algebraic invariants of the o 2 gauge transformation the authors consider the o 2 gauge transformation for a two state vertex model on a lattice and derive its fundamental algebraic invariants the minimal set of homogeneous polynomials of the vertex weights which are invariant under o 2 transformations explicit expressions of the fundamental invariants are given for symmetric vertex models on lattices with coordination number p 2 3 4 5 6 generalising p 3 results obtained previously from more elaborate considerations

discrete riemann surfaces and the ising model we define a new theory of discrete riemann surfaces and present its basic results the key idea is to consider not only a cellular decomposition of a surface but the union with its dual discrete holomorphy is defined by a straightforward discretisation of the cauchy riemann equation a lot of classical results in riemann theory have a discrete counterpart hodge star harmonicity hodge theorem weyl s lemma cauchy integral formula existence of holomorphic forms with prescribed holonomies giving a geometrical meaning to the construction on a riemann surface we define a notion of criticality on which we prove a continuous limit theorem we investigate its connection with criticality in the ising model we set up a dirac equation on a discrete universal spin structure and we prove that the existence of a dirac spinor is equivalent to criticality

diagonalization of the quadratic boson hamiltonian with zero modes i mathematical the necessary mathematical equipment is developed for an analysis of the zero modes connected with hamiltonians quadratic in boson creation and annihilation operators a cross matrix being a matrix of a certain partitioned form we consider the group g of conjuctivity transformations t where t is a 2m square cross matrix subjected to the restriction t it i i diag i i i is the m square unit matrix with respect to this group the concept of standard form is introduced for the set of positive semidefinite hermitian cross matrices d it is proved that any such matrix d can be transformed into a matrix e of the standard form according to t dt e t g an algorithm suitable as a basis for computer programs is given for finding standardized and standardizing matrices e and t for any given d

a comparison of minimax tree search algorithms abstract although theoretic performance measures of most game searching algorithms exist for various reasons their practicality is limited this paper examines and extends the existing search methods and reports on empirical performance studies on trees with useful size and ordering properties emphasis is placed on trees that are strongly ordered i e similar to those produced by many current game playing programs

diagrammatic construction of an irreducible basis of algebraic invariants for the sixteen vertex model according to a fundamental theorem by hilbert the partition function and other physically relevant properties of the general sixteen vertex model must be expressible algebraically in terms of a small number of basic invariants with respect to the symmetry group of the model the construction of such an irreducible set of algebraic invariants has been described in two earlier papers by graff and hijmans1 2 in the present paper it is shown that this basic set can be obtained in a simpler and more elegant way by means of a diagrammatic technique based on scalar and vectorial multiplication of three kinds of construction elements and the use of six reduction rules for diagrams

semiparametric estimation of censored selection models with a nonparametric selection mechanism abstract in this paper estimation of the coefficients in a single index selectivity bias model is considered under the assumption that the selection correction function depends on the conditional mean of some observable selection variable the estimation method follows a familiar two step strategy the first step uses a nonparametric regression estimator for the selection variable while the second step uses a weighted instrumental variables estimator for the coefficients in the equation of interest the paper gives conditions under which the proposed estimator is root n consistent and asymptotically normal the proposed method is applied to data on labor supply

hyperbolic coxeter groups for triangular potts models the symmetry groups generated by the inversion relations of lattice models of statistical mechanics on triangular lattices are analysed for vertex models and for the standard scalar potts model with two and three site interactions these groups are generated by three inversion relations and are seen to be generically very large ones hyperbolic groups two situations for which the representations of these groups degenerate into smaller ones hopefully compatible with integrability are considered the first reduction for the vertex triangular model corresponds to the situation where the vertex of the triangular model coincides with the left or right hand side of a yang baxter relation in this case the representation of the group is isomorphic up to a semi direct product by a finite group to z z the second reduction for q state ports models occurs for particular values of q the so called tutte beraha numbers for this model algebraic varieties including the known ferromagnetic critical variety happen to be invariant under such large groups of symmetries as a byproduct this analysis provides nice birational representations of hyperbolic coxeter groups

free fermion checkerboard and z invariant lattice models in statistical mechanics it is shown that the two dimensional free fermion model is equivalent to a checkerboard ising model which is a special case of the general z invariant ising model expressions are given for the partition function and local correlations in terms of those of the regular square lattice ising model corresponding results are given for the self dual potts model and the application of the methods to the three dimensional zamolodchikov model is discussed the paper ends with a discussion of the critical and disorder surfaces of the checkerboard potts model

