Large Dimensions Research Articles

Fast Fourier transforms and fast Wigner and Weyl functions in large quantum systems

Two methods for fast Fourier transforms are used in a quantum context. The first method is for systems with dimension of the Hilbert space D=dn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D=d^n$$\\end{document} with d an odd integer, and is inspired by the Cooley-Tukey formalism. The ‘large Fourier transform’ is expressed as a sequence of n ‘small Fourier transforms’ (together with some other transforms) in quantum systems with d-dimensional Hilbert space. Limitations of the method are discussed. In some special cases, the n Fourier transforms can be performed in parallel. The second method is for systems with dimension of the Hilbert space D=d0...dn-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D=d_0...d_{n-1}$$\\end{document} with d0,...,dn-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d_0,...,d_{n-1}$$\\end{document} odd integers coprime to each other. It is inspired by the Good formalism, which in turn is based on the Chinese reminder theorem. In this case also the ‘large Fourier transform’ is expressed as a sequence of n ‘small Fourier transforms’ (that involve some constants related to the number theory that describes the formalism). The ‘small Fourier transforms’ can be performed in a classical computer or in a quantum computer (in which case we have the additional well known advantages of quantum Fourier transform circuits). In the case that the small Fourier transforms are performed with a classical computer, complexity arguments for both methods show the reduction in computational time from O(D2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{O}(D^2)$$\\end{document} to O(DlogD)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{O}(D\\log D)$$\\end{document}. The second method is also used for the fast calculation of Wigner and Weyl functions, in quantum systems with large finite dimension of the Hilbert space.

Large extra dimensions from higher-dimensional inflation

Large extra dimensions from higher-dimensional inflation

Improvement Synthesis of Graphene Oxide Yield in Two Steps of Intercalation and Oxidation of Flexible Graphite Foil by Electrochemical Exfoliation

Synthesis of high quality and quantity of graphene by cost-effective methods are highly desirable for various application. In electrochemical exfoliation, graphite foil has been used as carbon source for the synthesis of high yield of graphene flakes. Electrochemical exfoliation is one of the faster and cheaper method to synthesize graphene sheets. In this work, five different types of concentration of sulphuric acid were used for electrochemical exfoliation. The electrochemical cell design where graphite foil as anode and copper foil as cathode which were connected to DC power supply of 5V. To examine the morphology scanning electron microscope (SEM) was employed in which the sheet structures with large lateral dimension and thin graphene flakes. Furthermore, X-ray diffraction (XRD) revealed that exfoliated graphene samples showed a significant peak at about 2θ = 26º corresponded to graphite.

Microseismic Observation Enabled by High-Sensitivity Micromechanical Interferometers

High-sensitivity accelerometry has historically been employed to explore Earth sciences and advance resource-related industries, such as petroleum exploitation. The devices capable of such measurements, however, traditionally involve precise mechanical structures and consequent large dimensions. In this work, combined by micromechanical systems and grating-assisted interferometry, a closed-loop optical accelerometer with nano-g (ng) sensitivity is developed for microseismic observations. In order to lower the intrinsic thermal noise, a modified 8.84 Hz micromechanical spring-mass oscillator is designed and fabricated. Additionally, an active control system is equipped to stabilize the device temperature and thus enhance the low-frequency stability. Field tests demonstrate that the prototype has achieved a scale factor of 1195 V/g, along with a dynamic range of 1.12 mg and a bandwidth of about 7 Hz. Further, under the controlled 45 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\pm$</tex-math></inline-formula> 0.01 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^\circ$</tex-math></inline-formula> C temperature condition, complete terrestrial microsesimic peaks from 0.1 Hz to 3 Hz are tracked. After calibration by a reference seismometer, the device self-noise is determined as 2 ng/ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\sqrt{Hz}$</tex-math></inline-formula> from 0.2 Hz to 4 Hz with a bias stability of 7.9 ng. The transducer and control circuits are both packaged within a 13.6 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\times 13.6\times$</tex-math></inline-formula> 12.8 cm <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{3}$</tex-math></inline-formula> insulated enclosure, making it advantageous for outdoor observations.

