characteristic submanifold theory and toroidal dehn filling the exceptional dehn filling conjecture of the second author concerning the re lationship between exceptional slopes on the boundary of a hyperbolic knot manifold m has been verified in all cases other than small seifert filling slopes in this paper we verify it whenis a small seifert filling slope andis a toroidal filling slope in the generic case where m admits no punctured torus fibre or semi fibre and there is no incompressible torus in m which intersects m in one or two components under these hypotheses we show that 5 our proof is based on an analysis of the relationship between the topology of m the combinatorics of the intersection graph of an immersed disk or torus in m and the two sequences of characteristic subsurfaces associated to an essential punctured torus properly embedded in m

lens spaces and toroidal dehn fillings we show that if m is a hyperbolic 3 manifold with m a torus such that m r 1 is a lens space and m r 2 is toroidal then r 1 r 2 4

knot floer homology detects fibred knots ozsvath and szabo conjectured that knot floer homology detects fibred knots in s 3 we will prove this conjecture for null homologous knots in arbitrary closed 3 manifolds namely if k is a knot in a closed 3 manifold y y k is irreducible and hat hfk y k is monic then k is fibred the proof relies on previous works due to gabai ozsvath szabo ghiggini and the author a corollary is that if a knot in s 3 admits a lens space surgery then the knot is fibred

nonextensive entropies from information content and stabilities abstract we consider a family of nonextensive entropies derived from information contents which are a basic ingredient in information theory to give a deeper insight into a certain class of stability of generalized entropies and into recent discussion on it we present a criterion for stability which is satisfied by a minimum discrepancy against infinitesimal shift of distributions

on culler shalen seminorms and dehn filling if f is a finitely generated discrete group and g a complex algebraic lie group the g character variety of r is an affine algebraic variety whose points correspond to characters of representations of r with values in g marc culler and peter shalen developed the theory of sl2 c character varieties of finitely generated groups and applied their results to study the topology of 3 dimensional manifolds in the papers 6 7 8 consider the exterior m of a hyperbolic knot lying in a closed connected orientable 3 manifold the mostow rigidity theorem implies that the holonomy representation p iri m isom h3 psl2 c is unique up to conjugation and taking complex conjugates the orientability of m can be used to show 1 lifts to a representation p e hom ri m sl2 c whose character determines an essentially unique point of xp of x iri m the sl2 c character variety of irl m culler and shalen 8 proved that the component x0 of x x1ri m which contains x is a curve one of their major contributions was to show how x0 determines a norm on h1 wm r which encodes many topological properties of m in particular it provides information on the dehn fillings of m their construction may be applied to arbitrary curves in the sl2 c character variety of a connected compact orientable irreducible 3manifold whose boundary is a torus though in this generality one can only guarantee that it will define a seminorm the first half of this paper is devoted to the development of the general theory of culler shalen seminorms defined for curves of psl2 c characters by working over psl2 c we obtain a theory that is more generally applicable than its sl2 c counterpart while being only mildly more difficult to set up in the second half of this paper we apply the theory of culler shalen seminorms to study the dehn filling operation in particular we examine the relationship between fillings which yield manifolds having a positive dimen

scaling theorems for zero crossings we characterize some properties of the zero crossings of the laplacian of signals in particular images filtered with linear filters as a function of the scale of the filter extending recent work by witkin 16 we prove that in any dimension the only filter that does not create generic zero crossings as the scale increases is the gaussian this result can be generalized to apply to level crossings of any linear differential operator it applies in particular to ridges and ravines in the image intensity in the case of the second derivative along the gradient there is no filter that avoids creation of zero crossings unless the filtering is performed after the derivative is applied

biorthogonal bases of compactly supported wavelets orthonormal bases of compactly supported wavelet bases correspond to subband coding schemes with exact reconstruction in which the analysis and synthesis filters coincide we show here that under fairly general conditions exact reconstruction schemes with synthesis filters different from the analysis filters give rise to two dual riesz bases of compactly supported wavelets we give necessary and sufficient conditions for biorthogonality of the corresponding scaling functions and we present a sufficient condition for the decay of their fourier transforms we study the regularity of these biorthogonal bases we provide several families of examples all symmetric corresponding to linear phase filters in particular we can construct symmetric biorthogonal wavelet bases with arbitrarily high preassigned regularity we also show how to construct symmetric biorthogonal wavelet bases close to a nonsymmetric orthonormal basis

a hardware algorithm for modular multiplication division a mixed radix 4 2 algorithm for modular multiplication division suitable for vlsi implementation is proposed the algorithm is based on montgomery method for modular multiplication and on the extended binary gcd algorithm for modular division both algorithms are modified and combined into the proposed algorithm so that almost all the hardware components are shared the new algorithm carries out both calculations using simple operations such as shifts additions and subtractions the radix 2 signed digit representation is used to avoid carry propagation in all additions and subtractions a modular multiplier divider based on the algorithm performs an n bit modular multiplication division in o n clock cycles where the length of the clock cycle is constant and independent of n the modular multiplier divider has a linear array structure with a bit slice feature and can be implemented with much smaller hardware than that necessary to implement both multiplier and divider separately

