Excellent Statistical Properties Research Articles

A constant-per-iteration likelihood ratio test for online changepoint detection for exponential family models

Online changepoint detection algorithms that are based on (generalised) likelihood-ratio tests have been shown to have excellent statistical properties. However, a simple online implementation is computationally infeasible as, at time T, it involves considering O(T) possible locations for the change. Recently, the FOCuS algorithm has been introduced for detecting changes in mean in Gaussian data that decreases the per-iteration cost to O(logT)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$O(\\log T)$$\\end{document}. This is possible by using pruning ideas, which reduce the set of changepoint locations that need to be considered at time T to approximately logT\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\log T$$\\end{document}. We show that if one wishes to perform the likelihood ratio test for a different one-parameter exponential family model, then exactly the same pruning rule can be used, and again one need only consider approximately logT\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\log T$$\\end{document} locations at iteration T. Furthermore, we show how we can adaptively perform the maximisation step of the algorithm so that we need only maximise the test statistic over a small subset of these possible locations. Empirical results show that the resulting online algorithm, which can detect changes under a wide range of models, has a constant-per-iteration cost on average.

Secure image encryption algorithm using chaos-based block permutation and weighted bit planes chain diffusion

Aiming at the problem of insufficient security of image encryption technology, a secure image encryption algorithm using chaos-based block permutation and weighted bit planes chain diffusion is proposed, which is based on a variant structure of classical permutation-diffusion. During the permutation phase, the encryption operations of dividing an image into sub-block, block scrambling, block rotation and block inversion, negative-positive transformation, color component shuffling are performed sequentially with chaotic sequences of plaintext association. In the chain diffusion stage, different encryption strategies are adopted for the high and low 4-bit planes according to the weight of image information. Theoretical analyses and empirical results substantiate that the algorithm conforms to the cryptographic requirements of confusion, diffusion, and avalanche effects, while possessing excellent numerical statistical properties with a large cryptographic space. Therefore, the cryptanalysis-propelled security enhancement mechanism proposed in this paper effectively amplifies the aptitude of the algorithm to withstand cryptographic attacks.

Structure-odor relationship in pyrazines and derivatives: A physicochemical study using 3D-QSPR, HQSPR, Monte Carlo, molecular docking, ADME-Tox and molecular dynamics

In this study, using both 2D-QSPR and 3D-QSPR approaches, to understand the structure-odor relationship of 78 1–4-pyrazine odorant molecules and to use this knowledge for the design of new food and flavor products. According to our results, the developed models have good predictability such as the HQSPR/BC model with QLOO2=0.832, R2 = 0.916, CoMSIA/SEH model with Q2 = 0.624, Rcv2 = 0.590, Rncv2 = 0.932, Rbs2 = 0.963, and Topomer CoMFA model withRtraining2 = 0.899, Rtest2 = 0.916. The Monte Carlo method was used in the creation of a Quantitative Structure-Property Relationship (QSPR) model. The molecular structure is represented using optimized Simplified Molecular Input Line Entry System (SMILES) and molecular descriptors. The performance of the model is evaluated using the Correlation Ideality Index (IIC) and the Correlation Contradiction Index (CCI). The best model, designated as TF2, boasts excellent statistical properties with a training R-squared value of 0.957 and a test R-squared value of 0.834. The model was then used to determine promoter activity levels, which formed the basis for the design of 36 new odorant molecules. Molecular docking and pharmacokinetic properties were used to explain the mode of binding between the proposed compounds and the active site of the Porcine Odorant Binding Protein complexed with pyrazine (2-isobutyl-3-methoxypyrazine). Molecular dynamic simulation was used to assess and justify the stability of the ligand in the active site of the receptor. The results of this study provide a basis for the discovery of new compounds with lower olfactory thresholds and diverse pharmacological properties.

