optimal interpolation for linear stochastic systems let y satisfying dy cxdt ddw y 0 0 represent the noisy observation of the gauss markov process x generated by dx axdt bdw x 0 x 0 on the finite interval 0 t in this paper we solve the following interpolation problem determine the best least squares estimate of x t t in 0 t given the increments of y on the intervals 0 t 1 and t 2 t where 0 t 1 t 2 t and the statistics of x 0 several alternative expressions for the optimal interpolator are derived some of which are phrased in terms of two kalman bucy estimates as a by product we also solve the interpolation problem for the missing increments of y

a non archimedean ohsawa takegoshi extension theorem we prove an ohsawa takegoshi type extension theorem on the berkovich closed unit disc over certain non archimedean fields as an application we establish a non archimedean analogue of demailly s regularization theorem for quasisubharmonic functions on the berkovich unit disc

on discrete algebraic riccati equations a rank characterization of solutions abstract we give a rank characterization of the solution set of discrete algebraic riccati equations dares involving real matrices our characterization involves the use of invariant subspaces of the system matrix we observe that a dare can be considered as a specific type of a non symmetric continuous time algebraic riccati equation we show how to extract the low rank solutions from the full rank solution of a homogeneous dare we also study the eigen structure of various feedback closed loop matrices associated with solutions of a dare we show as a consequence of our observations that a solution x of a dare for controllable systems and certain specific types of uncontrollable systems satisfies the inequality x m i n x x m a x we characterize conditions under which the solution set of dare is bounded unbounded we use the method of invariant subspaces to identify some invariant sets of a difference riccati equation

analytic approximations of plurisubharmonic singularities we study several classes of isolated singularities of plurisubharmonic functions that can be approximated by analytic singularities with control over their residual monge ampere masses they are characterized in terms of green functions for demailly s approximations relative types and valuations furthermore the classes are shown to appear when studying graded families of ideals of analytic functions and the corresponding asymptotic multiplier ideals

linear estimation of boundary value stochastic processes part i the role and construction of complementary models this paper presents a substantial extension of the method of complementary models for minimum variance linear estimation introduced by weinert and desai in their important paper 1 specifically the method of complementary models is extended to solve estimation problems for both discrete and continuous parameter linear boundary value stochastic processes in one and higher dimensions a major contribution of this paper is an application of green s identity in deriving a differential operator representation of the estimator to clarify the development and to illustrate the range of applications of our approach two brief examples are provided one is a 1 d discrete two point boundary value process and the other is a 2 d process governed by poisson s equation on the unit disk

some comments on conditionally markov and reciprocal gaussian processes corresp mehr and mcfadden s conditionally markov processes and jamison s reciprocal processes are two independent extensions of slepian s work on a particular stationary gaussian process the relationship between them and their relationship with gauss markov processes are discussed

a sharp effectiveness result of demailly s strong openness conjecture abstract in this article we establish a sharp effectiveness result of demailly s strong openness conjecture we also establish a sharp effectiveness result related to a conjecture posed by demailly and kollar

model parameter estimation for reciprocal gaussian random processes the problem of estimating the model parameters of a discrete index reciprocal gaussian random process from a limited number of noisy observations is addressed the general case of a first order multivariate process is analyzed stating its basic properties and deriving a linear equation set that relates the model parameters including the unknown variance of the observation noise to the generally nonstationary autocorrelation function of the observed process it generalizes to the reciprocal processes the so called high order yule walker equations for ar processes based on these results a practical estimation algorithm is proposed

smoothing error dynamics and their use in the solution of smoothing and mapping problems martingale decomposition techniques are used to derive markovian models for the error in smoothed estimates of processes described by linear models driven by white noise these models together with some simple hilbert space decomposition ideas provide a simple unified framework for examining a variety of problems involving the efficient assimilation of spatial data which we refer to as mapping problems algorithms for several different mapping problems are derived a specific example of map updating for a two dimensional random field is included

minimal realization and dynamic properties of optimal smoothers smoothing algorithms of various kinds have been around for several decades however some basic issues regarding the dynamical structure and the minimal dimension of the steady state algorithm are still poorly understood in this paper we derive a realization of minimal dimension of the optimal smoother for a signal admitting a state space description of dimension n it is shown that the dimension of the smoothing algorithm can vary from n to 2n depending on the zero structure of the signal model the dynamics pole structure of the steady state smoother is also characterized explicitly and is related to the zero structure of the model we use several recent ideas from stochastic realization theory in particular a minimal markovian representation of the smoother is derived which requires solving a nonsymmetric wiener hopf factorization problem in this way the smoother is naturally expressed as the cascade of a whitening filter and a linear filter of least possible dimension whose state space is a minimal markovian subspace containing the smoothed estimate x spl i cap this among other aspects affords a very simple calculation of the error covariance matrix of the smoother a reduced order two filter implementation of the type due to mayne 1966 and fraser 1967 is obtained by solving a riccati equation of reduced dimension which is in general smaller than the dimension of the riccati equations considered in the literature