discrete wavelet transform and data expansion reduction in homomorphic encrypted domain signal processing in the encrypted domain is a new technology with the goal of protecting valuable signals from insecure signal processing in this paper we propose a method for implementing discrete wavelet transform dwt and multiresolution analysis mra in homomorphic encrypted domain we first suggest a framework for performing dwt and inverse dwt idwt in the encrypted domain then conduct an analysis of data expansion and quantization errors under the framework to solve the problem of data expansion which may be very important in practical applications we present a method for reducing data expansion in the case that both dwt and idwt are performed with the proposed method multilevel dwt idwt can be performed with less data expansion in homomorphic encrypted domain we propose a new signal processing procedure where the multiplicative inverse method is employed as the last step to limit the data expansion taking a 2 d haar wavelet transform as an example we conduct a few experiments to demonstrate the advantages of our method in secure image processing we also provide computational complexity analyses and comparisons to the best of our knowledge there has been no report on the implementation of dwt and mra in the encrypted domain

group entropies correlation laws and zeta functions the notion of group entropy is proposed it enables the unification and generaliztion of many different definitions of entropy known in the literature such as those of boltzmann gibbs tsallis abe and kaniadakis other entropic functionals are introduced related to nontrivial correlation laws characterizing universality classes of systems out of equilibrium when the dynamics is weakly chaotic the associated thermostatistics are discussed the mathematical structure underlying our construction is that of formal group theory which provides the general structure of the correlations among particles and dictates the associated entropic functionals as an example of application the role of group entropies in information theory is illustrated and generalizations of the kullback leibler divergence are proposed a new connection between statistical mechanics and zeta functions is established in particular tsallis entropy is related to the classical riemann zeta function

a generalization of the kullback leibler divergence and its properties a generalized kullback leibler relative entropy is introduced starting with the symmetric jackson derivative of the generalized overlap between two probability distributions the generalization retains much of the structure possessed by the original formulation we present the fundamental properties including positivity metricity concavity bounds and stability in addition a connection to shift information and behavior under liouville dynamics are discussed

dehn fillings of knot manifolds containing essential once punctured tori in this paper we study exceptional dehn fillings on hyperbolic knot manifolds which contain an essential once punctured torus let m be such a knot manifold and let be the boundary slope of such an essential once punctured torus we prove that if dehn filling m with slope produces a seifert fibred manifold then 5 furthermore we classify the triples m when 4 more precisely when 5 then m is the unique manifold w h 3 2 obtained by dehn filling one boundary component of the whitehead link exterior with slope 3 2 and is the pair of slopes 5 0 further 4 if and only if m is the triple w h 2n 1 n 4 0 for some integer n with n 1 combining this with known results we classify all hyperbolic knot manifolds m and pairs of slopes on m where is the boundary slope of an essential once punctured torus in m and is an exceptional filling slope of distance 4 or more from refined results in the special case of hyperbolic genus one knot exteriors in s3 are also given

the montgomery modular inverse revisited we modify an algorithm given by kaliski to compute the montgomery inverse of an integer modulo a prime number we also give a new definition of the montgomery inverse and introduce efficient algorithms for computing the classical modular inverse the kaliski montgomery inverse and the new montgomery inverse the proposed algorithms are suitable for software implementations on general purpose microprocessors

interpretation of the extreme physical information principle in terms of shift information it is shown that fisher information fi can be considered as a limiting case of a related form of kullback information char22 a shift information si the compatibility of the use of si with a basic physical principle of uncertainty is demonstrated the scope of fi based theory is extended to the nonlinear klein gordon equation

characteristic subsurfaces and dehn filling let m be a simple knot manifold using the characteristic submanifold theory and the combinatorics of graphs in surfaces we develop a method for bounding the distance between the boundary slope of an essential surface in m which is not a fiber or a semi fiber and the boundary slope of a certain type of singular surface applications include bounds on the distances between exceptional dehn surgery slopes it is shown that if the fundamental group of m has no non abelian free subgroup and if m is a reducible manifold which is not homeomorphic to s 1 s 2 or p 3 p 3 then 5 under the same condition on m it is shown that if m is seifert fibered then 6 moreover in the latter situation character variety techniques are used to characterize the topological types of m and m in case the bound of 6 is attained

conditions for the existence of a generalization of renyi divergence abstract we give necessary and sufficient conditions for the existence of a generalization of renyi divergence which is defined in terms of a deformed exponential function if the underlying measure is non atomic we found that not all deformed exponential functions can be used in the generalization of renyi divergence a condition involving the deformed exponential function is provided in the case is purely atomic the counting measure on the set of natural numbers we show that any deformed exponential function can be used in the generalization

the maximal number of exceptional dehn surgeries thurston s hyperbolic dehn surgery theorem is one of the most important results in 3 manifold theory and it has stimulated an enormous amount of research if m is a compact orientable hyperbolic 3 manifold with boundary a single torus then the theorem asserts that for all but finitely many slopes s on m the manifold m s obtained by dehn filling along s also admits a hyperbolic structure the slopes s where m s is not hyperbolic are known as exceptional a major open question has been what is the maximal number of exceptional slopes on such a manifold m when m is the exterior of the figure eight knot the number of exceptional slopes is 10 and this was conjectured by gordon in 19 to be an upper bound that holds for all m in this paper we prove this conjecture

