Parametric models have been widely used in pertinent literature for reconstructing, modifying and representing a wide range of airfoil and/or hydrofoil profile geometries. Design spaces corresponding to these models can be exploited for modeling and profile-shape optimization under various performance criteria. Accuracy requirements, along with the need for modeling local features, often lead to high-dimensional design spaces that hinder the process of shape optimization and design through analysis. In this work, we propose a shape-informed dimensional reduction approach that attempts to tackle this deficiency by producing low-dimensional latent design spaces that can be efficiently used in shape representation and optimization. Furthermore, geometric moments are introduced in an attempt to cost-effectively capture analysis-relevant information that is generally expensive to produce. Specifically, geometric integral properties, although intrinsic features of the shape, are quite commonly related to performance indicators employed in performance optimization and therefore provide a cost-effective physics-informed component in the description of the design in the latent space. To this end, we employ the generalized Karhunen-Loeve expansion to produce a shape- and physics-informed subspace retaining the highest possible geometric variance and robustness, that is, lack of invalid designs. At the same time, a series of shape discretizations, encoding the foil's shape profile, are examined with regards to their effect on the resulting latent space's quality and efficiency. Our results demonstrate a significant reduction in the dimensionality of the original design space while maintaining a high representational capacity and a large percentage of valid geometries that facilitate fast convergence to optimal solutions in performance-based optimization.

In this research, an attempt was made to reduce the dimension of wavelet-ANFIS/ANN (artificial neural network/adaptive neuro-fuzzy inference system) models toward reliable forecasts as well as to decrease computational cost. In this regard, the principal component analysis was performed on the input time series decomposed by a discrete wavelet transform to feed the ANN/ANFIS models. The models were applied for dissolved oxygen (DO) forecasting in rivers which is an important variable affecting aquatic life and water quality. The current values of DO, water surface temperature, salinity, and turbidity have been considered as the input variable to forecast DO in a three-time step further. The results of the study revealed that PCA can be employed as a powerful for dimension reduction of input variables and also to detect inter-correlation of input variables. Results of the PCA-Wavelet-ANN models are compared with those obtained from Wavelet-ANN models while the earlier one has the advantage of less computational time than the later models. Dealing with ANFIS models, PCA is more beneficial to avoid Wavelet-ANFIS models creating too many rules which deteriorate the efficiency of the ANFIS models. Moreover, manipulating the Wavelet-ANFIS models utilizing PCA leads to a significant decreasing in computational time. Finally, it was found that the PCA-Wavelet-ANN/ANFIS models can provide reliable forecasts of dissolved oxygen as an important water quality indicators in rivers.

Unmanned Aerial Vehicles (UAVs) have become increasingly important in various applications, including environmental monitoring, disaster response, and surveillance, due to their flexibility, efficiency, and ability to access hard-to-reach areas. Effective path planning for multiple UAVs exploring a target area is crucial for maximizing coverage and operational efficiency. This study presents a novel approach to optimizing collaborative navigation for UAVs using Multi-Agent Reinforcement Learning (MARL). To enhance the efficiency of this process, we introduce the Adaptive Dimensionality Reduction (ADR) framework, which includes Autoencoders (AEs) and Principal Component Analysis (PCA) for dimensionality reduction and feature extraction. The ADR framework significantly reduces computational complexity by simplifying high-dimensional state spaces while preserving crucial information. Additionally, we incorporate communication modules to facilitate inter-UAV coordination, further improving path planning efficiency. Our experimental results demonstrate that the proposed approach significantly enhances exploration performance and reduces computational complexity, showcasing the potential of combining MARL with ADR techniques for advanced UAV navigation in complex environments.

With the rapid advancements in remote sensing technology, the spectral information from hyperspectral remote sensing images has become increasingly rich, facilitating detailed spectral analysis of the Earth's surface objects. However, this abundance of spectral data poses significant challenges in data processing, such as the curse of dimensionality leading to the “Hughes” phenomenon, "strong correlation" due to high resolution, and "non-linear characteristics" caused by varied surface reflectance rates. Therefore, dimensionality reduction of hyperspectral data has become a crucial task. This paper, grounded in manifold theory and manifold learning techniques, and considering the non-linear structures and features in hyperspectral remote sensing data, elucidates the principles and processes of dimensionality reduction in hyperspectral remote sensing images using manifold learning, with a formalized expression of the process. This article introduces spectral information divergence (SID) into the nearest neighbor graph computation of manifold learning algorithms. The principles and computational processes of nearest neighbor graph algorithms based on Euclidean distance (ED), spectral angle mapping (SAM), and SID are studied, and a comparative analysis of the dimensionality reduction effects under these three metrics in hyperspectral data is conducted. Experiments on feature extraction under different metrics were performed using the publicly available Indian Pines hyperspectral dataset. The intrinsic features obtained post-dimensionality reduction were used as inputs for classification algorithms in ground objects classification experiments, with algorithm runtime, overall accuracy, and Kappa coefficient as evaluation metrics for dimensionality reduction quality. The results demonstrate that nearest neighbor graph computation based on SAM and SID outperforms traditional ED methods; SAM-based computation has the lowest time complexity, while SID-based manifold learning yields the highest accuracy in ground objects classification. Thus, manifold learning based on SAM and SID metrics proves to be an effective method for feature extraction in hyperspectral remote sensing data, underscoring the potential of manifold learning techniques in the dimensionality reduction of hyperspectral remote sensing images.

