superresolution reconstruction through object modeling and parameter estimation a method based on object modeling and parameter estimation is proposed to achieve superresolution reconstruction an efficient method for solving for the model parameters is given that uses linear prediction theory and linear least squares fitting reconstruction results from simulated and real magnetic resonance data are also presented to demonstrate its capability for gibbs ringing reduction and resolution enhancement

weak approachability in this paper we study repeated games with vector payoffs following blackwell 2 we define weak approachability and its dual property weak excludability we use results from differential games with fixed duration to prove that every set is either weakly approachable or weakly excludable

the complexity of mean payoff games on graphs abstract we study the complexity of finding the values and optimal strategies of mean payoff games on graphs a family of perfect information games introduced by ehrenfeucht and mycielski and considered by gurvich karzanov and khachiyan we describe a pseudo polynomial time algorithm for the solution of such games the decision problem for which is in np conp finally we describe a polynomial reduction from mean payoff games to the simple stochastic games studied by condon these games are also known to be in np conp but no polynomial or pseudo polynomial time algorithm is known for them

a generalization of the darcy forchheimer equation involving an implicit pressure dependent relation between the drag force and the velocity abstract we study mathematical properties of steady flows described by the system of equations generalizing the classical porous media models of darcy and forchheimer the considered generalizations are outlined by implicit relations between the drag force and the velocity that are in addition parametrized by the pressure we analyze such drag force velocity relations which are described through a maximal monotone graph varying continuously with the pressure large data existence of a solution to this system is established whereupon we show that under certain assumptions on data the pressure satisfies a maximum or minimum principle even if the drag coefficient depends on the pressure exponentially

regularized iterative image restoration with ringing reduction linear space invariant image restoration algorithms often introduce ringing effects near sharp intensity transitions it is shown that these artifacts are attributable to the regularization of the ill posed image restoration problem two possible methods to reduce the ringing effects in restored images are proposed the first method incorporates deterministic a priori knowledge about the original image into the restoration algorithm the second method locally regulates the severity of the noise magnification and the ringing phenomenon depending on the edge information in the image a regularized iterative image restoration algorithm is proposed in which both ringing reduction methods are included by making use of the theory of the projections onto convex sets and the concept of norms in a weighted hilbert space both the numerical performance and the visual evaluation of the results are improved by the use of ringing reduction

unsteady flows of fluids with pressure dependent viscosity in this short paper we consider the unsteady flows of fluids with pressure dependent viscosities when the effect of gravity has to be taken into account such a situation presents itself in many technologically relevant flows after developing the appropriate governing equations we establish qualitative results concerning the nature of the solutions to the governing equations as well as uniqueness results we then obtain explicit exact solutions for two initial boundary value problems namely modified stokes first and second problems such explicit solutions serve a dual purpose they present exact results for idealized problems that reflect practical situations and they provide a means for checking the numerical schemes that are developed for flows in more complex situations

the reconstruction of a multidimensional sequence from the phase or magnitude of its fourier transform this paper addresses two fundamental issues involved in the reconstruction of a multidimensional sequence from either the phase or magnitude of its fourier transform the first issue relates to the uniqueness of a multidimensional sequence in terms of its phase or magnitude although phase or magnitude information alone is not sufficient in general to uniquely specify a sequence a large class of sequences are shown to be recoverable from their phase or magnitude the second issue which is addressed in this paper concerns the actual reconstruction of a multidimensional sequence from its phase or magnitude for those sequences which are uniquely specified by their phase several practical algorithms are described which may be used to reconstruct a sequence from its phase several examples of phase only reconstruction are also presented unfortunately however even for those sequences which are uniquely defined by their magnitude it appears that a practical algorithm is yet to be developed for reconstructing a sequence from only its magnitude nevertheless an iterative procedure which has been proposed is briefly discussed and evaluated

