conservative arrays multidimensional modulation codes for holographic recording in holographic storage two dimensional arrays of binary data is optically recorded in a medium via an interference process to ensure optimum operation of a holographic recording system it is desirable that the patterns of 1s light and 0s no light in the recorded array satisfy the following modulation constraint in each row and column of the array there are at least t transitions of the type 1 spl rarr 0 or 0 spl rarr 1 for a prescribed integer t a two dimensional array with this property is said to be a conservative array of strength t in general an n dimensional conservative array of strength t is a binary array having at least t transitions in each column extending in any of the n dimensions of the array we present an algorithm for encoding unconstrained binary data into an n dimensional conservative array of strength t the algorithm employs differential coding and error correcting codes using n binary codes one per dimension with minimum hamming distance d spl ges 2t 3 we apply a certain transformation to an arbitrary information array which ensures that the number of transitions in each dimension is determined by the minimum distance of the corresponding code

the positive capacity region of two dimensional run length constrained channels a binary sequence satisfies a one dimensional d k constraint if every run of zeros with possible exception of the first and the last runs has length at least d and at most k a binary two dimensional array satisfies a d k constraint if each row and each column satisfies the one dimensional d k constraint few models have been proposed in the literature to handle two dimensional data the diamond model the square model the hexagonal model and the triangular model the constraints in the different directions might be asymmetric and hence many kind of constraints are defined depending on the number of directions in the model for example a two dimensional array in the diamond model satisfies a d1 k1 d2 k 2 constraint if it satisfies the one dimensional d1 k1 constraint horizontally and the one dimensional d 2 k2 constraint vertically in this correspondence the region in which the capacity is zero or positive in the various models is examined asymmetric constraints in the diamond model and symmetric constraints in the other models are considered in particular an almost complete solution for asymmetric constraints in the diamond model is provided

on generalized predictive control two alternative formulations two alternative solutions to the generalized predictive control gpc design problem are given for the case when the output horizon is larger than or equal to the plant order first using multirate models of the discrete time plant we present a state space solution that does not require state observers or riccati equation iterations for its implementation second it is shown via simple algebraic manipulations that the key prediction equation used for gpc can be easily derived from the transfer function coefficients effectively replacing the diophantine equation recursions by the inversion of a lower triangular matrix

two dimensional runlength constrained arrays with equal horizontal and vertical constraints a binary array is a d1 k1 d2 k 2 runlength constrained array if the runs of zeros in every row and column have length at least d1 and at most k1 and the runs of ones in every row and column have length at least d2 and at most k2 such arrays arise in the context of digital storage devices writing n m n d1 k1 d2 k2 for the number of d1 k 1 d2 k2 runlength constrained arrays of size mtimesn the capacity c d1 k1 d2 k2 is defined to be limm nrarrinfin 1 mn log2n m n d1 k 1 d2 k2 let d2 be an integer such that d2 ges 1 the paper shows that c 1 d2 delta d2 d2 is positive when delta ges 2 but is zero when delta les 1

partial characterization of the positive capacity region of two dimensional asymmetric run length constrained channels a binary sequence satisfies a one dimensional d k run length constraint if every run of zeros has length at least d and at most k a two dimensional binary pattern is d sub 1 k sub 1 d sub 2 k sub 2 constrained if it satisfies the one dimensional d sub 1 k sub 1 run length constraint horizontally and the one dimensional d sub 2 k sub 2 run length constraint vertically for given d sub 1 k sub 1 d sub 2 and k sub 2 the asymmetric two dimensional capacity is defined as c sub d1 k1 d2 k2 lim sub m n spl rarr spl infin 1 mn log sub 2 n sub m n sup d1 k1 d2 k2 where n sub m n sup d1 k1 d2 k2 denotes the number of d sub 1 k sub 1 d sub 2 k sub 2 constrained m spl times n binary patterns we determine whether the capacity is positive or is zero for many choices of d sub 1 k sub 1 d sub 2 k sub 2

entropy bounds for constrained two dimensional random fields the maximum entropy and thereby the capacity of two dimensional 2 d fields given by certain constraints on configurations is considered upper and lower bounds are derived a new class of 2 d processes yielding good lower bounds is introduced asymptotically the process achieves capacity for constraints with limited long range effects the processes are general and may also be applied to e g data compression of digital images results are given for the binary hard square model which is a 2 d run length limited model and some other 2 d models with simple constraints

existence of stationary distributions for kolmogorov systems of competitive type under telegraph noise abstract this work focuses on population dynamics of two species described by kolmogorov systems of competitive type under telegraph noise that is formulated as a continuous time markov chain with two states our main effort is on establishing the existence of an invariant or a stationary probability measure in addition the convergence in total variation of the instantaneous measure to the stationary measure is demonstrated under suitable conditions moreover the limit set of a model in which each species is dominant in a state of the telegraph noise is examined in detail

