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We define inclusive scattering matrix in the framework of a geometric approach to quantum field theory. We review the definitions of scattering theory in the algebraic approach and relate them to the definitions in the geometric approach. [ABSTRACT FROM AUTHOR]

The definitions of scattering matrix and inclusive scattering matrix in the framework of formulation of quantum field theory in terms of associative algebras with involution are presented. The scattering matrix is expressed in terms of Green functions on shell (LSZ formula), and the inclusive scattering matrix is expressed in terms of generalized Green functions on shell. The expression for inclusive scattering matrix can be used also for quasi-particles (for elementary excitations of any translation-invariant stationary state, for example, for elementary excitations of equilibrium state). An interesting novelty is the consideration of associative algebras over real numbers. [ABSTRACT FROM AUTHOR]

In this paper, six kinds of periodic optical waveguide networks are designed to study the influence of three‐order parity–time‐symmetric (PT‐symmetric) substructures on the singular optical characteristics. It is found that different characteristics correspond to different PT‐symmetric substructures, and new singular optical characteristics are produced by adjusting the PT‐symmetric substructures. This work demonstrates that these six kinds of systems can create novel quasi‐blackbody, super reflection, and new total reflection, which are significantly different from the corresponding traditional properties and have not been reported yet. These findings may deepen the understanding of PT‐symmetric optical systems and optical waveguide networks, and these new characteristics may possess potential applications in the design of multifunctional optical structures with efficient information processing. [ABSTRACT FROM AUTHOR]

A thorough understanding of the scattering mechanism of Lamb waves at discontinuities is of interest for quantitative evaluation of structural properties and mode control. This study extends the generalized scattering matrix method to investigate the interaction of straight crested Lamb waves with multiple cascaded rectangular notches. Based on the orthogonality and completeness of Lamb modes, the mode matching method is utilized to determine the scattering matrices of downward and upward step discontinuities. After that, the generalized scattering matrix method is employed to determine the scattering matrices of a single rectangular notch and the recurrence relations between the scattering matrices of n + 1 cascaded notches and those of n cascaded notches. Finally, the scattering matrices of multiple cascaded notches can be easily obtained taking advantage of the recurrence relations. As the number of cascaded notches increases, more and sharper peaks appear in the scattering coefficient curves. The finite element simulations conducted in the time domain validate the theoretical results for cascaded notches with identical or different depths, which demonstrate that this method can be applied to find the scattering coefficients at piece-wise periodic or nonperiodic waveguides. The generalized scattering matrix method may have potential applications in quantitative nondestructive evaluation and mode control. [ABSTRACT FROM AUTHOR]

We compare two methods for obtaining the parameters of overlapping resonances. The convenience of the Breit–Wigner (BW) approach is based on the fact that it operates with the masses and widths of the states. For several resonances with the same quantum numbers, a sum of BW functions violates the unitarity of the S-matrix. However, unitarity can be maintained by introducing interference phases to a BW implementation of scattering matrix formalism. A background can be added to the BW amplitudes in the standard way by using background phases. The K-matrix method is often used to analyze data related to several resonances with the same quantum numbers. It guarantees the unitarity of the S-matrix, but its parameters can be considered as resonance masses and widths only for well-spaced states. It also does not allow the separation of the resonant and background contributions in scattering amplitudes, which is critically important for determining parameters of wide resonances. To demonstrate the features of these methods, we consider several examples using simulated data. [ABSTRACT FROM AUTHOR]

To study the olfactory perceptual interaction of odorants (OPIO) in binary mixtures containing maltol, a simple and efficient analysis method was developed. This method correlated three variables of the binary mixture: two rates of change in perceived odor intensities of two odorants within the binary mixtures, and the degree of overall odor synergy exhibited by the binary mixtures. By creating a three-dimensional scatter matrix with the variables, the changes in odor intensity of the binary mixture due to OPIO were visualized. The results revealed that the proportions of mutual antagonism, opposite effect, mutual independence, and mutual synergy in the binary mixtures were 64.7%, 32.9%, 1.9%, and 0.5%, respectively. The odor of maltol was mainly masked, and those of esters (68%), aldehydes and ketones (33%) in the mixture were enhanced. In terms of overall odor intensity, 67% of cases involved partial addition, followed by 22.2% overshadowing, and 19.6% stronger component effect. • Olfactory perceptual interactions of maltol with key odorants were studied. • >100,000 data points of 388 groups of binary mixtures were obtained. • A new method was used to analyze perceptual odor intensity of binary mixtures. • In terms of the overall odor intensity, 67% of cases involved partial addition. [ABSTRACT FROM AUTHOR]

