one way hash function construction based on 2d coupled map lattices an algorithm for constructing one way hash function based on spatiotemporal chaos is proposed a two dimensional coupled map lattices 2d cml with parameters leading to the largest lyapunov exponent is employed the state of the 2d cml is dynamically determined by its previous state and the message bit at the corresponding positions the hash value is obtained by a linear transform on the final state of the 2d cml theoretical analysis and computer simulation indicate that our algorithm has good statistical properties strong collision resistance and high flexibility it is practical and reliable with high potential to be adopted as a strong hash function for providing data integrity

an algorithm for computing some heegaard floer homologies in this paper we give an algorithm to compute the hat version of heegaard floer homology of a closed oriented three manifold this method also allows us to compute the filtration coming from a null homologous link in a three manifold

λ aluthge transforms and schatten ideals abstract let t l h and let t u t t u be the polar decomposition of t then for every 0 1 the aluthge transform is defined by t t u t 1 we show that several properties which are known for the usual aluthge transform i e the case 1 2 also hold for aluthge transforms with 0 1 moreover we get several results which are new even for the usual aluthge transform

symplectic tori in rational elliptic surfaces let e 1 p denote the rational elliptic surface with a single multiple fiber fp of multiplicity p we construct an infinite family of homologous non isotopic symplectic tori representing the primitive 2 dimensional homology class fp in e 1 p when p 1 as a consequence we get infinitely many non isotopic symplectic tori in the fiber class of the rational elliptic surface open image in new window we also show how these tori can be non isotopically embedded as homologous symplectic submanifolds in other symplectic 4 manifolds

non isotopic symplectic tori in the same homology class for any pair of integers n 1 and q 2 we construct an infinite family of mutually non isotopic symplectic tori representing the homology class q f of an elliptic surface e n where f is the homology class of the fiber we also show how such families can be non isotopically and symplectically embedded into a more general class of symplectic 4 manifolds

color image encryption based on one time keys and robust chaotic maps we designed a stream cipher algorithm based on one time keys and robust chaotic maps in order to get high security and improve the dynamical degradation we utilized the piecewise linear chaotic map as the generator of a pseudo random key stream sequence the initial conditions were generated by the true random number generators the md5 of the mouse positions we applied the algorithm to encrypt the color image and got the satisfactory level security by two measures npcr and uaci when the collision of md5 had been found we combined the algorithm with the traditional cycle encryption to ensure higher security the ciphered image is robust against noise and makes known attack unfeasible it is suitable for application in color image encryption

exotic smooth structures on small 4 manifolds let m be either mathbb cp 2 3 overline mathbb cp 2 or 3 mathbb cp 2 5 overline mathbb cp 2 we construct the first example of a simply connected irreducible symplectic 4 manifold that is homeomorphic but not diffeomorphic to m

milnor fibers and symplectic fillings of quotient surface singularities abstract we determine a one to one correspondence between milnor fibers and minimal symplectic fillings of a quotient surface singularity up to diffeomorphism type by giving an explicit algorithm to compare them mainly via techniques from the minimal model program for 3 folds and pinkham s negative weight smoothing as by products we show that milnor fibers associated to irreducible components of the reduced versal deformation space of a quotient surface singularity are not diffeomorphic to each other with a few obvious exceptions for this we classify minimal symplectic fillings of a quotient surface singularity up to diffeomorphism any symplectic filling of a quotient surface singularity is obtained by a sequence of rational blow downs from a special resolution so called the maximal resolution of the singularity which is an analogue of the one to one correspondence between the irreducible components of the reduced versal deformation space and the so called p resolutions of a quotient surface singularity

combinatorial cobordism maps in hat heegaard floer theory in a previous article sarkar and wang 15 gave a combinatorial description of the hat version of heegaard floer homology for three manifolds given a cobordism between two connected three manifolds there is an induced map between their heegaard floer homologies assume that the first homology group of each boundary component surjects onto the first homology group of the cobordism modulo torsion under this assumption we present a procedure for finding the rank of the induced heegaard floer map combinatorially in the hat version

