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By Foissy's work, the bidendriform structure of the Word Quasisymmetric Functions Hopf algebra (WQSym) implies that it is isomorphic to its dual. However, the only known explicit isomorphism due to Vargas does not respect the bidendriform structure. This structure is entirely determined by so-called totally primitive elements (elements such that the two half-coproducts vanish). In this paper, we construct two bases indexed by two new combinatorial families called red (dual side) and blue (primal side) biplane forests in bijection with packed words. In those bases, primitive elements are indexed by biplane trees and totally primitive elements by a certain subset of trees. We carefully combine red and blue forests to get bicolored forests. A simple recoloring of the edges allows us to obtain the first explicit bidendriform automorphism of WQSym.Mathematics Subject Classifications: 05A05, 05A19, 05E05, 05E18Keywords: Bidendriform Hopf algebras, Word Quasisymmetric Functions, packed words, permutation, primitive elements, duality, tree, forest, global descents

The internal kink mode is one of the crucial factors affecting the stability of magnetically confined fusion devices. This paper explores the key features influencing the growth rate of internal kink modes using machine learning techniques such as Random Forest, Extreme Gradient Boosting (XGboost), Permutation, and SHapley Additive exPlanations (SHAP). We conduct an in-depth analysis of the significant physical mechanisms by which these key features impact the growth rate of internal kink modes. Numerical simulation data were used to train high-precision machine learning models, namely Random Forest and XGBoost, which achieved coefficients of determination values of 95.07% and 94.57%, respectively, demonstrating their capability to accurately predict the growth rate of internal kink modes. Based on these models, key feature analysis was systematically performed with Permutation and SHAP methods. The results indicate that resistance, pressure at the magnetic axis, viscosity, and plasma rotation are the primary features influencing the growth rate of internal kink modes. Specifically, resistance affects the evolution of internal kink modes by altering current distribution and magnetic field structure; pressure at the magnetic axis impacts the driving force of internal kink modes through the pressure gradient directly related to plasma stability; viscosity modifies the dynamic behavior of internal kink modes by regulating plasma flow; and plasma rotation introduces additional shear forces, affecting the stability and growth rate of internal kink modes. This paper describes the mechanisms by which these four key features influence the growth rate of internal kink modes, providing essential theoretical insights into the behavior of internal kink modes in magnetically confined fusion devices. [ABSTRACT FROM AUTHOR]

ABSTRACT Image based screening is now routinely available for early detection of cancer and other diseases. Quantitative analysis for effects of risk factors on digital images is important to extract biological insights for modifiable factors in prevention studies and understand pathways for targets in preventive drugs. However, current approaches are restricted to summary measures within the image with the assumption that all relevant features needed to characterize an image can be identified and appropriately quantified. Motivated by data challenges in breast cancer, we propose a nonparametric statistical framework for risk factor screening that uses the whole mammogram image as outcome. The proposed permutation test allows assessment of whether a set of scalar risk factors is associated with the whole image in the presence of correlated residuals across the spatial domain. We provide extensive simulation studies and illustrate an application to the Joanne Knight Breast Health Cohort using the mammogram imaging data. [ABSTRACT FROM AUTHOR]

In 2016, Y. Kumar et al. in the paper 'Affine equivalence and non-linearity of permutations over Z n ' conjectured that: For n ≥ 3 , the nonlinearity of any permutation on Z n , the ring of integers modulon, cannot exceed n - 2 . For an odd prime p, we settle the above conjecture when n = 2 p and for p ≡ 3 (mod 4) we prove the above conjecture with an improved upper bound. Further, we derive a lower bound on max N L n when n is an odd prime or twice of an odd prime where max N L n denotes the maximum possible nonlinearity of any permutation on Z n . [ABSTRACT FROM AUTHOR]

A permutation is said to be cycle-alternating if it has no cycle double rises, cycle double falls or fixed points; thus each index i is either a cycle valley ( σ - 1 (i) > i < σ (i) ) or a cycle peak ( σ - 1 (i) < i > σ (i) ). We find Stieltjes-type continued fractions for some multivariate polynomials that enumerate cycle-alternating permutations with respect to a large (sometimes infinite) number of simultaneous statistics that measure cycle status, record status, crossings and nestings along with the parity of the indices. Our continued fractions are specializations of more general continued fractions of Sokal and Zeng. We then introduce alternating Laguerre digraphs, which are generalization of cycle-alternating permutations, and find exponential generating functions for some polynomials enumerating them. We interpret the Stieltjes–Rogers and Jacobi–Rogers matrices associated to some of our continued fractions in terms of alternating Laguerre digraphs. [ABSTRACT FROM AUTHOR]