a solution to the ghi problem for best first search in a search graph a node s value may be dependent on the path leading to it different paths may lead to different values hence it is difficult to determine the value of any node unambiguously the problem is known as the graph history interaction ghi problem this paper provides a solution for best first search first we give a precise formulation of the problem then for best first search and for other searches we review earlier proposals to overcome the problem next our solution is given in detail here we introduce the notion of twin nodes enabling a distinction of nodes according to their history the implementation called bta base twin algorithm is performed for pn search a best first search algorithm it is generally applicable to other best first search algorithms experimental results in the field of computer chess confirm the claim that the ghi problem has been solved for best first search

proof number search abstract proof number search pn search is designed for finding the game theoretical value in game trees it is based on ideas derived from conspiracy number search and its variants such as applied cn search and cn search while in cn search the purpose is to continue searching until it is unlikely that the minimax value of the root will change pn search aims at proving the true value of the root therefore pn search does not consider interim minimax values pn search selects the next node to be expanded using two criteria the potential range of subtree values and the number of nodes which must conspire to prove or disprove that range of potential values these two criteria enable pn search to treat efficiently game trees with a non uniform branching factor it is shown that in non uniform trees pn search outperforms other types of search such as iterative deepening search even when enhanced with transposition tables move ordering for the full principal variation etc pn search has been used to establish the game theoretical values of connect four qubic and go moku there pn search was able to find a forced win for the player to move first the experiments described here are in the domain of awari a game which has not yet been solved the experiments are repeatable for other games with a non uniform branching factor this article describes the underlying principles of pn search presents an appropriate implementation and provides an analysis of its strengths and weaknesses

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

simplified bifurcation analysis of the sixteen vertex model based on the standard representation of equivalence classes of models the search for bifurcation points in the parameter space of sixteen vertex models as described in three papers by gaaff and hijmans1 and hijmans and schram2 3 canbe considerably simplified and clarified by representing the equivalence classes of models having the same partition function by their standard models instead of by their normal models the preference for the standard model arises from the fact that it is characterized by parameters belonging to the irreducible representations of the symmetry group of the partition function whereas the parameters defining the normal model belong to a mixed representation the standard model defined in terms of 10 characteristic parameters is unique apart from a finite stargroup of 96 operations arising from the freedom to permute the eigenvalues and eigenvectors of a characteristic 4 x 4 matrix qss bifurcations occur whenever the set of 10 characteristic parameters is invariant with respect to a non trivial little group of operations from the stargroup

on the bifurcations occurring in the parameter space of the sixteen vertex model ii bifurcations arising from degeneracies in the n matrix the analysis of the bifurcation structure in the 16 dimensional parameter space of homogeneous sixteen vertex models started in part i is completed in this paper as before equivalence classes of models having the same partition function are identified by means of a 4 4 diagonal matrix n and a pair of characteristic 2 2 matrices a and b the bifurcation classes of models studied in this part include also classes for which the n matrix shows degeneracies the four primary bifurcation classes uncovered in part i i e the general and complementary eight vertex models and the one sided and doubly cyclic models each give rise to a hierarchy of two kinds of subbifurcations on the one hand the models corresponding to the different patterns of degeneracies of the n matrix and on the other hand the models for which the rotation angles and characterizing the matrices a and b have values 2 na and 2 nb respectively with na and nb integers

on zamolodchikov s solution of the tetrahedron equations the tetrahedron equations arise in field theory as the condition for thes matrix in 2 1 dimensions to be factorizable and in statistical mechanics as the condition that the transfer matrices of three dimensional models commute zamolodchikov has proposed what appear from numerical evidence and special cases to be non trivial particular solutions of these equations but has not fully verified them here it is proved that they are indeed solutions

accurate determination of the critical line of the square ising antiferromagnet in a field several points on the critical line of the simple quadratic antiferromagnetic ising model in a field are located with high precision this is accomplished by means of finite size scaling of the magnetic correlation length of n infinity strips the latter quantities were determined by means of the transfer matrix method for strip widths up to n 20 an expression possibly with the exact form is constructed which reproduces the critical line with an accuracy to the order of 10 10

