block based progressive visual secret sharing block based progressive visual secret sharing bpvss is an encryption technique that utilizes the human visual system to recover a secret image the recovery method is based on building up different image blocks step by step in the last few years several research projects have been devoted to the study of bpvss however they have some common drawbacks their dispatching matrices are chaotically designed by adding some redundant 0 1s in order to maintain the size as a fixed value which makes the methods hard to be implemented in addition the pixel expansion ratio grows faster when the number of participants increases and the visual quality of the restored image is quite poor in this paper we propose a non expanded block based progressive visual secret sharing scheme with noise like and meaningful shares respectively experimental results demonstrate the feasibility of this scheme our design has several advantages over other related methods 1 the model is concise easy to implement and the number of participants need not be restricted 2 with noise like shares the contrast of the restored image is 50 which means that the hidden message can be clearly recognized by the naked eye 3 when transparencies are transferred from noise like patterns into a meaningful cover image the contrast in the shares and the restored image is 25 which is still superior to that obtained in other studies 4 our scheme is more suitable for grayscale and color secret images and 5 the size of the transparencies is the same as that of the secret image

large deviations for stochastic pde with levy noise abstract we prove a large deviation principle result for solutions of abstract stochastic evolution equations perturbed by small levy noise we use general large deviations theorems of varadhan and bryc coupled with the techniques of feng and kurtz 2006 15 viscosity solutions of integro partial differential equations in hilbert spaces and deterministic optimal control methods the laplace limit is identified as a viscosity solution of a hamilton jacobi bellman equation of an associated control problem we also establish exponential moment estimates for solutions of stochastic evolution equations driven by levy noise general results are applied to stochastic hyperbolic equations perturbed by subordinated wiener process

statistical analysis of airport network of china through the study of airport network of china anc composed of 128 airports nodes and 1165 flights edges we show the topological structure of anc conveys two characteristics of small worlds a short average path length 2 067 and a high degree of clustering 0 733 the cumulative degree distributions of both directed and undirected anc obey two regime power laws with different exponents i e the so called double pareto law in degrees and out degrees of each airport have positive correlations whereas the undirected degrees of adjacent airports have significant linear anticorrelations it is demonstrated both weekly and daily cumulative distributions of flight weights frequencies of anc have power law tails besides the weight of any given flight is proportional to the degrees of both airports at the two ends of that flight it is also shown the diameter of each subcluster consisting of an airport and all those airports to which it is linked is inversely proportional to its density of connectivity efficiency of anc and of its subclusters is measured through a simple definition in terms of that the efficiency of anc s subclusters increases as the density of connectivity does anc is found to have an efficiency of 0 484

visual multiple secret sharing based upon turning and flipping the secret sharing schemes in conventional visual cryptography are capable of sharing one secret image into a set of random transparencies called shares in the form of rectangles which reveal the secret image to the human visual system when they are superimposed recently visual secret sharing schemes involving multiple secrets have attracted much attention by adopting rotations on one of the two encoded circle shares more than two secrets could be shared yet the encoding and decoding processes of circle shares need more sophisticated mechanisms than those of rectangular or square ones in this paper we explore the possibilities of visual multiple secret sharing using simply two rectangular or square shares specifically we define some operations onto a transparency based upon turning over or flipping around then we propose visual cryptographic schemes that are able to encode two or four secrets into two rectangular shares and up to eight secrets into two square shares such that the secrets cannot be obtained from any single share whereas they are revealed by stacking the two shares under various combinations of turning or flipping operations the proposed schemes which solidly elaborate the relationship between the encoded shares and the shared secrets broaden the research scope and enrich the flexibility and applicability of visual cryptography or image encryption theoretically and practically

new bounds on the average information rate of secret sharing schemes for graph based weighted threshold access structures a secret sharing scheme is a protocol by which a dealer distributes shares of a secret key among a set of n participants in such a way that only qualified subsets of participants can reconstruct the secret key from the shares they received while unqualified subsets have no information about the secret key the collection of all qualified subsets is called the access structure of this scheme the information rate resp average information rate of a secret sharing scheme is the ratio between the size of the secret key and the maximum size resp average size of the shares in a weighted threshold scheme each participant has his or her own weight a subset is qualified if and only if the sum of the weights of participants in the subset is not less than the given threshold morillo et al 19 considered the schemes for weighted threshold access structure that can be represented by graphs called k weighted graphs they characterized this kind of access structures and derived a result on the information rate in this paper we deal with the average information rate of the secret sharing schemes for these structures two sophisticated constructions are presented each of which has its own advantages and both of them perform very well when n k is large