concurrent games with tail objectives we study infinite stochastic games played by two players over a finite state space with objectives specified by sets of infinite traces the games are concurrent players make moves simultaneously and independently stochastic the next state is determined by a probability distribution that depends on the current state and chosen moves of the players and infinite proceed for an infinite number of rounds the analysis of concurrent stochastic games can be classified into quantitative analysis analyzing the optimum value of the game and e optimal strategies that ensure values within e of the optimum value and qualitative analysis analyzing the set of states with optimum value 1 and e optimal strategies for the states with optimum value 1 we consider concurrent games with tail objectives i e objectives that are independent of the finite prefix of traces and show that the class of tail objectives is strictly richer than that of the w regular objectives we develop new proof techniques to extend several properties of concurrent games with w regular objectives to concurrent games with tail objectives we prove the positive limit one property for tail objectives the positive limit one property states that for all concurrent games if the optimum value for a player is positive for a tail objective f at some state then there is a state where the optimum value is 1 for the player for the objective f we also show that the optimum values of zero sum strictly conflicting objectives games with tail objectives can be related to equilibrium values of nonzero sum not strictly conflicting objectives games with simpler reachability objectives a consequence of our analysis presents a polynomial time reduction of the quantitative analysis of tail objectives to the qualitative analysis for the subclass of one player stochastic games markov decision processes

compositional strategy synthesis for stochastic games with multiple objectives abstract design of autonomous systems is facilitated by automatic synthesis of controllers from formal models and specifications we focus on stochastic games which can model interaction with an adverse environment as well as probabilistic behaviour arising from uncertainties our contribution is twofold first we study long run specifications expressed as quantitative multi dimensional mean payoff and ratio objectives we then develop an algorithm to synthesise e optimal strategies for conjunctions of almost sure satisfaction for mean payoffs and ratio rewards in general games and boolean combinations of expected mean payoffs in controllable multi chain games second we propose a compositional framework together with assume guarantee rules which enables winning strategies synthesised for individual components to be composed to a winning strategy for the composed game the framework applies to a broad class of properties which also include expected total rewards and has been implemented in the software tool prism games

supervisory control of a class of discrete event processes this paper studies the control of a class of discrete event processes i e processes that are discrete asynchronous and possibly nondeter ministic the controlled process is described as the generator of a formal language while the controller or supervisor is constructed from the grammar of a specified target language that incorporates the desired closed loop system behavior the existence problem for a supervisor is reduced to finding the largest controllable language contained in a given legal language two examples are provided

looking at mean payoff and total payoff through windows we consider two player games played on weighted directed graphs with mean payoff and total payoff objectives two classical quantitative objectives while for single dimensional games the complexity and memory bounds for both objectives coincide we show that in contrast to multi dimensional mean payoff games that are known to be conp complete multi dimensional total payoff games are undecidable we introduce conservative approximations of these objectives where the payoff is considered over a local finite window sliding along a play instead of the whole play for single dimension we show that i if the window size is polynomial deciding the winner takes polynomial time and ii the existence of a bounded window can be decided in np conp and is at least as hard as solving mean payoff games for multiple dimensions we show that i the problem with fixed window size is exptime complete and ii there is no primitive recursive algorithm to decide the existence of a bounded window

on the c1 γ ω w2 2 ω regularity for a class of electro rheological fluids abstract we are concerned with a system of nonlinear partial differential equations with p x structure 1 p p x p 0 and no slip boundary conditions we prove the existence and uniqueness of a c 1 w 2 2 solution corresponding to small data without further restrictions on the bounds p p 0 in particular this result is applicable to the steady motion of shear dependent electro rheological fluids

