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

on the security of a visual cryptography scheme for color images hou visual cryptography for color images pattern recognition 36 2003 1619 1629 proposed a four share visual cryptography scheme for color images the scheme splits a dithered eight color secret image into four shares the black mask and other three shares it was claimed that without knowing the black mask no information about the secret image can be obtained even if all the other three shares are known in this paper we show that this may be true for a few specific two color secret images only in all other cases however security cannot be guaranteed we show that an attacker can compromise a randomly chosen two color secret image from any two of the other three shares with probability 47 by completely recovering the shape and pattern of the secret image the advantage will increase to 67 if all the three shares are known if the secret image has three or four colors we show that the attacker can compromise it with probability 47 and 835 respectively finally we show that our technique can be extended to compromising secret images with more than four colors

last syzygies of 1 generic spaces abstract we consider determinantal varieties x of expected codimension defined by the maximal minors of a matrix m of linear forms representing a linear map eisenbud and popescu have conjectured that 1 generic linear maps have the property that the syzygy ideals i s of all last syzygies s of x coincide with i x we prove a geometric version of this conjecture for 1 generic linear maps the syzygy varieties syz s v i s of all last syzygies have the same support as x

dynamical grobner bases over dedekind rings abstract in this paper we extend the notion of dynamical grobner bases introduced by the second author to dedekind rings with zero divisors as an application we dynamically solve the ideal membership problem and compute a generating set for the syzygy module over multivariate polynomial rings with coefficients in dedekind rings we also give a partial positive answer to a conjecture about grobner rings

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

sharing a verifiable secret image using two shadows in this paper we propose a novel 2 2 verifiable secret sharing vss scheme which not only protects a secret image but also allows users to verify the restored secret image in the revealing and verifying phase for all binary grayscale and color images error diffusion and image clustering techniques are adopted to achieve our objective experimental results and discussions show that the proposed scheme with its smaller shadow size and lower computational complexity obviously outperforms previous vss schemes designed either with or without the cheating prevention mechanism moreover the use of a halftone logo gives an efficient solution to verifying whether the restored secret image is correct by using a halftone logo

flocking of the cucker smale model on general digraphs in the literature the study of the cucker smale c s flocking model is all restricted to connected undirected graphs or digraphs of some special types containing only a single root in this technical note we establish the flocking behavior of the c s model on general digraphs which contain all existing interaction topologies in relation to the c s model as special cases in particular the topology with multiple leaders is included the flocking results are guaranteed under some conditions on the initial state of the flock only the critical exponent below which unconditional convergence holds is given depending only on the interaction topology it is consistent with the ones obtained under some known special topologies in the literature

an adaptive secret image sharing with a new bitwise steganographic property recently numerous studies have been conducted in the area of secret image sharing and steganography the main objective of these schemes is to produce high quality tampering resistant stego images a number of these methods are based on least significant bit embedding and hence the presence of hidden data can be detected by well designed steganalysis algorithms this paper proposes a new sharing scheme for critical images so that stego images are obtained with better visual quality and at the same time the authentication ability can be adjusted to any desired level adaptive in order to achieve these objectives the construction of cellular automata is modified so that visual quality is improved although authentication bits are hidden in cover images furthermore authentication bits are computed in such a way that any tampering with one block affects more than one block for steganographic purposes least significant bit replacement is substituted with a new blockwise xor operation so that the scheme can withstand steganalysis attacks the other interesting property of the proposed method is that the size of blocks is determined dynamically therefore our approach can be adapted with secret cover images of different sizes

linear syzygies of curves with prescribed gonality abstract we prove two statements concerning the linear strand of the minimal free resolution of a k gonal curve c of genus g firstly we show that a general curve c of genus g of non maximal gonality k g 1 2 satisfies schreyer s conjecture that is b g k 1 c c g k this statement goes beyond green s conjecture and predicts that all highest order linear syzygies in the canonical embedding of c are determined by the syzygies of the k 1 dimensional scroll containing c secondly we prove an optimal effective version of the gonality conjecture for general k gonal curves which makes more precise the asymptotic gonality conjecture proved by ein lazarsfeld and improves results of rathmann

