down scaling for better transform compression the most popular lossy image compression method used on the internet is the jpeg standard jpeg s good compression performance and low computational and memory complexity make it an attractive method for natural image compression nevertheless as we go to low bit rates that imply lower quality jpeg introduces disturbing artifacts it is known that at low bit rates a down sampled image when jpeg compressed visually beats the high resolution image compressed via jpeg to be represented by the same number of bits motivated by this idea we show how down sampling an image to a low resolution then using jpeg at the lower resolution and subsequently interpolating the result to the original resolution can improve the overall psnr performance of the compression process we give an analytical model and a numerical analysis of the down sampling compression and up sampling process that makes explicit the possible quality compression trade offs we show that the image auto correlation can provide a good estimate for establishing the down sampling factor that achieves optimal performance given a specific budget of bits we determine the down sampling factor necessary to get the best possible recovered image in terms of psnr

cartan decomposition subgroups of 2 for g sl 3 r and g so 2 n we give explicit practical conditions that determine whether or not a closed connected subgroup h of g has the property that there exists a compact subset c of g with chc g to do this we fix a cartan decomposition g ka k of g and then carry out an approximate calculation of khk n a for each closed connected subgroup h of g

a preparation theorem for weierstrass systems it is shown that lion and rolin s preparation theorem for globally subanalytic functions holds for the collection of definable functions in any expansion of the real ordered field by a weierstrass system

approximate generalizations and computational experiments in this paper i demonstrate how one can generalize finitely many examples to statements about infinite classes of economic models if there exist upper bounds on the number of connected components of one dimensional linear subsets of the set of parameters for which a conjecture is true one can conclude that it is correct for all parameter values in the class considered except for a small residual set once one has verified the conjecture for a predetermined finite set of points i show how to apply this insight to computational experiments and spell out assumptions on the economic fundamentals that ensure that the necessary bounds on the number of connected components exist

closed asymptotic couples the derivation of a hardy field induces on its value group a certain function if a hardy field extends the real field and is closed under powers then its value group is also a vector space over such ordered vector spaces with function are called h couples we define closed h couples and show that every h couple can be embedded into a closed one the key fact is that closed h couples have an elimination theory solvability of an arbitrary system of equations and inequalities built up from vector space operations the function parameters and the unknowns to be solved for is equivalent to an effective condition on the parameters of the system the h couple of a maximal hardy field is closed and this is also the case for the h couple of the field of logarithmic exponential series over we analyze in detail finitely generated extensions of a given h couple

vapnik chervonenkis density in some theories without the independence property ii we study the vapnik chervonenkis vc density of denable families in certain stable rst order theories in particular we obtain uniform bounds on vc density of denable families in nite u rank theories without the nite cover property and we characterize those abelian groups for which there exist uniform bounds on the vc density of denable families

multiplicity of fixed points and growth of e neighborhoods of orbits abstract we study the relationship between the multiplicity of a fixed point of a function g and the dependence on e of the length of e neighborhood of any orbit of g tending to the fixed point the relationship between these two notions was discovered in elezovic ubrinic and upanovic 2007 5 in the differentiable case and related to the box dimension of the orbit here we generalize these results to non differentiable cases introducing a new notion of critical minkowski order we study the space of functions having a development in a chebyshev scale and use multiplicity with respect to this space of functions with the new definition we recover the relationship between multiplicity of fixed points and the dependence on e of the length of e neighborhoods of orbits in non differentiable cases applications include in particular poincare maps near homoclinic loops and hyperbolic 2 cycles and abelian integrals this is a new approach to estimate the cyclicity by computing the length of the e neighborhood of one orbit of the poincare map for example numerically and by comparing it to the appropriate scale

