Search Results (32)

This paper explores the implications of modifying the canonical Heisenberg commutation relations over two simple systems, such as the free particle and the tunnel effect generated by a step-like potential. The modified commutation relations include position-dependent and momentum-dependent terms analyzed separately. For the position deformation case, the corresponding free wave functions are sinusoidal functions with a variable wave vector $k(x)$. In the momentum deformation case, the wave function has the usual sinusoidal behavior, but the energy spectrum becomes non-symmetric in terms of momentum. Tunneling probabilities depend on the deformation strength for both cases. Also, surprisingly, the quantum mechanical model generated by these modified commutation relations is related to the Black–Scholes model in finance. In fact, by taking a particular form of a linear position deformation, one can derive a Black–Scholes equation for the wave function when an external electromagnetic potential is acting on the particle. In this way, the Scholes model can be interpreted as a quantum-deformed model. Furthermore, by identifying the position coordinate x in quantum mechanics with the underlying asset S, which in finance satisfies stochastic dynamics, this analogy implies that the Black–Scholes equation becomes a quantum mechanical system defined over a random spatial geometry. If the spatial coordinate oscillates randomly about its mean value, the quantum particle’s mass would correspond to the inverse of the variance of this stochastic coordinate. Further, because this random geometry is nothing more than gravity at the microscopic level, the Black–Scholes equation becomes a possible simple model for understanding quantum gravity. Full article

U-statistics are fundamental in modeling statistical measures that involve responses from multiple subjects. They generalize the concept of the empirical mean of a random variable X to include summations over each m-tuple of distinct observations of X. W. Stute introduced conditional U-statistics, extending the Nadaraya–Watson estimates for regression functions. Stute demonstrated their strong pointwise consistency with the conditional expectation $r^{\left(m\right)}(\phi ,\mathbf{t})$, defined as $\mathbb{E}\left[\phi (Y_1,\dots ,Y_m)\right|(X_1,\dots ,X_m)=\mathbf{t}]$ for $\mathbf{t}\in {\mathcal{X}}^m$. This paper focuses on estimating functional single index (FSI) conditional U-processes for regular time series data. We propose a novel, automatic, and location-adaptive procedure for estimating these processes based on k-Nearest Neighbor (kNN) principles. Our asymptotic analysis includes data-driven neighbor selection, making the method highly practical. The local nature of the kNN approach improves predictive power compared to traditional kernel estimates. Additionally, we establish new uniform results in bandwidth selection for kernel estimates in FSI conditional U-processes, including almost complete convergence rates and weak convergence under general conditions. These results apply to both bounded and unbounded function classes, satisfying certain moment conditions, and are proven under standard Vapnik–Chervonenkis structural conditions and mild model assumptions. Furthermore, we demonstrate uniform consistency for the nonparametric inverse probability of censoring weighted (I.P.C.W.) estimators of the regression function under random censorship. This result is independently valuable and has potential applications in areas such as set-indexed conditional U-statistics, the Kendall rank correlation coefficient, and discrimination problems. Full article

We propose a secure user pairing (UP) and power allocation (PA) strategy for a downlink Non-Orthogonal Multiple Access (NOMA) system when there exists an external eavesdropper. The secure transmission of data through the downlink is constructed to optimize both UP and PA. This optimization aims to maximize the achievable sum secrecy rate (ASSR) while adhering to a limit on the rate for each user. However, this poses a challenge as it involves a mixed integer nonlinear programming (MINLP) problem, which cannot be efficiently solved through direct search methods due to its complexity. To handle this gracefully, we first divide the original problem into two smaller issues, i.e., an optimal PA problem for two paired users and an optimal UP problem. Next, we obtain the closed-form optimal solution for PA between two users and UP in a simplified NOMA system involving four users. Finally, the result is extended to a general $2K$-user NOMA system. The proposed UP and PA method satisfies the minimum rate constraints with an optimal ASSR as shown theoretically and as validated by numerical simulations. According to the results, the proposed method outperforms random UP and that in a standard OMA system in terms of the ASSR and the average ASSR. It is also interesting to find that increasing the number of user pairs will bring more performance gain in terms of the average ASSR. Full article