We study a family of separable potentials with and without added contact interactions by solving the associated Lippmann–Schwinger equation with two coupled partial waves. The matching of the resulting amplitude matrix with the effective-range expansion is studied in detail. When a counterterm is included in the potential we also carefully discuss its renormalization. Next, we use the matrix N / D method and study whether the amplitude matrices from the potentials considered admit an N / D representation in matrix form. As a novel result we show that it is typically not possible to find such matrix representation for the coupled partial-wave case. However, a separate N / D representation for each coupled partial wave — a valid option known in the literature — is explicitly implemented and numerically solved in cases where the matrix N / D method is unavailable. [ABSTRACT FROM AUTHOR]

• Capability for processing photonuclear data is developed in nuclear data processing code NECP-Atlas. • The newly developed capability is verified. • NECP-Atlas can provide comprehensive data for photon-neutron coupling transport calculations. In the present work, NECP-Atlas has been developed to feature a capability for processing photonuclear data, providing ACE format library for Monte Carlo codes, alongside multi-group data for deterministic transport calculation codes. The work emphasizes the development of a capability responsible for generating multi-group data, including the multi-group photonuclear reaction cross-sections and scattering matrix. The capability for generating a multi-group scattering matrix, which is lacking in conventional nuclear data processing codes, enables NECP-Atlas to provide comprehensive data for photon-neutron coupling transport calculations. The photonuclear ACE library and multi-group photonuclear absorption cross-sections generated by NECP-Atlas are verified with the results obtained by NJOY21. To verify the photonuclear scattering matrix, the photon and neutron leakage spectra of a one-dimensional spherical shell problem and the photon and neutron dose equivalent rates of an electron linear accelerator are calculated and compared with the results from the Monte Carlo simulations. The numerical results affirm that NECP-Atlas has the capability for processing photonuclear data with high accuracy. [ABSTRACT FROM AUTHOR]

Scattering matrices of particle ensembles are analytically decomposed into sums of pure Mueller matrices. The ensembles are assumed to have equal numbers of particles and their mirror particles, both in random orientation. In the general case, there are four pure Mueller matrices in the decomposition. In the present spectral decomposition, of these four matrices, there is a single matrix that qualifies as a scattering matrix, whereas the remaining three matrices represent other classes of pure matrices. For ensembles of spherical particles, there are two pure Mueller matrices in the decomposition. Again, there is a single matrix qualifying as a scattering matrix. The analytical decomposition unveils the explicit dependencies of the pure Mueller matrices on the ensemble-averaged scattering matrix. Applications are identified in scattering by single particles and by random media of particles. • Scattering matrices are analytically decomposed into pure Mueller matrices. • Pure matrices are characterized in terms of explicit matrix-element dependencies. • Scattering matrix purity is measured for particle ensembles. • A single pure scattering matrix is identified for spherical and nonspherical particles. [ABSTRACT FROM AUTHOR]

Samples of soils collected by the Apollo 11 mission (10084,2036) and the Apollo 14 mission (14163,940) were obtained from the NASA Curation and Analysis Planning Team for Extraterrestrial Materials (CAPTEM) program. The particle size, shape, and internal porosity were characterized in three dimensions (3D) using a combination of X-ray computed tomography (XCT) and mathematical analysis, with various size and shape parameters measured and calculated for each particle. High-resolution scanning electron microscopy (SEM) was used to image the particles that were too small for the two XCT instruments used. Similar characterization was carried out on samples of JSC-1A lunar soil simulant, updating a previous analysis. Approximately 14,000 lunar regolith particles and 128,000 JSC1-A particles, covering a wide range of size and shape, were characterized for this paper and the results stored in a publicly accessible database. This large number of particles enabled, for the first time, statistically valid particle shape distributions to be generated. The 3D shape distributions of the two regoliths and JSC-1A were quantitatively compared and it was found that the way particle shape and porosity depends on particle size was different between regolith and simulant. The measured size distribution of particles in the lunar soils was applied to estimate the relative contributions of different sizes to the ensemble average particle single scattering albedo and phase function. By linking our particle counts to published sieve weight fractions for the lunar samples, we find that ∼80% of the total cross-section area is contributed by particles <20 μm diameter and ∼ 50% by particles <8 μm diameter. The orientation-averaged two-dimensional projected areas of the actual regolith particles were computed so that this estimate was also based on real particle shapes. Such small sizes dominating the total cross-section area suggest that calculations of the elements of the scattering matrix for individual particles may be possible with modest computing capabilities leading to the development of improved models for the quantitative interpretation of remote sensing spectrophotometry and polarimetry. This 3D characterization and database will enable other computational work to be done with real lunar regolith particle shapes, including discrete element method mechanical modeling, packing simulations, further light scattering calculations, dust contamination modeling, and modeling of lunar rover interactions with collected and packed regolith particles. • 14,000 lunar regolith and 128,000 JSC-1A particles characterized in 3D. • Lunar regolith particles came from Apollo 11 (10084) and Apollo 14 (14163). • All 3D particle shapes and geometrical information stored in NIST database. • Data useful for mechanical simulations, light-scattering, and packing simulations. • Particles <20 μm give ∼80% of the total light-scattering cross-section area. [ABSTRACT FROM AUTHOR]

