random constraint satisfaction easy generation of hard satisfiable instances in this paper we show that the models of random csp instances proposed by xu and li k xu w li exact phase transitions in random constraint satisfaction problems journal of artificial intelligence research 12 2000 93 103 k xu w li many hard examples in exact phase transitions with application to generating hard satisfiable instances technical report corr report cs cc 0302001 revised version in theoretical computer science 355 2006 291 302 are of theoretical and practical interest indeed these models called rb and rd present several nice features first it is quite easy to generate random instances of any arity since no particular structure has to be integrated or property enforced in such instances then the existence of an asymptotic phase transition can be guaranteed while applying a limited restriction on domain size and on constraint tightness in that case a threshold point can be precisely located and all instances have the guarantee to be hard at the threshold i e to have an exponential tree resolution complexity next a formal analysis shows that it is possible to generate forced satisfiable instances whose hardness is similar to unforced satisfiable ones this analysis is supported by some representative results taken from an intensive experimentation that we have carried out using complete and incomplete search methods

a general model and thresholds for random constraint satisfaction problems in this paper we study the relation among the parameters in their most general setting that define a large class of random csp models d k csp where d is the domain size and k is the length of the constraint scopes the model d k csp unifies several related models such as the model rb and the model k csp we prove that the model d k csp exhibits exact phase transitions if klnd increases no slower than the logarithm of the number of variables a series of experimental studies with interesting observations are carried out to illustrate the solubility phase transition and the hardness of instances around phase transitions

on the order of borel subgroups of group amalgams and an application to locally transitive graphs abstract a permutation group is called semiprimitive if each of its normal subgroups is either transitive or semiregular given nontrivial finite transitive permutation groups l 1 and l 2 with l 1 not semiprimitive we construct an infinite family of rank two amalgams of permutation type l 1 l 2 and borel subgroups of strictly increasing order as an application we show that there is no bound on the order of edge stabilisers in locally l 1 l 2 graphs we also consider the corresponding question for amalgams of rank k 3 we completely resolve this by showing that the order of the borel subgroup is bounded by the permutation type l 1 l k only in the trivial case where each of l 1 l k is regular

finite permutation groups with a transitive minimal normal subgroup a finite permutation group is said to be innately transitive if it contains a transitive minimal normal subgroup in this paper we give a characterisation and structure theorem for the finite innately transitive groups as well as describing those innately transitive groups which preserve a product decomposition the class of innately transitive groups contains all primitive and quasiprimitive groups

efficient computation of the discrete pseudo wigner distribution a description is given of a novel algorithm the fast fourier transform in part fftp for the computation of the discrete pseudo wigner distribution dpwd the fftp computes the cosine and sine parts of the discrete fourier transform dft separately by employing real inverse sinusoidal twiddle factors unlike the conventional methods which directly utilize the complex dft the fftp yields real output since the dpwd is always real in addition the new method reduces the computational cost by making full use of symmetries and removing redundancies in the fftp computation the authors also describe a simple algorithm for computing the discrete hilbert transform dht to produce the nonaliased dpwd a pipeline structure for real time and a bulk processing technique for offline implementations of the method are presented

combinatorial sharpness criterion and phase transition classification for random csps we investigate the nature of the phase transition sharp or coarse for random constraint satisfaction problems we first give a sharp threshold criterion specified for csps which is derived from friedgut bourgain s one thus we get a complete and precise classification of the nature of the threshold for symmetric boolean csps in particular we show that it is governed by two local properties strongly related to the problems 1 sat and 2 xor sat

imprimitive permutations in primitive groups abstract the goal of this paper is to study primitive groups that are contained in the union of maximal in the symmetric group imprimitive groups the study of types of permutations that appear inside primitive groups goes back to the origins of the theory of permutation groups however this is another instance of a situation common in mathematics in which a very natural problem turns out to be extremely difficult fortunately the enormous progresses of the last few decades seem to allow a new momentum on the attack to this problem in this paper we prove that there are infinite families of primitive groups contained in the union of imprimitive groups and propose a new hierarchy for primitive groups based on that fact in addition we introduce some algorithms to handle permutations provide the corresponding gap implementation solve some open problems and propose a large list of open problems

