darboux transformations for the two dimensional toda system binary darboux transformations are constructed for the two dimensional a toda lattice and for a generalized non abelian toda lattice invariance of these transformations under certain reductions produces the b and c toda lattices as well as various periodic reductions corresponding to kac moody algebras the reduction to the d lattice from the non abelian lattice is studied in some detail

on the τ functions of the reduced ostrovsky equation and the a 2 2 two dimensional toda system the reciprocal link between the reduced ostrovsky equation and the a 2 2 two dimensional toda 2d toda system is used to construct the n soliton solution of the reduced ostrovsky equation the n soliton solution of the reduced ostrovsky equation is presented in the form of pfaffian through a hodograph reciprocal transformation the bilinear equations and the function of the reduced ostrovsky equation are obtained from the period 3 reduction of the b or c 2d toda system i e the a 2 2 2d toda system one of the functions of the a 2 2 2d toda system becomes the square of a pfaffian which also becomes a solution of the reduced ostrovsky equation there is another bilinear equation which is a member of the 3 reduced extended bkp hierarchy using this bilinear equation we can also construct the same pfaffian solution

on the τ functions of the degasperis procesi equation the degasperis procesi dp equation is investigated from the point of view of determinant pfaffian identities the reciprocal link between the dp equation and the pseudo 3 reduction of the c two dimensional toda system is used to construct the n soliton solution of the dp equation the n soliton solution of the dp equation is presented in the form of pfaffian through a hodograph reciprocal transformation the bilinear equations the identities between determinants and pfaffians and the functions of the dp equation are obtained from the pseudo 3 reduction of the c two dimensional toda system

temporal constraint networks abstract this paper extends network based methods of constraint satisfaction to include continuous variables thus providing a framework for processing temporal constraints in this framework called temporal constraint satisfaction problem tcsp variables represent time points and temporal information is represented by a set of unary and binary constraints each specifying a set of permitted intervals the unique feature of this framework lies in permitting the processing of metric information namely assessments of time differences between events we present algorithms for performing the following reasoning tasks finding all feasible times that a given event can occur finding all possible relationships between two given events and generating one or more scenarios consistent with the information provided we distinguish between simple temporal problems stps and general temporal problems the former admitting at most one interval constraint on any pair of time points we show that the stp which subsumes the major part of vilain and kautz s point algebra can be solved in polynomial time for general tcsps we present a decomposition scheme that performs the three reasoning tasks considered and introduce a variety of techniques for improving its efficiency we also study the applicability of path consistency algorithms as preprocessing of temporal problems demonstrate their termination and bound their complexities

the complexity of some polynomial network consistency algorithms for constraint satisfaction problems abstract constraint satisfaction problems play a central role in artificial intelligence a class of network consistency algorithms for eliminating local inconsistencies in such problems has previously been described we analyze the time complexity of several node arc and path consistency algorithms and prove that arc consistency is achievable in time linear in the number of binary constraints the waltz filtering algorithm is a special case of the arc consistency algorithm in the edge labelling computational vision application the constraint graph is planar and so the time complexity is linear in the number of variables

modelling and solving temporal reasoning as propositional satisfiability representing and reasoning about time dependent information is a key research issue in many areas of computer science and artificial intelligence one of the best known and widely used formalisms for representing interval based qualitative temporal information is allen s interval algebra ia the fundamental reasoning task in ia is to find a scenario that is consistent with the given information this problem is in general np complete in this paper we investigate how an interval based representation or ia network can be encoded into a propositional formula of boolean variables and or predicates in decidable theories our task is to discover whether satisfying such a formula can be more efficient than finding a consistent scenario for the original problem there are two basic approaches to modelling an ia network one represents the relations between intervals as variables and the other represents the end points of each interval as variables by combining these two approaches with three different boolean satisfiability sat encoding schemes we produced six encoding schemes for converting ia to sat in addition we also showed how ia networks can be formulated into satisfiability modulo theories smt formulae based on the quantifier free integer difference logic qf idl these encodings were empirically studied using randomly generated ia problems of sizes ranging from 20 to 100 nodes a general conclusion we draw from these experimental results is that encoding ia into sat produces better results than existing approaches more specifically we show that the new point based 1 d support sat encoding of ia produces consistently better results than the other alternatives considered in comparison with the six different sat encodings the smt encoding came fourth after the point based and interval based 1 d support schemes and the point based direct scheme further we observe that the phase transition region maps directly from the ia encoding to each sat or smt encoding but surprisingly the location of the hard region varies according to the encoding scheme our results also show a fixed performance ranking order over the various encoding schemes

iwasawa theory for k 1 local spectra the iwasawa algebra is a power series ring in one variable over the adic integers it has long been studied by number theorists in the context of extensions of number fields it also arises however as a ring of operations in adic topological theory in this paper we study local stable homotopy theory using the structure theory of modules over the iwasawa algebra in particular for odd we classify local spectra up to pseudo equivalence the analogue of pseudo isomorphism for modules and give an iwasawa theoretic classification of the thick subcategories of the weakly dualizable spectra