hiding data in images by simple lsb substitution in this paper a data hiding scheme by simple lsb substitution is proposed by applying an optimal pixel adjustment process to the stego image obtained by the simple lsb substitution method the image quality of the stego image can be greatly improved with low extra computational complexity the worst case mean square error between the stego image and the cover image is derived experimental results show that the stego image is visually indistinguishable from the original cover image the obtained results also show a significant improvement with respect to a previous work

avoiding collisions in flocks among the many models for flocking systems of interacting particles the one introduced by cucker and smale has attracted attention due to the fact that a convergence to flocking i e to a common velocity could be established depending on conditions on the initial state of the system in this note we extend this model by adding to it a repelling force between particles we show that for this modified model convergence to flocking is established along the same lines while in addition avoidance of collisions i e the respect of a minimal distance between particles is ensured

projective subvarieties having large green lazarsfeld index abstract let x p n c be a nondegenerate projective irreducible subvariety of degree d and codimension c 1 the green lazarsfeld index of x denoted by index x is defined as the largest p such that the homogeneous ideal of x is generated by quadrics and the syzygies among them are generated by linear syzygies until the p 1 th stage thus index x is an important invariant in order to describe the minimal free resolution of x recently it is shown that d c 1 if and only if index x c and x is a del pezzo variety if and only if index x c 1 in this paper we prove that index x c 2 c 3 if and only if x is either a complete intersection of three quadrics or else an arithmetically cohen macaulay variety with d c 3 theorem 1 1 also we classify x with index x c 3 c 4 for the cases when d c 2 theorem 4 1 and when x is a smooth surface theorem 4 3

sharing secrets in stego images with authentication recently lin and tsai and yang et al proposed secret image sharing schemes with steganography and authentication which divide a secret image into the shadows and embed the produced shadows in the cover images to form the stego images so as to be transmitted to authorized recipients securely in addition these schemes also involve their authentication mechanisms to verify the integrity of the stego images such that the secret image can be restored correctly unfortunately these schemes still have two shortcomings one is that the weak authentication cannot well protect the integrity of the stego images so the secret image cannot be recovered completely the other shortcoming is that the visual quality of the stego images is not good enough to overcome such drawbacks in this paper we propose a novel secret image sharing scheme combining steganography and authentication based on chinese remainder theorem crt the proposed scheme not only improves the authentication ability but also enhances the visual quality of the stego images the experimental results show that the proposed scheme is superior to the previously existing methods

hierarchical cucker smale model subject to random failure consider a system of autonomous interacting agents in r3 where each agent adjusts its velocity according to its own past velocity and a weighted mean of the relative velocities of its superiors in a certain prescribed hierarchy furthermore each agent at each time step can fail to see any of its superiors with a certain probability the failure rate probability we prove that for agent interactions with linear or sub linear distance dependent rate of decay the flocking results valid for the non failure deterministic model introduced by shen also hold true independently of the failure rate probability

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

algorithm for computing the moduli space of pointed gorenstein curves with weierstrass gap sequence 1 2 g 2 λ 2g 3 abstract an algorithm for computing the moduli space of pointed gorenstein curves with weierstrass gap sequence 1 2 g 2 2 g 3 where 3 g 5 g 8 and g 6 is given this algorithm consists in deforming a nonreduced reducible canonical curve by the method of stohr

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

consensus conditions of multi agent systems with time varying topologies and stochastic communication noises this paper investigates the average consensus problem of first order discrete time multi agent networks in uncertain communication environments each agent can only use its own and neighbors information to design its control input to attenuate the communication noises a distributed stochastic approximation type protocol is used by using probability limit theory and algebraic graph theory consensus conditions for this kind of protocols are obtained a for the case of fixed topologies a necessary and sufficient condition for mean square average consensus is given which is also sufficient for almost sure consensus b for the case of time varying topologies sufficient conditions for mean square average consensus and almost sure consensus are given respectively especially if the network switches between jointly containing spanning tree instantaneously balanced graphs then the designed protocol can guarantee that each individual state converges both almost surely and in mean square to a common random variable whose expectation is right the average of the initial states of the whole system and whose variance describes the static maximum mean square error between each individual state and the average of the initial states of the whole system

