sharp estimates for solutions of multi bubbles in compact riemann surfaces in this paper we consider a sequence of multibubble solutions u k of the equation 0 1 0 u k k he uk f m he u k d 1 0 in m where h is a c 2 positive function in a compact riemann surface m and k is a constant satisfying lim k k 8m for some positive integer m 1 we prove among other things that k 8m 2 m m j 1h 1 p k j 0 log h p k j 8m 2k p k j k j e k j o e k j where p k j are centers of the bubbles of u k and k j are the local maxima of u k after adding a constant this yields a uniform bound of solutions as k converges to 8m from below provided that 0 log h p k j 8m 2k p k j 0 it generalizes a previous result due to ding jost li and wang 18 and nolasco and tarantello 31 which says that any sequence of minimizers u k is uniformly bounded if k 0 for any maximum point p of the sum of 2 log h and the regular part of the green function where k is the gaussian curvature of m the analytic work of this paper is the first step toward computing the topological degree of 0 1 which was initiated by li 24

on the negative k theory of schemes in finite characteristic abstract we show that if x is a d dimensional scheme of finite type over an infinite perfect field k of characteristic p 0 then k i x 0 and x is k i regular for i d 2 whenever the resolution of singularities holds over k this proves the k dimension conjecture of weibel c weibel k theory and analytic isomorphisms invent math 61 1980 177 197 2 9 except for d 1 i d 2 in all characteristics assuming the resolution of singularities

a high payload frequency based reversible image hiding method to provide both a high payload capacity and a good stego image quality a high payload frequency based reversible image hiding hpfrih method was presented in this paper these performances can be achieved by transforming a cover image from the spatial domain into the frequency domain through haar digital wavelet transform hdwt method followed by an adaptive arithmetic coding method to encode the hdwt coefficients in a high frequency band the hpfrih method was used to conceal both the compressed data and the secret data in the high frequency band this simple method can completely reconstruct the cover image only from the stego image moreover experimental results showed that the hpfrih method offers both impressive hiding capacity and satisfied stego image quality

an improved approach to steganalysis of jpeg images steganography secretly embeds additional information in digital products the potential for covert dissemination of malicious software mobile code or information is great to combat the threat posed by steganography steganalysis aims at the exposure of the stealthy communication in this paper a new scheme is proposed for steganalysis of jpeg images which being the most common image format is believed to be widely used for steganography purposes as there are many free or commercial tools for producing steganography using jpeg covers first a recently proposed markov approach 27 is expanded to the inter block of the discrete cosine transform dct and to the discrete wavelet transform dwt the features on the joint distributions of the transform coefficients and the features on the polynomial fitting errors of the histogram of the dct coefficients are also extracted all features are called original expanded features epf next the epf features are extracted from the calibrated version these are called reference epf features the difference between the original and the reference epf features is calculated and then the original epf features and the difference are merged to form the feature vector for classification to handle the large number of developed features the feature selection method of support vector machine recursive feature elimination svm rfe and a method of multi class support vector machine recursive feature elimination msvm rfe are used to select features for binary classification and multi class classification respectively finally support vector machines are applied to the selected features for detecting stego images experimental results show that in comparison to the markov approach 27 this new scheme remarkably improves the detection performance on several jpeg based steganographic systems including jphs cryptobola f5 steghide and model based steganography

effective watermarking scheme in the encrypted domain for buyer seller watermarking protocol in most watermarking schemes for copyright protection a seller usually embeds a watermark in multimedia content to identify a buyer when an unauthorized copy is found by the seller the traitor s identity can be traced by the embedded watermark however it incurs both repudiation issue and framing issue to solve these problems some buyer seller watermarking protocols have been proposed based on watermarking scheme in the encrypted domain in this paper an enhanced watermarking scheme is presented compared with solanki et al s scheme the enhanced scheme increases effective watermarking capacity avoids additional overhead and overcomes an inherent flaw that watermarking capacity depends on the probability distribution of input watermark sequence based on the security requirements of buyer seller watermarking protocols a new watermarking scheme in the encrypted domain with flexible watermarking capacity is proposed it improves the robustness of watermark sequence against image compressions and enables image tampering detection watermark extraction is blind which employs the same threshold criterion and secret keys as watermark embedding experimental results demonstrate that the enhanced watermarking scheme eliminates the drawbacks of solanki et al s scheme and that the proposed watermarking scheme in the encrypted domain outperforms kuribayashi and tanaka s scheme

high capacity image hiding scheme based on vector quantization a novel grayscale image hiding scheme that is capable of hiding multiple secret images into a host image of the same size is proposed in this paper the secret images to be hidden are first compressed by vector quantization with additional index compression process then the compressed secret images are encrypted and embedded into the least significant bits of the host pixels to provide good image quality of the stego image the modulus function and the image property are employed to hide the secret bits into the host pixels and determine the number of hidden bits in each host pixel respectively according to the results the proposed scheme provides a higher hiding capacity and a higher degree of security than that of the virtual image cryptosystem