densities for piecewise deterministic markov processes with boundary abstract we study the existence of densities for distributions of piecewise deterministic markov processes we also obtain relationships between invariant densities of the continuous time process and that of the process observed at jump times in our approach we use functional analytic methods and the theory of linear operator semigroups by imposing general conditions on the characteristics of a given markov process we show the existence of a substochastic semigroup describing the evolution of densities for the process and we identify its generator our main tool is a new perturbation theorem for substochastic semigroups where we perturb both the action of the generator and of its domain allowing to treat general transport type equations with non local boundary conditions a couple of particular examples illustrate our general results

stabilizability of linear systems over a commutative normed algebra with applications to spatially distributed and parameter dependent systems the problem of achieving stabilization by using state feedback is considered for linear systems given by a pair of matrices whose entries belong to a real or complex commutative normed algebra this framework is applicable to various types of linear systems including spatially distributed systems systems depending on parameters and infinite dimensional systems necessary and sufficient conditions for stabilizability are derived in terms of solutions to an associated riccati equation defined in the gelfand transform domain necessary and sufficient conditions for stabilizability are also given in terms of a local rank criterion involving the gelfand transform of the system coefficients the results are applied to the problem of positioning a long seismic cable

on the capacity of two dimensional run length constrained channels two dimensional binary patterns that satisfy one dimensional d k run length constraints both horizontally and vertically are considered for a given d and k the capacity c sub d k is defined as c sub d k lim sub m n spl rarr spl infin log sub 2 n sub m n sup d k mn where n sub m n sup d k denotes the number of m spl times n rectangular patterns that satisfy the two dimensional d k run length constraint bounds on c sub d k are given and it is proven for every d spl ges 1 and every k d that c sub d k 0 if and only if k d 1 encoding algorithms are also discussed

spectral gaps for hyperbounded operators abstract we consider a positive and power bounded linear operator t on l p over a finite measure space and prove that if t l p l q for some q p then the essential spectral radius of t is strictly smaller than 1 as a special case we obtain a recent result of miclo who proved this assertion for self adjoint ergodic markov operators in the case p 2 and thereby solved a long open problem of simon and hoegh krohn our methods draw a connection between spectral theory and the geometry of banach spaces they rely on a result going back to groh that encodes spectral gap properties via ultrapowers and on the fact that an infinite dimensional l p space cannot be isomorphic to an l q space for q p we also prove a number of variations of our main result i it follows from theorems of lotz and martinez that the condition t l p l q can be replaced with the weaker assumption that t maps the positive part of the l p unit ball into a uniformly p integrable set ii while it is known that the positivity assumption on t cannot in general be omitted we show that we can replace it with the assumption that t is contractive both on l p and on l q iii we prove a version of the theorem which allows us under appropriate circumstances to also consider non finite measures spaces iv our result also has a uniform version there exists an upper bound c 0 1 for the essential spectral radius of t where c depends on certain quantitative properties of t l p and l q

asymptotic behavior of distributions of mrna and protein levels in a model of stochastic gene expression abstract the paper is devoted to a stochastic process introduced in the recent paper by lipniacki et al t lipniacki p paszek a marciniak czochra a r brasier m kimmel transcriptional stochasticity in gene expression j theor biol 238 2006 348 367 in modelling gene expression in eukaryotes starting from the full generator of the process we show that its distributions satisfy a fokker planck type system of partial differential equations then we construct a c 0 markov semigroup in l 1 space corresponding to this system the main result of the paper is asymptotic stability of the involved semigroup in the set of densities

almost everywhere convergence of powers of some positive lp contractions abstract we extend the solution of burkholder s conjecture for products of conditional expectations obtained by delyon and delyon for l 2 and by cohen for l p 1 p to the context of badea and lyubich let t be a finite convex combination of operators t j which are products of finitely many conditional expectations then t n f converges a e for every f l p 1 p with sup n t n f l p the proof uses the work of le merdy and xu on positive l p contractions satisfying ritt s resolvent condition as another application of the work of le merdy and xu we extend a result of bellow jones and rosenblatt proving that if a probability a k k z has bounded angular ratio then for every positive invertible isometry s of an l p space 1 p the operator t k z a k s k is a positive l p contraction such that for every f l p t n f converges a e and sup n t n f l p if a k is supported on n the same result is true when s is only a positive contraction of l p similar results are obtained for averages of bounded continuous representations of a compact lca group by positive operators in one l p space 1 p for a positive contraction t on l p which satisfies ritt s condition and f i t l p 0 1 we prove that n t n f 0 a e and sup n n t n f l p

robust adaptive regulation without persistent excitation a globally convergent adaptive regulator for minimum or nonminimum phase systems subject to bounded disturbances is presented the control strategy is designed for a particular input output representation obtained from the state space representation of the system the leading coefficient of the novel representation is the product of the observability and controllability matrices of the system the controller scheme uses a least squares identification algorithm with a dead zone the dead zone is chosen to obtain convergence properties on the estimates and on the covariance matrix as well this allows the definition of modified estimates which secure well conditioned matrices in the adaptive control law explicit bounds on the plant output are given