a scalable variational inequality approach for flow through porous media models with pressure dependent viscosity abstract mathematical models for flow through porous media typically enjoy the so called maximum principles which place bounds on the pressure field it is highly desirable to preserve these bounds on the pressure field in predictive numerical simulations that is one needs to satisfy discrete maximum principles dmp unfortunately many of the existing formulations for flow through porous media models do not satisfy dmp this paper presents a robust scalable numerical formulation based on variational inequalities vi to model non linear flows through heterogeneous anisotropic porous media without violating dmp vi is an optimization technique that places bounds on the numerical solutions of partial differential equations to crystallize the ideas a modification to darcy equations by taking into account pressure dependent viscosity will be discretized using the lowest order raviart thomas rt0 and variational multi scale vms finite element formulations it will be shown that these formulations violate dmp and in fact these violations increase with an increase in anisotropy it will be shown that the proposed vi based formulation provides a viable route to enforce dmp moreover it will be shown that the proposed formulation is scalable and can work with any numerical discretization and weak form a series of numerical benchmark problems are solved to demonstrate the effects of heterogeneity anisotropy and non linearity on dmp violations under the two chosen formulations rt0 and vms and that of non linearity on solver convergence for the proposed vi based formulation parallel scalability on modern computational platforms will be illustrated through strong scaling studies which will prove the efficiency of the proposed formulation in a parallel setting algorithmic scalability as the problem size is scaled up will be demonstrated through novel static scaling studies the performed static scaling studies can serve as a guide for users to be able to select an appropriate discretization for a given problem size

a general formulation for iterative restoration methods information theory based techniques for signal or image restoration and resolution enhancement are now considered a viable alternative to other popular techniques in this correspondence we present a general iterative mapping derived using an information theoretic criterion of optimality a mathematical structure is defined followed by an analysis of the mapping based on this structure the convergence of the mapping is considered both in the general formulation and for a particular example some popular techniques are shown to be special cases of this general mapping

opportunistic approachability and generalized no regret problems blackwell s theory of approachability introduced in 1956 has since proved a useful tool in the study of a range of repeated multiagent decision problems given a repeated matrix game with vector payoffs a target set s is approachable by a certain player if he can ensure that the average payoff vector converges to that set for any strategy of the opponent in this paper we consider the case where a set need not be approachable in general but may be approached if the opponent played favorably in some sense in particular we consider nonconvex sets that satisfy blackwell s dual condition namely can be approached when the opponent plays a stationary strategy whereas the convex hull of such a set is approachable this is not generally the case for the original nonconvex set itself we start by defining a sense of restricted play of the opponent with stationary strategies being a special case and then formulate appropriate goals for an opportunistic approachability algorithm that can take advantage

regularization theory in image restoration the stabilizing functional approach several aspects of the application of regularization theory in image restoration are presented this is accomplished by extending the applicability of the stabilizing functional approach to 2 d ill posed inverse problems inverse restoration is formulated as the constrained minimization of a stabilizing functional the choice of a particular quadratic functional to be minimized is related to the a priori knowledge regarding the original object through a formulation of image restoration as a maximum a posteriori estimation problem this formulation is based on image representation by certain stochastic partial differential equation image models the analytical study and computational treatment of the resulting optimization problem are subsequently presented as a result a variety of regularizing filters and iterative regularizing algorithms are proposed a relationship between the regularized solutions proposed and optimal wiener estimation is identified the filters and algorithms proposed are evaluated through several experimental results

weighted lq estimates for stationary stokes system with partially bmo coefficients abstract we prove the unique solvability of solutions in sobolev spaces to the stationary stokes system on a bounded reifenberg flat domain when the coefficients are partially bmo functions i e locally they are merely measurable in one direction and have small mean oscillations in the other directions using this result we establish the unique solvability in muckenhoupt type weighted sobolev spaces for the system with partially bmo coefficients on a reifenberg flat domain we also present weighted a priori l q estimates for the system when the domain is the whole euclidean space or a half space