a self adaptive moving mesh method for the camassa holm equation a self adaptive moving mesh method is proposed for the numerical simulations of the camassa holm equation it is an integrable scheme in the sense that it possesses the exact n soliton solution it is named a self adaptive moving mesh method because the non uniform mesh is driven and adapted automatically by the solution once the non uniform mesh is evolved the solution is determined by solving a tridiagonal linear system due to these two superior features of the method several test problems give very satisfactory results even if by using a small number of grid points

two dimensional generalized toda lattice the zero curvature representation is obtained for the two dimensional generalized toda lattices connected with semisimple lie algebras the reduction group and conservation laws are found and the mass spectrum is calculated

morava modules and brown comenetz duality fix a prime number p and let x be a finite spectrum whose n 1 st morava k theory is trivial but whose n th morava k theory is nontrivial n 0 we prove following a method outlined to us by m j hopkins that if 2 p n 2 n 2 the morava module of the brown comenetz dual of the e n localization of x is isomorphic to a suspension of the pontryagin dual of the morava module of x to complete this proof we found it necessary to develop a more canonical construction of certain modified adams spectral sequences this construction should be of independent interest

arc and path consistence revisited mackworth and freuder have analyzed the time complexity of several constraint satisfaction algorithms 5 we present here new algorithms for arc and path consistency and show that the arc consistency algorithm is optimal in time complexity and of the same order space complexity as the earlier algorithms a refined solution for the path consistency problem is proposed however the space complexity of the path consistency algorithm makes it practicable only for small problems these algorithms are the result of the synthesis techniques used in image a general constraint satisfaction system and local consistency methods 3

twenty one large tractable subclasses of allen s algebra abstract this paper continues nebel and burckert s investigation of allen s interval algebra by presenting nine more maximal tractable subclasses of the algebra provided that p np in addition to their previously reported ord horn subclass furthermore twelve tractable subclasses are identified whose maximality is not decided four of them can express the notion of sequentiality between intervals which is not possible in the ord horn algebra all of the algebras are considerably larger than the ord horn subclass the satisfiability algorithm which is common for all the algebras is shown to be linear furthermore the path consistency algorithm is shown to decide satisfiability of interval networks using any of the algebras

combining qualitative and quantitative constraints in temporal reasoning abstract this paper presents a general model for temporal reasoning that is capable of handling both qualitative and quantitative information this model allows the representation and processing of many types of constraints discussed in the literature to date including metric constraints restricting the distance between time points and qualitative disjunctive constraints specifying the relative position of temporal objects reasoning tasks in this unified framework are formulated as constraint satisfaction problems and are solved by traditional constraint satisfaction techniques such as backtracking and path consistency new classes of tractable problems are characterized involving qualitative networks augmented by quantitative domain constraints some of which can be solved in polynomial time using arc and path consistency

processing disjunctions in temporal constraint networks temporal constraint satisfaction problems tcsps provide a formal framework for representing and processing temporal knowledge deciding the consistency of tcsps is known to be intractable we demonstrate that even local consistency algorithms like path consistency pc can be exponential on tcsps due to the fragmentation problem we present two new polynomial approximation algorithms upper lower tightening ult and loose path consistency lpc which are efficient yet effective in detecting inconsistencies and reducing fragmentation our experiments on hard problems in the transition region show that lpc has the best effectiveness efficiency tradeoff for processing tcsps when incorporated within backtrack search lpc is capable of improving search performance by orders of magnitude

combining topological and size information for spatial reasoning information about the size of spatial regions is often easily accessible and when combined with other types of spatial information it can be practically very useful in this paper we introduce four classes of qualitative and metric size constraints and we study their integration with the region connection calculus rcc 8 a well known approach to qualitative spatial reasoning with topological relations we propose a new path consistency algorithm for combining rcc 8 relations and qualitative size relations the algorithm is complete for deciding satisfiability of an input set of topological constraints over one of the three maximal tractable subclasses of rcc 8 containing all the basic relations moreover its time complexity is cubic and is the same as the complexity of the best known method for deciding satisfiability when only these topological relations are considered we also provide results on finding a consistent scenario in cubic time for these combined classes regarding metric size constraints we first study their combination with rcc 8 and we show that deciding satisfiability for the combined sets of constraints is np hard even when only the rcc 8 basic relations are used then we introduce rcc 7 a subalgebra of rcc 8 that can be used for applications where spatial regions cannot partially overlap we show that reasoning with the seven rcc 7 basic relations and the universal relation is intractable but that reasoning with the rcc 7 basic relations combined with metric size information is tractable finally we give a polynomial algorithm for the latter case and a backtracking algorithm for the general case

