on the existence of a limit value in some nonexpansive optimal control problems we investigate the limit of the average value of an optimal control problem when the horizon converges to infinity for this aim we suppose suitable nonexpansive like assumptions which does not imply that the limit is independent of the initial state as is usually done in the literature

on optimal finite state digital transmission systems the digital transmission of signals by transmitters and receivers that are time invariant finite state machines were investigated in general form an average distortion criterion is used some general structure theorems are proved and some examples given that show improvement in performance as the memories of the transmitter and receiver are increased many conjectures and unsolved problems are mentioned and areas for further study are indicated

helicity and the calugareanu invariant the helicity of a localized solenoidal vector field i e the integrated scalar product of the field and its vector potential is known to be a conserved quantity under frozen field distortion of the ambient medium in this paper we present a number of results concerning the helicity of linked and knotted flux tubes particularly as regards the topological interpretation of helicity in terms of the gauss linking number and its limiting form the c lug reanu invariant the helicity of a single knotted flux tube is shown to be intimately related to the c lug reanu invariant and a new and direct derivation of this topological invariant from the invariance of helicity is given helicity is decomposed into writhe and twist contributions the writhe contribution involving the gauss integral for definition see equation 4 8 which admits interpretation in terms of the sum of signed crossings of the knot averaged over all projections part of the twist contribution is shown to be associated with the torsion of the knot and part with what may be described as intrinsic twist of the field lines in the flux tube around the knot see equations 5 13 and 5 15 the generic behaviour associated with the deformation of the knot through a configuration with points of inflexion points at which the curvature vanishes is analysed and the role of the twist parameter is discussed the derivation of the c lug reanu invariant from first principles of fluid mechanics provides a good demonstration of the relevance of fluid dynamical techniques to topological problems

the value of repeated games with an informed controller we consider the general model of zero sum repeated games or stochastic games with signals and assume that one of the players is fully informed and controls the transitions of the state variable we prove the existence of the uniform value generalizing several results of the literature a preliminary existence result is obtained for a particular class of stochastic games played with pure strategies

packings of a charged line on a sphere we find equilibrium configurations of open and closed lines of charge on a sphere and track them with respect to varying sphere radius closed lines transition from a circle to a spiral like shape through two low wave number bifurcations char22 baseball seam and twist char22 which minimize coulomb energy the spiral shape is the unique stable equilibrium of the closed line other unstable equilibria arise through tip splitting events an open line transitions smoothly from an arc of a great circle to a spiral as the sphere radius decreases under repulsive potentials with faster than coulomb power law decay the spiral is tighter in initial stages of sphere shrinkage but at later stages of shrinkage the equilibria for all repulsive potentials converge on a spiral with uniform spacing between turns multiple stable equilibria of the open line are observed

the value of markov chain games with lack of information on one side we consider a two player zero sum game given by a markov chain over a finite set of states and a family of matrix games indexed by states the sequence of states follows the markov chain at the beginning of each stage only player 1 is informed of the current state then the corresponding matrix game is played and the actions chosen are observed by both players before proceeding to the next stage we call such a game a markov chain game with lack of information on one side this model generalizes the model of aumann and maschler of zero sum repeated games with lack of information on one side which corresponds to the case where the transition matrix of the markov chain is the identity matrix we generalize the proof of aumann and maschler and from the definition and the study of appropriate nonrevealing auxiliary games with infinitely many stages show the existence of the uniform value an important difference with aumann and maschler s model is that here the notions for player 1 of using the information and revealing a relevant information are distinct

long term values in markov decision processes and repeated games and a new distance for probability spaces we study long term markov decision processes mdps and gambling houses with applications to any partial observation mdps with finitely many states and zero sum repeated games with an informed controller we consider a decision maker who is maximizing the weighted sum t 1 x1d703 trt where rt is the expected reward of the t th stage we prove the existence of a very strong notion of long term value called general uniform value representing the fact that the decision maker can play well independently of the evaluations x1d703 t t 1 over stages provided the total variation or impatience t 1 x1d703 t 1 x1d703 t is small enough this result generalizes previous results of the literature that focus on arithmetic means and discounted evaluations moreover we give a variational characterization of the general uniform value via the introduction of appropriate invariant measures for the decision problems generalizing the fundamental theorem of gambling or the aumann maschler cav u formula for repeated games with incomple