two generalizations of homogeneity in groups with applications to regular semigroups let x be a finite set such that x n and let i 6 j 6 n a group g 6 sn is said to be i j homogeneous if for every i j x such that i i and j j there exists g g such that ig j clearly i i homogeneity is i homogeneity in the usual sense a group g 6 sn is said to have the k universal transversal property if given any set i x with i k and any partition p of x into k blocks there exists g g such that ig is a section for p that is the orbit of each k subset of x contains a section for each k partition of x in this paper we classify the groups with the k universal transversal prop erty with the exception of two classes of 2 homogeneous groups and the k 1 k homogeneous groups for 2 k 6 n 1 as a corollary of the clas sification we prove that a k 1 k homogeneous group is also k 2 k 1 homogeneous with two exceptions and similarly but with no exceptions groups having the k universal transversal property have the k 1 universal transversal property a corollary of all the previous results is a classification of the groups that together with any rank k transformation on x generate a regular semigroup for 1 6 k 6 n 1 the paper ends with a number of challenges for experts in number theory group and or semigroup theory linear algebra and matrix theory

on the mumford tate group of an abelian variety with complex multiplication let k be a primitive cm type with k o 2n for definitions and previous results see section 1 1 fix n and consider the collection s n rank where rank counts the number of independent translates of qi under the galois action and k ranges over all primitive types the smallest element of s n denoted by b n is referred to as the sharp lower bound for the rank in dimension n as was brought to the author s attention by ribet bounds on b n of the form p 1 for p a prime dividing n follow directly from the proof of ribet s nondegeneracy theorem 21 this is recorded as theorem 1 4 ribet s method also gives bounds of the form 2q for q a prime with q2 dividing n as is observed in theorem 1 12 when combined with the author s constructions of abelian varieties in s 91 we obtain the precise value of b n for many values of n corollaries 1 5 to 1 8 and 1 13 we recall that these constructions use the analytic method of weil and shimura together with new results on the reflex field from an investigation suggested to the author by shim ura the interest of the rank comes from the theory of complex multiplication if a is an abelian variety of cm type k then the kubota rank of a is rank and controls properties of the classfields constructed from a as in kubota 161 and ribet 20 this is connected with the fact that the rank of is also the dimension of the mumford tate group of a and with the relation of this group to the i adic representations of a as in serre 24 251 the main body of the paper contains results that provide information on s n the main result theorem 2 5 asserts that when n is odd there is a computable subset s n of s n that accounts for the ranks of many cm types on most cm fields more precisely let k be the maximal totally real subfield of k and kg be the galois closure of k we consider the per

on the phase transitions of random k constraint satisfaction problems constraint satisfaction has received increasing attention over the years intense research has focused on solving all kinds of constraint satisfaction problems csps in this paper first we propose a random csp model named k csp that guarantees the existence of phase transitions under certain circumstances the exact location of the phase transition is quantified and experimental results are provided to illustrate the performance of the proposed model second we revise the model k csp to a random linear csp by incorporating certain linear structure to constraint relations we also prove the existence of the phase transition and exhibit its exact location for this random linear csp model

identification of image and blur parameters in frequency domain using the em algorithm we extend a method presented previously which considers the problem of the semicausal autoregressive ar parameter identification for images degraded by observation noise only we propose a new approach to identify both the causal and semicausal ar parameters and blur parameters without a priori knowledge of the observation noise power and the psf of the degradation we decompose the image into 1 d independent complex scalar subsystems resulting from the vector state space model by using the unitary discrete fourier transform dft then by applying the expectation maximization em algorithm to each subsystem we identify the ar model and blur parameters of the transformed image the ar parameters of the original image are then identified by using the least squares ls method the restored image is obtained as a byproduct of the em algorithm

blind deconvolution using a variational approach to parameter image and blur estimation following the hierarchical bayesian framework for blind deconvolution problems in this paper we propose the use of simultaneous autoregressions as prior distributions for both the image and blur and gamma distributions for the unknown parameters hyperparameters of the priors and the image formation noise we show how the gamma distributions on the unknown hyperparameters can be used to prevent the proposed blind deconvolution method from converging to undesirable image and blur estimates and also how these distributions can be inferred in realistic situations we apply variational methods to approximate the posterior probability of the unknown image blur and hyperparameters and propose two different approximations of the posterior distribution one of these approximations coincides with a classical blind deconvolution method the proposed algorithms are tested experimentally and compared with existing blind deconvolution methods