on general construction for extended visual cryptography schemes numerous visual cryptography schemes vcss have been proposed to protect a secret image with share images most vcss use random looking shares to code a single binary secret image some schemes are designed for color secret images droste s new results on visual cryptography in advances in cryptology crypto 96 lecture notes in computer science vol 1109 springer berlin 1996 pp 401 415 n n vcs is introduced for multiple binary secret images extended vcs evcs by ateniese et al extended capabilities for visual cryptography theoretical computer science 250 2001 143 161 for binary secret image uses meaningful innocent looking shares in this paper we start with a more concise derivation of matrix extension in the ecvs model this is implemented by concatenating an extended matrix to each basis matrix we then present a general construction method for single or multiple binary grayscale color secret images using matrix extension utilizing meaningful shares the result k n visual secret sharing schemes are more general than most existing schemes in terms of the secret share image types using our matrix extension algorithm any existing vcs with random looking shares can be easily modified to utilize meaningful shares the effectiveness of our schemes is demonstrated by real examples

mutual attraction model for both assortative and disassortative weighted networks for most complex networks the connection between a pair of nodes is the result of their mutual affinity and attachment in this letter we will propose a mutual attraction model to characterize weighted evolving networks by introducing the initial attractiveness a and the general mechanism of mutual attraction controlled by parameter m our model can naturally reproduce scale free distributions of degree weight and strength as found in many real systems also simulation results are consistent with theoretical predictions interestingly we obtain nontrivial clustering coefficient c and tunable degree assortativity r depending on the values of m and a our model appears as a more general one that unifies the characterization of both assortative and disassortative weighted networks

modeling the coevolution of topology and traffic on weighted technological networks for many technological networks the network structures and the traffic taking place on them mutually interact the demands of traffic increment spur the evolution and growth of the networks to maintain their normal and efficient functioning in parallel a change of the network structure leads to redistribution of the traffic in this paper we perform an extensive numerical and analytical study extending results of wang phys rev lett 94 188702 2005 by introducing a general strength coupling interaction driven by the traffic increment between any pair of vertices our model generates networks of scale free distributions of strength weight and degree in particular the obtained nonlinear correlation between vertex strength and degree and the disassortative property demonstrate that the model is capable of characterizing weighted technological networks moreover the generated graphs possess both dense clustering structures and an anticorrelation between vertex clustering and degree which are widely observed in real world networks the corresponding theoretical predictions are well consistent with simulation results

two secret sharing schemes based on boolean operations traditional secret sharing schemes involve complex computation a visual secret sharing vss scheme decodes the secret without computation but each shadow is m times as big as the original probabilistic vss solved the computation complexity and space complexity problems at once in this paper we propose a probabilistic 2 n scheme for binary images and a deterministic n n scheme for grayscale images both use simple boolean operations and both have no pixel expansion the 2 n scheme provides a better contrast and significantly smaller recognized areas than other methods the n n scheme gives an exact reconstruction

eliminating the texture features in visually meaningful cipher images generally most image encryption algorithms transform original images into texture like or noise like ones unfortunately the feature like texture or noise is just a hint of the existence of encryption for attackers to solve this problem bao et al inf sci 324 2015 197 207 proposed a new image encryption algorithm which can transform original images into visually meaningful ones however the resulting cipher images have some texture features which may be a hint of the existence of encryption to some extent to overcome this flaw we present a new visually meaningful image encryption algorithm based on discrete wavelet transform and discrete quantum walks numerical simulation security analysis and performance comparison demonstrate that our proposal is superior to bao et al s scheme it promotes the combination of image encryption and quantum computation

well posedness and large deviations for a class of spdes with levy noise abstract in this paper a class of stochastic partial differential equations spdes with levy noise is concerned firstly the local well posedness is established by the iterative approximation then the large deviation principle ldp for the regularized spdes is obtained by the weak convergence approach to get the ldp for spdes here an exponential equivalence of the probability measures is proved the results can be applied to some types of spdes such as stochastic burgers equation stochastic b family equation stochastic modified novikov equation and stochastic hunter saxton equation

large deviations for a reaction diffusion equation with non gaussian perturbations in this paper we establish a large deviations principle for the non gaussian stochastic reaction diffusion equation srde partial t nu varepsilon mathscr l nu varepsilon f x nu varepsilon varepsilon sigma x nu varepsilon ddot w tx as a random perturbation of the deterministic rde partial t nu 0 mathscr l nu 0 f x nu 0 here the space variable takes values on the unit circle s 1 and mathscr l is a strongly elliptic second order operator with constant coefficients the functions f and sigma are sufficiently regular so that there is a unique solution to the above srde for any continuous initial condition we also assume that there are positive constants m and m such that m leq sigma x y leq m for all x in s 1 and all y in mathbb r the perturbation ddot w tx is the formal derivative of a brownian sheet it is known that if the initial condition is continuous then the solution will also be continuous and moreover if the initial condition is assumed to be holder continuous of exponent kappa for some 0 kappa frac 1 2 then the solution will be holder continuous of exponent kappa 2 as a function of t x in this paper we establish the large deviations principle for nu varepsilon in the holder norm of exponent kappa 2 when the initial condition is holder continuous of exponent kappa for any 0 kappa frac 1 2 and when the initial condition is assumed only to be continuous we establish the large deviations principle for nu varepsilon in the supremum norm moreover we prove that these large deviations principles are uniform with respect to the initial condition

