analytical and belief propagation studies of random constraint satisfaction problems with growing domains we study solution space structure and solution finding algorithms of a representative hard random constraint satisfaction problem with growing domains known as model rb using rigorous methods we show that solutions are grouped into disconnected clusters before the theoretical satisfiability phase transition point using the cavity method it is shown that the entropy density obtained by belief propagation bp on random model rb instances which corresponds well to the analytical results vanishes as the control parameter constraint tightness approaches the satisfiability threshold from an algorithmic point of view we find that reinforced bp which performs much better than all existing algorithms allows us to find solutions efficiently for instances in the regime that is very close to the satisfiability transition these results also can shed light on the effectiveness of bp reinforcement on problems with a large number of states

spectral gmm estimation of continuous time processes abstract this paper derives a methodology for the estimation of continuous time stochastic models based on the characteristic function the estimation method does not require discretization of the stochastic process and it is simple to apply in practice the method is essentially generalized method of moments on the complex plane hence it shares the efficiency and distribution properties of gmm estimators we illustrate the method with some applications to relevant estimation problems in continuous time finance we estimate a model of stochastic volatility a jump diffusion model with constant volatility and a model that nests both the stochastic volatility model and the jump diffusion model we find that negative jumps are important to explain skewness and asymmetry in excess kurtosis of the stock return distribution while stochastic volatility is important to capture the overall level of this kurtosis positive jumps are not statistically significant once we allow for stochastic volatility in the model we also estimate a non affine model of stochastic volatility and find that the power of the diffusion coefficient appears to be between one and two rather than the value of one half that leads to the standard affine stochastic volatility model however we find that including jumps into this non affine stochastic volatility model reduces the power of the diffusion coefficient to one half finally we offer an explanation for the observation that the estimate of persistence in stochastic volatility increases dramatically as the frequency of the observed data falls based on a multiple factor stochastic volatility model

social balance as a satisfiability problem of computer science reduction of frustration was the driving force in an approach to social balance as it was recently considered by antal t antal p l krapivsky and s redner phys rev e 72 036121 2005 we generalize their triad dynamics to k cycle dynamics for arbitrary integer k we derive the phase structure determine the stationary solutions and calculate the time it takes to reach a frozen state the main difference in the phase structure as a function of k is related to k being even or odd as a second generalization we dilute the all to all coupling as considered by antal to a random network with connection probability w 1 interestingly this model can be mapped to a satisfiability problem of computer science the phase of social balance in our original interpretation then becomes the phase of satisfaction of all logical clauses in the satisfiability problem in common to the cases we study the ideal solution without any frustration always exists but the question actually is as to whether this solution can be found by means of a local stochastic algorithm within a finite time the answer depends on the choice of parameters after establishing the mapping between the two classes of models we generalize the social balance problem to a diluted network topology for which the satisfiability problem is usually studied on the other hand in connection with the satisfiability problem we generalize the random local algorithm to a p random local algorithm including a parameter p that corresponds to the propensity parameter in the social balance problem the qualitative effect of the inclusion of this parameter is a bias towards the optimal solution and a reduction of the needed simulation time

structural induction in institutions abstract we develop a general logic independent structural induction proof method at the level of abstract institutions this provides a solid and uniform mathematical foundation to induction proof methodologies for a wide variety of actual logic based formal specification frameworks our development is based technically upon an axiomatic approach to substitutions within institution theory

nonparametric estimation for a class of levy processes we consider estimation for a class of levy processes modelled as a sum of a drift a symmetric stable process and a compound poisson process we propose a nonparametric approach to estimating unknown parameters of our model including the drift the scale and index parameters in the stable law the mean of the poisson process and the underlying jump size distribution we show that regression and nonparametric deconvolution methods based on the empirical characteristic function can be used for inference interesting connections are shown to exist between properties of our estimators and of those found in conventional deconvolution

asymptotic properties of monte carlo estimators of diffusion processes abstract this paper studies the limit distributions of monte carlo estimators of diffusion processes we examine two types of estimators based on the euler scheme one applied to the original processes the other to a doss transformation of the processes we show that the transformation increases the speed of convergence of the euler scheme we also study estimators of conditional expectations of diffusions after characterizing expected approximation errors we construct second order bias corrected estimators we also derive new convergence results for the mihlstein scheme illustrations of the results are provided in the context of simulation based estimation of diffusion processes

ultraproducts and possible worlds semantics in institutions we develop possible worlds kripke semantics at the categorical abstract model theoretic level provided by the so called institutions our general abstract modal logic framework provides a method for systematic kripke semantics extensions of logical systems from computing science and logic we also extend the institution independent method of ultraproducts of r diaconescu institution independent ultraproducts fundamenta informaticae 55 3 4 2003 321 348 to possible worlds semantics and prove a fundamental preservation result for abstract modal satisfaction as a consequence we develop a generic compactness result for possible worlds semantics

estimation of stable distributions by indirect inference this article deals with the estimation of the parameters of an stable distribution by the indirect inference method with the skewed t distribution as an auxiliary model the latter distribution appears as a good candidate for an auxiliary model since it has the same number of parameters as the stable distribution with each parameter playing a similar role to improve the properties of the estimator in finite sample we use a variant of the method called constrained indirect inference in a monte carlo study we show that this method delivers estimators with good properties in finite sample in particular they are much more efficient than two other prevalent methods based on the characteristic function and the empirical quantiles we provide an empirical application to hedge fund returns

estimation of stochastic volatility models via monte carlo maximum likelihood this paper discusses the monte carlo maximum likelihood method of estimating stochastic volatility sv models the basic sv model can be expressed as a linear state space model with log chi square disturbances the likelihood function can be approximated arbitrarily accurately by decomposing it into a gaussian part constructed by the kalman filter and a remainder function whose expectation is evaluated by simulation no modifications of this estimation procedure are required when the basic sv model is extended in a number of directions likely to arise in applied empirical research this compares favorably with alternative approaches the finite sample performance of the new estimator is shown to be comparable to the monte carlo markov chain mcmc method