an analysis of the conspiracy numbers algorithm abstract mcallester s conspiracy numbers algorithm is a minimax search procedure that builds game trees to variable depths without application dependent knowledge the algorithm gathers information to determine how likely it is that the search of a sub tree will produce a useful result likeliness is measured by the conspiracy numbers the minimum number of leaf nodes that must change their value by being searched deeper to cause the minimax value of a sub tree to change the search is controlled by the conspiracy threshold ct the minimum number of conspirators beyond which it is considered unlikely that a sub tree s value can be changed this paper analyzes the best case performance for the algorithm mcallester s original algorithm is shown to build a tree of size o w ct w 1 where w is the branching factor of the tree a new improvement to the algorithm is shown to reduce this complexity to o ct 2 hence for a given fixed w the algorithm s best case can be improved from exponential to quadratic growth although the minimal tree case is not necessarily representative of the search trees built in practice experimental results are presented that demonstrate the improvement appears to be significant in the expected case as well

local instrumental variables and latent variable models for identifying and bounding treatment effects this paper examines the relationship between various treatment parameters within a latent variable model when the effects of treatment depend on the recipient s observed and unobserved characteristics we show how this relationship can be used to identify the treatment parameters when they are identified and to bound the parameters when they are not identified

a minimax algorithm better than alpha beta yes and no this paper contains a probabilistic analysis of the performance of the game searching sss algorithm which has been shown to be superior to a b necessary and sufficient conditions for node expansion are established and an expression for the average number of nodes expanded is derived the branching factor of sss is shown to coincide with that of a b thus rendering the two algorithms asymptotically equivalent numerical comparison of the expected complexities of the two algorithms is finally carried out over a wide spectrum of search depths and branching degrees the latter shows that the savings in the number of positions evaluated by sss relative to that of a b is rather limited and is not enough to offset the increase in other computational resources

the vertex formulation of the bazhanov baxter model in this paper we formulate an integrable model on the simple cubic lattice then valued spin variables of the model belong to edges of the lattice the boltzmann weights of the model obey the vertex type tetrahedron equation in the thermodynamic limit our model is equivalent to the bazhanov baxter model in the case whenn 2 we reproduce korepanov s and hietarinta s solutions of the tetrahedron equation as special cases

on the bifurcations occuring in the parameter space of the sixteen vertex model i discrete bifurcations abstract the 16 dimensional parameter space of homogeneous sixteen vertex models is scanned for bifurcation points i e points corresponding to models which possess extra symmetries not existing in nearby points equivalence classes of models having the same partition function are identified by means of a characteristic normal model represented by a 4 x 4 diagonal matrix n and a pair of 2 x 2 matrices a and b in this paper the matrix n is assumed to be non degenerate and the only bifurcations found are those associated with special types of matrices a and b i e matrices whose decomposition in terms of pauli matrices corresponds to a vector a a 1 a 2 a 3 or b b 1 b 2 b 3 that is invariant with respect to one or more elements of the cubic symmetry group the various bifurcation classes of models found include a the families of general and complementary eight vertex models b discrete sets of doubly and one sided cyclic models and c a number of secondary bifurcation classes within the eight vertex families among which is baxters symmetric eight vertex model

the history heuristic and alpha beta search enhancements in practice many enhancements to the alpha beta algorithm have been proposed to help reduce the size of minimax trees a recent enhancement the history heuristic which improves the order in which branches are considered at interior nodes is described a comprehensive set of experiments is reported which tries all combinations of enhancements to determine which one yields the best performance in contrast previous work on assessing their performance has concentrated on the benefits of individual enhancements or a few combinations the aim is to find the combination that provides the greatest reduction in tree size results indicate that the history heuristic combined with transposition tables significantly outperforms other alpha beta enhancements in application generated game trees for trees up to depth 8 this combination accounts for 99 of the possible reductions in tree size with the other enhancements yielding insignificant gains

analysis of treatment response data without the joint distribution of potential outcomes in this paper we show how it is possible to develop a bayesian framework for analyzing structural models for treatment response data without the joint distribution of the potential outcomes that this is possible has not been noticed in the literature we also discuss the computation of the model marginal likelihood and present recipes for finding relevant treatment effects averaged over both parameters and covariates as compared to an approach in which the counterfactuals are part of the prior posterior analysis as in the work to date the approach we suggest is simpler in terms of the required prior inputs computational burden and extensibility to more complex settings

fa yueh wu s contributions in physics abstract we sketch a subset of professor f y wu s contributions in lattice statistical mechanics solid state physics graph theory enumerative combinatorics and other domains of physics and mathematics we will recall some of f y wu s most important and well known classic results and we will also sketch some of his most recent researches dedicated to the connections of lattice statistical mechanical models with deep problems in pure mathematics

