bayesian estimation of dirichlet mixture model with variational inference in statistical modeling parameter estimation is an essential and challengeable task estimation of the parameters in the dirichlet mixture model dmm is analytically intractable due to the integral expressions of the gamma function and its corresponding derivatives we introduce a bayesian estimation strategy to estimate the posterior distribution of the parameters in dmm by assuming the gamma distribution as the prior to each parameter we approximate both the prior and the posterior distribution of the parameters with a product of several mutually independent gamma distributions the extended factorized approximation method is applied to introduce a single lower bound to the variational objective function and an analytically tractable estimation solution is derived moreover there is only one function that is maximized during iterations and therefore the convergence of the proposed algorithm is theoretically guaranteed with synthesized data the proposed method shows the advantages over the em based method and the previously proposed bayesian estimation method with two important multimedia signal processing applications the good performance of the proposed bayesian estimation method is demonstrated

variational inference for watson mixture model this paper addresses modelling data using the watson distribution the watson distribution is one of the simplest distributions for analyzing axially symmetric data this distribution has gained some attention in recent years due to its modeling capability however its bayesian inference is fairly understudied due to difficulty in handling the normalization factor recent development of markov chain monte carlo mcmc sampling methods can be applied for this purpose however these methods can be prohibitively slow for practical applications a deterministic alternative is provided by variational methods that convert inference problems into optimization problems in this paper we present a variational inference for watson mixture models first the variational framework is used to side step the intractability arising from the coupling of latent states and parameters second the variational free energy is further lower bounded in order to avoid intractable moment computation the proposed approach provides a lower bound on the log marginal likelihood and retains distributional information over all parameters moreover we show that it can regulate its own complexity by pruning unnecessary mixture components while avoiding over fitting we discuss potential applications of the modeling with watson distributions in the problem of blind source separation and clustering gene expression data sets

one way permutations computational asymmetry and distortion abstract computational asymmetry i e the discrepancy between the complexity of transformations and the complexity of their inverses is at the core of one way transformations we introduce a computational asymmetry function that measures the amount of one wayness of permutations we also introduce the word length asymmetry function for groups which is an algebraic analogue of computational asymmetry we relate combinational circuits to words in a thompson monoid over a fixed generating set in such a way that circuit size is equal to word length moreover combinational circuits have a representation in terms of elements of a thompson group in such a way that circuit size is polynomially equivalent to word length we show that circuits built with gates that are not constrained to have fixed length inputs and outputs are at most quadratically more compact than circuits built from traditional gates with fixed length inputs and outputs finally we show that the computational asymmetry function is closely related to certain distortion functions the computational asymmetry function is polynomially equivalent to the distortion of the path length in schreier graphs of certain thompson groups compared to the path length in cayley graphs of certain thompson monoids we also show that the results of razborov and others on monotone circuit complexity lead to exponential lower bounds on certain distortions

the isomorphism conjecture fails relative to a random oracle berman and hartmanis 1977 conjectured that there is a polynomial time computable isomorphism between any two languages complete for np with respect to polynomial time computable many one karp reductions joseph and young 1985 gave a structural definition of a class of np complete sets the k creative sets and defined a class of sets the k f k s that are necessarily k creative they went on to conjecture that certain of these k f t s are not isomorphic to the standard np complete sets clearly the berman hartmanis and joseph young conjectures cannot both be correct we introduce a family of strong one way functions the scrambling functions if f is a scrambling function then k f k is not isomorphic to the standard np complete sets as joseph and young conjectured and the berman hartmanis conjecture fails indeed if scrambling functions exist then the isomorphism also fails at higher complexity classes such as exp and nexp as evidence for the existence of scrambling functions we show that much more powerful one way functions the annihilating functions exist relative to a random oracle random oracles are the first examples of oracles relative to which the isomorphism conjecture fails with respect to higher classes such as exp and nexp

survey of disjoint np pairs and relations to propositional proof systems we survey recent results on disjoint np pairs in particular we survey the relationship of disjoint np pairs to the theory of proof systems for propositional calculus

hard promise problems and nonuniform complexity for every recursive set a let pp a denote the following promise problem input x and y promise x a y a property x a we show that if l is a solution of pp a then a p l poly from this result it follows that if a is t p hard for np then all solutions of pp a are hard for np under a reduction that generalizes both t p and t sn specifically if a is np hard then all solutions of pp a are generalized high2 bbs86b the main theorem that leads to this result states that if b is a self reducible set b t p a and a p l poly then 2 p b 2 p l several interesting connections between uniform and nonuniform complexity follow directly from this theorem

