twisted dual group algebras equivariant deformations of c0 g abstract we consider a family of twisted fourier algebras a g of a locally compact group g which in the case of a abelian group g are the fourier transforms of the usual twisted group algebras of over cap g o the corresponding c algebras c g o are deformations of c 0 g which are equivariant in the sense that g still acts by left translation the main examples come from cocycles on the dual of an abelian subgroup h of g we prove that for such cocycles the twisted dual group algebras c g o are induced from the twisted group algebras c h o and we give detailed formulas for the multiplication on a g which extend to larger dense subalgebras of c 0 g and c b g we anticipate that these larger subalgebras will be useful for constructing deformations of homogeneous spaces c 0 g

the atiyah singer index theorem as passage to the classical limit in quantum mechanics a new approach to the atiyah singer index theorem is described using the technique of continuous fields ofc algebras the proof is given in the case of elliptic pseudodifferential operators on n

a gibbs sampler for learning dags we propose a gibbs sampler for structure learning in directed acyclic graph dag models the standard markov chain monte carlo algorithms used for learning dags are random walk metropolis hastings samplers these samplers are guaranteed to converge asymptotically but often mix slowly when exploring the large graph spaces that arise in structure learning in each step the sampler we propose draws entire sets of parents for multiple nodes from the appropriate conditional distribution this provides an efficient way to make large moves in graph space permitting faster mixing whilst retaining asymptotic guarantees of convergence the conditional distribution is related to variable selection with candidate parents playing the role of covariates or inputs we empirically examine the performance of the sampler using several simulated and real data examples the proposed method gives robust results in diverse settings outperforming several existing bayesian and frequentist methods in addition our empirical results shed some light on the relative merits of bayesian and constraint based methods for structure learning

constrained likelihood for reconstructing a directed acyclic gaussian graph directed acyclic graphs are widely used to describe directional pairwise relations such relations are estimated by reconstructing a directed acyclic graph s structure which is challenging when the ordering of nodes of the graph is unknown in such a situation existing methods such as the neighbourhood and search and score methods have high estimation errors or computational complexities especially when a local or sequential approach is used to enumerate edge directions by testing or optimizing a criterion locally as a local method may break down even for moderately sized graphs we propose a novel approach to simultaneously identifying all estimable directed edges and model parameters using constrained maximum likelihood with nonconvex constraints we develop a constraint reduction method that constructs a set of active constraints from super exponentially many constraints this coupled with an alternating direction method of multipliers and a difference convex method permits efficient computation for large graph learning we show that the proposed method consistently reconstructs identifiable directions of the true graph and achieves the optimal performance in terms of parameter estimation numerically the method compares favourably with competitors a protein network is analysed to demonstrate that the proposed method can make a difference in identifying the network s structure

large sample learning of bayesian networks is np hard in this paper we provide new complexity results for algorithms that learn discrete variable bayesian networks from data our results apply whenever the learning algorithm uses a scoring criterion that favors the simplest structure for which the model is able to represent the generative distribution exactly our results therefore hold whenever the learning algorithm uses a consistent scoring criterion and is applied to a sufficiently large dataset we show that identifying high scoring structures is np hard even when any combination of one or more of the following hold the generative distribution is perfect with respect to some dag containing hidden variables we are given an independence oracle we are given an inference oracle we are given an information oracle we restrict potential solutions to structures in which each node has at most k parents for all k 3 our proof relies on a new technical result that we establish in the appendices in particular we provide a method for constructing the local distributions in a bayesian network such that the resulting joint distribution is provably perfect with respect to the structure of the network

learning linear cyclic causal models with latent variables identifying cause effect relationships between variables of interest is a central problem in science given a set of experiments we describe a procedure that identifies linear models that may contain cycles and latent variables we provide a detailed description of the model family full proofs of the necessary and sufficient conditions for identifiability a search algorithm that is complete and a discussion of what can be done when the identifiability conditions are not satisfied the algorithm is comprehensively tested in simulations comparing it to competing algorithms in the literature furthermore we adapt the procedure to the problem of cellular network inference applying it to the biologically realistic data of the dreamchallenges the paper provides a full theoretical foundation for the causal discovery procedure first presented by eberhardt et al 2010 and hyttinen et al 2010

the generalized distributive law we discuss a general message passing algorithm which we call the generalized distributive law gdl the gdl is a synthesis of the work of many authors in information theory digital communications signal processing statistics and artificial intelligence it includes as special cases the baum welch algorithm the fast fourier transform fft on any finite abelian group the gallager tanner wiberg decoding algorithm viterbi s algorithm the bcjr algorithm pearl s belief propagation algorithm the shafer shenoy probability propagation algorithm and the turbo decoding algorithm although this algorithm is guaranteed to give exact answers only in certain cases the junction tree condition unfortunately not including the cases of gtw with cycles or turbo decoding there is much experimental evidence and a few theorems suggesting that it often works approximately even when it is not supposed to

multi domain sampling with applications to structural inference of bayesian networks when a posterior distribution has multiple modes unconditional expectations such as the posterior mean may not offer informative summaries of the distribution motivated by this problem we propose to decompose the sample space of a multimodal distribution into domains of attraction of local modes domain based representations are defined to summarize the probability masses of and conditional expectations on domains of attraction which are much more informative than the mean and other unconditional expectations a computational method the multi domain sampler is developed to construct domain based representations for an arbitrary multimodal distribution the multi domain sampler is applied to structural learning of protein signaling networks from high throughput single cell data where a signaling network is modeled as a causal bayesian network not only does our method provide a detailed landscape of the posterior distribution but also improves the accuracy and the predictive power of estimated net

equivariant deformations of homogeneous spaces abstract c algebraic deformations of homogeneous spaces g are constructed by completing dense subspaces of c 0 g in a different multiplication and c norm these deformations are equivariant in the sense that they still carry a natural action of g by left translation the motivating examples are the noncommutative heisenberg manifolds of rieffel but the construction given here is based on the authors twisted dual group algebras which are equivariant deformations of c 0 g the procedure is general enough to give other recently studied families of noncommutative spaces and some interesting new examples of simple c algebras