knots links and 4 manifolds in this paper we investigate the relationship between isotopy classes of knots and links in s and the di eomorphism types of homeomorphic smooth 4 manifolds as a corollary of this initial investigation we begin to uncover the surprisingly rich structure of di eomorphism types of manifolds homeomorphic to the k3 surface in order to state our theorems we need to view the seiberg witten invariant of a smooth 4 manifold as a multivariable laurent polynomial to do this recall that the seiberg witten invariant of a smooth closed oriented 4 manifold x with b2 x 1 is an integer valued function which is de ned on the set of spinc structures over x cf w km ko1 t1 in case h1 x z has no 2 torsion which will be the situation in this paper there is a natural identi cation of the spinc structures of x with the characteristic elements of h2 x z in this case we view the seiberg witten invariant as

jordan product maps commuting with the λ aluthge transform abstract let b h be the algebra of all bounded linear operators acting on a hilbert space h the main purpose in this paper is to obtain a characterization of bijective maps b h b k k hilbert space satisfying the following condition a b a b for all a b b h where t stands the aluthge transform of the operator t b h and a b 1 2 a b b a is the jordan product of a and b we prove that a bijective map satisfies the above condition if and only if there exists a unitary linear bounded operator u h k such that has the form a u a u for all a b h

on weakly unitarily invariant norm and the λ aluthge transformation for invertible operator abstract let t b h be an invertible operator with polar decomposition t up and b b h commute with t in this paper we prove that p bup 1 bt where is a weakly unitarily invariant norm on b h and 0 1 as the consequence of this result we have f p up 1 f t for any polynomial f

a construction of horikawa surface via q gorenstein smoothings we prove that the fintushel stern construction of a horikawa surface which is obtained from elliptic surface via a rational blow down surgery in the smooth category can be performed in the complex category the main technique involved is mathbb q gorenstein smoothings

product commuting maps with the λ aluthge transform let h and k be two hilbert spaces and b h be the algebra of all bounded linear operators from h into itself the main purpose of this paper is to obtain a characterization of bijective maps b h b k satisfying the following condition a b ab f orall a b b h where t stands the aluthge transform of the operator t b h more precisely we prove that a bijective map satisfies the above condition if and only if a u au for all a b h for some unitary operator u h k

the geography problem for irreducible spin four manifolds we study the geography problem for smooth irreducible simplyconnected spin four manifolds for a large class of hoinotopy types we exhibit both symplectic and non symplectic representatives we also compute the seiberg witten invariants of all the four manifolds we construct

new formulas for the spectral radius via λ aluthge transform abstract in this paper we give several expressions of spectral radius of a bounded operator on a hilbert space in terms of iterated aluthge transform numerical radius and the asymptotic behavior of the powers of this operator we also obtain several characterizations of normaloid operators

superconformal simple type and witten s conjecture abstract let x be a smooth closed connected orientable four manifold with b 1 x 0 and b x 3 and odd we show that if x has seiberg witten simple type then the so 3 monopole cobordism formula of 14 implies witten s conjecture relating the donaldson and seiberg witten invariants

on the diffeomorphism types of certain algebraic surfaces i l invariant de donaldson la geometrie de certaines surfaces rationnelles surfaces dolgachev generalites sur des formes de type 1 n la classe canonique d une chambre et un coin le cone de kahler d une bonne surface generique une etude de p cellules les super p cellules

2d sine logistic modulation map for image encryption because of the excellent properties of unpredictability ergodicity and sensitivity to their parameters and initial values chaotic maps are widely used in security applications in this paper we introduce a new two dimensional sine logistic modulation map 2d slmm which is derived from the logistic and sine maps compared with existing chaotic maps it has the wider chaotic range better ergodicity hyperchaotic property and relatively low implementation cost to investigate its applications we propose a chaotic magic transform cmt to efficiently change the image pixel positions combining 2d slmm with cmt we further introduce a new image encryption algorithm simulation results and security analysis demonstrate that the proposed algorithm is able to protect images with low time complexity and a high security level as well as to resist various attacks

small exotic rational surfaces without 1 and 3 handles we give new rational blowdown constructions of exotic cp 2 ncp 2 5 n 9 without using elliptic fibrations we also show that our 4 manifolds admit handle decompositions without 1 and 3 handles for 7 n 9 a strategy for rational blowdown constructions of exotic cp 2 ncp 2 1 n 4 is also proposed

