a remark on regularity criterion for the dissipative quasi geostrophic equations abstract this paper concerns with a regularity criterion of solutions to the 2d dissipative quasi geostrophic equations based on a logarithmic sobolev inequality in besov spaces the absence of singularities of in 0 t is derived for a solution on the interval 0 t satisfying the condition l r 0 t b p 0 for 2 p r 4 p this is an extension of earlier regularity results in the serrin s type space l r 0 t l p

independent valued minimax pathological or beneficial minimax search which is used by most game playing programs is considered pathological when deeper searches produce worse evaluations than shallower ones this phenomenon was first observed in theoretical analyses under seemingly reasonable conditions it was most commonly explained by the lack of dependence between nearby positions in the analyses if nearby positions have similar values as is typically the case in real games the pathology no longer occurs in this paper we show that the pathology can be eliminated even without position value dependence by assigning enough different values to the positions and modeling the heuristic error as normally distributed noise that is independent of the depth in the game tree this leads to the conclusion that minimax is less prone to the pathology than was previously thought and indicates the importance of the number of different position values

feedback decoupling of structured systems the feedback decoupling of structured linear systems is considered using results gathered on decoupling and the graph characterization of the structure at infinity a necessary and sufficient decoupling condition for structured systems is developed this condition has a graphical interpretation in terms of shortest input output paths

asymptotic convergence rate of supercritical surface quasi geostrophic equation in morrey space abstract in this paper the asymptotic convergence rate of the supercritical surface quasi geostrophic equation in morrey space is investigated it is shown that if the global solution x t of the supercritical surface quasi geostrophic equation satisfies the growth condition in critical morrey space 0 t m p q r 2 r d t for r 2 p 2 p then every perturbed weak solution x t of the perturbed quasi geostrophic equation converges asymptotically to x t with the optimal rate t t l 2 o 1 t 1 as t in particular the initial perturbation is allowed large the findings are based on the spectral decomposition methods of fractional laplace and morrey space technique

the design of a precompensator for multivariable adaptive control a network theoretic approach a network theoretic approach to the design of a dynamic precompensator c s for a multiinput multioutput plant t s is considered the design is based on the relative degree of each element of t s specifically an efficient algorithm is presented for determining whether a given plant t s has a diagonal precompensator c s such that for almost all cases t s c s has a diagonal interactor the algorithm also finds any optimal precompensator in the sense that the total relative degree is minimal the algorithm can be easily modified to work even when a t s represented by a nonsquare matrix is given

global well posedness for the critical 2d dissipative quasi geostrophic equation we give an elementary proof of the global well posedness for the critical 2d dissipative quasi geostrophic equation the argument is based on a non local maximum principle involving appropriate moduli of continuity

the effect of mobility on minimaxing of game trees with random leaf values abstract random minimaxing introduced by beal and smith icca j 17 1994 3 9 is the process of using a random static evaluation function for scoring the leaf nodes of a full width game tree and then computing the best move using the standard minimax procedure the experiments carried out by beal and smith using random minimaxing in chess showed that the strength of play increases as the depth of the lookahead is increased we investigate random minimaxing from a combinatorial point of view in an attempt to gain a better understanding of the utility of the minimax procedure and a theoretical justification for the results of beal and smith s experiments the concept of domination is central to our theory intuitively one move by white dominates another move when choosing the former move would give less choice for black when it is black s turn to move and subsequently more choice for white when it is white s turn to move we view domination as a measure of mobility and show that when one move dominates another then its probability of being chosen is higher we then investigate when the probability of a good move relative to the probability of a bad move increases with the depth of search we show that there exist situations when increased depth of search is beneficial but that this is not always the case under the assumption that each move is either good or bad we are able to state sufficient conditions to ensure that increasing the depth of search increases the strength of play of random minimaxing if the semantics of the game under consideration match these assumptions then it is fair to say that random minimaxing appears to follow a reasonably intelligent strategy in practice domination does not always occur so it remains an open problem to find a more general measure of mobility in the absence of domination

a new bernstein s inequality and the 2d dissipative quasi geostrophic equation we show a new bernstein s inequality which generalizes the results of cannone planchon danchin and lemarie rieusset as an application of this inequality we prove the global well posedness of the 2d quasi geostrophic equation with the critical and super critical dissipation for the small initial data in the critical besov space and local well posedness for the large initial data

structured systems within the transfer matrix approach application to decoupling abstract we consider a new approach to structured systems within the transfer matrix framework we associate with such a structured system a graph which concentrates both knowledge on structural properties of independent subsystems and on their interconnections the analysis of this associated graph allows to conclude on the decouplability of structured systems

best first fixed depth minimax algorithms abstract this article has three main contributions to our understanding of minimax search first a new formulation for stockman s sss algorithm based on alpha beta is presented it solves all the perceived drawbacks of sss finally transforming it into a practical algorithm in effect we show that sss alpha beta transposition tables the crucial step is the realization that transposition tables contain so called solution trees structures that are used in best first search algorithms like sss having created a practical version we present performance measurements with tournament game playing programs for three different minimax games yielding results that contradict a number of publications second based on the insights gained in our attempts at understanding sss we present a framework that facilitates the construction of several best first fixed depth game tree search algorithms known and new the framework is based on depth first null window alpha beta search enhanced with storage to allow for the refining of previous search results it focuses attention on the essential differences between algorithms third a new instance of this framework is presented it performs better than algorithms that are currently used in most state of the art game playing programs we provide experimental evidence to explain why this new algorithm mtd f performs better than other fixed depth minimax algorithms