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 optimal stationary policies in infinite state markov decision processes with unbounded costs we deal with infinite state markov decision processes with unbounded costs three simple conditions based on the optimal discounted value function guarantee the existence of an expected average cost optimal stationary policy sufficient conditions are the existence of a distinguished state of smallest discounted value and a single stationary policy inducing an irreducible ergodic markov chain for which the average cost of a first passage from any state to the distinguished state is finite a result to verify this is also given two examples illustrate the ease of applying the criteria

the complexity of stochastic games abstract we consider the complexity of stochastic games simple games of chance played by two players we show that the problem of deciding which player has the greatest chance of winning the game is in the class np co np

response based approachability with applications to generalized no regret problems blackwell s theory of approachability provides fundamental results for repeated games with vector valued payoffs which have been usefully applied in the theory of learning in games and in devising online learning algorithms in the adversarial setup a target set s is approachable by a player the agent in such a game if he can ensure that the average payoff vector converges to s no matter what the opponent does blackwell provided two equivalent conditions for a convex set to be approachable standard approachability algorithms rely on the primal condition which is a geometric separation condition and essentially require to compute at each stage a projection direction from a certain point to s here we introduce an approachability algorithm that relies on blackwell s dual condition which requires the agent to have a feasible response to each mixed action of the opponent namely a mixed action such that the expected payoff vector belongs to s thus rather than projections the proposed algorithm relies on computing the response to a certain action of the opponent at each stage we demonstrate the utility of the proposed approach by applying it to certain generalizations of the classical regret minimization problem which incorporate side constraints reward to cost criteria and so called global cost functions in these extensions computation of the projection is generally complex while the response is readily obtainable

deciding parity games in quasi polynomial time it is shown that the parity game can be solved in quasi polynomial time the parameterized parity game with n nodes and m distinct values a k a colors or priorities is proven to be in th

an iterative method for the extrapolation of band limited functions abstract we derive an iterative algorithm to extrapolate band limited functions using the operators of fourier transform and projection on convex subsets the algorithm allows the use of a priori knowledge in the extrapolation procedure

meet your expectations with guarantees beyond worst case synthesis in quantitative games abstract classical analysis of two player quantitative games involves an adversary modeling the environment of the system which is purely antagonistic and asks for strict guarantees while markov decision processes model systems facing a purely randomized environment the aim is then to optimize the expected payoff with no guarantee on individual outcomes we introduce the beyond worst case synthesis problem which is to construct strategies that guarantee some quantitative requirement in the worst case while providing a higher expected value against a particular stochastic model of the environment given as input we study the beyond worst case synthesis problem for two important quantitative settings the mean payoff and the shortest path in both cases we show how to decide the existence of finite memory strategies satisfying the problem and how to synthesize one if one exists we establish algorithms and we study complexity bounds and memory requirements

on steady flows of fluids with pressure and shear dependent viscosities there are many technologically important problems such as elastohydrodynamics which involve the flows of a fluid over a wide range of pressures while the density of the fluid remains essentially constant during these flows whereby the fluid can be approximated as being incompressible the viscosity varies significantly by several orders of magnitude it is also possible that the viscosity of such fluids depends on the shear rate here we consider the flows of a class of incompressible fluids with viscosity that depends on the pressure and shear rate we establish the existence of weak solutions for the steady flows of such fluids subjected to homogeneous dirichlet boundary conditions and to specific body forces that are not necessarily assumed to be small a novel aspect of the study is the manner in which we treat the pressure that allows us to establish its compactness as well as that of the velocity gradient the method draws upon the physics of the problem namely that the notion of incompressibility is an idealization that is attained by letting the compressibility of the fluid to tend to zero