self contained encrypted image folding the recently introduced approach for encrypted image folding is generalized to make it self contained the goal is achieved by enlarging the folded image so as to embed all the necessary information for the image recovery the need for extra size is somewhat compensated by considering a transformation with higher folding capacity numerical examples show that the size of the resulting cipher image may be significantly smaller than the plain text one the implementation of the approach is further extended to deal also with color images

symplectic rational blowdowns we prove that the rational blowdown a surgery on smooth 4 manifolds introduced by fintushel and stern can be performed in the symplectic category as a consequence interesting families of smooth 4 manifolds including the exotic k3 surfaces of gompf and mrowka admit symplectic structures a basic problem in symplectic topology is to understand what smooth manifolds admit a symplectic structure a closed non degenerate 2 form in this paper we focus on this question in dimension 4 currently the primary methods for constructing smooth irreducible 4 manifolds in such a way that one can distinguish them by donaldson or seiberg witten invariants are surgery constructions that use complex manifolds as building blocks these surgery methods are smooth logarithmic transforms rational blowdowns and connect sums along surfaces it is interesting to see when these surgeries can be performed in the symplectic category in this paper we prove that performing a rational blowdown of a symplectic manifold along symplectic surfaces yields a symplectic manifold this result establishes that certain exotic 4 manifolds including the exotic k3 surfaces of gompf and mrowka 9 are symplectic in any even dimension two symplectic manifolds can be summed along codimension 2 symplectic submanifolds to yield a symplectic manifold we refer to this symplectic operation which was proposed by gromov 11 as the symplectic sum gompf 8 used the symplectic sum to construct a plethora of interesting symplectic manifolds including the first examples of simply connected symplectic 4 manifolds that are not homotopic to any complex surface and some exotic k3 surfaces more recently fintushel and stern 6 have used the connect sum along smoothly embedded tori to produce a rich class of exotic 4 manifolds some homeomorphic to a k3 surface many of which cannot admit a symplectic structure the author is grateful for the support of an nsf post doctoral fellowship dsm9627749

computations of instanton invariants using donaldson floer theory we compute the donaldson su 2 invariants of the double cover of 2 branched over a smooth algebraic curve of degree eight from this we deduce a formula for the relative invariants of the blow up of the gompf nucleusn2 and we show how this gives a blow up formula for a class of 4 manifolds which includes essentially all the simply connected 4 manifolds known to have big diffeomorphism group we apply the result on the nucleus also to prove a formula for the invariants of minimal simply connected elliptic surfaces which reduces the computation to the case of geometric genus one in particular we compute all the donaldson invariants of minimal simply connected elliptic surfaces without multiple fibers our main tool is donaldson floer theory

many closed symplectic manifolds have infinite hofer zehnder capacity we exhibit many examples of closed symplectic manifolds on which there is an autonomous hamiltonian whose associated flow has no nonconstant periodic orbits the only previous explicit example in the literature was the torus t2n n 2 with an irrational symplectic structure the underlying smooth manifolds of our examples include for instance the k3 surface and also infinitely many smooth manifolds homeomorphic but not diffeomorphic to it infinitely many minimal four manifolds having any given finitely presented group as their fundamental group and simply connected minimal four manifolds realizing all but finitely many points in the first quadrant of the geography plane below the line corresponding to signature 3 the examples are constructed by performing symplectic sums along suitable tori and then perturbing the symplectic form in such a way that hypersurfaces near the neck in the symplectic sum have no closed characteristics we conjecture that any closed symplectic four manifold with b 1 admits symplectic forms with a similar property

subset selection in noise based on diversity measure minimization we develop robust methods for subset selection based on the minimization of diversity measures a bayesian framework is used to account for noise in the data and a maximum a posteriori map estimation procedure leads to an iterative procedure which is a regularized version of the focal underdetermined system solver focuss algorithm the convergence of the regularized focuss algorithm is established and it is shown that the stable fixed points of the algorithm are sparse we investigate three different criteria for choosing the regularization parameter quality of fit sparsity criterion l curve the l curve method as applied to the problem of subset selection is found not to be robust and we propose a novel modified l curve procedure that solves this problem each of the regularized focuss algorithms is evaluated through simulation of a detection problem and the results are compared with those obtained using a sequential forward selection algorithm termed orthogonal matching pursuit omp in each case the regularized focuss algorithm is shown to be superior to the omp in noisy environments