Delay in data transmission is one of key performance indicators (KPIs) of a network. The planning and project value of delay in network management is of crucial importance for the optimal allocation of network resources and their performance focuses. To create optimal solutions, predictive models, which are currently most often based on machine learning (ML), are used. This paper aims to investigate the training, testing and selection of the best predictive delay model for a VoIP service in an Long Term Evolution (LTE) network using three ML techniques - Neural Networks (NN), Support Vector Machines (SVM) and k-Nearest Neighbors (k-NN). The space of model input variables is optimized by dimensionality reduction techniques: RReliefF algorithm, Backward selection via the recursive feature elimination algorithm and the Pareto 80/20 rule. A three-segment road in the geo-space between the cities of Banja Luka (BL) and Doboj (Db) in the Republic of Srpska (RS), Bosnia and Herzegovina (BiH), covered by the cellular network (LTE) of the M:tel BL operator was chosen for the case study. The results show that, in all three optimization approaches, the k-NN model is selected as the best solution. For the RReliefF optimization algorithm, the best model has 6 inputs and minimum relative error (RE), RE=0.109; for the Backward selection via the recursive feature elimination algorithm, the best model has 4 inputs and RE=0.041; and for the Pareto 80/20 rule, the best model has 11 inputs and RE= 0.049. The comparative analysis of the results concludes that according to observed criteria for the selection of the final model, the best solution is an approach to optimizing the number of predictors based on the Backward selection via the recursive feature elimination algorithm.

In this study, our primary objective was to analyze the tradeoff between accuracy and complexity in machine learning models, with a specific focus on the impact of reducing complexity and entropy on the production of landslide susceptibility maps. We aimed to investigate how simplifying the model and reducing entropy can affect the capture of complex patterns in the susceptibility maps. To achieve this, we conducted a comprehensive evaluation of various machine-learning algorithms for classification tasks. We compared the performance of these algorithms in terms of accuracy and complexity, considering both "before" and "after" scenarios of dimensionality reduction using Principal Component Analysis (PCA). Our findings revealed that reducing complexity and lowering entropy can lead to an increase in model accuracy. However, we also observed that this reduction in complexity comes at the cost of losing important complex patterns in the produced landslide susceptibility maps. By simplifying the model and reducing entropy, certain intricate relationships and uncertain patterns may be overlooked, resulting in a loss of information and potentially compromising the accuracy of the susceptibility maps. The analysis encompassed a diverse range of machine learning algorithms, including Random Forest (RF), Extra Trees (EXT), XGboost, LightGBM, Catboost, Naive Bayes (NB), K-Nearest Neighbors (KNN), Gradient Boosting Machine (GBM), and Decision Trees (DT). Each algorithm was evaluated for its strengths and limitations, considering the tradeoff between accuracy and complexity. Before dimensionality reduction, the algorithms demonstrated promising results, with RF exhibiting excellent AUC/ROC scores and average accuracy. However, computational costs were noted as a potential drawback for RF, especially when dealing with large datasets. EXT showcased robust performance and good accuracy, while XGboost demonstrated its ability to handle complex relationships within large datasets, albeit requiring careful hyperparameter tuning. The efficiency and scalability of LightGBM made it a suitable choice for large datasets, although it displayed sensitivity to class imbalance. Catboost excelled in handling categorical features, but longer training times were observed for larger datasets. NB showcased simplicity and computational efficiency but assumed independence among features. KNN, known for its capability to capture local patterns and spatial relationships, was found to be sensitive to the choice of distance metric. GBM, while capturing complex relationships effectively, was prone to overfitting without proper regularization. DT, with its interpretability and ease of understanding, faced limitations in terms of overfitting and limited generalization. After dimensionality reduction, certain algorithms exhibited improvements in their AUC/ROC scores and average accuracy, including RF, EXT, XGboost, and LightGBM. However, for a few algorithms, such as NB and DT, a decrease in performance was observed. This study provides valuable insights into the performance characteristics, strengths, and limitations of various machine learning algorithms in classification tasks. Researchers and practitioners can utilize these findings to make informed decisions when selecting algorithms for their specific datasets and requirements. We also aim to identify the potential factors contributing to the high accuracy rates obtained from these ensembled algorithms and explore possible shortcomings of non-ensembled algorithms that may result in lower accuracy rates. By conducting a comprehensive analysis of these algorithms, we seek to provide valuable insights into the benefits and limitations of ensembled approaches for landslide susceptibility mapping. Our study sheds light on the challenges faced when balancing accuracy and complexity in machine learning models for landslide susceptibility mapping. It emphasizes the importance of carefully considering the level of complexity and entropy reduction in relation to the specific patterns and uncertainties present in the data. By providing insights into this tradeoff, our research aims to assist researchers and practitioners in making informed decisions regarding model complexity and entropy reduction, ultimately improving the quality and interpretability of landslide susceptibility maps.

