Double Mapping Research Articles

Action of Crossed Modules and Bar Construction

If a group $N$ acts on a set $X$, a simplicial set $Bar(X,N)$ using the usual bar construction has been provided. In this construction, if the group $N$ acts on a group $G$ via a homomorphism $f:N\rightarrow G$, then $Bar(G,N)$ has a simplicial set structure. In the case of $f$ has a crossed module structure, $Bar(G,N)$ has a normal simplicial group structure. In this work, by defining an action of a crossed module $\partial: N_1 \longrightarrow X_1$ on a homomorphism of groups $f: N_2 \longrightarrow X_2 $ via a double map $\alpha: \partial\rightarrow f$, we will construct a bisimplicial set, using the 2-dimensional version of the usual Bar construction.

Double kernel and minimum variance embedded broad learning system based autoencoder for one-class classification

One-class classification methods are often used for anomaly detection in healthcare, quality control in manufacturing, and fraud detection in financial services. Particularly in medical datasets, instances of rare cancers are considerably fewer in comparison to those of healthy individuals. One-class classification methods, which concentrate on learning models using just samples from a specified class, have drawn increasing attention as a solution to this problem. To enhance the model’s ability to capture essential feature information, we propose a novel strategy in this paper. This strategy involves the initial application of double kernel mapping, translating the original features into a new feature space. The autoencoder based on the Broad Learning System is then modified to incorporate the minimum variance so that the model can learn the potential feature information. We validated the effectiveness of our proposed strategy using UCI dataset and concordia digits dataset. To compare the performance with other one-class methods, the average F1 scores and the average G−mean are employed as comparative measures. Based on experimental results, it is evident that DKVBLS-AE not only outperforms but also demonstrates greater stability compared to the existing methods.

Uniform Positivity of the Lyapunov Exponent for Monotone Potentials Generated by the Doubling Map

We show that for any doubling map generated C1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C^1$$\\end{document} monotone potential with derivative uniformly bounded away from zero and infinity, the Lyapunov exponent of the associated Schrödinger operators is bounded below by logλ-C\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\log {\\lambda }-C$$\\end{document} for all energies, where C depends only on the potential. In particular, it answers an open question [D, Problem 5] raised by D. Damanik.

An efficient improved parrot optimizer for bladder cancer classification

Bladder Cancer (BC) is a common disease that comes with a high risk of morbidity, death, and expense. Primary risk factors for BC include exposure to carcinogens in the workplace or the environment, particularly tobacco. There are several difficulties, such as the requirement for a qualified expert in BC classification. The Parrot Optimizer (PO), is an optimization method inspired by key behaviors observed in trained Pyrrhura Molinae parrots, but the PO algorithm becomes stuck in sub-regions, has less accuracy, and a high error rate. So, an Improved variant of the PO (IPO) algorithm was developed using a combination of two strategies: (1) Mirror Reflection Learning (MRL) and (2) Bernoulli Maps (BMs). Both strategies improve optimization performance by avoiding local optimums and striking a compromise between convergence speed and solution diversity. The performance of the proposed IPO is evaluated against eight other competitor algorithms in terms of statistical convergence and other metrics according to Friedman’s test and Bonferroni–Dunn test on the IEEE Congress on Evolutionary Computation conducted in 2022 (CEC 2022) test suite functions and nine BC datasets from official repositories. The IPO algorithm ranked number one in best fitness and is more optimal than the other eight MH algorithms for CEC 2022 functions. The proposed IPO algorithm was integrated with the Support Vector Machine (SVM) classifier termed (IPO-SVM) approach for bladder cancer classification purposes. Nine BC datasets were then used to confirm the effectiveness of the proposed IPO algorithm. The experiments show that the IPO-SVM approach outperforms eight recently proposed MH algorithms. Using the nine BC datasets, IPO-SVM achieved an Accuracy (ACC) of 84.11%, Sensitivity (SE) of 98.10%, Precision (PPV) of 95.59%, Specificity (SP) of 95.98%, and F-score (F1) of 94.15%. This demonstrates how the proposed IPO approach can help to classify BCs effectively. The open-source codes are available at https://www.mathworks.com/matlabcentral/fileexchange/169846-an-efficient-improved-parrot-optimizer.