order sorted algebra i equational deduction for multiple inheritance overloading exceptions and partial operations abstract this paper generalizes many sorted algebra msa to order sorted algebra osa by allowing a partial ordering relation on the set of sorts this supports abstract data types with multiple inheritance in roughly the sense of object oriented programming several forms of polymorphism and overloading partial operations as total on equationally defined subsorts exception handling and an operational semantics based on term rewriting we give the basic algebraic constructions for osa including quotient image product and term algebra and we prove their basic properties including quotient homomorphism and initiality theorems the paper s major mathematical results include a notion of osa deduction a completeness theorem for it and an osa birkhoff variety theorem we also develop conditional osa including initiality completeness and mckinsey malcev quasivariety theorems and we reduce osa to conditional msa which allows lifting many known msa results to osa retracts which intuitively are left inverses to subsort inclusions provide relatively inexpensive run time error handling we show that it is safe to add retracts to any osa signature in the sense that it gives rise to a conservative extension a final section compares and contrasts many different approaches to osa this paper also includes several examples demonstrating the flexibility and applicability of osa including some standard benchmarks like stack and list as well as a much more substantial example the number hierarchy from the naturals up to the quaternions

simulated moments estimation of markov models of asset prices this paper provides a simulated moments estimator sme of the parameters of dynamic models in which the state vector follows a time homogeneous markov process conditions are provided for both weak and strong consistency as well as asymptotic normality various tradeoffs among the regularity conditions underlying the large sample properties of the sme are discussed in the context of an asset pricing model this paper provides conditions for the consistency and asymptotic normality of a simulated moments estimator sme of the parameters of asset pricing models with time homogeneous markov representations of the stochastic forc ing process sme s for economic models have been proposed by mcfadden 1989 and pakes and pollard 1989 for i i d environments and by lee and ingram 1991 for a time series environment the sme for time series models examined in this paper is as follows the state vector yt that determines asset prices is assumed to follow a time homogeneous markov process whose transi tion function depends on an unknown parameter vector 3 0 asset prices and possibly other relevant data are observed as f yt 0 for some given function f of the underlying state and parameter vector in parallel a simulated state process y is generated analytically or numerically from the economic model and corresponding simulated observations f yj3 13 are taken for a given parameter choice f3 the parameter is chosen so as to match moments that is to minimize the distance between sample moments of the data f y 8030 and those of the simulated series f yt f3 in a sense to be made precise the proposed sme extends the generalized method of moments gmm estimator hansen 1982 to a large class of asset pricing models for which the moment restrictions of interest do not have analytic representations in terms of observable variables and the unknown parameter vector we provide conditions on the transition function of yt and the observation function f under which the sme of 030 is consistent and characterize the normalized asymptotic distribu tion of the estimator for two reasons neither the regularity conditions underly ing hansen s 1982 analysis of gmm estimators for time series models without

fisher s information for discretely sampled levy processes this paper studies the asymptotic behavior of the fisher information for a levy process discretely sampled at an increasing frequency we show that it is possible to distinguish not only the continuous part of the process from its jumps part but also different types of jumps and derive the rates of convergence of efficient estimators

efficient estimation of general dynamic models with a continuum of moment conditions there are two difficulties with the implementation of the characteristic function based estimators first the optimal instrument yielding the ml efficiency depends on the unknown probability density function second the need to use a large set of moment conditions leads to the singularity of the covariance matrix we resolve the two problems in the framework of gmm with a continuum of moment conditions a new optimal instrument relies on the double indexing and as a result has a simple exponential form the singularity problem is addressed via a penalization term we introduce hac type estimators for non markov models a simulated method of moments is proposed for non analytical cases

observational logic constructor based logic and their duality observability and reachability are important concepts for formal software development while observability concepts are used to specify the required observable behavior of a program or system reachability concepts are used to describe the underlying data in terms of datatype constructors in this paper we first reconsider the observational logic institution which provides a logical framework for dealing with observability then we develop in a completely analogous way the constructor based logic institution which formalizes a novel treatment of reachability both institutions are tailored to capture the semantically correct realizations of a specification from either the observational or the reachability point of view we show that there is a methodological and even formal duality between both frameworks in particular we establish a correspondence between observer operations and datatype constructors observational and constructor based algebras fully abstract and reachable algebras and observational and inductive consequences of specifications the formal duality between the observability and reachability concepts is established in a category theoretic setting

a test of separate families of distributions based on the empirical moment generating function summary in testing an hypothesis that a population has a specified distribution against the alternative that its distribution belongs to a separate family it is well known that the likelihood ratio test does not apply we propose a test based on the difference between the sample moment generating function and its theoretical counterpart under ho the argument of the moment generating function is chosen to maximize the test s largesample power small sample properties of the test in two applications are studied by simulation

spanning trees in random satisfiability problems working with tree graphs is always easier than with loopy ones and spanning trees are the closest tree like structures to a given graph we find a correspondence between the solutions of random k satisfiability problem and those of spanning trees in the associated factor graph we introduce a modified survey propagation algorithm which returns null edges of the factor graph and helps us to find satisfiable spanning trees this allows us to study organization of satisfiable spanning trees in the space spanned by spanning trees

module algebra an axiomatic algebraic calculus of modules is given that is based on the operators combination union export renaming and taking the visible signature four different models of module algebra are discussed and compared

on some fourier methods for inference abstract common statistical procedures such as maximum likelihood and m estimation admit generalized representations in the fourier domain the fourier domain provides fertile ground for approaching a number of difficult problems in inference in particular the empirical characteristic function and its extension for stationary time series are shown to be fundamental tools which support numerically simple inference procedures having arbitrarily high asymptotic efficiency and certain robustness features as well a numerical illustration involving the symmetric stable laws is given

estimation of affine asset pricing models using the empirical characteristic function abstract the known functional form of the conditional characteristic function ccf of discretely sampled observations from an affine diffusion is used to develop computationally tractable and asymptotically efficient estimators of the parameters of affine diffusions and of asset pricing models in which the state vectors follow affine diffusions both time domain estimators based on fourier inversion of the ccf and frequency domain estimators based directly on the ccf are constructed a method of moments estimator based on the ccf is shown to approximate the efficiency of maximum likelihood for affine diffusion and asset pricing models

