Permutation Arrays Research Articles

Improved bounds for permutation arrays under Chebyshev distance

Improved bounds for permutation arrays under Chebyshev distance

Multiple contractions of permutation arrays

Multiple contractions of permutation arrays

Time domain speech scrambler based on particle swarm optimization

Abstract Speech scrambler is used to transform clear speech into an unintelligible signal to prevent eavesdropping. The speech scrambling algorithm involves the permutation of speech segments depending on a specific permutation matrix which may be fixed or dynamic during encryption. A fixed permutation matrix is easy to break and has given high residual intelligibility in the scrambled signal. The proposed scheme used a particle swarm optimization algorithm to generate a dynamic permutation array that can attain a high degree of security. The outcome of the scrambled speech signal does not have any residual intelligibility, and the quality of the descrambled speech is extremely satisfying, with zero mean squared error.

Supply Chain Design for Blending Technologies

When optimizing blending technologies, the main objective is to determine the right mixing ratio of the raw materials, depending on the different qualities and costs of the raw materials available. It can be concluded that research is mainly focused on answering technological questions, and only very few studies take into account the logistics processes related to blending technologies, their design, cost-efficiency, utilization and sustainability including energy efficiency and environmental impact. Based on this fact, within the frame of this research the authors describe a new approach, extending the basic model of blending problems by adding new supply chain efficiency-related components that makes it possible to take logistics parameters related to the raw materials supply (available stocks, batch sizes, transport and storage costs, supply chain structure) into consideration. A mathematical model of this supply chain optimization problem for blending technologies is described including routing and assignment problems in the supply chain, while technological objectives are also taken into consideration as technological objective functions and constraints. The optimization problem described in the model is a problem with non-deterministic polynomial-time hardness (NP-hard), which means that there are no known efficient analytical methods to solve the logistics-related supply chain optimization of blending technologies. As a solution algorithm, the authors have used an evolutive solver and a new metrics, which improved the efficiency of the comparison of distances between solutions of routing problems represented by permutation arrays. The scenario analysis, which focuses on the integrated optimization of technological and logistics problems validates the model and evaluates the solution algorithm and the new metrics. Using the mentioned algorithm, the supply chain processes of the blending technologies can be improved from availability, efficiency, sustainability point of view.

Using permutation rational functions to obtain permutation arrays with large hamming distance

Using permutation rational functions to obtain permutation arrays with large hamming distance

A polynomial‐time algorithm for simple undirected graph isomorphism

A polynomial‐time algorithm for simple undirected graph isomorphism

Distance increasing mapping for variable distance block code

A new idea regarding the generation of a block code for a code rate of 1/2 and less than 1/2 is developed here. The minimum distance between the codewords can be maximised using a suitable transformation of the P matrix in the generator matrix G of the block code. This study gives the construction of distance increasing mapping (DIM) such that the proposed code is a variable distance modified block code with a code rate equal to 1/2. An algorithm for such DIM is developed here. The construction for distance preserving mapping (DPM) is also generalised in an algorithmic way. Further, to achieve DIM from the proposed DPM, for the established codes with a code rate less than 1/2, transformation is developed with the help of permutation arrays. The performance of the codes has also been evaluated. Decoding of this code is also simple and can be carried out using the existing techniques of decoding of block codes. The probability of undetected error is found to be better than the existing block codes.

Some explicit constructions of type-II, III, IV, V QCLDPC codes with girth 6

Multi-type quasi-cyclic (QC) low-density parity-check (LDPC) codes can be considered as multiple-edge protograph QC-LDPC codes having some advantages in the minimum Hamming distance bound over single-edge protograph codes or type-I QC-LDPC codes when the base matrices have the same size. In this paper, we investigate a class of multi-type QC-LDPC codes whose parity-check matrices contain just one blockrow of circulants and we obtain the generator matrix of such codes in general form. Using the permutation arrays and defining injection arrays, we present a new approach to construct a class of high-rate type-I QC-LDPC codes with girth 6 from the constructed 4-cycle free multi-type QC-LDPC codes. In continue, for 2 ≤ w ≤ 6, some type-w QC-LDPC codes with girth 6 are constructed explicitly such that the constructed codes are flexible in terms of rate and length. To the best of our knowledge, for w = 5,6, this is the first paper which deals with the explicit construction of type-w QC-LDPC codes with girth 6 and high rates. Moreover, for w = 3,4, the constructed type-w QC-LDPC codes have better (6,8)-cycle multiplicities than the codes with minimum achievable length recently constructed by cyclic difference families (CDFs). Simulation results show that the binary and non-binary constructed codes outperform the constituent underlying QC-LDPC codes.