Thermodynamics of chaotic relaxation processes.

The established thermodynamic formalism of chaotic dynamics, valid at statistical equilibrium, is here generalized to systems out of equilibrium that have yet to relax to a steady state. A relation between information, escape rate, and the phase-space average of an integrated observable (e.g., Lyapunov exponent, diffusion coefficient) is obtained for finite time. Most notably, the thermodynamic treatment may predict the phase-space profile of any integrated observable for finite time, from the leading and subleading eigenfunctions of the Perron-Frobenius or Koopman transfer operator. Examples of that equivalence are shown, and the theory is tested analytically on the Bernoulli map while numerically on the perturbed cat map, the Hénon map, and the Ikeda map, all paradigms of chaos.

Revolutionizing optimization: An innovative nutcracker optimizer for single and multi-objective problems

Nutcracker Optimization Algorithm (NOA) is a recently proposed meta-heuristic algorithm inspired by foraging and storing behavior of nutcracker birds. NOA demonstrates strong performance across various test sets and optimization problems. However, it faces challenges in effectively balancing exploration and exploitation, particularly in high-dimensional and complex applications. In this paper, an improved variant of NOA based on Bernoulli map strategy and seasonal behavior strategy, called INOA, is proposed. Firstly, the Bernoulli map strategy enhances the quality of the initial population during the initialization process. Secondly, the seasonal behavior strategy is employed to balance the exploration and exploitation of NOA, enabling it to effectively handle high-dimensional problems by improving convergence and exploration capabilities. Additionally, this paper extends INOA to a multi-objective version called MONOA, enabling the algorithm to solve multi-objective problems. The proposed algorithm, INOA, undergoes evaluation using 30 classical benchmark problems, CEC-2014, CEC-2017, CEC-2019 test suites, and two real-world engineering design problems. INOA’s performance is compared with three categories of optimization methods: (1) recently-developed algorithms, i.e., NOA, BWO, DBO, RIME, MGO, HBA, and SO, (2) highly-cited algorithms, i.e., SMA, MPA, GWO, and (3) high-performing optimizers and winners of CEC competition, i.e., CJADE, L-SHADE-RSP, L-SHADE, and EBOwithCMAR. The proposed algorithm, MONOA, undergoes evaluation using well-known ZDT and DTLZ suites, as well as six constrained and engineering design problems. MONOA’s performance is compared with some state-of-the-art approaches such as MOPSO, NSSO, MOGOA, MOSMA, and MOMGA. Five performance indicators are employed for comparison purposes. Experimental results and comparisons affirm the efficacy of INOA in solving complex and higher-dimensional optimization problems. Similarly, the findings underscore the effectiveness of MONOA in solving diverse multi-objective problems with distinct characteristics.

Hybrid deep architecture for intrusion detection in cyber‐physical system: An optimization‐based approach

SummaryIntrustion Detection System (IDS) refers to the gear or software that monitors a network or system for malicious activity or policy violations. Periodically, the system records any intrusion action or breach, which frequently modifies the administrator. Cyber Physical System (CPS) is particularly called as networked connected system, in which the system components are spatially distributed and integrated via the communication network. The control mechanism ensures computation significance; however, the system does affect attacks. Researchers are trying to handle this issue via the existing anomaly datasets. In this way, this paper follows an intrusion detection system under three major stages including extraction of features, selection of feature, and detection. The primary stage is the extraction of Statistical features like standard deviation, mean, mode, variance, and median, as well as higher‐order statistical features like moment, percentile, improved correlation, kurtosis, mutual information, skewness, flow‐based features, and information gain‐based features. The curse of dimensionality becomes a significant problem in this scenario, so it is crucial to choose the right features. Improved Linear Discriminant Analysis (LDA) is utilized to choose the right features. The selected features are subjected to a Hybrid classifier for final detection. Here, models like CNN (Convolutional Neural Network) and Bi‐GRU (Bidirectional Gated Recurrent Unit) are combined. A new Bernoulli Map Estimated Arithmetic Optimization Algorithm (BMEAOA) is added to train the system by adjusting the ideal weights of the two classifiers, leading to improved detection outcomes. Ultimately, the effectiveness is assessed in comparison to the other traditional techniques.