This work is driven by a practical question, corrections of Artificial Intelligence (AI) errors. Systematic re-training of a large AI system is hardly possible. To solve this problem, special external devices, correctors, are developed. They should provide quick and non-iterative system fix without modification of a legacy AI system. A common universal part of the AI corrector is a classifier that should separate undesired and erroneous behavior from normal operation. Training of such classifiers is a grand challenge at the heart of the one- and few-shot learning methods. Effectiveness of one- and few-short methods is based on either significant dimensionality reductions or the blessing of dimensionality effects. Stochastic separability is a blessing of dimensionality phenomenon that allows one-and few-shot error correction: in high-dimensional datasets under broad assumptions each point can be separated from the rest of the set by simple and robust linear discriminant. The hierarchical structure of data universe is introduced where each data cluster has a granular internal structure, etc. New stochastic separation theorems for the data distributions with fine-grained structure are formulated and proved. Separation theorems in infinite-dimensional limits are proven under assumptions of compact embedding of patterns into data space. New multi-correctors of AI systems are presented and illustrated with examples of predicting errors and learning new classes of objects by a deep convolutional neural network.

We extend the concept of metallic ratios to the real argument n considered as a dimension by analytic continuation showing that they are defined by an argument of a normalized complex number, and for rational n ≠ {0, ±2}, they are defined by Pythagorean triples. We further extend the concept of metallic ratios to metallic angles.

Photoplethysmography (PPG) signals, which measure blood volume changes through light absorption, are increasingly used for non-invasive Cardiovascular Disease (CVD) detection. Analyzing PPG signals can help identify irregular heart patterns and other indicators of CVD. This research involves a thorough analysis of CVD classification using the Capnobase dataset, which includes data from 20 CVD subjects and 21 normal subjects. In the initial stage, heuristic optimization algorithms, such as ABC-PSO, the Cuckoo Search algorithm (CSA), and the Dragonfly algorithm (DFA), were applied to reduce the dimension of the PPG data. Next, these Dimensionally Reduced (DR) PPG data are then fed into various classifiers such as Linear Regression(LR), Linear Regression with Bayesian Linear Discriminant Classifier (LR-BLDC), K-Nearest Neighbors (KNN), PCA-Firefly, Linear Discriminant Analysis (LDA), Kernel LDA (KLDA), Probabilistic LDA (ProbLDA), SVM-Linear, SVM-Polynomial, SVM-RBF, to identify CVD. Classifier performance is evaluated using Accuracy, Kappa, MCC, F1 Score, Good Detection Rate(GDR), Error rate, and Jaccard Index(JI). The SVM-RBF classifier for ABC PSO dimensionality reduced values outperforms other classifiers, achieving an accuracy of 95.12% with a MCC of 0.90.

Abstract: Urban regeneration decision-making is a complex process, as it involves a wide range of decision-makers, public-private partnerships in finance and implementation, including the inevitable considerable amount of risk on a long-term basis. There are a multitude of stakeholders, the citizens being the key stakeholders. It is necessary to involve the citizens in the planning process. Such involvement allows the communities to express their needs and aspirations, which is useful in the policymaking, delivery of planning programs, and in the monitoring process. In such a context, Factor analysis was the statistical technique used (1) Carry out factor analysis based on the principal component analysis method using the software XLSTAT 2021.4.1.1205 - (2) Construct a factor model of Urban Regeneration. (3) Interpret and label the factor dimensions. The results of the analysis indicated that the first two principal components accounted for 60.04% of the total variance of the original dataset. All variables seemed to be, positively correlated to each other and contributed similarly to principal components PC1 &PC2. The observations were well clustered; except for very few outliers. The limitation of the work was that the perceptions of the citizens were limited to the variables derived by the researcher.

As a system becomes more complex, at first, its description and analysis becomes more complicated. However, a further increase in the system’s complexity often makes this analysis simpler. A classical example is Central Limit Theorem: when we have a few independent sources of uncertainty, the resulting uncertainty is very difficult to describe, but as the number of such sources increases, the resulting distribution get close to an easy-to-analyze normal one – and indeed, normal distributions are ubiquitous. We show that such limit theorems make analysis of complex systems easier – i.e., lead to blessing of dimensionality phenomenon – for all the aspects of these systems: the corresponding transformation, the system’s uncertainty, and the desired result of the system’s analysis.