baxter equations and the zamolodchikov model abstract a summary is given of the significance of the star triangle or yang baxter equations in the solution of two dimensional statistical mechanical models the extension to the three dimensional tetrahedron relations is quoted and it is shown how this can be used to obtain the partition function of the zamolodchikov model for an n lattice the n result differs from that recently obtained by bazhanov and stroganov

random matrix theory and higher genus integrability the quantum chiral potts model we perform a random matrix theory rmt analysis of the quantum fourstate chiral potts chain for different sizes of the chain up to size l 8 ou ra nalysis gives clear evidence of a gaussian orthogonal ensemble goe statistics suggesting the existence of a generalized time reversal invariance furthermore a change from the generic goe distribution to a poisson distribution occurs when the integrability conditions are met the chiral potts model is known to correspond to a star triangle integrability associated with curves of genus higher than zero or one therefore the rmt analysis can also be seen as a detector of higher genus integrability

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

phase diagram of a six state chiral potts model abstract we study the phase diagram of an isotropic six state chiral potts model on a square lattice by means of both exact and numerical methods the phase diagram of this model presents many similarities with the phase diagrams of the ashkin teller model or the models studied by zamolodchikov and monarstirskii a remarkable line globally invariant under a transformation generalizing the kramers wannier duality seems to correspond to a first order transition line up to a bifurcation point where this line splits into two second order lines all the numerical calculations are compared with exact results which can be performed using a canonical elliptic parametrization of this model the bifurcation point is found to correspond to the intersection of a generalized self dual line with an algebraic curve this curve corresponds to the set of points of the phase diagram for which a non trivial infinite symmetry group of the model degenerates into a finite group of order six the agreement between numerical and analytical results is very good

inversion relations and disorder solutions on potts models the inversion symmetry and the automorphy group generated by the latter when combined with the spatial symmetries are studied for the anisotropic potts models on the triangular and checkerboard lattices the exact expression of the partition function which is known on some particular disorder subvarieties of the triangular model is checked and a generalisation is proposed for the checkerboard lattice the automorphy group is then used to extend the disorder solutions to the infinity of transformed subvarieties

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

the o 3 gauge transformation and 3 state vertex models the authors consider the o 3 gauge transformation for three state vertex models on lattices of coordination number three using an explicit mapping between o 3 and sl 2 they establish that there exist exactly six polynomials of the vertex weights which are fundamentally invariant under the o 3 transformation explicit expressions of these fundamental invariants are obtained in the case of symmetric vertex weights

random matrix theory and classical statistical mechanics spin models a connection between integrability properties and general statistical properties of the spectra of symmetric transfer matrices of the asymmetric eight vertex model is studied using random matrix theory eigenvalue spacing distribution and spectral rigidity for yang baxter integrable cases including free fermion solutions we found a poissonian behavior whereas level repulsion close to the wigner distribution is found for nonintegrable models for the asymmetric eight vertex model however the level repulsion can also disappear and the poisson distribution be recovered on non yang baxter integrable algebraic varieties the so called disorder varieties we also present an infinite set of algebraic varieties which are stable under the action of an infinite discrete symmetry group of the parameter space these varieties are possible loci for free parafermions using our numerical criterion we tested the generic calculability of the model on these algebraic varieties

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

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

topological representations of the quantum groupuq sl2 we define a topological action of the quantum groupuq sl2 on a space of homology cycles with twisted coefficients on the configuration space of the punctured disc this action commutes with the monodromy action of the braid groupoid which is given by ther matrix ofuq sl2

models for nonresponse in sample surveys abstract the literature on the analysis of incomplete data using models is reviewed in the context of nonresponse in sample surveys the modeling approach provides a large body of methods for handling unit and item nonresponse some of which cannot be derived from the randomization theory of inference for surveys key concepts from the literature on incomplete data such as factorizations of the likelihood for special data patterns the em algorithm for general data patterns and ignorability of the response mechanism are discussed within the survey context model based procedures are related to common methods for handling nonresponse in surveys such as weighting or imputation of means within subclasses of the population

hidden quantum group symmetry and integrable perturbations of conformal field theories the hidden quantum group symmetry in the quantum sine gordon model is found this symmetry provides the possibility to restrict the operator algebra of the model to subalgebras it is shown that these subalgebras are massive deformations of minimal conformal field theories