COMPARATIVE ANALYSIS OF DIFFERENT VARIANTS OF AZIMUTHAL CONFORMAL PROJECTION FOR THE TERRITORY OF THE REPUBLIC OF SERBIA

<p>The paper analyzes four variants of conformal azimuthal projections for the territory of the Republic of Serbia. In the procedure, a double conformal mapping was applied. As it is common practice to perform mapping in azimuthal projections from a sphere to a plane, it was initially necessary to perform a conformal mapping from the ellipsoid to the sphere, after which a conformal mapping from the sphere to the plane was executed. The central point of the projection is a point with a value of 44° north latitude and 21° east longitude. The mapping territory is trapezoidal in shape, defined by the values of the geographic latitudes and longitudes of the southernmost (41°53'), northernmost (46°11'), westernmost (18°49'), and easternmost (23°) points in the territory of the Republic of Serbia. The mapping variants are defined based on different values of linear scale at the central point of the projection. Data processing was carried out within the Jupyter Notebook component, part of the Anaconda software package, using the Python programming language. The results are presented numerically, graphically, and visualized using AutoCAD software.</p>

Adaptive soft sensor using stacking approximate kernel based BLS for batch processes

To deal with the highly nonlinear and time-varying characteristics of Batch Process, a model named adaptive stacking approximate kernel based broad learning system is proposed in this paper. This model innovatively introduces the approximate kernel based broad learning system (AKBLS) algorithm and the Adaptive Stacking framework, giving it strong nonlinear fitting ability, excellent generalization ability, and adaptive ability. The Broad Learning System (BLS) is known for its shorter training time for effective nonlinear processing, but the uncertainty brought by its double random mapping results in poor resistance to noisy data and unpredictable impact on performance. To address this issue, this paper proposes an AKBLS algorithm that reduces uncertainty, eliminates redundant features, and improves prediction accuracy by projecting feature nodes into the kernel space. It also significantly reduces the computation time of the kernel matrix by searching for approximate kernels to enhance its ability in industrial online applications. Extensive comparative experiments on various public datasets of different sizes validate this. The Adaptive Stacking framework utilizes the Stacking ensemble learning method, which integrates predictions from multiple AKBLS models using a meta-learner to improve generalization. Additionally, by employing the moving window method—where a fixed-length window slides through the database over time—the model gains adaptive ability, allowing it to better respond to gradual changes in industrial Batch Process. Experiments on a substantial dataset of penicillin simulations demonstrate that the proposed model significantly improves predictive accuracy compared to other common algorithms.

Confusion and Diffusion Techniques for Image Encryption Process Based on Chaos System

Face recognition uses biometric technologies to identify humans based on their facial characteristics. This method is commonly used to restrict information access control. The benefits of face recognition systems encompass their ease of use and security. The human face recognition process consists of face detection, face tracking, and face recognition. The process uses some algorithms: the Viola-Jones for face detection, the Kanade-Lucas-Tomasi (KLT) for face tracking, and the principal component analysis (PCA) for face recognition. Furthermore, this research proposed face recognition with an encryption process to protect the data stored in a database. The encryption process consists of two main processes: confusion and diffusion. The confusion process is randomizing the position of the original image pixels. This research utilized the Arnold’s cat map (ACM) for the confusion process, and the diffusion process was performed using the XOR operation with the key generated from the 1D chaos system. Three different 1D chaos systems, namely logistic map, Bernoulli map, and tent map, were compared to see which chaos system had the best encryption results. Tests were conducted by comparing various parameters on the three proposed 1D chaos systems, including correlation coefficient, histogram analysis, entropy value, number of pixel rate changes (NPCR), and unified average change intensity (UACI). Based on testing the image encryption results, the diffusion process utilizing the tent map produced the best image encryption compared to other chaotic systems.