principles of proof scores in cafeobj this paper describes the theoretical principles of a verification method with proof scores in the cafeobj algebraic specification language the verification method focuses on specifications with conditional equations and realizes systematic theorem proving or interactive verification the method is explained using a simple but instructive example and the necessary theoretical foundations which justify every step of the verification are described with precise mathematical definitions some important theorems that result from the definitions are also presented

density approximations for multivariate affine jump diffusion processes we introduce closed form transition density expansions for multivariate affine jump diffusion processes the expansions rely on a general approximation theory which we develop in weighted hilbert spaces for random variables which possess all polynomial moments we establish parametric conditions which guarantee existence and differentiability of transition densities of affine models and show how they naturally fit into the approximation framework empirical applications in option pricing credit risk and likelihood inference highlight the usefulness of our expansions the approximations are extremely fast to evaluate and they perform very accurately and numerically stable

fuzzy lattice operations on first order terms over signatures with similar constructors a constraint based approach abstract unification and generalization are operations on two terms computing respectively their greatest lower bound and least upper bound when the terms are quasi ordered by subsumption up to variable renaming i e t 1 t 2 iff t 1 t 2 for some variable substitution when term signatures are such that distinct functor symbols may be related with a fuzzy equivalence called a similarity these operations can be formally extended to tolerate mismatches on functor names and or arity or argument order we reformulate and extend previous work with a declarative approach defining unification and generalization as sets of axioms and rules forming a complete constraint normalization proof system these include the reynolds plotkin term generalization procedures maria sessa s weak unification with partially fuzzy signatures and its corresponding generalization as well as novel extensions of such operations to signatures with weaker functor similarities i e with possibly different arities one advantage of this approach is that it requires no modification of the conventional data structures for terms and substitutions this and the fact that these declarative specifications are efficiently executable conditional horn clauses offers great practical potential for fuzzy information handling applications

volatility estimators for discretely sampled levy processes this paper studies the estimation of the volatility parameter in a model where the driving process is a brownian motion or a more general symmetric stable process that is perturbed by another levy process we distinguish between a parametric case where the law of the perturbing process is known and a semiparametric case where it is not in the parametric case we construct estimators which are asymptotically efficient in the semiparametric case we can obtain asymptotically efficient estimators by sampling at a sufficiently high frequency and these estimators are efficient uniformly in the law of the perturbing process

a martingale approach for testing diffusion models based on infinitesimal operator abstract i develop an omnibus specification test for diffusion models based on the infinitesimal operator the infinitesimal operator based identification of the diffusion process is equivalent to a martingale hypothesis for the processes obtained by a transformation of the original diffusion model my test procedure is then constructed by checking the martingale hypothesis via a multivariate generalized spectral derivative based approach that delivers a n 0 1 asymptotical null distribution for the test statistic the infinitesimal operator of the diffusion process is a closed form function of drift and diffusion terms consequently my test procedure covers both univariate and multivariate diffusion models in a unified framework and is particularly convenient for the multivariate case moreover different transformed martingale processes contain separate information about the drift and diffusion specifications this motivates me to propose a separate inferential test procedure to explore the sources of rejection when a parametric form is rejected simulation studies show that the proposed tests have reasonable size and excellent power performance an empirical application of my test procedure using eurodollar interest rates finds that most popular short rate models are rejected and the drift misspecification plays an important role in such rejections

relating casl with other specification languages the institution level in this work we investigate various specification languages and their relation to casl the recently developed common algebraic specification language in particular we consider the languages larch obj3 and functional cafeobj act one asf and hep theories as well as various sublanguages of casl all these languages are translated to an appropriate sublanguage of casl the translation mainly concerns the level of specification in the small the logics underlying the languages are formalized as institutions and representations among the institutions are developed however it is also considered how these translations interact with specification in the large thus we obtain on the one hand translations of any of the above mentioned specification languages to an appropriate sublanguage of casl this allows us to take libraries and case studies that have been developed for other languages and re use them in casl on the other hand we set up institution representations going from the casl institution and some of its subinstitutions to simpler subinstitutions given a theorem proving tool for such a simpler subinstitution with the help of a representation it can also be used for a more complex institution thus first order theorem provers and conditional term rewriting tools become usable for casl

on the satisfiability threshold and clustering of solutions of random 3 sat formulas we study the structure of satisfying assignments of a random 3 sat formula in particular we show that a random formula of density a 4 453 almost surely has no non trivial core assignments core assignments are certain partial assignments that can be extended to satisfying assignments and have been studied recently in connection with the survey propagation heuristic for random sat their existence implies the presence of clusters of solutions and they have been shown to exist with high probability below the satisfiability threshold for k sat with k 9 d achlioptas f ricci tersenghi on the solution space geometry of random constraint satisfaction problems in proc 38th acm symp theory of computing stoc 2006 pp 130 139 our result implies that either this does not hold for 3 sat or the threshold density for satisfiability in 3 sat lies below 4 453 the main technical tool that we use is a novel simple application of the first moment method

the equational theory of parameterized specifications abstract equational theorems that are valid in a given parameterized data type can be derived in the inductive theory of the corresponding specification certain syntactical requirements to the specification guarantee that its equational theory agrees with the set of those equations which are satisfied by all consistent models of the specification

random subcubes as a toy model for constraint satisfaction problems we present an exactly solvable random subcube model inspired by the structure of hard constraint satisfaction and optimization problems our model reproduces the structure of the solution space of the random k satisfiability and k coloring problems and undergoes the same phase transitions as these problems the comparison becomes quantitative in the large k limit distance properties as well the x satisfiability threshold are studied the model is also generalized to define a continuous energy landscape useful for studying several aspects of glassy dynamics

is sp bp the survey propagation sp algorithm for solving k sat problems has been shown recently as an instance of the belief propagation bp algorithm in this paper we show that for general constraint satisfaction problems sp may not be reducible from bp we also establish the conditions under which such a reduction is possible along our development we present a unification of the existing sp algorithms in terms of a probabilistically interpretable iterative procedure weighted probabilistic token passing