on the classification of the homogeneous 16 vertex models on a square lattice ii connection with a new type of phase transition abstract in the previous paper we have shown that the classification problem of the homogeneous real 16 vertex models on a square lattice as proposed by gaaff and hijmans is closely connected with the similar problem corresponding to the boson bogoliubov transformation in quantum mechanics this insight leads us in the present paper to use arguments and examples from papers dealing with the latter problem in a further study of the classification problem of the real 16 vertex models we also use a somewhat modified concept of standard or normal 16 vertex model which was introduced by hijmans and schram in a similar study concerning the complex 16 vertex models we show that rather than the single family found by hijmans and schram for the complex variant of the problem the set of equivalence classes of real 16 vertex models can be divided up into seven families this strongly suggests the existence of a new type of phase transitions which manifest themselves when the physical system in the 16 parameter space moves from one family to another

distribution free estimation of the random coefficient dummy endogenous variable model this paper considers the estimation of the random coefficient dummy endogenous variable model under a symmetry and index condition for the error distribution we follow a two step approach the selection equation is estimated first in the second step an instrumental variables estimator is proposed for the ourcome equation through a pairwise comparison method our approach can be readily extended to the general switching regression model in constrast to the existing literature on sample selection models the exclusion restriction is not needed here for model identification furthermore the intercept term for the outcome equation can be estimated at the usual parametric rate

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

a generalised quiescence search algorithm abstract this paper describes how the concept of a null move may be used to define a generalised quiescence search applicable to any minimax problem experimental results in the domain of chess tactics show major gains in cost effectiveness over full width searches and it is suggested that null move quiescence may be almost as widely useful as the alpha beta mechanism the essence of the mechanism is that null moves give rise to bounds on position values which are more reliable than evaluations when opposing bounds touch they create a single value which is more reliable than ordinary evaluations and the search is terminated at that point these terminations are prior to any alpha beta cutoffs and can lead to self terminating searches

symmetry complexity and multicritical point of the two dimensional spin glass we analyse models of spin glasses on the two dimensional square lattice by exploiting symmetry arguments the replicated partition functions of the ising and related spin glasses are shown to have many remarkable symmetry properties as functions of the edge boltzmann factors it is shown that the applications of homogeneous and hadamard inverses to the edge boltzmann matrix indicate reduced complexities when the elements of the matrix satisfy certain conditions suggesting that the system has special simplicities under such conditions using these duality and symmetry arguments we present a conjecture on the exact location of the multicritical point in the phase diagram

labelling schemes for tetrahedron equations and dualities between them zamolodchikov s tetrahedron equations which were derived by considering the scattering of straight strings can be written in three different labelling schemes one can use as labels the states of the vacua between the strings the states of the string segments or the states of the particles at the intersections of the strings we give a detailed derivation of the three corresponding tetrahedron equations and also show how the frenkel moore equations fits in as a non local string labelling we then discuss how an analogue of the wu kadanoff duality can be defined between each pair of the above three labelling schemes it turns out that there are two cases for which one can simultaneously construct a duality between all three pairs of labellings

quantum group structure in the fock space resolutions of widehat sl n representations we describe a complex of wakimoto type fock space modules for the affine kac moody algebra widehat sl n the intertwining operators that build the complex are obtained from contour integrals of so called screening operators we show that a quantum group structure underlies the algebra of screening operators this observation greatly facilitates the explicit determination of the intertwiners we conjecture that the complex provides a resolution of an irreducible highest weight module in terms of fock spaces

tetrahedron equations and the relativistic s matrix of straight strings in 2 1 dimensions the quantums matrix theory of straight strings infinite one dimensional objects like straight domain walls in 2 1 dimensions is considered thes matrix is supposed to be purely elastic and factorized the tetrahedron equations which are the factorization conditions are investigated for the special two colour model the relativistic three strings matrix which apparently satisfies this tetrahedron equation is proposed

exact solution of generalized t j models in one dimension a relation between the anisotropic t j model and a generalized six vertex model has been established on the basis of this relation we obtain the exact bethe ansatz solution for the ground state energy of anisotropic t j model for arbitrary spin and special values of coupling parameters we consider also the anisotropic generalization of t j model with localons

rational dynamical zeta functions for birational transformations we propose a conjecture for the exact expression of the unweighted dynamical zeta function for a family of birational transformations of two variables depending on two parameters this conjectured function is a simple rational expression with integer coecients this yields an algebraic value for the topological entropy furthermore the generating function for the arnold complexity is also conjectured to be a rational expression with integer coecients with the same singularities as for the dynamical zeta function this leads at least in this example to an equality between the asymptotic of the arnold complexity and the exponential of the topological entropy we also give a semi numerical method to eectively compute the arnold complexity c 1999 published by elsevier science b v all rights reserved