classifying quadratic maps from plane to plane let v be a 2 dimensional vector space over an algebraically closed field f of characteristic 2 3 the elements in s 2 v v under the natural action of gl 2 f are classified generi

holomorphic disks and three manifold invariants properties and applications in 27 we introduced floer homology theories hf y s hf y s hf y t hf y s and hf red y s associated to closed oriented three manifolds y equipped with a spiny structures s spin c y in the present paper we give calculations and study the properties of these invariants the calculations suggest a conjectured relationship with seiberg witten theory the properties include a relationship between the euler characteristics of hf and turaev s torsion a relationship with the minimal genus problem thurston norm and surgery exact sequences we also include some applications of these techniques to three manifold topology

absolutely continuous invariant measures for one parameter families of one dimensional maps given a one parameter familyf x of maps of the interval 0 1 we consider the set of parameter values for whichf has an invariant measure absolutely continuous with respect to lebesgue measure we show that this set has positive measure for two classes of maps i f x f x where 0 4 andf x is a functionc3 near the quadratic mapx 1 x and ii f x f x mod 1 wheref isc3 f 0 f 1 0 andf has a unique nondegenerate critical point in 0 1

spectral radius inequalities for sums of operators with an application to the problem of bounding the zeros of polynomials abstract we prove spectral radius inequalities for sums of operators our results are employed to establish a new bound for the zeros of polynomials

weighted homogeneous singularities and rational homology disk smoothings we classify the resolution graphs of weighted homogeneous surface singularities which admit rational homology disk smoothings the nonexistence of rational homology disk smoothings is shown by symplectic geometric methods while the existence is verified via smoothings of negative weight

gray code permutation algorithm for high dimensional data encryption abstract we present a novel permutation algorithm for fast encryption of a large amount of data such as 3d images and real time videos the proposed p box algorithm takes advantage of gray code properties and allows fast encryption with high information diffusion the algorithm is optimized for integer q bit operations q 8 16 32 allowing a direct implementation in almost any hardware platform while avoiding rounding errors of floating point operations by combining the p box with chaotic s box based on the logistic map we design a complete highly secure and fast cryptosystem

a combinatorial description of knot floer homology given a grid presentation of a knot or link k in the three sphere we describe a heegaard diagram for the knot complement in which the heegaard surface is a torus and all elementary domains are squares using this diagram we obtain a purely combinatorial description of the knot floer homology of k

tour of bordered floer theory heegaard floer theory is a kind of topological quantum field theory tqft assigning graded groups to closed connected oriented 3 manifolds and group homomorphisms to smooth oriented four dimensional cobordisms bordered heegaard floer homology is an extension of heegaard floer homology to 3 manifolds with boundary with extended tqft type gluing properties in this survey we explain the formal structure and construction of bordered floer homology and sketch how it can be used to compute some aspects of heegaard floer theory

fractal sets attached to homogeneous quadratic maps in two variables abstract the fractal set attached to the iteration of a generic homogeneous quadratic map from the plane to itself is studied and depicted by using a two parametric family of normal forms obtained from the theory of invariants of symmetric bilinear maps f r r r under the full linear group of the plane while invariant theory classifies maps f c c c on the complex plane we confine ourselves to consider maps on the real plane in order to include the results obtained from the theory of two dimensional discrete dynamical systems a discrete number of topological types for such fractals is conjectured to exist

the constrained bilinear form and the c numerical range abstract let v be an n dimentional unitary space with inner product and s the set x v x x 1 for any a hom v v and q c with q 1 we define w a q ax y x y s x y q if q 1 then w a q is just the classical numerical range ax x x s the convexity of which is well known another generalization of the numerical range is the c numerical range which is defined to be the set w c a tr cu au u unitary where c hom v v in this note we prove that w a q is always convex and that wc a is convex for all a if rank c 1 or n 2

on numerical range of the aluthge transformation let t u t be the polar decomposition of an operator t aluthge defined an operator transformation t t 1 2u t 1 2 of t which is called aluthge transformation in this paper we shall discuss the numerical range of t and show the following results 1 i w t w t 2 ii if t is an n n matrix then w t w t 3 iii if n t n t then w t w t moreover we shall obtain some applications of above results