bi relative algebraic k theory and topological cyclic homology it is well known that algebraic k theory preserves products of rings however in general algebraic k theory does not preserve fiber products of rings and one defines bi relative algebraic k theory so as to measure the deviation it was proved recently by cortinas 6 that rationally bi relative algebraic k theory and bi relative negative cyclic homology agree in this paper we show that with finite coefficients bi relative algebraic k theory and bi relative topological cyclic homology agree as an application we show that for a possibly singular curve over a perfect field k of positive characteristic p the cyclotomic trace map induces an isomorphism of the p adic algebraic k groups and the p adic topological cyclic homology groups in non negative degrees as a further application we show that the difference between the p adic k groups of the integral group ring of a finite group and the p adic k groups of a maximal z order in the rational group algebra can be expressed entirely in terms of topological cyclic homology let f be a functor that to a unital associative ring a associates a symmetric spectrum f a if i a is a two sided ideal the relative term f a i is defined to be the homotopy fiber of the map f a f a i induced from the canonical projection if further f a b is a ring homomorphism such that f i f i is an isomorphism onto a two sided ideal of b there is an induced map f a i f b f i and the bi relative term f a b i is defined to be the homotopy fiber of this map then there is a distinguished triangle in the stable homotopy category

a novel image hiding scheme based on block difference to transmit a secret image securely by embedding it into a cover image without drawing the unintended observer s attention a novel image hiding scheme is proposed by exploring the block correlation between the cover image and the secret image the stego image quality can be greatly improved experimental results demonstrate that the stego image has a high peak signal to noise ratio and the stego image is almost the same as the cover image

reversible data hiding based on block median preservation this paper proposes a reversible data hiding scheme for gray level images it exploits the high correlation among image block pixels to produce a difference histogram secret data is embedded based on a multi level histogram shifting mechanism with reference to the integer median of each block the image blocks are divided into four categories due to four corresponding embedding strategies aiming at preserving the medians during data embedding in decoder the median pixels are retrieved first followed by the hidden data extraction and the host image can be accurately recovered via an inverse histogram shifting mechanism after removing the secret data from the marked image experimental results validate the effectiveness of our scheme and demonstrate that it outperforms several previous methods in terms of capacity and marked image s quality

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

an improved geometric inequality via vanishing moments with applications to singular liouville equations we consider a class of singular liouville equations on compact surfaces motivated by the study of electroweak and self dual chern simons theories the gaussian curvature prescription with conical singularities and onsager s description of turbulence we analyse the problem of existence variationally and show how the angular distribution of the conformal volume near the singularities may lead to improvements in the moser trudinger inequality and in turn to lower bounds on the euler lagrange functional we then discuss existence and non existence results

hiding secret data in images via predictive coding this paper presents a prediction based image hiding scheme that embeds secret data into compression codes during image compression this scheme employs a two stage structure a prediction stage and an entropy coding stage the secret data is embedded into the difference values of a given image after the prediction stage is performed according to the experimental results the image quality is better than jpeg jsteg and its improved scheme inform sci 141 1 2 2002 123 the average image quality of the stego images in the proposed scheme is greater than 50db when the hiding capacity is 1 bit per pixel whereas those values in jpeg jsteg and scheme in chang et al inform sci 141 1 2 2002 123 are 37 04 and 33 73db respectively the hiding capacity of the proposed scheme is 65 536 bits when the hiding capacity is 1 bit per pixel whereas it is 53 248 bits in scheme inform sci 141 1 2 2002 123 and less than 3000 bits in jpeg jsteg

joint coding and embedding techniques for multimedia images hiding data in digital images is a technique for secret data communication it involves embedding important data into a cover image in digital form with minimal perceptible degradation in this paper we first propose an improved data hiding method for side match vector quantization smvq compressed images which utilizes the codeword pairing procedure to modulate the index code of each image block in order to take it a step further and obtain a larger embedding capacity we remodel the first proposed method into a new one with the power of variable rate data embedding through the use of a multiple base notational system according to the experimental results the two proposed methods are indeed capable of providing a larger embedding capacity without causing noticeable distortions of stego images in comparison with previous methods moreover our methods also maintain a low compression bit rate without auxiliary data

the obstruction to excision in k theory and in cyclic homology let f a b be a ring homomorphism of not necessarily unital rings and i triangleleft a an ideal which is mapped by f isomorphically to an ideal of b the obstruction to excision in k theory is the failure of the map between relative k groups k a i k b f i to be an isomorphism it is measured by the birelative groups k a b i similarly the groups hn a b i measure the obstruction to excision in negative cyclic homology we show that the rational jones goodwillie chern character induces an isomorphism ch k a b i otimes mathbb q overset sim to hn a otimes mathbb q b otimes mathbb q i otimes mathbb q

two dimensional solutions of a mean field equation on flat tori abstract we study the mean field equation on the flat torus t c z z u e u t e u 1 t 0 where is a real parameter for a general flat torus we obtain the existence of two dimensional solutions bifurcating from the trivial solution at each eigenvalue up to a multiplicative constant t of laplace operator on the torus in the space of even symmetric functions we further characterize the subset of all eigenvalues through which only one bifurcating curve passes finally local convexity near bifurcating points of the solution curves are obtained

perceptually adaptive spread transform image watermarking scheme using hadamard transform the present paper proposes a digital image watermarking scheme using the characteristics of the human visual system hvs spread transform technique and statistical information measure spread transform st scheme is implemented using the transform coefficients of both the host and the watermark signal watermark embedding strength is adaptively adjusted using frequency sensitivity luminance contrast and entropy masking of hvs model the choice of hadamard transform as watermark embedding domain offers several advantages such as low loss in image information higher image fidelity greater reliability of watermark detection and higher data hiding capacity at high degree of compression performance of the proposed method is compared with a number of recently reported watermarking schemes based on spread spectrum ss and quantization index modulation qim