generating structured networks based on a weight dependent deactivation mechanism motivated by the degree dependent deactivation model generating networks with high clustering coefficient k klemm et al phys rev e 65 036123 2002 a weight dependent version is studied to model evolving networks the growth dynamics of the network is based on a naive weight driven deactivation mechanism which couples the establishment of new active vertices and the weights dynamical evolution both analytical solutions and numerical simulations show that the generated networks possess a high clustering coefficient larger than that for regular lattices of the same average connectivity weighted structured scale free networks are obtained as the deactivated vertex is target selected at each time step and weighted structured exponential networks are realized for the random selected case

colored visual cryptography scheme based on additive color mixing a t n visual cryptography scheme vcs encodes a secret image into n shadow images shadows distributed among n participants when any qualified set of at least t participants stack their shadows the secret image can be visually revealed the first vcs proposed by naor and shamir was only designed for encrypting a black and white secret image subsequently some colored vcss cvcss for sharing colored images were proposed to enhance the applicability in cvcss we usually use several color subpixels to represent a secret pixel where the number of subpixels is referred to as the pixel expansion generally the cvcs requires a larger pixel expansion to produce more colors however this expansion will increase the shadow size we therefore study the additive color mixing in a probabilistic way and propose a new cvcs whose pixel expansion is fixed and improves on the previous cvcss at the price of reducing the contrast quality to certain level

large deviations for stochastic reaction diffusion systems with multiplicative noise and non lipshitz reaction term following classical work by freidlin trans amer math soc 1988 305 665 657 and subsequent works by sowers ann probab 1992 20 504 537 and peszat probab theory related fields 1994 98 113 136 we prove large deviation estimates for the small noise limit of systems of stochastic reaction diffusion equations with globally lipschitz but unbounded diffusion coefficients however assuming the reaction terms to be only locally lipschitz with polynomial growth this generalizes results of the above mentioned authors our results apply in particular to systems of stochastic ginzburg landau equations with multiplicative noise

from scale free to erdos renyi networks we analyze a model that interpolates between scale free and erdos r enyi networks the model introduced generates a one parameter family of networks and allows one to analyze the role of structural heterogeneity analytical calculations are compared with extensive numerical simulations in order to describe the transition between these two important classes of networks finally an application of the proposed model to the study of the percolation transition is presented

mixing patterns in networks we study assortative mixing in networks the tendency for vertices in networks to be connected to other vertices that are like or unlike them in some way we consider mixing according to discrete characteristics such as language or race in social networks and scalar characteristics such as age as a special example of the latter we consider mixing according to vertex degree i e according to the number of connections vertices have to other vertices do gregarious people tend to associate with other gregarious people we propose a number of measures of assortative mixing appropriate to the various mixing types and apply them to a variety of real world networks showing that assortative mixing is a pervasive phenomenon found in many networks we also propose several models of assortatively mixed networks both analytic ones based on generating function methods and numerical ones based on monte carlo graph generation techniques we use these models to probe the properties of networks as their level of assortativity is varied in the particular case of mixing by degree we find strong variation with assortativity in the connectivity of the network and in the resilience of the network to the removal of vertices

large deviation principles for 2 d stochastic navier stokes equations driven by levy processes abstract in this paper we establish a large deviation principle for the two dimensional stochastic navier stokes equations driven by levy processes which involves the study of the levy noise and the investigation of the effect of the highly nonlinear unbounded drifts

color visual cryptography schemes for black and white secret images in this paper we propose the use of colors to improve visual cryptography schemes for black and white secret images the resulting model is called colored black and white visual cryptography cbw vc model using this new model we exploit colors to obtain schemes to share bw this is a direct consequence of the definition of contrast which distinguishes only black and non black pixels we discuss an alternative measure of contrast that takes into account the distance between colors we conjecture that also with this definition of contrast there exist schemes that use only full intensity colors and achieve optimal contrast

sample path properties of the stochastic flows we consider a stochastic flow driven by a finite dimensional brownian motion we show that almost every realization of such a flow exhibits strong statistical properties such as the exponential convergence of an initial measure to the equilibrium state and the central limit theorem the proof uses new estimates of the mixing rates of the multi point motion

large deviation for diffusions and hamilton jacobi equation in hilbert spaces large deviation for markov processes can be studied by hamilton jacobi equation techniques the method of proof involves three steps first we apply a nonlinear transform to generators of the markov processes and verify that limit of the transformed generators exists such limit induces a hamilton jacobi equation second we show that a strong form of uniqueness the comparison principle holds for the limit equation finally we verify an exponential compact containment estimate the large deviation principle then follows from the above three verifications this paper illustrates such a method applied to a class of hilbert space valued small diffusion processes the examples include stochastically perturbed allen cahn cahn hilliard pdes and a one dimensional quasilinear pde with a viscosity term we prove the comparison principle using a variant of the tataru method we also discuss different notions of viscosity solution in infinite dimensions in such context