AbstractWe prove that an element of the symmetric group of degree n>3 can be represented as the commutator of two permutations whose supports intersect at exactly p≤n points if and only if it is the product of p cycles of length 3. As an accompanying result, and also as a step of the main result’s proof, we give a lower bound for p to express an even permutation as the product of p cycles of length 3, in terms of its decomposition into disjoint cycles. [ABSTRACT FROM AUTHOR]

AbstractWe propose a two-step procedure to model and predict high-dimensional functional time series, where the number of function-valued time series p is large in relation to the length of time series n. Our first step performs an eigenanalysis of a positive definite matrix, which leads to a one-to-one linear transformation for the original high-dimensional functional time series, and the transformed curve series can be segmented into several groups such that any two subseries from any two different groups are uncorrelated both contemporaneously and serially. Consequently in our second step those groups are handled separately without the information loss on the overall linear dynamic structure. The second step is devoted to establishing a finite-dimensional dynamical structure for all the transformed functional time series within each group. Furthermore the finite-dimensional structure is represented by that of a vector time series. Modelling and forecasting for the original high-dimensional functional time series are realized via those for the vector time series in all the groups. We investigate the theoretical properties of our proposed methods, and illustrate the finite-sample performance through both extensive simulation and two real datasets. [ABSTRACT FROM AUTHOR]

ABSTRACT The first Adaptive COVID‐19 Treatment Trial (ACTT‐1) showed that remdesivir improved COVID‐19 recovery time compared with placebo in hospitalized adults. The secondary outcome of mortality was almost significant overall (p = 0.07) and highly significant for people receiving supplemental oxygen at enrollment (p = 0.002), suggesting a mortality benefit concentrated in this group. We explore analysis methods that are helpful when a single subgroup benefits from treatment and apply them to ACTT‐1, using baseline oxygen use to define subgroups. We consider two questions: (1) is the remdesivir effect for people receiving supplemental oxygen real, and (2) does this effect differ from the overall effect? For Question 1, we apply a Bonferroni adjustment to subgroup‐specific hypothesis tests and the Westfall and Young permutation test, which is valid when small cell counts preclude normally distributed test statistics (a frequently unexamined condition in subgroup analyses). For Question 2, we introduce Qmax, the largest standardized difference between subgroup‐specific effects and the overall effect. Qmax simultaneously tests whether any subgroup effect differs from the overall effect and identifies the subgroup benefitting most. We demonstrate that Qmax strongly controls the familywise error rate (FWER) when test statistics are normally distributed with no mean–variance relationship. We compare Qmax to a related permutation test, SEAMOS, which was previously proposed but not extensively applied or tested. We show that SEAMOS can have inflated Type 1 error under the global null when control arm event rates differ between subgroups. Our results support a mortality benefit from remdesivir in people receiving supplemental oxygen. [ABSTRACT FROM AUTHOR]

In the last few years, the volume of internet traffic has increased enormously. A significant portion of the internet traffic is constituted by applications that stream multimedia data from one part of the world to another. The enormity of the video data requires the Content Delivery Network to distribute the content efficiently and securely among the consumers. The secure and authenticated distribution can be achieved by the end-to-end encryption of video. In this paper, one time random key algorithm and the algorithms and methods based on permutation techniques have been proposed to encrypt the video frames selectively and these encrypted frames are transmitted over the network along with the other video frames. The proposed encryption methods extract the colour channels like Red, Green and Blue from the video frames, and they are encrypted by applying row-column permutation cipher, One Time Pad cipher and row permutation cipher. Encryption of the video frames has been performed at two levels by combining the one-time random key algorithm and permutation techniques to provide security to the video. These encryption techniques have been applied on the twenty-five, thirty, and thirty-five, and so on, up to fifty per cent of the total frames available in the video. The experimental results, histogram analysis and parameters like average Peak Signal-to-noise Noise Ratio (PSNR) and Structural Similarity Index (SSIM) values measure the quality of the video obtained after the application of the proposed methods on the video to be transmitted over the network. [ABSTRACT FROM AUTHOR]