continuous markov semigroups and stability of transport equations a new theorem for asymptotic stability of markov semigroups is proved this result is applied to transport equations connected with diffusion and jumping processes and randomly perturbed dynamical systems

stability of markov semigroups and applications to parabolic systems abstract a new theorem for asymptotic stability of markov semigroups is proved this result is applied to semigroups generated by parabolic systems describing the evolution of densities of two state diffusion processes

asymptotic decomposition of substochastic operators and semigroups abstract theorems on asymptotic decomposition of substochastic operators and semigroups are given general results are applied to show asymptotic periodicity asymptotic stability and sweeping of substochastic operators and semigroups

bounds on the capacity of constrained two dimensional codes bounds on the capacity of constrained two dimensional 2 d codes are presented the bounds of calkin and wilf see siam j discr math vol 11 no 1 p 54 60 1998 apply to first order symmetric constraints the bounds are generalized in a weaker form to higher order and nonsymmetric constraints results are given for constraints specified by run length limits or a minimum distance between pixels of a given value

shannon capacity of m ary redundant multitrack runlength limited codes we consider multiamplitude multitrack runlength limited d k constrained channels with and without clock redundancy we calculate the shannon capacities of these channels and present some simple 100 efficient codes to compute capacity a constraint graph equivalent to the usual runlength limited constraint graph is used the introduced graph model has the vertex labeling independent of number of tracks to be written on in parallel which provides computational savings when the number of tracks is large we show that increasing the number of tracks written on in parallel provides significant increase of per track capacity for the more restrictive clocking constraint case i e when k d but it does not have much influence on the channel capacity when k spl ges d

block form control of linear time invariant discrete time systems defined over commutative rings abstract a new approach based on a block input block output state model is developed for the study of linear time invariant discrete time systems whose coefficients belong to a commutative ring with 1 it is well known that such systems arise in the study of various classes of complex linear systems including systems depending on parameters and multidimentional systems by time compressing the block input state representation new results are obtained on the construction of a memoryless block form state feedback control law that yields a type of assignability and or deadbeat control these results are then dualized to yield results on a new type of state observer based on a block of output measurements the observer and state feedback controller are then combined to yield new results on input output regulation and set point tracking for systems defined over an arbitrary commutative ring in the last part of the paper the block input form is utilized to study the stabilization of systems defined over a normed algebra

design of a stable state feedback controller based on the multirate sampling of the plant output a new type of controller is proposed which detects the ith plant output n sub i times during a period of t sub 0 and changes the plant inputs once during t sub 0 it is shown that an arbitrary state feedback can be realized by such controllers if the plant is observable this implies for instance that arbitrary symmetric pole assignment is possible if the plant is controllable it is also shown that if the plant has no zeros at the origin the state transition matrix of the controller itself can be set arbitrarily without changing the state feedback to be realized that is to say inversely expressed any state feedback can be equivalently realized by a controller with any prescribed degree of stability

capacity bounds for the three dimensional 0 1 run length limited channel the capacity c sub 0 1 sup 8 of a three dimensional 0 1 run length constrained channel is shown to satisfy 0 522501741838 spl les c sub 0 1 sup 8 spl les 0 526880847825

feedback linearization of sampled data systems it is shown that feedback linearizability of a continuous time system can be destroyed through the introduction of the usual sample and hold devices a method whereby a feedback linearizable discrete time model can be recovered is given

iterative positive definite solutions of the two nonlinear matrix equations x a t x 2 a i in this paper iterative methods for obtaining positive definite solutions of the two matrix equations x a t x 2a i are proposed we show that under some conditions on the real square matrix a the constructed iterative methods converge to positive definite solutions for the two equations numerical examples are given to test and illustrate the performance of the algorithms in terms of convergence accuracy as well as the efficiency

writing sequences on the plane the problem of arranging two dimensional arrays of data into one dimensional sequences comes up in image processing color quantization and optical and magnetic data recording a good arrangement should enable the one dimensional sequences to be modeled as markov chains or shifts of finite type since this is not possible in general two dimensional data is most commonly scanned by rows columns or diagonals we look into three unusual ways to write a sequence in the plane by penrose tilings by space filling curves and by cylindrical and spiral lattices we show how penrose tilings can be used to record information and how some spiral lattices can be used for quantization of color spaces

regulation of split linear systems over rings coefficient assignment and observers a theory of regulators is developed for finite free split linear systems over a commutative ring k this is achieved by developing a theory of coefficient assignment and observers it is shown that the problem of coefficient assignment can be solved for reachable systems by using dynamic state feedback for strongly observable systems it is shown that observers with arbitrary dynamics can be constructed internal stability of observer and state feedback configuration is considered explicitly some examples are given to illustrate these techniques