subdimensional expansion for multirobot path planning abstract planning optimal paths for large numbers of robots is computationally expensive in this paper we introduce a new framework for multirobot path planning called subdimensional expansion which initially plans for each robot individually and then coordinates motion among the robots as needed more specifically subdimensional expansion initially creates a one dimensional search space embedded in the joint configuration space of the multirobot system when the search space is found to be blocked during planning by a robot robot collision the dimensionality of the search space is locally increased to ensure that an alternative path can be found as a result robots are only coordinated when necessary which reduces the computational cost of finding a path we present the m algorithm an implementation of subdimensional expansion that adapts the a planner to perform efficient multirobot planning m is proven to be complete and to find minimal cost paths simulation results are presented that show that m outperforms existing optimal multirobot path planning algorithms

partial order bounding a new approach to evaluation in game tree search abstract in computer game playing the established method for constructing an evaluation function uses a scalar value computed as a weighted sum of features this paper advocates the use of partial order evaluation and describes an efficient new search method called partial order bounding pob previous tree search algorithms using a partial order evaluation have attempted to propagate partially ordered values through the search tree which leads to many problems in practice such as the complexity of backing up sets of incomparable evaluations pob compares partially ordered values only in the leaves of a game tree and backs up boolean values through the tree a closely related new algorithm linear extension partial order bounding le pob uses a standard scalar alpha beta search with values from a suitably chosen linear extension of the partial order evaluation as an application the effectiveness of partial order evaluation is shown in the case of modeling capturing races called semeai in the game of go

breadth first heuristic search recent work shows that the memory requirements of a and related graph search algorithms can be reduced substantially by only storing nodes that are on or near the search frontier using special techniques to prevent node regeneration and recovering the solution path by a divide and conquer technique when this approach is used to solve graph search problems with unit edge costs we show that a breadth first search strategy can be more memory efficient than a best first strategy we also show that a breadth first strategy allows a technique for preventing node regeneration that is easier to implement and can be applied more widely the breadth first heuristic search algorithms introduced in this paper include a memory efficient implementation of breadth first branch and bound search and a breadth first iterative deepening a algorithm that is based on it computational results show that they outperform other systematic search algorithms in solving a range of challenging graph search problems

global well posedness in the super critical dissipative quasi geostrophic equations we consider the quasi geostrophic equation with the dissipation term in the case constantin cordoba wu 6 proved the global existence of strong solution in h 1 and h 2 under the assumption of small l norm of initial data in this paper we prove the global existence in the scale invariant besov space b 2 2 2 1 for initial data small in the b 2 2 2 1 norm we also prove a global stability result in b 1 2 1

game tree algorithms and solution trees in this paper a theory of game tree algorithms is presented entirely based upon the concept of a solution tree two types of solution trees are distinguished max and min trees every game tree algorithm tries to prune as many nodes as possible from the game tree a cut off criterion in terms of solution trees will be formulated which can be used to eliminate nodes from the search without affecting the result further we show that any algorithm actually constructs a superposition of a max and a min solution tree finally we will see how solution trees and the related cutoff criterion are applied in major game tree algorithms like alphabeta and mtd

real time heuristic search abstract we apply the two player game assumptions of limited search horizon and commitment to moves in constant time to single agent heuristic search problems we present a variation of minimax lookahead search and an analog to alpha beta pruning that significantly improves the efficiency of the algorithm paradoxically the search horizon reachable with this algorithm increases with increasing branching factor in addition we present a new algorithm called real time a for interleaving planning and execution we prove that the algorithm makes locally optimal decisions and is guaranteed to find a solution we also present a learning version of this algorithm that improves its performance over successive problem solving trials by learning more accurate heuristic values and prove that the learned values converge to their exact values along every optimal path these algorithms effectively solve significantly larger problems than have previously been solvable using heuristic evaluation functions

hopf bifurcation in quasi geostrophic channel flow in this article we conduct a rigorous stability and bifurcation analysis for a highly idealized model of planetary scale atmospheric and oceanic flows the model is governed by the two dimensional quasi geostrophic equation for the conservation of vorticity in an east west oriented periodic channel the main result is the existence of hopf bifurcation of the flow as the reynolds number crosses a critical value the key idea in proving this result is translating the eigenvalue problem into a difference equation and treating the latter by continued fraction methods numerical results are obtained by using a finite difference scheme with high spatial resolution and these results agree closely with the theoretical predictions the spatio temporal structure of the limit cycle corresponds to a wave that propagates slowly westward and is symmetric about the midaxis of the channel for plausible paramater values that correspond to midlatitude atmospheric flows the period of this wave is 20 25 days

on the structure at infinity of a structured system abstract we develop a graph theoretic characterization of the generic structure at infinity of the transfer matrix of a structured system we show that the generic structure at infinity can be determined by means of algorithms from combinatorial optimization based on the max flow min cut theorem and on results concerning minimal cost flows as an application of the obtained characterization we propose a structural version of two well known disturbance decoupling problems and we derive graph theoretic necessary and sufficient conditions for the solvability of each of the two problems