classes of representable disjoint np pairs for a propositional proof system p we introduce the complexity class dnpp p of all disjoint np pairs for which the disjointness of the pair is efficiently provable in the proof system p we exhibit structural properties of proof systems which make canonical np pairs associated with these proof systems hard or complete for dnpp p moreover we demonstrate that non equivalent proof systems can have equivalent canonical pairs and that depending on the properties of the proof systems different scenarios for dnpp p and the reductions between the canonical pairs exist

variational inference for large scale models of discrete choice discrete choice models are commonly used by applied statisticians in numerous fields such as marketing economics finance and operations research when agents in discrete choice models are assumed to have differing preferences exact inference is often intractable markov chain monte carlo techniques make approximate inference possible but the computational cost is prohibitive on the large datasets now becoming routinely available variational methods provide a deterministic alternative for approximation of the posterior distribution we derive variational procedures for empirical bayes and fully bayesian inference in the mixed multinomial logit model of discrete choice the algorithms require only that we solve a sequence of unconstrained optimization problems which are shown to be convex one version of the procedures relies on a new approximation to the variational objective function based on the multivariate delta method extensive simulations along with an analysis of real world data demonstr

enumerative counting is hard abstract an n variable boolean formula may have anywhere from 0 to 2n satisfying assignments can a polynomial time machine given such a formula reduce this exponential number of possibilities to a small number of possibilities we call such a machine an enumerator and prove that if there is a good polynomial time enumerator for p i e one where for every boolean formula f the small set has at most o f 1 e numbers then p np p p and probabilistic polynomial time equals polynomial time furthermore we show that p polynomial time turing reduces to enumerating p

universal groups for point sets and tilings abstract we study the universal groups of inverse semigroups associated with point sets and with tilings we focus our attention on two classes of examples the first class consists of point sets which are obtained by a cut and projection scheme so called model sets here we introduce another inverse semigroup which is given in terms of the defining data of the projection scheme and related to the model set by the empire congruence the second class is given by one dimensional tilings

quasiperiodic tilings with tenfold symmetry and equivalence with respect to local derivability two 2d quasiperiodic tilings with generalized tenfold symmetry are derived from the lattice a4r the reciprocal of the root lattice a4 both tilings are built from four tiles triangles in one case rhombi and hexagons in the other after a brief description of the tilings and their structures the authors introduce the equivalence concept of mutual local derivability they present its key properties and its application to several tenfold tilings and discuss some implications on a future classification of tilings in position space

resource bounded immunity and simplicity revisiting the 30 years old notions of resource bounded immunity and simplicity we investigate the structural characteristics of various immunity notions strong immunity almost immunity and hyperimmunity as well as their corresponding simplicity notions we also study limited immunity and simplicity called k immunity and feasible k immunity and their simplicity notions finally we propose the k immune hypothesis as a working hypothesis that guarantees the existence of simple sets in np

separation of np completeness notions we use hypotheses of structural complexity theory to separate various np completeness notions in particular we introduce an hypothesis from which we describe a set in np that is mbox leq rm p rm t complete but not mbox leq rm p tt complete we provide fairly thorough analyses of the hypotheses that we introduce

nondeterministic functions and the existence of optimal proof systems we provide new characterizations of two previously studied questions on nondeterministic function classes q1 do nondeterministic functions admit efficient deterministic refinements q2 do nondeterministic function classes contain complete functions we show that q1 for the class npmv t is equivalent to the question whether the standard proof system for sat is p optimal and to the assumption that every optimal proof system is p optimal assuming only the existence of a p optimal proof system for sat we show that every set with an optimal proof system has a p optimal proof system under the latter assumption we also obtain a positive answer to q2 for the class npmv t an alternative view on nondeterministic functions is provided by disjoint sets and tuples we pursue this approach for disjoint np pairs and its generalizations to tuples of sets from np and conp with disjointness conditions of varying strength in this way we obtain new characterizations of q2 for the class npsv question q1 for npsv is equivalent to the question of whether every disjoint np pair is easy to separate in addition we characterize this problem by the question of whether every propositional proof system has the effective interpolation property again these interpolation properties are intimately connected to disjoint np pairs and we show how different interpolation properties can be modeled by np pairs associated with the underlying proof system

characterizing the existence of one way permutations we establish a condition necessary and sufficient for the existence of one way permutations one way permutations exist if and only if there exist total one one one way functions whose range is p rankable