relational queries over interpreted structures we rework parts of the classical relational theory when the underlying domain is a structure with some interpreted operations that can be used in queries we identify parts of the classical theory that go through as before when interpreted structure is present parts that go through only for classes of nicely behaved structures and parts that only arise in the interpreted case the first category include a number of results on language equivalence and expressive power characterizations for the active domain semantics for a variety of logics under this semantics quantifiers range over elements of a relational database the main kind of results we prove here are generic collapse results for generic queries adding operations beyond order does not give us extra power the second category includes results on the natural semantics under which quantifiers range over the entire interpreted structure we prove for a variety of structures natural active collapse results showing that using unrestricted quantification does not give us any extra power moreover for a variety of structures including the real field we give a set of algorithms for eliminating unbounded quantifications in favor of bounded ones furthermore we extend these collapse results to a new class of higher order logics that mix unbounded and bounded quantification we give a set of normal forms for these logics under special conditions on the interpreted structures as a by product we obtain an elementary proof of the fact that parity test is not definable in the relational calculus with polynomial inequality constraints we also give examples of structures with nice model theoretic properties over which the natural active collapse fails

the topology of locales and its effects on position uncertainty the precision to which the position of a target in a digital image can be estimated may be analyzed by considering the possible digital representations of the target such an analysis leads to regions of indistinguishable target position referred to as locales by considering the density distribution and shape of these locales the available precision can be estimated previously such analyses have presumed an absence of noise in the digital image it is shown how the noise tolerance for position estimation is affected by the topological properties of locales such as locale connectivity adjacency and clustering

integrability of oscillatory functions on local fields transfer principles for oscillatory functions on local fields coming from motivic exponential functions we show that integrability over q n p implies integrability over f p t n for large p and vice versa more generally the integrability only depends on the isomorphism class of the residue field of the local field once the characteristic of the residue field is large enough this principle yields general local integrability results for harish chandra characters in positive characteristic as we show in other work transfer principles for related conditions such as boundedness and local integrability are also obtained the proofs rely on a thorough study of loci of integrability to which we give a geometric meaning by relating them to zero loci of functions of a specific kind

definable sets in ordered structures i this paper introduces and begins the study of a well behaved class of linearly ordered structures the minimal structures the definition of this class and the corresponding class of theories the strongly dlminlmal theories is made in analogy with the notions from stability theory of minimal structures and strongly minimal theories theorems 2 1 and 2 3 respectively provide characterizations of 41 minimal ordered groups and rings several other simple results are collected in 3 the primary tool in the analysis of minimal structures is a strong analogue of ii forking symmetry given by theorem 4 2 this result states that any parametri cally definable unary function in an yminimal structure is piecewise either constant or an ore er preserving or reversing bijection of intervals the results that follow include the existence and uniqueness of prime models over sets theorem 5 1 and a characterization of all bto categorical aminimal structures theorem 6 1 1 introduction the class of linearly ordered structures has long been an im portant subject of concern to model theorists impressive results have been obtained in the study of models of several particular theories that extend the theory of linear order among those theories that have been approached successfully are peano arithmetic the theory of ordered abelian groups that of real closed fields and that of linear order itself yet very little has been done in the way of developing a general model theory for ordered structures in this paper we develop the model theory for a class of linearly ordered structures that we isolate by demanding that a structure in this class satisfy a condition whose effect is that the linear ordering and the algebraic part of the structure behave quite well with respect to one another let l be a finitary first order language and w an l structure a set of n tuples a c x is said to be parametrically definable if there is some l formula

towers of complements to valuation rings and truncation closed embeddings of valued fields abstract we study necessary and sufficient conditions for a valued field k with value group g and residue field k with char k char k to admit a truncation closed embedding in the field of generalized power series k g f with factor set f we show that this is equivalent to the existence of a family tower of complements of k subspaces of k which are complements of the possibly fractional ideals of the valuation ring and satisfying certain natural conditions if k is a henselian field of characteristic 0 or more generally an algebraically maximal kaplansky field we give an intrinsic construction of such a family which does not rely on a given truncation closed embedding we also show that towers of complements and truncation closed embeddings can be extended from an arbitrary field to at least one of its maximal immediate extensions

the differential rank of a differential valued field we develop a notion of principal differential rank for differential valued fields in analog of the exponential rank developed in kuhlmann the fields institute monograph series 12 2000 and of the difference rank developed in kuhlmann groups modules and model theory surveys and recent developments in memory of rdiger gbel pp 399 414 2017 we give several characterizations of this rank we then give a method to define a derivation on a field of generalized power series and use this method to show that any totally ordered set can be realized as the principal differential rank of a h field