Diabetes becomes a life threatening non-communicable disease in the world, according to International Diabetic Federation (IDF) in 2023, an estimated 537 million adults (20-79 years) are living with diabetes, which is equivalent to 9.3% of the global adult population. This number is predicted to rise to 643 million by 2030 and 783 million by 2045. Over 3 in 4 adults with diabetes live in low- and middle-income countries. Diabetes is a persistent metabolic condition marked by increased levels of glucose in the bloodstream. It is a significant global health concern, affecting millions of individuals worldwide. It having the symptoms of drowsiness for the whole day if not properly examined or treated well. It is targeted to spread over the younger age community and the number is growing in the exponential fashion. Even day to day many advancements have come from the researcher to diagnose, to find solutions to prevent from newer entry. Authors have taken a dataset with 57 non diabetic and 20 diabetic patients with the total 28735 micro array gene to undergone pre-processing process and reduced up to 22960 gene data using Dimensionality Reduction (DR) such as Detrend Fluctuation Analysis (DFA), Chi square probability density function (Chi2PDF), Firefly algorithm Cuckoo search were used in this research. Meta heuristic algorithms like Particle swarm Optimization (PSO) and Harmonic Search (HS) are used for feature selection. Further seven classification techniques such as Non-Linear Regression (NLR), Linear Regression (LR), Logistics Regression (LoR), Gaussian Mixture Model (GMM), Bayesian Linear Discriminant Classifier (BLDC), Softmax Discriminant Classifier (SDC), Support Vector Machine – Radial Basis Function (SVM-RBF) are using to make a decision, predictive analysis and segregate the data according to the level of blood glucose as Diabetic Patient (DP) and Non-Diabetic Patient (NDP).

In the era of big data, feature engineering has proved its efficiency and importance in dimensionality reduction and useful information extraction from original features. Feature engineering can be expressed as dimensionality reduction and is divided into two types of methods such as feature selection and feature extraction. Each method has its pros and cons. There are a lot of studies to combine these methods. Sparse autoencoder (SAE) is a representative deep feature learning method that combines feature selection with feature extraction. However, existing SAEs do not consider the feature importance during training. It causes extracting irrelevant information. In this paper, we propose a parallel guiding sparse autoencoder (PGSAE) to guide the information by two parallel guiding layers and sparsity constraints. The parallel guiding layers keep the main distribution using Wasserstein distance which is a metric of distribution difference, and it suppresses the leverage of guiding features to prevent overfitting. We perform our experiments using four datasets that have different dimensionality and number of samples. The proposed PGSAE method produces a better classification performance compared to other dimensionality reduction methods.

Complex systems can be described as the network of interactions between their components. In directed networks, information, energy and matter flow in dominant directions. Undirected networks, on the other hand, cannot easily capture these asymmetries. The local flow of information depends on the node spin, which is a function of the number of incoming and outgoing links attached to it. And yet, how the heterogeneous association between in-degree and out-degree constraints global dynamics remains poorly understood. Here, we develop a new theoretical model to study the relationship between node directionality and global flow dynamics. Our computational analysis of random and scale-free directed networks indicates that structural diversity constrains the dimensionality of reachable dynamical space. These results suggest how local directionality might be an universal driver of global dynamics in many systems, from social networks, to technological systems to the connectome.

Hund's rule of maximum multiplicity is a powerful empirical tool for determining the electron population of electronic shells. It was recently discovered that it is also the rule of minimum Shannon entropy. This study extends these findings to the Aufbau rule and discusses them from the perspective of emergent dimensionality, providing a monotonically increasing entropy function. We observed that some elements that violate the Aufbau rule have the same entropies in the actual and Aufbau electron configurations. On the other hand, lower entropies of all actual elements' configurations are associated with higher or equal numbers of unpaired electrons in these configurations compared to the Aufbau configurations. The only exception to this rule is palladium.

Autism spectrum disorder (ASD) is a heterogeneous neuropsychiatric problem with a few core symptoms: weaknesses in social behavior, verbal impairments, repetitive behavior and restricted interests. Beyond the core symptoms, autism has strong association with other disorders such as intellectual disability, epilepsy, schizophrenia among many others. This paper outlines a theory of ASD with capacity to connect heterogeneous ‘core’ symptoms, medical and psychiatric comorbidities as well as other etiological theories of autism in a unifying cognitive framework rooted in neuroscience and genetics. Cognition is embedded into an ever-developing structure modified by experiences, including the outcomes of environment influencing behaviors. We introduce the hypothesis that autism is caused by deficits in component-based cognition and the internal learning reinforcing machinery. Specifically, we outline our Cartesian Factor forming autoencoder like model that supports cognition by breaking combinatorial explosion and discuss the cognitive and neural processes behind our model. The high dimensionality of sensory information poses serious problems, since the brain can handle only 7±2 relevant variables at a time making processes, such as the extraction and encoding of the relevant variables and their efficient manipulation critical. These processes are influenced by previous experiences and the internal reward system. In addition, large delays of distributed information processing should be counteracted by learned predictive models to synchronize sensory, proprioceptive, and cognitive signals and have timely and accurate model-based actions. Impairments in any of these aspects may disrupt learning and execution. Combinations of small impairments may allow the solving of low complexity tasks but may become visible if learned variables and the related metric are improper and imprecise, respectively, especially if their number is large. We claim that social interactions are amongst the most challenging cognitive tasks in terms of the number of variables involved. In turn, they are highly susceptible to combinations of small impairments. We consider impairments as the basic colors of autism, whereas the combinations of diverse impairments make the palette of autism. In turn, social processes can be spoiled in many ways and can lead to diverse comorbidities.