Hybrid Classifier for Crowd Anomaly Detection with Bernoulli Map Evaluation

Automatically detecting unusual behavior in a crowded environment greatly improves public safety. Unusual behaviors are those that depend on the rules established in the environment under consideration and cannot be properly described. This paper proposes a new deep feature-based crowd anomaly detection method. Priorly, the input image is preprocessed using the Weiner filtering method. Subsequently, AlexNet, VGGnet, and ResNet-based deep features are extracted. During this process, all three models were optimally tuned. For optimization, a new hybrid optimization method called Hybrid COOT and Bald Eagle with Bernoulli Map Evaluation (HCBEBME) is introduced in this work. This improves the performance of extracting features from the input. Finally, based on the proposed feature set, anomalies are detected by the hybrid detection model that combines LSTM and Bi-GRU models, respectively. Finally, the performance of the proposed model is validated over the conventional models. The detection accuracy of the suggested approach is 96.59%, whereas the minimal accuracy scores for the other methods BRCASO, GNNN, CNN-BILSTM, LSTM, BIGRU, BILSTM, CNN, and RNN are 93.63%, 79.16%, 87.57%, 73.85%, 70.59%, 77.08%, 81.44%, and 84.66% respectively.

Exploring Simplicity Bias in 1D Dynamical Systems.

Arguments inspired by algorithmic information theory predict an inverse relation between the probability and complexity of output patterns in a wide range of input-output maps. This phenomenon is known as simplicity bias. By viewing the parameters of dynamical systems as inputs, and the resulting (digitised) trajectories as outputs, we study simplicity bias in the logistic map, Gauss map, sine map, Bernoulli map, and tent map. We find that the logistic map, Gauss map, and sine map all exhibit simplicity bias upon sampling of map initial values and parameter values, but the Bernoulli map and tent map do not. The simplicity bias upper bound on the output pattern probability is used to make a priori predictions regarding the probability of output patterns. In some cases, the predictions are surprisingly accurate, given that almost no details of the underlying dynamical systems are assumed. More generally, we argue that studying probability-complexity relationships may be a useful tool when studying patterns in dynamical systems.

Advances in Breeding for Oil Quality Enhancement in Indian Mustard (Brassica spp. L.): Achievements, Challenges, and Research Opportunities

Major objectives in oil crop improvement are enhancement of seed and oil yield, quality of oil according to its use, i.e. edible or industrial uses, breeding of varieties that fit in different cropping systems and breeding biotic and abiotic stress resistant/tolerant varieties. Despite traditional breeding approaches, including pure line breeding, yielding only modest gains in productivity, recent advancements in mustard breeding have led to significant breakthroughs in both productivity and oil quality. This review discusses the innovative breeding strategies that have contributed to these advancements, with a focus on hybrid development, oil quality enhancement, and biotechnological approaches. To enhance productivity, researchers at the University of Delhi have developed hybrid seed production techniques using transgenic Barnase-barstar systems and cytoplasmic male sterility (CMS) systems. These systems enable large-scale hybrid seed production, with field trials demonstrating significant yield heterosis ranging from 31% to 55% compared to national check varieties. In addition to productivity, improving oil and meal quality has been a key objective. By integrating genes from canola-quality mustard lines, breeders have achieved reductions in erucic acid and glucosinolates, enhancing the health profile and industrial applicability of mustard oil. A high-density linkage map developed using an F1 double haploid mapping population has facilitated the marker-assisted backcross breeding of desirable traits, enabling precise transfer of key quality traits. Transgenic approaches, such as antisense RNA technology, have led to the development of high-oleic, low-linoleic mustard lines with improved fatty acid profiles. These advancements reflect a strategic combination of conventional and biotechnological methods, demonstrating a clear pathway for boosting mustard yields while enhancing oil quality. Molecular markers reported for genetic diversity assessment, mapping and tagging genes/QTLs for different qualitative and quantitative traits and their use in marker-assisted selection have been presented. This progress not only addresses current challenges but also sets the stage for future research aimed at further optimizing productivity, oil quality, and resistance to pests and diseases in mustard cultivation.