APPLICATION OF GENETIC ALGORITHM FOR IMAGE TRANSFER

For images transfer, different embedding system exist which works by creating a mosaic image from the source image and recovery from the target image using some sort of algorithm. In current study, a method is proposed using the genetic algorithm for recovery of image from the source image. The algorithm utilized is genetic algorithm which is a search method along with another additional technique for obtaining higher robustness and security. The proposed methodology works by dividing the source image into smaller parts which are fitted into target image using the lossless compression. The mosaic image is recovered at retrieving side by the permutation array which is recovered and mapped using the pre-select key.

The Construction of Permutation Group Codes for Communication Systems: Prime or Prime Power?

This paper focuses on correcting a theorem relating to the construction of permutation group codes (PGCs). The theorem in question assumed that affine transformation could be used to enumerate all the code words of a permutation array with a minimum Hamming distance (MHD) of n - 1 for any n > 1. This assumption was founded upon the proposition that, if the code length, n, is a prime power, then the maximum cardinality of the code will be n(n - 1) and its MHD will be n - 1. However, two typical algebraic methods, one relying on affine transformation and another upon the composite operation of two small subgroups of a symmetric group, can violate this proposition. This is because it is only when n is a prime rather than a prime power that they can enumerate all the code words of an (n; n (n - 1) ; n - 1)-PGC. By investigating how the range of n impacts upon the cardinality and MHD of a code, we provide a corrective theorem that stipulates the construction of (p q ; p 2q (1 - 1/p); p q (1 - 1/p))-PGCs when n = pq is a prime power, wherep is a prime and q > 1. On the basis of this theorem, and under the condition of n being the power of 2, we construct a (2 q ; 2 2q-1 ; 2 q-1 )-PGC and present an encoder that can map a k-bit binary information sequence to an n = 2 2q -dimension permutation code word. The natural array structure of (2 q ; 2 2q-1 ; 2 q-1 )-PGCs makes them especially well-suited to forming the basis of low-complexity encoders. We present simulation-based experiments that show that, as the code length increases, the performance of these codes improves. The best performance is for a (16; 128; 8)-PGC, which can achieve -3.8 dB with a word error rate of 10 -7 .

Constructing permutation arrays using partition and extension

We give new lower bounds for M(n, d), for various positive integers n and d with $$n>d$$, where M(n, d) is the largest number of permutations on n symbols with pairwise Hamming distance at least d. Large sets of permutations on n symbols with pairwise Hamming distance d are needed for constructing error correcting permutation codes, which have been proposed for power-line communications. Our technique, partition and extension, is universally applicable to constructing such sets for all n and all d, $$d<n$$. We describe three new techniques, sequential partition and extension, parallel partition and extension, and a modified Kronecker product operation, which extend the applicability of partition and extension in different ways. We describe how partition and extension gives improved lower bounds for $$M(n,n-1)$$ using mutually orthogonal Latin squares (MOLS). We present efficient algorithms for computing new partitions: an iterative greedy algorithm and an algorithm based on integer linear programming. These algorithms yield partitions of positions (or symbols) used as input to our partition and extension techniques. We report many new lower bounds for M(n, d) found using these techniques for n up to 600.

Allylative Approaches to the Synthesis of Complex Guaianolide Sesquiterpenes from Apiaceae and Asteraceae.

With hundreds of unique members isolated to date, guaianolide lactones represent a particularly prolific class of terpene natural products. Given their extensive documented therapeutic properties and fascinating chemical structures, these metabolites have captivated the synthetic chemistry community for many decades. As a result of divergent biosynthetic pathways, which produce a wide array of stereochemical and oxidative permutations, a unifying synthetic pathway to this broad family of natural products is challenging. Herein we document the evolution of a chiral-pool-based synthetic program aimed at accessing an assortment of guaianolides, particularly those from the plant family Apiaceae as well as Asteraceae, members of which possess distinct chemical substructures and necessitate deviating synthetic platforms. An initial route employing the linear monoterpene linalool generated a lower oxidation state guaianolide but was not compatible with the majority of family members. A double-allylation disconnection using a carvone-derived fragment was then developed to access first an Asteraceae-type guaianolide and then various Apiaceae congeners. Finally, using these findings in conjunction with a tandem polyoxygenation cascade, we developed a pathway to highly oxygenated nortrilobolide. A variety of interesting observations in metal-mediated aldehyde allylation and alkene polyoxygenation are reported and discussed.