strategies anticipating a difference in search depth using opponent model search in this contribution we propose a class of strategies which focus on the game as well as on the opponent preference is given to the thoughts of the opponent so that the strategy under investigation might be speculative we describe a generalization of om search called d d om search where d stands for the depth of search by the player and d for the opponent s depth of search a known difference in search depth can be exploited by purposely choosing a suboptimal variation with the aim to gain a larger advantage than when playing the objectively best move the difference in search depth may have the result that the opponent does not see the variation in sufficiently deep detail we then give a pruning alternative for d d om search denoted by 2 pruning a best case analysis shows that 2 prunes very efficiently comparable to the efficiency of with regard to minimax the effectiveness of the proposed strategy is confirmed by simulations using a game tree model including an opponent model and by experiments in the domain of othello

integrable boundary conditions for multi species asep the first result of the present paper is to provide classes of explicitsolutions for integrable boundary matrices for the multi species asep with anarbitrary number of species all the solutions we have obtained can be seen as representations of a newalgebra that contains the boundary hecke algebra the boundary hecke algebra isnot sufficient to build these solutions this is the second result of ourpaper

no free ends method for lattice animals and vertex models with arbitrary number of states abstract a new no free ends method for generating power series expansions for vertex models with arbitrary number of states is described it is based on first order differential equations providing a recurrent relation connecting the free ends part of the series expansion in the n 1 th order with the nth and n 1 th order of the complete expansion the number of necessary no free ends graphs can be further reduced for symmetric systems by eliminating the nodes which have two neighbors and their incident bonds are in different states

representations of the quantum doubles of finite group algebras and spectral parameter dependent solutions of the yang baxter equation quantum doubles of finite group algebras form a class of quasitriangular hopf algebras that algebraically solve the yang baxter equation each representation of the quantum double then gives a matrix solution of the yang baxter equation such solutions do not depend on a spectral parameter and to date there has been little investigation into extending these solutions such that they do depend on a spectral parameter here we first explicitly construct the matrix elements of the generators for all irreducible representations of quantum doubles of the dihedral groups dn these results may be used to determine constant solutions of the yang baxter equation we then discuss baxterization ansatze to obtain solutions of the yang baxter equation with a spectral parameter and give several examples including a new 21 vertex model we also describe this approach in terms of minimal dimensional representations of the quantum doubles of the alternating group a4 and the symmetric group s4

a flexible parametric approach for estimating switching regime models and treatment effect parameters in this paper we propose a flexible parametric class of switching regime models allowing for both skewed and fat tailed outcome and selection errors specifically we model the joint distribution of each outcome error and the selection error via a newly constructed class of multivariate distributions which we call generalized normal mean variance mixture distributions we extend heckman s two step estimation procedure for the gaussian switching regime model to the new class of models when the distributions of the outcome errors are asymmetric we show that an additional correction term accounting for skewness in the outcome error distribution besides the analogue of the well known inverse mill s ratio needs to be included in the second step regression we use the two step estimators of parameters in the model to construct simple estimators of average treatment effects and establish their asymptotic properties simulation results confirm the importance of accounting for skewness in the outcome errors in estimating both model parameters and the average treatment effect and the treatment effect for the treated

identification and estimation of local average treatment effects we investigate conditions sufficient for identification of average treatment effects using instrumental variables first we show that the existence of valid instruments is not sufficient to identify any meaningful average treatment effect we then establish that the combination of an instrument and a condition on the relation between the instrument and the participation status is sufficient for identification of a local average treatment effect for those who can be induced to change their participation status by changing the value of the instrument finally we derive the probability limit of the standard iv estimator under these conditions it is seen to be a weighted average of local average treatment effects this abstract was borrowed from another version of this item

discrete symmetry groups of vertex models in statistical mechanics we analyze discrete symmetry groups of vertex models in lattice statistical mechanics represented as groups of birational transformations they can be seen as generated by involutions corresponding respectively to two kinds of transformations onq q matrices the inversion of theq q matrix and an involutive permutation of the entries of the matrix we show that the analysis of the factorizations of the iterations of these transformations is a precious tool in the study of lattice models in statistical mechanics this approach enables one to analyze two dimensionalq4 state vertex models as simply as three dimensional vertex models or higher dimensional vertex models various examples of birational symmetries of vertex models are analyzed a particular emphasis is devoted to a three dimensional vertex model the 64 state cubic vertex model which exhibits a polynomial growth of the complexity of the calculations a subcase of this general model is seen to yield integrable recursion relations we also concentrate on a specific two dimensional vertex model to see how the generic exponential growth of the calculations reduces to a polynomial growth when the model becomes yang baxter integrable it is also underlined that a polynomial growth of the complexity of these iterations can occur even for transformations yielding algebraic surfaces or higher dimensional algebraic varieties