boundary maps for c crossed products with r with an application to the quantum hall effect the boundary map in k theory arising from the wiener hopf extension of a crossed product algebra with r is the connes thom isomorphism in this article the wiener hopf extension is combined with the heisenberg group algebra to provide an elementary construction of a corresponding map on higher traces and cyclic cohomol ogy it then follows directly from a non commutative stokes theorem that this map is dual w r t connes pairing of cyclic cohomology with k theory as an application we prove equality of quantized bulk and edge conductivities for the integer quantum hall effect described by continuous magnetic schrodinger operators 1 motivation and main result in a commonly used approach to study aperiodic solids particles in the bulk of the medium are described by covariant families of one particle schrodinger operators h whereis the probability space of configurations furnished with an ergodic action of space translations crossed product algebras provide a natural framework for such families be86 in particular their bounded functions are represented by elements of a c crossed product the so called bulk algebra the non commutative topology of the c algebra is a useful tool to construct topological invariants resulting from pairings between k group elements and higher traces some of these invariants may be physi cally interpreted as topologically quantised quantities the quantised hall conductivity is such an example the physics near a boundary of the solid can also be described by a c algebra the so called edge algebra the bulk algebra being essentially a crossed product of the edge algebra with r or with z in the tight binding approximation krs02 both algebras are tied together in the wiener hopf extension or respectively the toeplitz extension this extension gives rise to boundary maps between the k groups and the higher traces of the bulk and edge algebra which allow one to equate bulk and edge in variants this topological relation and its physical interpretations is our main objective we discuss one prominent physical example of this the quantum hall effect where the

jointly interventional and observational data estimation of interventional markov equivalence classes of directed acyclic graphs summary in many applications we have both observational and randomized interventional data we propose a gaussian likelihood framework for joint modelling of such different data types based on global parameters consisting of a directed acyclic graph and corresponding edge weights and error variances thanks to the global nature of the parameters maximum likelihood estimation is reasonable with only one or few data points per intervention we prove consistency of the bayesian information criterion for estimating the interventional markov equivalence class of directed acyclic graphs which is smaller than the observational analogue owing to increased partial identifiability from interventional data such an improvement in identifiability has immediate implications for tighter bounds for inferring causal effects besides methodology and theoretical derivations we present empirical results from real and simulated data

the two stage assembly scheduling problem complexity and approximation this paper introduces a new two stage assembly scheduling problem there are m machines at the first stage each of which produces a component of a job when all m components are available a single assembly machine at the second stage completes the job the objective is to schedule jobs on the machines so that the makespan is minimized we show that the search for an optimal solution may be restricted to permutation schedules the problem is proved to be np hard in the strong sense even when m 2 a schedule associated with an arbitrary permutation of jobs is shown to provide a worst case ratio bound of two and a heuristic with a worst case ratio bound of 2 1 m is presented the compact vector summation technique is applied for finding approximation solutions with worst case absolute performance guarantees

matricial quantum gromov hausdorff distance abstract we develop a matricial version of rieffel s gromov hausdorff distance for compact quantum metric spaces within the setting of operator systems and unital c algebras our approach yields a metric space of isometric unital complete order isomorphism classes of metrized operator systems which in many cases exhibits the same convergence properties as those in the quantum metric setting as for example in rieffel s approximation of the sphere by matrix algebras using berezin quantization within the metric subspace of metrized unital c algebras we establish the convergence of sequences which are cauchy with respect to a larger leibniz distance and we also prove an analogue of the precompactness theorems of gromov and rieffel

finding optimal bayesian network given a super structure classical approaches used to learn bayesian network structure from data have disadvantages in terms of complexity and lower accuracy of their results however a recent empirical study has shown that a hybrid algorithm improves sensitively accuracy and speed it learns a skeleton with an independency test it approach and constrains on the directed acyclic graphs dag considered during the search and score phase subsequently we theorize the structural constraint by introducing the concept of super structure s which is an undirected graph that restricts the search to networks whose skeleton is a subgraph of s we develop a super structure constrained optimal search cos its time complexity is upper bounded by o m n where m 2 depends on the maximal degree m of s empirically complexity depends on the average degree m and sparse structures allow larger graphs to be calculated our algorithm is faster than an optimal search by several orders and even finds more accurate results when given a sound super structure practically s can be approximated by it approaches significance level of the tests controls its sparseness enabling to control the trade off between speed and accuracy for incomplete super structures a greedily post processed version cos still enables to significantly outperform other heuristic searches

causal inference by using invariant prediction identification and confidence intervals summary what is the difference between a prediction that is made with a causal model and that with a non causal model suppose that we intervene on the predictor variables or change the whole environment the predictions from a causal model will in general work as well under interventions as for observational data in contrast predictions from a non causal model can potentially be very wrong if we actively intervene on variables here we propose to exploit this invariance of a prediction under a causal model for causal inference given different experimental settings e g various interventions we collect all models that do show invariance in their predictive accuracy across settings and interventions the causal model will be a member of this set of models with high probability this approach yields valid confidence intervals for the causal relationships in quite general scenarios we examine the example of structural equation models in more detail and provide sufficient assumptions under which the set of causal predictors becomes identifiable we further investigate robustness properties of our approach under model misspecification and discuss possible extensions the empirical properties are studied for various data sets including large scale gene perturbation experiments

learning causal bayesian network structures from experimental data we propose a method for the computational inference of directed acyclic graphical structures given data from experimental interventions order space markov chain monte carlo equi energy sampling importance weighting and stream based computation are combined to create a fast algorithm for learning causal bayesian network structures

systemes dynamiques non commutatifs et moyennabilite on introduit la notion de fonction de type positif relativement a un systeme dynamique c dont les proprietes sont analogues a celles des fonctions de type positif classiques on montre que dans le cas d un groupe discret g agissant sur une algebre de von neumann m la moyennabilite de l action est equivalente a l existence d une suite bornee de fonctions de type positif sur g a support fini a valeurs dans le centre z m de m qui converge vers 1 pour la topologie de la convergence simple ultrafaible

harmonic analysis approach to gromov hausdorff convergence for noncommutative tori we show that the rotation algebras are limits of matrix algebras in a very strong sense of convergence for algebras with additional lipschitz structure our results generalize to higher dimensional noncommutative tori and operator valued coefficients in contrast to previous results by rieffel li kerr and latremoliere we use lipschitz norms induced by the carre du champ of certain natural dynamical systems including the heat semigroup