enforcing and defying associativity commutativity totality and strong noninvertibility for worst case one way functions rabi and sherman m rabi a sherman an observation on associative one way functions in complexity theory information processing letters 64 5 1997 239 244 m rabi a sherman associative one way functions a new paradigm for secret key agreement and digital signatures tech rep cs tr 3183 umiacs tr 93 124 department of computer science university of maryland college park md 1993 proved that the hardness of factoring is a sufficient condition for there to exist one way functions i e p time computable honest p time noninvertible functions this paper is in the worst case model not the average case model that are total commutative and associative but not strongly noninvertible in this paper we improve the sufficient condition to p np more generally in this paper we completely characterize which types of one way functions stand or fall together with plain one way functions equivalently stand or fall together with p np we look at the four attributes used in rabi and sherman s seminal work on algebraic properties of one way functions see m rabi a sherman an observation on associative one way functions in complexity theory information processing letters 64 5 1997 239 244 m rabi a sherman associative one way functions a new paradigm for secret key agreement and digital signatures tech rep cs tr 3183 umiacs tr 93 124 department of computer science university of maryland college park md 1993 and subsequent papers strongness of noninvertibility totality commutativity and associativity and for each attribute we allow it to be required to hold required to fail or don t care in this categorization there are 3 4 81 potential types of one way functions we prove that each of these 81 feature laden types stands or falls together with the existence of plain one way functions

bayesian estimation of the von mises fisher mixture model with variational inference this paper addresses the bayesian estimation of the von mises fisher vmf mixture model with variational inference vi the learning task in vi consists of optimization of the variational posterior distribution however the exact solution by vi does not lead to an analytically tractable solution due to the evaluation of intractable moments involving functional forms of the bessel function in their arguments to derive a closed form solution we further lower bound the evidence lower bound where the bound is tight at one point in the parameter distribution while having the value of the bound guaranteed to increase during maximization we derive an analytically tractable approximation to the posterior distribution which has the same functional form as the assigned prior distribution the proposed algorithm requires no iterative numerical calculation in the re estimation procedure and it can potentially determine the model complexity and avoid the over fitting problem associated with conventional approaches based on the expectation maximization moreover we derive an analytically tractable approximation to the predictive density of the bayesian mixture model of vmf distributions the performance of the proposed approach is verified by experiments with both synthetic and real data

unambiguous computations and locally definable acceptance types abstract hertrampf s locally definable acceptance types show that many complexity classes can be defined in terms of polynomial time bounded ntms with simple local conditions on the nodes of its computation tree rather than global concepts like number of accepting paths etc we introduce a modification of hertrampf s locally definable acceptance types which allows to get a larger number of characterizable complexity classes among others the newly characterizable classes are up and mod z k p it is shown how different types of oracle access e g guarded access can be characterized by this model this sheds new light on the discussion on how to access unambiguous computation we present simple functions that describe precisely objects of current research as the unambiguous oracle alternation and promise hierarchies we exhibit the new class uap which seems to be an unambiguous analogue of wagner s p uap and thus p contains few and is currently the smallest class known with this property

complexity measures for public key cryptosystems a general theory of public key cryptography is developed that is based on the mathematical framework of complexity theory two related approaches are taken to the development of this theory and th

insights into multiple single lower bound approximation for extended variational inference in non gaussian structured data modeling for most of the non gaussian statistical models the data being modeled represent strongly structured properties such as scalar data with bounded support e g beta distribution vector data with unit length e g dirichlet distribution and vector data with positive elements e g generalized inverted dirichlet distribution in practical implementations of non gaussian statistical models it is infeasible to find an analytically tractable solution to estimating the posterior distributions of the parameters variational inference vi is a widely used framework in bayesian estimation recently an improved framework namely the extended vi evi has been introduced and applied successfully to a number of non gaussian statistical models evi derives analytically tractable solutions by introducing lower bound approximations to the variational objective function in this paper we compare two approximation strategies namely the multiple lower bounds mlbs approximation and the single lower bound slb approximation which can be applied to carry out the evi for implementation two different conditions the weak and the strong conditions are discussed convergence of the evi depends on the selection of the lower bound regardless of the choice of weak or strong condition we also discuss the convergence properties to clarify the differences between mlb and slb extensive comparisons are made based on some evi based non gaussian statistical models theoretical analysis is conducted to demonstrate the differences between the weak and strong conditions experimental results based on real data show advantages of the slb approximation over the mlb approximation

scd patterns have singular diffraction among the many families of nonperiodic tilings known so far scd tilings are still a bit mysterious here we determine the diffraction spectra of point sets derived from scd tilings and show that they have no absolutely continuous part that they have a uniformly discrete pure point part on the axis re3 and that they are otherwise supported on a set of concentric cylinder surfaces around this axis for scd tilings with additional properties more detailed results are given