multilevel reversible data hiding based on histogram modification of difference images reversible data hiding has drawn considerable attention in recent years reversibility allows original media to be completely recovered from marked media without distortion after embedded message has been extracted in this paper we propose a multilevel reversible data hiding scheme based on the difference image histogram modification that uses the peak point to hide messages through a joint imperceptibility and hiding capacity evaluation we show that our proposed scheme uses a multilevel hiding strategy to achieve large hiding capacity and keep distortion low performance comparisons with other existing reversible hiding schemes are provided to demonstrate the validity of our proposed scheme

constant q curvature metrics in arbitrary dimension working in a given conformal class we prove existence of constant q curvature metrics on compact manifolds of arbitrary dimension under generic assumptions the problem is equivalent to solving a nth order non linear elliptic differential or integral equation with variational structure where n is the dimension of the manifold since the corresponding euler functional is in general unbounded from above and below we use critical point theory jointly with a compactness result for the above equation

high performance jpeg steganography using complementary embedding strategy a high performance jpeg steganography should be secure enough to resist modern steganalysis in this paper we propose a high performance jpeg steganographic method the proposed method adopts the complementary embedding strategy to avoid the detections of several statistical attacks to show the effectiveness of the proposed method several statistical attacks are simulated and used to detect the stego images created by the proposed method several famous jpeg steganographic algorithms are also simulated for comparisons with the proposed method experimental results show that the proposed steganographic method has superior performance both in capacity and security and is practical for the application of secret communication

asymptotic estimate for a perturbed scalar curvature equation abstract we consider the equation u v u n 2 n 2 w u with n n 2 n 2 n 2 and we give some minimal conditions on v and w for having a uniform estimate for their solutions when 0

on the solutions of liouville systems for some prescribed m 0 together with the dirichlet boundary condition u 0 on 0 the liouville equation finds applications in various fields of physics and mathematics to name a few it represents the newtonian potential of a cluster of self gravitating mass distribution where a 0 1 6 36 37 the electric potential induced by charge carriers in the theory of electrolytes where a 0 31 and maximal entropy solutions of the incompressible euler equation 23 9 in the field of differential geometry it stands for the problem of finding a metric corresponding to a prescribed gaussian curvature 3 10 the system analog of l takes the form

reversible data hiding with oriented and minimized distortions using cascading trellis coding a novel cascading trellis coding algorithm is proposed a novel data hiding scheme with oriented and minimized distortions is proposed an application scheme that develops the dom algorithm in dwt domain is proposed reversible data hiding technique usually generates low quality images when the relative payload is high this paper proposes a novel reversible data hiding scheme that provides improved performances first a distortion oriented minimized dom embedding algorithm is proposed by using a cascading trellis coding algorithm the overall modifications to the host coefficients are minimal and some specified host coefficients are kept intact following that the proposed dom algorithm is used in the discrete wavelet transform dwt domain to increase the payload both the scaling coefficients and the wavelet coefficients are involved in computation however by using the dom algorithm the scaling coefficients are kept unchanged by these approaches the proposed scheme provides high quality to the stego image and reversibility to the host image without the problems of overflow and underflow furthermore by using a multi round embedding operation a high payload is achieved experimental results show that the proposed scheme outperforms the state of the art reversible hiding schemes

lossless data hiding for color images based on block truncation coding in this paper we present a novel reversible steganographic method which can reconstruct an original image effectively after extracting the embedded secret data the proposed reversible hiding method aims at btc block truncation coding compressed color images conventionally each block of a color image compressed by btc requires three bitmaps and three pairs of quantization levels for reconstruction in order to improve the compression rate a genetic algorithm ga is applied to find an approximate optimal common bitmap to replace the original three the secret data then are embedded in the common bitmap and the quantization levels of each block use the properties of side matching and the order of these quantization levels to achieve reversibility the experimental results demonstrate that the proposed method is practical for btc compressed color images and can embed more than three bits in each btc encoded block on average

compactness of solutions to some geometric fourth order equations we prove compactness of solutions to some fourth order equations with exponential nonlinearities on four manifolds the proof is based on a refined bubbling analysis for which the main estimates are given in integral form our result is used in a subsequent paper to find critical points via minimax arguments of some geometric functional which give rise to conformal metrics of constant q curvature as a byproduct of our method we also obtain compactness of such metrics

wavelet based copyright protection scheme for digital images based on local features a lossless robust copyright protection scheme for digital images based on cryptography and watermarking is proposed in the proposed wavelet based scheme the logo image is not embedded into the protected image the secret key is generated during the embedding process using local features extracted from the perceptually prominent components of the host image after the digital wavelet transform digital signature and time stamping technologies are then used for further protection with the secret key the logo image extraction process can be completed without the host image experimental results show that the proposed scheme is effective and robust against common image processing and geometric distortions

the nilpotence conjecture in k theory of toric varieties it is shown that all nontrivial elements in higher k groups of toric varieties are annihilated by iterations of the natural frobenius type endomorphisms this is a higher analog of the triviality of vector bundles on affine toric varieties

reversible data hiding for depth maps using the depth no synthesis error model when embedding hidden data in 3d images conventional reversible data hiding methods which are designed for 2d gray and color images can be applied to color and depth maps however directly applying these methods to depth maps may cause synthesis errors and lead to visual artifacts in the rendered virtual views two novel reversible data hiding methods based on the depth no synthesis error d nose model are proposed to embed hidden data in the depth maps of 3d images the proposed methods can preserve the quality of the rendered virtual view and achieve substantially higher embedding capacity experimental results show that the proposed methods achieve better performance than the existing state of the art methods in terms of both embedding capacity and the quality of the rendered virtual views