discrete time controlled markov processes with average cost criterion a survey this work is a survey of the average cost control problem for discrete time markov processes the authors have attempted to put together a comprehensive account of the considerable research on this problem over the past three decades the exposition ranges from finite to borel state and action spaces and includes a variety of methodologies to find and characterize optimal policies the authors have included a brief historical perspective of the research efforts in this area and have compiled a substantial yet not exhaustive bibliography the authors have also identified several important questions that are still open to investigation

a uniform tauberian theorem in dynamic programming we prove that in dynamic programming framework uniform convergence of v implies uniform convergence of vn and vice versa moreover both have the same limit

stochastic games with a single controller and incomplete information we study stochastic games with incomplete information on one side in which the transition is controlled by one of the players we prove that if the informed player also controls the transitions the game has a value whereas if the uninformed player controls the transitions the max min value as well as the min max value exist but they may differ we discuss the structure of the optimal strategies and provide extensions to the case of incom plete information on both sides

average cost dynamic programming equations for controlled markov chains with partial observations the value function for the average cost control of a class of partially observed markov chains is derived as the vanishing discount limit in a suitable sense of the value functions for the corresponding discounted cost problems the limiting procedure is justified by bounds derived using a simple coupling argument

dynamic programming for ergodic control of markov chains under partial observations a correction a gap in the author s work on dynamic programming for ergodic control of partially observed markov chains v s borkar siam j control optim 39 2000 pp 673 681 is pointed out and a correction is provided

robust estimation when more than one variable per equation of condition has error summary it is well known that in the errors in variables estimation problem the results will have unnecessary asymptotic bias unless the algorithm is properly formulated similar difficulties can be expected with robust estimation techniques that are based on extending least squares to a noneuclidean metric this paper presents an algorithm for robust estimation for the nonlinear model errors in variables case the properties of the estimates produced by the algorithm are investigated and a numerical example using data on galaxies is given

on optimal causal coding of partially observed markov sources in single and multiterminal settings the optimal causal zero delay coding of a partially observed markov process is studied where the cost to be minimized is a bounded nonnegative additive measurable single letter function of the source and the receiver output a structural result is obtained extending witsenhausen s and walrand varaiya s structural results on optimal causal coders to more general state spaces and to a partially observed setting the decentralized multiterminal setup is also considered for the case where the source is an i i d process it is shown that an optimal solution to the decentralized causal coding of correlated observations problem is memoryless for markov sources a counterexample to a natural separation conjecture is presented

robust line estimation with errors in both variables abstract the estimator holding the central place in the theory of the multivariate errors in the variables ev model results from performing orthogonal regression on variables rescaled according to the covariance matrix of the errors our simulations on the univariate model essentially relegate this estimator to use only in large samples on data with no trace of outlier contamination a modification requiring a robust preliminary slope is proposed that essentially sets out the generalization to ev of the robust w estimator in regression it is demonstrated that the modification is robust to outlier contamination even in small samples given a sufficiently good preliminary estimator candidates for a preliminary slope estimator based on the data are discussed and the performance of one under simulation is examined

the energy spectrum of a twisted flexible string under elastic relaxation a full investigation of the energy spectrum of a twisted flexible string under elastic relaxation is presented and discussed in detail for the first time new polynomial expressions for critical energy states are derived and the whole spectrum of critical states minima maxima and inflexion points of the elastic energy is found and discussed in relation to superhelicity and elastic characteristics of the string the study is carried out in the context of the theory of linear elasticity and the thin rod approximation the relaxation mechanism is studied by using conservation of linking difference by the formula delta lk wr delta tw we show how specific geometric quantities such as pitch angle writhe and twist contributions as well as physical quantities such as torsional and bending energy depend on superhelicity given by the specific linking difference and elastic characteristics of the string given by bending and torsional rigidity these quantities expressed per unit length are examined and compared at each critical energy state starting from a supertwisted configuration we show that the string relaxes by twist reduction through two different intermediate helical states which correspond to different local minima to reach the lowest minimum energy state in a supercoiled configuration the case of a generic kink formation and consequent passage through an inflexional configuration is then examined and new expressions for the energy change in the vicinity of the inflexion point are derived

blackwell optimality in markov decision processes with partial observation a blackwell epsilon optimal strategy in a markov decision process is a strategy that is epsilon optimal for every discount factor sufficiently close to 1 we prove the existence of blackwell epsilon optimal strategies in finite markov decision processes with partial observation