the field of reals with multisummable series and the exponential function we show that the field of real numbers with multisummable real power series is model complete o minimal and polynomially bounded further expansion by the exponential function yields again a model complete and o minimal structure which is exponentially bounded and in which the gamma function on the positive real line is definable 2000 mathematics subject classification primary 03c10 32b05 32b20 secondary 26e05

on optimal image digitization nielsen et al recently addressed the problem of determining the optimal discretization grid and quantization depth when a given bivariate function f x y has to be described with a predetermined number of bits this was done under the assumption that the function value range and mean fluctuation rates in the x and y direction are given and that ideal point sampling with zero order hold interpolation is used in reconstructing the image this correspondence outlines an alternative approach based on the assumption that f x y is the sample function of a 2 d stationary stochastic process with a known covariance function we use standard integral sampling and obtain closed form solutions under the assumption that f x y is the sample of a homogeneous and separable markov process

hardy type derivations on generalised series fields abstract we consider the valued field k r of generalised series with real coefficients and monomials in a totally ordered multiplicative group we investigate how to endow k with a series derivation that is a derivation that satisfies some natural properties such as commuting with infinite sums strong linearity and an infinite version of leibniz rule we characterise when such a derivation is of hardy type that is when it behaves like differentiation of germs of real valued functions in a hardy field we provide a necessary and sufficient condition for a series derivation of hardy type to be surjective

definable sets in ordered structures on introduit la notion de theorie o minimale des structures ordonnees une telle theorie etant telle que les sous ensembles definissables de ses modeles soient particulierement simples

differential galois theory of linear difference equations we present a galois theory of difference equations designed to measure the differential dependencies among solutions of linear difference equations with this we are able to reprove holder s theorem that the gamma function satisfies no polynomial differential equation and are able to give general results that imply for example that no differential relationship holds among solutions of certain classes of q hypergeometric equations

o minimal hauptvermutung for polyhedra i milnor discovered two compact polyhedra which are homeomorphic but not pl homeomorphic a counterexample to the hauptvermutung he constructed the homeomorphism by a finite procedure repeated infinitely often informally we call a procedure constructive if it consists of an explicit procedure that is repeated only finitely many times in this sense milnor did not give a constructive procedure to define the homeomorphism between the two polyhedra in the case where the homeomorphism is semialgebraic the author and yokoi proved that the polyhedra in r n are pl homeomorphic in that article the required pl homeomorphism was not constructively defined from the given homeomorphism in the present paper we obtain the pl homeomorphism by a constructive procedure starting from the homeomorphism we prove in fact that for any ordered field r equipped with any o minimal structure two definably homeomorphic compact polyhedra in r n are pl homeomorphic the o minimal hauptvermutung theorem 1 1 together with the fact that any compact definable set is definably homeomorphic to a compact polyhedron we can say that o minimal topology is tame

ilyashenko algebras based on transserial asymptotic expansions abstract we construct a hardy field that contains ilyashenko s class of germs at of almost regular functions found in 12 as well as all log exp analytic germs this implies non oscillatory behaviour of almost regular germs with respect to all log exp analytic germs in addition each germ in this hardy field is uniquely characterized by an asymptotic expansion that is an le series as defined by van den dries et al 7 as these series generally have support of order type larger than the notion of asymptotic expansion itself needs to be generalized

generalized markoff maps and mcshane s identity abstract we study the relative sl 2 c character varieties of the one holed torus and the action of the mapping class group on the relative character variety we show that the subset of characters satisfying two simple conditions called the bowditch q conditions is open in the relative character variety and that the mapping class group acts properly discontinuously on this subset furthermore this is the largest open subset for which this holds we also show that a generalization of mcshane s identity holds for all characters satisfying the bowditch q conditions finally we show that further variations of the mcshane bowditch identity hold for characters which are fixed by an anosov element of the mapping class group and which satisfy a relative version of the bowditch q conditions with applications to identities for incomplete hyperbolic structures on punctured torus bundles over the circle and also for closed hyperbolic 3 manifolds which are obtained by hyperbolic dehn surgery on such manifolds