Comparison of Tiktok Application Users Between the Implementation of Creativity and Addictive Behavior

TikTok application users have now reached all levels of society, especially teenagers who use the TikTok application as a medium to express themselves. Teenagers who access TikTok are considered to have the opportunity to use creative abilities in creating content on TikTok, but the Tiktok application, in fact, will also have a bad impact on individuals, especially teenagers who are still very unstable. Tiktok can have a negative impact where it makes its users more and more addicted every day. This study aims to understand and analyze the implementation of creativity and addictive behavior of TikTok users. Implementation using Torrance Test of Creative Thinking (TTCT) and addictive behavior using Bergen Social Media Addiction Scale. There are four aspects of creativity, namely fluency, flexibility, elaboration, and originality. While addictive behavior there are aspects of importance, tolerance, mood swings, withdrawal and relapse. The method used is quantitative descriptive, to find out more between creativity and addiction that TikTok users use. Based on the findings, 85% were able to implement their creativity on the TikTok application with the biggest aspect lying in the flexibility in utilizing the ability to identify problems or provide solutions to their problems by utilizing the features and visualizations available on TikTok. As for addictive behavior, it was found that 75% of addictive behavior existed, with the largest dimension in mood swings, this is because TikTokers are looking for fun and entertainment to forget for a moment about the problem.

Machine learning classification of sphalerons and black holes at the LHC

In models with large extra dimensions, “miniature” black holes (BHs) might be produced in high-energy proton–proton collisions at the Large Hadron Collider (LHC). In the semi-classical regime, those BHs thermally decay, giving rise to large-multiplicity final states with jets and leptons. On the other hand, similar final states are also expected in the production of electroweak sphaleron/instanton-induced processes. We investigate whether one can discriminate these scenarios when BH or sphaleron-like events are observed in the LHC using machine learning (ML) methods. Classification among several BH scenarios with different numbers of extra dimensions and the minimal BH masses is also examined. In this study we consider three ML models: XGBoost algorithms with (1) high- and (2) low-level inputs, and (3) a Residual Convolutional Neural Network. In the latter case, the low-level detector information is converted into an input format of three-layer binned event images, where the value of each bin corresponds to the energy deposited in various detector subsystems. We demonstrate that only a small number of detected events are sufficient to effectively discriminate between the sphaleron and BH processes. Separation between BH scenarios with different minimal masses is possible with an order of 10 events passing the preselection. A sufficient number of events could be observed in combined Run-2 and -3 data, if the production cross section is not much smaller than the present limit ∼0.1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sim 0.1$$\\end{document} fb. We find, however, that a large number of events is needed to discriminate between BH hypotheses with the same minimal BH mass, but different numbers of extra dimensions.

An Optimised Hoffman Algorithm for Testing Linear Code Equivalency

The Hoffman’s algorithm to test equivalency of linear codes is one of the techniques that have been used over the years; it is achieved by a comparison of codewords of the linear codes. However, this comparison technique becomes ineffective in instances where it is applied to linear codes with larger dimensions as it requires much run time complexity, space and size in comparing the codewords of each linear code. This paper proposes an optimised algorithm for testing the equivalency of linear codes, specifically addressing the limitations of the Hoffman method. To assess and compare the efficiencies of the Hoffman algorithm and the optimised algorithm, a set of nine carefully selected linear codes were subjected to equivalency testing. The CPU runtime of both algorithms was recorded using the C++ chrono library. The recorded runtime data was then utilized to create a scatter plot, offering a visual representation of the contrasting trends in CPU runtime between the two algorithms. The plot clearly indicate exponential growth in CPU runtime for the Hoffman algorithm as the length and dimension of the linear codes increases, in contrast, the proposed algorithm showcased a minimal growth in CPU runtime, indicating its superior efficiency and optimised performance.