on locally semiprimitive graphs and a theorem of weiss abstract in this paper we investigate graphs that admit a group acting arc transitively such that the local action is semiprimitive with a regular normal nilpotent subgroup this type of semiprimitive group is a generalisation of an affine group we show that if the graph has valency coprime to six then there is a bound on the order of the vertex stabilisers depending on the valency alone we also prove a detailed structure theorem for the vertex stabilisers in the remaining case this is a contribution to an ongoing project to investigate the validity of the potocnik spiga verret conjecture

classifying the complexity of constraints using finite algebras many natural combinatorial problems can be expressed as constraint satisfaction problems this class of problems is known to be np complete in general but certain restrictions on the form of the constraints can ensure tractability here we show that any set of relations used to specify the allowed forms of constraints can be associated with a finite universal algebra and we explore how the computational complexity of the corresponding constraint satisfaction problem is connected to the properties of this algebra hence we completely translate the problem of classifying the complexity of restricted constraint satisfaction problems into the language of universal algebra we introduce a notion of tractable algebra and investigate how the tractability of an algebra relates to the tractability of the smaller algebras which may be derived from it including its subalgebras and homomorphic images this allows us to reduce significantly the types of algebras which need to be classified using our results we also show that if the decision problem associated with a given collection of constraint types can be solved efficiently then so can the corresponding search problem we then classify all finite strictly simple surjective algebras with respect to tractability obtaining a dichotomy theorem which generalizes schaefer s dichotomy for the generalized satisfiability problem finally we suggest a possible general algebraic criterion for distinguishing the tractable and intractable cases of the constraint satisfaction problem

on groups with every normal subgroup transitive or semiregular we investigate finite solvable permutation groups in which all normal subgroups are transitive or semiregular the motivation comes from universal algebra such groups are examples of collapsing transformation monoids

on the orders of primitive groups abstract almost all primitive permutation groups of degree n have order at most n i 0 log 2 n 1 n 2 i 1 log 2 n or have socle isomorphic to a direct power of some alternating group the mathieu groups m11 m12 m23 and m24 are the four exceptions as a corollary the sharp version of a theorem of praeger and saxl is established where m12 turns out to be the largest primitive group for an application a bound on the orders of permutation groups without large alternating composition factors is given this sharpens a lemma of babai cameron palfy and generalizes a theorem of dixon

distance transitive graphs and finite simple groups introductionthis paper represents the first step in the classification of finite primitive distancetransitive graphs in it we reduce the problem to the case where the automorph ism group is either almost simple or affine let be a simple connected undirected graph with verte oc x se t q e q i fthen d a j8 denotes the distance between 3 a i ann

on the order of uniprimitive permutation groups one of the central problems of 19th century group theory was the estimation of the order of a primitive permutation group g of degree n where g x an we prove i g i exp 4v n log2 n for the case when g is not doubly transitive this result is best possible apart from an o log n factor in the exponent the best result previously known was i g i el h wielandt a similar estimate for the doubly transitive case follows in a subsequent paper for rank 3 groups with subdegree p n 2 we obtain i gi exp 4 n p log2 n in the proof we develop some new combinatorial properties of coherent configurations the results also have relevance to theoretical estimates on the computational complexity of graph isomorphism testing

primitive permutation groups of odd degree and an application to finite projective planes one of the most beautiful and important results concerning finite projective planes is the ostrom wagner theorem 26 such a plane admitting a 2 transitive collineation group must be desarguesian it has long been conjectured that the same conclusion must hold if it is only assumed that there is a collineation group transitive on incident point line pairs ll pp 208 214 171 the starting point for this paper was a proof of this conjecture modulo a degenerate situation

a classification of primitive permutation groups with finite stabilizers abstract we classify all infinite primitive permutation groups possessing a finite point stabilizer thus extending the seminal aschbacher o nan scott theorem to all primitive permutation groups with finite point stabilizers