quasi injective reductions abstract a reduction is said to be quasi injective if no element of the range is mapped to by infinitely many elements via two natural families of quasi injective reductions we study the connection between degree of injectivity and strength of reduction in particular we completely determine the relative strengths of polynomial time n to reductions and of polynomial time k to k reductions

if p np then some strongly noninvertible functions are invertible rabi rivest and sherman alter the standard notion of noninvertibility to a new notion they call strong noninvertibility and show via explicit cryptographic protocols for secret key agreement rabi and sherman attribute this protocol to rivest and sherman and digital signatures rabi and sherman that strongly noninvertible functions are very useful components in protocol design their definition of strong noninvertibility has a small twist respecting the argument given that is needed to ensure cryptographic usefulness in this paper we show that this small twist has a consequence unless p np some strongly noninvertible functions are invertible

projection of the danzer tiling we derive the icosahedrally symmetric octahedral tiling of danzer 1991 denoted by t d locally from the tiling t 2f of kramer et al 1989 obtained by icosahedral projection from the root lattice d6 moreover we determine all windows such that the tiling t d can be obtained by projection from the 6d root lattice d6 we reconstruct all vertex configurations of the tiling t d using the tools of the projection method

quasiperiodic icosahedral tilings from the six dimensional bcc lattice the cell geometry of the six dimensional bcc lattice is investigated via klotz construction two different classes of icosahedrally projected quasiperiodic tilings are defined for both cases we determine the acceptance domains of tiles and give a detailed description of the geometry of all tiles

diagonalization uniformity and fixed point theorems abstract we derive new fixed point theorems for subrecursive classes together with a theorem on the uniformity of certain reductions from a general formulation of the technique of delayed diagonalization this formulation extends the main theorem of u schoning theoret comput sci 18 1982 95 103 to cases which involve infinitely many diagonal classes c k and which allow each c k to contain uncountably many members the main technical work ties the familiar concept of a witness function directly to the often studied cantor set topology on languages and provides a delay construction which refines those due to schoning s breidtbart and d schmidt our a e fixed point theorems do not require that the programming system for the subrecursive class in question be well behaved we compare them to results which do the other theorem is similar to the uniform boundedness theorem of classical analysis and extends work of j grollmann and a selman

a dirichlet process mixture of generalized dirichlet distributions for proportional data modeling in this paper we propose a clustering algorithm based on both dirichlet processes and generalized dirichlet distribution which has been shown to be very flexible for proportional data modeling our approach can be viewed as an extension of the finite generalized dirichlet mixture model to the infinite case the extension is based on nonparametric bayesian analysis this clustering algorithm does not require the specification of the number of mixture components to be given in advance and estimates it in a principled manner our approach is bayesian and relies on the estimation of the posterior distribution of clusterings using gibbs sampler through some applications involving real data classification and image databases categorization using visual words we show that clustering via infinite mixture models offers a more powerful and robust performance than classic finite mixtures

on polynomial time turing and many one completeness in pspace meyer and paterson 1979 investigated pm reducibility of pspace complete sets to sparse sets we point out that their observation indicates the difference between the powers of pt and pm reducibilities and establish a machinery that uses this difference for separating pt completeness from pm completeness in pspace by using this machinery we show the difference between pt and pm completeness notions in pspace from each of the following assumptions i a randomized completeness notion differs from a deterministic one in pspace and ii pspace has a dense set almost every element of which is hard to produce by any polynomial time computation

canonical disjoint np pairs of propositional proof systems we prove that every disjoint np pair is polynomial time many one equivalent to the canonical disjoint np pair of some propositional proof system therefore the degree structure of the class of disjoint np pairs and of all canonical pairs is identical we show that this degree structure is not superficial assuming there exist p inseparable disjoint np pairs every countable distributive lattice can be embedded into every interval of polynomial np degrees of disjoint pairs by maps that preserve the least and greatest element respectively as one consequence of this embedding under the same assumption there exist intermediate disjoint np pairs that is if a b is a p separable disjoint np pair and c d is a p inseparable disjoint np pair then there exist p inseparable incomparable np pairs e f and g h whose degrees lie strictly between a b and c d furthermore between any two disjoint np pairs that are comparable and inequivalent such a diamond exists

reductions between disjoint np pairs disjoint np pairs are pairs a b of nonempty disjoint sets in np we prove that all of the following assertions are equivalent there is a many one complete disjoint np pair there is a strongly many one complete disjoint np pair there is a turing complete disjoint np pair such that all reductions are smart reductions there is a complete disjoint np pair for one to one invertible reductions the class of all disjoint np pairs is uniformly enumerable let a b c and d be nonempty sets belonging to np a smart reduction between the disjoint np pairs a b and c d is a turing reduction with the additional property that if the input belongs to a b then all queries belong to c d we prove under the reasonable assumption that up co up has a p bi immune set that there exist disjoint np pairs a b and c d such that a b is truth table reducible to c d but there is no smart reduction between them this paper contains several additional separations of reductions between disjoint np pairs we exhibit an oracle relative to which distnp has a truth table complete disjoint np pair but has no many one complete disjoint np pair