Subdata Selection With a Large Number of Variables

Subdata selection from big data is an active area of research that facilitates inferences based on big data with limited computational expense. For linear regression models, the optimal design-inspired Information-Based Optimal Subdata Selection (IBOSS) method is a computationally efficient method for selecting subdata that has excellent statistical properties. But the method can only be used if the subdata size, k, is at last twice the number of regression variables, p. In addition, even when $k\ge 2p$, under the assumption of effect sparsity, one can expect to obtain subdata with better statistical properties by trying to focus on active variables. Inspired by recent efforts to extend the IBOSS method to situations with a large number of variables p, we introduce a method called Combining Lasso And Subdata Selection (CLASS) that, as shown, improves on other proposed methods in terms of variable selection and building a predictive model based on subdata when the full data size n is very large and the number of variables p is large. In terms of computational expense, CLASS is more expensive than recent competitors for moderately large values of n, but the roles reverse under effect sparsity for extremely large values of n.

The Self-Shrinking Conflation Generator: A Proposed Improvement to the Self-Shrinking Generator

The backbone of many cybersecurity applications and algorithms require random numbers.  One of the most commonly used pseudo-random number generators is the Linear Feedback Shift Register (LFSR), which is fast, computationally inexpensive, and has excellent statistical properties. Unfortunately LFSRs have a number of weaknesses, some of which were addressed by decimation-based sequence generators such as the self-shrinking generator (SSG). Regrettably, the SSG was also found to be vulnerable to attack. In this paper, we propose an improvement to the SSG called the self-shrinking conflation generator (SSCG).  Our approach is based on the observation that what is discarded during the self-shrinking process of the SSG, is from a cryptographic perspective, just as good as that which is kept.  By combining the bits the SSG would normally discard with those it retains, using the exclusive OR (XOR) operation, we create a modified SSG bitstream with several improved characteristics. To highlight these improvements, we provide some mathematical security analysis associated with this approach, apply the NIST statistical test suite to several different bitstreams created using LFSRs driven by different degree primitive polynomials, and compare our results to that of the SSG.

Optimizing Leaching of Rare Earth Elements from Red Mud and Spent Fluorescent Lamp Phosphors Using Levulinic Acid

Although various hydrometallurgical and solvometallurgical efforts have been made to extract REEs from end-of-life (EoL) products and waste, a systematic and statistical analysis of the impacts of leaching parameters to optimize the leaching process using organic acids is necessary, but lacking in the literature. This study employed the response surface methodology to develop mathematical models for optimal leaching by levulinic acid (LevA) of REEs in two waste materials, namely red mud and spent fluorescent lamp phosphors. The established models exhibited excellent statistical properties, in terms of significance, fitting, prediction, and error distribution. For red mud, the optimal conditions of liquid-to-solid ratio (L/S; v/w) of 40, temperature of 70 °C, and duration of 60 h led to 100% leaching of REEs excluding Sc. At the same L/S and temperature, >98.7% of REEs were leached from fluorescent phosphors after 96 h. The SEM–EDS analysis of the waste materials revealed and confirmed morphological and compositional changes after leaching under the optimal conditions.

Multi Chaotic System to Generate Novel S-Box for Image Encryption

A novel method on the basis of multi chaos theory is suggested in the presented study. Also, the study used two different dimensions to generate S-Box to get a strong cipher that is difficult to break. The suggested image cryptosystem includes an identical (decryption and encryption) process, which involves a single keystream generator, shifting process (based on 3D Lorenz map) related diffusion operations, and generate S-Box (based on 2D Henon map) that related confusion operation. The comparative analysis and the simulate test show that the suggested image cryptosystem has a few properties, like high-sensitivity, fast encryption/decryption, large keyspace, excellent statistical properties related to the ciphertext, and so on. The suggested cryptosystem is considered as an alternative for practical secure communications.