locating the phase transition in binary constraint satisfaction problems abstract the phase transition in binary constraint satisfaction problems i e the transition from a region in which almost all problems have many solutions to a region in which almost all problems have no solutions as the constraints become tighter is investigated by examining the behaviour of samples of randomly generated problems in contrast to theoretical work which is concerned with the asymptotic behaviour of problems as the number of variables becomes larger this paper is concerned with the location of the phase transition in finite problems the accuracy of a prediction based on the expected number of solutions is discussed it is shown that the variance of the number of solutions can be used to set bounds on the phase transition and to indicate the accuracy of the prediction a class of sparse problems for which the prediction is known to be inaccurate is considered in detail it is shown that for these problems the phase transition depends on the topology of the constraint graph as well as on the tightness of the constraints

the structure of galois groups of fields a cm field k defines a triple c h p where c is the galois group of the galois closure of k h is the subgroup of c fixing k and p e c is induced by complex conjugation a 4p structure identifies cm fields when their triples are identified under the action of the group of automorphisms of c a classification of the p structures is given and a general formula for the degree of the reflex field is obtained complete lists of p structues and reflex fields are provided for k cl 2 n with n 3 4 5 and 7 in addition simple degenerate abelian varieties of cm type are constructed in every composite dimension the collection of reflex fields is also determined for the dihedral group c d2n with n odd and h of order 2 and a relative class number formula is found

understanding blind deconvolution algorithms blind deconvolution is the recovery of a sharp version of a blurred image when the blur kernel is unknown recent algorithms have afforded dramatic progress yet many aspects of the problem remain challenging and hard to understand the goal of this paper is to analyze and evaluate recent blind deconvolution algorithms both theoretically and experimentally we explain the previously reported failure of the naive map approach by demonstrating that it mostly favors no blur explanations we show that using reasonable image priors a naive simulations map estimation of both latent image and blur kernel is guaranteed to fail even with infinitely large images sampled from the prior on the other hand we show that since the kernel size is often smaller than the image size a map estimation of the kernel alone is well constrained and is guaranteed to succeed to recover the true blur the plethora of recent deconvolution techniques makes an experimental evaluation on ground truth data important as a first step toward this experimental evaluation we have collected blur data with ground truth and compared recent algorithms under equal settings additionally our data demonstrate that the shift invariant blur assumption made by most algorithms is often violated

blind image restoration by anisotropic regularization this paper presents anisotropic regularization techniques to exploit the piecewise smoothness of the image and the point spread function psf in order to mitigate the severe lack of information encountered in blind restoration of shift invariantly and shift variantly blurred images the new techniques which are derived from anisotropic diffusion adapt both the degree and direction of regularization to the spatial activities and orientations of the image and the psf this matches the piecewise smoothness of the image and the psf which may be characterized by sharp transitions in magnitude and by the anisotropic nature of these transitions for shift variantly blurred images whose underlying psfs may differ from one pixel to another we parameterize the psf and then apply the anisotropic regularization techniques this is demonstrated for linear motion blur and out of focus blur alternating minimization is used to reduce the computational load and algorithmic complexity

generalized satisfiability problems minimal elements and phase transitions we develop a probabilistic model on the generalized satisfiability problems defined by schaefer in proceedings of the 10th stoc san diego ca usa association for computing machinery new york 1978 pp 216 226 for which the arity of the constraints is fixed in order to study the associated phase transition we establish new results on minimal elements associated with such generalized satisfiability problems these results are the keys of the exploration we conduct on the location and on the nature of the phase transition for generalized satisfiability we first prove that the phase transition occurs at the same scale for every reasonable problem and we provide lower and upper bounds for the associated critical ratio our framework allows one to get these bounds in a uniform way in particular we obtain a lower bound proportional to the number of variables for k sat without analyzing any algorithm finally we reveal the seed of coarseness for the phase transition of generalized satisfiability 2 xor sat

constructing an asymptotic phase transition in random binary constraint satisfaction problems the standard models used to generate random binary constraint satisfaction problems are described at the problem sizes studied experimentally a phase transition is seen as the constraint tightness is varied however achlioptas et al showed that if the problem size number of variables increases while the remaining parameters are kept constant asymptotically almost all instances are unsatisfiable in this paper an alternative scheme for one of the standard models is proposed in which both the number of values in each variable s domain and the average degree of the constraint graph are increased with problem size it is shown that with this scheme there is asymptotically a range of values of the constraint tightness in which instances are trivially satis able with probability at least 0 5 and a range in which instances are almost all unsatisfiable hence there is a crossover point at some value of the constraint tightness between these two ranges this scheme is compared to a similar scheme due to xu and li