a virtual image cryptosystem based upon vector quantization we propose a new image cryptosystem to protect image data it encrypts the original image into another virtual image since both original and virtual images are significant our new cryptosystem can confuse illegal users besides the camouflage this new cryptosystem has three other benefits first our cryptosystem is secure even if the illegal users know that our virtual image is a camouflage second this cryptosystem can compress image data finally our method is more efficient than a method that encrypts the entire image directly

a reversible compression code hiding using soc and smvq indices reversible data hiding recovers the original images without distortion after the secret data are extracted so it has received considerable attention among researchers in recent years this work presents a novel reversible data hiding scheme based on the search order coding soc algorithm and side match vector quantization smvq the compression performance is improved by encoding the index with either soc or smvq during the data embedding phase the index of an image block also is encoded by using a few bits thus improving the compression rate during the extracting phase the receiver uses simple steps to extract the secret data and reconstruct the original smvq compression code our experimental results indicated that using a size 64 state codebook the average compression rate with our scheme was 0 41bpp which is much better than the compression rates of chang et al s yang and lin s and yang et al s schemes i e 0 50 0 54 and 0 56bpp respectively furthermore in addition to reducing the time required for the embedding and extracting phases the proposed scheme yields a higher embedding rate than the schemes of yang and lin and yang et al

a steganographic method based upon jpeg and particle swarm optimization algorithm in this paper a novel steganographic method based on jpeg and particle swarm optimization algorithm pso is proposed in order to improve the quality of stego images an optimal substitution matrix for transforming the secret messages is first derived by means of the pso algorithm the standard jpeg quantization table is also modified to contain more secret messages the transformed messages are then hidden in the dc to middle frequency components of the quantized dct coefficients of the cover image finally a jpeg file with secret messages is generated through jpeg entropy coding we compare our algorithm with chang et al s jpeg based steganographic algorithm the experimental results show that our proposed method has larger message capacity and better image quality than chang et al s in addition our method also has a high security level

a novel joint data hiding and compression scheme based on smvq and image inpainting in this paper we propose a novel joint data hiding and compression scheme for digital images using side match vector quantization smvq and image inpainting the two functions of data hiding and image compression can be integrated into one single module seamlessly on the sender side except for the blocks in the leftmost and topmost of the image each of the other residual blocks in raster scanning order can be embedded with secret data and compressed simultaneously by smvq or image inpainting adaptively according to the current embedding bit vector quantization is also utilized for some complex blocks to control the visual distortion and error diffusion caused by the progressive compression after segmenting the image compressed codes into a series of sections by the indicator bits the receiver can achieve the extraction of secret bits and image decompression successfully according to the index values in the segmented sections experimental results demonstrate the effectiveness of the proposed scheme

excision in algebraic k theory introduction 1 excision and the homology of affine groups 2 volodin s spaces 3 excision for rings with the triple factorization property 4 lie analogue of volodin s construction 5 the homology of nilpotent groups and nilpotent lie algebras 6 a proof of the main theorems 7 the tensor product of h unital algebras 8 the matrix ring of a small category 9 the acyclicity of triangular complexes 10 a proof of karoubi s conjecture

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

lossless data hiding for vq indices based on neighboring correlation data hiding is one of the protective techniques for authentication or secret communication through a public and open channel such as the internet in this study a novel lossless data hiding by embedding secret data into a vector quantization vq compressed image is proposed to achieve secret communication and data compression simultaneously the correlation of neighboring blocks of a vq compressed image is explored it is shown that the neighboring blocks of a vq compressed image normally have high mutual correlation thus this scheme employs the neighboring processed compression indices to generate specific sub codebooks required for encoding and hiding data simultaneously since the sizes of sub codebooks are smaller than that of the original vq codebook the encoded size of each index can be significantly reduced as a result a great deal of extra free space can be created moreover the original vq compressed images can be perfectly recovered after data extraction to evaluate the effectiveness of this approach various test images are employed in the experiments as documented in the experimental results it is shown that the performance of the proposed scheme is superior to the former schemes in terms of compression ratio embedding rate execution time and embedding capacity

supercritical mean field equations on convex domains and the onsager s statistical description of two dimensional turbulence we are motivated by the study of the microcanonical variational principle within onsager s description of two dimensional turbulence in the range of energies where the equivalence of statistical ensembles fails we obtain sufficient conditions for the existence and multiplicity of solutions for the corresponding mean field equation on convex and thin enough domains in the supercritical with respect to the moser trudinger inequality regime this is a brand new achievement since existence results in the supercritical region were previously known only on multiply connected domains we then study the structure of these solutions by the analysis of their linearized problems and we also obtain a new uniqueness result for solutions of the mean field equation on thin domains whose energy is uniformly bounded from above finally we evaluate the asymptotic expansion of those solutions with respect to the thinning parameter and combining it with all the results obtained so far we solve the microcanonical variational principle in a small range of supercritical energies where the entropy is shown to be concave