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

statistical distribution host for encrypted information the statistical distribution when determined from an incomplete set of constraints is shown to be suitable as host for encrypted information we design an encoding decoding scheme to embed such a distribution with hidden information the encryption security is based on the extreme instability of the encoding procedure the essential feature of the proposed system lies in the fact that the key for retrieving the code is generated by random perturbations of very small value the security of the proposed encryption relies on the security to interchange the secret key hence it appears as a good complement to the quantum key distribution protocol

the blowup formula for donaldson invariants k k which is calculated in 4 below this formula has been the target of much recent work the abstract fact that there exists such a formula which is independent of x was first proved by c taubes using techniques of t j bryan b and p ozsvath o have independently calculated the coefficients throughb10 x quite recently j morgan and ozsvath have announced a scheme which can recursively compute all of the bk x the special case of the blowup formula for manifolds of simple type see 5 below was first given by p kronheimer and t mrowka however none of the techniques in these cases approach the simplicity of that offered here before presenting the formula we shall first establish notation for the donaldson in variants of a simply connected 4 manifold x with b 1 and odd the hypothesis of simple connectivity is not necessary but makes the exposition easier an orientation of x together with an orientation of h 2 x r is called a homology orientation of x such a homology orientation determines the su 2 donaldson invariant a linear function d dx a x sym h0 x h2 x r

comment on image encryption with chaotically coupled chaotic maps this paper studies the security of a recently proposed chaos based cryptosystem it is shown that the encryption architecture of this cryptosystem exhibits some important problems related to its implementation and its robustness against noise some security problems are also highlighted

reply to comment on image encryption with chaotically coupled chaotic maps physica d 2010 abstract we respond to the comment by arroyo et al on our paper image encryption with chaotically coupled chaotic maps

simply connected symplectic 4 manifolds with b2 1 and c12 2 in this article we construct a new simply connected symplectic 4 manifold with b2 1 and c12 2 which is homeomorphic but not diffeomorphic to a rational surface by using rational blow down technique as a corollary we conclude that a rational surface mathbf c p 2 sharp 7 overline mathbf c p 2 admits an exotic smooth structure

a rigorous lower bound for the stability regions of the quadratic map abstract we establish a lower bound on the measure of the set of stable parameters a for the quadratic map q a x a x 1 x for these parameters we prove that q a either has a single stable periodic orbit or a period doubling bifurcation from this result we also obtain a non trivial upper bound on the set of stochastic parameters for q a

symplectic surgeries along certain singularities and new lefschetz fibrations abstract we define a new 4 dimensional symplectic cut and paste operations arising from the generalized star relations t a 0 t a 1 t a 2 t a 2 g 1 2 g 1 t b 1 t b 2 g t b 3 also known as the trident relations in the mapping class group g 3 of an orientable surface of genus g 1 with 3 boundary components we also construct new families of lefschetz fibrations by applying the generalized star relations and the chain relations to the families of words t c 1 t c 2 t c 2 g 1 t c 2 g t c 2 g 1 2 t c 2 g t c 2 g 1 t c 2 t c 1 2 n 1 t c 1 t c 2 t c 2 g t c 2 g 1 2 g 2 n 1 and t c 1 t c 2 t c 2 g 1 t c 2 g 2 2 g 1 n 1 in the mapping class group g of the closed orientable surface of genus g 1 and n 1 furthermore we show that the total spaces of some of these lefschetz fibrations are irreducible exotic symplectic 4 manifolds using the degenerate cases of the generalized star relations we also realize all elliptic lefschetz fibrations and genus two lefschetz fibrations over s 2 with non separating vanishing cycles

on weakly unitarily invariant norm and the aluthge transformation abstract in this paper we show that f p up 1 max f t u f t u f 0 i u u where t b h is a semi norm on b h which satisfies some conditions t up polar decomposition 0 1 and f is a polynomial as a consequence of this fact we will show that some semi norms including the radii 0 f p up 1 f t we also give some related results