Supervised feature selection (FS) as an interpretable dimensionality reduction technique has received increasing attention, where linear discriminative analysis (LDA)-based method can select informative features discriminatively and obtain promising performance. When original data has more features than samples, however, LDA-based method generally encounters degradation since the appearance of irreversible scatter matrix. This situation is called the small sample size (SSS) problem. To overcome it and enhance the discriminant power of selected feature subsets, in this paper, we design an elegant LDA-based FS model referred to as Top- k Discriminative FS (TDFS), which is constructed by seamlessly integrating the ℓ 2 , 0 -norm equation constraint into uncorrelated LDA model. More concretely, the ℓ 2 , 0 -norm equation constraint can explicitly characterize the number of selective features k to ensure the sparsity of projected matrix and select top features. The uncorrelated LDA model aims to improve discriminative ability based on uncorrelated data in projected subspace. Given the formidable nature of solving this non-convex model, a novel optimization algorithm is further developed and the SSS problem can be efficaciously addressed during the optimization process. We first decompose projection matrix into a discrete selection matrix and its corresponding nonzero projection matrix, then concurrently optimize above two matrices by employing a column-by-column update scheme, during which the reversibility of scatter matrix in selective feature subspace can be easily guaranteed to solve SSS problem. The extensive experiments on four synthetic data sets and eight real-world data sets show that the proposed method outperforms eight competitors validated by three classifiers. Moreover, although the theoretical analysis proves that our algorithm has quartic time complexity on the number of selected features k , the running time experiments verify that TDFS is still efficient and applicable in scenarios where only a small number of features need to be selected. From above perspectives, our algorithm shows desirable performance to achieve discriminative FS. [ABSTRACT FROM AUTHOR]

We present theory for calculating state-to-state differential cross sections (DCS) of triatomic reactive scattering in hyperspherical coordinates using a quantum wavepacket method. The adiabatically adjusting, principal axes hyperspherical coordinates proposed by Pack and Parker [J. Chem. Phys. 87, 3888 (1987)] are applied, which deal with all arrangement channels equivalently, allowing the analysis of the products in all three arrangement channels with one main propagation. The propagated wavepacket is analyzed by projecting it onto the product ro-vibrational states at a fixed, asymptotic radius, R, of the corresponding Jacobi coordinates; thus, the channel-specified S-matrix elements can be calculated by matching the projections with the boundary conditions in the Jacobi coordinates. For numerical demonstrations, state-to-state DCS of the H + HD (v 0 = 0, j0 = 0) reaction and state-to-state reaction probabilities of the O + O2 (v 0 = 0, j0 = 0) reaction and the F + HCl (v 0 = 0, j0 = 0) → HF + Cl reaction for zero total angular momentum are presented. The second order split operator method and the Chebyshev polynomial expansion method were applied to propagate the wavefunction. The relative numerical efficiencies for calculating the state-to-state information of triatomic reactive scattering using the hyperspherical coordinate and the reactant Jacobi coordinate are discussed. [ABSTRACT FROM AUTHOR]

Multi band, high spatial resolution and information redundancy are the most significant characteristics of hyperspectral image. These remarkable characteristics are mainly caused by the high-dimensional image data. In view of these characteristics, feature extraction of hyperspectral image has naturally become one of the research hotspots in this field. However, it is impossible to fully describe the intrinsic geometric structure of hyperspectral image only by using spectral information. To improve the subsequent forecasting accuracy, spatial information should be mined to further describe the geometric structure of hyperspectral image. Therefore, an effective feature extraction method (SSF_HM) was proposed via using harmonic mean and spectral-spatial filter. This investigation divides the SSF_HM into three steps. First, the pi principal components were extracted by using principal components analysis (PCA) skill and subsequent the pi spatial filtering features were obtained via using area median filter (AMF) method. Then, the original spectral features and extracted spatial filtering features combine to form the fusion feature matrix, and then the scatter matrix S b H M (based on harmonic mean (HM) spectral-spatial filter inter-class) and scatter matrix S w H M (based on harmonic mean (HM) spectral-spatial filter intra-class) can be established in the fusion feature space, respectively. Finally, combining the Fisher discriminant analysis model and regularization technique, a new feature extraction method SSF_HM is developed. The proposed SSF_HM method combines spectral information and spatial information. At the same time, the range of feature extraction is expanded from spectral space to spectral-spatial fusion space. The experimental results on three real-world hyperspectral image data sets show the better performance of SSF_HM in comparison with other feature extraction methods in small sample size situation by using maximum likelihood classifier (MLC). [ABSTRACT FROM AUTHOR]