Within the context of Indian religions, Jainism has long been recognized for its extensive use of permutations and combinations. However, the application of these principles within Buddhist scriptures has received relatively little scholarly attention. This paper introduces a new example of the specific application of permutations and combinations in Buddhist scriptures. In this paper, we focus on the first saṅghādisesa rule in the Theravāda-vinaya, which lists a series of element sets and arranges these elements according to a certain pattern known as "ten-roots" (mūla), and we discover that these arrangements form a regular numerical sequence, called "oblong numbers". Moreover, similar patterns with different quantities are also found in the fourth Pārājika and the fifth saṅghādisesa rules. This indicates that the compilers of the Theravāda-vinaya did not use this mathematical knowledge without basis. Interestingly, we also found the use of this sequence in the Bakhshālī manuscript. Therefore, in this article, after summarizing and verifying the arrangement rules of the Theravāda-vinaya, we discuss whether the oblong numbers were influenced by Greek mathematics. [ABSTRACT FROM AUTHOR]

We consider representations of an arbitrary permutation π of degree 2n, n ⩾ 3, by products of the so-called (2n)-permutations (any cycle of such a permutation has length 2). We show that any even permutation is represented by the product of four (2n)-permutations. Products of three (2n)-permutations cannot represent all even permutations. Any odd permutation is realized (for odd n) by a product of five (2n)-permutations. [ABSTRACT FROM AUTHOR]

Given a finite set of points C ⊆ R d , we say that an ordering of C is protrusive if every point lies outside the convex hull of the points preceding it. We give an example of a set C of 5 points in the Euclidean plane possessing a protrusive ordering that cannot be obtained by ranking the points of C according to the sum of their distances to a finite multiset of points. This answers a question of Alon, Defant, Kravitz, and Zhu. [ABSTRACT FROM AUTHOR]

We consider the problem of determining which matrices are permutable to be supmodular. We show that for small dimensions any matrix is permutable by a universal permutation or by a pair of permutations, while for higher dimensions no universal permutation exists. We raise several questions including to determine the dimensions in which every matrix is permutable. [ABSTRACT FROM AUTHOR]

For a Coxeter system (W, S) and a subset J ⊆ S, fix u ∈ WJ and ξ ∈ WJ, let λ(−, u) : WJ → W and λ(ξ, −) : WJ → W be the mappings defined by λ(x, u) = xu and λ(ξ, y) = ξy, respectively. We show that λ(−, u) is left weak Bruhat order preserving for all u ∈ WJ, and that λ(ξ,−) is left weak Bruhat order-preserving if and only if it is a convex embedding, if and only if `(y) = `(ξyξ−1 ) for all y ∈ WJ. For the Coxeter groups of types A and B, we explicitly describe the ξ that satisfies the previous equivalent conditions in a purely combinatorial manner. [ABSTRACT FROM AUTHOR]

Test of independence is of fundamental importance in modern data analysis, with broad applications in variable selection, graphical models, and causal inference. When the data is high dimensional and the potential dependence signal is sparse, independence testing becomes very challenging without distributional or structural assumptions. In this article, we propose a general framework for independence testing by first fitting a classifier that distinguishes the joint and product distributions, and then testing the significance of the fitted classifier. This framework allows us to borrow the strength of the most advanced classification algorithms developed from the modern machine learning community, making it applicable to high dimensional, complex data. By combining a sample split and a fixed permutation, our test statistic has a universal, fixed Gaussian null distribution that is independent of the underlying data distribution. Extensive simulations demonstrate the advantages of the newly proposed test compared with existing methods. We further apply the new test to a single cell dataset to test the independence between two types of single cell sequencing measurements, whose high dimensionality and sparsity make existing methods hard to apply. for this article are available online. [ABSTRACT FROM AUTHOR]