dynamical compactifications of c 2 we find good dynamical compactifications for arbitrary polynomial mappings of c 2 and use them to show that the degree growth sequence satisfies a linear integral recursion formula for maps of low topological degree we prove that the green function is well behaved for maps of maximum topological degree we give normal forms

remarks on linear and nonlinear filtering this communication tries to give some insight into relationships existing between viterbi and the forward backward algorithm used in the context of hidden markov models on the one hand and kalman filtering and rauch tung striebel smoothing on the other we give a unifying view which shows how those algorithms are related and give an example of a nonlinear hybrid system that can be filtered through a mixed algorithm

discrete time complementary models and smoothing abstract the fact that the smoothing error is a wide sense markov process is somehow surprising since smoothed estimates depend upon both past and future data in this paper we first give a simple and general proof of this fact then we use the so called complementary models introduced by weinert and desai to derive forwards and backwards markovian models for the smoothing error in state space models by exploring the structure of the complementary models we show that under certain restrictions only two simple structured models exist one that runs forwards in time and the other that runs backwards in time the forwards complementary model leads to the forward rauch tung striebel rts smoothing formula and to a backwards markovian model for the error whereas the backwards model leads to the backward rts formula and to a forwards error model the two models for the smoothing error can be derived one from the other by a forward backward transformation that preserves the sample paths finally by using

on the relative entropy of discrete time markov processes with given end point densities given a markov process x k defined over a finite interval i 0 n i spl sub z we construct a process x k with the same initial density as x but a different end point density which minimizes the relative entropy of x and x it is shown that x is a markov process in the same reciprocal class as x in the gaussian case the minimum relative entropy problem is related to a minimum energy lqg optimal control problem

a new inversion free method for a rational matrix equation abstract motivated by the classical newton schulz method for finding the inverse of a nonsingular matrix we develop a new inversion free method for obtaining the minimal hermitian positive definite solution of the matrix rational equation x a x 1 a i where i is the identity matrix and a is a given nonsingular matrix we present convergence results and discuss stability properties when the method starts from the available matrix aa we also present numerical results to compare our proposal with some previously developed inversion free techniques for solving the same rational matrix equation

the circulant rational covariance extension problem the complete solution the rational covariance extension problem to determine a rational spectral density given a finite number of covariance lags can be seen as a matrix completion problem to construct an infinite dimensional positive definite toeplitz matrix the northwest corner of which is given the circulant rational covariance extension problem considered in this paper is a modification of this problem to partial stochastic realization of periodic stationary process which are better represented on the discrete unit circle rather than on the discrete real line the corresponding matrix completion problem then amounts to completing a finite dimensional toeplitz matrix that is circulant another important motivation for this problem is that it provides a natural approximation involving only computations based on the fast fourier transform for the ordinary rational covariance extension problem potentially leading to an efficient numerical procedure for the latter the circulant rational covariance extension problem is an inverse problem with infinitely many solutions in general each corresponding to a bilateral arma representation of the underlying periodic process in this paper we present a complete smooth parameterization of all solutions and convex optimization procedures for determining them a procedure to determine which solution that best matches additional data in the form of logarithmic moments is also presented

imperfect model reference adaptive control deadbeat output error approach it is well known that while the perfect model matching condition i e unstable plant zeros must be zeros of the reference model is not met the model reference adaptive control cannot easily be implemented in adaptive control systems since the plant is assumed to be unknown previously it is a difficult task to choose an adequate reference model such that the perfect model matching condition is guaranteed in every adaptive step in this paper a new design algorithm for model reference adaptive control systems is proposed to synthesize an adaptive controller such that the error between the reference model output and the plant output can vanish in a deadbeat manner in this situation the stringent matching condition can be relaxed in every adaptive step so our design algorithm is also suitable for unstable or non minimum phase systems several simulation results are presented to illustrate the good behaviour of our design algorithm

identification of 2 d noncausal gauss markov random fields parameter identification of multidimensional noncausal markov random fields is an important paradigm in multidimensional signal processing and modeling and the solutions to this problem are employed in many areas of image processing an original procedure for estimating the model parameters of discrete index 2 d noncausal gauss markov random fields gmrfs from noisy observations is proposed valid for both finite and infinite lattices and for any kind of boundary conditions starting from a suitable local representation of the gmrf and taking into account the symmetry property of so called field potentials a linear equation set relating the model parameters to the 2 d autocorrelation function known or estimated of the observed field is derived its solution gives the parameter estimates of the gmrf together with the estimate of the possibly unknown variance of the observation noise