on the k theory of twisted higher rank graph c algebras abstract we investigate the k theory of twisted higher rank graph algebras by adapting parts of elliott s computation of the k theory of the rotation algebras we show that each 2 cocycle on a higher rank graph taking values in an abelian group determines a continuous bundle of twisted higher rank graph algebras over the dual group we use this to show that for a circle valued 2 cocycle on a higher rank graph obtained by exponentiating a real valued cocycle the k theory of the twisted higher rank graph algebra coincides with that of the untwisted one

ideal parent structure learning for continuous variable bayesian networks bayesian networks in general and continuous variable networks in particular have become increasingly popular in recent years largely due to advances in methods that facilitate automatic learning from data yet despite these advances the key task of learning the structure of such models remains a computationally intensive procedure which limits most applications to parameter learning this problem is even more acute when learning networks in the presence of missing values or hidden variables a scenario that is part of many real life problems in this work we present a general method for speeding structure search for continuous variable networks with common parametric distributions we efficiently evaluate the approximate merit of candidate structure modifications and apply time consuming exact computations only to the most promising ones thereby achieving significant improvement in the running time of the search algorithm our method also naturally and efficiently facilitates the addition of useful new hidden variables into the network structure a task that is typically considered both conceptually difficult and computationally prohibitive we demonstrate our method on synthetic and real life data sets both for learning structure on fully and partially observable data and for introducing new hidden variables during structure search

efficient structure learning of bayesian networks using constraints this paper addresses the problem of learning bayesian network structures from data based on score functions that are decomposable it describes properties that strongly reduce the time and memory costs of many known methods without losing global optimality guarantees these properties are derived for different score criteria such as minimum description length or bayesian information criterion akaike information criterion and bayesian dirichlet criterion then a branch and bound algorithm is presented that integrates structural constraints with data in a way to guarantee global optimality as an example structural constraints are used to map the problem of structure learning in dynamic bayesian networks into a corresponding augmented bayesian network finally we show empirically the benefits of using the properties with state of the art methods and with the new algorithm which is able to handle larger data sets than before

quantum heisenberg manifolds as twisted groupoid c algebras abstract the quantum heisenberg manifolds are noncommutative manifolds constructed by m rieffel as strict deformation quantizations of heisenberg manifolds and have been studied by various authors rieffel constructed the quantum heisenberg manifolds as the generalized fixed point algebras of certain crossed product c algebras and they also can be realized as crossed products of c t 2 by hilbert c bimodules in the sense of abadie et al in this paper we describe how the quantum heisenberg manifolds can also be realized as twisted groupoid c algebras in the final section for a transformation groupoid x z with x compact and e p x a locally trivial principal g bundle where g is a compact abelian group we form a groupoid that is a locally trivial principal g bundle over x z which reduces to the twist groupoid of the second author when g t

sampling based approaches to calculating marginal densities abstract stochastic substitution the gibbs sampler and the sampling importance resampling algorithm can be viewed as three alternative sampling or monte carlo based approaches to the calculation of numerical estimates of marginal probability distributions the three approaches will be reviewed compared and contrasted in relation to various joint probability structures frequently encountered in applications in particular the relevance of the approaches to calculating bayesian posterior densities for a variety of structured models will be discussed and illustrated

metric aspects of noncommutative homogeneous spaces for a closed cocompact subgroup of a locally compact group g given a compact abelian subgroup k of g and a homomorphism k g satisfying certain conditions landstad and raeburn constructed equivariant noncommutative deformations c g of the homogeneous space g generalizing rieffel s construction of quantum heisenberg manifolds we show that when g is a lie group and g is connected given any norm on the lie algebra of g the seminorm on c g induced by the derivation map of the canonical g action defines a compact quantum metric furthermore it is shown that this compact quantum metric space depends on continuously with respect to quantum gromov hausdorff distances

continuous fields of c algebras coming from group cocycles and actions recently i have been attempting to formulate a suitable c algebraic framework for the subject of deformation quantization 3 19 continuous fields of c algebras provide one of the key elements for this framework the main examples of deformation quantizations which i have constructed up to now in this c algebra framework come from letting either cocycles on groups or actions of groups vary it has thus become necessary to show that one obtains in this way fields of c aigebras that are indeed continuous since this material is of a general nature and can be useful in other situations 4 6 11 13 it has seemed appropriate to give a separate exposition of it in the present article section 1 of this article contains a review of the published results on continuous fields which we will need as well as a discussion of the fact that the approach which we will take involves treating upper and lower semi continuity separately in sect 2 we discuss the continuity of fields of c algebras which arise from varying cocycles on groups while in sect 3 we do the same for actions which vary

yang mills connections on quantum heisenberg manifolds abstract we investigate critical points and minimizers of the yang mills functional ym on quantum heisenberg manifolds d c where the yang mills functional is defined on the set of all compatible linear connections on finitely generated projective modules over d c a compatible linear connection which is both a critical point and minimizer of ym is called a yang mills connection in this paper we investigate yang mills connections with constant curvature we are interested in yang mills connections on the following classes of modules over d c i abadie s module of trace 2 and its submodules ii modules of trace 2 iii tensor product modules of the form p e c where e c is morita equivalent to d c and p is a projection in e c we present a characterization of critical points and minimizers of ym and provide a class of new yang mills connections with constant curvature on over d c via concrete examples in particular we show that every yang mills connection on over d c with constant curvature should have a certain form of the curvature such as x y x z 0 and y z i id e also we show that these yang mills connections with constant curvature do not provide global minima but only local minima we do this by constructing a set of compatible connections that are not critical points but their values are smaller than those of yang mills connections with constant curvature our other results include i an example of a compatible linear connection with constant curvature on d c such that the corresponding connection on an isomorphic projective module does not have constant curvature and ii the construction of a compatible linear connection with constant curvature which neither attains its minimum nor is a critical point of ym on d c consequently the critical points and minimizers of ym depend crucially on the geometric structure of d c and of the projective modules over d c furthermore we construct the grassmannian connection on the projective modules with trace 2 over d c and compute its corresponding curvature finally we construct tensor product connections on p e c whose coupling constant is 2 and characterize the critical points of ym for this projective module

traces on noncommutative homogeneous spaces abstract we study properties of c algebraic deformations of homogeneous spaces g which are equivariant in the sense that they preserve the natural action of g by left translation the center is shown to be isomorphic to c g g 0 for a certain subgroup g 0 of g and there is a 1 1 correspondence between normalised traces and probability measures on g g 0 this makes it possible to represent the deformed algebra as operators over l 2 g applications to k theory are also mentioned