We initiate the investigation of the parameterized complexity of Diameter and Connectivity in the streaming paradigm. On the positive end, we show that knowing a vertex cover of size k allows for algorithms in the Adjacency List (AL) streaming model whose number of passes is constant and memory is O (log n) for any fixed k. Underlying these algorithms is a method to execute a breadth-first search in O (k) passes and O (k log n) bits of memory. On the negative end, we show that many other parameters lead to lower bounds in the AL model, where Ω (n / p) bits of memory is needed for any p-pass algorithm even for constant parameter values. In particular, this holds for graphs with a known modulator (deletion set) of constant size to a graph that has no induced subgraph isomorphic to a fixed graph H, for most H. For some cases, we can also show one-pass, Ω (n log n) bits of memory lower bounds. We also prove a much stronger Ω (n 2 / p) lower bound for Diameter on bipartite graphs. Finally, using the insights we developed into streaming parameterized graph exploration algorithms, we show a new streaming kernelization algorithm for computing a vertex cover of size k. This yields a kernel of 2k vertices (with O (k 2) edges) produced as a stream in poly (k) passes and only O (k log n) bits of memory. [ABSTRACT FROM AUTHOR]

We write $\mathcal {S}_n(A)$ for the set of permutations of a set A with n non-fixed points and $\mathrm {{seq}}^{1-1}_n(A)$ for the set of one-to-one sequences of elements of A with length n where n is a natural number greater than $1$. With the Axiom of Choice, $|\mathcal {S}_n(A)|$ and $|\mathrm {{seq}}^{1-1}_n(A)|$ are equal for all infinite sets A. Among our results, we show, in ZF, that $|\mathcal {S}_n(A)|\leq |\mathrm {{seq}}^{1-1}_n(A)|$ for any infinite set A if ${\mathrm {AC}}_{\leq n}$ is assumed and this assumption cannot be removed. In the other direction, we show that $|\mathrm {{seq}}^{1-1}_n(A)|\leq |\mathcal {S}_{n+1}(A)|$ for any infinite set A and the subscript $n+1$ cannot be reduced to n. Moreover, we also show that " $|\mathcal {S}_n(A)|\leq |\mathcal {S}_{n+1}(A)|$ for any infinite set A " is not provable in ZF. [ABSTRACT FROM AUTHOR]

Smart door locks pose a large number of threats such as network attacks. Its storage area and power of cipher are severely limited because the wireless nodes of smart door locks are mostly battery‐powered. Therefore, effective security solutions are urgently needed. In this paper, a new lightweight block cipher with low power named LPHD is proposed to ensure the security of the master control chip of the smart door lock terminal. We design a scheme of low power S‐box and construct the two‐stage permutation layer (TP structure) suitable for LPHD by filtering the sets of 8‐bit permutations. LPHD proposes a variant of the 8‐branch generalized Feistel structure (GFS) to realize that the bits of all branches are affected in one encryption round. The problem of slow diffusion in the standard Feistel structure is solved. The key schedule adopts the nonlinear design and reuses the encryption process of LPHD. It improves the security of the cipher and reduces hardware overhead. Moreover, we evaluate the hardware implementation and security of LPHD. The results show that LPHD for the unified encryption and decryption circuits requires only 1276 Gate Equivalents (GEs) and 1.914 μW on UMC 0.18 μm, which is better than other lightweight block ciphers such as SKINNY, PRESENT, and IVLBC. In summary, LPHD provides sufficient security for the master control chip of the smart door lock terminal. [ABSTRACT FROM AUTHOR]

We characterize the permutative automorphisms of the Cuntz algebra \mathcal {O}_n (namely, stable permutations) in terms of two sequences of graphs that we associate to any permutation of a discrete hypercube [n]^t. As applications we show that in the limit of large t (resp. n) almost all permutations are not stable, thus proving Conj. 12.5 of Brenti and Conti [Adv. Math. 381 (2021), p. 60], characterize (and enumerate) stable quadratic 4 and 5-cycles, as well as a notable class of stable quadratic r-cycles, i.e. those admitting a compatible cyclic factorization by stable transpositions. Some of our results use new combinatorial concepts that may be of independent interest. [ABSTRACT FROM AUTHOR]