on the classification of the homogeneous 16 vertex models on a square lattice i connection with the boson bogoliubov transformation abstract we consider the classification of all homogeneous 16 vertex models on a square lattice which was proposed by gaaff and hijmans we show that this classification can be translated into that is reformulated in terms of a classification of matrices which closely resembles one already investigated with some success in the literature viz the classification connected with the boson bogoliubov transformation in quantum mechanics the main difference between our approach and the one of gaaff and hijmans who also made a reformulation is that we can keep our considerations in conformity with the actual physical problem within the field of real rather than complex numbers in the accompanying paper this leads to results with features not present in the analysis over c which point to a possible connection with a new kind of phase transitions

quantum backlund transformation for the integrable dst model for the integrable case of the discrete self trapping dst model we construct a backlund transformation the dual lax matrix and the corresponding dual backlund transformation are also found and studied the quantum analogue of the backlund transformation q operator is constructed as the trace of a monodromy matrix with an infinite dimensional auxiliary space we present the q operator as an explicit integral operator as well as describing its action on the monomial basis as a result we obtain a family of integral equations for multivariable polynomial eigenfunctions of the quantum integrable dst model these eigenfunctions are special functions of the heun class which is beyond the hypergeometric class the integral equations found are new and they shall provide a basis for efficient analytical and numerical studies of such complicated functions

factorization properties of birational mappings abstract we analyse birational mappings generated by transformations on q q matrices which correspond respectively to two kinds of transformations the matrix inversion and a permutation of the entries of the q q matrix remarkable factorization properties emerge for quite general involutive permutations it is shown that factorization properties do exist even for birational transformations associated with noninvolutive permutations of entries of q q matrices and even for more general transformation which are rational transformations but no longer birational the existence of factorization relations independent of q the size of the matrices is underlined the relations between the polynomial growth of the complexity of the iterations the existence of recursions in a single variable and the integrability of the mappings are sketched for the permutations yielding these properties all these results show that permutations of the entries of the matrix yielding factorization properties are not so rare in contrast the occurrence of recursions in a single variable or of the polynomial growth of the complexity are of course less frequent but not completely exceptional

rational mappings arborescent iterations and the symmetries of integrability we describe a class of nonlinear birational representations of groups generated by a finite number of involutions these groups are symmetries of the yang baxter equations and their higher dimensional generalizations they provide discrete dynamical systems with a variety of behaviors from chaotic to integrable according to the number of invariants of the representation

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

necessary versus sufficient conditions for exact solubility of statistical models on lattices it is shown that under rather mild conditions the triangle relation represents a necessary condition for the existence of commuting transfer matrices of arbitrary size the cases of spin models and vertex models are treated separately

let s baxterise we recall the concept of baxterisation of an r matrix or of a monodromy matrix which corresponds to build from one point in the r matrix parameter space the algebraic variety where the spectral parameter s live we show that the baxterisation which amounts to studying the iteration of a birational transformation is a win win strategy it enables to discard efficiently the non integrable situations focusing directly on the two interesting cases where the algebraic varieties are of the so called general type finite order iteration or are abelian varieties infinite order iteration we emphasize the heuristic example of the sixteen vertex model and provide a complete description of the finite order iterations situations for the baxter model we show that the baxterisation procedure can be introduced in much larger frameworks where the existence of some underlying yang baxter structure is not used we baxterise l operators local quantum lax matrices and quantum hamiltonians

growth complexity spectrum of some discrete dynamical systems we first study the iteration of birational mappings generated by the composition of the matrix inversion and of a permutation of the entries of 3 3 matrices and consider the degree d n of the numerators or denominators of the corresponding successive rational expressions for the nth iterate the growth of this degree is generically exponential with n d n n is called the growth complexity we introduce a semi numerical analysis which enables to compute these growth complexities for all the 9 possible birational transformations these growth complexities correspond to a spectrum of eighteen algebraic values we then drastically generalize these results replacing permutations of the entries by homogeneous polynomial transformations of the entries possibly depending on many parameters again it is shown that the associated birational or even rational transformations yield algebraic values for their growth complexities 1999 elsevier science b v all rights reserved

an effective two level proof number search algorithm the paper presents a new proof number pn search algorithm called pds pn it is a two level search like pn2 which performs at the first level a depth first proof number and disproof number search pds and at the second level a best first pn search hence pds pn selectively exploits the power of both pn2 and pds experiments in the domain of lines of action are performed they show that within an acceptable time frame pds pn is more effective for really hard endgame positions than and any other pn search algorithm