game tree searching by min max approximation abstract we present an iterative method for searching min max game trees based on the idea of approximating the min and max operators by generalized mean valued operators this approximation is used to guide the selection of the next leaf node to expand since the approximations allow one to select efficiently that leaf node upon whose value the approximate value at the root most highly depends experimental results from almost 1 000 games of connect four 1 suggest that our scheme is superior to minimax search with alpha beta pruning for the same number of calls to the move routine however our scheme has higher overhead so that further work is needed before it becomes competitive when cpu time per turn is the limiting resource

an incremental negamax algorithm abstract in certain models of game trees with erroneous evaluation functions the minimax algorithm does not reduce errors even under favourable assumptions about the size of the errors and the frequency of their occurrence we present an incremental negamax algorithm which uses estimates of all nodes in the tree rather than only those of the leaves to determine the root value under the assumption of independently occurring and sufficiently small errors the algorithm is shown to have exponentially reduced error probabilities with respect to the height of the tree

asymptotic stability of large solutions with large perturbation to the navier stokes equations abstract consider weak solutions w of the navier stokes equations in serrin s class w l 0 l q for 2 3 q 1 with 3 q where is a general unbounded domain in r 3 we shall show that although the initial and external disturbances from w are large every perturbed flow v with the energy inequality converges asymptotically to w as v t w t l 2 0 v t w t l 2 o t 1 2 as t

prior information in the design of multivariable adaptive controllers this note discusses the design of a dynamic precompensator w c s for an m times m mimo plant w p s such that for almost all cases w p s w c s has a diagonal hermite form

the pn search algorithm application to tsume shogi abstract this paper proposes a new search algorithm denoted pn for and or tree search the algorithm is based on proof number pn search a best first search algorithm proposed by allis et al artificial intelligence 66 1 1994 91 124 and on korf s rbfs algorithm artificial intelligence 62 1 1993 41 78 pn combines several existing ideas it transforms a best first pn search algorithm into an iterative deepening depth first approach moreover it is enhanced by methods such as recursive iterative deepening dynamic evaluation efficient successor ordering and pruning by dependency relations the resulting algorithm turns out to be highly efficient as witnessed by the experimental results the pn algorithm is implemented in a tsume shogi japanese chess mating problem program and evaluated by testing it on 295 notoriously difficult tsume shogi problems one problem has a depth of search of over 1500 plies the experimental results are compared with those of other programs the pn program shows by far the best results solving all problems but one needless to say it outperforms the best human tsume shogi problem solvers by far

decay of weak solutions to the 2d dissipative quasi geostrophic equation we address the decay of the norm of weak solutions to the 2d dissipative quasi geostrophic equation when the initial data 0 is in l2 only we prove that the l2 norm tends to zero but with no uniform rate that is there are solutions with arbitrarily slow decay for 0 in lp l2 with 1 p frac 2 2 alpha 1 have uniform decay rates this result allows us to prove decay for the lq norms for q geq frac 2 2 alpha 1 when 0 is in l 2 cap l frac 2 2 alpha 1

minimax search algorithms with and without aspiration windows investigation of several algorithms for computing exact minimax values of game trees utilizing backward pruning are discussed the focus is on trees with an ordering similar to that actually found in game playing practice the authors compare the algorithms using two different distributions of the static values the uniform distribution and a distribution estimated from practical data a systematic comparison of using aspiration windows for all of the usual minimax algorithms is presented the effects of aspiration windows of varying size and position are analyzed increasing the ordering of moves to near the optimum results in unexpectedly high savings algorithms with linear space complexity benefit most although the ordering of the first move is of predominant importance that of the remainder has only second order effects the use of an aspiration window not only makes alpha beta search competitive but there also exist dependencies of its effects on certain properties of the trees

on the structure at infinity of linear square decoupled systems the purpose of this note is to demonstrate that a square invertible linear system c a b is decouplable by static state feedback if and only if its infinite zero orders are respectively equal to the infinite zero orders of the subsystems c i a b where c i denotes the i th row of c until now only the necessity of this condition has been established 1

linear feedback decoupling transfer function analysis the problem of linear system decoupling is examined based on recent results on linear feedback new insight is obtained through which resolution of the decoupliug problem is accomplished by calculations performed directly on the given transfer matrix computation of the decoupling compensators follows by easy constructions the problem of feedback block decoupling with internal stability is also formulated and resolved

the multi player version of minimax displays game tree pathology abstract it is widely believed that by searching deeper in the game tree the decision maker is more likely to make a better decision dana nau and others have discovered pathology theorems that show the opposite searching deeper in the game tree causes the quality of the ultimate decision to become worse not better the models for these theorems assume that the search procedure is minimax and the games are two player zero sum this report extends nau s pathology theorem to multi player game trees searched with maxn the multi player version of minimax thus two player zero sum game trees and multi player game trees are shown to have an important feature in common

nonexistence of simple hyperbolic blow up for the quasi geostrophic equation the problem we are concerned with is whether singularities form in finite time in incompressible fluid flows it is well known that the answer is no in the case of euler and navier stokes equations in dimension two in dimension three it is still an open problem for these equations in this paper we focus on a two dimensional active scalar model for the 3d euler vorticity equation constantin majda and tabak 7 suggested by studying rigorous theorems and detailed numerical experiments a general principle if the level set topology in the temperature field for the 2d quasi geostrophic active scalar in the region of strong scalar gradients does not contain a hyperbolic saddle then no finite time singularity is possible numerical simulations showed evidence of singular behavior when the geometry of the level sets of the active scalar contain a hyperbolic saddle there is a naturally associated notion of simple hyperbolic saddle breakdown the main theorem we present in this paper shows that such breakdown cannot occur in finite time we also show that the angle of the saddle cannot close in finite time and it cannot be faster than a double exponential in time using the same techniques we see that analogous results hold for incompressible 2d and 3d euler these results were announced in 9 but with a slight difference in the definition of a simple hyperbolic saddle the definition given in section 4 generalizes the one given in the announcement see also constantin 4 discussed in section 7 remark 5 below the whole work described in this paper is basically part of the author s thesis i am particularly grateful to my thesis advisor charles fefferman for his attention support guidance and advice i am indebted to d christodoulou and p constantin for helpful corrections and suggestions i wish to thank a majda for suggesting the subject and e tabak for discussions and com