three stage flow shop scheduling with assembly operations to minimize the weighted sum of product completion times abstract a modified flow shop scheduling problem for a production system characterized by parts machining followed by their subsequent assembly joining operation is studied several products of different kinds are ordered each part for the products is processed on machine m 1 the first stage and then processed on machine m 2 the second stage each product is processed e g joined with the parts by one assembly operation on assembly stage m a the third stage the objective function to be minimized is the weighted sum of product completion times the decision variables are the sequence of products to be assembled and the sequence of parts to be processed in this paper we assume that if product h is assembled before product h then on each machine processing of any part for product h is done after processing of all parts for product h is completed we call this assumption assumption b 2 and call this problem sp constrained an efficient solution procedure using a branch and bound method is developed based on this assumption where johnson s algorithm is used as a part of the solution procedure computational experiments are provided to evaluate the performance of the solution procedure it has been found that the proposed solution procedure is effective to obtain an optimal or e optimal solution for larger scaled problems we further compare the optimal value for sp constrained with the optimal value for another problem sp unconstrained defined without assumption b 2 the optimal solution for sp unconstrained being significantly more difficult to obtain we offer three propositions to analyze some special cases in which the difference between the optimal value of sp constrained and the optimal value of sp unconstrained is zero for general cases we make some computational experiments to evaluate the difference between the optimal value of sp constrained and the optimal value of sp unconstrained it has been found that the difference is very small

controlling the false discovery rate of the association causality structure learned with the pc algorithm in real world applications graphical statistical models are not only a tool for operations such as classification or prediction but usually the network structures of the models themselves are also of great interest e g in modeling brain connectivity the false discovery rate fdr the expected ratio of falsely claimed connections to all those claimed is often a reasonable error rate criterion in these applications however current learning algorithms for graphical models have not been adequately adapted to the concerns of the fdr the traditional practice of controlling the type i error rate and the type ii error rate under a conventional level does not necessarily keep the fdr low especially in the case of sparse networks in this paper we propose embedding an fdr control procedure into the pc algorithm to curb the fdr of the skeleton of the learned graph we prove that the proposed method can control the fdr under a user specified level at the limit of large sample sizes in the cases of moderate sample size about several hundred empirical experiments show that the method is still able to control the fdr under the user specified level and a heuristic modification of the method is able to control the fdr more accurately around the user specified level the proposed method is applicable to any models for which statistical tests of conditional independence are available such as discrete models and gaussian models

order unit quantum gromov hausdorff distance we introduce a new distance distoq between compact quantum metric spaces we show that distoq is lipschitz equivalent to rieel s distance distq and give criteria for when a parameterized family of compact quantum metric spaces is continuous with respect to distoq as applications we show that the continuity of a parameterized family of quantum metric spaces induced by ergodic actions of a fixed compact group is determined by the multiplicities of the actions generalizing rieel s work on noncommutative tori and integral coadjoint orbits of semisimple compact connected lie groups we also show that the deformations of connes and landi are continuous in the parameter

optimal structure identification with greedy search in this paper we prove the so called meek conjecture in particular we show that if a dag h is an independence map of another dag g then there exists a finite sequence of edge additions and covered edge reversals in g such that 1 after each edge modification h remains an independence map of g and 2 after all modifications g h as shown by meek 1997 this result has an important consequence for bayesian approaches to learning bayesian networks from data in the limit of large sample size there exists a two phase greedy search algorithm that when applied to a particular sparsely connected search space provably identifies a perfect map of the generative distribution if that perfect map is a dag we provide a new implementation of the search space using equivalence classes as states for which all operators used in the greedy search can be scored efficiently using local functions of the nodes in the domain finally using both synthetic and real world datasets we demonstrate that the two phase greedy approach leads to good solutions when learning with finite sample sizes

a note on the two stage assembly flow shop scheduling problem with uniform parallel machines we study the problem of minimizing the makespan in a two stage assembly flow shop scheduling problem with uniform parallel machines this problem is a generalization of the assembly flow shop problem with concurrent operations in the first stage and a single assembly operation in the second stage we propose a heuristic with an absolute performance bound which becomes asymptotically optimal as the number of jobs becomes very large we show that our results slightly improve earlier results for the simpler assembly flow shop problem without uniform machines and for the two stage hybrid flow shop problem with uniform machines

some remarks on group bundles and c dynamical systems we introduce the notion of fibred action of a group bundle on a c x algebra by using such a notion a characterization in terms of induced c bundles is given for c dynamical systems such that the relative commutant of the fixed point c algebra is minimal i e it is generated by the centre of the given c algebra and the centre of the fixed point c algebra a class of examples in the setting of the cuntz algebra is given and connections with superselection structures with nontrivial centre are discussed

learning sparse causal gaussian networks with experimental intervention regularization and coordinate descent causal networks are graphically represented by directed acyclic graphs dags learning causal networks from data is a challenging problem due to the size of the space of dags the acyclicity constraint placed on the graphical structures and the presence of equivalence classes in this article we develop an l 1 penalized likelihood approach to estimate the structure of causal gaussian networks a blockwise coordinate descent algorithm which takes advantage of the acyclicity constraint is proposed for seeking a local maximizer of the penalized likelihood we establish that model selection consistency for causal gaussian networks can be achieved with the adaptive lasso penalty and sufficient experimental interventions simulation and real data examples are used to demonstrate the effectiveness of our method in particular our method shows satisfactory performance for dags with 200 nodes which have about 20 000 free parameters supplementary materials for this article are available online

equi energy sampler with applications in statistical inference and statistical mechanics we introduce a new sampling algorithm the equi energy sampler for efficient statistical sampling and estimation complementary to the widely used temperature domain methods the equi energy sampler utilizing the temperature energy duality targets the energy directly the focus on the energy function not only facilitates efficient sampling but also provides a powerful means for statistical estimation for example the calculation of the density of states and microcanonical averages in statistical mechanics the equi energy sampler is applied to a variety of problems including exponential regression in statistics motif sampling in computational biology and protein folding in biophysics we congratulate samuel kou qing zhou and wing wong referred to subsequently as kzw for this beautifully written paper which opens a new direction in monte carlo computation this discussion has two parts first we describe a very closely related method multicanonical sampling mcs and report a simulation example that compares the equi energy ee sampler with mcs overall we found the two algorithms to be of comparable efficiency for the simulation problem considered in the second part we develop some additional convergence results for the ee sampler novel sampling algorithms can significantly impact open questions in computational biology most notably the in silico protein folding problem by using computational methods protein folding aims to find the three dimensional structure of a protein chain given the sequence of its amino acid building blocks the complexity of the problem strongly depends on the protein representation and its energy function the more detailed the model the more complex its corresponding energy function and the more challenge it sets for sampling algorithms kou zhou and wong have introduced a novel sampling method which could contribute significantly to the field of structural prediction