Imaginary dimensions in physics require an imaginary set of base Planck units and some negative parameter $c_n$ corresponding to the speed of light in vacuum $c$. The second, negative fine-structure constant $\alpha_2^{-1} \approx -140.178$ present in Fresnel coefficients for the normal incidence of electromagnetic radiation on monolayer graphene leads to the imaginary Planck units. Furthermore, it sets $c_n \approx -3.06 \times 10^8~\text{[m/s]}$. It follows that electric charges are the same in real and imaginary dimensions. Neutron stars and white dwarfs, objects emitting perfect black-body radiation, need energy exceeding their mass-energy equivalence ratios. Complex energies are defined in terms of real and imaginary Planck units. Their imaginary parts, inaccessible for direct observation, store the excess of these energies. It follows that black holes are fundamentally uncharged, charged micro neutron stars and white dwarfs with masses lower than $5.7275 \times 10^{-10}~[\text{kg}]$ are unphysical, and the radii of white dwarfs' cores are limited to $R_{\text{WD}} < 6.7933~G M_{\text{WD}}/c^2$. It is conjectured that the maximum atomic number $Z=238$. A black-body object is in the equilibrium of complex energies of masses, charges, and wavelengths if its radius $R_\text{eq} \approx 2.7665~G M_{\text{BBO}}/c^2$, which corrects the value of the photon sphere radius $R_{\text{ps}}=3G M/c^2$, taking into account the value(s) of the fine-structure constant(s), which is otherwise neglected in general relativity.

This paper presents an innovative approach to dimensionality reduction and feature extraction in high-dimensional datasets, with a specific application focus on wood surface defect detection. The proposed framework integrates sparse modeling techniques, particularly Lasso and proximal gradient methods, into a comprehensive pipeline for efficient and interpretable feature selection. Leveraging pre-trained models such as VGG19 and incorporating anomaly detection methods like Isolation Forest and Local Outlier Factor, our methodology addresses the challenge of extracting meaningful features from complex datasets. Evaluation metrics such as accuracy and F1 score, alongside visualizations, are employed to assess the performance of the sparse modeling techniques. Through this work, we aim to advance the understanding and application of sparse modeling in machine learning, particularly in the context of wood surface defect detection.

Convolutional Neural Networks (CNNs) are often criticized for their lack of transparency, acting as 'black boxes' in decision-making, a challenge compounded by class imbalance in ECG datasets, which limits their clinical application. This study introduces a CNN-based ECG signal classification model that enhances interpretability and addresses class imbalance through the Synthetic Minority Over-sampling Technique (SMOTE). The model also integrates Uniform Manifold Approximation and Projection (UMAP) for dimensionality reduction and SHAP value analysis, facilitating the visualization of decision boundaries and the assessment of feature contributions. Our evaluation using the MIT-BIH Arrhythmia Database highlights the model's high performance, with accuracy and precision nearing 1.00 for Normal ECG (NOR), Left Bundle Branch Block (LBBB), Right Bundle Branch Block (RBBB), and Ventricular Premature Beat (PVC) in the six-class task. In the ten-class task, the model demonstrated robustness, particularly with an accuracy of 0.9846, precision of 0.9783, recall of 0.9736, and F1 score of 0.9760 in Pacemaker Fusion Beat (PFHB), supported by an AUC of 0.9999 and AP of 0.9885. These results underscore the model's efficacy in cardiac rhythm recognition and resilience to class imbalance. Future research will explore sophisticated model architectures and feature extraction methods to enhance the model's generalization and clinical applicability for early heart disease diagnosis and personalized treatment.

Spectral unmixing represents both an application per se and a pre-processing step for several applications involving data acquired by imaging spectrometers. However, there is still a lack of publicly available reference data sets suitable for the validation and comparison of different spectral unmixing methods. In this paper we introduce the DLR HyperSpectral Unmixing (DLR HySU) benchmark dataset, acquired over German Aerospace Center (DLR) premises in Oberpfaffenhofen. The dataset includes airborne hyperspectral and RGB imagery of targets of different materials and sizes, complemented by simultaneous ground-based reflectance measurements. The DLR HySU benchmark allows a separate assessment of all spectral unmixing main steps: dimensionality estimation, endmember extraction (with and without pure pixe assumption), and abundance estimation. Results obtained with traditional algorithms for each of these steps are reported. To the best of our knowledge, this is the first time that real imaging spectrometer data with accurately measured targets are made available for hyperspectral unmixing experiments. The DLR HySU benchmark dataset is openly available online and the community is welcome to use it for spectral unmixing and other applications.