a heuristic search algorithm with modifiable estimate abstract this paper describes an improved version of two previously published algorithms in the area a and b the new approach is based on considering the estimate n on node n as a variable rather than as a constant the new algorithm thus improves the estimate as it goes on avoiding some useless node expansions it is proved to never expand more nodes than b or a and to expand a much smaller number of them in some cases another result of the paper is a proof that no overall optimal algorithm exists if the cost of an algorithm is measured by the total number of node expansions

conspiracy numbers for min max search abstract a new procedure is presented for growing min max game trees in large games such as chess decisions must be based on incomplete search trees the new tree growth procedure is based on conspiracy numbers as a measure of the accuracy of the root minimax value of an incomplete tree conspiracy numbers measure the number of leaf nodes whose value must change in order to change the minimax root value by a given amount trees are grown in a way that maximizes the conspiracy required to change the root value the trees grown by this procedure are often deep and narrow however if all static values in a game are the same this new procedure reduces to d ply search with pruning unlike b search nonuniform growth is achieved without any modification of the static board evaluator

a maximum principle applied to quasi geostrophic equations we study the initial value problem for dissipative 2d quasi geostrophic equations proving local existence global results for small initial data in the super critical case decay of lp norms and asymptotic behavior of viscosity solution in the critical case our proofs are based on a maximum principle valid for more general flows

asymptotic stability of non newtonian flows with large perturbation in r2 consider asymptotic stability of weak solutions for the incompressible non newtonian fluid motion in whole spaces r 2 we shall show that although the initial data disturbance from u are large every perturbed flow v with the energy inequality converges asymptotically to u as v t u t 0 as t

analysis of linear structured systems using a primal dual algorithm in this paper we give a polynomial algorithm to compute the infinite structure of a structured system a directed graph is associated with such structured systems the infinite zero orders can be computed on the associated graph via the determination of the minimal length of vertex disjoint input output paths this search corresponds to a minimum cost flow determination on an appropriate directed graph the proposed algorithm is based on the primal dual algorithm linked to linear programming this polynomial algorithm is one of the most efficient for this type of problem moreover it allows an iterative determination of the generic infinite structure which is a key tool for solving numerous control problems

iterative version spaces an incremental depth first algorithm for computing the s and set of mitchell s candidate elimination and mellish s description identification algorithm is presented as in mellish s approach lowerbounds examples as well as upperbounds can be handled instead of storing the complete s and sets only one element s s and g is stored together with backtrack information the worst case space complexity of our algorithm is linear in the number of lower and upperbounds for the candidate elimination algorithm this can be exponential we introduce a test for membership of s and with a number of coverage tests linear in the number of examples consequently the worst case time complexity to compute s and for each example is only a linear factor worse than the candidate elimination algorithm s

conspiracy number search with relative sibling scores for some two player games e g go no accurate and inexpensive heuristic is known for evaluating leaves of a search tree for other games e g chess a heuristic is known sum of piece values for other games e g hex only a local heuristic one that compares children reliably but non siblings poorly is known cell voltage drop in the shannon anshelevich electric circuit model in this paper we introduce a search algorithm for a two player perfect information game with a reasonable local heuristic sibling conspiracy number search scns is an anytime best first version of conspiracy number search based not on evaluation of leaf states of the search tree but for each node on relative evaluation scores of all children of that node scns refines cns search value intervals converging to proof number search scns is a good framework for a game player we tested scns in the domain of hex with promising results we implemented an 11 by 11 scns hex bot deephex we competed deephex against current hex bot champion mohex a monte carlo tree search player and previous hex bot champion wolve an alpha beta search player deephex widely outperforms wolve at all time levels and narrowly outperforms mohex once time reaches 4 min move we tested the strength of scns features most critical is to initialize leaves via a multi step process also we show a simple parallel version of scns it scales well for 2 threads but less efficiently for 4 or 8 threads

on the speed of convergence of value iteration on stochastic shortest path problems we establish a bound on the convergence time of the value iteration algorithm on stochastic shortest path problems the bound which applies for admissible initial vectors as for example j equiv 0 implies a polynomial time convergence of value iteration for all problems with polynomially bounded vert j vert underline g this result gives a partial answer to the open problem of bounding the convergence time of value iteration on arbitrary initial vectors the proof is obtained by analyzing a stochastic process associated with the shortest path problem

comments on achieving diagonal interactor matrix for multivariable linear systems with uncertain parameters abstract in this note we propose a criterion for determining whether or not a multivariable linear system may be made to have a diagonal interactor with the possible use of diagonal precompensation we present a constructive procedure to achieve a diagonal interactor for multivariable linear systems when possible this procedure is simpler than that given in gibbens et al automatica 29 1547 1550 1993