superquasicrystals self similar ordered structures with non crystallographic point symmetries we present a systematic method of constructing limit quasiperiodic structures with non crystallographic point symmetries such structures are different aperiodic ordered structures from quasicrystals and we call them superquasicrystals they are sections of higher dimensional limit periodic structures constructed on super bravais lattices we enumerate important super bravais lattices superquasicrystals with strong self similarities form an important subclass the simplest example is a two dimensional octagonal superquasicrystal

deformed graph laplacian for semisupervised learning graph laplacian has been widely exploited in traditional graph based semisupervised learning ssl algorithms to regulate the labels of examples that vary smoothly on the graph although it achieves a promising performance in both transductive and inductive learning it is not effective for handling ambiguous examples shown in fig 1 this paper introduces deformed graph laplacian dgl and presents label prediction via dgl lpdgl for ssl the local smoothness term used in lpdgl which regularizes examples and their neighbors locally is able to improve classification accuracy by properly dealing with ambiguous examples theoretical studies reveal that lpdgl obtains the globally optimal decision function and the free parameters are easy to tune the generalization bound is derived based on the robustness analysis experiments on a variety of real world data sets demonstrate that lpdgl achieves top level performance on both transductive and inductive settings by comparing it with popular ssl algorithms such as harmonic functions anchorgraph regularization linear neighborhood propagation laplacian regularized least square and laplacian support vector machine

a hierarchy based on output multiplicity abstract the class np k v consists of those partial multivalued functions that can be computed by a nondeterministic polynomial time bounded transducer that has at most k distinct values on any input we define the output multiplicity hierarchy to consist of the collection of classes np k v for all positive integers k 1 in this paper we investigate the strictness of the output multiplicity hierarchy and establish three main results pertaining to this 1 1 if for any k 1 the class np k v collapses into the class np k 1 v then the polynomial hierarchy collapses to 2 p 2 2 if the converse of the above result is true then any proof of this converse cannot relativize we exhibit an oracle relative to which the polynomial hierarchy collapses to p np but the output multiplicity hierarchy is strict 3 3 relative to a random oracle the output multiplicity hierarchy is strict this result is in contrast to the still open problem of the strictness of the polynomial hierarchy relative to a random oracle in introducing the technique for the third result we prove a related result of interest relative to a random oracle up np

variational learning for finite dirichlet mixture models and applications in this paper we focus on the variational learning of finite dirichlet mixture models compared to other algorithms that are commonly used for mixture models such as expectation maximization our approach has several advantages first the problem of over fitting is prevented furthermore the complexity of the mixture model i e the number of components can be determined automatically and simultaneously with the parameters estimation as part of the bayesian inference procedure finally since the whole inference process is analytically tractable with closed form solutions it may scale well to large applications both synthetic and real data generated from real life challenging applications namely image databases categorization and anomaly intrusion detection are experimented to verify the effectiveness of the proposed approach

bayesian estimation of beta mixture models with variational inference bayesian estimation of the parameters in beta mixture models bmm is analytically intractable the numerical solutions to simulate the posterior distribution are available but incur high computational cost in this paper we introduce an approximation to the prior posterior distribution of the parameters in the beta distribution and propose an analytically tractable closed form bayesian approach to the parameter estimation the approach is based on the variational inference vi framework following the principles of the vi framework and utilizing the relative convexity bound the extended factorized approximation method is applied to approximate the distribution of the parameters in bmm in a fully bayesian model where all of the parameters of the bmm are considered as variables and assigned proper distributions our approach can asymptotically find the optimal estimate of the parameters posterior distribution also the model complexity can be determined based on the data the closed form solution is proposed so that no iterative numerical calculation is required meanwhile our approach avoids the drawback of overfitting in the conventional expectation maximization algorithm the good performance of this approach is verified by experiments with both synthetic and real data

fick s law assisted propagation for semisupervised learning how to propagate the label information from labeled examples to unlabeled examples is a critical problem for graph based semisupervised learning many label propagation algorithms have been developed in recent years and have obtained promising performance on various applications however the eigenvalues of iteration matrices in these algorithms are usually distributed irregularly which slow down the convergence rate and impair the learning performance this paper proposes a novel label propagation method called fick s law assisted propagation flap unlike the existing algorithms that are directly derived from statistical learning flap is deduced on the basis of the theory of fick s first law of diffusion which is widely known as the fundamental theory in fluid spreading we prove that flap will converge with linear rate and show that flap makes eigenvalues of the iteration matrix distributed regularly comprehensive experimental evaluations on synthetic and practical datasets reveal that flap obtains encouraging results in terms of both accuracy and efficiency