The so-called Born-Huang ansatz is a fundamental tool in the context of ab-initio molecular dynamics, viz., it allows to effectively separate fast and slow degrees of freedom and thus treating electrons and nuclei at different mathematical footings. Here we consider the use of a Born-Huang-like expansion of the three-dimensional time-dependent Schr\"odinger equation to separate transport and confinement degrees of freedom in electron transport problems that involve geometrical constrictions. The resulting scheme consists of an eigenstate problem for the confinement degrees of freedom (in the transverse direction) whose solution constitutes the input for the propagation of a set of coupled one-dimensional equations of motion for the transport degree of freedom (in the longitudinal direction). This technique achieves quantitative accuracy using an order less computational resources than the full dimensional simulation for a prototypical two-dimensional constriction.

Based on a very fast numerical procedure for the determination of the subsurface stress field beneath frictional contacts of axisymmetric elastic bodies under arbitrary 2D oblique loading, the contact mechanical influences of loading parameters and contact profile geometry on the Smith-Watson-Topper (SWT) fatigue crack initiation parameter in elastic fretting contacts with superimposed normal and tangential oscillations are studied in detail. The efficiency of the stress calculation allows for a comprehensive physical analysis of the multi-dimensional parameter space of influencing variables. It is found that a superimposed normal oscillation of the contact can significantly increase or decrease the SWT parameter, depending on the initial phase difference and frequency ratio between the normal and tangential oscillation. Written in proper non-dimensional variables, the rounded flat punch always exhibits smaller values of the SWT parameter, compared to a full paraboloid with the same curvature, while the truncated paraboloid exhibits larger values. A small superimposed profile waviness also significantly increased or decreased the SWT parameter, depending on the amplitude and wave length of the waviness. While both the load protocol and the profile geometry can significantly alter the SWT parameter, the coupling between both influencing factors is weak.

The Hertzian contact theory, as well as most of the other classical theories of normal and tangential contact, provides displacements and the distribution of normal and tangential stress components directly in the contact surface. However, other components of the full stress tensor in the material may essentially influence the material behaviour in contact. Of particular interest are principal stresses and the equivalent von Mises stress, as well as the gradient of the hydrostatic pressure. For many engineering and biomechanical problems, it would be important to find these stress characteristics at least in the contact plane. In the present paper, we show that the complete stress state in the contact plane can be easily found for axially symmetric contacts under very general assumptions. We provide simple explicit equations for all stress components and the normal component of the gradient of hydrostatic pressure in the form of one-dimensional integrals.

Using assembly theory, we investigate the assembly pathways of binary strings of length N formed by joining bits present in the assembly pool and the strings that entered the pool as a result of previous joining operations. We show that the string assembly index is bounded from below by the shortest addition chain for N, and we conjecture about the form of the upper bound. We define the degree of causation for the minimum assembly index and show that for certain N it features regularities that can be used to determine a shortest addition chain. We show that a string with the smallest assembly index for N can be assembled by a binary program of length equal to this index if the length of this string is expressible as a product of Fibonacci numbers. We conjecture that there is no binary program that has a length shorter than the length of the string having the largest assembly index for N that could assemble this string. The results confirm that four Planck areas provide a minimum information capacity that corresponds to a minimum thermodynamic (Bekenstein-Hawking) entropy. Knowing that the problem of determining the assembly index is at least NP-complete, we conjecture that this problem is NP-complete, while the problem of creating the string so that it would have a predetermined largest assembly index is NP-hard. The proof of this conjecture would imply P ≠ NP, since every computable problem and every computable solution can be encoded as a finite binary string.

The study shows that the volumes and surfaces of $n$-balls, $n$-simplices, and $n$-orthoplices are holomorphic functions of $n$, which makes those objects omnidimensional, that is well defined in any complex dimension. Applications of these formulas to the omnidimensional polytopes inscribed in and circumscribed about $n$-balls reveal previously unknown properties of these geometric objects. In particular, for $0 < n < 1$, the volumes of the omnidimensional polytopes are larger than those of circumscribing $n$-balls, and both their volumes and surfaces are smaller than those of inscribed $n$-balls. The surface of an $n$-simplex circumscribing unit diameter $n$-ball is spirally convergent to zero with real $n$ approaching negative infinity but first has a local maximum at $n=-3.5$. The surface of an $n$-orthoplex circumscribing unit diameter $n$-ball is spirally divergent with real $n$ approaching negative infinity but first has a local minimum at $n=-1.5$, where its real and imaginary parts are equal to each other; similarly, as its volume, where the similar local minimum occurs at $n=-3.5$. Reflection functions for volumes and surfaces of these polytopes inscribed in and circumscribed about $n$-balls are proposed. symmetries of products and quotients of volumes in complex dimensions $n$ and $-n$ and of surfaces in complex dimensions $n$ and $2-n$ are shown to be independent of the metric factor and the gamma function. Specific symmetries also hold between volumes and surfaces in dimensions $n = -1/2$ and $n = 1/2$.