a comprehensive weighted evolving network model abstract many social technological biological and economical systems are best described by weighted networks whose properties and dynamics depend not only on their structures but also on the connection weights among their nodes however most existing research work on complex network models are concentrated on network structures with connection weights among their nodes being either 1 or 0 in this paper we propose a new weighted evolving network model numerical simulations indicate that this network model yields three power law distributions for the node degrees connection weights and node strengths respectively particularly some other properties of the distributions such as the droop head and heavy tail effects can also be reflected by this model

recursive graphs with small world scale free properties we discuss a category of graphs recursive clique trees which have small world and scale free properties and allow a fine tuning of the clustering and the power law exponent of their discrete degree distribution we determine relevant characteristics of those graphs the diameter degree distribution and clustering parameter the graphs have also an interesting recursive property and generalize recent constructions with fixed degree distributions

a novel secret image sharing scheme in color images using small shadow images over the past several years secret image sharing techniques have become another branch of the effort to prevent secret images from being eavesdropped on in addition to traditional cryptography because smaller shadows can speed up the transmission of a secret color image in this paper we combine chang and wu s gradual search algorithm for a single bitmap btc gsbtc and shamir s k n threshold concept to propose a novel secret color image sharing scheme that generates smaller shadows experimental results confirm that the proposed scheme successfully reduces shadow size and that each shadow behaves as a random like image that prevents leakage of information about the secret color image furthermore the correlation between two vertically or horizontally adjacent pixels in each shadow is significantly less than those in a color secret image and the presented scheme also achieves on average an npcr 0 414 and auci 32 78 thus with our scheme one pixel difference could cause a significant difference in the corresponding shadows therefore the security of the presented scheme is also confirmed

distortionless visual multi secret sharing based on random grid we proposed an visual multi secret sharing without secret distortion we define the shape of share as pie not traditional doughnut shape number of secret sharing is more than two we adopt rg based for implementing vmss to void pixel expansion and complex codebook design because visual secret sharing vss has already been well defined visual multi secret sharing vmss is more practical for various fields in a vmss scheme n secret messages are encoded into two shares that appear to be noise and these are later stacked by rotating flipping and turning to visually recognize the secrets vmss is generally classified as visual cryptography vc based vmss or random grid rg based vmss however vc based vmss has the three main drawbacks of pixel expansion the cost of designing a complex codebook and shape distortion in the decoded secret image in order to stack shares at any angle during decoding secrets are encoded into doughnut shaped shares however the traditional doughnut share methods distort the secret after decoding because the shape of each share is doughnut this paper proposes a new rg based vmss scheme that defines the shape of each share as a pie shaped share that does not distort secrets so that multiple secrets are encoded into two pie shares and then decoded by stacking one pie share on another at different angles of rotation experimental results demonstrate the efficiency of the proposed method

extended color visual cryptography for black and white secret image recently de prisco and de santis introduced a k n colored black and white visual cryptography scheme cbw vcs which adopts colored pixels in shadow images to share a black and white secret image only k or more participants can reconstruct the secret image by combining their shadow images it seems that no one study k n cbw vcs with the extended ability revealing meaningful shadow images denoted as cbw extended vcs cbw evcs in this paper we extend the conventional evcs i e bw evcs to the cbw evcs this paper has two main contributions i we construct k n cwb evcss ii all constructions are proven to satisfy security contrast and cover image conditions we propose the k n colored black and white extended visual cryptography scheme cbw evcs our k n cbw evcs has the extended ability revealing meaningful shadow images we extend the conditions of k n cwb evcs to those of k n cwb evcs we prove that our constructions satisfy security contrast and cover image conditions

a discussion on the relationship between probabilistic visual cryptography and random grid abstract in a k n visual cryptography scheme vcs the dealer encodes the secret into n shadow images each pixel of the secret image is expanded into m sub pixels in each share in a k n vcs the secret can be visually reconstructed when k or more shares are available the reconstruction process employs the human visual system and no computations are required to solve the pixel expansion problem of vcss probabilistic vcss are directly converted from vcss with no pixel expansion another well known secret image sharing scheme random grid rg is also provided with this novel stacking to see property compared with vcs the most appealing benefit of rg is that there is no pixel expansion in this paper we use the probabilistic vcs without pixel expansion to study the construction and performance of rg this paper has two main results i we show that each step of the share generation process in all existing 2 2 rg 2 n rg n n rg k n rg incremental rg can be mapped to a corresponding step in pvcss and their shadow images between pvcs and rg are perfectly indistinguishable and the reconstructed images are the same also include our 2 n rg ii from the quality of reconstructed image pixel expansion recognized region size and image types to be considered for evaluating pvcss and rgs we point out that rg and pvcs have no difference other than the terminology furthermore rgs is a subset of pvcss