on pyber s base size conjecture let g be a permutation group on a finite set a subset of is a base for g if its pointwise stabilizer in g is trivial the base size of g denoted b g is the smallest size of a base a well known conjecture of pyber from the early 1990s asserts that there exists an absolute constant c such that b g c log g logn for any primitive permutation group g of degree n several special cases have been verified in recent years including the almost simple and diagonal cases in this paper we prove pyber s conjecture for all non affine primitive groups

an empirical study of phase transitions in binary constraint satisfaction problems abstract an empirical study of randomly generated binary constraint satisfaction problems reveals that for problems with a given number of variables domain size and connectivity there is a critical level of constraint tightness at which a phase transition occurs at the phase transition problems change from being soluble to insoluble and the difficulty of problems increases dramatically a theory developed by williams and hogg 44 and independently developed by smith 37 predicts where the hardest problems should occur it is shown that the theory is in close agreement with the empirical results except when constraint graphs are sparse

a kullback leibler divergence approach to blind image restoration a new algorithm for maximum likelihood blind image restoration is presented in this paper it is obtained by modeling the original image and the additive noise as multivariate gaussian processes with unknown covariance matrices the blurring process is specified by its point spread function which is also unknown estimations of the original image and the blur are derived by alternating minimization of the kullback leibler divergence between a model family of probability distributions defined using the linear image degradation model and a desired family of probability distributions constrained to be concentrated on the observed data the algorithm presents the advantage to provide closed form expressions for the parameters to be updated and to converge only after few iterations a simulation example that illustrates the effectiveness of the proposed algorithm is presented

large subgroups of simple groups abstract let g be a finite group a proper subgroup h of g is said to be large if the order of h satisfies the bound h 3 g in this note we determine all the large maximal subgroups of finite simple groups and we establish an analogous result for simple algebraic groups in this context largeness is defined in terms of dimension an application to triple factorisations of simple groups both finite and algebraic is discussed

nonedge specific adaptive scheme for highly robust blind motion deblurring of natural imagess blind motion deblurring estimates a sharp image from a motion blurred image without the knowledge of the blur kernel although significant progress has been made on tackling this problem existing methods when applied to highly diverse natural images are still far from stable this paper focuses on the robustness of blind motion deblurring methods toward image diversity a critical problem that has been previously neglected for years we classify the existing methods into two schemes and analyze their robustness using an image set consisting of 1 2 million natural images the first scheme is edge specific as it relies on the detection and prediction of large scale step edges this scheme is sensitive to the diversity of the image edges in natural images the second scheme is nonedge specific and explores various image statistics such as the prior distributions this scheme is sensitive to statistical variation over different images based on the analysis we address the robustness by proposing a novel nonedge specific adaptive scheme neas which features a new prior that is adaptive to the variety of textures in natural images by comparing the performance of neas against the existing methods on a very large image set we demonstrate its advance beyond the state of the art

a theory of semiprimitive groups abstract a transitive permutation group is semiprimitive if each of its normal subgroups is transitive or semiregular interest in this class of groups is motivated by two sources problems arising in universal algebra related to collapsing monoids and the graph restrictive problem for permutation groups here we develop a theory of semiprimitive groups which encompasses their structure their quotient actions and a method by which all finite semiprimitive groups are constructed we also extend some results from the theory of primitive groups to semiprimitive groups and conclude with open problems of a similar nature

parameter estimation of superimposed signals using the em algorithm a computationally efficient algorithm for parameter estimation of superimposed signals based on the two step iterative em estimate and maximize with an e step and an m step algorithm is developed the idea is to decompose the observed data into their signal components and then to estimate the parameters of each signal component separately the algorithm iterates back and forth using the current parameter estimates to decompose the observed data better and thus increase the likelihood of the next parameter estimates the application of the algorithm to the multipath time delay and multiple source location estimation problems is considered

synchronizing groups and automata pin showed that every p state automaton p a prime containing a cyclic permutation and a non permutation has a synchronizing word of length at most p 1 2 in this paper we consider permutation automata with the property that adding any nonpermutation will lead to a synchronizing word and establish bounds on the lengths of such synchronizing words in particular we show that permutation groups whose permutation character over the rationals splits into a sum of only two irreducible characters have the desired property