Malware complexity is rapidly increasing, causing catastrophic impacts on computer systems. Memory dump malware is gaining increased attention due to its ability to expose plaintext passwords or key encryption files. This paper presents an enhanced classification model based on One class SVM (OCSVM) classifier that can identify any deviation from the normal memory dump file patterns and detect it as malware. The proposed model integrates OCSVM and Principal Component Analysis (PCA) for increased model sensitivity and efficiency. An up-to-date dataset known as “MALMEMANALYSIS-2022” was utilized during the evaluation phase of this study. The accuracy achieved by the traditional one-class classification (TOCC) model was 55%, compared to 99.4% in the one-class classification with PCA (OCC-PCA) model. Such results have confirmed the increased performance achieved by the proposed model.

One challenging problem is the representation of three-dimensional datasets that vary with time. These datasets can be though as a cloud of points that gradually deforms. But point-wise variations lack of information about the overall deformation pattern, and more importantly, about the extreme deformation locations inside the cloud. The present article applies a technique in computational mechanics to derive the strain-rate state of a time-dependent and three-dimensional data distribution, by which one can characterize its main trends of shift. Indeed, the tensorial analysis methodology is able to determine the global deformation rates in the entire dataset. With the use of this technique, one can characterize the significant fluctuations in a reduced multivariate description of an urban system and identify the possible causes of those changes: calculating the strain-rate state of a PCA-based multivariate description of an urban system, we are able to describe the clustering and divergence patterns between the districts of the city and to characterize the temporal rate in which those variations happen.

This paper presents a model for archival and retrieval of the videos of natural flowers. To design an efficient video retrieval system the stages namely, keyframe selection, feature extraction, feature dimensionality reduction and indexing are essential for fast browsing and accessing of videos. Three different keyframe selection approaches are proposed using clustering algorithms after segmenting flower regions from its background. Deep Convolutional Neural Network is used as a feature extractor. After keyframe selection, a video is represented with a set of keyframes. To reduce the feature dimension of a video, two feature selection methods are utilized. For an efficient archival and fast retrieval of flower videos an indexing method called KD-tree is recommended. For a given query video, similar videos are retrieved both in relative and absolute search modalities. An extensive experimentation conducted on a relatively large flower video dataset. The data set consists of 7788 videos of 30 different species of flowers. The videos are captured with three different devices in different resolutions. The comparative study reveals proposed keyframe selection approaches gives better results. It has also been observed that the videos retrieved in absolute approach with features selected from Binormal separation metric and indexing gives good results.

This paper is concerned with developing an efficient numerical algorithm for fast implementation of the sparse grid method for computing the $d$-dimensional integral of a given function. The new algorithm, called the MDI-SG ({\em multilevel dimension iteration sparse grid}) method, implements the sparse grid method based on a dimension iteration/reduction procedure, it does not need to store the integration points, nor does it compute the function values independently at each integration point, instead, it reuses the computation for function evaluations as much as possible by performing the function evaluations at all integration points in a cluster and iteratively along coordinate directions. It is shown numerically that the computational complexity (in terms of CPU time) of the proposed MDI-SG method is of polynomial order $O(Nd^3 )$ or better, compared to the exponential order $O(N(\log N)^{d-1})$ for the standard sparse grid method, where $N$ denotes the maximum number of integration points in each coordinate direction. As a result, the proposed MDI-SG method effectively circumvents the curse of dimensionality suffered by the standard sparse grid method for high-dimensional numerical integration.

The importance and near ubiquity of the Golden Ratio in disciplines like chemistry and biology is well known, but only recently has it come to light in areas pertaining to the Quantum domain. By using a modified tool-kit of hyper-complex numbers (known as Dimensional Gate Operators) and numerical analysis, we uncover a connection between hyper-dimensional objects, the Fibonacci sequence and that of quasiparticles and excitations. The results show that dimensionality increases in step with the Fibonacci sequence.

Diabetes mellitus is a chronic disease that affects millions of people worldwide. Article focuses on detecting the presence of diabetes in patients using microarray gene data obtained from the pancreas. Handle the high-dimensional nature of the data, four different dimensionality reduction techniques, namely Bessel Function, Discrete Cosine Transform (DCT), Least Square Linear Regression (LSLR), and Artificial Algae Algorithm (AAA) are used. After reduced the data, Meta-heuristic algorithms are applied like Dragonfly Optimization Algorithm (DOA) and Elephant Herding Optimization Algorithm (EHO) for feature selection. Ten classification techniques are using to classify the data in both the format like without feature selection method and with feature selection method. The classification techniques are Non-Linear Regression (NLR), Linear Regression (LR), Gaussian Mixture Model (GMM), Expectation Maximum (EM), Bayesian Linear Discriminant Classifier (BLDC), Logistic Regression (LoR), Softmax Discriminant Classifier (SDC), Support Vector Machine (SVM) with linear kernel, Support Vector Machine (SVM) with polynomial kernel, and Support Vector Machine (SVM) with Radial Basis Function (RBF) kernel. Results showed that the AAA with SVM(RBF) achieved an accuracy of 90% without feature selection. However, when feature selection was applied, with EHO of AAA with SVM(RBF) exhibited the highest accuracy of 95.714%, followed closely by with DOA of AAA with SVM (RBF) at 94.28%.