viscosity solutions of hamilton jacobi equations in infinite dimensions iv hamiltonians with unbounded linear terms in this work we show how to interpret s and e in the viscosity sense when the solutions may be expected to be weakly sequentially continuous in particular we introduce notions which allow us to handle the terms and for which we can obtain existence and uniqueness results in a variety of circumstances

quantum cryptographic algorithm for color images using quantum fourier transform and double random phase encoding abstract a novel encryption decryption method for color images is proposed in which quantum fourier transform qft and double random phase encoding drpe techniques have been used the encryption process can be realized by performing two secret random phase encoding operations respectively in the input and the qft planes because all quantum operations are invertible the decryption process is the inverse of the encryption process supported by detailed numerical simulation and theoretical analysis the method has clarified its robustness security and computational complexity over its classical counterpart and it opens the door for introducing color image encryption into quantum scenarios

visual secret sharing for multiple secrets conventional visual secret sharing schemes are designed for a single secret image so it is inefficient to generate numerous share images for multiple secret images simultaneously therefore a novel visual secret sharing scheme for multiple secret images is proposed in this paper in the proposed encryption process a stacking relationship graph of secret pixels and share blocks is generated to indicate the encryption functions and a set of visual patterns is defined to produce two share images according to this graph based on the stacking properties of these patterns the secret images can be obtained from the two share images at aliquot stacking angles the proposed scheme makes the number of secret images not restricted and further extends it to be general as a result the proposed scheme enhances visual secret sharing schemes ability for multiple secrets

generalized local world models for weighted networks based on the weighted scale free network model proposed by barrat barth elemy and vespignani phys rev lett 92 228701 2004 and enlightened by our local world concept li and chen physica a 328 274 2003 we propose two generalized local world glw models for weighted complex networks theoretical analysis and numerical simulations show that the glw models generate weighted networks as a crossover between exponential and scale free weighted networks and exhibit an alteration from assortative networks to disassortative networks

from unweighted to weighted networks with local information abstract in this paper we analyze an evolving model with local information which can generate a class of networks by choosing different values of the parameter p the model introduced exhibits the transition from unweighted networks to weighted networks because the distribution of the edge weight can be widely tuned with the increase in the local information the degree correlation of the network transforms from assortative to disassortative we also study the distribution of the degree strength and edge weight which all show crossover between exponential and scale free finally an application of the proposed model to the study of the synchronization is considered it is concluded that the synchronizability is enhanced when the heterogeneity of the edge weight is reduced

sharing multiple secrets in visual cryptography the secret sharing schemes in conventional visual cryptography are characterized by encoding one shared secret into a set of random transparencies which reveal the secret to the human visual system when they are superimposed in this paper we propose a visual secret sharing scheme that encodes a set of x 2 secrets into two circle shares such that none of any single share leaks the secrets and the x secrets can be obtained one by one by stacking the first share and the rotated second shares with x different rotation angles this is the first true result that discusses the sharing ability in visual cryptography up to any general number of multiple secrets in two circle shares

a weighted local world evolving network model with aging nodes abstract in this paper the dynamical behaviors of a class of weighted local world evolving networks with aging nodes are investigated as the network grows each newly added node is connected to some existing nodes through strength age preferential attachment each time step the newly added node with randomly determined initial degree is connected to some existing nodes through a local strength age preferential attachment by using tools from stochastic analysis and continuous approximation it is theoretically proved that the strength distribution of the generated network has a power law form with exponent depending nontrivially on a decay factor 0 1 in addition the clustering coefficient correlation and small world properties of this class of networks are examined via simulations it is shown that clustering coefficient is a monotone decreasing function of the decay factor and the assortative degree correlation and small world properties appear simultaneously finally the new model is used to characterize the internet topology as a typical application

modeling the evolution of weighted networks we present a general model for the growth of weighted networks in which the structural growth is coupled with the edges weight dynamical evolution the model is based on a simple weight driven dynamics and a weights reinforcement mechanism coupled to the local network growth that coupling can be generalized in order to include the effect of additional randomness and nonlinearities which can be present in real world networks the model generates weighted graphs exhibiting the statistical properties observed in several real world systems in particular the model yields a nontrivial time evolution of vertices properties and scale free behavior with exponents depending on the microscopic parameters characterizing the coupling rules very interestingly the generated graphs spontaneously achieve a complex hierarchical architecture characterized by clustering and connectivity correlations varying as a function of the vertices degree