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

an optimal image watermarking approach based on a multi objective genetic algorithm in accordance with the multi objective nature of image watermarking an optimal image watermarking approach using a multi objective genetic algorithm is presented in this paper both watermarking parameters and embedding positions are often important factors affecting the performance of watermarking systems the proposed multi objective watermarking method can automatically optimize system parameters and a variable length mechanism is specially designed to search the most suitable positions for embedding watermarks the method can also remove the difficult issue of determining optimal watermarking parameters from previous watermarking algorithms the proposed multi objective watermarking method directly deals with the problem of optimizing watermarking under non dominated meaning thus it can effectively avoid the difficulty of determining the optimally weighted factor in existing single objective watermarking schemes in addition a pareto optimal set generated by multi objective optimization can provide flexibility in selecting the most suitable watermarking parameters according to practical requirements

pro unitality and pro excision in algebraic k theory and cyclic homology the purpose of this paper is to study pro excision in algebraic k theory and cyclic homology after suslin wodzicki cuntz quillen cortinas and geisser hesselholt as well as continuity properties of andre quillen and hochschild homology a key tool is first to establish the equivalence of various pro tor vanishing conditions which appear in the literature this allows us to prove that all ideals of commutative noetherian rings are pro unital in a suitable sense we show moreover that such pro unital ideals satisfy pro excision in derived hochschild and cyclic homology it follows hence and from the suslin wodzicki criterion that ideals of commutative noetherian rings satisfy pro excision in derived hochschild and cyclic homology and in algebraic k theory in addition our techniques yield a strong form of the pro hochschild kostant rosenberg theorem an extension to general base rings of the cuntz quillen excision theorem in periodic cyclic homology a generalisation of the f igin tsygan theorem a short proof of pro excision in topological hochschild and cyclic homology and new artin rees and continuity statements in andre quillen and hochschild homology msc 19d55 primary 16e40 13d03 secondary

a sup inf type inequality for conformal metrics on riemann surfaces with conical singularities abstract a sup inf type inequality is proved for the regular part of conformal factors for riemannian metrics on surfaces with conical singularities of positive order 0 the proof is based on the explicit representation formula for solutions of the singular liouville equation and generalizes to the singular case an argument by i shafrir

moving planes moving spheres and a priori estimates abstract in this paper we use the method of moving planes and the method of moving spheres to obtain a priori estimates for the solutions of semi linear elliptic equations using the method of moving planes we establish a sharper estimate on the solutions for prescribing scalar curvature equations with indefinite curvature functions and thus generalized a resent result of lin applying the method of moving spheres we give a different proof for a well known sup inf inequality established by brezis li and shafrir

a path optional lossless data hiding scheme based on vq joint neighboring coding data hiding is an important technique for covert communication that embeds secret data into a cover image with minimal perceptible degradation lossless data hiding is a special type of data hiding technique that guarantees not only the secret data but the cover media can be reconstructed without any distortion in this paper a novel path optional lossless data hiding scheme based on the joint neighboring coding jnc of the vector quantization vq index table is proposed the proposed scheme generates a vq index table based on the cover image first next according to an initial key and secret data content different adjacent indices may be chosen to perform joint neighboring coding for each index and hide secret data finally an appropriate output codestream is generated based on the minimal length principle our main contributions lie in three aspects 1 the method combines the novel path based shift method with the traditional jnc method to improve the capacity and stego image quality simultaneously 2 the secret data extraction and cover image recovering processes are separated and both can be publicized to users 3 the method is path optional to meet various users requirements to testify the superiority of the proposed method we compare it with the side match vq smvq based and modified fast correlation vq mfcvq based algorithms according to the experimental results the proposed scheme outperforms the smvq based and mfcvq based algorithms in four aspects i e hiding capacity stego image quality transmission efficiency and security level

reversible data hiding for vq compressed images based on search order coding and state codebook mapping abstract in the field of digital multimedia numerous researchers have exploited data hiding for providing secure communications because most multimedia is compressed in advance to save storage space and transmission time this paper presents a reversible data hiding scheme for vector quantization vq compressed images in the proposed scheme search order coding soc is first employed to reduce the size of the vq index table for image blocks that cannot be processed by soc a technique called state codebook mapping scm is used to map the blocks to the corresponding indices in their state codebooks which are generated by a set of neighborhood indices after soc and scm the size of the output code stream is reduced and a large amount of space is available for embedding sensitive data performance comparisons with similar recent studies are presented for demonstrating the superiority of the proposed scheme the experimental results indicated that the proposed scheme can achieve a high embedding capacity and a high compression bit rate

an estimate on the blowing up solutions of a fourth order equation abstract in this short paper i prove a harnack type inequality of the blowing up solutions for a class of fourth order equations with exponential growth on a compact four manifold the main method i use is the moving plane method

a sup inf inequality for some nonlinear elliptic equations involving exponential nonlinearities let u be a solution of the equation u v x eu in a domain r2 where 0 a v b and v is lipschitz continuous we prove that sup u can be controlled in terms of inf u more precisely supku inf u c a b k v l for any compact subset k this extends an earlier result of shafrir who obtained a similar conclusion when v 1

reversible hiding in dct based compressed images this paper presents a lossless and reversible steganography scheme for hiding secret data in each block of quantized discrete cosine transformation dct coefficients in jpeg images in this scheme the two successive zero coefficients of the medium frequency components in each block are used to hide the secret data furthermore the scheme modifies the quantization table to maintain the quality of the stego image experimental results also confirm that the proposed scheme can provide expected acceptable image quality of stego images and successfully achieve reversibility