p adic hurwitz groups abstract herrlich showed that a mumford curve of genus g 1 over the p adic complex field c p has at most 48 g 1 24 g 1 30 g 1 or 12 g 1 automorphisms as p 2 3 5 or p 5 the mumford curves attaining these bounds are uniformised by normal subgroups of finite index in certain p adic triangle groups p for p 5 or in a p adic quadrangle group p for p 5 the finite groups attaining these bounds are p adic analogues of the hurwitz groups arising from curves over c we construct explicit infinite families of such groups as quotients of p and p these include groups of type psl 2 q and pgl 2 q all arising as congruence quotients when p 5 and also various alternating and symmetric groups arising as noncongruence quotients of the groups p

thresholds of random quasi abelian codes for a q ary random quasi abelian code with fixed coindex and constant rate r it is shown that the gilbert varshamov gv bound is a threshold point if r is less than the gv bound at 0 1 q 1 then the probability of the relative distance of the random code being greater than approaches 1 as the index goes to infinity whereas if r is bigger than the gv bound at then the probability approaches 0 as a corollary there exist numerous asymptotically good quasi abelian codes attaining the gv bound

the use of cone shaped kernels for generalized time frequency representations of nonstationary signals generalized time frequency representations gtfrs which use cone shaped kernels for nonstationary signal analysis are presented the cone shaped kernels are formulated for the gtfrs to produce good resolution simultaneously in time and frequency specifically for a gtfr with a cone shaped kernel finite time support is maintained in the time dimension along with an enhanced spectrum in the frequency dimension and the cross terms are smoothed out experimental results on simulated data and real speech show the advantages of the gtfrs with the cone shaped kernels through comparisons to the spectrogram and the pseudo wigner distribution

on statistical identification of a class of linear space invariant image blurs using non minimum phase arma models an optimal statistical parameter estimation technique was previously presented by the authors ibid vol assp 34 p 963 72 for the identification of a class of unknown linear systems that can be modeled by a zero phase finite impulse response filter this technique is now extended to a more general case using a spectrally equivalent minimum phase semp representation of the system the original zero phase system parameters are computed from the semp model parameters

a variational approach for bayesian blind image deconvolution in this paper the blind image deconvolution bid problem is addressed using the bayesian framework in order to solve for the proposed bayesian model we present a new methodology based on a variational approximation which has been recently introduced for several machine learning problems and can be viewed as a generalization of the expectation maximization em algorithm this methodology reaps all the benefits of a full bayesian model while bypassing some of its difficulties we present three algorithms that solve the proposed bayesian problem in closed form and can be implemented in the discrete fourier domain this makes them very cost effective even for very large images we demonstrate with numerical experiments that these algorithms yield promising improvements as compared to previous bid algorithms furthermore the proposed methodology is quite general with potential application to other bayesian models for this and other imaging problems

the mean field theory in em procedures for blind markov random field image restoration a markov random field mrf model based em expectation maximization procedure for simultaneously estimating the degradation model and restoring the image is described the mrf is a coupled one which provides continuity inside regions of smooth gray tones and discontinuity at region boundaries constraints for the restoration problem which is in general ill posed the computational difficulty associated with the em procedure for mrfs is resolved by using the mean field theory from statistical mechanics an orthonormal blur decomposition is used to reduce the chances of undesirable locally optimal estimates experimental results on synthetic and real world images show that this approach provides good blur estimates and restored images the restored images are comparable to those obtained by a wiener filter in mean square error but are most visually pleasing

finite primitive permutation groups containing a permutation having at most four cycles we classify the finite primitive groups containing a permutation with at most four cycles including fixed points in its disjoint cycle representation

maximum likelihood blur identification and image restoration using the em algorithm the authors describe an algorithm for the identification of the blur and the restoration of a noisy blurred image the original image and the additive noise are modeled as zero mean gaussian random processes their covariance matrices are unknown parameters the blurring process is specified by its point spread function which is also unknown maximum likelihood estimation is used to find these unknown parameters in turn the expectation maximization em algorithm is exploited in computing the maximum likelihood estimates in applying the em algorithm the original image is part of the complete data its estimate is computed in the e step of the em iterations explicit iterative expressions are derived for the estimation experimental results on simulated and photographically blurred images are shown