Chaotic neural network for information security

The neural network-based key generator has been employed in this work. The chaotic binary sequences were created using one of the best and simplest chaotic Bernoulli maps. Additionally, chaotic sequences' randomness can be improved using neural networks, where the inputs and weights completely determine the output sequence. As the created sequences are based on the perceptron learning approach, the output sequence is unpredictable. The generated sequences passed each test that was conducted using the Diehard battery test and NIST 800–22. To strengthen the security of the images, DNA computing was also used for the ANN binary sequence and encryption.

Fast Dimension Spectrum for a Potential with a Logarithmic Singularity

We regard the classic Thue–Morse diffraction measure as an equilibrium measure for a potential function with a logarithmic singularity over the doubling map. Our focus is on unusually fast scaling of the Birkhoff sums (superlinear) and of the local measure decay (superpolynomial). For several scaling functions, we show that points with this behavior are abundant in the sense of full Hausdorff dimension. At the fastest possible scaling, the corresponding rates reveal several remarkable phenomena. There is a gap between level sets for dyadic rationals and non-dyadic points, and beyond dyadic rationals, non-zero accumulation points occur only within intervals of positive length. The dependence between the smallest and the largest accumulation point also manifests itself in a non-trivial joint dimension spectrum.

An image watermarking scheme: combining the transform domain and deep learning modality with an improved scrambling process

ABSTRACT This paper proposes a novel image watermarking scheme with the following two processes. In the embedding process, the cover image is subjected to NSCT to obtain the properties of multi-scale and directional characteristics and fed to DWT which decomposes the contourlet image into various sub-bands. The wavelet decomposition image is subjected to a region selection step, where the regions are selected based on the DL strategy for selecting the region from the contourlet of the cover image where the features, including LOOP feature, mean feature, Canny features, and ResNet features are extracted and subjected to the DNN classifier. Conversely, the watermark image performs NSCT and DWT as the cover image and is fed into further steps to eliminate the correlation of pixels. For that, it proposes the FTTS approach to scramble the contourlet of watermark images, in which tent map and dyadic transformation are employed to eliminate the correlation among pixels. Then the resultants of region selection and FTTS are embedded to obtain the watermarked image. On the other hand, the extraction process takes place, which extracts the embedded watermarked image and applies inverse scrambling and inverse an NSCT approach to recover the watermark image against any malicious attack.

Quantitative double echo steady state T2 mapping of upper extremity peripheral nerves and muscles.

T2 mapping can characterize peripheral neuropathy and muscle denervation due to axonal damage. Three-dimensional double echo steady-state (DESS) can simultaneously provide 3D qualitative information and T2 maps with equivalent spatial resolution. However, insufficient signal-to-noise ratio may bias DESS-T2 values. Deep learning reconstruction (DLR) techniques can reduce noise, and hence may improve quantitation of high-resolution DESS-T2. This study aims to (i) evaluate the effect of DLR methods on DESS-T2 values, and (ii) to evaluate the feasibility of using DESS-T2 maps to differentiate abnormal from normal nerves and muscles in the upper extremities, with abnormality as determined by electromyography. Analysis of images from 25 subjects found that DLR decreased DESS-T2 values in abnormal muscles (DLR = 37.71 ± 9.11 msec, standard reconstruction = 38.56 ± 9.44 msec, p = 0.005) and normal muscles (DLR: 27.18 ± 6.34 msec, standard reconstruction: 27.58 ± 6.34 msec, p < 0.001) consistent with a noise reduction bias. Mean DESS-T2, both with and without DLR, was higher in abnormal nerves (abnormal = 75.99 ± 38.21 msec, normal = 35.10 ± 9.78 msec, p < 0.001) and muscles (abnormal = 37.71 ± 9.11 msec, normal = 27.18 ± 6.34 msec, p < 0.001). A higher DESS-T2 in muscle was associated with electromyography motor unit recruitment (p < 0.001). These results suggest that quantitative DESS-T2 is improved by DLR and can differentiate the nerves and muscles involved in peripheral neuropathies from those uninvolved.