French adaptation and validation of the Speech, Spatial and Qualities of Hearing scale for Parents (SSQ-P) and for Children (SSQ-Ch)

Objectives Hearing loss can seriously impact children’s daily life. This study aims to translate and validate the French versions of the hearing performance questionnaires, SSQ-Parent (for 5–18 years old children), and SSQ-Children (for 11–18 years old children). Design This controlled prospective trial was conducted between April and October 2020. The forward-backward translation method was used, and a test-retest procedure was carried out on a case and a control population. Cases had at least 30 dBHL hearing loss. Study sample 54 cases (mean age 10.4 years old) and 32 controls (mean age 12.5 years old) answered the SSQ-Parent. 35 cases (mean age 13.1 years old) and 35 controls (mean age 14.3 years old) answered the SSQ-Children. Results Spearman’s correlation coefficients between global scores of the test and re-test were 0.91 (p < 0.001) for SSQ-Parent, and 0.89 (p < 0.001) for SSQ-Children. Both tests were discriminant (respectively, global score 57.8 vs 92 p < 0.001, 61.2 vs 92.6 p < 0.001), and internally consistent (Cronbach’s alpha 0.94 and 0.97). Items-global score correlation was satisfactory. ROC curves showed high area under curve for the SSQ-Children (0.990), and SSQ-Parent (0.988). Conclusion The SSQ-Parent and SSQ-Children revealed excellent statistical properties, and can be used for the evaluation of hearing performance of children.

Constructing Prediction Intervals Using the Likelihood Ratio Statistic

Statistical prediction plays an important role in many decision processes, such as university budgeting (depending on the number of students who will enroll), capital budgeting (depending on the remaining lifetime of a fleet of systems), the needed amount of cash reserves for warranty expenses (depending on the number of warranty returns), and whether a product recall is needed (depending on the number of potentially life-threatening product failures). In statistical inference, likelihood ratios have a long history of use for decision making relating to model parameters (e.g., in evidence-based medicine and forensics). We propose a general prediction method, based on a likelihood ratio (LR) involving both the data and a future random variable. This general approach provides a way to identify prediction interval methods that have excellent statistical properties. For example, if a prediction method can be based on a pivotal quantity, our LR-based method will often identify it. For applications where a pivotal quantity does not exist, the LR-based method provides a procedure with good coverage properties for both continuous or discrete-data prediction applications.

Modelling the COVID-19 Mortality Rate with a New Versatile Modification of the Log-Logistic Distribution.

The goal of this paper is to develop an optimal statistical model to analyze COVID-19 data in order to model and analyze the COVID-19 mortality rates in Somalia. Combining the log-logistic distribution and the tangent function yields the flexible extension log-logistic tangent (LLT) distribution, a new two-parameter distribution. This new distribution has a number of excellent statistical and mathematical properties, including a simple failure rate function, reliability function, and cumulative distribution function. Maximum likelihood estimation (MLE) is used to estimate the unknown parameters of the proposed distribution. A numerical and visual result of the Monte Carlo simulation is obtained to evaluate the use of the MLE method. In addition, the LLT model is compared to the well-known two-parameter, three-parameter, and four-parameter competitors. Gompertz, log-logistic, kappa, exponentiated log-logistic, Marshall–Olkin log-logistic, Kumaraswamy log-logistic, and beta log-logistic are among the competing models. Different goodness-of-fit measures are used to determine whether the LLT distribution is more useful than the competing models in COVID-19 data of mortality rate analysis.