estimating stochastic volatility diffusion using conditional moments of integrated volatility we exploit the distributional information contained in high frequency intraday data in constructing a simple conditional moment estimator for stochastic volatility diffusions the estimator is based on the analytical solutions of the first two conditional moments for the latent integrated volatility the realization of which is effectively approximated by the sum of the squared high frequency increments of the process our simulation evidence indicates that the resulting gmm estimator is highly reliable and accurate our empirical implementation based on high frequency five minute foreign exchange returns suggests the presence of multiple latent stochastic volatility factors and possible jumps

an improved version of the quandt ramsey mgf estimator for mixtures of normal distributions and switching regressions quandt and ramsey have suggested an estimator for normal mixtures and switching regressions which minimizes a sum of squared differences between empirical and theoretical values of the moment generating function this paper demonstrates how their estimator can be improved by minimizing a generalized sum of squares rather than an ordinary sum of squares when this is done more points of evaluation moments are unambiguously better than less most of the results presented are also applicable to method of moments estimators in general

some fundamental algebraic tools for the semantics of computation part 3 indexed categories abstract this paper presents indexed categories which model uniformly defined families of categories and suggests that they are a useful tool for the working computer scientist an indexed category gives rise to a single flattened category as a disjoint union of its component categories plus some additional morphisms similarly an indexed functor which is a uniform family of functors between the components categories induces a flattened functor between the corresponding flattened categories under certain assumptions flattened categories are co complete if all their components are and flattened functors have left adjoints if all their components do several examples are given although this paper is part 3 of the series some fundamental algebraic tools for the semantics of computation it is entirely independent of parts 1 and 2

behavior of heuristics on large and hard satisfiability problems we study the behavior of a heuristic for solving random satisfiability problems by stochastic local search near the satisfiability threshold the heuristic for average satisfiability asat is si

a semantic approach to interpolation craig interpolation is investigated for various types of formulae by shifting the focus from syntactic to semantic interpolation we generate prove and classify a series of interpolation results for first order logic a few of these results non trivially generalize known interpolation results all the others are new we also discuss some applications of our results to the theory of institutions and of algebraic specifications and a craig robinson version of these results

some fundamental algebraic tools for the semantics of computation part 2 signed and abstract theories les theories algebriques dans le sens de lawvere sont abstraites en ce qui concerne les presentations operation donnee ni equations particulieres ne sont determinees par la classe d isomorphisme d une theorie de ce fait pas meme les rangs ou le nombre total d operations ne sont determines ce degre d abstraction n est pas approprie a la specification des concepts de programmation on a donc donne une signature particuliere

possible sets of autocorrelations and the simplex algorithm the problem of imposing a set of correlations of any order on binary sequences is addressed the entropy of infinitely long sequences obeying such a given set was calculated in previous works using the saddle point method and it was observed that a finite fraction of sets are characterized by a non extensive entropy in this paper the region of finite entropy the allowed region of sets of correlations is found to be a convex hyper polygon in the space of correlation sets using the simplex algorithm outside of this region the simplex solution indicates that sequences obeying the correlations cannot be found therefore the entropy is in particular the boundaries of the allowed region for c1 cm are presented at the boundaries the entropy drops in a first order phase transition fashion and this drop can be explained from a combinatorial point of view finally we observe that the fraction of the volume occupied by allowed correlation sets drops exponentially with the number of correlations imposed and a qualitative explanation of this scaling phenomenon is provided

a method for calculating bounds on the asymptotic covariance matrices of generalized method of moments estimators abstract for many time series estimation problems there is an infinite dimensional class of generalized method of moments estimators that are consistent and asymptotically normal this paper suggests a procedure for calculating the greatest lower bound for the asymptotic covariance matrices of such estimators the analysis focuses on estimation problems in which the data are generated by a stochastic process that is stationary and ergodic the calculation of the bound uses martingale difference approximations as suggested by gordon 1969 and a matrix version of hilbert space methods

maximally flexible solutions of a random k satisfiability formula random k satisfiability k sat is a paradigmatic model system for studying phase transitions in constraint satisfaction problems and for developing empirical algorithms the statistical properties of the random k sat solution space have been extensively investigated but most earlier efforts focused on solutions that are typical here we consider maximally flexible solutions which satisfy all the constraints only using the minimum number of variables such atypical solutions have high internal entropy because they contain a maximum number of null variables which are completely free to choose their states each maximally flexible solution indicates a dense region of the solution space we estimate the maximum fraction of null variables by the replica symmetric cavity method and implement message passing algorithms to construct maximally flexible solutions for single k sat instances

testing for jumps and jump intensity path dependence abstract in this paper we develop a jump test for the null hypothesis that the probability of a jump is zero building on earlier work by ait sahalia 2002 the test is based on realized third moments and uses observations over an increasing time span the test offers an alternative to standard finite time span tests and is designed to detect jumps in the data generating process rather than detecting realized jumps over a fixed time span more specifically we make two contributions first we introduce our largely model free jump test for the null hypothesis of zero jump intensity second under the maintained assumption of strictly positive jump intensity we introduce two self excitement tests for the null of constant jump intensity against the alternative of path dependent intensity these tests have power against autocorrelation in the jump component and are direct tests for hawkes diffusions see e g ait sahalia et al 2015 the limiting distributions of the proposed statistics are analyzed via use of a double asymptotic scheme wherein the time span goes to infinity and the discrete interval approaches zero and the distributions of the tests are normal and half normal the results from a monte carlo study indicate that the tests have reasonable finite sample properties an empirical illustration based on the analysis of 11 stock price series indicates the prevalence of jumps and self excitation