lie group convolution algebras as deformation quantizations of linear poisson structures introduction let l be a finite dimensional lie algebra over the real numbers r and let l be its dual vector space it is well known 24 that the lie algebra structure on l defines a natural poisson structure on l in fact this was already known to lie 24 and these poisson structures are exactly what are now called the linear poisson structures given a manifold m equipped with a poisson structure one can seek deformation quantizations in the direction of as first studied in 3 these are loosely speaking one parameter families h ler of deformations of the pointwise multiplication on c m or an appropriate subalgebra such that

approximating a two machine flow shop scheduling under discrete scenario uncertainty abstract this paper deals with the two machine permutation flow shop problem with uncertain data whose deterministic counterpart is known to be polynomially solvable in this paper it is assumed that job processing times are uncertain and they are specified as a discrete scenario set for this uncertainty representation the min max and min max regret criteria are adopted the min max regret version of the problem is known to be weakly np hard even for two processing time scenarios in this paper it is shown that the min max and min max regret versions of the problem are strongly np hard even for two scenarios furthermore the min max version admits a polynomial time approximation scheme if the number of scenarios is constant and it is approximable with performance ratio of 2 and not 4 3 approximable for any 0 unless p np if the number of scenarios is a part of the input on the other hand the min max regret version is not at all approximable even for two scenarios

a vector sum theorem and its application to improving flow shop guarantees we prove that if a closed polygonal path in rd consists of a finite number of line segments of at most unit length then it is possible to transpose the segments in such a way that the new polygonal path is contained in a ball of radius frac 3 2 d using this result we give a near optimal algorithm for the np complete flow shop problem the error of the algorithm cannot exceed a constant depending on the maximal execution time and the number of machines but not depending on the number of jobs our theorems improve earlier results of the same type by belov and stolin

exact bayesian structure discovery in bayesian networks learning a bayesian network structure from data is a well motivated but computationally hard task we present an algorithm that computes the exact posterior probability of a subnetwork e g a directed edge a modified version of the algorithm finds one of the most probable network structures this algorithm runs in time o n 2n nk 1c m where n is the number of network variables k is a constant maximum in degree and c m is the cost of computing a single local marginal conditional likelihood for m data instances this is the first algorithm with less than super exponential complexity with respect to n exact computation allows us to tackle complex cases where existing monte carlo methods and local search procedures potentially fail we show that also in domains with a large number of variables exact computation is feasible given suitable a priori restrictions on the structures combining exact and inexact methods is also possible we demonstrate the applicability of the presented algorithm on four synthetic data sets with 17 22 37 and 100 variables

the flow shop problem with no idle constraints a review and approximation the makespan minimization problem in flow shops with no idle constraints on machines is considered the latter means that each machine once started must process all its operations without intermediate idle time until all those operations are completed the problem is known to be strongly np hard already for three machines while being based on a geometrical approach we propose several polynomial time heuristics for the general case and for special cases of 3 and 4 machines which provide asymptotically optimal solutions for the increasing number of jobs a comprehensive review of relevant results is also presented

probability inequalities for likelihood ratios and convergence rates of sieve mles let y 1 y n be independent identically distributed with density p 0 and let f be a space of densities we show that the supremum of the likelihood ratios i 1 n p y i p 0 y i where the supremum is over p f with p l 2 p 0 1 2 2 e is exponentially small with probability exponentially close to 1 the exponent is proportional to ne 2 the only condition required for this to hold is that e exceeds a value determined by the bracketing hellinger entropy of f a similar inequality also holds if we replace f by f n and p 0 by q n where q n is an approximation to p 0 in a suitable sense these results are applied to establish rates of convergence of sieve mles furthermore weak conditions are given under which the optimal rate e n defined by h e n f ne n 2 where h f is the hellinger entropy of f is nearly achievable by sieve estimators

a branch and bound algorithm for the two stage assembly scheduling problem this paper develops a branch and bound algorithm for the two stage assembly scheduling problem in this problem there are m machines at the first stage each of which produces a component of a job when all m components are available a single assembly machine at the second stage completes the job the objective is to schedule the jobs on the machines so that the maximum completion time or makespan is minimized a lower bound based on solving an artificial two machine flow shop problem is derived also several dominance theorems are established and incorporated into the branch and bound algorithm computational experience with the algorithm is reported for problems with up to 8000 jobs and 10 first stage machines

deformation quantization and the baum connes conjecture alternative titles of this paper would have been index theory without index or the baum connes conjecture without baum

on inclusion driven learning of bayesian networks two or more bayesian network structures are markov equivalent when the corresponding acyclic digraphs encode the same set of conditional independencies therefore the search space of bayesian network structures may be organized in equivalence classes where each of them represents a different set of conditional independencies the collection of sets of conditional independencies obeys a partial order the so called inclusion order this paper discusses in depth the role that the inclusion order plays in learning the structure of bayesian networks in particular this role involves the way a learning algorithm traverses the search space we introduce a condition for traversal operators the inclusion boundary condition which when it is satisfied guarantees that the search strategy can avoid local maxima this is proved under the assumptions that the data is sampled from a probability distribution which is faithful to an acyclic digraph and the length of the sample is unbounded the previous discussion leads to the design of a new traversal operator and two new learning algorithms in the context of heuristic search and the markov chain monte carlo method we carry out a set of experiments with synthetic and real world data that show empirically the benefit of striving for the inclusion order when learning bayesian networks from data

expansion of solution in terms of generalized eigenfunctions for a hyperbolic system with static boundary condition this paper studies a linear hyperbolic system with static boundary condition that was first studied in neves et al j funct anal 67 1986 320 344 it is shown that the spectrum of the system consists of zeros of a sine type function and the generalized eigenfunctions of the system constitute a riesz basis with parentheses for the root subspace the state space thereby decomposes into topological direct sum of root subspace and another invariant subspace in which the associated semigroup is superstable that is to say the semigroup is identical to zero after a finite time period