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

on a sharp sobolev type inequality on two dimensional compact manifolds motivated by the asymptotic analysis of double vortex condensates in the chern simons higgs theory we construct a suitable minimizing sequence for a sharp sobolev inequality a la moser for two dimensional compact manifolds as a consequence we first obtain a direct proof of the sharp character of such an inequality secondly and more interestingly we use such minimizing sequence to show that for the flat torus the corresponding extremal problem attains its infimum

excision in cyclic homology and in rational algebraic k theory for a precise definition see 1 below by replacing everywhere k by k q one obtains the corresponding notion in rational algebraic k theory the above definition has an obvious counterpart for cyclic homology and algebras over a fixed field in the case of a general commutative ground ring k some restrictions on the class of allowable extensions seem inevitable due to the well known limitations of cyclic homology considered as a homology functor for algebras not flat over a ground ring an extension of k algebras will be called pure if it is pure as an extension of k modules in the sense of p m cohn 6 cf also appendix a 3 below the class of pure extensions contains e g i extensions which admit a k module splitting ii extensions a e r s with s flat over k in fact one among the several possible characterizations of purity says that an extension is pure if and only if the underlying extension of k modules is an inductive limit of split extensions see theorem a 4 of appendix a below everywhere in this paper the word excision used in the context of cyclic homology will mean excision with respect to the class of pure extensions the second purpose of the present paper is to give a complete characterization of the class of algebras possessing the excision property in cyclic homology before stating the corresponding result we need the following definition let us

reversible steganographic method using smvq approach based on declustering reversible steganography allows an original image to be completely restored after the extraction of hidden data embedded in a cover image in this paper we propose a reversible scheme for vq compressed images that is based on a declustering strategy and takes advantage of the local spatial characteristics of the image the main advantages of our method are ease of implementation low computational demands and no requirement for auxiliary data the experimental results show that the embedding capacity of the proposed method is controlled by the number of declustered groups and the spatial characteristics of the cover image the results also show that the proposed method has the best embedding capacity and the least running time compared with other methods

side match and overlap match vector quantizers for images a class of vector quantizers with memory that are known as finite state vector quantizers fsvqs in the image coding framework is investigated two fsvq designs namely side match vector quantizers smvqs and overlap match vector quantizers omvqs are introduced these designs take advantage of the 2 d spatial contiguity of pixel vectors as well as the high spatial correlation of pixels in typical gray level images smvq and omvq try to minimize the granular noise that causes visible pixel block boundaries in ordinary vq for 512 by 512 gray level images smvq and omvq can achieve communication quality reproduction at an average of 1 2 b pixel per image frame and acceptable quality reproduction because block boundaries are less visible the perceived improvement in quality over ordinary vq is even greater owing to the structure of smvq and omvq simple variable length noiseless codes can achieve as much as 60 bit rate reduction over fixed length noiseless codes

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

a quantization property for blow up solutions of singular liouville type equations abstract motivated by the study of self dual vortices in gauge field theory cf vortices and monopoles birkhauser boston 1980 solitons in field theory and nonlinear analysis monographs in mathematics springer new york 2001 we consider a concentrating solution sequence u k satisfying u k z 2 k v k z e u k in b 1 z 2 k v k z e u k z 0 weakly in the sense of measures in b 1 where i k r k ii v k c 0 1 b 1 0 a v k b and v k a in b 1 we prove that necessarily 8 n 8 1 8 z the result is sharp as shown by explicit examples and should be compared with that obtained by li shafrir ind univ math j 43 4 1994 1255 concerning the situation where k 0 k n

a two codebook combination and three phase block matching based image hiding scheme with high embedding capacity image hiding is a technique that embeds the important images into a cover image such that the important images are imperceptible and can be securely transmitted to the receiver in such research the common goals are to enlarge the embedding capacity as much as possible since the visual quality of the cover image is degraded slightly and to keep high visual quality of the important images when they are extracted from the stego image in this paper we propose an image hiding method based on the two codebook combination the three phase block matching procedure and the modulus substitution the proposed method can achieve these benefits 1 multiple relatively large important images can be embedded into a relatively small cover image 2 the quality of the stego image after embedding the secret data is not distorted significantly 3 the important images have an acceptable visual quality after they are extracted the experimental results also show that the proposed method is more flexible than previous methods

the steinberg group of a monoid ring nilpotence and algorithms for a regular ring r and an affine monoid m the homotheties of m act nilpotently on the milnor unstable groups of r m this strengthens the k2 part of the main result of j gubeladze the nilpotence conjecture in k theory of toric varieties invent math 160 2005 173 216 in two ways the coefficient field of characteristic 0 is extended to any regular ring and the stable k2 group is substituted by the unstable ones the proof is based on a polyhedral combinatorial technique computations in steinberg groups and a substantially corrected version of an old result on elementary matrices by mushkudiani z mushkudiani k2 groups of monoid algebras over regular rings proc a razmadze math inst 113 1995 120 137 a similar stronger nilpotence result for k1 and algorithmic consequences for factorization of high frobenius powers of invertible matrices are also derived

adaptive data hiding for vector quantization images based on overlapping codeword clustering in this paper an overlapping codeword clustering based data hiding scheme is presented in this scheme a mapping table is designed to determine the overlapping codeword clustering and to indicate the index modification in the secret embedding the mapping table explores the relationship among the sub codebook s size the codeword s order and the embedding secret message to which the codeword overlapping in sub codebooks with different sizes is permitted in addition the secret embedding is also determined according to the mapping table the experimental results showed that the number of partitioned sub codebooks was increased significantly the average hiding capacity was about 30k bits while the average embedding distortion was about 1 2db in comparison to similar methods the proposed scheme provided a larger hiding capacity than others while preserving a similar stego image quality furthermore the proposed scheme offered a better proportion of hiding compared to image distortion