Fermat’s two squares theorem asserts that a prime one more than a multiple of 4 is a sum of two squares. There are many proofs of this gem in number theory, including a remarkable one-sentence proof by Don Zagier based on two involutions on a finite set built from such a prime. Applying the two involutions alternatively leads to an iterative algorithm to find the two squares for the prime. Moreover, a detailed analysis of the computation reveals that it is possible to jump through the iteration nodes, leading to a better hopping algorithm. Here is a formalisation of Zagier’s proof, deriving the involutions using windmill patterns. Theories developed for the formal proof are used to establish the correctness of both algorithms. [ABSTRACT FROM AUTHOR]

Permutation techniques have been used extensively in machine learning algorithms for evaluating variable importance. In ordinary regression, however, variables are often removed to gauge their importance. In this paper, we compared the results for permuting variables to removing variables in regression to assess relations between these two methods. We compared permute-and-predict (PaP) methods with leave-one-covariate-out (LOCO) techniques. We also compared these results with conventional metrics such as regression coefficient estimates, t-statistics, and random forest out-of-bag (OOB) PaP importance. Our results indicate that permutation importance metrics are practically equivalent to those obtained from removing variables in a regression setting. We demonstrate a strong association between the PaP metrics, true coefficients, and regression-estimated coefficients. We also show a strong relation between the LOCO metrics and the regression t-statistics. Finally, we illustrate that manual PaP methods are not equivalent to the OOB PaP technique and suggest prioritizing the use of manual PaP methods on validation data.

AbstractFor a natural number n, the permutation (n!) is defined as the left-to-right product of the first n cycles, namely, . In this article, we prove that for any natural number n, 2 is a primitive root of 2n + 1 if and only if 2n + 1 = pk for some odd prime number p and for some natural number k such that the permutation (n!) has exactly k orbits. We also prove that a prime number p is a Sophie Germain prime if and only if the permutation (p!) has at most two orbits. [ABSTRACT FROM AUTHOR]

The substitution box (S-box) is one of the extremely important components in the design of block cipher. An excellent S-box is necessary for the block cipher algorithm, and its cipher strength directly affects the security of the cipher algorithm. The differential uniformity of the S-box generated by the chaotic system is 10 or 12, which cannot effectively resist differential cryptanalysis. Aiming at the high differential uniformity of the S-box constructed by the chaotic system, a novel efficient S-box construction scheme based on a new chaotic map and permutation is proposed in this paper. In this scheme, the chaotic matrix is generated by a new chaotic map, and then is replaced by permutation sequences to generate S-boxes. Comparative analysis shows that the generated S-boxes have high nonlinearity, low differential uniformity, and satisfy SAC and BIC criteria, which can improve the ability of the algorithm to resist differential cipher attacks and linear cryptographic analysis. [ABSTRACT FROM AUTHOR]

Complete non-ambiguous trees (CNATs) are combinatorial objects which appear in various contexts. Recently, Chen and Ohlig studied the notion of permutations associated to these objects, and proposed a series of nice conjectures. Most of themwere proved by Selig and Zhu, through a connection with the abelian sandpile model. But one conjecture remained open, about the distribution of a natural statistic named determinant. We prove this conjecture, in a bijective way. [ABSTRACT FROM AUTHOR]

Permutation techniques have been used extensively in machine learning algorithms for evaluating variable importance. In ordinary regression, however, variables are often removed to gauge their importance. In this paper, we compared the results for permuting variables to removing variables in regression to assess relations between these two methods. We compared permute-and-predict (PaP) methods with leave-one-covariate-out (LOCO) techniques. We also compared these results with conventional metrics such as regression coefficient estimates, t-statistics, and random forest out-of-bag (OOB) PaP importance. Our results indicate that permutation importance metrics are practically equivalent to those obtained from removing variables in a regression setting. We demonstrate a strong association between the PaP metrics, true coefficients, and regression-estimated coefficients. We also show a strong relation between the LOCO metrics and the regression t-statistics. Finally, we illustrate that manual PaP methods are not equivalent to the OOB PaP technique and suggest prioritizing the use of manual PaP methods on validation data. [ABSTRACT FROM AUTHOR]