detecting the solution space of vertex cover by mutual determinations and backbones to solve the combinatorial optimization problems especially the minimal vertex cover problem with high efficiency is a significant task in theoretical computer science and many other subjects aiming at detecting the solution space of vertex cover a new structure named mutual determination is defined and discovered for vertex cover on general graphs which results in the emergence of strong correlations among the unfrozen nodes based on the backbones and mutual determinations with node ranks by leaf removal we propose a mutual determination and backbone evolution algorithm to achieve the reduced solution graph which provides a graphical expression of the solution space of vertex cover by this algorithm the whole solution space and detailed structures such as backbones can be obtained strictly when there is no leaf removal core on the given graph compared with the current algorithms the mutual determination and backbone evolution algorithm performs as well as the replica symmetry one in a certain interval but has a small gap higher than the replica symmetric breaking one and has a relatively small error for the exact results the algorithm with the mutual determination provides a new viewpoint to solve vertex cover and understand the organizations of the solution spaces and the reduced solution graph gives an alternative way to catch detailed information of the ground steady states

instrumental variable estimation of nonlinear errors in variables models this paper establishes that instruments enable the identification of nonparametric regression models in the presence of measurement error by providing a closed form solution for the regression function in terms of fourier transforms of conditional expectations of observable variables for parametrically specified regression functions we propose a root n consistent and asymptotically normal estimator that takes the familiar form of a generalized method of moments estimator with a plugged in nonparametric kernel density estimate both the identification and the estimation methodologies rely on fourier analysis and on the theory of generalized functions the finite sample properties of the estimator are investigated through monte carlo simulations

gibbs states and the set of solutions of random constraint satisfaction problems abstract an instance of a random constraint satisfaction problem defines a random subset the set of solutions of a large product space x n the set of assignments we consider two prototypical problem ensembles random k satisfiability and q coloring of random regular graphs and study the uniform measure with support on s as the number of constraints per variable increases this measure first decomposes into an exponential number of pure states clusters and subsequently condensates over the largest such states above the condensation point the mass carried by the n largest states follows a poisson dirichlet process for typical large instances the two transitions are sharp we determine their precise location further we provide a formal definition of each phase transition in terms of different notions of correlation between distinct variables in the problem the degree of correlation naturally affects the performances of many search sampling algorithms empirical evidence suggests that local monte carlo markov chain strategies are effective up to the clustering phase transition and belief propagation up to the condensation point finally refined message passing techniques such as survey propagation may also beat this threshold message passing algorithms phase transitions random graphs

clustering of solutions in the random satisfiability problem using elementary rigorous methods we prove the existence of a clustered phase in the random k sat problem for k geq 8 in this phase the solutions are grouped into clusters which are far away from each other the results are in agreement with previous predictions of the cavity method and give a rigorous confirmation to one of its main building blocks it can be generalized to other systems of both physical and computational interest

empirical likelihood methods based on characteristic functions with applications to levy processes levy processes have been receiving increasing attention in financial modeling one distinctive feature of such models is that their characteristic functions are readily available inference based on characteristic functions is very useful for studying levy processes by incorporating the recent advances in nonparametric approaches empirical likelihood methods based on characteristic functions are developed in this paper for parameter estimation testing a particular parametric class including the presence of a jump component in the levy process and testing for symmetry of a distribution simulation and case studies confirm the effectiveness of the proposed method

efficient estimation and filtering for multivariate jump diffusions abstract this paper develops estimators of the transition density filters and parameters of multivariate jump diffusion models the drift volatility jump intensity and jump magnitude are allowed to be state dependent and non affine it is not necessary to diagonalize the volatility matrix our density and filter estimators converge at the canonical rate typically associated with exact monte carlo estimation our parameter estimators have the same asymptotic distribution as maximum likelihood estimators which are often intractable for the class of models we consider the results of this paper enable the empirical analysis of previously intractable models of asset prices and economic time series

closed form likelihood approximation and estimation of jump diffusions with an application to the realignment risk of the chinese yuan this paper provides closed form likelihood approximations for multivariate jump diffusion processes widely used in finance for a fixed order of approximation the maximum likelihood estimator mle computed from this approximate likelihood achieves the asymptotic efficiency of the true yet uncomputable mle as the sampling interval shrinks this method is used to uncover the realignment probability of the chinese yuan since february 2002 the market implied realignment intensity has increased fivefold the term structure of the forward realignment rate which completely characterizes future realignment probabilities is hump shaped and peaks at mid 2004 the realignment probability responds quickly to economic news releases and government interventions r 2007 elsevier b v all rights reserved

phase transitions in the q coloring of random hypergraphs we study in this paper the structure of solutions in the random hypergraph coloring problem and the phase transitions they undergo when the density of constraints is varied hypergraph coloring is a constraint satisfaction problem where each constraint includes k variables that must be assigned one out of q colors in such a way that there are no monochromatic constraints i e there are at least two distinct colors in the set of variables belonging to every constraint this problem generalizes naturally coloring of random graphs k 2 and bicoloring of random hypergraphs q 2 both of which were extensively studied in past works the study of random hypergraph coloring gives us access to a case where both the size q of the domain of the variables and the arity k of the constraints can be varied at will our work provides explicit values and predictions for a number of phase transitions that were discovered in other constraint satisfaction problems but never evaluated before in hypergraph coloring among other cases we revisit the hypergraph bicoloring problem q 2 where we find that for k 3 and k 4 the colorability threshold is not given by the one step replica symmetry breaking analysis as the latter is unstable towards more levels of replica symmetry breaking we also unveil and discuss the coexistence of two different 1rsb solutions in the case of q 2 k 4 finally we present asymptotic expansions for the density of constraints at which various phase transitions occur in the limit where q and or k diverge

realized laplace transforms for estimation of jump diffusive volatility models a b s t r a c t we develop an efficient and analytically tractable method for estimation of parametric volatility models that is robust to price level jumps the method entails first integrating intra day data into the realized laplace transform of volatility which is a model free estimate of the daily integrated empirical laplace transform of the unobservable volatility the estimation is then done by matching moments of the integrated joint laplace transform with those implied by the parametric volatility model in the empirical application the best fitting volatility model is a non diffusive two factor model where low activity jumps drive its persistent component and more active jumps drive the transient one