A memetic algorithm with competition for the capacitated green vehicle routing problem

In this paper, a memetic algorithm with competition &#x0028 MAC &#x0029 is proposed to solve the capacitated green vehicle routing problem &#x0028 CGVRP &#x0029. Firstly, the permutation array called traveling salesman problem &#x0028 TSP &#x0029 route is used to encode the solution, and an effective decoding method to construct the CGVRP route is presented accordingly. Secondly, the k-nearest neighbor &#x0028 kNN &#x0029 based initialization is presented to take use of the location information of the customers. Thirdly, according to the characteristics of the CGVRP, the search operators in the variable neighborhood search &#x0028 VNS &#x0029 framework and the simulated annealing &#x0028 SA &#x0029 strategy are executed on the TSP route for all solutions. Moreover, the customer adjustment operator and the alternative fuel station &#x0028 AFS &#x0029 adjustment operator on the CGVRP route are executed for the elite solutions after competition. In addition, the crossover operator is employed to share information among different solutions. The effect of parameter setting is investigated using the Taguchi method of design-of-experiment to suggest suitable values. Via numerical tests, it demonstrates the effectiveness of both the competitive search and the decoding method. Moreover, extensive comparative results show that the proposed algorithm is more effective and efficient than the existing methods in solving the CGVRP.

New lower bounds for permutation arrays using contraction

A permutation array A is a set of permutations on a finite set $$\Omega $$ , say of size n. Given distinct permutations $$\pi , \sigma \in \Omega $$ , we let $$hd(\pi , \sigma ) = |\{ x\in \Omega : \pi (x) \ne \sigma (x) \}|$$ , called the Hamming distance between $$\pi $$ and $$\sigma $$ . Now let $$hd(A) =$$ min $$\{ hd(\pi , \sigma ): \pi , \sigma \in A \}$$ . For positive integers n and d with $$d\le n$$ we let M(n, d) be the maximum number of permutations in any array A satisfying $$hd(A) \ge d$$ . There is an extensive literature on the function M(n, d), motivated in part by suggested applications to error correcting codes for message transmission over power lines. A basic fact is that if a permutation group G is sharply k-transitive on a set of size $$n\ge k$$ , then $$M(n,n-k+1) = |G|$$ . Motivated by this we consider the permutation groups AGL(1, q) and PGL(2, q) acting sharply 2-transitively on GF(q) and sharply 3-transitively on $$GF(q)\cup \{\infty \}$$ respectively. Applying a contraction operation to these groups, we obtain the following new lower bounds for prime powers q satisfying $$q\equiv 1$$ (mod 3). These results resolve a case left open in a previous paper (Bereg et al. in Des Codes Cryptogr 86(5):1095–1111, 2018), where it was shown that $$M(q-1, q-3) \ge q^{2} - q$$ and $$M(q,q-3) \ge q^{3} - q$$ for all prime powers q such that $$q\not \equiv 1$$ (mod 3). We also obtain lower bounds for M(n, d) for a finite number of exceptional pairs n, d, by applying this contraction operation to the sharply 4 and 5-transitive Mathieu groups.

In Silico Engineering of Synthetic Binding Proteins from Random Amino Acid Sequences

SummarySynthetic proteins with high affinity and selectivity for a protein target can be used as research tools, biomarkers, and pharmacological agents, but few methods exist to design such proteins de novo. To this end, the In-Silico Protein Synthesizer (InSiPS) was developed to design synthetic binding proteins (SBPs) that bind pre-determined targets while minimizing off-target interactions. InSiPS is a genetic algorithm that refines a pool of random sequences over hundreds of generations of mutation and selection to produce SBPs with pre-specified binding characteristics. As a proof of concept, we design SBPs against three yeast proteins and demonstrate binding and functional inhibition of two of three targets in vivo. Peptide SPOT arrays confirm binding sites, and a permutation array demonstrates target specificity. Our foundational approach will support the field of de novo design of small binding polypeptide motifs and has robust applicability while offering potential advantages over the limited number of techniques currently available.

Increasing the Minimum Distance of Codes by Twisting

Twisted permutation codes, introduced recently by the second and third authors, belong to the family of frequency permutation arrays. Like some other codes in this family, such as the repetition permutation codes, they are obtained by a repetition construction applied to a smaller code (but with a "twist" allowed). The minimum distance of a twisted permutation code is known to be at least the minimum distance of a corresponding repetition permutation code, but in some instances can be larger. We construct two new infinite families of twisted permutation codes with minimum distances strictly greater than those for the corresponding repetition permutation codes. These constructions are based on two infinite families of finite groups and their representations. The first is a family of $p$-groups, for an odd prime $p$, while the second family consists of the $4$-dimensional symplectic groups over a finite field of even order. In the latter construction, properties of the graph automorphism of these symplectic groups play an important role.

