Watermarking Images in the Frequency Domain by Exploiting Self-Inverting Permutations

In this work we propose efficient codec algorithms for watermarking images that are intended for uploading on the web under intellectual property protection. Headed to this direction, we recently suggested a way in which an integer number w which being transformed into a self-inverting permutation, can be represented in a two dimensional (2D) object and thus, since images are 2D structures, we have proposed a watermarking algorithm that embeds marks on them using the 2D representation of w in the spatial domain. Based on the idea behind this technique, we now expand the usage of this concept by marking the image in the frequency domain. In particular, we propose a watermarking technique that also uses the 2D representation of self-inverting permutations and utilizes marking at specific areas thanks to partial modifications of the image’s Discrete Fourier Transform (DFT). Those modifications are made on the magnitude of specific frequency bands and they are the least possible additive information ensuring robustness and imperceptiveness. We have experimentally evaluated our algorithms using various images of different characteristics under JPEG compression. The experimental results show an improvement in comparison to the previously obtained results and they also depict the validity of our proposed codec algorithms.

Double Derangement Permutations

Let n be a positive integer. A permutation a of the symmetric group of permutations of is called a derangement if for each . Suppose that x and y are two arbitrary permutations of . We say that a permutation a is a double derangement with respect to x and y if and for each . In this paper, we give an explicit formula for , the number of double derangements with respect to x and y. Let and let and be two subsets of with and . Suppose that denotes the number of derangements x such that . As the main result, we show that if and z is a permutation such that for and for , then where .

Walsh Spectral Characteristics and the Auto-Correlation Function Characteristics of Forming Orthomorphic Permutations of Multi-Output Functions

Orthomorphic permutations have good characteristics in cryptosystems. In this paper, by using of knowledge about relation between orthomorphic permutations and multi-output functions, and conceptions of the generalized Walsh spectrum of multi-output functions and the auto-correlation function of multi-output functions to investigate the Walsh spectral characteristics and the auto-correlation function characteristics of orthormophic permutations, several results are obtained.

Singly Covered Minimal Elements of Linked Partitions and Cycles of Permutations

Linked partitions were introduced by Dykema(Dykema K J. Multilinear function series and transforms in free probability theory. Adv. Math., 2005, 208(1):351–407) in the study of the unsymmetrized T-transform in free probability theory.Permutation is one of the most classical combinatorial structures. According to the linear representation of linked partitions, Chen et al.(Chen W Y C, Wu S Y J, Yan C H. Linked partitions and linked cycles. European J. Combin., 2008, 29(6): 1408–1426) de?ned the concept of singly covered minimal elements. Let L(n, k) denote the set of linked partitions of [n] with k singly covered minimal elements and let P(n, k) denote the set of permutations of [n] with k cycles. In this paper, we mainly establish two bijections between L(n, k) and P(n, k). The two bijections from a different perspective show the one-to-one correspondence between the singly covered minimal elements in L(n, k) and the cycles in P(n, k).

Chrestenson Spectrum and Auto-Correlation Function of Inverse Permutations of Quick Trickle Permutations

In this paper, a sufficient and necessary condition of quick trickle permutations is given from the point of inverse permutations. The bridge is built between quick trickle permutations and m-value logic functions. By the methods of the Chrestenson spectrum of m-value logic functions and the auto-correlation function of m-value logic functions to investigate the Chrestenson spectral characteristics and the auto-correlation function charac- teristics of inverse permutations of quick trickle permutations, a determinant arithmetic of quick trickle permutations is given. Using the results, it becomes easy to judge that a permutation is a quick trickle permutation or not by using computer. This gives a new pathway to study constructions and enumerations of quick trickle permutations.

PERMUTATIONS(排列)AND COMBINATIONS(组合)

In this article,we shall explore some techniques of permutations(排列)and combi- nations.This is going to be a slightly long ar- ticle,but is very much educative,and I'll try to cover the entire thing from front to back. You can skip bits if you know them,but

AGGREGATE SPECIAL FUNCTIONS TO APPROXIMATE PERMUTING TRI-HOMOMORPHISMS AND PERMUTING TRI-DERIVATIONS ASSOCIATED WITH A TRI-ADDITIVEψ-FUNCTIONAL INEQUALITY IN BANACH ALGEBRAS

In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better estimation for permuting tri-homomorphisms and permuting tri-derivations in unital C*-algebras and Banach algebras by the vector-valued alternative fixed point theorem.