testing distributional assumptions using a continuum of moments abstract we propose specification tests for parametric distributions that compare the potentially complex theoretical and empirical characteristic functions using the continuum of moment conditions analogue to an overidentifying restrictions test which takes into account the correlation between influence functions for different argument values we derive its asymptotic distribution for fixed regularization parameter and when this vanishes with the sample size we show its consistency against any deviation from the null study its local power and compare it with existing tests an extensive monte carlo exercise confirms that our proposed tests display good power in finite samples against a variety of alternatives

a new look at survey propagation and its generalizations this article provides a new conceptual perspective on survey propagation which is an iterative algorithm recently introduced by the statistical physics community that is very effective in solving random k sat problems even with densities close to the satisfiability threshold we first describe how any sat formula can be associated with a novel family of markov random fields mrfs parameterized by a real number 0 1 we then show that applying belief propagation a well known message passing technique for estimating marginal probabilities to this family of mrfs recovers a known family of algorithms ranging from pure survey propagation at one extreme e 1 to standard belief propagation on the uniform distribution over sat assignments at the other extreme e 0 configurations in these mrfs have a natural interpretation as partial satisfiability assignments on which a partial order can be defined we isolate cores as minimal elements in this partial ordering which are also fixed points of survey propagation and the only assignments with positive probability in the mrf for e 1 our experimental results for k e 3 suggest that solutions of random formulas typically do not possess non trivial cores this makes it necessary to study the structure of the space of partial assignments for 0 can be viewed as a smoothed version of the uniform distribution over satisfying assignments e 0 finally we isolate properties of gibbs sampling and message passing algorithms that are typical for an ensemble of k sat problems

on fuzzification of topological categories this paper shows that l m fuzzy topology of u hohle t kubiak and a sostak is an instance of a general fuzzification procedure for topological categories which amounts to the construction of a new topological category from a given one this fuzzification procedure motivates a partial dualization of the machinery of tower extension of topological constructs of d zhang thereby providing the procedure of tower extension of topological categories with the help of this dualization we arrive at the meta mathematical result that the concept of l m fuzzy topology and the notion of approach space of r lowen are dual to each other

a quantum lovasz local lemma the lovasz local lemma lll is a powerful tool in probability theory to show the existence of combinatorial objects meeting a prescribed collection of weakly dependent criteria we show that the lll extends to a much more general geometric setting where events are replaced with subspaces and probability is replaced with relative dimension which allows to lower bound the dimension of the intersection of vector spaces under certain independence conditions our result immediately applies to the k qsat problem quantum analog of k sat for instance we show that any collection of rank 1 projectors with the property that each qubit appears in at most 2k e k of them has a joint satisfiable state we then apply our results to the recently studied model of random k qsat recent works have shown that the satisfiable region extends up to a density of 1 in the large k limit where the density is the ratio of projectors to qubits using a hybrid approach building on work by laumann et al 2009 2010 we greatly extend the known satisfiable region for random k qsat to a density of 2k k2 since our tool allows us to show the existence of joint satisfying states without the need to construct them we are able to penetrate into regions where the satisfying states are conjectured to be entangled avoiding the need to construct them which has limited previous approaches to product states

spectral estimation of the fractional order of a levy process we consider the problem of estimating the fractional order of a levy process from low frequency historical and options data an estimation methodology is developed which allows us to treat both estimation and calibration problems in a unified way the corresponding procedure consists of two steps the estimation of a conditional characteristic function and the weighted least squares estimation of the fractional order in spectral domain while the second step is identical for both calibration and estimation the first one depends on the problem at hand minimax rates of convergence for the fractional order estimate are derived the asymptotic normality is proved and a data driven algorithm based on aggregation is proposed the performance of the estimator in both estimation and calibration setups is illustrated by a simulation study

generalized spectral testing for multivariate continuous time models we develop an omnibus specification test for multivariate continuous time models using the conditional characteristic function which often has a convenient closed form or can be accurately approximated for many multivariate continuous time models in finance and economics the proposed test fully exploits the information in the joint conditional distribution of underlying economic processes and hence is expected to have good power in a multivariate context a class of easy to interpret diagnostic procedures is supplemented to gauge possible sources of model misspecification our tests are also applicable to discrete time distribution models simulation studies show that the tests provide reliable inference in finite samples

interpolation in grothendieck institutions it is well known that interpolation properties of logics underlying specification formalisms play an important rule in the study of structured specifications they have also many other useful logical consequences in this paper we solve the interpolation problem for grothendieck institutions which have recently emerged as an important mathematical structure underlying heterogenous multilogic specification our main result can be used in the applications in several different ways it can be used to establish interpolation properties for multi logic grothendieck institutions but also to lift interpolation properties from unsorted logics to their many sorted variants the importance of the latter resides in the fact that unlike other structural properties of logics many sorted interpolation is a non trivial generalisation of unsorted interpolation the concepts results and the applications discussed in this paper are illustrated with several examples from conventional logic and algebraic specification theory

the realized laplace transform of volatility we introduce and derive the asymptotic behavior of a new measure constructed from high frequency data which we call the realized laplace transform of volatility the statistic provides a nonparametric estimate for the empirical laplace transform function of the latent stochastic volatility process over a given interval of time and is robust to the presence of jumps in the price process with a long span of data that is under joint long span and infill asymptotics the statistic can be used to construct a nonparametric estimate of the volatility laplace transform as well as of the integrated joint laplace transform of volatility over different points of time we derive feasible functional limit theorems for our statistic both under fixed span and infill asymptotics as well as under joint long span and infill asymptotics which allow us to quantify the precision in estimation under both sampling schemes

characterizing specification languages which admit initial semantics abstract the paper proposes an axiomatic approach to specification languages and introduces notions of reducibility and equivalence as tools for their study and comparison algebraic specification languages are characterized up to equivalence they are shown to be limited in expressive power by implicational languages

institutional semantics for many valued logics we develop many valued logic including a generic abstract model theory over a fully abstract syntax we show that important many valued logic model theories such as traditional first order many valued logic and fuzzy multi algebras may be conservatively embedded into our abstract framework our development is technically based upon the so called theory of institutions of goguen and burstall and may serve as a template for defining at hand many valued logic model theories over various concrete syntaxes or from another perspective to combine many valued logic with other logical systems we also show that our generic many valued logic abstract model theory enjoys a couple of important institutional model theory properties that support the development of deep model theory methods