bnc pso structure learning is a very important problem in the field of bayesian networks bns it is also an active research area for more than 2 decades therefore many approaches have been proposed in order to find an optimal structure based on training samples in this paper a particle swarm optimization pso based algorithm is proposed to solve the bn structure learning problem named bnc pso bayesian network construction algorithm using pso edge inserting deleting is employed in the algorithm to make the particles have the ability to achieve the optimal solution while a cycle removing procedure is used to prevent the generation of invalid solutions then the theorem of markov chain is used to prove the global convergence of our proposed algorithm finally some experiments are designed to evaluate the performance of the proposed pso based algorithm experimental results indicate that bnc pso is worthy of being studied in the field of bns construction meanwhile it can significantly increase nearly 15 in the scoring metric values comparing with other optimization based algorithms

quantized gromov hausdorff distance abstract a quantized metric space is a matrix order unit space equipped with an operator space version of rieffel s lip norm we develop for quantized metric spaces an operator space version of quantum gromov hausdorff distance we show that two quantized metric spaces are completely isometric if and only if their quantized gromov hausdorff distance is zero we establish a completeness theorem as applications we show that a quantized metric space with 1 exact underlying matrix order unit space is a limit of matrix algebras with respect to quantized gromov hausdorff distance and that matrix algebras converge naturally to the sphere for quantized gromov hausdorff distance

geometric invariants of the quantum hall effect we study the two dimensional hall effect with a random potential the hall conductivity is identified as a geometric invariant associated with an algebra of observables using the pairing betweenk theory and cyclic cohomology theory we identify this geometric invariant with a topological index thereby giving the hall conductivity a new interpretation

approximation of quantum tori by finite quantum tori for the quantum gromov hausdorff distance we establish that given a compact abelian group g endowed with a continuous length function l and a sequence hn n n of closed subgroups of g converging to g for the hausdorff distance induced by l then c g is the quantum gromov hausdorff limit of any sequence c hn nn n for the natural quantum metric structures and when the lifts of n to g converge pointwise to this allows us in particular to approximate the quantum tori by finite dimensional c algebras for the quantum gromov hausdorff distance moreover we also establish that if the length function l is allowed to vary we can collapse quantum metric spaces to various quotient quantum metric spaces

optimal search on clustered structural constraint for learning bayesian network structure we study the problem of learning an optimal bayesian network in a constrained search space skeletons are compelled to be subgraphs of a given undirected graph called the super structure the previously derived constrained optimal search cos remains limited even for sparse super structures to extend its feasibility we propose to divide the super structure into several clusters and perform an optimal search on each of them further to ensure acyclicity we introduce the concept of ancestral constraints acs and derive an optimal algorithm satisfying a given set of acs finally we theoretically derive the necessary and sufficient sets of acs to be considered for finding an optimal constrained graph empirical evaluations demonstrate that our algorithm can learn optimal bayesian networks for some graphs containing several hundreds of vertices and even for super structures having a high average degree up to four which is a drastic improvement in feasibility over the previous optimal algorithm learnt networks are shown to largely outperform state of the art heuristic algorithms both in terms of score and structural hamming distance

concurrent flowshop scheduling to minimize makespan abstract this paper considers the concurrent flowshop scheduling problem with the makespan objective function in this problem each job consists of several components each of which is processed on a dedicated flowshop equivalently each component requires a series of consecutive operations in a prespecified order as in the standard serial flowshop we assume that each component has the same number of indexed operations and that these operations must be processed in the same order for each component we first show that this problem is strongly np hard and then using compact vector summation techniques we construct schedules using a quadratic time heuristic with an absolute performance guarantee independent of the number of jobs this makes our schedules asymptotically optimal as the number of jobs becomes very large

spectral continuity for aperiodic quantum systems i general theory abstract how does the spectrum of a schrodinger operator vary if the corresponding geometry and dynamics change is it possible to define approximations of the spectrum of such operators by defining approximations of the underlying structures in this work a positive answer is provided using the rather general setting of groupoid c algebras a characterization of the convergence of the spectra by the convergence of the underlying structures is proved in order to do so the concept of continuous field of groupoids is slightly extended by adding continuous fields of cocycles with this at hand magnetic schrodinger operators on dynamical systems or delone systems fall into this unified setting various approximations used in computational physics like the periodic or the finite cluster approximations are expressed through the tautological groupoid which provides a universal model for fields of groupoids the use of the hausdorff topology turns out to be fundamental in understanding why and how these approximations work

compact quantum metric spaces and ergodic actions of compact quantum groups we show that for any co amenable compact quantum group a c g there exists a unique compact hausdorff topology on the set ea g of isomorphism classes of ergodic actions of g such that the following holds for any continuous field of ergodic actions of g over a locally compact hausdorff space t the map t ea g sending each t in t to the isomorphism class of the fibre at t is continuous if and only if the function counting the multiplicity of in each fibre is continuous over t for every equivalence class of irreducible unitary representations of g generalizations for arbitrary compact quantum groups are also obtained in the case g is a compact group the restriction of this topology on the subset of isomorphism classes of ergodic actions of full multiplicity coincides with the topology coming from the work of landstad and wassermann podle spheres are shown to be continuous in the natural parameter as ergodic actions of the quantum su 2 group we also introduce a notion of regularity for quantum metrics on g and show how to construct a quantum metric from any ergodic action of g starting from a regular quantum metric on g furthermore we introduce a quantum gromov hausdorff distance between ergodic actions of g when g is separable and show that it induces the above topology

finding optimal bayesian networks using precedence constraints we consider the problem of finding a directed acyclic graph dag that optimizes a decomposable bayesian network score while in a favorable case an optimal dag can be found in polynomial time in the worst case the fastest known algorithms rely on dynamic programming across the node subsets taking time and space 2n to within a factor polynomial in the number of nodes n in practice these algorithms are feasible to networks of at most around 30 nodes mainly due to the large space requirement here we generalize the dynamic programming approach to enhance its feasibility in three dimensions first the user may trade space against time second the proposed algorithms easily and efficiently parallelize onto thousands of processors third the algorithms can exploit any prior knowledge about the precedence relation on the nodes underlying all these results is the key observation that given a partial order p on the nodes an optimal dag compatible with p can be found in time and space roughly proportional to the number of ideals of p which can be significantly less than 2n considering sufficiently many carefully chosen partial orders guarantees that a globally optimal dag will be found aside from the generic scheme we present and analyze concrete tradeoff schemes based on parallel bucket orders