double node neighborhoods and families of simply connected 4 manifolds with b 1 journal of the american mathematical society volume 19 number 1 pages 171 180 s 0894 0347 05 00500 x article electronically published on august 15 2005 double node neighborhoods and families of simply connected 4 manifolds with b 1 ronald fintushel and ronald j stern 1 introduction a basic question of 4 manifold topology is whether the complex projective plane cp 2 admits exotic smooth structures thus one is interested in knowing the smallest m for which cp 2 m cp admits an exotic smooth structure in the late 1980s dieter kotschick k proved that the barlow surface which was known to be homeomorphic to cp 2 8cp is not di eomorphic to it in the following years the subject of simply connected smooth 4 manifolds with b 1 languished because of a lack of suitable examples however largely due to a beautiful paper of jongil park p who found the rst examples of exotic simply connected 4 manifolds with b 1 and b 7 the past year has found renewed interest in this subject peter ozsvath and zoltan szabo os proved that park s manifold is minimal and andras stipsicz and szabo ss used a technique similar to park s to construct an exotic manifold with b 1 and b 6 the rational elliptic surface e 1 cp 2 9 cp admits in nitely many distinct smooth structures up to now it has not been known whether cp 2 m cp can have an in nite family of smooth structures when m 9 it is the purpose of this paper to introduce a new technique which we use to show that for m 6 7 8 cp 2 m cp does have an in nite family of smooth structures the construction of these examples to some extent follows the ideas of park p after performing suitable knot surgeries fs3 on e 1 the essential new idea is that after certain knot surgeries on e 1 one is able to nd an immersed sphere of self intersection 1 representing the pseudo section this is accomplished by studying double node neighborhoods as described below shortly after the appearance of a preliminary version of this article park stip sicz and szabo pss used the techniques described herein to give even better examples an in nite family of pairwise nondi eomorphic smooth 4 manifolds all homeomorphic to cp 2 5 cp in the nal section of this paper we give a quick construction of such a family of examples received by the editors january 13 2005 2000 mathematics subject classi cation primary 14j26 53d05 57r55 57r57 key words and phrases 4 manifold seiberg witten invariant knot surgery rational blowdown the rst author was partially supported by nsf grant dms0305818 and the second author by nsf grant dms0204041 c 2005 american mathematical society reverts to public domain 28 years from publication

combinatorial heegaard floer homology and nice heegaard diagrams abstract we consider a stabilized version of hf of a 3 manifold y i e the u 0 variant of heegaard floer homology for closed 3 manifolds we give a combinatorial algorithm for constructing this invariant starting from a heegaard decomposition for y and give a topological proof of its invariance properties

geometric variational discretization of continuum theories this study derives geometric variational discretization of continuum theories arising in fluid dynamics magnetohydrodynamics mhd and the dynamics of complex fluids a central role in these discretizations is played by the geometric formulation of fluid dynamics which views solutions to the governing equations for perfect fluid flow as geodesics on the group of volume preserving diffeomorphisms of the fluid domain inspired by this framework we construct a finite dimensional approximation to the diffeomorphism group and its lie algebra thereby permitting a variational temporal discretization of geodesics on the spatially discretized diffeomorphism group the extension to mhd and complex fluid flow is then made through an appeal to the theory of euler poincare systems with advection which provides a generalization of the variational formulation of ideal fluid flow to fluids with one or more advected parameters upon deriving a family of structured integrators for these systems we test their performance via a numerical implementation of the update schemes on a cartesian grid among the hallmarks of these new numerical methods are exact preservation of momenta arising from symmetries automatic satisfaction of solenoidal constraints on vector fields good long term energy behavior robustness with respect to the spatial and temporal resolution of the discretization and applicability to irregular meshes

numerical range of aluthge transform of operator for any operator a on a hilbert space let a denote its aluthge transform in this paper we prove that the closure of the numerical range of a is always contained in that of a this supplements the recently proved case for dimkera dimkera by yamazaki and partially confirms a conjecture of jung ko and pearcy

personalized information encryption using ecg signals with chaotic functions the development of efficient data encryption to ensure high security of information transmission has long been a popular research subject because electrocardiogram ecg signals vary from person to person and can be used as a new tool for biometric recognition this study introduces an individual feature of ecg with chaotic henon and logistic maps for personalized cryptography this study also develops an encryption algorithm based on the chaos theory to generate initial keys for chaotic logistic and henon maps the proposed personalized encryption system uses a convenient handheld device to collect ecg signals from the user high quality randomness in ecg signals results in a widely expanded key space making it an ideal key generator for personalized data encryption the experiments reported in this study demonstrate the use of this approach in encrypting texts and images and applied of the proposed approach to secure communications