Robust asymptotic stability analysis for fractional-order systems with commensurate time delays: The 1 

The robust asymptotic stability problem for fractional-order linear systems with commensurate time delays (FOSCDs) and structured perturbations is investigated in this manuscript. Based on the properties of Kronecker products and μ-analysis, the necessary and sufficient conditions are given to guarantee the asymptotic stability of FOSCDs. Then, the necessary and sufficient conditions for the robust asymptotic stability of FOSCDs with structured perturbations are investigated. To reduce the computing complexity and deal with the problems of systems with larger dimensions, a sufficient condition on the robust asymptotic stability of FOSCDs with structured perturbations is given based on the properties of Kronecker products and 2-norm transformations. Finally, several examples are illustrated to test the effectiveness of the proposed results.

Measurement of the Impact Loads to Reduce Injuries in Acrobatic Gymnasts: Designing a Dedicated Platform

Background: The main objective of this study was the development of a specific load platform that would meet the needs of gymnasts and acrobatic coaches. This new platform has larger dimensions and is an identical structure to the plywood floor surface normally used; it was designed to make competitions with gymnasts safer and more like a real training situation. During a landing, there is high body stiffness, especially in the knees and ankles, which can cause injuries due to the number of repetitions performed in this gymnastics specialty. Methods: A group of 10 volunteers, with a mean age of 14.7 ± 2.4 years, performed at least 10 valid vertical jumps on each platform. Results: Despite being a preliminary study, this specific platform was shown to be more suitable for gymnastic use, compared to the industrial one, which represents a significant advantage for the modality. In fact, this platform is similar to the surface used for training and competition, allowing athletes to perform the jump in a similar way, and for the results to be replicable during the practice of the sport. The standard deviation values were lower, which shows that the new platform was more suitable for acrobatic gymnastics. Conclusions: As the maximum vertical load induced during landing after a jump has a significant effect on the likelihood of gymnasts suffering injuries, the development of a new load platform specifically for acrobatic gymnastics is clearly an improvement in this discipline. Knowledge of the load transmitted to the body can help coaches and athletes in defining training, and avoiding the possible occurrence of injuries. Therefore, it is necessary to use a platform that can accurately evaluate the load transmitted to the acrobatic gymnasts during real training and competition conditions, which is achieved with this new platform.

Lifting of superconformal descendants in the D1-D5 CFT

We consider D1-D5-P states in the untwisted sector of the D1-D5 orbifold CFT where we excite one copy of the seed CFT with a left-moving superconformal descendant. When the theory is deformed away from this region of moduli space these states can ‘lift’, despite being BPS at the orbifold point. For descendants formed from the supersymmetry \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${G}_{\\dot{A},-s}^{\\alpha }$$\\end{document} and R-symmetry \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${J}_{-n}^{a}$$\\end{document} current modes we obtain explicit results for the expectation value of the lifts for various subfamilies of states at second order in the deformation parameter. A smooth ∼ \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sqrt{h}$$\\end{document} behaviour is observed in the lifts of these subfamilies for large dimensions. Using covering space Ward identities we then find a compact expression for the lift of the above \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${J}_{-n}^{a}$$\\end{document} descendant states valid for arbitrary dimensions. In the large-dimension limit this lift scales as ∼ \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sqrt{h}$$\\end{document}, strengthening the conjecture that this is a universal property of the lift of D1-D5-P states. We observe that the lift is not simply a function of the total dimension, but depends on how the descendant level is partitioned amongst modes.

Iterative synthesis method for high‐directivity symmetrical stepped‐impedance microstrip parallel‐line coupler

AbstractTraditional quarter‐wavelength parallel‐line couplers (QWPLC) in microstrip form suffer heavily in low directivity because of unbalanced even‐mode and odd‐mode phase velocities. Related schemes to improve directivity lead to complex structures and large dimensions. This study derives and validates an iterative synthesis method to design a high‐directivity microstrip coupler adopting a symmetric stepped‐impedance microstrip coupled line (SSIMCL). Given that the even‐mode and odd‐mode effective dielectric constants (EDCs) vary with the characteristic impedances, the authors take the EDCs of traditional QWPLC as the initial values for an SSIMCL, and the characteristic impedances and EDCs can be computed and converged in several iterations, resulting in good phase delay balance and high coupler directivity. A 20‐dB microstrip coupler working at 1 GHz with high directivity is designed, fabricated, and measured. The obtained maximum directivity is 47 dB and approximately 1 GHz, while the relative bandwidth with a directivity higher than 20 dB and a return loss better than 20 dB is larger than 70%. The novel microstrip coupler also features a compact, simple structure shorter than λg/4.