an image hiding method with high hiding capacity based on best block matching and k means clustering this paper presents a novel image hiding method that exhibits a high hiding capacity that allows the embedded important image to be larger than the cover image a facility that is seldom described in the literature in the proposed method the entire important image is divided into many nonoverlapping blocks for each block of the important image a block matching procedure is used to search for the best similar block from a series of numbered candidate blocks the obtained indices of the best matching blocks are encoded using huffman coding scheme and then recorded in the least significant bit planes of the cover image through a monoalphabetic transposition cipher the proposed method exhibits the following advantages over existing methods 1 a high hiding capacity such that the embedded important image can be larger than the cover image 2 a stego image with a high quality which improves the secrecy of the hidden image and 3 a small error between the extracted important image and the original important image indicating that the extracted important image is of acceptable quality

topological degree for solutions of fourth order mean field equations we consider the following fourth order mean field equation with navier boundary condition delta 2 u rho frac h x e u int omega h e u rm in omega quad u delta u 0 rm on partial omega quad quad quad quad quad quad quad quad quad quad where h is a c2 positive function is a bounded and smooth domain in mathbb r 4 we prove that for rho in 32m sigma 3 32 m 1 sigma 3 the degree counting formula for is given by d rho left begin array ll frac 1 m chi omega 1 cdot cdot cdot chi omega m rm for m 0 1 rm for m 0 end array right where is the euler characteristic of similar result is also proved for the corresponding dirichlet problem delta 2 u rho frac h x e u int omega h e u quad rm in omega quad u nabla u 0 quad rm on partial omega quad quad quad quad quad quad quad quad quad quad

temporal and spatial correlation based reversible data hiding for rgb cfa videos abstract considering a mosaic video in which each mosaic image could be captured by any of the existing eleven rgb color filter array cfa structures and each mosaic pixel contains only one primary color this paper proposes a novel spatial and temporal correlation based reversible data hiding rdh method in the proposed rdh method an intellectual switching strategy to select the spatial correlation based or the temporal prediction scheme to maximize the quality improvement of the marked mosaic videos under fixed embedding capacity based on eight test mosaic videos the experimental results demonstrate that in terms of peak signal to noise ratio psnr color psnr cpsnr structure similarity ssim index motion based video integrity evaluation movie index and human perceptual effect the proposed rdh method clearly outperforms the spatial correlation based rdh method by yang et al and the other four state of the art rdh methods

a sup inf inequality near r 0 let be a domain in r2 not necessarily bounded consider the semi linear elliptic equation u r x eu x we prove that for any compact subset k of there is a constant c such that the inequality 1 supku inf u c holds for all solutions u this type of inequality was first established by brezis li and shafrir h brezis y y li i shafrir a sup inf inequality for some nonlinear elliptic equations involving exponential nonlinearities j funct anal 115 1993 344 358 under the assumption that r x is positive and bounded away from zero it has become a useful tool in estimating the solutions of semi linear elliptic equations either in euclidean spaces or on riemannian manifolds see h brezis y y li i shafrir a sup inf inequality for some nonlinear elliptic equations involving exponential nonlinearities j funct anal 115 1993 344 358 c c chen c s lin a sharp sup inf inequality for a nonlinear elliptic equation in r2 comm anal geom 6 1998 1 19 w chen c li gaussian curvature in the negative case proc amer math soc 131 2003 741 744 w chen c li indefinite elliptic problems with critical exponent in advances in non linear pde and related areas world scientific 1998 pp 67 79 y y li i shafrir blow up analysis for solutions of u veu in dimension two indiana univ math j 43 1994 1255 1270 in brezis li and shafrir s result the constant c depends on the lower bound of the function r x in this paper we remove this restriction and extend the inequality to the case where r x is allowed to have zeros so that it can be applied to obtain a priori estimates for a broader class of equations as we will illustrate in the last section the key to prove this inequality is the analysis of asymptotic decay near infinity of solutions for a corresponding limiting equation in r2 which is interesting and useful in its own right

infinitesimal cohomology and the chern character to negative cyclic homology there is a chern character from k theory to negative cyclic homology we show that it preserves the decomposition coming from adams operations at least in characteristic zero

the k theory of toric varieties recent advances in computational techniques for k theory allow us to describe the k theory of toric varieties in terms of the k theory of fields and simple cohomological data

a novel reversible image data hiding scheme based on pixel value ordering and dynamic pixel block partition recently various efficient reversible data hiding schemes based on pixel value ordering have been proposed for embedding messages into high fidelity images in these schemes after dividing the cover image into equal sized blocks the pixels within a given block are ordered according to their values and data embedding is achieved by modifying the maximum and minimum values of each block for a given embedding capacity the optimal block size is exhaustively searched so that the embedding distortion is minimized these pixel value ordering based schemes perform fairly well especially for low embedding capacity however to obtain a larger embedding capacity a smaller block size should be used which usually leads to a dramatic quality degradation of the marked image in this paper to address this drawback and to enhance the performance of pixel value ordering based embedding further a novel reversible data hiding method is proposed instead of using equal sized blocks a dynamic blocking strategy is used to divide the cover image adaptively into various sized blocks specifically flat image areas are preferentially divided into smaller blocks to retain high embedding capacity whereas rough areas are divided into larger blocks to avoid decreasing peak signal to noise ratio as a result the proposed scheme can provide a larger embedding capacity than current pixel value ordering based schemes while keeping distortion low the superiority of the proposed method is also experimentally verified