projective structures with degenerate holonomy and the bers density conjecture we prove the bers density conjecture for singly degenerate kleinian surface groups without parabolics

the degeneration of convex ℝℙ2 structures on surfaces let m be a compact surface of negative euler characteristic and let c m be the deformation space of convex real projective structures on m with positive hyperbolic holonomy for every choice of pants decomposition for m there is a well known parameterization of c m known as the goldman parameterization in this paper we study how some geometric properties of the real projective structure on m degenerate as we deform it so that the internal parameters of the goldman parameterization leave every compact set while the boundary invariants remain bounded away from zero and infinity

a game theoretic approach to fault diagnosis and identification of hybrid systems physical systems can fail for this reason the problem of identifying and reacting to faults has received a lot of attention in the control and computer science communities in this paper we study the fault diagnosis problem for hybrid systems from a game theoretical point of view a hybrid system is a system mixing continuous and discrete behaviours that cannot be faithfully modelled neither by using a formalism with continuous dynamics only nor by a formalism including only discrete dynamics we model hybrid systems as hybrid automata and add distinguished actions to describe faults we define a fault identification game on them using two players the environment and the identifier the environment controls the evolution of the system and chooses whether and when a fault occurs the identifier observes the external behaviour of the system and announces whether a fault has occurred or not existence of a winning strategy for the identifier implies that faults can be detected correctly while computing such a winning strategy corresponds to implementing an identifier for the system we will show how to determine the existence of a winning strategy and how to compute it for all decidable classes of hybrid automata that admit a finite bisimulation quotient

comparison theorems for o minimal singular co homology fct grant sfrh bpd 6015 2001 european research and training network hprn ct 2001 00271 raag

the real field with convergent generalized power series we construct a model complete and o minimal expansion of the field of real numbers in which each real function given on 0 1 by a series cnxn with 0 n and cn r n 1 is definable this expansion is polynomially bounded

the six grothendieck operations on o minimal sheaves in this paper we develop the formalism of the grothendieck six operations on o minimal sheaves the grothendieck formalism allows us to obtain o minimal versions of i derived projection formula ii universal coefficient formula iii derived base change formula iv kunneth formula v local and global verdier duality

quasiconformal homeomorphisms and dynamics ii structural stability implies hyperbolicity for kleinian groups sous groupe de psl 2 c familles holomorphes d homeomorphismes de c lemme champs de ligne invariants familles holomorphes de groupes abstraitement isomorphes car finiment genere la stabilite structurelle implique geometriquement fini ou rigide theoreme a avec paraboles stabilite structurelle au sens de la dynamique differentiable

characteristic cycles of constructible sheaves in his paper k kashiwara introduced the notion of characteristic cycle for complexes of constructible sheaves on manifolds let x be a real analytic manifold and f a complex of sheaves of c vector spaces on x whose cohomology is constructible with respect to a subanalytic strati cation the characteristic cycle cc f is a subanalytic lagrangian cycle with in nite support and with values in the orientation sheaf of x in the cotangent bundle t x the de nition of cc f is morse theoretic heuristically cc f encodes the in nitesimal change of the euler characteristic of the stalks of f along the various directions in x it tends to be di cult in practice to calculate cc f explicitly for all but the simplest complexes f on the other hand the characteristic cycle construction has good functorial properties the behavior of cc f with respect to the operations of proper direct image verdier duality and non characteristic inverse image of f is well understood ks in this paper we describe the e ect of the operation of direct image by an open embedding combining our result with those that were previously known we obtain descriptions of cc rf f and cc f f analogous to those in ks for arbitrary morphisms f x y in the semi algebraic category and complexes f with semi algebraically constructible cohomology in e ect this provides an axiomatic characterization of the functor cc at least in the semi algebraic context our arguments do apply more generally in the subanalytic case but because statements become quite convoluted we shall not strive for the greatest degree of generality as a concrete application we consider the case of the ag manifold x of a complex semisimple lie algebra g here the weyl group w of g operates