New DNA Coded Fuzzy Based (DNAFZ) S-Boxes: Application to Robust Image Encryption Using Hyper Chaotic Maps

This article proposes a novel approach of improvising the cryptographic features of substitution-boxes (S-Box) based on the Choquet Fuzzy Integral (CFI) and DNA techniques. First, we propose a strong structure for the construction of four S-Boxes using CFI. The key for generating the CFI based (FZ) S-Boxes consists of two parts, namely, an external secret key and a secret image. Each of these FZ S-boxes is then encoded using DNA techniques, with dynamic rules selection which is dictated by a secret control code. The resultant four S-boxes are designated as DNAFZ S-Boxes. To apply for image encryption, the plain image is, at first 8-bit binary-coded, shuffled by an M-sequence, and down-sampled into four sub-images. Subsequently, the pixel values of each sub-image are replaced with the corresponding values of one of the four DNAFZ S-Boxes. Next, each DNAFZ encoded sub-image is diffused with a different DNA encoded chaotic sequence from Chen’s hyper-chaotic map. Finally, the four DNAFZ/Chaotic encoded sub-images are combined to build the final encrypted image. The proposed DNAFZ S-boxes shows excellent statistical properties under majority logic criterions such as correlation, homogeneity, energy, entropy, and contrast. Moreover, numerical simulation is used to examine the efficacy of encrypted images against different attacks. In particular, the values of the pixel correlation coefficient are found to be quite small either horizontally, vertically, or diagonally (between 7.8597e-04 and 0.00527, between 8.7856e-04 and 0.00452, and between 0.00241 and 0.00021, respectively). In addition, the information entropy of the encrypted image is found to be within the range of (7.9965:7.9989) which is very near to the ideal value of 8. As for the UACI and the NPCR, they are in the ranges between 33.46 and 33.32 and between 99.58 and 99.62, respectively. These values are also very close to the optimum ones. The results are compared to those of other encryption algorithms and proved that the proposed encryption method delivers better results than other conventional ones including LSS chaotic map, Arnold transforms, Dynamic Henon map, Hybrid chaotic map optimized substitution, and cubic S-Box.

Shrinking generators based on [formula omitted]-LFSRs

The word-based LFSRs called σ-LFSRs are very attractive as they take advantage of the modern word-based processor and thus increase the throughput. Secondly, the bitstream produced by σ-LFSR has excellent statistical properties with a high period except for low linear complexity. In order to increase the linear complexity, the concept of both bit-oriented shrinking and self-shrinking generators is introduced in case of σ-LFSRs. In both the cases, the lower bound for the period as well as for the linear complexity of the bitstream are shown to be exponential. Further, we have experimented and investigated more results on the periodicity and statistical properties of the bitstream in self-shrinking σ-LFSRs. This helps to find and prove the exact period of the bitstream produced by self-shrinking generators.

Highly efficient stepped wedge designs for clusters of unequal size.

The stepped wedge design (SWD) is a form of cluster randomized trial, usually comparing two treatments, which is divided into time periods and sequences, with clusters allocated to sequences. Typically all sequences start with the standard treatment and end with the new treatment, with the change happening at different times in the different sequences. The clusters will usually differ in size but this is overlooked in much of the existing literature. This paper considers the case when clusters have different sizes and determines how efficient designs can be found. The approach uses an approximation to the variance of the treatment effect, which is expressed in terms of the proportions of clusters and of individuals allocated to each sequence of the design. The roles of these sets of proportions in determining an efficient design are discussed and illustrated using two SWDs, one in the treatment of sexually transmitted diseases and one in renal replacement therapy. Cluster-balanced designs, which allocate equal numbers of clusters to each sequence, are shown to have excellent statistical and practical properties; suggestions are made about the practical application of the results for these designs. The paper concentrates on the cross-sectional case, where subjects are measured once, but it is briefly indicated how the methods can be extended to the closed-cohortdesign.

Forecasting Class I Railroad Fuel Consumption by Train Type

Fuel efficiency is an important consideration in evaluating public-sector investments in multimodal corridors. Two approaches are typically used in corridor studies to forecast railroad diesel fuel consumption: (1) system-average efficiency factors, and (2) detailed analytical estimates derived from train performance calculators. The former method is easy to apply but may not be reflective of the actual mix of trains used. The second method is data- and time-intensive and can only be effectively implemented with specialized software that is not publicly available. An intermediate method is introduced in this paper which allows distinctions among the types of trains that might be utilized in a corridor (e.g., unit, way, and through). A model is estimated from publicly available data that has excellent statistical properties and quantifies the absolute and relative fuel efficiencies of train options. The analysis demonstrates that using system-average fuel consumption factors may significantly understate railroad fuel economy when traffic moves in unit trains instead of mixed train service. The new method offers greater accuracy than system-average comparisons yet is much less data-intensive than train performance calculators or analytical methods.