data hiding for vector quantization images using mixed base notation and dissimilar patterns without loss of fidelity data hiding without loss of fidelity also called reversible data hiding allows an original image to be restored completely after extraction of hidden data embedded in a cover image in this paper we propose a reversible scheme based on mixed base notation and dissimilar pattern strategies for vector quantization vq compressed images the dissimilar patterns resulting from the declustering process make the proposed hiding method more efficient our experimental results show that the time required for the embedding process in the proposed method is much less than that in the side matched vq smvq based reversible method in addition the use of declustering can reduce many more prediction errors than traditional clustering methods the results also show that the number of declustered groups and the spatial characteristics of the cover image will affect the embedding capacity and the size of the stego vq index table

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

compression unimpaired batch image encryption combining vector quantization and index compression as the network bandwidth has grown rapidly it has become common to share a large number of still images via the internet by means of batch transmission unfortunately most existing methods encrypt only a single image so there is room for improvement in our ability to send batches of images at one time a complete reconstruction of the methods is sometimes necessary especially when considering performance criteria this paper presents a novel batch image encryption algorithm that combines vector quantization vq and additional index compression process to benefit from their computational efficiency and low transmission bandwidth without affecting the original compression rate the experimental results show the performance of this new scheme in terms of compression rate and computational cost

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

efficient reversible data hiding for color filter array images a reversible data hiding algorithm which uses prediction errors in the color difference domain for mosaic images with the bayer color filter array cfa is proposed furthermore the proposed algorithm can be extended to deal with the digital time delay and integration dtdi mosaic images and lukac and plataniotis lp mosaic images experimental results on cfa dtdi and lp mosaic images demonstrate that the proposed algorithm can achieve high embedding capacity while maintaining good image quality

adaptive embedding techniques for vq compressed images an embedding algorithm which can adaptively embed a binary message into a vq compressed image is proposed in this paper the proposed algorithm is divided into three phases in the codeword grouping phase a new group of codewords is initiated by the two most similar codewords which do not belong to any group for each codeword which does not belong to any group if the codeword is similar to all of the codewords in the group it will be added to the group in the embedding phase each codeword in a group will be assigned to embed a certain sub message whose length is determined by the number of codewords in the group the more codewords a group has the higher the embedding capacity of a codeword in the group will be in the extracting phase given a codeword and the number of codewords in the group to which the codeword belongs the embedded message can be extracted from the codeword by simply determining the order of the codeword in the group experimental results show that the proposed algorithm performs better than previous algorithms with regard to embedding capacity and image quality for the test images when the embedding capacity is less than 5bits per codeword index the difference of the psnr values between the stego image and its vq compressed cover image will be no more than 5db on average

comparison between algebraic and topological k theory of locally convex algebras abstract this paper is concerned with the algebraic k theory of locally convex c algebras stabilized by operator ideals and its comparison with topological k theory we show that if l is locally convex and j a frechet operator ideal then all the different variants of topological k theory agree on the completed projective tensor product l j and that the obstruction for the comparison map k l j k top l j to be an isomorphism is absolute algebraic cyclic homology we prove the existence of an exact sequence theorem 6 2 1 we show that cyclic homology vanishes in the case when j is the ideal of compact operators and l is a frechet algebra whose topology is generated by a countable family of sub multiplicative seminorms and admits an approximate right or left unit which is totally bounded with respect to that family theorem 8 3 3 this proves the generalized version of karoubi s conjecture due to mariusz wodzicki and announced in his paper m wodzicki algebraic k theory and functional analysis in first european congress of mathematics vol ii paris 1992 in progr math vol 120 birkhauser basel 1994 pp 485 496 we also consider stabilization with respect to a wider class of operator ideals called sub harmonic every frechet ideal is sub harmonic but not conversely for example the schatten ideal l p is sub harmonic for all p 0 but is frechet only if p 1 we prove a variant of the exact sequence above which essentially says that if a is a c algebra and j is sub harmonic then the obstruction for the periodicity of k a c j is again cyclic homology theorem 7 1 1 this generalizes to all algebras a result of wodzicki for h unital algebras announced in m wodzicki algebraic k theory and functional analysis in first european congress of mathematics vol ii paris 1992 in progr math vol 120 birkhauser basel 1994 pp 485 496 the main technical tools we use are the diffeotopy invariance theorem of cuntz and the second author which we generalize in theorem 6 1 6 and the excision theorem for infinitesimal k theory due to the first author

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

an intelligent chaotic embedding approach to enhance stego image quality steganography s role in secret communication extends from concealing information to communication as one of several possible approaches to embed confidential information in digital images the least significant bit lsb technique has been widely used however maintaining the imperceptibility of the stego image is still a serious concern in this paper an adaptive random ar k bit embedding approach has been attempted to enhance the quality of stego images the original cover is divided into nonoverlapping blocks of equal size the encrypted confidential data are embedded in each block through four different random walks the best random walk which provides the minimum degradation for a particular block is identified and is fixed for that block the decision on the fixed random walk for each block is recorded and kept as the secret key the ar method has also been combined with the inverted pattern approach referred to as the adaptive random inverted pattern arip approach to further enhance the quality of the stego image the estimated peak signal to noise ratio psnr value for the arip method yields 1db enhancement