ax lindemann for mathcal a _g we prove the ax lindemann theorem for the coarse moduli space a g of principally polarized abelian varieties of dimension g 1 we affirm the andre oort conjecture unconditionally for a g for g 6 and under grh for all g

hyperbolic structures on 3 manifolds i deformation of acylindrical manifolds this is the first in a series of papers showing that haken manifolds have hyperbolic structures this first was published the second two have existed only in preprint form and later preprints were never completed this eprint is only an approximation to the published version which is the definitive form for part i and is provided for convenience only all references and quotations should be taken from the published version since the theorem numbering is different and not all corrections have been incorporated into the present version parts ii and iii will be made available as eprints shortly

quasi isometric classification of graph manifold groups we show that the fundamental groups of any two closed irreducible nongeometric graph manifolds are quasi isometric we also classify the quasi isometry types of fundamental groups of graph manifolds with boundary in terms of certain finite twocolored graphs a corollary is the quasi isometric classification of artin groups whose presentation graphs are trees in particular any two right angled artin groups whose presentation graphs are trees of diameter greater than 2 are quasi isometric further this quasi isometry class does not include any other right angled artin groups a finitely generated group can be considered geometrically when endowed with a word metric up to quasi isometric equivalence such metrics are unique in this article only finitely generated groups are considered given a collection of groups g gromov 11 proposed the fundamental questions of identifying which groups are quasi isometric to those in g rigidity and which groups in g are quasi isometric to each other classification in this article we focus on the classification question for graph manifold groups and right angled artin groups a compact 3 manifold m is called geometric if m m admits a geometric structure in the sense of thurston i e a complete locally homogeneous riemannian metric of finite volume thurston s geometrization conjecture see 29 17 21 23 22 provides that every irreducible 3 manifold of zero euler characteristic i e with boundary consisting only of tori and klein bottles admits a decomposition along tori and klein bottles into geometric pieces the minimal such decomposition being called the geometric decomposition there is a considerable literature on quasi isometric rigidity and classification of 3 manifold groups the rigidity results can be briefly summarized in the following form

a hardy field extension of szemeredi s theorem abstract in 1975 szemeredi proved that a set of integers of positive upper density contains arbitrarily long arithmetic progressions bergelson and leibman showed in 1996 that the common difference of the arithmetic progression can be a square a cube or more generally of the form p n where p n is any integer polynomial with zero constant term we produce a variety of new results of this type related to sequences that are not polynomial we show that the common difference of the progression in szemeredi s theorem can be of the form n where is any positive real number and x denotes the integer part of x more generally the common difference can be of the form a n where a x is any function that is a member of a hardy field and satisfies a x x k and a x x k 1 0 for some non negative integer k the proof combines a new structural result for hardy sequences techniques from ergodic theory and some recent equidistribution results of sequences on nilmanifolds

isomorphism theorem for bss recursively enumerable sets over real closed fields the main result of this paper lies in the framework of bss computability it shows roughly that any recursively enumerable set s in rn n where r is a real closed field is isomorphic to rdims by a bijection which is decidable over s moreover the map s is computable some related matters are also considered like characterization of the real closed fields with a r e set of infinitesimals and the dimension of r e sets

the rational points of a definable set let x r n be a set that is definable in an o minimal structure over r this article shows that in a suitable sense there are very few rational points of x which do not lie on some connected semialgebraic subset of x of positive dimension

convergence of freely decomposable kleinian groups we consider a compact orientable hyperbolic 3 manifold with a compressible boundary suppose that we are given a sequence of geometrically finite hyperbolic metrics whose conformal boundary structures at infinity diverge to a projective lamination we prove that if this limit projective lamination is doubly incompressible then the sequence has compact closure in the deformation space as a consequence we generalise thurston s double limit theorem and solve his conjecture on convergence of function groups affirmatively

on the density of geometrically finite kleinian groups the density conjecture of bers sullivan and thurston predicts that each complete hyperbolic 3 manifold m with finitely generated fundamental group is an algebraic limit of geometrically finite hyperbolic 3 manifolds we prove that the conjecture obtains for each complete hyperbolic 3manifold with no cusps and incompressible ends