holomorphic disks and knot invariants abstract we define a floer homology invariant for knots in an oriented three manifold closely related to the heegaard floer homologies for three manifolds defined in an earlier paper we set up basic properties of these invariants including an euler characteristic calculation and a description of the behavior under connected sums then we establish a relationship with hf for surgeries along the knot applications include calculation of hf of three manifolds obtained by surgeries on some special knots in s 3 and also calculation of hf for certain simple three manifolds which fiber over the circle

on symplectic fillings of lens spaces le st be the contact structure naturally induced on the lens space l p q s 3 z pz by the standard contact structure st on the three sphere s 3 we obtain a complete classification of the symplectic fillings of l p q st up to orientation preserving diffeomorphisms in view of our results we formulate a conjecture on the diffeomorphism types of the smoothings of complex two dimensional cyclic quotient singularities

image encryption with chaotically coupled chaotic maps abstract we present a novel secure cryptosystem for direct encryption of color images based on chaotically coupled chaotic maps the proposed cipher provides good confusion and diffusion properties that ensures extremely high security because of the chaotic mixing of pixels colors information is mixed and distributed over a complete image using a complex strategy that makes known plaintext attack unfeasible the encryption algorithm guarantees the three main goals of cryptography strong cryptographic security short encryption decryption time and robustness against noise and other external disturbances due to the high speed the proposed cryptosystem is suitable for application in real time communication systems

holomorphic disks and topological invariants for closed three manifolds the aim of this article is to introduce certain topological invariants for closed oriented three manifolds y equipped with a spiny structure given a heegaard splitting of y u 0o u u 1 these theories are variants of the lagrangian floer homology for the g fold symmetric product of relative to certain totally real subspaces associated to u 0 and u 1

a symmetric image encryption algorithm based on mixed linear nonlinear coupled map lattice abstract we propose a new image encryption algorithm based on the spatiotemporal chaos of the mixed linear nonlinear coupled map lattices this spatiotemporal chaotic system has more outstanding cryptography features in dynamics than the logistic map or the system of coupled map lattices does in the proposed image encryption we employ the strategy of bit level pixel permutation which enables the lower bit planes and higher bit planes of pixels permute mutually without any extra storage space simulations have been carried out and the results demonstrate the superior security and high efficiency of the proposed algorithm

small lefschetz fibrations and exotic 4 manifolds we explicitly construct genus 2 lefschetz fibrations whose total spaces are minimal symplectic 4 manifolds homeomorphic to complex rational surfaces mathbb cp 2 p overline mathbb cp 2 for p 7 8 9 and to 3 mathbb cp 2 q overline mathbb cp 2 for q 12 ldots 19 complementarily we prove that there are no minimal genus 2 lefschetz fibrations whose total spaces are homeomorphic to any other simply connected 4 manifold with b le 3 with one possible exception when b 3 meanwhile we produce positive dehn twist factorizations for several new genus 2 lefschetz fibrations with small number of critical points including the smallest possible example which follow from a reverse engineering procedure we introduce for this setting we also derive exotic minimal symplectic 4 manifolds in the homeomorphism classes of mathbb cp 2 4 overline mathbb cp 2 and 3 mathbb cp 2 6 overline mathbb cp 2 from small lefschetz fibrations over surfaces of higher genera

a simply connected surface of general type with p g 0 and k 2 2 in this paper we construct a simply connected minimal complex surface of general type with pg 0 and k2 2 using a rational blow down surgery and a gorenstein smoothing theory

on generalized numerical range of the aluthge transformation abstract in this paper the authors show that the aluthge transformation t of a matrix t and a polynomial f satisfy the inclusion relation w c f t w c f t for the generalized numerical range if c is a hermitian matrix or a rank one matrix

algebraic break of image ciphers based on discretized chaotic map lattices in this paper we provide an algebraic cryptanalysis of a recently proposed chaotic image cipher we show that the secret parameters of the algorithm can be revealed using chosen plaintext attacks our attack uses the orbit properties of the permutation maps to deduce encryption values for a single round once a single round encryption is revealed the secret parameters are obtained using simple assignments