a new approach to cyclic ordering of 2d orientations using ternary relation algebras abstract in tarski s formalisation the universe of a relation algebra ra consists of a set of binary relations a first contribution of this work is the introduction of ras whose universe is a set of ternary relations these support rotation as an operation in addition to those present in tarski s formalisation then we propose two particular ras a binary ra cyc b whose universe is a set of binary relations on 2d orientations and a ternary ra cyc t whose universe is a set of ternary relations on 2d orientations the ra cyc t more expressive than cyc b constitutes a new approach to cyclic ordering of 2d orientations an atom of cyc t expresses for triples of orientations whether each of the three orientations is equal to to the left of opposite to or to the right of each of the other two orientations cyc t has 24 atoms and the elements of its universe consist of all possible 2 24 subsets of the set of all atoms amongst other results 1 we provide for cyc t a constraint propagation procedure computing the closure of a problem under the different operations and show that the procedure is polynomial and complete for a subset including all atoms 2 we prove that another subset expressing only information on parallel orientations is np complete 3 we show that provided that a subset s of cyc t includes two specific elements deciding consistency for a problem expressed in the closure of s can be polynomially reduced to deciding consistency for a problem expressed in s and 4 we derive from the previous result that for both ras we jump from tractability to intractability if we add the universal relation to the set of all atoms a comparison to the most closely related work in the literature indicates that the approach is promising

integrable discretizations for the short wave model of the camassa holm equation the link between the short wave model of the camassa holm equation sche and bilinear equations of the two dimensional toda lattice equation is clarified the parametric form of the n cuspon solution of the sche in casorati determinant is then given based on the above finding integrable semi discrete and full discrete analogues of the sche are constructed the determinant solutions of both semi discrete and fully discrete analogues of the sche are also presented

an integrable semi discretization of the camassa holm equation and its determinant solution an integrable semi discretization of the camassa holm ch equation is presented the keys of its construction are bilinear forms and determinant structure of solutions of the ch equation determinant formulas of n soliton solutions of the continuous and semi discrete camassa holm equations are presented based on determinant formulas we can generate multi soliton multi cuspon and multi soliton cuspon solutions numerical computations using the integrable semi discrete camassa holm equation are performed it is shown that the integrable semi discrete camassa holm equation gives very accurate numerical results even in the cases of cuspon cuspon and soliton cuspon interactions the numerical computation for an initial value condition which is not an exact solution is also presented

integrable semi discretizations of the reduced ostrovsky equation based on our previous work on the reduced ostrovsky equation j phys a math theor 45 355203 we construct its integrable semi discretizations since the reduced ostrovsky equation admits two alternative representations one being its original form the other the differentiated form the short wave limit of the degasperis procesi equation two semi discrete analogues of the reduced ostrovsky equation are constructed possessing the same n loop soliton solution the relationship between these two versions of semi discretizations is also clarified

integrable discretizations of the short pulse equation in this paper we propose integrable semi discrete and full discrete analogues of the short pulse sp equation the key construction is the bilinear form and determinant structure of solutions of the sp equation we also give the determinant formulas of n soliton solutions of the semi discrete and full discrete analogues of the sp equations from which the multi loop and multi breather solutions can be generated in the continuous limit the full discrete sp equation converges to the semi discrete sp equation and then to the continuous sp equation based on the semi discrete sp equation an integrable numerical scheme i e a self adaptive moving mesh scheme is proposed and used for the numerical computation of the short pulse equation

backtracking algorithms for disjunctions of temporal constraints abstract we extend the framework of simple temporal problems studied originally by dechter meiri and pearl to consider constraints of the form x 1 y 1 r 1 x n y n r n where x 1 x n y 1 y n are variables ranging over the real numbers r 1 r n are real constants and n 1 this is a wide class of temporal constraints that can be used to model a variety of problems in temporal reasoning scheduling planning and temporal constraint databases we have implemented several progressively more efficient algorithms for the consistency checking problem for this class of temporal constraints backtracking backjumping three variations of forward checking and forward checking with backjumping we have partially ordered the above algorithms according to the number of visited search nodes and the number of performed consistency checks although our problem is non binary our results agree with the results of kondrak and van beek who consider only binary constraints we have also studied the performance of the above algorithms experimentally using randomly generated sets of data and job shop scheduling problems the experiments with random instances allowed us to locate the hard region for this class of problems the results show that hard problems occur at a critical value of the ratio of disjunctions to variables

on the asymptotic complexity of matrix multiplication the main results of this paper have the following flavor given one algorithm for multiplying matrices there exists another better algorithm a consequence of these results is that omega the exponent for matrix multiplication is a limit point that is it cannot be realized by any single algorithm we also use these results to construct a new algorithm which shows that omega 2 495548

effective solution of qualitative interval constraint problems abstract we present a fast algorithm for solving qualitative interval constraint problems which returns solutions of random problems in less than half a second on average with the hardest problem taking only half a minute on a risc workstation this is a surprising result considering the problem is np complete the fast solution time is attributed to the extraordinary pruning power of the path consistency computation and to the fact that all our randomly generated interval networks of size 14 were found to be inconsistent which is rapidly detected by a path consistency computation while inconsistency is relatively easy to prove our algorithm also solves large consistent networks with 100 edges we conclude that our algorithm suffices for solving qualitative interval constraint problems in practice other conclusions are that path consistency reduces the solution search to an almost linear selection of atomic labels and that path consistency is by itself an excellent consistency heuristic for random networks with fewer than 6 or more than 15 nodes