Testing zero variance components is of utmost importance in various applications empowered by the use of mixed-effects models. Focusing on generalized linear models, this article proposes a permutation test using an analogue of the ANOVA test statistic that merely requires fitting the null model with independent observations. Monte Carlo simulations reveal that the new test has correct Type-I error rate and that its power compares favorably to an existing bootstrap score test. A real data application illustrates the advantageous capability of the proposed test in detecting the need for random effects. [ABSTRACT FROM AUTHOR]

Affiliative relationships are well documented in a wide range of wild animals. However, there is limited evidence of their existence in social farm animals, despite potential significant animal welfare implications. We aimed to determine whether pigs have preferential partners for affiliative interactions and associations and whether these preferences remain stable over time or are influenced by sex, dominance rank or litter of origin (i.e. kinship or familiarity). Two pens of 12 domestic pigs, Sus scrofa , two males and two females from three litters, were weaned at 28 days of age and observed from 42 to 57 days (postweaning phase) and from 70 to 85 days (finishing phase) following a change of housing at 62 days. Sociopositive behaviours, including nose-to-nose and nose-to-body contacts, allogrooming and associations while lying were scored on video observations over 6 days per phase. Using social network analysis methods, we found nonrandom social preferences for allogrooming in both pens of pigs, which remained stable between the postweaning and finishing phases. We also observed nonrandom associations for proximities while lying, although these patterns were not found in both pens of pigs and did not systematically persist between phases. In contrast, nose-to-nose interactions were expressed randomly in both pens and phases. Depending on the housing conditions, social preferences for grooming interactions or proximity while lying were only weakly influenced by sex, dominance rank or litter of origin. We did not find any correlation between social networks for grooming interactions and associations while lying. In summary, our study highlights the existence of durable affiliative relationships based on grooming interactions and proximity while lying within stable pig groups. These relationships appear to be minimally affected by sex, dominance, kinship or familiarity. Taking these relationships into account, particularly from a young age, could be pivotal in improving the welfare of pigs on farms. • Pigs showed preferential partners for allogrooming and lying together. • Social preferences for allogrooming persisted after a change of housing. • Lying proximity and social interactions were distinct facets of social affiliation. • Nose-to-nose contacts occurred randomly within groups of pigs. • Affiliation in pigs was not primarily driven by sex, dominance or kinship. [ABSTRACT FROM AUTHOR]

Most semi-quantum secret sharing protocols are suitable for the application with three participants. Based on the n-level states, a multiparty semi-quantum secret sharing protocol is proposed. Compared with similar protocols, it has the merits as follows. (1) The dealer only needs to prepare the single photon sequence without using any product state or entangle state. (2) To share a secret, the classical parties need not have the ability of measurement. They only need to reorder the photon sequence and send it to the receiver. (3) The dealer knows nothing about any agent's secret shadow. Therefore, it is infeasible for the dealer to impersonate the classical participant to pool the secret shadow during the secret recovering phase. (4) Theoretically, the qubit efficiency of the proposed protocol is asymptotically 100%. The protocol is secure against famous attacks such as intercept-resend attack, measurement-resend attack and entangle-measure attack. [ABSTRACT FROM AUTHOR]

Let n be any natural number such that 2 is a primitive root of 2 n + 1 . In this article, we prove that the permutation (n!) has two orbits if and only if 2 n + 1 = p 2 for some odd prime p, where (n !) = ∏ k = 0 n - 1 (1 , 2 , ⋯ , (n - k)) . [ABSTRACT FROM AUTHOR]

In the rapid evolving digital landscape, the imperative to ensure data security has never been more crucial. This paper addresses the pressing challenges in data security by introducing a file encryption management system, leveraging a modified advanced encryption standard (AES) algorithm with reduced round iterations and bit permutation. This system aims to comprehensively secure various file types, providing a dependable solution for file exchange. Our findings reveal substantial improvements in both encryption and decryption processes using the reduced-round permutationbased AES (RRPBA). The adapted algorithm demonstrates a significant 38.8% acceleration in encryption time and a remarkable 44.86% improvement in decryption time, positioning it as a pivotal component for efficient file operations within the management system. Moreover, the throughput assessments showcase a remarkable 33.73% improvement in encryption and 23.72% in decryption, outperforming the original AES, emphasizing the algorithm's superior computational effectiveness, signaling positive implications for future high-performance applications. In conclusion, the study not only addresses critical security challenges but also presents a viable solution with tangible speed advantages for file encryption and decryption processes within digital file management systems. [ABSTRACT FROM AUTHOR]

The internal kink mode is one of the crucial factors affecting the stability of magnetically confined fusion devices. This paper explores the key features influencing the growth rate of internal kink modes using machine learning techniques such as Random Forest, Extreme Gradient Boosting (XGboost), Permutation, and SHapley Additive exPlanations (SHAP). We conduct an in-depth analysis of the significant physical mechanisms by which these key features impact the growth rate of internal kink modes. Numerical simulation data were used to train high-precision machine learning models, namely Random Forest and XGBoost, which achieved coefficients of determination values of 95.07% and 94.57%, respectively, demonstrating their capability to accurately predict the growth rate of internal kink modes. Based on these models, key feature analysis was systematically performed with Permutation and SHAP methods. The results indicate that resistance, pressure at the magnetic axis, viscosity, and plasma rotation are the primary features influencing the growth rate of internal kink modes. Specifically, resistance affects the evolution of internal kink modes by altering current distribution and magnetic field structure; pressure at the magnetic axis impacts the driving force of internal kink modes through the pressure gradient directly related to plasma stability; viscosity modifies the dynamic behavior of internal kink modes by regulating plasma flow; and plasma rotation introduces additional shear forces, affecting the stability and growth rate of internal kink modes. This paper describes the mechanisms by which these four key features influence the growth rate of internal kink modes, providing essential theoretical insights into the behavior of internal kink modes in magnetically confined fusion devices.

Abstract Background Although many studies have been done to reveal artificial selection signatures in commercial and indigenous chickens, a limited number of genes have been linked to specific traits. To identify more trait-related artificial selection signatures and genes, we re-sequenced a total of 85 individuals of five indigenous chicken breeds with distinct traits from Yunnan Province, China. Results We found 30 million non-redundant single nucleotide variants and small indels (

The confusion-creating ability of a substitution box is indispensable. Its utmost involvement in the block cipher motivates researchers to investigate methods and construct cryptographically strong and efficient substitution boxes. In this paper, we define an isogeny that maps the elements of the base curve to the second curve. The points that can generate the maximal order subgroup of the elliptic curve points are the generators of the base curve. A group action is applied to the generators of the base curve to construct the initial S-boxes. The images of the generator points are established through isogeny and used to generate initial S-boxes from the second curve. The idea is cost-effective regarding computation, as both curves share the same prime field, and we only need to find a few generator points and the corresponding images. A suitable permutation from S n is applied to the selected initial substitution box to improve the nonlinearity. The suggested S-box is balanced and highly nonlinear. We assessed the cryptographic strength of the suggested S-box against linear and differential probabilities. The smaller values of these tests ensure that the suggested S-box is cryptographically strong and can be used securely in any block cipher. [ABSTRACT FROM AUTHOR]

A proposed algorithm for digital image encryption is presented in this paper. It combines permutation and substitution techniques. Logistic map which is a chaos function is used in both techniques. Before encrypting, the keystream is generated first from the logistics map. Then, the plain image's pixel positions are shuffled with perfect shuffle permutation based on ascending keystream order, thereby executing the permutation process. Next, the pixel values are substituted using the XOR operation with a keystream which is also generated from the logistic map. Pixels are operated in cipher block chain mode. This research aim is to develop an image encryption algorithm, especially in the permutation process, that has high resistance to attacks by crackers. The attack types observed in this research include statistical attacks, permutation matrix attacks, differential attacks, as well as brute force attacks. From the experimental results and analysis of the proposed algorithm indicate that it has high resistance from all those attacks. [ABSTRACT FROM AUTHOR]

In this note, we give four representations of 1/π as the limits of four sequences formed by the number of permutations of n elements with k cycles. [ABSTRACT FROM AUTHOR]

Permutation rational functions over finite fields have attracted high interest in recent years. However, only a few of them have been exhibited. This article studies a class of permutation rational functions constructed using trace maps on extensions of finite fields, especially for the cases of quadratic and cubic extensions. Our achievements are obtained by investigating absolute irreducibility of some polynomials in two indeterminates. [ABSTRACT FROM AUTHOR]

Background: Although many studies have been done to reveal artificial selection signatures in commercial and indigenous chickens, a limited number of genes have been linked to specific traits. To identify more trait-related artificial selection signatures and genes, we re-sequenced a total of 85 individuals of five indigenous chicken breeds with distinct traits from Yunnan Province, China. Results: We found 30 million non-redundant single nucleotide variants and small indels (< 50 bp) in the indigenous chickens, of which 10 million were not seen in 60 broilers, 56 layers and 35 red jungle fowls (RJFs) that we compared with. The variants in each breed are enriched in non-coding regions, while those in coding regions are largely tolerant, suggesting that most variants might affect cis-regulatory sequences. Based on 27 million bi-allelic single nucleotide polymorphisms identified in the chickens, we found numerous selective sweeps and affected genes in each indigenous chicken breed and substantially larger numbers of selective sweeps and affected genes in the broilers and layers than previously reported using a rigorous statistical model. Consistent with the locations of the variants, the vast majority (~ 98.3%) of the identified selective sweeps overlap known quantitative trait loci (QTLs). Meanwhile, 74.2% known QTLs overlap our identified selective sweeps. We confirmed most of previously identified trait-related genes and identified many novel ones, some of which might be related to body size and high egg production traits. Using RT-qPCR, we validated differential expression of eight genes (GHR, GHRHR, IGF2BP1, OVALX, ELF2, MGARP, NOCT, SLC25A15) that might be related to body size and high egg production traits in relevant tissues of relevant breeds. Conclusion: We identify 30 million single nucleotide variants and small indels in the five indigenous chicken breeds, 10 million of which are novel. We predict substantially more selective sweeps and affected genes than previously reported in both indigenous and commercial breeds. These variants and affected genes are good candidates for further experimental investigations of genotype-phenotype relationships and practical applications in chicken breeding programs. [ABSTRACT FROM AUTHOR]

The selection of group features is a critical aspect in reducing model complexity by choosing the most essential group features, while eliminating the less significant ones. The existing group feature selection methods select a set of important group features, without providing the relative importance of all group features. Moreover, few methods consider the relative importance of group features in the selection process. This study introduces a permutation-based group feature selection approach specifically designed for high-dimensional multiclass datasets. Initially, the least absolute shrinkage and selection operator (lasso) method was applied to eliminate irrelevant individual features within each group feature. Subsequently, the relative importance of the group features was computed using a random-forest-based permutation method. Accordingly, the process selected the highly significant group features. The performance of the proposed method was evaluated using machine learning algorithms and compared with the performance of other approaches, such as group lasso. We used real-world, high-dimensional, multiclass microarray datasets to demonstrate its effectiveness. The results highlighted the capability of the proposed method, which not only selected significant group features but also provided the relative importance and ranking of all group features. Furthermore, the proposed method outperformed the existing method in terms of accuracy and F1 score. [ABSTRACT FROM AUTHOR]

Topological transformations and permutations of proteins have attracted significant interest as strategies to generate new protein functionalities or stability. These efforts have mainly been inspired by naturally occurring post‐translational modifications, such as head‐to‐tail cyclization, circular permutation, or lasso‐like entanglement. Such approaches can be realized experimentally via genetic encoding, in the case of circular permutation, or via enzymatic processing, in the case of cyclization. Notably, these previously described strategies leave the polypeptide backbone orientation unaltered. Here we describe an unnatural protein permutation, the protein domain inversion, whereby a C‐terminal portion of a protein is enzymatically inverted from the canonical N‐to‐C to a C‐to‐C configuration with respect to the N‐terminal part of the protein. The closest conceptually analogous biological process is perhaps the inversion of DNA segments as catalyzed by recombinases. We achieve these inversions using an engineered sortase A, a widely used transpeptidase. Our reactions proceed efficiently under mild conditions at 4–25 °C and are compatible with entirely heterologously‐produced protein substrates. [ABSTRACT FROM AUTHOR]

We consider multipermutations and a certain partial order, the weak Bruhat order, on this set. This generalizes the Bruhat order for permutations, and is defined in terms of containment of inversions. Different characterizations of this order are given. We also study special multipermutations called Stirling multipermutations and their properties. [ABSTRACT FROM AUTHOR]