a lefschetz fibration on minimal symplectic fillings of a quotient surface singularity in this article we construct a genus 0 or genus 1 positive allowable lefschetz fibration on any minimal symplectic filling of the link of non cyclic quotient surface singularities as a byproduct we also show that any minimal symplectic filling of the link of quotient surface singularities can be obtained from a sequence of rational blowdowns from its minimal resolution

absolutely graded floer homologies and intersection forms for four manifolds with boundary abstract in ozsvath and szabo holomorphic triangles and invariants for smooth four manifolds math sg 0110169 2001 we introduced absolute gradings on the three manifold invariants developed in ozsvath and szabo holomorphic disks and topological invariants for closed three manifolds math sg 0101206 ann of math 2001 to appear coupled with the surgery long exact sequences we obtain a number of three and four dimensional applications of this absolute grading including strengthenings of the complexity bounds derived in ozsvath and szabo holomorphic disks and three manifold invariants properties and applications math sg 0105202 ann of math 2001 to appear restrictions on knots whose surgeries give rise to lens spaces and calculations of hf for a variety of three manifolds moreover we show how the structure of hf constrains the exoticness of definite intersection forms for smooth four manifolds which bound a given three manifold in addition to these new applications the techniques also provide alternate proofs of donaldson s diagonalizability theorem and the thom conjecture for cp 2

holomorphic triangles and invariants for smooth four manifolds abstract in earlier articles the authors introduced invariants for closed oriented three manifolds defined using a variant of lagrangian floer homology in the symmetric products of riemann surfaces the aim of this article is to introduce invariants of oriented smooth four manifolds built using these floer homology groups this four dimensional theory also endows the corresponding three dimensional theories with additional structure an absolute grading of certain of its floer homology groups

surgery in cusp neighborhoods and the geography of irreducible 4 manifolds since its inception the theory of smooth 4 manifolds has relied upon complex surface theory to provide its basic examples this is especially true for simply connected 4 manifolds a longstanding conjecture held that every smooth simply connected closed 4 manifold is the connected sum of manifolds each admitting a complex structure with one of its orientations for this conjecture the 4 sphere was considered as the empty connected sum quite recently this was disproved by gompf and mrowka gm1 who produced infinite families of examples of 4 manifolds homeomorphic to the k3 surface and which admit no complex structure with either orientation the discovery of these dramatic counterexamples to the h cobordism theorem in dimension 4 was the most recent success in a long line of applications of donaldson invariants to the study of smooth structures on 4 manifolds beginning with donaldson s d4 and followed by fm1 ko ov1 ov2 which depended on donaldson s f invariant or a suitable generalization and fmm dk e2 eo1 mn2 sa using donaldson s polynomial invariant a common thread running through many of these counterexamples to the h cobordism conjecture is the process of logarithmic transformation which introduces multiple fibres in an elliptic surface in controlled situations this process will change the diffeomorphism type of a given elliptic surface while keeping its homotopy type fixed taking advantage of the complex structure on an elliptic surface this change can often be detected by using the relationship between anti self dual connections over a complex surface and stable holomorphic bundles d2 an alternative and more differential geometric

the geography of spin symplectic 4 manifolds in this paper we construct a family of simply connected spin non complex symplectic 4 manifolds which cover all but finitely many allowed lattice points chi mathbf c lying in the region 0 leq mathbf c leq 8 76 chi furthermore as a corollary we prove that there exist infinitely many exotic smooth structures on 2n 1 s 2 times s 2 for all n large enough

true random number generator based on mouse movement and chaotic hash function a true random number generator trng makes use of a non deterministic source to produce randomness it is considered as more secure than a pseudorandom number generator as the degree of randomness is higher in this letter we propose a novel trng which generates random bits by moving the mouse casually it is convenient universal and low cost for the personal computer pc platform to eliminate the regular patterns of mouse movements caused by the habit of the same user we propose three trngs based on chaotic hash functions experiments are conducted to evaluate the speed diffusion and randomness performance of these trngs the results show that two of them possess satisfactory performance and can be implemented on common pc platform