sharp thresholds of graph properties and the sat problem consider g n p to be the probability space of random graphs on n vertices with edge probability p we will be considering subsets of this space defined by monotone graph properties a monotone graph property p is a property of graphs such that a p is invariant under graph automorphisims b if graph h has property p then so does any graph g having h as a subgraph a monotone symmetric family of graphs is a family defined by such a property one of the first observations made about random graphs by erdos and renyi in their seminal work on random graph theory 12 was the existence of threshold phenomena the fact that for many interesting properties p the probability of p appearing in g n p exhibits a sharp increase at a certain critical value of the parameter p bollobas and thomason proved the existence of threshold functions for all monotone set properties 6 and in 14 it is shown that this behavior is quite general and that all monotone graph properties exhibit threshold behavior i e the probability of their appearance increases from values very close to 0 to values close to 1 in a very small interval more precise analysis of the size of the threshold interval is done in 7 this threshold behavior which occurs in various settings which arise in combinatorics and computer science is an instance of the phenomenon of phase transitions which is the subject of much interest in statistical physics one of the main questions that arises in studying phase transitions is how sharp is the transition for example one of the motivations for this paper arose from the question of the sharpness of the phase transition for the property of satisfiability of a random kcnf boolean formula nati linial who introduced me to this problem suggested that although much concrete analysis was being performed on this problem the best approach would be to find general conditions for sharpness of the phase transition answering the question posed in 14 as to the relation between the length of the threshold interval and the value of the critical probability in this paper we indeed introduce a simple condition and prove it is sufficient stated roughly in the setting of random graphs the main theorem states that if a property has a coarse threshold then it can be approximated by the property of having certain given graphs as a subgraph this condition can be applied in a more

blind image restoration with eigen face subspace performance of conventional image restoration methods is sensitive to signal to noise ratios for heavily blurred and noisy human facial images information contained in the eigen face subspace can be used to compensate for the lost details the blurred image is decomposed into the eigen face subspace and then restored with a regularized total constrained least square method with generalized cross validation a cost function is deduced to include two unknown parameters the regularization factor and one parameter relevant to point spread function it is shown that in minimizing the cost function the cost function dependence of any one unknown parameter can be separated from the other one which means the cost function can be considered roughly depending on single variable in an iterative algorithm with realistic constraints on the regularized factor a global minimum for the cost function is achieved to determine the unknown parameters experiments are presented to demonstrate the effectiveness and robustness of the new method

a regularization approach to joint blur identification and image restoration the primary difficulty with blind image restoration or joint blur identification and image restoration is insufficient information this calls for proper incorporation of a priori knowledge about the image and the point spread function psf a well known space adaptive regularization method for image restoration is extended to address this problem this new method effectively utilizes among others the piecewise smoothness of both the image and the psf it attempts to minimize a cost function consisting of a restoration error measure and two regularization terms one for the image and the other for the blur subject to other hard constraints a scale problem inherent to the cost function is identified which if not properly treated may hinder the minimization blind restoration process alternating minimization is proposed to solve this problem so that algorithmic efficiency as well as simplicity is significantly increased two implementations of alternating minimization based on steepest descent and conjugate gradient methods are presented good performance is observed with numerically and photographically blurred images even though no stringent assumptions about the structure of the underlying blur operator is made

clustering phase of a general constraint satisfaction problem model d k csp abstract relation between problem hardness and solution space structure is an important research aspect model d k csp is a random model of constraint satisfaction problem which generates very hard instances when r 1 or r is near 1 where r represents normalized constraint density we study the clustering phase of the model and find that if r is below and close to 1 the solution space contains many widely distributed and well separated small frozen clusters which should be the reason why the generated instances are hard to solve

identification of image and blur parameters for the restoration of noncausal blurs an optimal statistical parameter estimation technique is presented for the identification of unknown image and blur model parameters the development leads to an autoregressive moving average arma model identification problem where the image model coefficients define the ar part and the blur parameters define the ma part conditional maximum likelihood estimates of the unknown parameters are derived both in the absence and in the presence of observation noise the proposed algorithms constitute a generalization of previous work on blur identification in that they are able to locate the zero loci of the blurred image spectrum on the entire z 1 z 2 plane simulation results as well as photographically blurred images processed with the proposed algorithms are shown as examples