multi image encryption by circular random grids visual secret sharing vss can encode a secret image into several share images where the original secret can be reconstructed and recognized by sight by stacking all share images there are two categories of vss schemes visual cryptography vc and random grids rg vc has three main drawbacks the large size the need for the codebook to be redesigned for specific applications and the ability to encode only one secret image at a time rg removes the first two drawbacks this paper proposes a novel rg based vss scheme that encodes multiple secret images at a time the scheme encrypts multiple secret images into two circular cipher grids and decrypts the images by stacking two circular cipher grids to obtain the first secret and gradually rotating one circular cipher grid at a fixed degree based on the quantity of the secret images encrypted to disclose other secrets compared with conventional vc based vss the proposed scheme has no pixel expansion a higher capacity for secret sharing and no need for a complex vc codebook to be redesigned theoretical analysis of visual quality and security is demonstrated

probabilistic visual secret sharing schemes for grey scale images and color images visual secret sharing vss scheme is an encryption technique that utilizes the human visual system in recovering the secret image and does not require any cryptographic computation pixel expansion has been a major issue of vss schemes a number of probabilistic vss schemes with minimum pixel expansion have been proposed for binary secret images this paper presents a general probabilistic k n vss scheme for grey scale images and another scheme for color images with our schemes the pixel expansion can be set to a user defined value when this value is 1 there is no pixel expansion at all the quality of reconstructed secret images measured by average contrast or average relative difference is equivalent to the contrast of existing deterministic vss schemes previous probabilistic vss schemes for black and white images can be viewed as special cases in the schemes proposed here

a multiple level visual secret sharing scheme without image size expansion in traditional vss schemes the size of the share image is substantially expanded since each pixel of the secret image is mapped onto a block consisting of several pixels in addition the quality of the reconstructed secret image is normally degraded in contrast especially for halftone images this study proposes a vss scheme that maps a block in a secret image onto one corresponding equal sized block in each share image without image size expansion two types of techniques including histogram width equalization and histogram depth equalization are proposed to generate the corresponding share blocks containing multiple levels rather than two levels based on the density of black pixels on the blocks for a secret block in the former technique the gray scale image histogram is obtained by uniformly splitting the range of the pixel gray levels in the secret image while in the latter the buckets are created so that the area of each bucket is roughly constant by containing approximately the same number of pixels the proposed schemes significantly improve the quality of the reconstructed secret image compared to several previous investigations

image cryptographic algorithm based on the haar wavelet transform lossless encryption methods are more applicable than lossy encryption methods when marginal distortion is not tolerable in this research the authors propose a novel lossless symmetric key encryption decryption technique in the proposed algorithm the image is transformed into the frequency domain using the haar wavelet transform then the image sub bands are encrypted in a such way that guarantees a secure reliable and an unbreakable form the encryption involves scattering the distinguishable frequency data in the image using a reversible weighting factor amongst the rest of the frequencies the algorithm is designed to shuffle and reverse the sign of each frequency in the transformed image before the image frequencies are transformed back to the pixel domain the results show a total deviation in pixel values between the original and encrypted image the decryption algorithm reverses the encryption process and restores the image to its original form the proposed algorithm is evaluated using standard security and statistical methods results show that the proposed work is resistant to most known attacks and more secure than other algorithms in the cryptography domain

efficient visual secret sharing scheme for color images a k out of n visual secret sharing scheme vsss resolves the visual variant of the k out of n secret sharing problem where only k or more out of n participants can reveal the secret by human visual system without any cryptographic computation the best pixel expansion of the general k out of n vsss for c colored images was cxm by yang and laih new colored visual secret sharing schemes des codes cryptogr 24 2000 325 335 where m is the pixel expansion of an existing binary k out of n vsss regarding the c colored n out of n scheme the best pixel expansion is c 1 2 n 1 c 2 and c c 1 2 n 2 c when n is odd and even respectively by blundo et al improved schemes for visual cryptography des codes cryptogr 24 2001 255 278 in this paper we propose a new c colored k out of n vsss by using a pixel expansion of log 2c xm that is more efficient than ever

large deviations for a class of stochastic partial differential equations we consider the random fields x e t q t 0 q o governed by stochastic partial differential equations driven by a gaussian white noise in space time where o is a bounded domain in lid with regular boundary to study the continuity of the random fields x e in space and time variables we prove an analogue of garsia s theorem we then derive the large deviation results based on the methods used by the second author in another paper this article provides an alternative proof of sowers result for the case of d 1

image encryption by multiple random grids in this paper we first give a formal definition to the visual cryptograms of n 2 random grids vcrg n for encrypting an image specifically a set of vcrg n with respect to image p consists of n random grids printed on transparencies such that only when the n transparencies are superimposed altogether can p be recognized by human vision without any computing device while any group of less than n transparencies obtains no information about p then we design novel vcrg n encryption schemes for binary gray level and color images validate the correctness by formal proofs and demonstrate the feasibility by computer simulations our schemes do not require any extra pixel expansion neither any encoding basis matrix which are necessary and inevitable in the approaches of conventional visual cryptography these attractive advantages make our schemes more informative in theoretical interests and much applicable in practical applications

image encryption to protect image contents most existing encryption algorithms are designed to transform an original image into a texture like or noise like image which is however an obvious visual sign indicating the presence of an encrypted image and thus results in a significantly large number of attacks to address this problem this paper proposes a new image encryption concept to transform an original image into a visually meaningful encrypted one as an example of the implementation of this concept we introduce an image encryption system simulation results and security analysis demonstrate excellent encryption performance of the proposed concept and system