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

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

emergent behavior of a cucker smale type particle model with nonlinear velocity couplings in this note we present a cucker smale type flocking model with nonlinear velocity couplings and derive sufficient conditions for the formation of flocking in terms of communication weight and initial spatial velocity standard deviations

cucker smale flocking under hierarchical leadership and random interactions consider a flock of birds that fly interacting between them this flock is a hierarchical system in which each bird at each time step adjusts its own velocity according to its past velocity and a linear combination of the relative velocities of its superiors in the hierarchy this linear combination has nonnegative random coefficients including the case in which each of the birds can fail to see any of its superiors with certain probability for this model with random interactions we prove that the flocking results obtained for similar deterministic models hold true

on the vanishing of higher syzygies of curves ii we verify green s conjecture for a generic k gonal curve of genus g for g geq k k 1 2

scrollar syzygies of general canonical curves with genus le 8 we prove that for a general canonical curve c c z 9 1 of genus g the space of g 5 2 th last scrollar syzygies is isomorphic to the brill noether locus c 1 g 2 2 schreyer has conjectured that these scrollar syzygies span the space of all g 5 2 th last syzygies of c using mukai varieties we prove this conjecture for genus 6 7 and 8

convergence rates of distributed average consensus with stochastic link failures we consider a distributed average consensus algorithm over a network in which communication links fail with independent probability in such stochastic networks convergence is defined in terms of the variance of deviation from average we first show how the problem can be recast as a linear system with multiplicative random inputs which model link failures we then use our formulation to derive recursion equations for the second order statistics of the deviation from average in networks with and without additive noise we give expressions for the convergence behavior in the asymptotic limits of small failure probability and large networks we also present simulation free methods for computing the second order statistics in each network model and use these methods to study the behavior of various network examples as a function of link failure probability

a simple and high hiding capacity method for hiding digit by digit data in images based on modulus function this study presents a simple method for high hiding capacity the basic concept uses a modulus operation the proposed method has the following advantages 1 the proposed method outperforms the simple lsb substitution method given the same range 0 m 1 of data digits in the embedded data 2 the proposed method achieves good image vision quality without the need for post processing 3 the proposed method is almost as simple as the lsb method in both coding and decoding 4 the smaller error advantage over the simple lsb substitution method can also be mathematically verified 5 the error is smaller than m 1 2 for almost every pixel 6 the proposed method has high hiding capacity for example the proposed method can hide a 256 256 or 256 512 image in a 512 512 host image

green s conjecture for curves on rational surfaces with an anticanonical pencil green s conjecture is proved for smooth curves c lying on a rational surface s with an anticanonical pencil under some mild hypotheses on the line bundle l mathcal o s c constancy of clifford dimension clifford index and gonality of curves in the linear system vert l vert is also obtained

birational morphisms of rational surfaces abstract a fairly complete characterization on anticanonical rational surfaces of the divisor classes whose sections define birational morphisms is given most results are proven over an algebraically closed field of arbitrary characteristic

image hiding scheme with modulus function and dynamic programming strategy on partitioned pixels in this paper we shall propose a novel image hiding scheme our new scheme classifies the host image pixels into two groups of pixels according to the pixel values for each group of pixels the corresponding secret pixel values go through an optimal substitution process and are transformed into other pixel values by following the dynamic programming strategy then we can embed the transformed pixel values in the host pixels by using the modulus functions and obtain the stego image extensive experimental results demonstrate that our new method is capable of offering better stego image quality than a number of well accepted schemes

finding optimal least significant bit substitution in image hiding by dynamic programming strategy abstract the processing of simple least significant bit lsb substitution embeds the secret image in the least significant bits of the pixels in the host image this processing may degrade the host image quality so significantly that grabbers can detect that there is something going on in the image that interests them to overcome this drawback an exhaustive least significant bit substitution scheme was proposed by wang et al but it takes huge computation time wang et al then proposed another method that uses a genetic algorithm to search approximate optimal solutions and computation time is no longer so huge in this paper we shall use the dynamic programming strategy to get the optimal solution the experimental results will show that our method consumes less computation time and also gets the optimal solution

cucker smale flocking under rooted leadership with fixed and switching topologies in recent years a number of articles have focused on mathematical models for emergent phenomena for instance the flocking of birds or the schooling of fish in 2007 cucker and smale proposed an ingenious model which captures many of the observed features of moving animals subsequently shen extended the result to hierarchically structured flocks motivated by these works in this paper we study the discrete cucker smale flocking under rooted leadership which means that there exists an overall leader such that any other agent is led directly or indirectly by the leader the feature of our proposal departing from the existing models is that both the assumption of symmetry and the partial ordering of a hierarchy are dropped the rooted leadership topology is a necessary condition for the group to converge towards a single leader s fixed constant velocity the rates of convergence are established for flocks with fixed and switching topologies the results may reveal the applicability and advantage o