A Rare Case of a Malignant Epithelioid Neoplasm With an Underlying Novel EWSR1::ZBT44 Fusion, Identified on Next-Generation Sequencing (NGS).

The clinicopathological spectrum of undifferentiated round cell sarcomas of bone and soft tissues is expanding after the 5th edition of the WHO classification. A 23-year-old male patient presented with a lump in his left thigh of 3 months' duration. Radiological examination revealed a well-defined, solid-cystic lobulated, soft tissue lesion in the proximal medial region of his left thigh, measuring 7.7 cm in the largest dimension. The referring diagnosis was an epithelioid sarcoma. Histopathological review of the tumor sections revealed a cellular tumor composed of malignant epithelioid to focally "rhabdoid-like" cells in a variable hyalinized and myxoid stroma with geographic areas of necrosis. In addition, there were areas reminiscent of hemangiopericytomatous vasculature. By immunohistochemistry, the tumor cells were diffusely positive for CD34, focally and distinctly for pan keratin (AE1/AE3). INI1/SMARCB1 and SMARCA4 (BRG1) were diffusely positive (normal). Next-generation sequencing with a wide sarcoma panel revealed EWSR1exon8::ZBT44exon4 fusion. The present example constitutes the first malignant epithelioid tumor with a hemangiopericytomatous growth pattern, exhibiting this rare fusion. The differential diagnoses of this tumor and their corresponding immunohistochemical profile are discussed. This example highlights the value of NGS in unraveling rare fusions and in differentiating these tumors from their several mimics.

Dual-Responsive MXene-Functionalized Wool Yarn Artificial Muscles.

Fiber-based artificial muscles are promising for smart textiles capable of sensing, interacting, and adapting to environmental stimuli. However, the application of current artificial muscle-based textiles in wearable and engineering fields has largely remained a constraint due to the limited deformation, restrictive stimulation, and uncomfortable. Here, dual-responsive yarn muscles with high contractile actuation force are fabricated by incorporating a very small fraction (<1wt.%) of Ti3C2Tx MXene/cellulose nanofibers (CNF) composites into self-plied and twisted wool yarns. They can lift and lower a load exceeding 3400 times their own weight when stimulated by moisture and photothermal. Furthermore, the yarn muscles are coiled homochirally or heterochirally to produce spring-like muscles, which generated over 550% elongation or 83% contraction under the photothermal stimulation. The actuation mechanism, involving photothermal/moisture-mechanical energy conversion, is clarified by a combination of experiments and finite element simulations. Specifically, MXene/CNF composites serve as both photothermal and hygroscopic agents to accelerate water evaporation under near-infrared (NIR) light and moisture absorption from ambient air. Due to their low-cost facile fabrication, large scalable dimensions, and robust strength coupled with dual responsiveness, these soft actuators are attractive for intelligent textiles and devices such as self-adaptive textiles, soft robotics, and wearable information encryption.

HE-Gaston algorithm for frequent subgraph mining with hadoop framework

Graph mining contributes a key role in data mining and as the size of the data increases, it becomes complicated. Identifying the interesting subgraphs in the graph is a commonly researched issue, where the subgraphs denote the commonly occurring pattern exhibiting a particular structure. Frequent Subgraph Mining (FSM) is an important task for exploratory data analysis on graph data.Though many techniques are proposed for FSM, the large dimension of the data makes FSM complex. This research proposes a novel technique for performing FSM in a Hadoop framework. Here, FSM is carried out using the proposed Holoentropy Gaston algorithm (HE-Gaston), which is developed by incorporating the Holoentropy support measure instead of the Recurrent support measure in the Recurrent-Gaston (R-Gaston) technique. Here, the weblog files are considered for FSM and are fed to the Spark framework, which encompasses a master and several slaves. The slave nodes generate the frequent subgraphs based on the Holoentropy support measure and the generated frequent subgraphs are applied to the master node which produces the final frequent subgraphs by utilizing an aggregate Holoentropy support measure. Further, the HE-Gaston shows that it recorded execution time of 43 ms, memory of 2.161 MB, and number of structures mined as 117.