model averaging for prediction with discrete bayesian networks in this paper we consider the problem of performing bayesian model averaging over a class of discrete bayesian network structures consistent with a partial ordering and with bounded in degree k we show that for n nodes this class contains in the worst case at least distinct network structures and yet model averaging over these structures can be performed using operations furthermore we show that there exists a single bayesian network that defines a joint distribution over the variables that is equivalent to model averaging over these structures although constructing this network is computationally prohibitive we show that it can be approximated by a tractable network allowing approximate model averaged probability calculations to be performed in o n time our result also leads to an exact and linear time solution to the problem of averaging over the 2n possible feature sets in a naive bayes model providing an exact bayesian solution to the troublesome feature selection problem for naive bayes classifiers we demonstrate the utility of these techniques in the context of supervised classification showing empirically that model averaging consistently beats other generative bayesian network based models even when the generating model is not guaranteed to be a member of the class being averaged over we characterize the performance over several parameters on simulated and real world data

noncommutative finite dimensional manifolds ii moduli space and structure of noncommutative 3 spheres this paper contains detailed proofs of our results on the moduli space and the structure of noncommutative 3 spheres we develop the notion of central quadratic form for quadratic algebras and a general theory which creates a bridge between noncommutative differential geometry and its purely algebraic counterpart it allows to construct a morphism from an involutive quadratic algebra to a c algebra constructed from the characteristic variety and the hermitian line bundle associated to the central quadratic form we apply the general theory in the case of noncommutative 3 spheres and show that the above morphism corresponds to a natural ramified covering by a noncommutative 3 dimensional nilmanifold we then compute the jacobian of the ramified covering and obtain the answer as the product of a period of an elliptic integral by a rational function we describe the real and complex moduli spaces of noncommutative 3 spheres relate the real one to root systems and the complex one to the orbits of a birational cubic automorphism of three dimensional projective space we classify the algebras and establish duality relations between them

on finding optimal polytrees we study the np hard problem of finding a directed acyclic graph dag on a given set of nodes so as to maximize a given scoring function the problem models the task of inferring a probabilistic network from data which has been studied extensively in the fields of artificial intelligence and machine learning several variants of the problem where the output dag is constrained in several ways are np hard as well for example when the dag is required to have bounded in degree or when it is required to be a polytree polynomial time algorithms are known only for rare special cases perhaps most notably for branchings that is polytrees in which the in degree of every node is at most one in this paper we generalize this polynomial time result to polytrees that can be turned into a branching by deleting a constant number of arcs our algorithm stems from a matroid intersection formulation as the order of the polynomial time bound depends on the number of deleted arcs the algorithm does not establish fixed parameter tractability when parameterized by that number we show that certain additional constraints on the sought polytree render the problem fixed parameter tractable we contrast this positive result by showing that if we parameterize by the number of deleted nodes a somewhat more powerful parameter the problem is not fixed parameter tractable subject to a complexity theoretic assumption

open block scheduling in optical communication networks in this paper the process of data transmission in star coupled optical communication networks is modelled as a shop type scheduling problem where channels wavelengths are treated as machines we formulate an open block problem with the minimum makespan objective o b cmax in which a relation of a new type between the operations of each job is introduced any two operations of a job have identical processing times and may be processed either simultaneously in a common block or alternatively at disjoint time intervals we show that the problem is polynomially solvable for 4 machines np hard for 6 machines and strongly np hard for a variable number of machines for the case of a variable number of machines we present a polynomial time 2 approximation algorithm and prove that there is no polynomial time approximation algorithm with 11 10 unless p np for the case when the number of machines is fixed we show that the problem admits a linear time ptas in addition we show that the two machine problem with release dates is np hard in the strong sense

partition mcmc for inference on acyclic digraphs abstractacyclic digraphs are the underlying representation of bayesian networks a widely used class of probabilistic graphical models learning the underlying graph from data is a way of gaining insights about the structural properties of a domain structure learning forms one of the inference challenges of statistical graphical models markov chain monte carlo mcmc methods notably structure mcmc to sample graphs from the posterior distribution given the data are probably the only viable option for bayesian model averaging score modularity and restrictions on the number of parents of each node allow the graphs to be grouped into larger collections which can be scored as a whole to improve the chain s convergence current examples of algorithms taking advantage of grouping are the biased order mcmc which acts on the alternative space of permuted triangular matrices and nonergodic edge reversal moves here we propose a novel algorithm which employs the underlying combinatorial structure of dags t

on the structure of twisted group c algebras we first give general structural results for the twisted group algebras c g of a locally compact group g with large abelian subgroups in particular we use a theorem of williams to realise c g as the sections of a c bundle whose fibres are twisted group algebras of smaller groups and then give criteria for the simplicity of these algebras next we use a device of rosenberg to show that when is a discrete subgroup of a solvable lie group g the k groups k c are isomorphic to certain twisted k groups k g of the homogeneous space g and we discuss how the twisting class h 3 g z depends on the cocycle

the three machine proportionate open shop and mixed shop minimum makespan problems abstract we first consider the ordinary np hard three machine proportionate open shop minimum makespan o 3 prpt c max problem and show that it is solvable in o n log n time when certain conditions on the total machine load are met when these conditions are not met we derive an approximate solution by implementing the optimal solution for the o 3 prpt c max problem when the two longest jobs are of equal length in that case both absolute and ratio worst case bounds are derived we also consider the more general mixed shop problem m 3 prpt c max in which a given job subset must be processed as in a flow shop while the remaining jobs can be processed as in the o 3 prpt c max problem we show that our open shop solution techniques can be implemented to derive exact and approximate solutions for the m 3 prpt c max problem finally we discuss the applicability of our open shop results to the proportionate open shop problem with unequal machine speeds

a branch and bound algorithm for a production scheduling problem in an assembly system under due date constraints abstract this paper focuses on a production scheduling problem in a tree structured assembly system operating on a make to order basis due dates are considered as constraints in the problem that is tardiness is not allowed the objective of the problem is to minimize holding costs of final product inventory as well as work in process inventory a mixed integer linear programming model is given and a branch and bound b b algorithm based on a lagrangian relaxation method is developed in the algorithm a subgradient method is used for obtaining good lower bounds of subproblems or partial solutions while a lagrangian heuristic is used for upper bounds results of computational experiments on randomly generated test problems showed that the b b algorithm found optimal solutions of problems of moderate sizes in a reasonable amount of computation time