self tuning deadbeat controllers abstract a deterministic self tuning deadbeat control scheme is presented which is extremely simple to implement in the single variable and multivariable cases its convergence properties are analysed by straightforward application of de larminat s convergence results

degenerations of amoebae and berkovich spaces we prove a continuity result for the fibers of the berkovich analytification of a complex algebraic variety with respect to the maximum of the archimedean norm and the trivial norm as a consequence we obtain generalizations of a result of mikhalkin and rullgard about degenerations of amoebae onto tropical varieties

valuative analysis of planar plurisubharmonic functions we show that valuations on the ring r of holomorphic germs in dimension 2 may be naturally evaluated on plurisubharmonic functions giving rise to generalized lelong numbers in the sense of demailly any plurisubharmonic function thus defines a real valued function on the set mathcal v of valuations on r and by way of a natural laplace operator defined in terms of the tree structure on mathcal v a positive measure on mathcal v this measure contains a great deal of information on the singularity at the origin under mild regularity assumptions it yields an exact formula for the mixed monge ampere mass of two plurisubharmonic functions as a consequence any generalized lelong number can be interpreted as an average of valuations using our machinery we also show that the singularity of any positive closed 1 1 current t can be attenuated in the following sense there exists a finite composition of blowups such that the pull back of t decomposes into two parts the first associated to a divisor with normal crossing support the second having small lelong numbers

valuations and multiplier ideals this article is the third of a series of work on a new approach to the study of singularities of various objects in a local two dimensional setting our focus in the present paper is on multiplier ideals and singularity exponents in the discussion below we fix an equicharacteristic zero two dimensional regular local ring r m with algebraically closed residue field an important example is the ring r do o holomorphic germs at the origin in c2 in fj1 we introduced the space v consisting of all r u 00 valued valuations on r centered at m and normalized by m 1 this space is naturally a tree it is a union of uncountably many real segments patched together in such a way that v remains homotopic to a point it is also an r tree in the classical sense for a natural metric we hence call v the valuative tree it encodes in a natural way all possible blowups of r centered at m and therefore gives a way of measuring quite precisely singularities of different kinds of objects the points in v that are not ends form the subtree vqm of quasimonomial valuations these valuations which can alternatively be characterized as abhyankar valuations of rank 1 or as

optimal smoothing for finite state hidden reciprocal processes this technical note addresses modelling and estimation of a class of finite state random processes called hidden reciprocal chains hrc a hidden reciprocal chain consists of a finite state reciprocal process together with an observation process conditioned on the reciprocal process much as in the case of a hidden markov model hmm the key difference between markov models and reciprocal models is that reciprocal models are non causal the technical note presents a characterization of a hrc by a finite set of hidden markov bridges which are hmms with the final state fixed the technical note then uses this characterization to derive the optimal fixed interval smoother for a hrc performance of linear and optimal smoothers derived for both hmm and hrc are compared using simulations for a class of hrc derived from underlying markov transitions these experiments suggest that not surprisingly the performance of the optimal hmm and hrc smoothers are signifcantly better than their linear counterparts and that some performance improvement is obtained using the hrc smoothers compared to the hmm smoothers the technical note concludes by mentioning some ongoing and future work which exploits this new markov bridge characterization of a hrc

modeling and estimation of discrete time gaussian reciprocal processes discrete time gaussian reciprocal processes are characterized in terms of a second order two point boundary value nearest neighbor model driven by a locally correlated noise whose correlation is specified by the model dynamics this second order model is the analog for reciprocal processes of the standard first order state space models for markov processes the model is used to obtain a solution to the smoothing problem for reciprocal processes the resulting smoother obeys second order equations whose structure is similar to that of the kalman filter for gauss markov processes it is shown that the smoothing error is itself a reciprocal process

effectiveness of demailly s strong openness conjecture and related problems in this article stimulated by the effectiveness in berndtsson s solution of the openness conjecture and continuing our solution of demailly s strong openness conjecture we discuss conditions to guarantee the effectiveness of the conjecture and establish such an effectiveness result we explicitly point out a lower semicontinuity property of plurisubharmonic functions with a multiplier which is implicitly contained in guan and zhou 2014 arxiv 1401 7158 we also obtain optimal effectiveness of the conjectures of demailly kollar and jonsson mustat respectively