variational bayesian matrix factorization for bounded support data a novel bayesian matrix factorization method for bounded support data is presented each entry in the observation matrix is assumed to be beta distributed as the beta distribution has two parameters two parameter matrices can be obtained which matrices contain only nonnegative values in order to provide low rank matrix factorization the nonnegative matrix factorization nmf technique is applied furthermore each entry in the factorized matrices i e the basis and excitation matrices is assigned with gamma prior therefore we name this method as beta gamma nmf bg nmf due to the integral expression of the gamma function estimation of the posterior distribution in the bg nmf model can not be presented by an analytically tractable solution with the variational inference framework and the relative convexity property of the log inverse beta function we propose a new lower bound to approximate the objective function with this new lower bound we derive an analytically tractable solution to approximately calculate the posterior distributions each of the approximated posterior distributions is also gamma distributed which retains the conjugacy of the bayesian estimation in addition a sparse bg nmf can be obtained by including a sparseness constraint to the gamma prior evaluations with synthetic data and real life data demonstrate the good performance of the proposed method

quaternion michelson descriptor for color image classification in this paper we develop a simple yet powerful framework called quaternion michelson descriptor qmd to extract local features for color image classification unlike traditional local descriptors extracted directly from the original raw image space qmd is derived from the michelson contrast law and the quaternionic representation qr of color images the michelson contrast is a stable measurement of image contents from the viewpoint of human perception while qr is able to handle all the color information of the image holisticly and to preserve the interactions among different color channels in this way qmd integrates both the merits of michelson contrast and qr based on the qmd framework we further propose two novel quaternionic michelson contrast binary pattern descriptors from different perspectives experiments and comparisons on different color image classification databases demonstrate that the proposed framework and descriptors outperform several state of the art methods

a second step towards complexity theoretic analogs of rice s theorem abstract rice s theorem states that every nontrivial language property of the recursively enumerable sets is undecidable borchert and stephan 1997 initiated the search for complexity theoretic analogs of rice s theorem in particular they proved that every nontrivial counting property of circuits is up hard and that a number of closely related problems are spp hard the present paper studies whether their up hardness result itself can be improved to spp hardness we show that their up hardness result cannot be strengthened to spp hardness unless unlikely complexity class containments hold nonetheless we prove that every p constructibly bi infinite counting property of circuits is spp hard we also raise their general lower bound from unambiguous nondeterminism to constant ambiguity nondeterminism

the shrinking property for np and conp we study the shrinking and separation properties two notions well known in descriptive set theory for np and conp and show that under reasonable complexity theoretic assumptions both properties do not hold for np and the shrinking property does not hold for conp in particular we obtain the following results 1 np and conp do not have the shrinking property unless ph is finite in general s n p and p n p do not have the shrinking property unless ph is finite this solves an open question posed by selivanov 1994 33 2 the separation property does not hold for np unless email protected conp 3 the shrinking property does not hold for np unless there exist np hard disjoint np pairs existence of such pairs would contradict a conjecture of even et al 1984 6 4 the shrinking property does not hold for np unless there exist complete disjoint np pairs moreover we prove that the assumption np conp is too weak to refute the shrinking property for np in a relativizable way for this we construct an oracle relative to which email protected conp np conp and np has the shrinking property this solves an open question posed by blass and gurevich 1984 3 who explicitly ask for such an oracle

structural transformations in quasicrystals induced by higher dimensional lattice transitions we study the structural transformations induced via the cut and project method in quasicrystals and tilings by lattice transitions in higher dimensions with a focus on transition paths preserving at least some symmetry in intermediate lattices we discuss the effect of such transformations on planar aperiodic penrose tilings and on three dimensional aperiodic ammann tilings with icosahedral symmetry we find that locally the transformations in the aperiodic structures occur through the mechanisms of tile splitting tile flipping and tile merger and we investigate the origin of these local transformation mechanisms within the projection framework

a general method to construct oracles realizing given relationships between complexity classes we present a method to prove oracle results of the following type let k 1 ldots k 2n and l 1 ldots l 2m be complexity classes our method provides a general framework for constructing an oracle a such that k a 2i 1 neq k a 2i for i 1 ldots n and l a 2j 1 l a 2j for j 1 ldots m using that method we prove several results of this kind the hardest of them is the existence of an oracle a such that p a neq np a p a bpp a and both conp a sets and np a sets are p a separable we exhibit also two theorems that cannot be proved by that method