Gauge-Optimal Approximate Learning for Small Data Classification.

Small data learning problems are characterized by a significant discrepancy between the limited number of response variable observations and the large feature space dimension. In this setting, the common learning tools struggle to identify the features important for the classification task from those that bear no relevant information and cannot derive an appropriate learning rule that allows discriminating among different classes. As a potential solution to this problem, here we exploit the idea of reducing and rotating the feature space in a lower-dimensional gauge and propose the gauge-optimal approximate learning (GOAL) algorithm, which provides an analytically tractable joint solution to the dimension reduction, feature segmentation, and classification problems for small data learning problems. We prove that the optimal solution of the GOAL algorithm consists in piecewise-linear functions in the Euclidean space and that it can be approximated through a monotonically convergent algorithm that presents-under the assumption of a discrete segmentation of the feature space-a closed-form solution for each optimization substep and an overall linear iteration cost scaling. The GOAL algorithm has been compared to other state-of-the-art machine learning tools on both synthetic data and challenging real-world applications from climate science and bioinformatics (i.e., prediction of the El Niño Southern Oscillation and inference of epigenetically induced gene-activity networks from limited experimental data). The experimental results show that the proposed algorithm outperforms the reported best competitors for these problems in both learning performance and computational cost.

On the lengths of descendingly flexible and descendingly alternative algebras

We introduce the classes of descendingly flexible and descendingly alternative algebras over an arbitrary field F. We suggest a new method based on the sequence of differences between the dimensions of the linear spans of words, which allows us to obtain upper bounds on the lengths of these algebras. We also present an example of an algebra of arbitrarily large dimension such that these bounds are achieved on it asymptotically.

Fractal Characteristics and Microstructure of Coal with Impact of Starch-Polymerized Aluminum Sulfate Fracturing Fluids

The degree of irregularity and complexity of the pore structure are comprehensively reflected in the fractal dimension. The porosity of coal was determined by its fractal dimension, where a larger dimension indicates a lower porosity. Fractal theory and the Frenkel–Halsey–Hill (FHH) model were applied to explore the variation rules of concentration on functional groups and pore structure in this study. Combined with infrared spectroscopy (FTIR) and low-temperature nitrogen adsorption, a starch-polymerized aluminum sulfate composite fracturing fluid was prepared, which plays an important role in methane adsorption and permeability of coal samples. The test results showed that, compared with the original coal, the pore volume and specific surface area of each group of coal samples were reduced, the average pore diameter was initially enlarged and then declined, and fractal dimension D1 dropped by 5.4% to 15.4%, while fractal dimension D2 gained 1.2% to 7.9%. Moreover, the nitrogen adsorption of each group of coal samples was obviously lower than the original coal, and the concentration of starch-polymerized aluminum sulfate solution existed at a critical optimal concentration for the modification of the coal samples, and the nitrogen adsorption reached a minimum value of 0.6814 cm3/g at a concentration of 10%. The novel composite solution prepared by the combination of starch and flocculant in this paper enhanced the permeability of the coal seam, which is of great significance in improving the efficiency of coalbed methane mining.