quantitative fair simulation games simulation is an attractive alternative for language inclusion for automata as it is an under approximation of language inclusion but usually has much lower complexity for non deterministic automata while language inclusion is pspace complete simulation can be computed in polynomial time simulation has also been extended in two orthogonal directions namely 1 fair simulation for simulation over specified set of infinite runs and 2 quantitative simulation for simulation between weighted automata again while fair trace inclusion is pspace complete fair simulation can be computed in polynomial time for weighted automata the quantitative language inclusion problem is undecidable for mean payoff automata and the decidability is open for discounted sum automata whereas the quantitative simulation reduce to mean payoff games and discounted sum games which admit pseudo polynomial time algorithms in this work we study quantitative simulation for weighted automata with buchi acceptance conditions i e we generalize fair simulation from non weighted automata to weighted automata we show that imposing buchi acceptance conditions on weighted automata changes many fundamental properties of the simulation games for example whereas for mean payoff and discounted sum games the players do not need memory to play optimally we show in contrast that for simulation games with buchi acceptance conditions i for mean payoff objectives optimal strategies for both players require infinite memory in general and ii for discounted sum objectives optimal strategies need not exist for both players while the simulation games with buchi acceptance conditions are more complicated e g due to infinite memory requirements for mean payoff objectives as compared to their counterpart without buchi acceptance conditions we still present pseudo polynomial time algorithms to solve simulation games with buchi acceptance conditions for both weighted mean payoff and weighted discounted sum automata

a fuzzy approach to markov decision processes with uncertain transition probabilities in this paper markov decision models with uncertain transition matrices which allow a matrix to fluctuate at each step in time is described by the use of fuzzy sets we find a pareto optimal policy maximizing the infinite horizon fuzzy expected discounted reward fedr over all stationary policies under some partial order the pareto optimal policies are characterized by maximal solutions of an optimal inclusion including efficient set functions as a numerical example a machine maintenance problem is considered

a geometric approach to multi criterion reinforcement learning we consider the problem of reinforcement learning in a controlled markov environment with multiple objective functions of the long term average reward type the environment is initially unknown and furthermore may be affected by the actions of other agents actions that are observed but cannot be predicted beforehand we capture this situation using a stochastic game model where the learning agent is facing an adversary whose policy is arbitrary and unknown and where the reward function is vector valued state recurrence conditions are imposed throughout in our basic problem formulation a desired target set is specified in the vector reward space and the objective of the learning agent is to approach the target set in the sense that the long term average reward vector will belong to this set we devise appropriate learning algorithms that essentially use multiple reinforcement learning algorithms for the standard scalar reward problem which are combined using the geometric insight from the theory of approachability for vector valued stochastic games we then address the more general and optimization related problem where a nested class of possible target sets is prescribed and the goal of the learning agent is to approach the smallest possible target set which will generally depend on the unknown system parameters a particular case which falls into this framework is that of stochastic games with average reward constraints and further specialization provides a reinforcement learning algorithm for constrained markov decision processes some basic examples are provided to illustrate these results

global analysis of the flows of fluids with pressure dependent viscosities to describe the flows of fluids over a wide range of pressures it is necessary to take into account the fact that the viscosity of the fluid depends on the pressure that the viscosity depends on the pressure has been verified by numerous careful experiments while the existence of solutions local in time to the equations governing the flows of such fluids are available for small special data and rather unrealistic dependence of the viscosity on the pressure no global existence results are in place our interest here is to establish the existence of weak solutions for spatially periodic three dimensional flows that are global in time for a large class of physically meaningful viscosity pressure relationships

an optimal technique for constraint based image restoration and reconstruction a new technique for finding an optimal feasible solution to the general image reconstruction and restoration problem is described this method allows the use of prior knowledge of the properties of both the solution and any noise present on the data the problem is formulated as the optimization of a cost function over the intersection of a number of convex constraint sets each set being defined as containing those solutions consistent with a particular constraint a duality theorem is then applied to yield a dual problem in which the unknown image is replaced by a model defined in terms of a finite dimensional parameter vector and the kernels of the integral equations relating the data and solution the dual problem may then be solved for the model parameters using a gradient descent algorithm this method serves as an alternative to the primal constrained optimization and projection onto convex sets pocs algorithms problems in which this new approach is appropriate are discussed an example is given for image reconstruction from noisy projection data applying the dual method results in a fast nonlinear algorithm simulation results demonstrate the superiority of the optimal feasible solution over one obtained using a suboptimal approach