Heart and blood vessel disorders are referred to as cardiovascular diseases (CVDs). It is one of the leading global causes of death and consists of many disorders that harm the cardiovascular system. The World Health Organization (WHO) estimates that in 2019, 18 million deaths worldwide were caused by CVDs, accounting for about 32% of all deaths. Therefore, the early detection and prediction of cardiovascular disease can be beneficial in identifying high-risk individuals and enabling timely interventions to reduce the disease’s impact and improve patient outcomes. This study provides a machine learning (ML)-based framework CVD detection to satisfy this criterion. The proposed model includes data preprocessing, hyperparameter optimization using GridSearchCV, and classification using supervised learning approaches, such as support vector machine (SVM), K-nearest neighbors (KNN), XGBoost, random forest (RF), LightBoost (LB), and stochastic gradient descent (SGD). All these models are carried out on the publicly accessed database, namely Kaggle. The experimental results demonstrate that the suggested ML technique has attained a 92.76% detection rate with the SGD classifier on the 80:20 training/testing ratios, which is superior to the well-received approaches. Full article

Polymer composites are a class of material that are gaining a lot of attention in demanding tribological applications due to the ability of manipulating their performance by changing various factors, such as processing parameters, types of fillers, and operational parameters. Hence, a number of samples under different conditions need to be repeatedly produced and tested in order to satisfy the requirements of an application. However, with the advent of a new field of triboinformatics, which is a scientific discipline involving computer technology to collect, store, analyze, and evaluate tribological properties, we presently have access to a variety of high-end tools, such as various machine learning (ML) techniques, which can significantly aid in efficiently gauging the polymer’s characteristics without the need to invest time and money in a physical experimentation. The development of an accurate model specifically for predicting the properties of the composite would not only cheapen the process of product testing, but also bolster the production rates of a very strong polymer combination. Hence, in the current study, the performance of five different machine learning (ML) techniques is evaluated for accurately predicting the tribological properties of ultrahigh molecular-weight polyethylene (UHMWPE) polymer composites reinforced with silicon carbide (SiC) nanoparticles. Three input parameters, namely, the applied pressure, holding time, and the concentration of SiCs, are considered with the specific wear rate (SWR) and coefficient of friction (COF) as the two output parameters. The five techniques used are support vector machines (SVMs), decision trees (DTs), random forests (RFs), k-nearest neighbors (KNNs), and artificial neural networks (ANNs). Three evaluation statistical metrics, namely, the coefficient of determination (R²-value), mean absolute error (MAE), and root mean square error (RMSE), are used to evaluate and compare the performances of the different ML techniques. Based upon the experimental dataset, the SVM technique was observed to yield the lowest error rates—with the RMSE being 2.09 × 10⁻⁴ and MAE being 2 × 10⁻⁴ for COF and for SWR, an RMSE of 2 × 10⁻⁴ and MAE of 1.6 × 10⁻⁴ were obtained—and highest R²-values of 0.9999 for COF and 0.9998 for SWR. The observed performance metrics shows the SVM as the most reliable technique in predicting the tribological properties—with an accuracy of 99.99% for COF and 99.98% for SWR—of the polymer composites. Full article

In order to reduce the pumping threshold and achieve a short-cavity single-mode transmission with a narrow-linewidth random fiber laser, we propose a tunable random fiber laser based on the combination of random grating and highly reflective fiber Bragg grating (FBG). Theoretical modeling of a random refractive index-modulated fiber grating was carried out. Random grating is regarded as a linear combination of uniform fiber gratings with different periods. Simulation calculations were performed using the transfer matrix method to determine the preparation parameters. Under the premise of satisfying light localization, a point-by-point method was used to write a random grating in a single-mode fiber using a femtosecond laser according to the simulated parameters. We constructed a random fiber laser with a linewidth of 1.68 kHz and a threshold of 29.2 mW using a random grating and a highly reflective FBG combined with an erbium-doped fiber. Due to the broad scattered wavelength range of the random grating, by changing the central wavelength of the high-reflection FBG, the tunable wavelength of the output laser was realized, and the tunable range was 0.847 nm (1549.110–1549.957 nm). Moreover, the laser’s central wavelength and output power are stable for a long time. Compared with other lasers, the proposed laser has the advantages of a lower threshold, shorter cavity length, narrower linewidth, and a relatively simple structure. Full article