best first minimax search we describe a very simple selective search algorithm for two player games called best first minimax it always expands next the node at the end of the expected line of play which determines the minimax value of the root it uses the same information as alpha beta minimax and takes roughly the same time per node generation we present an implementation of the algorithm that reduces its space complexity from exponential to linear in the search depth but at significant time cost our actual implementation saves the subtree generated for one move that is still relevant after the player and opponent move pruning subtrees below moves not chosen by either player we also show how to efficiently generate a class of incremental random game trees on uniform random game trees best first minimax outperforms alpha beta when both algorithms are given the same amount of computation on random trees with random branching factors best first outperforms alpha beta for shallow depths but eventually loses at greater depths we obtain similar results in the game of othello finally we present a hybrid best first extension algorithm that combines alpha beta with best first minimax and performs significantly better than alpha beta in both domains even at greater depths in othello it beats alpha beta in two out of three games

drift diffusion equations with fractional diffusion and the quasi geostrophic equation motivated by the critical dissipative quasi geostrophic equation we prove that drift diffusion equations with l 2 initial data and minimal assumptions on the drift are locally holder continuous as an application we show that solutions of the quasi geostrophic equation with initial l 2 data and critical diffusion 1 2 are locally smooth for any space dimension

predicting optimal solution costs with bidirectional stratified sampling in regular search spaces optimal planning and heuristic search systems solve state space search problems by finding a least cost path from start to goal as a byproduct of having an optimal path they also determine the optimal solution cost in this paper we focus on the problem of determining the optimal solution cost for a state space search problem directly i e without actually finding a solution path of that cost we present an algorithm biss which is a hybrid of bidirectional search and stratified sampling that produces accurate estimates of the optimal solution cost biss is guaranteed to return the optimal solution cost in the limit as the sample size goes to infinity we show empirically that biss produces accurate predictions in several domains in addition we show that biss scales to state spaces much larger than can be solved optimally in particular we estimate the average solution cost for the 6 6 7 7 and 8 8 sliding tile puzzle and provide indirect evidence that these estimates are accurate as a practical application of biss we show how to use its predictions to reduce the time required by another system to learn strong heuristic functions from days to minutes in the domains tested

performance of linear space search algorithms abstract search algorithms that use space linear in the search depth are widely employed in practice to solve difficult problems optimally such as planning and scheduling in this paper we study the average case performance of linear space search algorithms including depth first branch and bound dfbnb iterative deepening id and recursive best first search rbfs to facilitate our analyses we use a random tree t b d that has mean branching factor b depth d and node costs that are the sum of the costs of the edges from the root to the nodes we prove that the expected number of nodes expanded by dfbnb on a random tree is no more than bd times the expected number of nodes expanded by best first search bfs on the same tree which usually requires space that is exponential in depth d we also show that dfbnb is asymptotically optimal when bfs runs in exponential time and id and rbfs are asymptotically optimal when the edge costs of t b d are integers if bp 0 is the expected number of children of a node whose costs are the same as that of their parent then the expected number of nodes expanded by these three linear space algorithms is exponential when bp o d 4 when bp 0 1 and at most quadratic when bp 0 1 in addition we study the heuristic branching factor of t b d and the effective branching factor of bfs dfbnb id and rbfs on t b d furthermore we use our analytic results to explain a surprising anomaly in the performance of these algorithms and to predict the existence of a complexity transition in the asymmetric traveling salesman problem

perimeter search in restricted memory abstract in this paper we consider the problem of finding a minimum cost path in a graph in particular we consider the perimeter search technique and we investigate the possibility of using very large perimeters we present an algorithm designed to use perimeters of arbitrary size our algorithm generates the perimeter incrementally and makes use of a technique called backward pruning for reducing the search effort a qualitative analysis and experimental results show that our algorithm can effectively use perimeters of very large size

reducing reexpansions in iterative deepening search by controlling cutoff bounds abstract it is known that a best first search algorithm like a 5 6 requires too much space which often renders it unusable and a depth first search strategy does not guarantee an optimal cost solution the iterative deepening algorithm ida 4 achieves both space and cost optimality for a class of tree searching problems however for many other problems it takes too much of computation time due to excessive reexpansion of nodes this paper presents a modification of ida to an admissible iterative depth first branch and bound algorithm ida cr for trees which overcomes this drawback of ida and operates much faster using the same amount of storage algorithm ida cra a bounded suboptimal cost variation of ida cr is also presented in order to reduce the execution time still further results with the 0 1 knapsack problem traveling salesman problem and the flow shop scheduling problem are shown

a two dimensional model for quasigeostrophic flow comparison with the two dimensional euler flow abstract a simple two dimensional model for quasigeostrophic flow is contrasted with the two dimensional incompressible euler equations the model arises under the assumptions of fast rotation uniform stratification and uniform potential vorticity it is found that the more loca feed back of the quasigeostrophic model gives rise to strongly nonlinear front formation as opposed to two dimensional euler where the steepening process of mature fronts obeys a nonlocal nearly linear mechanism

existence and uniqueness of the solution to the dissipative 2d quasi geostrophic equations in the sobolev space we study the two dimensional dissipative quasi geostrophic equations in the sobolev space open image in new window existence and uniqueness of the solution local in time is proved in h s when s 2 1 existence and uniqueness of the solution global in time is also proved in h s when s 2 1 and the initial data open image in new window is small for the case s 2 1 we also obtain the unique large global solution in h s provided that open image in new window is small enough