pairs of sat assignments in random boolean formulae we investigate geometrical properties of the random k satisfiability problem using the notion of x satisfiability a formula is x satisfiable is there exist two sat assignments differing in nx variables we show the existence of a sharp threshold for this property as a function of the clause density for large enough k we prove that there exists a region of clause density below the satisfiability threshold where the landscape of hamming distances between sat assignments experiences a gap pairs of sat assignments exist at small x and around x 12 but they do not exist at intermediate values of x this result is consistent with the clustering scenario which is at the heart of the recent heuristic analysis of satisfiability using statistical physics analysis the cavity method and its algorithmic counterpart the survey propagation algorithm our method uses elementary probabilistic arguments first and second moment methods and might be useful in other problems of computational and physical interest where similar phenomena appear

functorial theory of parameterized specifications in a general specification framework abstract a general specification framework based on the notion of indexed categories is introduced in order to study the structural aspects of specifications independent of the underlying logics similar to institutions this concept of specification frames allows to formulate a unified structural theory of various kinds of algebraic specifications which have been studied separately in the literature before in contrast to institutions we do not require to have satisfaction relations and conditions which allows to handle also behavioural specifications and semantics and various concepts of constraints in this framework in this framework we generalize the well known theory of parameterized algebraic specifications with initial semantics from the equational case to specification frames satisfying mainly three basic axioms the existence of pushouts free constructions and amalgamation moreover an axiomatic treatment of restriction is presented which allows to study in addition to refinement also implementations of parameterized specifications including restrictions finally we present an axiomatic framework for functorial semantics which opens the way to apply the theory not only to initial semantics but also to other kinds of functorial semantics including final and specific kinds of loose semantics

predictive density construction and accuracy testing with multiple possibly misspecified diffusion models this paper develops tests for comparing the accuracy of predictive densities derived from possibly misspecified diffusion models in particular we first outline a simple simulation based framework for constructing predictive densities for one factor and stochastic volatility models then we construct accuracy assessment tests that are in the spirit of diebold and mariano 1995 and white 2000 in order to establish the asymptotic properties of our tests we also develop a recursive variant of the nonparametric simulated maximum

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

simulated likelihood estimators for discretely observed jump diffusions abstract this paper develops an unbiased monte carlo approximation to the transition density of a jump diffusion process with state dependent drift volatility jump intensity and jump magnitude the approximation is used to construct a likelihood estimator of the parameters of a jump diffusion observed at fixed time intervals that need not be short the estimator is asymptotically unbiased for any sample size it has the same large sample asymptotic properties as the true but uncomputable likelihood estimator numerical results illustrate its properties

estimating stochastic differential equations efficiently by minimum chi squared summary we propose a minimum chi squared estimator for the parameters of an ergodic system of stochastic differential equations with partially observed state we prove that the efficiency of the estimator approaches that of maximum likelihood as the number of moment functions entering the chi squared criterion increases and as the number of past observations entering each moment function increases the minimised criterion is asymptotically chi squared and can be used to test system adequacy when a fitted system is rejected inspecting studentised moments suggests how the fitted system might be modified to improve the fit the method and diagnostic tests are applied to daily observations on the u s dollar to deutschmark exchange rate from 1977 to 1992

phase transitions in the coloring of random graphs we consider the problem of coloring the vertices of a large sparse random graph with a given number of colors so that no adjacent vertices have the same color using the cavity method we present a detailed and systematic analytical study of the space of proper colorings solutions we show that for a fixed number of colors and as the average vertex degree number of constraints increases the set of solutions undergoes several phase transitions similar to those observed in the mean field theory of glasses first at the clustering transition the entropically dominant part of the phase space decomposes into an exponential number of pure states so that beyond this transition a uniform sampling of solutions becomes hard afterward the space of solutions condenses over a finite number of the largest states and consequently the total entropy of solutions becomes smaller than the annealed one another transition takes place when in all the entropically dominant states a finite fraction of nodes freezes so that each of these nodes is allowed a single color in all the solutions inside the state eventually above the coloring threshold no more solutions are available

on the freezing of variables in random constraint satisfaction problems the set of solutions of random constraint satisfaction problems zero energy groundstates of mean field diluted spin glasses undergoes several structural phase transitions as the amount of constraints is increased this set first breaks down into a large number of well separated clusters at the freezing transition which is in general distinct from the clustering one some variables spins take the same value in all solutions of a given cluster in this paper we introduce and study a message passing procedure that allows to compute for generic constraint satisfaction problems the sizes of the rearrangements induced in response to the modification of a variable these sizes diverge at the freezing transition with a critical behavior which is also investigated in details we apply the generic formalism in particular to the random satisfiability of boolean formulas and to the coloring of random graphs the computation is first performed in random tree ensembles for which we underline a connection with percolation models and with the reconstruction problem of information theory the validity of these results for the original random ensembles is then discussed in the framework of the cavity method

foundations of logic programming in hybrid logics with user defined sharing abstract the present contribution advances an abstract notion of hybrid logic by supplementing the definition of institution with an additional structure to extract frames the foundation of logic programming is set in the general framework proposed by defining the basic concepts such as horn clause query and solution and proving fundamental results such as the existence of initial model of horn clauses and herbrand s theorem the abstract results are then applied to hybrid logics with user defined sharing where the possible worlds share a common domain and the variables used for quantification are interpreted uniformly across the worlds

on the efficiency of empirical characteristic function procedures summary the asymptotic normality and arbitrarily high efficiency of some new statistical procedures based on the empirical characteristic function is established under general conditions