growth properties of functions in hardy fields this paper continues the author s earlier work on the notion of rank in a hardy field further results are given on functions in hardy fields of finite rank including extensions of hardy s results on the rates of growth of his logarithmicoexponential functions 1 comparability classes nonzero elements a b of an ordered abelian group are called comparable if there are positive integers m n such that mlal iilt and n1 i1 lal nonzero elements f g of a hardy field k are accordingly called comparable if both lim f x and limxx g x are 0 or no and their rates of approach to 0 or xo or xo as x no are comparable that is if the nonzero elements v f v g of the value group v k of k are comparable as in 5 3 we assume some familiarity with 5 whose notation we employ more generally germs f g of continuous real valued functions on positive half lines in r which are nowhere zero on some half line and are such that lim x x f x and lim x x g x are either 0 or no or o will be called comparable if on some half line each of if l lgl is bounded above and below by suitable integral powers of the other comparability is an equivalence relation among such germs in particular comparability is an equivalence relation among all nonzero elements f of hardy fields with the property that lim5 f x is one of 0 oo or oo that is among all nonzero elements f such that v f 0 for f a germ of a nowhere zero continuous real valued function on a positive half line that approaches 0 oo or oo as x no denote the comparability class of f by cl f noting that f f 1 f and 1 f are comparable and that precisely one of these is infinitely increasing that is approaches no we define cl f cl v if and only if v u u v v v which holds if and only if v log u v log v received by the editors september 20 1985 1980 mathematics subject classification 1985 revision primary 34e05 41a60 secondary 12h05 13n05 26a12 research supported by national science foundation grant number dms 8303286 31987 american mathematical society 0002 9947 87 1 00 25 per page

an exact solution of the analytic equation of image quality from optimum quantization of microwave imaging data an exact solution is presented of the analytic equation of image quality in terms of the entropy of the quantized aperture data previously published work provides an optimum quantization scheme that obtains the best image quality for a given distribution of complex aperture data and a given number of bits into which each complex data sample is to be quantized an extension is provided to determine the number of bits required of the quantized signal for the image to achieve a given quality or conversely what quality of image can be obtained for a given number of quantized levels it is shown that the theory imposes substantially no constraints on the distributions of amplitude and phase in the microwave data it is also shown that the optimum quantization design derived from the theory is nearly scene independent and may achieve real time performance

a theory of the effect of hard limiting and other distortions upon the quality of microwave images this paper adds quantitative confirmation to the assertions of previous writers that the phase of the signal received in the aperture contains the preponderance of the information useful for image formation an easily calculable metric is established for judging the extent of the alteration of an image due to an arbitrary distortion of the signal in the aperture or of the imaging kernel in the signal processor given some known or measurable amplitude or phase nonlinearity in the detector at the front end of the measurement system it is possible to judge whether such nonlinearity is tolerable or whether it must be removed subjective viewing tests confirm the validity of the metric high angular resolution microwave images are used to test the theory it is demonstrated that hard limiting the input signals to a phased array preserves much of the image integrity amplitude only information on the other hand destroys it only one bit of phase information sometimes suffices two bits of signal phase and 2 bit phase quantization of the exponential kernel in the signal processor results in an extraordinarily simple signal processor that produces surprisingly good imagery

transseries as germs of surreal functions we show that ecalle s transseries and their variants le and el series can be interpreted as functions from positive infinite surreal numbers to surreal numbers the same holds for a much larger class of formal series here called omega series omega series are the smallest subfield of the surreal numbers containing the reals the ordinal omega and closed under the exp and log functions and all possible infinite sums they form a proper class can be composed and differentiated and are surreal analytic the surreal numbers themselves can be interpreted as a large field of transseries containing the omega series but unlike omega series they lack a composition operator compatible with the derivation introduced by the authors in an earlier paper

the classification of kleinian surface groups ii the ending lamination conjecture thurston s ending lamination conjecture states that a hyperbolic 3manifold n with nitely generated fundamental group is uniquely determined by its topological type and its end invariants in this paper we prove this conjecture for kleinian surface groups the general case when n has incompressible ends relative to its cusps follows readily the main ingredient is a uniformly bilipschitz model for the quotient of h 3 by a kleinian surface group