on a markov game with one sided information we apply the average cost optimality equation to zero sum markov games by considering a simple game with one sided incomplete information that generalizes an example of aumann and maschler aumann r j m b maschler 1995 repeated games with incomplete information mit press cambridge ma we determine the value and identify the optimal strategies for a range of parameters

fixed length lossy compression in the finite blocklength regime this paper studies the minimum achievable source coding rate as a function of blocklength n and probability that the distortion exceeds a given level d tight general achievability and converse bounds are derived that hold at arbitrary fixed blocklength for stationary memoryless sources with separable distortion the minimum rate achievable is shown to be closely approximated by r d v d n q 1 where r d is the rate distortion function v d is the rate dispersion a characteristic of the source which measures its stochastic variability and q 1 is the inverse of the standard gaussian complementary cumulative distribution function

optimal zero delay coding of markov sources stationary and finite memory codes the optimal zero delay coding of a finite state markov source is considered the existence and structure of optimal codes are studied using a stochastic control formulation prior results in the literature established the optimality of deterministic markov walrand varaiya type coding policies for the finite time horizon problem and the optimality of both deterministic nonstationary and randomized stationary policies for the infinite time horizon problem our main result here shows that for any irreducible and aperiodic markov source with a finite alphabet deterministic and stationary markov coding policies are optimal for the infinite horizon problem in addition the finite block length time horizon performance of an optimal stationary and markov coding policy is shown to approach the infinite time horizon optimum at a rate o 1 t the results are extended to systems where zero delay communication takes place across a noisy channel with noiseless feedback

measurement error model collinearities collinearities can occur among the error free true predictors in measurement error models just as they occur among predictors in traditional regression models the coefficient estimators for measurement error models suffer the same ill effects of collinearities as do least squares estimators for linear measurement error models collinearities are a property of the secondorder moment matrix of the unobservable error free predictors for nonlinear models they are a property of the second order moment matrix of derivatives of the nonlinear function in this article collinearities among the predictors in measurement error models are defined and diagnostics for their detection are discussed the collinearity diagnostics introduced are similar to those used in traditional regression models but they are applied to estimated second order moment matrices of the error free predictors rather than to the second order moment matrix of the observed predictors examples are discussed one of which demonstrates th

multiple folding and packing in dna modeling in this paper we introduce and analyze a set of equations to study geometric and energetic aspects associated with the kinematics of multiple folding and coiling of closed filaments for dna modeling by these equations we demonstrate that a high degree of coiling may be achieved at relatively low energy costs through appropriate writhe and twist distribution and independently from the number of coils formed for sufficiently high twist we show that coiling is actually favoured by elastic energy relaxation when the deformation energy is due to curvature and the mean twist of the filament we give estimates for the writhing process based purely on curvature information and the number of coils produced we also determine the packing rate associated with filament compaction in the case of a hierarchical helical coiling these results find useful applications in dna biology especially in modeling dna wrapping in proteic regions where there is a strong connection between high coiling efficient compaction and energy localization

the capacity of channels with feedback in this paper we introduce a general framework for treating channels with memory and feedback first we prove a general feedback channel coding theorem based on massey s concept of directed information second we present coding results for markov channels this requires determining appropriate sufficient statistics at the encoder and decoder we give a recursive characterization of these sufficient statistics third a dynamic programming framework for computing the capacity of markov channels is presented fourth it is shown that the average cost optimality equation acoe can be viewed as an implicit single letter characterization of the capacity fifth scenarios with simple sufficient statistics are described sixth error exponents for channels with feedback are presented

robust estimation in the errors in variables model summary orthogonal regression analogues of m estimates of regression called here orthogonal regression m estimates are defined these estimates are shown to be consistent at elliptical errors in variables models and robust if the corresponding loss function is bounded the orthogonal regression analogues of regression scale estimates called here orthogonal regression s estimates are considered as well in particular they provide a robust estimate for the scale of the orthogonal residuals a crucial quantity in the computation of orthogonal regression m estimates finally we present an algorithm for computing orthogonal regression s and m estimates and the results of a small monte carlo experiment

fitting data with errors in all variables using the huber m estimator this article is concerned with the problem of data fitting where the model is nonlinear in the free parameters using the huber m estimator under the assumption that there are significant errors in all the variables an efficient algorithm is developed some numerical examples are given