Constructing permutation arrays from groups

Let M(n, d) be the maximum size of a permutation array on n symbols with pairwise Hamming distance at least d. We use various combinatorial, algebraic, and computational methods to improve lower bounds for M(n, d). We compute the Hamming distances of affine semilinear groups and projective semilinear groups, and unions of cosets of AGL(1, q) and PGL(2, q) with Frobenius maps to obtain new, improved lower bounds for M(n, d). We give new randomized algorithms. We give better lower bounds for M(n, d) also using new theorems concerning the contraction operation. For example, we prove a quadratic lower bound for $$M(n,n-2)$$ for all $$n\equiv 2 \pmod 3$$ such that $$n+1$$ is a prime power.

Group Coaching, Grounded in Theory and Evidence, Deployed through the National Research Mentoring Network (NRMN) to Complement Research Mentoring and Increase Diversity

Biomedical research training has historically relied almost exclusively on mentoring by research advisors as the vehicle for developing the talents of young scientists. Following an apprenticeship model, it affords almost a limitless array of permutations and combinations among mentors and trainees. It also allows for maximum variations in approaches to mentoring. However, it also leads to extreme variability in terms of what is ‘taught’ and opportunities made available to those in training, often leading to unpredictable outcomes, and/or underdevelopment or loss of scientific talent. This potential loss of talent can have especially high impact for individuals from underrepresented groups. As an alternative and complementary approach to more fully develop scientific talent, several variations of group coaching processes have been created and studied. All incorporate both practical and theoretical underpinnings and have established evidence of efficacy, and in one case intensive analysis through a randomized controlled trial. Based on both evidence of impact and theoretical strengths, they are now being expanded beyond their home institutions or limited missions to national impact through the National Research Mentoring Network (NRMN) funded by NIH.This presentation will highlight the theoretical basis, designs, and impacts to date of 4 different grant writing group coaching models being deployed and compared through NRMN. The presentation will also describe the career coaching group model with an expanded focus beyond grant writing that has evolved from a randomized controlled trial. The refined career coaching model is being tested in collaboration with the American Society for Pharmacology and Experimental Therapeutics (ASPET). All of the coaching models augment and complement research and other mentoring trainees are receiving. The models also all employ coaches who are highly skilled and successful scientists, usually with extensive mentoring experience, who are provided with additional training in the respective group coaching models. The models differ in the time each group operates (ranging from 3–12 months), and the career stages and readiness of participants to be actively writing a proposal. Unique to these group coaching models, they all acknowledge and make visible the underlying social science theories and practices that influence the environments where research training takes place. Evidence to date supports these group coaching models as valuable adjuncts to classical research mentoring, with the ability to positively impact maximal development of research talent and increase contributions from underrepresented groups.Support or Funding InformationSupported by NIH DP4 GM0096807, R01 GM107701, R35 GM118184, U54 GM119023 and ASPET Big Idea Award

( n , n ( n − 1), n − 1) Permutation codes based on packing and Mendelsohn designs

Mendelsohn design was first used to construct n − 1 blocks of one optimal 2−(n, n, 2) packing which is isomorphic to an (n, n − 1, n − 1) permutation array. The n-ary shift register (SR) formed by a group of k binary SRs of length n was constructed and then used to operate n − 1 blocks of the 2−(n, n, 2) packing which can generate n(n − 1) blocks of another optimal 2−(n, n, 2n) packing from which a family of (n, n(n − 1), n − 1) permutation codes can be constructed.

Extending permutation arrays: improving MOLS bounds

A permutation array (PA) A is a set of permutations on $$Z_n=\{0,1,\dots ,n-1\}$$Zn={0,1,ź,n-1}, for some n. A PA A has pairwise Hamming distance at least d, if for every pair of permutations $$\sigma $$ź and $$\tau $$ź in A, there are at least d integers i in $$Z_n$$Zn such that $$\sigma (i)\ne \tau (i)$$ź(i)źź(i). Let M(n, d) denote the maximum number of permutations in any PA with pairwise Hamming distance at least d. Recently considerable effort has been devoted to improving known lower bounds for M(n, d) for all $$n>d>3$$n>d>3. We give a partition and extension operation that enables the production of a new PA $$A'$$Aź for $$M(n+1,d)$$M(n+1,d) from an existing PA A for $$M(n,d-1)$$M(n,d-1). In particular, this operation allows for improvements for PA's for $$M(q+1,q)$$M(q+1,q) for powers of prime numbers q, as well as for many other choices of n and d, where n is not a power of a prime. Finally, for prime numbers p, the partition and extension technique provides an asymptotically better lower bound for $$M(p+1,p)$$M(p+1,p) than that given by current knowledge about mutually orthogonal Latin squares. We prove a new asymptotic lower bound for the set of primes p, namely, $$M(p+1,p)\ge p^{1.5}/2-O(p)$$M(p+1,p)źp1.5/2-O(p).