A novel efficient image encryption algorithm based on affine transformation combine with linear fractional transformation

Algebraic structures and their hardware–software implementation gain considerable attention in the field of information security and coding theory. Research progress in the applications of arithmetic properties of algebraic structures is being frequently made. These structures are mostly useful in improvement of the cryptographic algorithms. A novel technique is given to design a cryptosystem responsible for lossless for image encryption. The proposed scheme is for the RGB image whose pixels are considered as 24 binary bits, accordingly a unique arrangement for the construction of S-boxes over a Galois field $$ GF\left( {2^{9} } \right) $$ is employed. Consequently, it generates multiple different S-boxes with excellent cryptographic characteristic and hence confusing process of the cryptosystem has been working. Whereas the diffusion process in this cryptosystem is based on Affine transformation over a unit elements of an integers modulo ring $$ {\mathbb{Z}}_{n} $$ . The scrambling of the image data through the Affine transformation escalate the security asset, avoid computational effort and abbreviated the time complexity. In addition, the simulation test and comparative scrutinize illustrate that the proposed scheme is highly sensitive, large keyspace, excellent statistical properties and secure against differential attacks. Therefore, the proposed algorithm is valuable for confidential communication. Furthermore, due to the arithmetic properties of algebraic structures, the proposed scheme would be easily implemented, secure and fast enough to be utilized in real-world applications.

Construction of Cryptographic S-Boxes Based on Mobius Transformation and Chaotic Tent-Sine System

Over the last few decades, different mediums of secure communication use chaos which is demonstrated by some nonlinear dynamical systems. Chaos shows unpredictable behavior and this characteristic is quite helpful in different encryption techniques and for multimedia security. In this work, the chaotic behavior of the improved Tent-Sine map is conferred and ultimately a new method to construct substitution-boxes is proposed. This new method explores the features of chaos through TSS map and algebraic Mobius transformation to generate strong S-boxes. The S-boxes are assessed using standard tests suit which includes nonlinearity, strict avalanche criterion, bit independence criterion, linear approximation probability and differential uniformity. Moreover, the proposed S-boxes show excellent statistical properties under majority logic criterions such as correlation, homogeneity, energy, entropy, contrast. The statistical encryption results are demonstrate the better performance of the proposed S-boxes when compared with some of state of the art S-boxes including AES, Gray, APA S8 AES, Skipjack and validate the suitability of anticipated method.

An Image Encryption Method Based on the Feistel Network and Dynamic DNA Encoding

Based on the Feistel network and dynamic deoxyribonucleic acid (DNA) encoding technology, an image encryption method is proposed using the “permutation-diffusion-scrambling” structure. First, the SHA-3 algorithm is used to calculate the hash value of the plaintext image as the initial value of the hyperchaotic system, and the chaos-generated sequence is used to generate the Hill cipher matrix to replace the image pixel. Second, the DNA sequence operation is used as the F function of the Feistel network. The DNA sequence database is used as the key K of Feistel network, and the image pixel value diffusion is realized by the Feistel network. Finally, further diffusion is carried out through the ciphertext feedback and through the ciphertext confusion and diffusion of three rounds of “chaotic scrambling-DNA encoding-Feistel transformation-DNA decoding,” making the ciphertext more random and resistant to attacks and ensuring that the encrypted ciphertext is more secure. The experimental results show that the proposed method can effectively encrypt the image and has prominent characteristics, such as strong plaintext sensitivity, a large key space, and excellent ciphertext statistical properties.