Water availability is a key factor in territorial sustainable development. Moreover, groundwater constitutes the survival element of human life and ecosystems in arid oasis areas. Therefore, groundwater potential (GWP) identification represents a crucial step for its management and sustainable development. This study aimed to map the GWP using ten algorithms, i.e., shallow models comprising: multilayer perceptron, k-nearest neighbor, decision tree, and support vector machine algorithms; hybrid models comprising: voting, random forest, adaptive boosting, gradient boosting (GraB), and extreme gradient boosting; and the deep learning neural network. The GWP inventory map was prepared using 884 binary data, with “1” indicating a high GWP and “0” indicating an extremely low GWP. Twenty-three GWP-influencing factors have been classified into numerical data using the frequency ration method. Afterwards, they were selected based on their importance and multi-collinearity tests. The predicted GWP maps show that, on average, only 11% of the total area was predicted as a very high GWP zone and 17% and 51% were estimated as low and very low GWP zones, respectively. The performance analyses demonstrate that the applied algorithms have satisfied the validation standards for both training and validation tests with an average area under curve of 0.89 for the receiver operating characteristic. Furthermore, the models’ prioritization has selected the GraB model as the outperforming algorithm for GWP mapping. This study provides decision support tools for sustainable development in an oasis area. Full article

Recently, a variety of non-systematic satisfiability studies on Discrete Hopfield Neural Networks have been introduced to overcome a lack of interpretation. Although a flexible structure was established to assist in the generation of a wide range of spatial solutions that converge on global minima, the fundamental problem is that the existing logic completely ignores the probability dataset’s distribution and features, as well as the literal status distribution. Thus, this study considers a new type of non-systematic logic termed S-type Random k Satisfiability, which employs a creative layer of a Discrete Hopfield Neural Network, and which plays a significant role in the identification of the prevailing attribute likelihood of a binomial distribution dataset. The goal of the probability logic phase is to establish the logical structure and assign negative literals based on two given statistical parameters. The performance of the proposed logic structure was investigated using the comparison of a proposed metric to current state-of-the-art logical rules; consequently, was found that the models have a high value in two parameters that efficiently introduce a logical structure in the probability logic phase. Additionally, by implementing a Discrete Hopfield Neural Network, it has been observed that the cost function experiences a reduction. A new form of synaptic weight assessment via statistical methods was applied to investigate the effect of the two proposed parameters in the logic structure. Overall, the investigation demonstrated that controlling the two proposed parameters has a good effect on synaptic weight management and the generation of global minima solutions. Full article

The common feature for a nontrivial hard problem is the existence of nontrivial topological structures, non-planarity graphs, nonlocalities, or long-range spin entanglements in a model system with randomness. For instance, the Boolean satisfiability (K-SAT) problems for K ≥ 3 ${\mathrm{M}}_{\mathrm{SAT}}^{\mathrm{K}\ge 3}$ are nontrivial, due to the existence of non-planarity graphs, nonlocalities, and the randomness. In this work, the relation between a spin-glass three-dimensional (3D) Ising model ${ \mathrm{M}}_{\mathrm{SGI}}^{3\mathrm{D}}$ with the lattice size N = mnl and the K-SAT problems is investigated in detail. With the Clifford algebra representation, it is easy to reveal the existence of the long-range entanglements between Ising spins in the spin-glass 3D Ising lattice. The internal factors in the transfer matrices of the spin-glass 3D Ising model lead to the nontrivial topological structures and the nonlocalities. At first, we prove that the absolute minimum core (AMC) model ${\mathrm{M}}_{\mathrm{AMC}}^{3\mathrm{D}}$ exists in the spin-glass 3D Ising model, which is defined as a spin-glass 2D Ising model interacting with its nearest neighboring plane. Any algorithms, which use any approximations and/or break the long-range spin entanglements of the AMC model, cannot result in the exact solution of the spin-glass 3D Ising model. Second, we prove that the dual transformation between the spin-glass 3D Ising model and the spin-glass 3D Z₂ lattice gauge model shows that it can be mapped to a K-SAT problem for K ≥ 4 also in the consideration of random interactions and frustrations. Third, we prove that the AMC model is equivalent to the K-SAT problem for K = 3. Because the lower bound of the computational complexity of the spin-glass 3D Ising model ${\mathrm{C}}_{\mathrm{L}}\left({\mathrm{M}}_{\mathrm{SGI}}^{3\mathrm{D}}\right)$ is the computational complexity by brute force search of the AMC model ${\mathrm{C}}^{\mathrm{U}}\left({\mathrm{M}}_{\mathrm{AMC}}^{3\mathrm{D}}\right)$, the lower bound of the computational complexity of the K-SAT problem for K ≥ 4 ${\mathrm{C}}_{\mathrm{L}}\left({\mathrm{M}}_{\mathrm{SAT}}^{\mathrm{K}\ge 4}\right)$ is the computational complexity by brute force search of the K-SAT problem for K = 3 ${ \mathrm{C}}^{\mathrm{U}}\left({\mathrm{M}}_{\mathrm{SAT}}^{\mathrm{K}=3}\right)$. Namely, ${\mathrm{C}}_{\mathrm{L}}\left({\mathrm{M}}_{\mathrm{SAT}}^{\mathrm{K}\ge 4}\right)={\mathrm{C}}_{\mathrm{L}}\left({\mathrm{M}}_{\mathrm{SGI}}^{3\mathrm{D}}\right)\ge {\mathrm{C}}^{\mathrm{U}}\left({\mathrm{M}}_{\mathrm{AMC}}^{3\mathrm{D}}\right)={\mathrm{C}}^{\mathrm{U}}\left({\mathrm{M}}_{\mathrm{SAT}}^{\mathrm{K}=3}\right)$. All of them are in subexponential and superpolynomial. Therefore, the computational complexity of the K-SAT problem for K ≥ 4 cannot be reduced to that of the K-SAT problem for K < 3. Full article