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

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

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

secret image sharing based on cellular automata and steganography recently lin and tsai secret image sharing with steganography and authentication the journal of systems and software 73 2004 405 414 and yang et al improvements of image sharing with steganography and authentication the journal of systems and software 80 2007 1070 1076 proposed secret image sharing schemes combining steganography and authentication based on shamir s polynomials the schemes divide a secret image into some shadows which are then embedded in cover images in order to produce stego images for distributing among participants to achieve better authentication ability chang et al sharing secrets in stego images with authentication pattern recognition 41 2008 3130 3137 proposed in 2008 an improved scheme which enhances the visual quality of the stego images as well and the probability of successful verification for a fake stego block is 1 16 in this paper we employ linear cellular automata digital signatures and hash functions to propose a novel t n threshold image sharing scheme with steganographic properties in which a double authentication mechanism is introduced which can detect tampering with probability 255 256 employing cellular automata instead of shamir s polynomials not only improves computational complexity from o nlog 2n to o n but obviates the need to modify pixels of cover images unnecessarily compared to previous methods c lin w tsai secret image sharing with steganography and authentication the journal of systems and software 73 2004 405 414 c yang t chen k yu c wang improvements of image sharing with steganography and authentication the journal of systems and software 80 2007 1070 1076 c chang y hsieh c lin sharing secrets in stego images with authentication pattern recognition 41 2008 3130 3137 we use fewer number of bits in each pixel of cover images for embedding data so that a better visual quality is guaranteed we further present some experimental results

syzygies of canonical curves and special linear series 0 introduction 105 1 line bundles on scrolls 109 2 scrolls and pencils 113 3 syzygies of a subvariety of a scroll 115 4 canonical curves 118 5 on the equation of rational surfaces 121 6 d gonal curves for d 5 126 7 proof of the main result 131 references 136

the gonality and the clifford index of curves on a toric surface abstract we determine the gonality and the clifford index for curves on a compact smooth toric surface moreover it is shown that their gonality is computed by pencils on the ambient surface from the geometrical viewpoint this means that the gonality can be read off from the lattice polygon associated to the curve

canonical curves with low apolarity abstract let k be an algebraically closed field and let c be a non hyperelliptic smooth projective curve of genus g defined over k since the canonical model of c is arithmetically gorenstein macaulay s theory of inverse systems allows us to associate to c a cubic form f in the divided power k algebra r g 3 in g 2 variables the apolarity ap c of c is the minimal number t of linear form l 1 l t r g 3 needed to write f as the sum of their divided power cubes it is easy to see that ap c g 2 and p de poi and f zucconi classified curves with ap c g 2 when k c in this paper we give a complete characteristic free classification of curves c with apolarity g 1 and g 2

high rank linear syzygies on low rank quadrics we study the linear syzygies of a homogeneous ideal i subseteq s rm sym bf k v focussing on the graded betti numbers b i i 1 rm dim bf k rm tor i s i bf k i 1 for a variety x and divisor d with v h 0 d what conditions on d ensure that b i i 1 ne 0 eisenbud has shown that a decomposition d sim a b such that a and b have at least two sections gives rise to determinantal equations and corresponding syzygies in i x and conjectured that if i 2 is generated by quadrics of rank le 4 then the last nonvanishing b i i 1 is a consequence of such equations we describe obstructions to this conjecture and prove a variant the obstructions arise from toric specializations of the rees algebra of koszul cycles and we give an explicit construction of toric varieties with minimal linear syzygies of arbitrarily high rank this gives one answer to a question posed by eisenbud and koh