blind deconvolution using generalized cross validation approach to regularization parameter estimation in this paper we propose and present an algorithm for total variation tv based blind deconvolution both the unknown image and blur can be estimated within an alternating minimization framework with the generalized cross validation gcv method the regularization parameters associated with the unknown image and blur can be updated in alternating minimization steps experimental results confirm that the performance of the proposed algorithm is better than variational bayesian blind deconvolution algorithms with student s t priors or a total variation prior

ant colony algorithm with a strengthened negative feedback mechanism for constraint satisfaction problems describing the definition and usage of negative feedback in ant colony optimization proposing a new negative pheromone matrix and combined with positive pheromone matrix in probability formula a novel strengthening negative feedback mechanism is proposed to improve efficiency and avoid local optimal detail experiment design has been given for evaluating the proposed approaches based on different standard real datasets and synthetically generated datasets ant colony optimization aco is an efficient way to solve binary constraint satisfaction problems csps in recent years new improvements have only considered enhancing the positive feedback to increase the convergence speed however through the study and analysis of these enhanced aco algorithms we determined that they still suffer from the problem of easily getting in locally optimal solutions thus an improved aco algorithm with a strengthened negative feedback mechanism is designed to tackle csps this new algorithm takes advantage of search history information and continually obtains failure experience to guide the ant swarm exploring the unknown space during the optimization process the starting point of this algorithm is to utilize the negative feedback to improve the diversity of solutions finally we use 24 csp samples and 25 queen samples to perform experiments compare this algorithm with other related algorithms and conduct performance assessment the preliminary results show that aco with negative feedback outperforms the compared algorithms in identifying high quality solutions

a joint estimation approach for two tone image deblurring by blind deconvolution a new statistical method is proposed for deblurring two tone images i e images with two unknown grey levels that are blurred by an unknown linear filter the key idea of the proposed method is to adjust a deblurring filter until its output becomes two tone two optimization criteria are proposed for the adjustment of the deblurring filter a three step iterative algorithm tsia is also proposed to minimize the criteria it is proven mathematically that by minimizing either of the criteria the original nonblurred image along with the blur filter will be recovered uniquely only with possible scale shift ambiguities at high snr the recovery is guaranteed not only for i i d images but also for correlated and nonstationary images it does not require a priori knowledge of the statistical parameters or the tone values of the original image neither does it require a priori knowledge of the phase or other special information e g fir symmetry nonnegativity etc about the blur filter numerical experiments are carried out to test the method on synthetic and real images

the scaling window of the model d k csp abstract consider the model d k csp which consists of a set of n variables with the domain size d and a set of t r n ln d ln p constraints where each constraint binds k distinct variables and permits p d k tuples of values we prove that the exact phase transition of the model d k csp occurs at r c 1 as long as k ln d ln n where satisfies that 1 2 1 2 2 k 1 e 1 e 0 is a sufficiently small constant more importantly we establish the finite size scaling about this transition specifically let 0 be a given constant the probability of satisfiability of the model d k csp is greater than 1 if r 1 1 n 1 ln d is dependent on the control parameters and is less than if r 1 1 n ln d

primitive groups graph endomorphisms and synchronization the third author has been partially supported by the fundacao para a ciencia e a tecnologia through the project cemat ciencias uid multi 04621 2013

normalizers of primitive permutation groups abstract let g be a transitive normal subgroup of a permutation group a of finite degree n the factor group a g can be considered as a certain galois group and one would like to bound its size one of the results of the paper is that a g n if g is primitive unless n 3 4 54 38 58 or 316 this bound is sharp when n is prime in fact when g is primitive out g n unless g is a member of a given infinite sequence of primitive groups and n is different from the previously listed integers many other results of this flavor are established not only for permutation groups but also for linear groups and galois groups

many hard examples in exact phase transitions this paper analyzes the resolution complexity of two random constraint satisfaction problem csp models i e model rb rd for which we can establish the existence of phase transitions and identify the threshold points exactly by encoding csps into cnf formulas it is proved that almost all instances of model rb rd have no tree like resolution proofs of less than exponential size thus we not only introduce new families of csps and cnf formulas hard to solve which can be useful in the experimental evaluation of csp and sat algorithms but also propose models with both many hard instances and exact phase transitions finally conclusions are presented as well as a detailed comparison of model rb rd with the hamiltonian cycle problem and random 3 sat which respectively exhibit three different kinds of phase transition behavior in np complete problems