Machine learning (ML) has found increasing use in research on energy conversion and storage technologies, in particular, so-called sustainable technologies. While often ML is used to directly optimize the parameters or phenomena of interest in the space of features, in this perspective, we focus on using ML to construct objects and methods that help in or enable the modeling of the underlying phenomena. We highlight the need for machine learning from very sparse and unevenly distributed numeric data in multidimensional spaces in these applications. After a brief introduction of some common regression-type machine learning techniques, we will focus on more advanced ML techniques which use these known methods as building blocks of more complex schemes and thereby allow working with extremely sparse data and also allow generating insight. Specifically, we will highlight the utility of using representations with sub-dimensional functions by combining the high-dimensional model representation ansatz with machine learning methods like neural networks or Gaussian process regressions in applications ranging from heterogeneous catalysis to nuclear energy.

Variational Auto-Encoders (VAEs) are deep generative models used for unsupervised learning, however their standard version is not topology-aware in practice since the data topology may not be taken into consideration. In this paper, we propose two different approaches with the aim to preserve the topological structure between the input space and the latent representation of a VAE. Firstly, we introduce InvMap-VAE as a way to turn any dimensionality reduction technique, given an embedding it produces, into a generative model within a VAE framework providing an inverse mapping into original space. Secondly, we propose the Witness Simplicial VAE as an extension of the Simplicial Auto-Encoder to the variational setup using a witness complex for computing the simplicial regularization, and we motivate this method theoretically using tools from algebraic topology. The Witness Simplicial VAE is independent of any dimensionality reduction technique and together with its extension, Isolandmarks Witness Simplicial VAE, preserves the persistent Betti numbers of a data set better than a standard VAE.

Motivated by assumptions that Quantum Mechanics (QM) is not the basement of reality and that additional dimensionality (XD) is required to complete and extend the Standard Models (SM) of Particle Physics and Cosmology, experimental protocols utilizing putative properties of Kaluza-Klein-like (KK) cyclicality embedded within Dirac’s electron hypertube model in conjunction with a Dirac covariant polarized vacuum is developed to produce a new type of low-energy tabletop cross section based on topological phase transitions rather than high energy collision sprays as in the LHC. The model is presented in a highly theoretical axiomatic manner utilizing off-the-shelf parameters generally marginalized by the mainstream physics community. When successful the protocol leads to obsolescence of the highly efficacious 100-year supercollider run producing a paradigm shift with an inherent new set of Unified Field (UF) transformations beyond the Galilean Lorentz-Poincaré transformations of the SM to 3rd regime natural science: Classical – Quantum - UF.

Microarray gene expression-based detection and classification of medical conditions have been prominent in research studies over the past few decades. However, extracting relevant data from the high-volume microarray gene expression with inherent nonlinearity and inseparable noise components raises significant challenges during data classification and disease detection. So, this paper proposes a two-level strategy involving feature extraction and selection methods before the classification step. The feature extraction step utilizes Short Term Fourier Transform (STFT), and the feature selection step employs Particle Swarm Optimization (PSO) and Harmonic Search (HS) metaheuristic methods. The classifiers employed are Non-Linear Regression, Gaussian Mixture Model, Softmax Discriminant, Naive Bayes, SVM (Linear), SVM (Polynomial), and SVM (RBF). The two-level extracted relevant features are compared with raw data classification results, including Convolutional Neural Network (CNN) Methodology. Among the methods, STFT with PSO feature selection and SVM (RBF) classifier produced the highest accuracy of 94.47%.

Using multi-color flow cytometry analysis, we studied the immunophenotypical differences between leukemic blasts/LSCs from patients with AML/MDS and hematopoietic stem and progenitor cells (HSPCs) from patients in complete remission (CR) following their successful treatment. The panel of markers included CD34, CD38, CD45RA, CD123 as representatives for a hierarchical hematopoietic stem and progenitor cell (HSPC) classification as well as programmed death ligand 1 (PD-L1). Rather than restricting the evaluation on a 2- or 3-dimensional analysis, we applied a t-distributed stochastic neighbor embedding (t-SNE) approach to get a deeper insight and segregation between leukemic and normal HPSCs. For that purpose, we created a t-SNE map, which resulted in the visualization of 27 cell clusters based on their similarity concerning the composition and intensity of antigen expression. Two of these clusters were “leukemia-related” containing a great proportion of CD34⁺/CD38^- hematopoietic stem cells (HSCs) or CD34⁺ cells with a strong coexpression of CD45RA/CD123, respectively. CD34⁺ cells within the latter cluster were also highly positive for PD-L1 reflecting their immunosuppressive capacity. Beyond this proof of principle study, the inclusion of additional markers will be helpful to refine the differentiation between normal HSPCs and leukemic cells, particularly in the context of minimal disease detection and antigen-targeted therapeutic interventions. Furthermore, we suggest a protocol for the assignment of new cell ensembles in quantitative terms, via a numerical value, the Pearson coefficient, based on a similarity comparison of the t-SNE pattern with a reference.