unambiguous computation boolean hierarchies and sparse turing complete sets this paper studies for up two topics that have been intensely studied for np boolean hierarchies and the consequences of the existence of sparse turing complete sets unfortunately as is often the case the results for np draw on special properties of np that do not seem to carry over straightforwardly to up for example it is known for np and more generally for any class containing sigma and emptyset and closed under union and intersection that the symmetric difference hierarchy the boolean hierarchy and the boolean closure all are equal we prove that closure under union is not needed for this claim for any class cal k that contains sigma and emptyset and is closed under intersection e g up us and fewp the symmetric difference hierarchy over cal k the boolean hierarchy over cal k and the boolean closure of cal k all are equal on the other hand we show that two hierarchies the hausdorff hierarchy and the nested difference hierarchy which in the np case are equal to the boolean closure fail to be equal for the up case in some relativized worlds regarding sparse turing complete sets for up we prove that if up has sparse turing complete sets then the levels of the unambiguous polynomial hierarchy are simpler than one would otherwise expect they collapse one level in terms of their location in the promise unambiguous polynomial hierarchy we obtain related results under the weaker assumption that up has sparse turing hard sets

inverting onto functions we look at the hypothesis that all honest onto polynomial time computable functions have a polynomial time computable inverse we show this hypothesis equivalent to several other complexity conjectures including in polynomial time one can find accepting paths of nondeterministic polynomial time turing machines that accept every total multivalued nondeterministic function has a polynomial time computable refinement in polynomial time one can compute satisfying assignments for any polynomial time computable set of satisfiable formulae in polynomial time one can convert the accepting computations of any nondeterministic turing machine that accepts sat to satisfying assignments we compare these hypotheses with several other important complexity statements we also examine the complexity of these statements where we only require a single bit instead of the entire inverse

generalised 2d penrose tilings structural properties usual penrose tilings are defined by a set of five phases gamma j which add up to an integer the authors study the general case where the phases add up to any number and show that these generalised tilings can be obtained with four tiles two thick rhombi and two thin rhombi with different colourings of the edges the consideration of generalised tilings is relevant for the study of phase distortions local structural transitions and therefore various defects of the usual things

count data modeling and classification using finite mixtures of distributions in this paper we consider the problem of constructing accurate and flexible statistical representations for count data which we often confront in many areas such as data mining computer vision and information retrieval in particular we analyze and compare several generative approaches widely used for count data clustering namely multinomial multinomial dirichlet and multinomial generalized dirichlet mixture models moreover we propose a clustering approach via a mixture model based on a composition of the liouville family of distributions from which we select the beta liouville distribution and the multinomial the novel proposed model which we call multinomial beta liouville mixture is optimized by deterministic annealing expectation maximization and minimum description length and strives to achieve a high accuracy of count data clustering and model selection an important feature of the multinomial beta liouville mixture is that it has fewer parameters than the recently proposed multinomial generalized dirichlet mixture the performance evaluation is conducted through a set of extensive empirical experiments which concern text and image texture modeling and classification and shape modeling and highlights the merits of the proposed models and approaches

automating resolution is np hard we show that the problem of finding a resolution refutation that is at most polynomially longer than a shortest one is np hard in the parlance of proof complexity resolution is not automatable unless p np indeed we show that it is np hard to distinguish between formulas that have resolution refutations of polynomial length and those that do not have subexponential length refutations this also implies that resolution is not automatable in subexponential time or quasi polynomial time unless np is included in subexp or qp respectively

an oracle builder s toolkit we show how to use various notions of genericity as tools in oracle creation in particular 1 we give an abstract definition of genericity that encompasses a large collection of different generic notions 2 we consider a new complexity class awpp which contains bqp quantum polynomial time and infer several strong collapses relative to sp generics 3 we show that under additional assumptions these collapses also occur relative to cohen generics 4 we show that relative to sp generics ulin co ulin dtime n k for any k where ulin is unambiguous linear time despite the fact that up np co np p relative to these generics 5 we show that there is an oracle relative to which np 1 co np 1 np co np poly and 6 we use a specialized notion of genericity to create an oracle relative to which np bpp ma