the cancellation theorem for projective modules over irrational rotation c algebras on montre que deux modules projectifs sur a qui sont isomorphes de facon stable sont en fait isomorphes

structure discovery in bayesian networks by sampling partial orders we present methods based on metropolis coupled markov chain monte carlo mc3 and annealed importance sampling ais for estimating the posterior distribution of bayesian networks the methods draw samples from an appropriate distribution of partial orders on the nodes continued by sampling directed acyclic graphs dags conditionally on the sampled partial orders we show that the computations needed for the sampling algorithms are feasible as long as the encountered partial orders have relatively few down sets while the algorithms assume suitable modularity properties of the priors arbitrary priors can be handled by dividing the importance weight of each sampled dag by the number of topological sorts it has we give a practical dynamic programming algorithm to compute these numbers our empirical results demonstrate that the presented partial order based samplers are superior to previous markov chain monte carlo methods which sample dags either directly or via linear orders on the nodes the results also suggest that the convergence rate of the estimators based on ais are competitive to those of mc3 thus ais is the preferred method as it enables easier large scale parallelization and in addition supplies good probabilistic lower bound guarantees for the marginal likelihood of the model

objective bayesian search of gaussian directed acyclic graphical models for ordered variables with non local priors directed acyclic graphical dag models are increasingly employed in the study of physical and biological systems to model direct influences between variables identifying the graph from data is a challenging endeavor which can be more reasonably tackled if the variables are assumed to satisfy a given ordering in this case we simply have to estimate the presence or absence of each potential edge working under this assumption we propose an objective bayesian method for searching the space of gaussian dag models which provides a rich output from minimal input we base our analysis on non local parameter priors which are especially suited for learning sparse graphs because they allow a faster learning rate relative to ordinary local parameter priors when the true unknown sampling distribution belongs to a simple model we implement an efficient stochastic search algorithm which deals effectively with data sets having sample size smaller than the number of variables and apply our method to a variety of simulated and real data sets our approach compares favorably in terms of the roc curve for edge hit rate versus false alarm rate to current state of the art frequentist methods relying on the assumption of ordered variables under this assumption it exhibits a competitive advantage over the pc algorithm which can be considered as a frequentist benchmark for unordered variables importantly we find that our method is still at an advantage for learning the skeleton of the dag when the ordering of the variables is only moderately mis specified prospectively our method could be coupled with a strategy to learn the order of the variables thus dropping the known ordering assumption

improving structure mcmc for bayesian networks through markov blanket resampling algorithms for inferring the structure of bayesian networks from data have become an increasingly popular method for uncovering the direct and indirect influences among variables in complex systems a bayesian approach to structure learning uses posterior probabilities to quantify the strength with which the data and prior knowledge jointly support each possible graph feature existing markov chain monte carlo mcmc algorithms for estimating these posterior probabilities are slow in mixing and convergence especially for large networks we present a novel markov blanket resampling mbr scheme that intermittently reconstructs the markov blanket of nodes thus allowing the sampler to more effectively traverse low probability regions between local maxima as we can derive the complementary forward and backward directions of the mbr proposal distribution the metropolis hastings algorithm can be used to account for any asymmetries in these proposals experiments across a range of network sizes show that the mbr scheme outperforms other state of the art algorithms both in terms of learning performance and convergence rate in particular mbr achieves better learning performance than the other algorithms when the number of observations is relatively small and faster convergence when the number of variables in the network is large

deformation quantization of heisenberg manifolds form a smooth manifold equipped with a poisson bracket we formulate ac algebra framework for deformation quantization including the possibility of invariance under a lie group of diffeomorphisms preserving the poisson bracket we then show that the much studied non commutative tori give examples of such deformation quantizations invariant under the usual action of ordinary tori going beyond this the main results of the paper provide a construction of invariant deformation quantizations for those poisson brackets on heisenberg manifolds which are invariant under the action of the heisenberg lie group and for various generalizations suggested by this class of examples interesting examples are obtained of simplec algebras on which the heisenberg group acts ergodically

semiprojectivity with and without a group action abstract the equivariant version of semiprojectivity was recently introduced by the first named author we study properties of this notion in particular its relation to ordinary semiprojectivity of the crossed product and of the algebra itself we show that equivariant semiprojectivity is preserved when the action is restricted to a cocompact subgroup thus if a second countable compact group acts semiprojectively on a c algebra a then a must be semiprojective this fails for noncompact groups we construct a semiprojective action of z on a nonsemiprojective c algebra we also study equivariant projectivity and obtain analogous results however with fewer restrictions on the subgroup for example if a discrete group acts projectively on a c algebra a then a must be projective this is in contrast to the semiprojective case we show that the crossed product by a semiprojective action of a finite group on a unital c algebra is a semiprojective c algebra we give examples to show that this does not generalize to all compact groups

a new family of noncommutative 2 spheres abstract we give new examples of noncommutative manifolds in particular we construct a strong deformation of c s 2 consisting of a family of noncommutative 2 spheres and study their analytic and topological properties

rates of convergence of posterior distributions we compute the rate at which the posterior distribution concentrates around the true parameter value the spaces we work in are quite general and include infinite dimensional cases the rates are driven by two quantities the size of the space as measured by bracketing entropy and the degree to which the prior concentrates in a small ball around the true parameter we consider two examples

θ deformations as compact quantum metric spaces let m be a compact spin manifold with a smooth action of the n torus connes and landi constructed deformations m of m parameterized by n n real skew symmetric matrices the m s together with the canonical dirac operator d open image in new window on m are an isospectral deformation of m the dirac operator d defines a lipschitz seminorm on c m which defines a metric on the state space of c m we show that when m is connected this metric induces the weak topology this means that m is a compact quantum metric space in the sense of rieffel

vector summation in banach space and polynomial algorithms for flow shops and open shops we consider the flow shop and the open shop problems with m machines and n jobs m is the total processing time of the most loaded machine t is the maximum operation length two functions are defined m is the minimum number such that the optimum of any flow shop is at most m m t m is the minimum number for which the inequality m m t ensures that the optimum of the open shop is equal to m upper and lower bounds for functions m and m are derived and two polynomial algorithms are suggested the first one delivers an optimal schedule of an open shop provided m m t for some function m m the second one computes a near optimal approximation schedule of a flow shop both algorithms are based on a vector summation algorithm in m dimensional banach space