benefits of using multivalued functions for minimaxing abstract minimaxing has been very successful in game playing practice although a complete explanation of why it has been that successful has not yet been given in particular it has not been shown why it should be useful as it is in practice to use multivalued evaluation functions such functions have many distinct values as their result and can discriminate between positions according to the heuristic knowledge represented in these values in this paper we modify a basic pathological model by adding two assumptions regarding multivalued evaluation functions these assumptions non uniformity of error distribution and dependency of heuristic values directly relate to the properties of multivalued evaluation functions as used in practice simulation studies of our multivalued model have exhibited sharp error reductions for deeper searches using minimaxing this behavior corresponds to observations in practice the error reductions are primarily due to the improved evaluation quality as search depth increases this phenomenon of lower probability of static evaluation errors with increasing search depth is revealed through our model although the same evaluation function is used at all levels of the tree and although its general error probability is independent of the depth essentially with increasing search depth the evaluation function is more frequently used on such positions which can be more reliably evaluated by a multivalued function with the assumed properties this effect together with the ability to discriminate between positions of different goodness leads to the benefits of using multivalued evaluation functions of appropriate granularity for minimaxing

searching for an optimal path in a tree with random costs we consider the problem of finding an optimal path leading from the root of a tree to any of its leaves the tree is known to be uniform binary and of height n and each branch independently may have a cost of 1 or 0 with probability p and 1 p respectively we show that for p 1 2 every algorithm which guarantees finding an exact cheapest path or even a path within a fixed cost ratio of the cheapest must run in exponential average time if however we are willing to accept a near optimal solution almost always then a pruning algorithm exists which finds such a solution in linear expected time the algorithm employs a depth first strategy which stops at regular intervals to appraise its progress and if the progress does not meet a criterion based on domain specific knowledge the current node is irrevocably pruned

frontier search the critical resource that limits the application of best first search is memory we present a new class of best first search algorithms that reduce the space complexity the key idea is to store only the open list of generated nodes but not the closed list of expanded nodes the solution path can be recovered by a divide and conquer technique either as a bidirectional or unidirectional search for many problems frontier search dramatically reduces the memory required by best first search we apply frontier search to breadth first search of sliding tile puzzles and the 4 peg towers of hanoi problem dijkstra s algorithm on a grid with random edge costs and the a algorithm on the fifteen puzzle the four peg towers of hanoi problem and optimal sequence alignment in computational biology

l2 stability for solutions of subcritical quasi geostrophic equation with large perturbations abstract this paper concerns with the asymptotic stability for the weak solution of the two dimensional dissipative subcritical quasi geostrophic equation in the class l p 0 t l q r 2 for p 2 q 2 q 1 2 it is proved that although the initial data and external force perturbations from are large every perturbed weak solution converges asymptotically to in l 2 r 2 as t as a byproduct we also obtain the weak strong uniqueness criterion of subcritical quasi geostrophic equation which improves the earlier results

the maximum principle and the global attractor for the dissipative 2d quasi geostrophic equations the long time behavior of the solutions to the two dimensional dissipative quasi geostrophic equations is studied we obtain a new positivity lemma which improves a previous version of a cordoba and d cordoba 10 and 11 as an application of the new positivity lemma we obtain the new maximum principle i e the decay of the solution in l p for any p 2 when f is zero as a second application of the new positivity lemma for the sub critical dissipative case with open image in new window the existence of the global attractor for the solutions in the space h s for any s 2 1 is proved for the case when the time independent f is non zero therefore the global attractor is infinitely smooth if f is this significantly improves the previous result of berselli 2 which proves the existence of an attractor in some weak sense for the case 1 the global attractor exists in h s for any s 0 and the estimate of the hausdorff and fractal dimensions of the global attractor is also available

depth first iterative deepening an optimal admissible tree search abstract the complexities of various search algorithms are considered in terms of time space and cost of solution path it is known that breadth first search requires too much space and depth first search can use too much time and doesn t always find a cheapest path a depth first iterative deepening algorithm is shown to be asymptotically optimal along all three dimensions for exponential tree searches the algorithm has been used successfully in chess programs has been effectively combined with bi directional search and has been applied to best first heuristic search as well this heuristic depth first iterative deepening algorithm is the only known algorithm that is capable of finding optimal solutions to randomly generated instances of the fifteen puzzle within practical resource limits

real time bidirectional search coordinated problem solving in uncertain situations this paper investigates real time bidirectional search rtbs algorithms where two problem solvers starting from the initial and goal states physically move toward each other to evaluate the rtbs performance two kinds of algorithms are proposed and are compared to real time unidirectional search one is called centralized rtbs where a supervisor always selects the best action from all possible moves of the two problem solvers the other is called decoupled rtbs where no supervisor exists and the two problem solvers independently select their next moves experiments on mazes and n puzzles show that 1 in clear situations decoupled rtbs performs better while in uncertain situations centralized rtbs becomes more efficient and 2 rtbs is more efficient than real time unidirectional search for 15 and 24 puzzles but not for randomly generated mazes it is shown that the selection of the problem solving organization is the selection of the problem space which determines the baseline of the organizational efficiency once a difficult problem space is selected the local coordination among problem solvers hardly overcome the deficit