the complexity of computing the size of an interval given a p order a over a universe of strings i e a transitive reflexive antisymmetric relation such that if x y in a then x is polynomially bounded by y an interval size function of a returns for each string x in the universe the number of strings in the interval between strings b x and t x with respect to a where b x and t x are functions that are polynomial time computable in the length of x by choosing sets of interval size functions based on feasibility requirements for their underlying p orders we obtain new characterizations of complexity classes we prove that the set of all interval size functions whose underlying p orders are polynomial time decidable is exactly mp we show that the interval size functions for orders with polynomial time adjacency checks are closely related to the class fpspace poly indeed fpspace poly is exactly the class of all nonnegative functions that are an interval size function minus a polynomial time computable function we study two important functions in relation to interval size functions the function mdiv maps each natural number n to the number of nontrivial divisors of n we show that mdiv is an interval size function of a polynomial time decidable partial p order with polynomial time adjacency checks the function mmonsat maps each monotone boolean formula f to the number of satisfying assignments of f we show that mmonsat is an interval size function of a polynomial time decidable total p order with polynomial time adjacency checks finally we explore the related notion of cluster computation

self similar quasilattices with windows having fractal boundaries the point inflation rule is presented as a powerful scheme to produce a self similar quasilattice with a non crystallographic point symmetry alternatively the conjugate point inflation rule which is a set map acting on the internal space has the unique fixed point which is a compact set w and the quasilattice ql is obtained with the projection method by taking w as the window the fixed point w is the attractor of the set map if w is topologically a disc a ball for a three dimensional case its boundary is usually fractal we investigate conditions for the boundary of the window to be a von koch curve a practical method of constructing windows and the relevant qls is presented a lot of windows with fractal boundaries are determined on the basis of this method we introduce isomerism which has priority of rank to the mutual local derivability as a classification scheme for self similar qls it is argued that the pir and isomerism can be the key points of classification of self similar qls

an oracle separating conjectures about incompleteness in the finite domain abstract pudlak 19 lists several major complexity theoretic conjectures relevant to proof complexity and asks for oracles that separate pairs of corresponding relativized conjectures among these conjectures are disjnp the class of all disjoint np pairs does not have many one complete problems sat np does not contain many one complete sets that have p optimal proof systems up up does not have many one complete problems np conp np conp does not have many one complete problems as one answer to this question we construct an oracle relative to which among others disjnp sat up and np conp hold hence there is no relativizable proof for the implication disjnp up np conp sat in particular regarding the conjectures by pudlak this extends a result by khaniki 11

on the linearity of bayesian interpolators for non gaussian continuous time ar 1 processes bayesian estimation problems involving gaussian distributions often result in linear estimation techniques nevertheless there are no general statements as to whether the linearity of the bayesian estimator is restricted to the gaussian case the two common strategies for non gaussian models are either finding the best linear estimator or numerically evaluating the bayesian estimator by monte carlo methods in this paper we focus on bayesian interpolation of non gaussian first order autoregressive ar processes where the driving innovation can admit any symmetric infinitely divisible distribution characterized by the levy khintchine representation theorem we redefine the bayesian estimation problem in the fourier domain with the help of characteristic forms by providing analytic expressions we show that the optimal interpolator is linear for all symmetric stable distributions the bayesian interpolator can be expressed in a convolutive form where the kernel is described in terms of exponential splines we also show that the limiting case of levy type ar 1 processes the system of which has a pole at the origin always corresponds to a linear bayesian interpolator made of a piecewise linear spline irrespective of the innovation distribution finally we show the two mentioned cases to be the only ones within the family for which the bayesian interpolator is linear

matching rules and growth rules for pentagonal quasicrystal tilings preuve de l existence de ces regles pour un ensemble infini de pavages pentagonaux 2d autres que le pavage de peurose

conjugacies for tiling dynamical systems we consider tiling dynamical systems and topological conjugacies between them we prove that the criterion of being of finite type is invariant under topological conjugacy for substitution tiling systems under rather general conditions including the penrose and pinwheel systems we show that substitutions are invertible and that conjugacies are generalized sliding block codes

one way functions and the nonisomorphism of np complete sets abstract the one way conjecture states that the existence of nonisomorphic np complete sets implies the existence of one way functions this paper gives a relativized counterexample to the conjecture by constructing a relativized world that has nonisomorphic np complete sets but lacks one way functions

dualisation of voronoi domains and klotz construction a general method for the generation of proper space fillings the authors present a general method for the generation of proper space fillings of euclidean spaces with convex polytopes by projection from higher dimensional spaces as a special case quasiperiodic tilings are obtained by the projection of periodic structures the concept is general enough for the treatment of defects in quasiperiodic tilings by placing defects in high dimensional translation lattices

canonical substitutions tilings of ammann beenker type we present a large class of parallelogram tilings that have two important features in common with the ammann beenker tiling they can be constructed by canonical projection from z4 r4 to a plane and they admit substitution rules