on the existence of free models in abstract algebraic institutions abstract to provide a formal framework for discussing specifications of abstract data types we restrict the notion of institution due to goguen and burstall 1984 which formalises the concept of a logical system for writing specifications and deal with abstract algebraic institutions these are institutions equipped with a notion of submodel which satisfy a number of technical conditions our main results concern the problem of the existence of free constructions in abstract algebraic institutions we generalise a characterization of algebraic specification languages that guarantee the existence of reachable initial models for any consistent set of axioms given by mahr and makowsky 1984 then the more general problem of the existence of free functors left adjoints to forgetful functors for any theory morphism is analysed we give a construction of a free model of a theory over a model of a subtheory with respect to an arbitrary theory morphism which requires only the existence of initial models this yields a characterization of strongly liberal abstract algebraic institutions we also show how to specialise there characterisation results for the partial algebras

validating forecasts of the joint probability density of bond yields can affine models beat random walk most existing empirical studies on affine term structure models atsms have mainly focused on in sample goodness of fit of historical bond yields and ignored out of sample forecast of future bond yields using an omnibus nonparametric procedure for density forecast evaluation in a continuous time framework we provide probably the first comprehensive empirical analysis of the out of sample performance of atsms in forecasting the joint conditional probability density of bond yields we find that although the random walk models tend to have better forecasts for the conditional mean dynamics of bond yields some atsms provide better forecasts for the joint probability density of bond yields however all atsms considered are still overwhelmingly rejected by our tests and fail to provide satisfactory density forecasts there exists room for further improving density forecasts for bond yields by extending atsms

on the functional estimation of jump diffusion models abstract we provide a general asymptotic theory for the fully functional estimates of the infinitesimal moments of continuous time models with discontinuous sample paths of the jump diffusion type minimal requirements are placed on the dynamic properties of the underlying jump diffusion process i e stationarity is not required our theoretical framework justifies consistent in a statistical sense nonparametric extraction of the parameters and functions that drive the dynamic evolution of the process of interest i e the potentially nonaffine and level dependent intensity of the jump arrival being an example from the estimated infinitesimal conditional moments as suggested in johannes 2003 the statistical and economic role of jumps in continuous time interest rate models journal of finance forthcoming

an axiomatic approach to structuring specifications in this paper we develop an axiomatic approach to structured specifications in which both the underlying logical system and corresponding institution of the structured specifications are treated as abstract institutions which means two levels of institution independence this abstract axiomatic approach provides a uniform framework for the study of structured specifications independently from any actual choice of specification building operators and moreover it unifies the theory and the model oriented approaches within this framework we develop concepts and results about abstract structured specifications such as co limits model amalgamation compactness interpolation sound and complete proof theory and pushout style parameterization with sharing all of them in a top down manner dictated by the upper level of institution independence

conditional rewriting logic as a unified model of concurrency abstract rewriting with conditional rewrite rules modulo a set e of structural axioms provides a general framework for unifying a wide variety of models of concurrency concurrent rewriting coincides with logical deduction in conditional rewriting logic a logic of actions whose models are concurrent systems this logic is sound and complete and has initial models in addition to general models interpreted as concurrent systems which provide a more operational style of semantics more restricted semantics with an incresingly denotational flavor such as preorder poset cpo and standard algebraic models appear as special cases of the model theory this permits dealing with operational and denotational issues within the same model theory and logic a programming language called maude whose modules are rewriting logic theories is defined and given denotational and operational semantics maude provides a simple unification of concurrent programming with functional and object oriented programming and supports high level declarative programming of concurrent systems

statistical properties and economic implications of jump diffusion processes with shot noise effects abstract the shot noise jump diffusion snjd model aims to reflect how economic variables respond to the arrival of sudden information this paper analyzes the snjd model providing its statistical distribution and closed form expressions for the characteristic function and moments we also analyze the dynamics of the model concluding that the degree of serial autocorrelation is related to the occurrence and magnitude of abnormal information in addition we provide some useful approximations in a particular case that considers exponential type decay empirically we propose a gmm approach to estimate the parameters of the model and present an empirical application for the stocks included in the dow jones averaged index our findings seem to confirm the presence of shot noise effects in 73 of the stocks and a strong relationship between the shot noise process and the autocorrelation pattern embedded in data

the surprise element jumps in interest rates abstract that information surprises result in discontinuous interest rates is no surprise to participants in the bond markets we develop a class of poisson gaussian models of the fed funds rate to capture surprise effects and show that these models offer a good statistical description of short rate behavior and are useful in understanding many empirical phenomena jump poisson processes capture empirical features of the data which would not be captured by gaussian models and there is strong evidence that existing gaussian models would be well enhanced by jump and arch type processes the analytical and empirical methods in the paper support many applications such as testing for fed intervention effects which are shown to be an important source of surprise jumps in interest rates the jump model is shown to mitigate the non linearity of interest rate drifts so prevalent in pure diffusion models day of week effects are modelled explicitly and the jump model provides evidence of bond market overreaction rejecting the martingale hypothesis for interest rates jump models mixed with markov switching processes predicate that conditioning on regime is important in determining short rate behavior

empirical reverse engineering of the pricing kernel abstract this paper proposes an econometric procedure that allows the estimation of the pricing kernel without either any assumptions about the investors preferences or the use of the consumption data we propose a model of equity price dynamics that allows for i simultaneous consideration of multiple stock prices ii analytical formulas for derivatives such as futures options and bonds and iii a realistic description of all of these assets the analytical specification of the model allows us to infer the dynamics of the pricing kernel the model calibrated to a comprehensive dataset including the s p 500 index individual equities t bills and gold futures yields the conditional filter of the unobservable pricing kernel as a result we obtain the estimate of the kernel that is positive almost surely i e precludes arbitrage consistent with the equity risk premium the risk free discounting and with the observed asset prices by construction the pricing kernel estimate involves a highly nonlinear function of the contemporaneous and lagged returns on the s p 500 index this contradicts typical implementations of capm that use a linear function of the market proxy return as the pricing kernel hence the s p 500 index does not have to coincide with the market portfolio if it is used in conjunction with nonlinear asset pricing models we also find that our best estimate of the pricing kernel is not consistent with the standard time separable utilities but potentially could be cast into the stochastic habit formation framework of campbell and cochrane j political economy 107 1999 205