controlling the learning process of real time heuristic search real time search provides an attractive framework for intelligent autonomous agents as it allows us to model an agent s ability to improve its performance through experience however the behavior of real time search agents is far from rational during the learning convergence process in that they fail to balance the efforts to achieve a short term goal i e to safely arrive at a goal state in the present problem solving trial and a long term goal to find better solutions through repeated trials as a remedy we introduce two techniques for controlling the amount of exploration both overall and per trial the weighted real time search reduces the overall amount of exploration and accelerates convergence it sacrifices admissibility but provides a nontrivial bound on the converged solution cost the real time search with upper bounds insures solution quality in each trial when the state space is undirected these techniques result in a convergence process more stable compared with that of the learning real time a algorithm

asymptotic properties of levelregular decision trees with randomly evaluated leaves game trees are an important model of decision making situations both in artificial intelligence and decision analysis the model most frequently investigated in theoretical research consists of a uniform tree of heighh and a constant branching factorb where the terminal positions are assigned the values of independent identically distributed random variables 1 3 10 our paper investigates two generalizations

linear space best first search abstract best first search is a general heuristic search algorithm that always expands next a frontier node of lowest cost it includes as special cases breadth first search dijkstra s single source shortest path algorithm and the a algorithm its applicability however is limited by its exponential memory requirement previous approaches to this problem such as iterative deepening do not expand nodes in best first order if the cost function can decrease along a path we present a linear space best first search algorithm rbfs that always explores new nodes in best first order regardless of the cost function and expands fewer nodes than iterative deepening with a nondecreasing cost function on the sliding tile puzzles rbfs with a nonmonotonic weighted evaluation function dramatically reduces computation time with only a small penalty in solution cost in general rbfs reduces the space complexity of best first search from exponential to linear at the cost of only a constant factor in time complexity in our experiments

achieving diagonal interactor matrix for multivariable linear systems with uncertain parameters abstract the notion of interactor matrix or equivalently the hermite normal form is a generalization of relative degree to multivariable systems and is crucial in problems such as decoupling inverse dynamics and adaptive control in order for a system to be input output decoupled using static state feedback the existence of a diagonal interactor matrix must first be established for a multivariable linear system which does not have a diagonal interactor matrix dynamic precompensation or dynamic state feedback is required for achieving a diagonal interactor matrix for the compensated system such precompensation often depends on the parameters of system and is thus difficult to implement with accuracy when the system is subject to parameter uncertainty in this paper we characterize a class of linear systems which can be precompensated to achieve a diagonal interactor matrix without the exact knowledge of the system parameters more precisely we present necessary and sufficient conditions on the transfer matrix of the system under which there exists a diagonal dynamic precompensator such that the compensated system has a diagonal interactor matrix these conditions are associated with the so called non generic singularity of certain matrix related to the system structure but independent of the system parameters the result of this paper is expected to be useful in robust and adaptive designs

on the nature of pathology in game searching abstract game playing programs usually process the estimates attached to game positions through repeated minimax operations as if these were true terminal payoffs this process introduces a spurious noise which degrades the quality of the decisions and in the extreme case may cause a pathological phenomenon the deeper we search the worse we play using a probabilistic game model this paper examines the nature of this distortion quantifies its magnitude determines the conditions when its damage is curtailed and explains why search depth pathology the extreme manifestation of minimax distortion is rarely observed in common games

cut and solve an iterative search strategy for combinatorial optimization problems branch and bound and branch and cut use search trees to identify optimal solutions to combinatorial optimization problems in this paper we introduce an iterative search strategy which we refer to as cut and solve and prove optimality and termination for this method this search is different from traditional tree search as there is no branching at each node in the search path a relaxed problem and a sparse problem are solved and a constraint is added to the relaxed problem the sparse problems provide incumbent solutions when the constraining of the relaxed problem becomes tight enough its solution value becomes no better than the incumbent solution value at this point the incumbent solution is declared to be optimal this strategy is easily adapted to be an anytime algorithm as an incumbent solution is found at the root node and continuously updated during the search cut and solve enjoys two favorable properties since there is no branching there are no wrong subtrees in which the search may get lost furthermore its memory requirement is negligible for these reasons it has potential for problems that are difficult to solve using depth first or best first search tree methods in this paper we demonstrate the cut and solve strategy by implementing a generic version of it for the asymmetric traveling salesman problem atsp our unoptimized implementation outperformed state of the art solvers for five out of seven real world problem classes of the atsp for four of these classes cut and solve was able to solve larger sometimes substantially larger problems our code is available at our websites

when is it better not to look ahead in situations where one needs to make a sequence of decisions it is often believed that looking ahead will help produce better decisions however it was shown 30 years ago that there are pathological situations in which looking ahead is counterproductive two long standing open questions are a what combinations of factors have the biggest influence on whether lookahead pathology occurs and b whether it occurs in real world decision making this paper includes simulation results for several synthetic game tree models and experimental results for three well known board games two chess endgames kalah with some modifications to facilitate experimentation and the 8 puzzle the simulations show the interplay between lookahead pathology and several factors that affect it and the experiments confirm the trends predicted by the simulation models the experiments also show that lookahead pathology is more common than has been thought all three games contain situations where it occurs