markov decision problems and state action frequencies consider a controlled markov chain with countable state and action spaces basic quantities that determine the values of average cost functionals are identified under some regularity conditions these turn out to be a collection of numbers one for each state action pair describing for each state the relative number of uses of each action these conditional frequencies which are defined pathwise are shown to determine the state action frequencies that in the finite case are known to determine the costs this is extended to the countable case allowing for unbounded costs the space of frequencies is shown to be compact and convex and the extreme points are identified with stationary deterministic policies conditions under which the search for optimality in several optimization problems may be restricted to stationary policies are given these problems include the standard markov decision process as well as constrained optimization both in terms of average cost functionals and variability sensitive optimization an application to a queueing problem is given where these results imply the existence and explicit computation of optimal policies in constrained optimization problems the pathwise definition of the conditional frequencies implies that their values can be controlled directly moreover they depend only on the limiting behavior of the control this has immediate application to adaptive control of markov chains including adaptive control under constraints

an asymptotically efficient simulation based algorithm for finite horizon stochastic dynamic programming we present a simulation based algorithm called simulated annealing multiplicative weights samw for solving large finite horizon stochastic dynamic programming problems at each iteration of the algorithm a probability distribution over candidate policies is updated by a simple multiplicative weight rule and with proper annealing of a control parameter the generated sequence of distributions converges to a distribution concentrated only on the best policies the algorithm is asymptotically efficient in the sense that for the goal of estimating the value of an optimal policy a provably convergent finite time upper bound for the sample mean is obtained

the complexity of multi mean payoff and multi energy games in mean payoff games the objective of the protagonist is to ensure that the limit average of an infinite sequence of numeric weights is nonnegative in energy games the objective is to ensure that the running sum of weights is always nonnegative multi mean payoff and multi energy games replace individual weights by tuples and the limit average resp running sum of each coordinate must be resp remain nonnegative we prove finite memory determinacy of multi energy games and show inter reducibility of multi mean payoff and multi energy games for finite memory strategies we improve the computational complexity for solving both classes with finite memory strategies we prove conp completeness improving the previous known expspace bound for memoryless strategies we show that deciding the existence of a winning strategy for the protagonist is np complete we present the first solution of multi mean payoff games with infinite memory strategies we show that mean payoff sup objectives can be decided in np conp whereas mean payoff inf objectives are conp complete

guaranteed performance regions in markovian systems with competing decision makers a decision maker is facing a dynamic system which is being controlled by himself herself as well as by other decision makers he she considers a vector of performance measures acceptable performance is defined through a set in the space of performance vectors whether this decision maker can guarantee a time averaged performance vector which approaches this desired set is considered for the worst case scenario in which other decision makers may for selfish reasons try to exclude his her vector from the desired set for a controlled markov model of the system a sufficient condition for approachability is given and appropriate control strategies are constructed under certain recurrence conditions a complete characterization of approachability is then provided for convex sets the mathematical formulation leads to a theory of approachability for stochastic games with vector payoffs a simple queuing example illustrates this approach

image restoration by the method of convex projections part 1ߞtheory a projection operator onto a closed convex set in hilbert space is one of the few examples of a nonlinear map that can be defined in simple abstract terms moreover it minimizes distance and is nonexpansive and therefore shares two of the more important properties of ordinary linear orthogonal projections onto closed linear manifolds in this paper we exploit the properties of these operators to develop several iterative algorithms for image restoration from partial data which permit any number of nonlinear constraints of a certain type to be subsumed automatically their common conceptual basis is as follows every known property of an original image f is envisaged as restricting it to lie in a well defined closed convex set thus m such properties place f in the intersection e0 ei of the corresponding closed convex sets e1 e2 em given only the projection operators pi onto the individual ei s i 1 m we restore f by recursive means clearly in this approach the realization of the pi s in a hilbert space setting is one of the major synthesis problems section i describes the geometrical significance of the three main theorems in considerable detail and most of the underlying ideas are illustrated with the aid of simple diagrams section ii presents rules for the numerical implementation of 11 specific projection operators which are found to occur frequently in many signal processing applications and the appendix contains proofs of all the major results

