problem is investigated for a general class of stochastic cohen grossberg neural networks with both markovian jumping parameters and mixed mode dependent time delays the mixed time delays consist of both discrete and distributed delays this paper aims to design a memoryless state feedback controller such that the closed loop system is stochastically exponentially stable in the mean square sense by introducing a new lyapunov krasovskii functional that accounts for the mode dependent mixed delays stochastic analysis is conducted in order to derive delay dependent criteria for the exponential stabilization problem three numerical examples are carried out to demonstrate the feasibility of our delay dependent stabilization criteria

exponential stabilization of memristive neural networks with time delays in this paper a general class of memristive neural networks with time delays is formulated and studied some sufficient conditions in terms of linear matrix inequalities are obtained in order to achieve exponential stabilization the result can be applied to the closed loop control of memristive systems in particular several succinct criteria are given to ascertain the exponential stabilization of memristive cellular neural networks in addition a simplified and effective algorithm is considered for design of the optimal controller these conditions are the improvement and extension of the existing results in the literature two numerical examples are given to illustrate the theoretical results via computer simulations

global exponential stability of memristive neural networks with mixed time varying delays this article investigates the lagrange exponential stability and the lyapunov exponential stability of memristive neural networks with discrete and distributed time varying delays dmnns by means of inequality techniques theories of the m matrix and the comparison strategy the lagrange exponential stability of the underlying dmnns is considered in the sense of filippov and the globally exponentially attractive set is estimated through employing the m matrix and external input especially when the external input is not concerned the lyapunov exponential stability of the corresponding dmnns is developed immediately in the form of an m matrix which contains some published outcomes as special cases furthermore by constructing an m matrix based differential system the lyapunov exponential stability of the dmnns is studied which is less conservative than some existing ones finally three simulation examples are carried out to examine the validness of the theories

a comprehensive review of stability analysis of continuous time recurrent neural networks stability problems of continuous time recurrent neural networks have been extensively studied and many papers have been published in the literature the purpose of this paper is to provide a comprehensive review of the research on stability of continuous time recurrent neural networks including hopfield neural networks cohen grossberg neural networks and related models since time delay is inevitable in practice stability results of recurrent neural networks with different classes of time delays are reviewed in detail for the case of delay dependent stability the results on how to deal with the constant variable delay in recurrent neural networks are summarized the relationship among stability results in different forms such as algebraic inequality forms m matrix forms linear matrix inequality forms and lyapunov diagonal stability forms is discussed and compared some necessary and sufficient stability conditions for recurrent neural networks without time delays are also discussed concluding remarks and future directions of stability analysis of recurrent neural networks are given

output feedback stabilization of stochastic high order nonlinear systems under weaker conditions under the weaker conditions on the power order and the nonlinear functions this paper investigates the output feedback stabilization problem for a class of stochastic high order nonlinear systems based on the backstepping design method and homogeneous domination technique the closed loop system can be proved to be globally asymptotically stable in probability

passivity and passification of memristor based recurrent neural networks with time varying delays this paper presents new theoretical results on the passivity and passification of a class of memristor based recurrent neural networks mrnns with time varying delays the casual assumptions on the boundedness and lipschitz continuity of neuronal activation functions are relaxed by constructing appropriate lyapunov krasovskii functionals and using the characteristic function technique passivity conditions are cast in the form of linear matrix inequalities lmis which can be checked numerically using an lmi toolbox based on these conditions two procedures for designing passification controllers are proposed which guarantee that mrnns with time varying delays are passive finally two illustrative examples are presented to show the characteristics of the main results in detail

semiparametric theory for causal mediation analysis efficiency bounds multiple robustness and sensitivity analysis whilst estimation of the marginal total causal effect of a point exposure on an outcome is arguably the most common objective of experimental and observational studies in the health and social sciences in recent years investigators have also become increasingly interested in mediation analysis specifically upon evaluating the total effect of the exposure investigators routinely wish to make inferences about the direct or indirect pathways of the effect of the exposure not through or through a mediator variable that occurs subsequently to the exposure and prior to the outcome although powerful semiparametric methodologies have been developed to analyze observational studies that produce double robust and highly efficient estimates of the marginal total causal effect similar methods for mediation analysis are currently lacking thus this paper develops a general semiparametric framework for obtaining inferences about so called marginal natural direct and indirect causal effects while appropriately accounting for a large number of pre exposure confounding factors for the exposure and the mediator variables our analytic framework is particularly appealing because it gives new insights on issues of efficiency and robustness in the context of mediation analysis in particular we propose new multiply robust locally efficient estimators of the marginal natural indirect and direct causal effects and develop a novel double robust sensitivity analysis framework for the assumption of ignorability of the mediator variable

hierarchy of stability criterion for time delay systems based on multiple integral approach abstract taking a class of time delay systems as research object this brief aims at developing a theoretical support on the hierarchy of stability criterion which is derived by the multiple integral approach and free weighting matrix technique the hierarchy implies that the conservatism of stability criterion can be reduced by increasing the ply of integral terms in lyapunov krasovskii functional lkf together with three numerical experiments the hierarchy of stability criterion is further shown

producing stable periodic solutions of switched impulsive delayed neural networks using a matrix based cubic convex combination approach this article is dedicated to designing a novel periodic impulsive control strategy for producing globally exponentially stable periodic solutions for switched neural networks with discrete and finite distributed time varying delays first tunable parameters and cubic convex combination approach are proposed to study the globally exponential convergence of switched neural networks second a sufficient criterion for the existence uniqueness and globally exponential stability of a periodic solution is demonstrated by using contraction mapping theorem and the impulse delay dependent lyapunov krasovskii functional method it is worth emphasizing that the addressed lyapunov krasovskii functional covers both triple integral terms and novel quadruple integral terms which makes the conservatism of the above criteria decrease even if the original neural network models are unstable or the impulsive effects are strong the addressed neural network model can produce a globally exponentially stable periodic solution these results here which include boundedness globally uniformly exponential convergence and globally exponentially stability of the periodic solution generalize and improve the earlier publications finally two numerical examples and their computer simulations are given to show the effectiveness of theoretical results

event triggered h_ infty state estimation for delayed stochastic memristive neural networks with missing measurements the discrete time case in this paper the event triggered h infty state estimation problem is investigated for a class of discrete time stochastic memristive neural networks dsmnns with time varying delays and missing measurements the dsmnn is subject to both the additive deterministic disturbances and the multiplicative stochastic noises the missing measurements are governed by a sequence of random variables obeying the bernoulli distribution for the purpose of energy saving an event triggered communication scheme is used for dsmnns to determine whether the measurement output is transmitted to the estimator or not the problem addressed is to design an event triggered h infty estimator such that the dynamics of the estimation error is exponentially mean square stable and the prespecified h infty disturbance rejection attenuation level is also guaranteed by utilizing a lyapunov krasovskii functional and stochastic analysis techniques sufficient conditions are derived to guarantee the existence of the desired estimator and then the estimator gains are characterized in terms of the solution to certain matrix inequalities finally a numerical example is used to demonstrate the usefulness of the proposed event triggered state estimation scheme