a new characterization for multivariate gaussian reciprocal processes established a new necessary and sufficient condition for a multivariate gaussian random process to be reciprocal this result is then used to prove that the state vector of a two point boundary value system is reciprocal the authors do not impose any nonsingularity conditions on the covariance function of the state vector

characterization of multiplier ideal sheaves with weights of lelong number one abstract in this article we characterize plurisubharmonic functions of lelong number one at the origin such that the germ of the associated multiplier ideal sheaf is nontrivial in arbitrary complex dimension their singularity must be the sum of a germ of smooth divisor and of a plurisubharmonic function with zero lelong number we also present a new proof of the related well known integrability criterion due to skoda

maximum likelihood sequence estimation for hidden reciprocal processes this paper addresses the problem of maximum likelihood sequence estimation mlse based on a hidden reciprocal chain hrc as the underlying target model hrcs are non causal discrete time finite state stochastic processes which can be regarded as the one dimensional version of a markov random field although they are not in general markov processes this paper describes a procedure for evaluating the mlse for hrc and compares the resultant estimator with its markov model equivalent the viterbi algorithm in addition the performance of the newly proposed reciprocal mlse is compared to a hrc based optimal smoother

an extremal problem for generalized lelong numbers we look for pointwise bounds on a plurisubharmonic function near its singularity point given the value of its generalized lelong number with respect to a plurisubharmonic weight to this end an extremal problem is considered in certain cases the problem is solved explicitly

a proof of demailly s strong openness conjecture in this article we solve the strong openness conjecture on the multiplier ideal sheaf associated to any plurisubharmonic function which was posed by demailly the multiplier ideal sheaf associated to a plurisubharmonic function which is an invariant of the singularities of the psh function plays an important role in several complex variables and complex geometry various properties about the multiplier ideal sheaves associated to plurisubharmonic functions have been discussed e g see 25 7 30 31 demailly s strong openness conjecture means that the strong openness property about the multiplier ideal sheaf holds in the present article we establish such a useful strong openness property on the multiplier ideal sheaf associated to any plurisubharmonic function i e demailly s strong openness conjecture is true 1 1 organization of the paper the paper is organized as follows in the present section we recall the statement of the strong openness conjecture posed by demailly and present the main result of the present paper a solution of the strong openness conjecture in section 2 we recall or give some preliminary lemmas used in the proof of the main result in section 3 we give the proof of the strong openness conjecture and present some consequences by combining the conjecture with some well known results

recursive structure of noncausal gauss markov random fields an approach is developed for noncausal gauss markov random fields gmrfs that enables the use of recursive procedures while retaining the noncausality of the field recursive representations are established that are equivalent to the original field this is achieved by first presenting a canonical representation for gmrfs that is based on the inverse of the covariance matrix which is called the potential matrix it is this matrix rather than the field covariance that reflects in a natural way the mrf structure from its properties two equivalent one sided representations are derived each of which is obtained as the successive iterates of a riccati type equation for homogeneous fields these unilateral descriptions are symmetrized versions of each other the study of only one riccati equation being required it is proven that this riccati equation converges at a geometric rate therefore the one sided representations are asymptotically invariant these unilateral representations make it possible to process the fields with well known recursive techniques such as kalman bucy filters and two point smoothers

degree growth of meromorphic surface maps we study the degree growth of iterates of meromorphic self maps of compact kahler surfaces using cohomology classes on the riemann zariski space we show that the degrees grow similarly to those of mappings that are algebraically stable on some bimeromorphic model 0 introduction let x be a compact kahler surface and let f x x be a dominant meromorphic mapping fix a kahler class on x normalized by x 1 and define the degree of f with respect to to be the positive real number deg f f x f x where x denotes the intersection form on h 1 1 r x when x p2 and is the class of a line this coincides with the usual algebraic degree of f one can show that deg f n m 2 deg f deg f for all m n hence the limit 1 lim n deg f exists we refer to it as the asymptotic degree of f it follows from standard arguments see proposition 3 1 that 1 does not depend on the choice of that 1 is invariant under bimeromorphic conjugacy and that 1 2 where 2 is the topological degree of f

adaptive control of nonminimum phase systems recent papers have established global convergence for a class of adaptive control algorithms for discrete time linear dynamic systems however in most cases studied to date it has been assumed that the system is stably invertible this assumption plays a major role in the proofs of convergence in this paper we consider the more general case in which it is not assumed that the system is either stable or stably invertible we establish local convergence for a class of adaptive control algorithms applied to general discrete deterministic linear time invariant systems by convergence in this context we mean that the system inputs and outputs remain bounded for all time and the closed loop poles are effectively assigned in the limit for a given desired trajectory