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

automorphisms of algebraic varieties and yang baxter equations it is shown that commuting transfer matrix models in statistical mechanics are parametrized by algebraic varieties having a set of automorphisms deduced from the so called inversion relation in general this set of automorphisms is infinite this shows that for algebraic varieties of dimension 1 the models are parametrized by algebraic curves of genus 0 or 1

a new braid like algebra for baxterisation we introduce a new baxterisation for r matrices that depend separately on two spectral parameters the baxterisation is based on a new algebra close to but different from the braid group we study representations of this new algebra on the vector space mathbb c m otimes n when the generators act locally the ones for m 2 are completely classified we also introduce some representations for generic m they allow us to recover the r matrix of the multi species generalization of the totally asymmetric simple exclusion process with different hopping rates

universal spectral parameter dependent lax operators for the drinfeld double of the dihedral group d3 two universal spectral parameter dependent lax operators are presented in terms of the elements of the drinfeld double d d3 of the dihedral group d3 applying representations of d d3 to these yields matrix solutions of the yang baxter equation with a spectral parameter

new integrable cases of a cremona transformation a finite order orbits analysis we analyse the properties of a particular birational mapping of two variables cremona transformation depending on two free parameters e and associated with the action of a discrete group of non linear birational transformations on the entries of a q q matrix this mapping originates from the analysis of birational transformations obtained from very simple algebraic calculations namely taking the inverse of q q matrices and permuting some of the entries of these matrices it has been seen to yield weak chaos and integrability we have found new integrable cases of this cremona transformation corresponding to the values of 0 when e 12 13 1 besides the already known values e 0 and e 1 and also arbitrary when e 0 for these cases one has a foliation of the parameter space in elliptic curves we give the equations of these elliptic curves based on this very example we show how one can find these integrability cases of the cremona transformation and actually integrate it using a method based on the systematic study of the finite order conditions of the cremona transformation the method is shown to be efficient and straightforward the various integrability cases are revisited using many different representations of this very mapping birational transformations recursion in one variable

square lattice ising model susceptibility series expansion method and differential equation for χ 3 in a previous paper 2004 j phys a math gen 37 9651 68 we have given the fuchsian linear differential equation satisfied by 3 the three particle contribution to the susceptibility of the isotropic square lattice ising model this paper gives the details of the calculations with some useful tricks and tools allowing one to obtain long series in polynomial time the method is based on series expansion in the variables that appear in the n 1 dimensional integrals representing the n particle contribution to the isotropic square lattice ising model susceptibility the integration rules are straightforward due to remarkable formulae we derived for these variables we obtain without any numerical approximation 3 as a fully integrated series in the variable w s 2 1 s2 where s sh 2k with k j kt the conventional ising model coupling constant we also give some perspectives and comments on these results

the ising model from elliptic curves to modular forms and calabi yau equations we show that almost all the linear differential operators factors obtained in the analysis of the n particle contributions s of the susceptibility of the ising model for n 6 are linear differential operators associated with elliptic curves beyond the simplest differential operators factors which are homomorphic to symmetric powers of the second order operator associated with the complete elliptic integral e the second and third order differential operators z2 f2 f3 can actually be interpreted as modular forms of the elliptic curve of the ising model a last order 4 globally nilpotent linear differential operator is not reducible to this elliptic curve modular form scheme this operator is shown to actually correspond to a natural generalization of this elliptic curve modular form scheme with the emergence of a calabi yau equation corresponding to a selected 4f3 hypergeometric function this hypergeometric function can also be seen as a hadamard product of the complete elliptic integral k with a remarkably simple algebraic pull back square root extension the corresponding calabi yau fourth order differential operator having a symplectic differential galois group the mirror maps and higher order schwarzian odes associated with this calabi yau ode present all the nice physical and mathematical ingredients we had with elliptic curves and modular forms in particular an exact isogenies representation of the generators of the renormalization group extending the modular group to a symmetry group