controlled markov set chains under average criteria in this paper applying an interval arithmetic analysis we consider the average case of controlled markov set chains whose process allows for fluctuating transition matrices at each step in time we introduce a v step contractive property for the average case under which a pareto optimal periodic policy is characterized as a maximal solution of optimality equation also in the class of stationary policies the behavior of the expected reward over t horizon as t approaches is investigated and the left and right hand side optimality equations are given by which a pareto optimal stationary policy is found as a numerical example the taxicab problem is considered

non zero sum two person repeated games with incomplete information characterization of all equilibria of nonzero sum two person repeated games with incomplete information in the standard one sided information case informally each such equilibrium is described by a sequence of communications between the players consisting of information transmission and coordination leading to some individually rational agreement formally the concept of a bi martingale is introduced

a discontinuous galerkin method for viscous compressible multifluids abstract we present a generalized discontinuous galerkin method for a multicomponent compressible barotropic navier stokes system of equations the system presented has a functional viscosity which depends on the pressure p p i of the flow with the density and the local concentration i high order runge kutta time discretization techniques are employed and different methods of dealing with arbitrary coupled boundary conditions are discussed analysis of the energy consistency of the scheme is performed in addition to inspection of the relative error of the solution compared to exact analytic test cases finally several examples comparisons generalizations and physical applications are presented

large data existence theory for unsteady flows of fluids with pressure and shear dependent viscosities abstract a generalization of navier stokes model is considered where the cauchy stress tensor depends on the pressure as well as on the shear rate in a power law like fashion for values of the power law index r 2 d d 2 2 we develop existence of generalized weak solutions for the resultant system of partial differential equations including also the so far uncovered cases r 2 d d 2 2 d 2 d 2 and r 2 by considering a maximal sensible range of the power law index r the obtained theory is in effect identical to the situation of dependence on the shear rate only

the principle of optimality in dynamic programming with returns in partially ordered sets a general sequential model is defined where returns are in a partially ordered set a distinction is made between maximal nondominated returns and greatest returns we show that bellman s principle of optimality is valid with respect to maximal returns and it leads to an algorithm to approximate these returns we argue that significantly greater effort is needed to apply this algorithm to maximal returns than to greatest returns

the empirical bayes envelope and regret minimization in competitive markov decision processes this paper proposes an extension of the regret minimizing framework from repeated matrix games to stochastic game models under appropriate recurrence conditions a decision maker p1 who wishes to maximize his long term average reward is facing a markovian environment which may also be affected by arbitrary actions of other agents the latter are collectively modeled as a second player p2 whose strategy is arbitrary both states and actions are fully observed by both players while p1 may obviously secure the min max value of the game he may wish to improve on that when the opponent is not playing a worst case strategy for repeated matrix games an achievable goal is presented by the bayes envelope that traces p1 s best response payoff against the observable frequencies of p2 s actions we propose a generalization to the stochastic game framework under recurrence conditions that amount to fixed state reachability the empirical bayes envelope ebe is defined as p1 s best response payoff against the stationary strategies of p2 that agree with the observed state action frequencies because the ebe may not be attainable in general we consider its lower convex hull the convex bayes envelope cbe which is proved to be achievable by p1 the analysis relies on blackwell s approachability theory the cbe is lower bounded by the value of the game and for irreducible games turns out to be strictly above the value whenever p2 s frequencies deviate from a worst case strategy in the special case of single controller games where p2 alone affects the state transitions the ebe itself is shown to be attainable