3d tamed navier stokes equations driven by multiplicative levy noise existence uniqueness and large deviations abstract in this paper we show the existence and uniqueness of a strong solution to stochastic 3d tamed navier stokes equations driven by multiplicative levy noise with periodic boundary conditions then we establish the large deviation principles of the strong solution on the state space d 0 t h 1 where the weak convergence approach plays a key role

viscosity solutions of hamilton jacobi equations in infinite dimensions v unbounded linear terms and b continuous solutions we continue the systematic study of first order hamilton jacobi equations in infinite dimensions begun in parts i iv of this series 121 our approach relies on as before an appropriate interpretation of the notion of viscosity solutions as introduced in 11 lo in the interim the strong development of viscosity solution theory in many directions has continued unabated in addition to the many references given in earlier papers in this series which we will not repeat here see 12 we would like to point out that a complete theory of second order fully nonlinear and possibly degenerate elliptic equations in finite dimensions has been made possible by the use of viscosity solutions s 9 18 20 22 19 32 331 for example and there is now a substantial body of work concerning second order equations in infinite dimensions 25 271 however in this work we come back to the particular situation studied in 12 part iv namely we come back to hamilton jacobi equations in

large deviation principle for stochastic evolution equations the large deviation principle obtained by freidlin and wentzell for measures associated with finite dimensional diffusions is extended to measures given by stochastic evolution equations with non additive random perturbations the proof of the main result is adopted from the priouret paper concerning finite dimensional diffusions exponential tail estimates for infinite dimensional stochastic convolutions are used as main tools

large deviation problem for some parabolic itǒ equations the large deviation problem of wentzell freidlin type is considered for a class of semilinear parabolic equations perturbed by a small multiplicative noise in a hilbert space setting it is proved that under suitable conditions the associated family of solution measures depending on a small parameter obeys the large deviation principle with respect to a certain rate function

image encryption by random grids a random grid in this paper is a transparency comprising a two dimensional array of pixels that are either transparent or opaque determined in a totally random way we design algorithms by using random grids to accomplish the encryption of the secret gray level and color images in such a way that neither of the two encrypted shares alone leaks the information of the secret image whereas the secret can be seen when these two shares are superimposed the decryption process is done by our visual system and no computation is required as compared to the approaches in visual cryptography our algorithms do not need the basis matrices to encode the shares so that the problem of pixel expansion exists no more that is the sizes of the secret image and the encrypted shares are the same

the architecture of complex weighted networks networked structures arise in a wide array of different contexts such as technological and transportation infrastructures social phenomena and biological systems these highly interconnected systems have recently been the focus of a great deal of attention that has uncovered and characterized their topological complexity along with a complex topological structure real networks display a large heterogeneity in the capacity and intensity of the connections these features however have mainly not been considered in past studies where links are usually represented as binary states i e either present or absent here we study the scientific collaboration network and the world wide air transportation network which are representative examples of social and large infrastructure systems respectively in both cases it is possible to assign to each edge of the graph a weight proportional to the intensity or capacity of the connections among the various elements of the network we define appropriate metrics combining weighted and topological observables that enable us to characterize the complex statistical properties and heterogeneity of the actual strength of edges and vertices this information allows us to investigate the correlations among weighted quantities and the underlying topological structure of the network these results provide a better description of the hierarchies and organizational principles at the basis of the architecture of weighted networks

on the cauchy problem for non local ornstein uhlenbeck operators abstract we study the cauchy problem involving non local ornstein uhlenbeck operators in finite and infinite dimensions we prove classical solvability without requiring that the levy measure corresponding to the large jumps part has a first finite moment moreover we determine a core of regular functions which is invariant for the associated transition markov semigroup such a core allows to characterize the marginal laws of the ornstein uhlenbeck stochastic process as unique solutions to fokker planck kolmogorov equations for measures

random perturbations of reaction diffusion equations the quasi deterministic approximation on considere des champs aleatoires u e t x u 1 e t x u n e t x definis comme les solutions d un systeme d equations aux derivees partielles u k e t l k u k e f k x u 1 e u n e e k t x les l k sont des operateurs elliptiques lineaires d ordre 2 k sont des champs gaussiens bruit blanc