基于EEMD、相关系数、排列熵和小波阈值去噪的新型水下声学信号去噪方法

The complexities of the marine environment and the unique characteristics of underwater channels pose challenges in obtaining reliable signals underwater,necessitating the filtration of underwater acoustic noise.Herein,an underwater acoustic signal denoising method based on ensemble empirical mode decomposition(EEMD),correlation coefficient(CC),permutation entropy(PE),and wavelet threshold denoising(WTD)is proposed.Furthermore,simulation experiments are conducted using simulated and real underwater acoustic data.The experimental results reveal that the proposed denoising method outperforms other previous methods in terms of signal-to-noise ratio,root mean square error,and CC.The proposed method eliminates noise and retains valuable information in the signal.

Single-Cycle Bit Permutations with MOMR Execution

Secure computing paradigms impose new architectural challenges for general-purpose processors. Cryptographic processing is needed for secure communications, storage, and computations. We identify two categories of operations in symmetric-key and public-key cryptographic algorithms that are not common in previous general-purpose workloads： advanced bit operations within a word and multi-word operations. We define MOMR （Multiple Operands Multiple Results） execution or datarich execution as a unified solution to both challenges. It allows arbitrary n-bit permutations to be achieved in one or two cycles, rather than O（n） cycles as in existing RISC processors. It also enables significant acceleration of multiword multiplications needed by public-key ciphers. We propose two implementations of MOMR： one employs only hardware changes while the other uses Instruction Set Architecture （ISA） support. We show that MOMR execution leverages available resources in typical multi-issue processors with minimal additional cost. Multi-issue processors enhanced with MOMR units provide additional speedup over standard multi-issue processors with the same datapath. MOMR is a general architectural solution for word-oriented processor architectures to incorporate datarich operations.

Null-free False Discovery Rate Control Using Decoy Permutations

The traditional approaches to false discovery rate(FDR)control in multiple hypothesis testing are usually based on the null distribution of a test statistic.However,all types of null distributions,including the theoretical,permutation-based and empirical ones,have some inherent drawbacks.For example,the theoretical null might fail because of improper assumptions on the sample distribution.Here,we propose a null distributionfree approach to FDR control for multiple hypothesis testing in the case-control study.This approach,named target-decoy procedure,simply builds on the ordering of tests by some statistic or score,the null distribution of which is not required to be known.Competitive decoy tests are constructed from permutations of original samples and are used to estimate the false target discoveries.We prove that this approach controls the FDR when the score function is symmetric and the scores are independent between different tests.Simulation demonstrates that it is more stable and powerful than two popular traditional approaches,even in the existence of dependency.Evaluation is also made on two real datasets,including an arabidopsis genomics dataset and a COVID-19 proteomics dataset.

Inverse problems of the Erdos-Ko-Rado type theorems for families of vector spaces and permutations

Ever since the famous Erd os-Ko-Rado theorem initiated the study of intersecting families of subsets,extremal problems regarding intersecting properties of families of various combinatorial objects have been extensively investigated.Among them,studies about families of subsets,vector spaces and permutations are of particular concerns.Recently,we proposed a new quantitative intersection problem for families of subsets:For F([n]k),define its total intersection number as I(F)=ΣF1;F2∈F|F1∩F2|.Then,what is the structure of F when it has the maximal total intersection number among all the families in([n]k)with the same family size?In a recent paper,Kong and Ge(2020)studied this problem and characterized extremal structures of families maximizing the total intersection number of given sizes.In this paper,we consider the analogues of this problem for families of vector spaces and permutations.For certain ranges of family sizes,we provide structural characterizations for both families of subspaces and families of permutations having maximal total intersection numbers.To some extent,these results determine the unique structure of the optimal family for some certain values of jFj and characterize the relationship between having the maximal total intersection number and being intersecting.Besides,we also show several upper bounds on the total intersection numbers for both families of subspaces and families of permutations of given sizes.