on the spectrum of fractional brownian motions fractional brownian motions fbms provide useful models for a number of physical phenomena whose empirical spectra obey power laws of fractional order however due to the nonstationary nature of these processes the precise meaning of such spectra remains generally unclear two complementary approaches are proposed which are intended to clarify this point the first one based on a time frequency analysis takes into account the nonstationary nature of fbm and puts emphasis on time averaged measurements the second one based on a time scale analysis is matched to self similarity properties of fbm and reveals an underlying stationary structure relative to each time scaling

quantum field theory in ninety minutes on presente divers aspects de la theorie quantique des champs la theorie p 2 a 2 dimensions la theorie 3 4 a 3 dimensions la theorie de yang mills a 4 dimensions

recursive quadrature mirror filters criteria specification and design method criteria are found for a pair of recursive infinite impluse response iir filters which have mirror image amplitude responses and whose outputs are in phase quadrature at all frequencies a method is suggested for designing filters with these characteristics and their performance and processing requirements are compared with a typical nonrecursive finite impluse response fir realization a particular filter is described in more detail and it is shown how it could be incorporated in a multiband processing scheme it is concluded that recursive quadrature mirror filters could offer considerable savings in terms of signal processing compared with nonrecursive filters with similar performances additionally it is suggested that because they can be designed to have relatively short absolute delays the performance of the iir filters may prove superior for certain applications

dehn surgery on knots in d dehn considered the following method for constructing 3 manifolds remove a solid torus neighborhood n k of some knot x in the 3 sphere s and sew it back differently in particular he showed that taking x to be the trefoil one could obtain infinitely many non simply connected homology spheres o in this way let mx s n k then the different resewings are parametrized by the isotopy class r of the simple closed curve on the torus omk that bounds a meridional disk in the re attached solid torus we denote the resulting closed oriented 3 manifold by mk and say that it is obtained by r dehn surgery on x more generally one can consider the manifolds ml obtained by r dehn surgery on a fc component link l xi u u kk in s where r r it turns out that every closed oriented 3 manifold can be constructed in this way wal lie thus a good understanding of dehn surgery might lead to progress on general questions about the structure of 3 manifolds starting with the case of knots it is natural to extend the context a little and consider the manifolds m r obtained by attaching a solid torus v to an arbitrary compact oriented irreducible every 2 sphere bounds a 3 ball 3 manifold m with dm an incompressible torus where r is the isotopy class slope on dm of the boundary of a meridional disk of v we say that m r is the result of r dehn filling on m an observed feature of this construction is that

distance between toroidal surgeries on hyperbolic knots in the 3 sphere for a hyperbolic knot in the 3 sphere at most finitely many dehn surgeries yield non hyperbolic 3 manifolds as a typical case of such an ex ceptional surgery a toroidal surgery is one that yields a closed 3 manifold containing an incompressible torus the slope corresponding to a toroidal surgery called a toroidal slope is known to be integral or half integral we show that the distance between two integral toroidal slopes for a hyperbolic knot except the figure eight knot is at most four

a block spin construction of ondelettes part i lemarie functions using block spin assignments we construct anl2 orthonormal basis consisting of dyadic scalings and translates of just a finite number of functions these functions have exponential localization and for even values of a construction parameterm one can make them classcm 1 with vanishing moments up to orderm inclusive such a basis has an important application to phase cell cluster expansions in quantum field theory

phase space gradient of dissipated work and information a role of relative fisher information we show that an information theoretic distance measured by the relative fisher information between canonical equilibrium phase densities corresponding to forward and backward processes is intimately related to the gradient of the dissipated work in phase space we present a universal constraint on it via the logarithmic sobolev inequality furthermore we point out that a possible expression of the lower bound indicates a deep connection in terms of the relative entropy and the fisher information of the canonical distributions

dehn fillings of large hyperbolic 3 manifolds let m be a compact connected orientable hyperbolic 3 manifold whose boundary is a torus and which contains an essential closed surface s i t is conjectured that 5 is an upper bound for the distance between two slopes on m whose associated fillings are not hyperbolic manifolds in this paper we verify the conjecture when the first betti number of m is at least 2 by showing that given a pseudo anosov mapping class f of a surface and an essential simple closed curve in the surface then 5 is an upper bound for the diameter of the set of integers n for which the composition of f with the n th power of a dehn twist along is not pseudo anosov this sharpens an inequality of albert fathi for large manifolds m of first betti number 1 we obtain partial results set

information gain within nonextensive thermostatistics we discuss the information theoretical foundations of the kullback information gain recently generalized within a nonextensive thermostatistical formalism general properties are studied and in particular a consistent test for measuring the degree of correlation between random variables is proposed in addition minimum entropy distributions are discussed and the h theorem is proved within the generalized context

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed