Permutations Of Order Research Articles

A Criterion for Decomposabilty in QYBE

Abstract In this paper, set theoretic solutions of the Quantum Yang–Baxter Equations are considered. Etingof et al. [ 8] defined the structure group for non-degenerate solutions and gave some properties of this group. In particular, they provided a criterion for decomposability of involutive solutions based on the transitivity of the structure group. In that paper, the diagonal permutation $T$ is also introduced. It is known that this permutation is trivial exactly when the solution is square free. Rump [ 12] proved that these solutions are decomposable except in the trivial case. Later, Ramirez and Vendramin [ 11] gave some criteria for decomposability related with the diagonal permutation $T$. In this paper it was proven that an involutive solution is decomposable when the number of symbols of the solution and the order of the diagonal permutation $T$ are coprime.

The peak and descent statistics over ballot permutations

A ballot permutation is a permutation π such that in any prefix of π the descent number is not more than the ascent number. By using a reversal-concatenation map, we (i) give a formula for the joint distribution (pk, des) of the peak and descent statistics over ballot permutations, (ii) connect this distribution and the joint distribution (pk, des) over ordinary permutations in terms of generating functions, and (iii) confirm Spiro's conjecture which finds the equidistribution of the descent statistic for ballot permutations and an analogue of the descent statistic for odd order permutations.

BioCPPNet: automatic bioacoustic source separation with deep neural networks

We introduce the Bioacoustic Cocktail Party Problem Network (BioCPPNet), a lightweight, modular, and robust U-Net-based machine learning architecture optimized for bioacoustic source separation across diverse biological taxa. Employing learnable or handcrafted encoders, BioCPPNet operates directly on the raw acoustic mixture waveform containing overlapping vocalizations and separates the input waveform into estimates corresponding to the sources in the mixture. Predictions are compared to the reference ground truth waveforms by searching over the space of (output, target) source order permutations, and we train using an objective function motivated by perceptual audio quality. We apply BioCPPNet to several species with unique vocal behavior, including macaques, bottlenose dolphins, and Egyptian fruit bats, and we evaluate reconstruction quality of separated waveforms using the scale-invariant signal-to-distortion ratio (SI-SDR) and downstream identity classification accuracy. We consider mixtures with two or three concurrent conspecific vocalizers, and we examine separation performance in open and closed speaker scenarios. To our knowledge, this paper redefines the state-of-the-art in end-to-end single-channel bioacoustic source separation in a permutation-invariant regime across a heterogeneous set of non-human species. This study serves as a major step toward the deployment of bioacoustic source separation systems for processing substantial volumes of previously unusable data containing overlapping bioacoustic signals.

The ‘D-Books’ of Daryaganj Sunday Book Market

Daryaganj Sunday Book Market, popularly known as Daryaganj Sunday Patri Kitab Bazaar, is a weekly informal market for used, rare, and pirated books that has been operating on the streets of Old Delhi for the past fifty years. In this essay, I focus on one of the circuits that has been flourishing in this market, that of pirated or ‘duplicate’ or D-books. In order to examine the forms in which piracy thrives in the present-day Patri Kitab Bazaar, and the reasons behind it, I compare two types of pirated books found here: a low-price self-help manual in Hindi and a ‘D’ copy of an English novel by popular Indian author Chetan Bhagat. As I examine the essential role that ‘randomness’ plays in the constitution of pirated texts, I suggest that there is organization to this apparent lack of pattern or unpredictability. Such permutation of order and chaos resonates with the location of the bazaar – a site that thrives on the serendipity of the streets.

Starter Set Generation Based on Factorial Numbers for Half Wing of Butterfly Representation

Permutation is an interesting subject to explore until today where it is widely applied in many areas. This paper presents the use of factorial numbers for generating starter sets where starter sets are used for listing permutation. Previously starter sets are generated by using their permutation under exchange-based and cycling based. However, in the new algorithm, this process is replaced by factorial numbers. The base theory is there are <img src=image/13491677_01.gif> number of distinct starter sets. Every permutation has its decimal number from zero until <img src=image/13491677_02.gif> for Lexicographic order permutation only. From a decimal number, it will be converted to a factorial number. Then the factorial number will be mapped to its corresponding starter sets. After that, the Half Wing of Butterfly will be presented. The advantage of the use of factorial numbers is the avoidance of the recursive call function for starter set generation. In other words, any starter set can be generated by calling any decimal number. This new algorithm is still in the early stage and under development for the generation of the half wing of butterfly representation. Case n=5 is demonstrated for a new algorithm for lexicographic order permutation. In conclusion, this new development is only applicable for generating starter sets as a lexicographic order permutation due to factorial numbers is applicable for lexicographic order permutation.

Lower bound on the size of a quasirandom forcing set of permutations

AbstractA set S of permutations is forcing if for any sequence $\{\Pi_i\}_{i \in \mathbb{N}}$ of permutations where the density $d(\pi,\Pi_i)$ converges to $\frac{1}{|\pi|!}$ for every permutation $\pi \in S$ , it holds that $\{\Pi_i\}_{i \in \mathbb{N}}$ is quasirandom. Graham asked whether there exists an integer k such that the set of all permutations of order k is forcing; this has been shown to be true for any $k\ge 4$ . In particular, the set of all 24 permutations of order 4 is forcing. We provide the first non-trivial lower bound on the size of a forcing set of permutations: every forcing set of permutations (with arbitrary orders) contains at least four permutations.

A Proposal of Quantum-Inspired Machine Learning for Medical Purposes: An Application Case

Learning tasks are implemented via mappings of the sampled data set, including both the classical and the quantum framework. Biomedical data characterizing complex diseases such as cancer typically require an algorithmic support for clinical decisions, especially for early stage tumors that typify breast cancer patients, which are still controllable in a therapeutic and surgical way. Our case study consists of the prediction during the pre-operative stage of lymph node metastasis in breast cancer patients resulting in a negative diagnosis after clinical and radiological exams. The classifier adopted to establish a baseline is characterized by the result invariance for the order permutation of the input features, and it exploits stratifications in the training procedure. The quantum one mimics support vector machine mapping in a high-dimensional feature space, yielded by encoding into qubits, while being characterized by complexity. Feature selection is exploited to study the performances associated with a low number of features, thus implemented in a feasible time. Wide variations in sensitivity and specificity are observed in the selected optimal classifiers during cross-validations for both classification system types, with an easier detection of negative or positive cases depending on the choice between the two training schemes. Clinical practice is still far from being reached, even if the flexible structure of quantum-inspired classifier circuits guarantees further developments to rule interactions among features: this preliminary study is solely intended to provide an overview of the particular tree tensor network scheme in a simplified version adopting just product states, as well as to introduce typical machine learning procedures consisting of feature selection and classifier performance evaluation.

Multilayer Dynamic Encryption for Security OFDM-PON Using DNA-Reconstructed Chaotic Sequences Under Cryptanalysis

In this paper, a multilayer dynamic encryption scheme using deoxyribonucleic acid reconstructed chaotic sequences (DNA-RCS) under cryptanalysis is firstly proposed, which aims at enhancing the security of orthogonal frequency division multiplexing passive optical network (OFDM-PON). We adopt DNA coding to reconstruct chaotic sequences, the selected coding rules and the number of chaotic sequence blocks divided are then random, the randomness and security of encryption sequences are improved. The transmitted signal is encrypted in two layers. The first layer is hybrid chaotic permutation and diffusion. Each symbol can be encrypted by the combination of a single non-repetitive permutation and plaintext-related diffusion. It makes encryption not only depend on the chaotic sequences but also relate to the order of permutation. The second layer is a dynamic Josephus permutation. By taking the unit as the permutation object, the scrambling efficiency is increased. Also, the counting period is randomly selected, which can enhance the security of the system. The number of tests needed to break a secure transmission for an attacker can reach up to $3.096\times 10^{106}$ . An encryption signal with 22.06Gb/s is successfully demonstrated over a 25-km standard single-mode fiber (SSMF) and a back-to-back (BTB) system. It is proved that the proposed scheme does not degrade the system performance and can effectively resist various attacks by the performance analysis model based on cryptanalysis.

Detecting Ordinal Subcascades

Ordinal classifier cascades are constrained by a hypothesised order of the semantic class labels of a dataset. This order determines the overall structure of the decision regions in feature space. Assuming the correct order on these class labels will allow a high generalisation performance, while an incorrect one will lead to diminished results. In this way ordinal classifier systems can facilitate explorative data analysis allowing to screen for potential candidate orders of the class labels. Previously, we have shown that screening is possible for total orders of all class labels. However, as datasets might comprise samples of ordinal as well as non-ordinal classes, the assumption of a total ordering might be not appropriate. An analysis of subsets of classes is required to detect such hidden ordinal substructures. In this work, we devise a novel screening procedure for exhaustive evaluations of all order permutations of all subsets of classes by bounding the number of enumerations we have to examine. Experiments with multi-class data from diverse applications revealed ordinal substructures that generate new and support known relations.

Geometry-attentive relational reasoning for robust facial landmark detection

In this paper, we propose a geometry-attentive relational reasoning approach to investigate the problem of robust facial landmark detection, especially when faces were captured in wild conditions. Unlike existing methods which usually cannot explicitly exploit the geometric relationship among different landmarks, our approach aims to reason about the intrinsic geometry-aware relations among landmarks for feature enhancement. To achieve this, we carefully develop an interpretable and plug-and-play module to reinforce the discriminativeness and uniqueness of feature maps, which typically operates on all possible pairs on the immediate inter-landmark heat maps. Among these pairing maps, our model learns to infer the meaningful relational clues in the transformed feature space on condition of holistic facial shape prior. For permutation order invariance, we pool these features as a single aggregated relational feature. To further improve the performance, we simply equip the proposed module inside the backbone hourglass networks. The experimental results on the standard benchmarking datasets indicate the effectiveness of our proposed approach.

Security analysis of multiple permutation encryption adopt in reversible data hiding

In order to improve the security of reversible data hiding algorithm in encrypted images, Liu designed an image multi-permutation encryption algorithm. By combining bit-plane permutation with pixel-block permutation, the embedding capacity of the algorithm is improved, and the ability of the encryption algorithm to resist existing Ciphertext-Only and Known-Plaintext attack is effectively improved. To analyze the security performance of the encryption algorithm, a Known-plaintext attack method based on the Root Mean Square(RMS) of image block is proposed in this paper. Firstly, the permutation order of bit plane is estimated by using the invariant distribution ratio of 0 and 1 before and after image encryption, the original pixel values is restored. Then, according to the characteristics that the pixel values of the image remain unchanged during block permutation and intra-block pixel permutation, the image block RMS feature is defined to search and estimate the block permutation sequence. Image block RMS equivalence class is defined by the image block RMS value, the ratio of the maximum number of elements in the equivalence class to the total number of pixels is p, which determines the difficulty of known plaintext attack. For the common image test set, 96% of the images have a p-value of less than 0.1, and only 4% of the images have a p-value greater than 0.1. Experimental results show that, When p 0.1, the attacker can crack more than 80% of the image content by two pairs of plaintext and ciphertext.

A remark about the anomalies of cyclic holomorphic permutation orbifolds

Using a result of Longo and Xu, we show that the anomaly arising from a cyclic permutation orbifold of order 3 of a holomorphic conformal net [Formula: see text] with central charge [Formula: see text] depends on the “gravitational anomaly” [Formula: see text]. In particular, the conjecture that holomorphic permutation orbifolds are non-anomalous and therefore a stronger conjecture of Müger about braided crossed [Formula: see text]-categories arising from permutation orbifolds of completely rational conformal nets are wrong. More generally, we show that cyclic permutations of order [Formula: see text] are non-anomalous if and only if [Formula: see text] or [Formula: see text]. We also show that all cyclic permutation gaugings of [Formula: see text] arise from conformal nets.

Robust fault estimation of discrete‐time nonlinear plants via a comprehensive partition‐based switching scheme

SummaryThe problem of robust fault estimation (FE) for a class of nonlinear systems in discrete‐time domain is studied via proposing a comprehensive partition‐based switching scheme. Both enhancement factors and attenuation factors are designed synchronously for accomplishing a comprehensive partition of the entire space spanned by the considered normalized fuzzy weighting functions. Thanks to the proposed comprehensive partition‐based switching scheme, six subspaces would be obtained by identifying the real‐time permutation order of the underlying parameters. Therefore, a novel fuzzy FE observer with six kinds of switching modes can be on‐line implemented. As a result, the robust H∞ performance index can be enhanced since much more information is employed than those reported results. Finally, simulation comparisons over the existing results are provided to show the obtained advantages of the article.

Compression-friendly Image Encryption Algorithm Based on Order Relation

In this paper, we introduce an image encryption algorithm that can be used in combination with compression algorithms. Existing encryption algorithms focus on either encryption strength or speed without compression, whereas the proposed algorithm improves compression efficiency while ensuring security. Our encryption algorithm decomposes images into pixel values and pixel intensity subsets, and computes the order of permutations. An encrypted image becomes unpredictable after permutation. Order permutation reduces the discontinuity between signals in an image, increasing compression efficiency. The experimental results show that the security strength of the proposed algorithm is similar to that of existing algorithms. Additionally, we tested the algorithm on the JPEG and the JPEG2000 with variable compression ratios. Compared to existing methods applied without encryption, the proposed algorithm significantly increases PSNR and SSIM values.

Pattern-avoiding permutation powers

Recently, Bóna and Smith defined strong pattern avoidance, saying that a permutation π strongly avoids a pattern τ if π and π2 both avoid τ. They conjectured that for every positive integer k, there is a permutation in Sk3 that strongly avoids 123⋯(k+1). We use the Robinson–Schensted–Knuth correspondence to settle this conjecture, showing that the number of such permutations is at least kk3∕2+O(k3∕logk) and at most k2k3+O(k3∕logk). We enumerate 231-avoiding permutations of order 3, and we give two further enumerative results concerning strong pattern avoidance. We also consider permutations whose powers all avoid a pattern τ. Finally, we study subgroups of symmetric groups whose elements all avoid certain patterns. This leads to several new open problems connecting the group structures of symmetric groups with pattern avoidance.

A Toeplitz Property of Ballot Permutations and Odd Order Permutations

We give a new semi-combinatorial proof for the equality of the number of ballot permutations of length $n$ and the number of odd order permutations of length $n$, which was originally proven by Bernardi, Duplantier and Nadeau. Spiro conjectures that the descent number of ballot permutations and certain cyclic weights of odd order permutations of the same length are equi-distributed. We present a bijection to establish a Toeplitz property for ballot permutations with any fixed number of descents, and a Toeplitz property for odd order permutations with any fixed cyclic weight. This allows us to refine Spiro's conjecture by tracking the neighbors of the largest letter in permutations.

S147. FUNCTIONAL BRAIN CONNECTIVITY DATA IMPROVE CLINICAL OUTCOME PREDICTION IN YOUTH AT RISK FOR PSYCHOSIS

BackgroundImproved outcome prediction in individuals at high risk for psychosis may facilitate targeted early intervention. Studies suggest that improved outcome prediction may be achieved through the use of neurocognitive or neuroimaging data, on their own or in addition to clinical data. This study examines whether adding resting-state functional connectivity data to validated clinical predictors of psychosis improve outcome prediction in the prodromal stage.MethodsThis study involves 137 adolescents and young adults at Clinical High Risk (CHR) for psychosis from the Shanghai At Risk for Psychosis (SHARP) program. Based on outcome after one-year follow-up, participants were separated into three outcome categories: good outcome (symptom remission, N = 71), intermediate outcome (ongoing CHR symptoms, N = 30), and poor outcome (conversion to psychosis or treatment-refractory, N = 36). Resting-state fMRI data were acquired for each participant and processed using the Conn toolbox, including rigorous motion correction. Multinomial logistic regression analysis and leave-one-out cross-validation were used to assess the performance of three prediction models: 1) a clinical-only model using validated clinical predictors from the NAPLS-2 psychosis-risk calculator, 2) an fMRI-only model using measures of functional connectome organization and within/between-network connectivity among established resting-state networks, and 3) a combined clinical and fMRI prediction model. Model performance was assessed using the harmonic mean of the positive predictive value and sensitivity for each outcome category. This F1 measure was compared to expected chance-levels using a permutation test with 1,000 sampled permutations in order to evaluate the statistical significance of the model’s prediction.ResultsThe clinical-only prediction model failed to achieve a significant level of outcome prediction (F1 = 0.32, F1-chance = 0.26 □ 0.06, p = .154). The fMRI-only model did predict clinical outcome to a significant degree (F1 = 0.41, F1-chance = 0.29 □ 0.06, p = .016), but the combined clinical and fMRI prediction model showed the best performance (F1 = 0.46, F1-chance = 0.29 □ 0.06, p < .001). On average, positive predictive values (reflecting the probability that an outcome label predicted by the model was correct) were 39% better than chance-level and 32% better than the clinical-only model. Analyzing the contribution of individual predictor variables showed that GAF functional decline, a family history of psychosis, and performance on the Hopkins Verbal Learning Test were the most influential clinical predictors, whereas modular connectome organization, default-mode and fronto-parietal within-network connectivity, and between-network connectivity among language, salience, dorsal attention, cerebellum, and sensorimotor networks were the leading fMRI predictors.DiscussionThis study’s findings suggest that functional brain abnormalities reflected by alterations in resting-state functional connectivity precede and may drive subsequent changes in clinical functioning. Moreover, the findings show that markers of functional brain connectivity may be useful for improving early identification and clinical decision-making in prodromal psychosis.

A Comparison of Complete Parts on m-Idempotent Hyperrings

On a particular class of m-idempotent hyperrings, the relation ξ m * is the smallest strongly regular equivalence such that the related quotient ring is commutative. Thus, on such hyperrings, ξ m * is a new representation for the α * -relation. In this paper, the ξ m -parts on hyperrings are defined and compared with complete parts, α -parts, and m-complete parts, as generalizations of complete parts in hyperrings. It is also shown how the ξ m -parts help us to study the transitivity property of the ξ m -relation. Finally, ξ m -complete hyperrings are introduced and studied, stressing on the fact that they can be characterized by ξ m -parts. The symmetry plays a fundamental role in this study, since the protagonist is an equivalence relation, defined using also the symmetrical group of permutations of order n.

Investigation of Polymer-70% Aluminum Powder Composite

Metals and polymers permutation in order to produce polymer metals composites attain new fascination and significance to several authors. The first effort to syndicate these two classes of materials was formulated in the earlier years of the 20^th era. In this article aluminum flakes were positively assimilated in polyethylene PE matrix to syndicate the valuable properties of metals and polymers. They extend to light weight, endurance to corrosion, brisk fabrication rates and a extensive range of moduli etc.

Order patterns, their variation and change points in financial time series and Brownian motion

Order patterns and permutation entropy have become useful tools for studying biomedical, geophysical or climate time series. Here we study day-to-day market data, and Brownian motion which is a good model for their order patterns. A crucial point is that for small lags (1 up to 6 days), pattern frequencies in financial data remain essentially constant. The two most important order parameters of a time series are turning rate and up-down balance. For change points in EEG brain data, turning rate is excellent while for financial data, up-down balance seems the best. The fit of Brownian motion with respect to these parameters is tested, providing a new version of a forgotten test by Bienaymé.