weighted scale free networks with stochastic weight assignments we propose a model of weighted scale free networks incorporating a stochastic scheme for weight assignments to the links taking into account both the popularity and fitness of a node as the network grows the weights of links are driven either by the connectivity with probability p or by the fitness with probability 1 ensuremath p numerical results show that the total weight exhibits a power law distribution with an exponent ensuremath sigma that depends on the probability p the exponent ensuremath sigma decreases continuously as p increases for p 0 the scaling behavior is the same as that of the connectivity distribution an analytical expression for the total weight is derived so as to explain the features observed in the numerical results numerical results are also presented for a generalized model with a fitness dependent link formation mechanism

viscosity solutions for a class of hamilton jacobi equations in hilbert spaces we study hamilton jacobi equations with an unbounded term in hilbert spaces we introduce a new variant of the notion of viscosity solution for a class of hamilton jacobi equations and obtain comparison and existence results for viscosity solutions we also examine the usefulness of the notion of viscosity solution in optimal control

mutual selection model for weighted networks for most networks the connection between two nodes is the result of their mutual affinity and attachment in this paper we propose a mutual selection model to characterize the weighted networks by introducing a general mechanism of mutual selection the model can produce power law distributions of degree weight and strength as confirmed in many real networks moreover we also obtained the nontrivial clustering coefficient c degree assortativity coefficient r and degree strength correlation depending on a single parameter m these results are supported by present empirical evidence studying the degree dependent average clustering coefficient c k and the degree dependent average nearest neighbors degree k nn k also provide us with a better description of the hierarchies and organizational architecture of weighted networks

weighted assortative and disassortative networks model abstract real world networks process structured connections since they have non trivial vertex degree correlation and clustering here we propose a toy model of structure formation in real world weighted network in our model a network evolves by topological growth as well as by weight change in addition we introduce the weighted assortativity coefficient which generalizes the assortativity coefficient of a topological network to measure the tendency of having a high weighted link between two vertices of similar degrees network generated by our model exhibits scale free behavior with a tunable exponent besides a few non trivial features found in real world networks are reproduced by varying the parameter ruling the speed of weight evolution most importantly by studying the weighted assortativity coefficient we found that both topologically assortative and disassortative networks generated by our model are in fact weighted assortative

a general non convex large deviation result with applications to stochastic equations we prove an abstract large deviation result for a sequence of random elements of a vector space satisfying an abstract exponential martingale condition the framework naturally generates non convex rate functions we apply the result to solutions of ito stochastic equations in r d driven by brownian motion and a poisson random measure

reduce shadow size in aspect ratio invariant visual secret sharing schemes using a square block wise operation an aspect ratio invariant visual secret sharing arivss scheme is a perfectly secure method for sharing secret images due to the nature of the vss encryption each secret pixel is expanded to m sub pixels in each of the generated shares the advantage of arivss is that the aspect ratio of the recovered secret image is fixed and thus there is no loss of information when the shape of the secret image is our information for example a secret image of a circle is compromised to an ellipse if m does not have a square value two arivss schemes based on processing one and four pixel blocks respectively were previously proposed in this paper we have generalized the square block wise approach to further reduce pixel expansion

meaningful secret sharing technique with authentication and remedy abilities lin and tasi yang et al and chang et al s meaningful secret sharing schemes provided authentication mechanisms but none included a remedy ability that would cause the secret image never to be completely obtained while some information of the stego images are losing or tampering with this paper proposes a meaningful secret sharing scheme which includes both authentication and remedy abilities that allow for detection of the corrupted area and use of the hidden information to repair the secret image with reasonable visual quality in comparison with previous schemes this approach results in superior visual qualities of the stego images by an average of more than 3db

almost aspect ratio invariant visual cryptography without adding extra subpixels we propose a k n almost aspect ratio invariant vcs aaivcs our k n aaivcs does not need extra subpixels our k n aaivcs does not find out a mapping pattern for arranging subpixels we theoretically prove that our scheme has the smallest aspect ratio difference a visual cryptographic scheme is a method to decompose a secret image into shadow images by expanding a secret pixel into m subpixels only legitimate subsets of participants can reconstruct the original image by combining their shadows because the size of the subpixel is the same as that of the pixel the shadow size is expanded m times in cases where m is not a square number the aspect ratio of the reconstructed image is distorted accordingly an aspect ratio invariant vcs arivcs was proposed to address this distortion problem however arivcs requires extra subpixels and a mapping pattern showing how to arrange the subpixels a large m creates a significant challenge when attempting to derive this pattern in this paper we propose the almost aspect ratio invariant vcs aaivcs which simulates the principle of a jigsaw puzzle the proposed aaivcs has the smallest loss of aspect ratio when we do not add extra subpixels

the dynamics of the stochastic shadow gierer meinhardt system we consider the dynamics of the stochastic shadow gierer meinhardt system with one dimensional standard brownian motion we establish the global existence and uniqueness of solutions we also prove a large deviation result