the curious moduli spaces of unmarked kleinian surface group fixing a closed hyperbolic surface s we define a moduli space rm a cal i s of unmarked hyperbolic 3 manifolds homotopy equivalent to s this 3 dimensional analogue of the moduli space cal m s of unmarked hyperbolic surfaces homeomorphic to s has bizarre local topology possessing many points that are not closed there is however a natural embedding iota cal m s rightarrow rm a cal i s and compactification rm a overline cal i s such that iota extends to an embedding of the deligne mumford compactification overline cal m s rightarrow rm a overline cal i s

a note on divisible points of curves let c be an irreducible algebraic curve defined over a number field and inside an algebraic torus of dimension at least 3 we partially answer a question posed by levin on points on c for which a non trivial power lies again on c our results have connections to zilber s conjecture on intersections with tori and yield to methods arising in transcendence theory and the theory of o minimal structures

optimal digitization of 2 d images the problem of representing an image by m n samples with b bits sample subject to the constraint of a fixed total number of bits is discussed reasonable assumptions are made in such a way that the optimization problem has a closed form solution the solution is tested experimentally and agrees well with human perception of visual quality the analytical solution brings out the dependence of the optimal digitization on image characteristics very clearly the results explain and agree with results of other subjective tests

h fields and their liouville extensions we introduce h fields as ordered differential fields of a certain kind hardy fields extending mathbb r as well as the field of logarithmic exponential series over mathbb r are h fields we study liouville extensions in the category of h fields as a step towards a model theory of h fields the main result is that an h field has at most two liouville closures

tropical varieties for exponential sums we study the complexity of approximating complex zero sets of certain n variate exponential sums we show that the real part r of such a zero set can be approximated by the n 1 dimensional skeleton t of a polyhedral subdivision of mathbb r n in particular we give an explicit upper bound on the hausdorff distance delta r t o left t 3 5 delta right where t and delta are respectively the number of terms and the minimal spacing of the frequencies of g on the side of computational complexity we show that even the n 2 case of the membership problem for r is undecidable in the blum shub smale model over mathbb r whereas membership and distance queries for our polyhedral approximation t can be decided in polynomial time for any fixed n

three dimensional manifolds kleinian groups and hyperbolic geometry 1 a conjectural picture of 3 manifolds a major thrust of mathematics in the late 19th century in which poincare had a large role was the uniformization theory for riemann surfaces that every conformai structure on a closed oriented surface is represented by a riemannian metric of constant curvature for the typical case of negative euler characteristic genus greater than 1 such a metric gives a hyperbolic structure any small neighborhood in the surface is isometric to a neighborhood in the hyperbolic plane and the surface itself is the quotient of the hyperbolic plane by a discrete group of motions the exceptional cases the sphere and the torus have spherical and euclidean structures three manifolds are greatly more complicated than surfaces and i think it is fair to say that until recently there was little reason to expect any analogous theory for manifolds of dimension 3 or more except perhaps for the fact that so many 3 manifolds are beautiful the situation has changed so that i feel fairly confident in proposing the

counting special points logic diophantine geometry and transcendence theory we expose a theorem of pila and wilkie on counting rational points in sets definable in o minimal structures and some applications of this theorem to problems in diophantine geometry due to masser peterzil pila starchenko and

relational expressive power of constraint query languages the expressive power of first order query languages with several classes of equality and inequality constraints is studied in this paper we settle the conjecture that recursive queries such as parity test and transitive closure cannot be expressed in the relational calculus augmented with polynomial inequality constraints over the reals furthermore noting that relational queries exhibit several forms of genericity we establish a number of collapse results of the following form the class of generic boolean queries expressible in the relational calculus augmented with a given class of constraints coincides with the class of queries expressible in the relational calculus with or without an order relation we prove such results for both the natural and active domain semantics as a consequence the relational calculus augmented with polynomial inequalities expresses the same classes of generic boolean queries under both the natural and active domain semantics in the course of proving these results for the active domin semantics we establish ramsey type theorems saying that any query involving certain kinds of constraints coincides with a constraint free query on databases whose elements come from a certain infinite subset of the domain to prove the collapse results for the natural semantics we make use of techniques from nonstandard analysis and from the model theory of ordered structures