Transition to anomalous dynamics in a simple random map.

The famous doubling map (or dyadic transformation) is perhaps the simplest deterministic dynamical system exhibiting chaotic dynamics. It is a piecewise linear time-discrete map on the unit interval with a uniform slope larger than one, hence expanding, with a positive Lyapunov exponent and a uniform invariant density. If the slope is less than one, the map becomes contracting, the Lyapunov exponent is negative, and the density trivially collapses onto a fixed point. Sampling from these two different types of maps at each time step by randomly selecting the expanding one with probability p, and the contracting one with probability 1-p, gives a prototype of a random dynamical system. Here, we calculate the invariant density of this simple random map, as well as its position autocorrelation function, analytically and numerically under variation of p. We find that the map exhibits a non-trivial transition from fully chaotic to completely regular dynamics by generating a long-time anomalous dynamics at a critical sampling probability pc, defined by a zero Lyapunov exponent. This anomalous dynamics is characterized by an infinite invariant density, weak ergodicity breaking, and power-law correlation decay.

New chaos function of composition function Gauss map and dyadic transformation map for digital image encryption

Encryption algorithms mostly use key-streams generated from random number generators. Several recent studies have shown that the random number generator used is a chaos function. In this paper, a new chaos function will be developed which can be used as a chaotic random number generator. The development is carried out by forming a new chaos function using the function composition method. The function that is composed is the Gauss Map function against the Dyadic Transformation Map. The results of the new chaos function are chaotic, this is based on the results of the analysis obtained from the results of the bifurcation diagram, the Lyapunov Exponent and the National Institute of Standard Technologies Test (NIST) standard randomness test. The results of the bifurcation diagram show that the density is for the value of α ∈ [−30,0] and has periodic properties to choose the values of β ∈ [−1.02, −0.75], β ∈ [−0.60, −0.30], β ∈ [0.10, 0.25] and β ∈ [0.55, 0.75]. A positive value of Lyapunov Exponential diagram will be employed alpha equal to negative value (α &lt; 0). The results of the NIST standard randomness test with values x0 = 0.9, α = −15 and β = 0.7 resulted in 100 % passing the test (16 tests).

Large deviations and conditioning for chaotic non-invertible deterministic maps: analysis via the forward deterministic dynamics and the backward stochastic dynamics

The large deviation properties of trajectory observables for chaotic non-invertible deterministic maps as studied recently by Smith (2022 Phys. Rev. E 106 L042202) and by Gutierrez et al (2023 arXiv:2304.13754) are revisited in order to analyze in detail the similarities and the differences with the case of stochastic Markov chains. More concretely, we focus on the simplest example displaying the two essential properties of local stretching and global folding, namely the doubling map xt+1=2xt[mod1] on the real-space interval x∈[0,1[ that can also be analyzed via the decomposition x=∑l=1+∞σl2l into binary coefficients σl=0,1 . The large deviation properties of trajectory observables can be studied either via deformations of the forward deterministic dynamics or via deformations of the backward stochastic dynamics. Our main conclusions concerning the construction of the corresponding Doob canonical conditioned processes are: (i) non-trivial conditioned dynamics can be constructed only in the backward stochastic perspective where the reweighting of existing transitions is possible, and not in the forward deterministic perspective; (ii) the corresponding conditioned steady state is not smooth on the real-space interval x∈[0,1[ and can be better characterized in the binary space σl=1,2,..,+∞ . As a consequence, the backward stochastic dynamics in the binary space are also the most appropriate framework to analyze higher levels of large deviations, and we obtain the explicit large deviations at level 2 for the probability of the empirical density of long backward trajectories.