Hazard ratio estimation and inference in clinical trials with many tied event times.

The medical literature contains numerous examples of randomized clinical trials with time-to-event endpoints in which large numbers of events accrued over relatively short follow-up periods, resulting in many tied event times. A generally common feature across such examples was that the logrank test was used for hypothesis testing and the Cox proportional hazards model was used for hazard ratio estimation. We caution that this common practice is particularly risky in the setting of many tied event times for two reasons. First, the estimator of the hazard ratio can be severely biased if the Breslow tie-handling approximation for the Cox model (the default in SAS and Stata software) is used. Second, the 95% confidence interval for the hazard ratio can include one even when the corresponding logrank test p-value is less than 0.05. To help establish a better practice, with applicability for both superiority and noninferiority trials, we use theory and simulations to contrast Wald and score tests based on well-known tie-handling approximations for the Cox model. Our recommendation is to report the Wald test p-value and corresponding confidence interval based on the Efron approximation. The recommended test is essentially as powerful as the logrank test, the accompanying point and interval estimates of the hazard ratio have excellent statistical properties even in settings with many tied event times, inferential alignment between the p-value and confidence interval is guaranteed, and implementation is straightforward using commonly used software.

A New Chaotic Map for Secure Transmission

The secure communication through synchronization between two identic chaotic systems have recently gained a lot of interest. To implement a robust secure system based on synchronization, there is always a need to generate new discrete dynamical systems and investigate their performances in terms of amount of randomness they have and the ability to achieve synchronization smoothly. In this work, a new chaotic system, named Nahrain, is proposed and tested for the possible use in secure transmission via chaos synchronization as well as in cryptography applications. The performance of the proposed chaotic system is tested using 0-1 test, while NIST suite tests are used to check the randomness statistical properties. The nonlinear control laws are used to verify the synchronization of master-slave parts of the proposed system. The simulation results show that Nahrain system has chaotic behavior and synchronizable, while the equivalent binary sequence of the system has excellent randomness statistical properties. The numerical results obtained using MATLAB for 0-1 test was 0.9864, and for frequency test was 0.4202, while for frequency test within a block was 0.4311. As a result, the new proposed system can be used to develop efficient encryption and synchronization algorithms for multimedia secure transmission applications.

NEW KEY EXPANSION FUNCTION OF RIJNDAEL 128-BIT RESISTANCE TO THE RELATED-KEY ATTACKS

A master key of special length is manipulated based on the key schedule to create round sub-keys in most block ciphers. A strong key schedule is described as a cipher that will be more resistant to various forms of attacks, especially in related-key model attacks. Rijndael is the most common block cipher, and it was adopted by the National Institute of Standards and Technology, USA in 2001 as an Advance Encryption Standard. However, a few studies on cryptanalysis revealed that a security weakness of Rijndael refers to its vulnerability to related-key differential attack as well as the related-key boomerang attack, which is mainly caused by the lack of nonlinearity in the key schedule of Rijndael. In relation to this, constructing a key schedule that is both efficient and provably secure has been an ongoing open problem. Hence, this paper presents a method to improve the key schedule of Rijndael 128-bit for the purpose of making it more resistance to the related-key differential and boomerang attacks. In this study, two statistical tests, namely the Frequency test and the Strict Avalanche Criterion test were employed to respectively evaluate the properties of bit confusion and bit diffusion. The results showed that the proposed key expansion function has excellent statistical properties and agrees with the concept of Shannon’s diffusion and confusion bits. Meanwhile, the Mixed Integer Linear Programming based approach was adopted to evaluate the resistance of the proposed approach towards the related-key differential and boomerang attacks. The proposed approach was also found to be resistant against the two attacks discovered in the original Rijndael. Overall, these results proved that the proposed approach is able to perform better compared to the original Rijndael key expansion function and that of the previous research.