Asymptotic performance of reconfigurable intelligent surface assisted MIMO communication for large systems using random matrix theory

AbstractReconfigurable intelligent surface (RIS) can provide unprecedented spectral efficiency gains and excellent ability to manipulate electromagnetic waves. This article considered a RIS‐assisted multiuser multiple‐input multiple‐output (MIMO) downlink system, where the beamforming at the base station and RIS are jointly designed to maximize the sum‐rate. For the large dimension scenario and high‐rank beamforming matrix, the accurate deterministic approximations from random matrix theory are then utilized to simplify the RIS‐assisted MIMO systems. The asymptotical signal‐to‐interference‐plus‐noise ratio values obtained through random matrix theory is infinitely close to the theoretical limits calculated by accurately iteration. And the performance of the proposed algorithm computed via the sharing second‐order channel statistics matches that of the RIS algorithm with sharing full channel state information asymptotically. The deterministic approximations are instrumental to get improvement into the structure of the optimal beamforming and to reduce the implementation complexity in large‐scale MIMO system. Numerical simulations results are provided to evaluate and verify the accuracy of the asymptotic results obtained from the proposed algorithm in the finite system regime. With the complex operation process of large dimension matrix reducing to the deterministic approximations, a lower computational complexity can be obtained compared with other methods.

Attention 3D central difference convolutional dense network for hyperspectral image classification.

Hyperspectral Images (HSI) classification is a challenging task due to a large number of spatial-spectral bands of images with high inter-similarity, extra variability classes, and complex region relationships, including overlapping and nested regions. Classification becomes a complex problem in remote sensing images like HSIs. Convolutional Neural Networks (CNNs) have gained popularity in addressing this challenge by focusing on HSI data classification. However, the performance of 2D-CNN methods heavily relies on spatial information, while 3D-CNN methods offer an alternative approach by considering both spectral and spatial information. Nonetheless, the computational complexity of 3D-CNN methods increases significantly due to the large capacity size and spectral dimensions. These methods also face difficulties in manipulating information from local intrinsic detailed patterns of feature maps and low-rank frequency feature tuning. To overcome these challenges and improve HSI classification performance, we propose an innovative approach called the Attention 3D Central Difference Convolutional Dense Network (3D-CDC Attention DenseNet). Our 3D-CDC method leverages the manipulation of local intrinsic detailed patterns in the spatial-spectral features maps, utilizing pixel-wise concatenation and spatial attention mechanism within a dense strategy to incorporate low-rank frequency features and guide the feature tuning. Experimental results on benchmark datasets such as Pavia University, Houston 2018, and Indian Pines demonstrate the superiority of our method compared to other HSI classification methods, including state-of-the-art techniques. The proposed method achieved 97.93% overall accuracy on the Houston-2018, 99.89% on Pavia University, and 99.38% on the Indian Pines dataset with the 25 × 25 window size.

Compact high-Q Ka-band sapphire distributed Bragg resonator

In a class of high quality (Q-) factor dielectric resonators with low radiative losses, including popular whispering-gallery mode (WGM) resonators with high azimuthal mode numbers, due to high confinement of modal field in dielectric, the Q-factor is limited by the value of inverse dielectric loss tangent of dielectric material. Metal enclosures necessary for device integration only marginally affect the Q-factor while eliminating the residual radiative loss and allowing the optimization of input and output coupling. While very high Q-factors ∼200000 are available in sapphire WGM resonators in X-band, at millimeter wave frequencies increasing dielectric loss limits the Q-factor to much smaller values, e.g. ∼50000 and ∼25000 for quasi-TE and quasi-TM modes, correspondingly, at 36 GHz. The use of distributed Bragg reflection (DBR) principle allows to push modal energy outside dielectric while also isolating it from Joule losses in metallic enclosure walls. Very high Q∼600000&amp;gt;tgδ has been demonstrated in X-band [C. A. Flory and R. C. Taber, IEEE Trans. Ultrason., Ferroelectr., Freq. Control 44, 486–495 (1997).] at the expense of impractically large dimensions. In this work, we report on the assembly and testing of a compact Ka-band sapphire distributed Bragg reflector cavity characterized with Q-factor seven times larger than one predicted by the material’s dielectric loss at the frequency of interest. An intrinsic Q-factor of ∼200000 is demonstrated at 36 GHz for the lowest order TM-mode of a sapphire DBR. The resonator has 50 cm3 volume, smaller than previously demonstrated DBRs.