The state-of-the-art design methods for railway prestressed concrete sleepers are currently based on the quasi-static stresses resulting from a simplification of dynamic wheel loads, and subsequently the quasi-static responses of concrete sleepers. This method has been widely used in practices to overcome the complexity of dynamic analysis and testing. A single load factor (or called dynamic impact factor) for a partial safety-factored design (or k factors for the test criteria) is commonly used to crudely account for dynamic train–track interactions over different levels of track irregularities. The dynamic impact factors for either design or testing are usually obtained from either (i) railway infrastructure managers (i.e., in EN 13230), or (ii) prescribed standardised factors (i.e., AS 1085.14, AREMA Chapter 30, JSA—JIS E 1201). The existing design concepts for prestressed concrete sleepers using either (i) an allowable stress design or (ii) the limit state design method require many iterations for calculations and optimisations. The design process to achieve optimal products suitable for track, operational, and environmental parameters is, thus, very time-consuming. On this ground, this study investigates the potential capability of machine learning (ML) to learn from large amounts of design data sets and then to facilitate the design and capacity prediction of railway prestressed concrete sleepers. Three ML algorithms are developed, namely deep learning, Bayesian Neural Network, and random forest. Through a combination of hand-calculated design data, industry design data, and experimental investigations in compliance with EN 13230, over 3000 sets of design data have been collected. These data sets are used to assimilate a comprehensive database for machine learning. Four indicators, namely mean squared error (MSE), root-mean-square error (RMSE), mean absolute error (MAE), and R² are used to benchmark the accuracy and precision of machine learning models. Our results reveal that the random forest algorithm offers the best performance. The values of MSE, RMSE, MAE, and R² are 0.54, 0.74, 0.25, and 0.99, respectively. Note that the Bayesian neural network also performs very well. In contrast, the deep learning algorithm performs worse than the others. The insight demonstrates machine learning’s capability to aid in the design of railway prestressed concrete sleepers, to satisfy both serviceability and ultimate limit states Full article

An automatic electrocardiogram (ECG) myocardial infarction detection system needs to satisfy several requirements to be efficient in real-world practice. These requirements, such as reliability, less complexity, and high performance in decision-making, remain very important in a realistic clinical environment. In this study, we investigated an automatic ECG myocardial infarction detection system and presented a new approach to evaluate its robustness and durability performance in classifying the myocardial infarction (with no feature extraction) under different noise types. We employed three well-known supervised machine learning models: support vector machine (SVM), k-nearest neighbors (KNN), and random forest (RF), and tested the performance and robustness of these techniques in classifying normal (NOR) and myocardial infarction (MI) using real ECG records from the PTB database after normalization and segmentation of the data, with a suggested inter-patient paradigm separation as well as noise from the MIT-BIH noise stress test database (NSTDB). Finally, we measured four metrics: accuracy, precision, recall, and F1-score. The simulation revealed that all of the models performed well, with values of over 0.50 at lower SNR levels, in terms of all the metrics investigated against different types of noise, indicating that they are encouraging and acceptable under extreme noise situations are are thus considered sustainable and robust models for specific forms of noise. All of the methods tested could be used as ECG myocardial infarction detection tools in real-world practice under challenging circumstances. Full article