GEOMETRIC CHARACTERISTICS OF FIBONACCI PERMUTATIONS AND A ONE-DIMENSIONAL LATTICE OF A QUASICRYSTAL

In November of 1984, D. Shechtman et al. obtained the first electron micrograph of a quasicrystal. In the high resolution electron micrograph, the bright dots along any straight line have Fibonacci permutations with two different distances, A and B.

ENUMERATION OF CERTAIN SETS OF PERMUTATIONS

Ⅰ. INTRODUCTION Let Zn = {1, 2, …, n}, and Pn be the set of n. permutations π = a1a2…an of Zn.We define the following conditions （ⅰ）—（ⅲ）:

ON THE NUMBER OF TDP PERMUTATIONS

A permutation is called a TDP permutation if i—a_i(?)j—a_j (mod n), for i≠j. It is easy to prove that a TDP permutation exists iff n is an odd number.C.Tompkins listed the number of TDP permutations for n≤11 in

Constructing Permutation Binomials from Permutations of Subfields

Permutation polynomials is a hot topic in finite fields,they have many applications in different areas.Permutation binomials and trinomials over finite fields were studied recently.In thispaper,by using a powerful lemma given by Zieve and some degree 5 and 6 permutation polynomials over Fq,we construct somepermutation binomials over Fqm.

On Increasing Subsequences of Minimal ErdSs-Szekeres Permutations

Let π be a minimal ErdSs-Szekeres permutation of 1, 2,..., n^2, and let ln,k be the length of the longest increasing subsequence in the segment （πr（1）,...,π（k））. Under uniform measure we establish an exponentially decaying bound of the upper tail probability for ln,k, and as a consequence we obtain a complete convergence, which is an improvement of Romik＇s recent result. We also give a precise lower exponential tail for ln,k.

A Relationship between the Partial Bell Polynomials and Alternating Run Polynomials

In this note, we first derive an exponential generating function of the alternating run polynomials. We then deduce an explicit formula of the alternating run polynomials in terms of the partial Bell polynomials.

A color image encryption algorithm based on hyperchaotic map and DNA mutation

We devise a color image encryption scheme via combining hyperchaotic map,cross-plane operation and gene theory.First,the hyperchaotic map used in the encryption scheme is analyzed and studied.On the basis of the dynamics of hyperchaotic map,a color image encryption scheme is designed.At the end of the encryption process,a DNA mutation operation is used to increase the encoding images’randomness and to improve the encryption algorithm’s security.Finally,simulation experiments,performance analysis,and attack tests are performed to prove the effectiveness and security of the designed algorithm.This work provides the possibility of applying chaos theory and gene theory in image encryption.

Modified 2 Satisfiability Reverse Analysis Method via Logical Permutation Operator

The effectiveness of the logic mining approach is strongly correlated to the quality of the induced logical representation that represent the behaviour of the data.Specifically,the optimum induced logical representation indicates the capability of the logic mining approach in generalizing the real datasets of different variants and dimensions.The main issues with the logic extracted by the standard logic mining techniques are lack of interpretability and the weakness in terms of the structural and arrangement of the 2 Satisfiability logic causing lower accuracy.To address the issues,the logical permutation serves as an alternative mechanism that can enhance the probability of the 2 Satisfiability logical rule becoming true by utilizing the definitive finite arrangement of attributes.This work aims to examine and analyze the significant effect of logical permutation on the performance of data extraction ability of the logic mining approach incorporated with the recurrent discrete Hopfield Neural Network.Based on the theory,the effect of permutation and associate memories in recurrent Hopfield Neural Network will potentially improve the accuracy of the existing logic mining approach.To validate the impact of the logical permutation on the retrieval phase of the logic mining model,the proposed work is experimentally tested on a different class of the benchmark real datasets ranging from the multivariate and timeseries datasets.The experimental results show the significant improvement in the proposed logical permutation-based logic mining according to the domains such as compatibility,accuracy,and competitiveness as opposed to the plethora of standard 2 Satisfiability Reverse Analysis methods.