sharing and hiding secret images with size constraint this paper presents a method for sharing and hiding secret images the method is modified from the t n threshold scheme comput graph 26 5 2002 765 the given secret image is shared and n shadow images are thus generated each shadow image is hidden in an ordinary image so as not to attract an attacker s attention any t of the n hidden shadows can be used to recover the secret image the size of each stego image in which a shadow image is hidden is about 1 t of that of the secret image avoiding the need for much storage space and transmission time in the sense that the total size of t stego images is about the size of the secret image experimental results indicate that the qualities of both the recovered secret image and the stego images that contain the hidden shadows are acceptable the photographers who work in enemy areas can use this system to transmit photographs

syzygies of torsion bundles and the geometry of the level l modular variety over overline mathcal m _ g we formulate and in some cases prove three statements concerning the purity or more generally the naturality of the resolution of various modules one can attach to a generic curve of genus g and a torsion point of l in its jacobian these statements can be viewed an analogues of green s conjecture and we verify them computationally for bounded genus we then compute the cohomology class of the corresponding non vanishing locus in the moduli space mathcal r g ell of twisted level l curves of genus g and use this to derive results about the birational geometry of mathcal r g ell for instance we prove that mathcal r g 3 is a variety of general type when g 11 and the kodaira dimension of mathcal r 11 3 is greater than or equal to 19 in the last section we explain probabilistically the unexpected failure of the prym green conjecture in genus 8 and level 2

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

on universal severi varieties of low genus k3 surfaces we prove the irreducibility of universal severi varieties parametrizing irreducible reduced nodal hyperplane sections of primitive k3 surfaces of genus g with 3 g 11 g 10

emergent behavior in flocks we provide a model for both continuous and discrete time describing the evolution of a flock our model is parameterized by a constant beta capturing the rate of decay which in our model is polynomial of the influence between birds in the flock as they separate in space our main result shows that when beta 1 2 convergence of the flock to a common velocity is guaranteed while for betages1 2 convergence is guaranteed under some condition on the initial positions and velocities of the birds only

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

steganography of capacity required using modulo operator for embedding secret image in this paper a novel mechanism using modulus operations to incorporate secret data with image form into a host image is proposed the used modulus is a threshold value that indicates how many bits of the secret image are being incorporated into the host image in our scheme there are two kinds of secret images processed the capacities of these two types are half the size and a quarter the size of the chosen host image respectively as can be seen in the result of our experiment not only can the secret images be totally embedded but the extra information such as the auxiliary table assisting the secret extraction is released as well even then there is still space remaining after the hiding procedure is completed the result is a higher capacity exploration for embedding the secret into a host image upon inspection of the quality of the stego image using the measurement of psnr it is noted that not only does the image display make the grade of the human vision system i e it is imperceptible by human eyes as far as the embedded secret is concerned but also the valued results of psnr remain sufficiently stable for a variety of host image selections therefore our proposal scheme is notably superior to those in the previous literature iee proc vision image signal process 147 1 2000 29 the advantages of this proposed scheme are the higher capacity exploration on secret embedding and better stability on stego image displays

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

image hiding by optimal lsb substitution and genetic algorithm in this paper we develop a novel method to embed important data in the host image so that the interceptors will not notice about the existence of the data the basic concept of the proposed method is by simple lsb substitution to prevent illicit access of data and increase the system performance the method of randomized process and the optimal lsb substitution are proposed the e ectiveness of the optimal lsb substitution in the worst case is proved we also develop a genetic algorithm to solve the problem of hiding important data in the rightmost k lsbs of the host image which may involve a huge computation time to nd the optimal result when k is large finally based on the concept of perceptual modeling an improved hiding technique is developed to obtain a high quality embedding result experimental results will reveal that the quality of the embedding result will not be seriously degraded and is near optimal by utilizing the proposed method 2001 pattern recognition society published by elsevier science ltd all rights reserved

determinantal characterization of canonical curves and combinatorial theta identities we characterize genus g canonical curves by the vanishing of combinatorial products of g 1 determinants of brill noether matrices this also implies the characterization of canonical curves in terms of g 2 g 3 2 theta identities a remarkable mechanism based on a basis of h 0 k c expressed in terms of szego kernels reduces such identities to a simple rank condition for matrices whose entries are logarithmic derivatives of theta functions such a basis together with the fay trisecant identity also leads to the solution of the question of expressing the determinant of brill noether matrices in terms of theta functions without using the problematic klein fay section