Hybridized algorithms are commonly employed to improve the performance of any existing method. However, an optimal learning algorithm composed of evolutionary and swarm intelligence can radically improve the quality of the final neuron states and has not received creative attention yet. Considering this issue, this paper presents a novel metaheuristics algorithm combined with several objectives—introduced as the Hybrid Election Algorithm (HEA)—with great results in solving optimization and combinatorial problems over a binary search space. The core and underpinning ideas of this proposed HEA are inspired by socio-political phenomena, consisting of creative and powerful mechanisms to achieve the optimal result. A non-systematic logical structure can find a better phenomenon in the study of logic programming. In this regard, a non-systematic structure known as Random k Satisfiability (RANkSAT) with higher-order is hosted here to overcome the interpretability and dissimilarity compared to a systematic, logical structure in a Discrete Hopfield Neural Network (DHNN). The novelty of this study is to introduce a new multi-objective Hybrid Election Algorithm that achieves the highest fitness value and can boost the storage capacity of DHNN along with a diversified logical structure embedded with RANkSAT representation. To attain such goals, the proposed algorithm tested four different types of algorithms, such as evolutionary types (Genetic Algorithm (GA)), swarm intelligence types (Artificial Bee Colony algorithm), population-based (traditional Election Algorithm (EA)) and the Exhaustive Search (ES) model. To check the performance of the proposed HEA model, several performance metrics, such as training–testing, energy, similarity analysis and statistical analysis, such as the Friedman test with convergence analysis, have been examined and analyzed. Based on the experimental and statistical results, the proposed HEA model outperformed all the mentioned four models in this research. Full article

One of the main problems in representing information in the form of nonsystematic logic is the lack of flexibility, which leads to potential overfitting. Although nonsystematic logic improves the representation of the conventional k Satisfiability, the formulations of the first, second, and third-order logical structures are very predictable. This paper proposed a novel higher-order logical structure, named G-Type Random k Satisfiability, by capitalizing the new random feature of the first, second, and third-order clauses. The proposed logic was implemented into the Discrete Hopfield Neural Network as a symbolic logical rule. The proposed logic in Discrete Hopfield Neural Networks was evaluated using different parameter settings, such as different orders of clauses, different proportions between positive and negative literals, relaxation, and differing numbers of learning trials. Each evaluation utilized various performance metrics, such as learning error, testing error, weight error, energy analysis, and similarity analysis. In addition, the flexibility of the proposed logic was compared with current state-of-the-art logic rules. Based on the simulation, the proposed logic was reported to be more flexible, and produced higher solution diversity. Full article

The coarse resolution of land surface temperatures (LSTs) retrieved from thermal-infrared (TIR) satellite images restricts their usage. One way to improve the resolution of such LSTs is downscaling using high-resolution remote sensing images. Herein, Gaofen-6 (GF-6) and Landsat-8 images were used to obtain original and retrieved LSTs (Landsat-8- and GF-6-retrieved-LSTs) to perform LST downscaling in the Ebinur Lake Watershed. Downscaling model was constructed, and the regression kernel was explored. The results of downscaling LST using the GF-6 normalized difference vegetation index with red-edge band 2, ratio built-up index, normalized difference sand index, and normalized difference water index as multi-remote sensing indices with multiple remote sensing indices with random forest regression method provided optimal downscaling results, with R² of 0.836, 0.918, and 0.941, root mean square difference of 1.04 K, 2.06 K, and 1.80 K, and the number of pixels with LST errors between −1 K and +1 K of 87.2%, 76.4%, and 81.9%, respectively. The expression of spatial distribution of 16 m-LST downscaling results corresponded with that of Landsat-8- and GF-6-retrieved-LST, and provided additional details spatial description of LST variations, which was absent in the Landsat-8- and GF-6-retrieved LSTs. The results of downscaling LST could satisfy the application requirements of LST spatial resolution. Full article

Let $\{{\xi }_i:i\ge 1\}$ be a sequence of independent, identically distributed (i.i.d. for short) centered random variables. Let $S_n={\xi }_1+\cdots +{\xi }_n$ denote the partial sums of $\{{\xi }_i\}.$ We show that sequence $\{{\displaystyle \frac{1}{n}}\underset{1\le k\le n}{max}|S_k|:n\ge 1\}$ satisfies the large deviation principle (LDP, for short) with a good rate function under the assumption that $P({\xi }_1\ge x)$ and $P({\xi }_1\le -x)$ have the same exponential decrease. Full article