learning heuristic functions for large state spaces we investigate the use of machine learning to create effective heuristics for search algorithms such as ida or heuristic search planners such as ff our method aims to generate a sequence of heuristics from a given weak heuristic h 0 and a set of unsolved training instances using a bootstrapping procedure the training instances that can be solved using h 0 provide training examples for a learning algorithm that produces a heuristic h 1 that is expected to be stronger than h 0 if h 0 is so weak that it cannot solve any of the given instances we use random walks backward from the goal state to create a sequence of successively more difficult training instances starting with ones that are guaranteed to be solvable by h 0 the bootstrap process is then repeated using h i in lieu of h i 1 until a sufficiently strong heuristic is produced we test this method on the 24 sliding tile puzzle the 35 pancake puzzle email protected s cube and the 20 blocks world in every case our method produces a heuristic that allows ida to solve randomly generated problem instances quickly with solutions close to optimal the total time for the bootstrap process to create strong heuristics for these large state spaces is on the order of days to make the process effective when only a single problem instance needs to be solved we present a variation in which the bootstrap learning of new heuristics is interleaved with problem solving using the initial heuristic and whatever heuristics have been learned so far this substantially reduces the total time needed to solve a single instance while the solutions obtained are still close to optimal

disturbance rejection for structured systems the disturbance rejection problem for structured systems is solved a graph is associated with such a structured system disturbance rejection is shown to be solvable by state feedback whenever the control inputs reach the outputs more quickly than the disturbances in the associated graph the infinite structure of a structured system is characterized in terms of input output paths in the associated graph

the last player theorem game trees are an important model of decision making situations both in artificial intelligence and decision analysis but many of the properties of game trees are not well understood one of these properties is known as biasing when a minimax search is done to an odd search depth all moves tend to look good and when it is done to an even search depth all modes tend to look bad one explanation sometimes proposed for biasing is that whenever a player makes a move his position is strengthened and that the evaluation function used in the minimax search reflects this however the mathematical results in this paper suggest that biasing may instead be due to the errors made by the evaluation function

heuristic search in restricted memory research note abstract this paper presents heuristic search algorithms which work within memory constraints these algorithms ma for ordinary graphs and mao for and or graphs guarantee admissible solutions within specified memory limitations above the minimum required the memory versus node expansions tradeoff is analyzed for the worst case in the case of ordinary graphs some experiments using the fifteen puzzle problem are carried out under various pruning conditions these parameterized algorithms are found to encompass a wide class of best first search algorithms

duality in permutation state spaces and the dual search algorithm geometrical symmetries are commonly exploited to improve the efficiency of search algorithms a new type of symmetry in permutation state spaces duality is introduced each state has a dual state both states share important attributes such as their distance to the goal given a state s it is shown that an admissible heuristic of the dual state of s is an admissible heuristic for s this provides opportunities for additional heuristic evaluations an exact definition of the class of problems where duality exists is provided a new search algorithm dual search is presented which switches between the original state and the dual state when it seems likely that the switch will improve the chance of reaching the goal faster the decision of when to switch is very important and several policies for doing this are investigated experimental results show significant improvements for a number of applications for using the dual state s heuristic evaluation and or dual search

inconsistent heuristics in theory and practice in the field of heuristic search it is usually assumed that admissible heuristics are consistent implying that consistency is a desirable attribute the term inconsistent heuristic has at times been portrayed negatively as something to be avoided part of this is historical early research discovered that inconsistency can lead to poor performance for a nodes might be re expanded many times however the issue has never been fully investigated and was not re considered after the invention of ida this paper shows that many of the preconceived notions about inconsistent heuristics are outdated the worst case exponential time of inconsistent heuristics is shown to only occur on contrived graphs with edge weights that are exponential in the size of the graph furthermore the paper shows that rather than being something to be avoided inconsistent heuristics often add a diversity of heuristic values into a search which can lead to a reduction in the number of node expansions inconsistent heuristics are easy to create contrary to the common perception in the ai literature to demonstrate this a number of methods for achieving effective inconsistent heuristics are presented pathmax is a way of propagating inconsistent heuristic values in the search from parent to children this technique is generalized into bidirectional pathmax bpmx which propagates values from a parent to a child node and vice versa bpmx can be integrated into ida and a when inconsistent heuristics are used with bpmx experimental results show a large reduction in the search effort required by ida positive results are also presented for a searches

decoupling of structured systems by parameter independent precompensation and state feedback in this paper structured systems described by state space models are considered for these systems the entries of the state space model matrices are assumed to be either fixed zeros or free independent parameters we study the dynamic decoupling of structured linear systems it turns out that a large class of systems which is not state feedback decouplable can be made decouplable by the addition of a simple structured precompensator such a precompensator then has the property to be independent of the system parameters we give a necessary and sufficient condition for a structured system to be made feedback decouplable using a parameter independent precompensator furthermore we prove that when such a solution exists the precompensator can be chosen to be diagonal in this case the precompensator is constructed via a simple combinatorial algorithm our approach is based on a graph representation of the structured system all the results of this paper are related to some particular shortest sets of input output paths in the graph associated with the structured system

on the equivalence of cost functions in the design of circuits by cost table in the cost table approach to logic design a function is realized as a combination of functions from a table the objective of the synthesis is to find the least cost realization where realization cost is the sum of the costs of the functions used plus the cost of combining them the costs of cost table functions are defined by a cost function which represents chip area speed power dissipation or a combination of these factors it is shown that there is an arbitrarily large set s of cost functions which yield the same cost table this implies for example that every minimal realization of any function over a cost function in s is independent of the actual cost function used with any cost function if the cost of combining functions from a cost table f is sufficiently large the realizations behave as if the cost function belonged to s that is any minimal realization of a function f using cost table f is one of the minimal realizations of f using f and a cost function in s the interpretation of these results is that there are not as many distinct cost tables as originally thought