hardy type derivations on fields of exponential logarithmic series abstract we consider the valued field k r of formal series with real coefficients and monomials in a totally ordered multiplicative group we investigate how to endow k with a logarithm l which satisfies some natural properties such as commuting with infinite products of monomials we studied derivations on k kuhlmann and matusinski in press km10 here we investigate compatibility conditions between the logarithm and the derivation i e when the logarithmic derivative is the derivative of the logarithm we analyze sufficient conditions on a given derivation to construct a compatible logarithm via integration of logarithmic derivatives in kuhlmann 2000 kuh00 the first author described the exponential closure k el of k l here we show how to extend such a log compatible derivation on k to k el

the asymptotic couple of the field of logarithmic transseries abstract the derivation on the differential valued field t log of logarithmic transseries induces on its value group log a certain map the structure log is a divisible asymptotic couple we prove that the theory t log th log admits elimination of quantifiers in a natural first order language all models of t log have an important discrete subset 0 we give explicit descriptions of all definable functions on and prove that is stably embedded in

inclusion dynamics hybrid automata hybrid systems are dynamical systems with the ability to describe mixed discrete continuous evolution of a wide range of systems consequently at first glance hybrid systems appear powerful but recalcitrant neither yielding to analysis and reasoning through a purely continuous time modeling as with systems of differential equations nor open to inferential processes commonly used for discrete state transition systems such as finite state automata a convenient and popular model called hybrid automata was introduced to model them and has spurred much interest on its tractability as a tool for inference and model checking in a general setting intuitively a hybrid automaton is simply a finite state automaton with each state augmented by continuous variables which evolve according to a set of well defined continuous laws each specified separately for each state this article investigates both the notion of hybrid automaton and the model checking problem over such a structure in particular it relates first order theories and analysis results on multivalued maps and reduces the bounded reachability problem for hybrid automata whose continuous laws are expressed by inclusions x f x t to a decidability problem for first order formulaeover the reals furthermore the paper introduces a class of hybrid automata for which the reachability problem can be decided and shows that the problem of deciding whether a hybrid automaton belongs to this class can be again decided using first order formulaeover the reals despite the fact that the bisimulation quotient for this class of hybrid automata can be infinite we show that our techniques permit effective model checking for a nontrivial fragment of ctl

schubert calculus on the grassmannian of hermitian lagrangian spaces abstract with an eye towards index theoretic applications we describe a schubert like stratification on the grassmannian of hermitian lagrangian spaces in c n c n this is a natural compactification of the space of hermitian n n matrices the closures of the strata define integral cycles and we investigate their intersection theoretic properties we achieve this by blending morse theoretic ideas with techniques from o minimal or tame geometry and geometric integration theory

markoff triples and quasifuchsian groups we study the global behaviour of trees of markoff triples over the complex numbers we relate this to the space of type preserving representations of the punctured torus group into psl 2 c in particular we explore which markoff triples correspond to quasifuchsian representations we derive a variation of mcshane s identity for quasifuchsian groups in the case of non discrete representations we attempt to relate the asymptotic behaviour of markoff triples to the realisability of laminations in hyperbolic 3 space we also consider how some of these issues might be related for more general surfaces

o minimality and the andre oort conjecture for mathbb c n we give an unconditional proof of the andre oort conjecture for arbitrary products of modular curves we establish two generalizations the first includes the manin mumford conjecture for arbitrary products of elliptic curves defined over q as well as lang s conjecture for torsion points in powers of the multiplicative group the second includes the manin mumford conjecture for abelian varieties defined over q our approach uses the theory of o minimal structures a part of model theory and follows a strategy proposed by zannier and implemented in three recent papers a new proof of the manin mumford conjecture by pila zannier a proof of a special but new case of pink s relative manin mumford conjecture by masser zannier and new proofs of certain known results of andre oort manin mumford type by pila 2010 mathematics subject classification 11g18 03c64