To solve the problem that the existing semi-supervised FISHER discriminant analysis algorithm (FDA) cannot effectively use both labeled and unlabeled data for learning, we propose a semi-supervised Kernel local FDA Algorithm based on density peak clustering pseudo-labels (SDPCKLFDA). First, the proposed algorithm adopts the density peak clustering algorithm to generate the pseudo cluster labels for labeled and unlabeled data, and then the generated pseudo-labels are explored to construct two regularization strategies. The two regularization strategies are used to regularize the corresponding within-class scatter matrix and between-class scatter matrix of the local Fisher discriminant analysis, and finally the optimal projection vector is obtained by solving the objective function of the local Fisher discriminant analysis. The two constructed regularization strategies can not only effectively enhance the discriminant performance of the extracted feature but also make the proposed algorithm suitable for multimodal and noisy data. In addition, to accommodate nonlinear and non-Gaussian datasets, we also develop a kernel version of the proposed algorithm with the help of kernel trick. In the experiment, the proposed algorithm is compared with the FDA and its improved algorithms on some benchmark artificial datasets and UCI datasets. The experimental results show that the discriminant performance of the proposed algorithm has been significantly improved compared with the other algorithms. [ABSTRACT FROM AUTHOR]

Infinite periodic arrays of antennas that can be individually described by means of spherical modes are analyzed starting from the generalized scattering matrix (GSM) of an isolated element. After computing the GSM of an isolated element with the finite-element method (FEM), a fast postprocessing can be carried out to calculate the response of the element in an infinite array environment by using addition theorems for spherical modes. For this purpose, an efficient computation of lattice sums of spherical harmonics is used. The main advantage of this method is that the antenna is analyzed only once whatever the array lattice or scan angle. In addition, fast frequency analysis can be performed since the starting point is the computation of the isolated antenna with the FEM, which is suitable for fast frequency sweep. The active reflection coefficient and the embedded radiation pattern of the infinite periodic array are calculated for several examples to show the capabilities of the proposed method. [ABSTRACT FROM AUTHOR]

The development of electromagnetic (EM)-based therapeutic and diagnostic tools, as well as safety assessment of EM interactions with the human body, requires adequate measurement of the complex permittivity of different biological tissues. Such measurement techniques must be low-cost, readily available, and easy to implement. In this study, a simple circuit with basic radio frequency electronics was used to implement the open-ended coaxial probe method for permittivity measurement, as opposed to the widely used vector network analyzers. The non-ideal behavior of the circuit due to spurious reflections and ohmic losses was accounted for by a scattering matrix (SM) that relates the measured reflection coefficient to the true reflection coefficient at the probe tip. Parameters of SM were obtained using three calibration standards, and the circuit was used to measure the complex permittivity of a standard, tissue-equivalent, American Society of Testing Materials (ASTM) polymer gel. A more intuitive approach to circuit analysis is also introduced. For both methods, the dielectric constant and electrical conductivity of the gel were found to agree with the recommended uncertainties of the ASTM standard and validate the utility of the circuit at the test frequency. [ABSTRACT FROM AUTHOR]

Evanescent waves are waves that decay or grow exponentially in regions of the space void of interaction. In potential scattering defined by the Schrödinger equation, (âˆ' ∇ 2 + v) ψ = k 2 ψ for a local potential v, they arise in dimensions greater than one and are generally present regardless of the details of v. The approximation in which one ignores the contributions of the evanescent waves to the scattering process corresponds to replacing v with a certain energy-dependent nonlocal potential V k ˆ . We present a dynamical formulation of the stationary scattering for V ˆ k in two dimensions, where the scattering data are related to the dynamics of a quantum system having a non-self-adjoint, unbounded, and nonstationary Hamiltonian operator. The evolution operator for this system determines a two-dimensional analog of the transfer matrix of stationary scattering in one dimension which contains the information about the scattering properties of the potential. Under rather general conditions on v, we establish the strong convergence of the Dyson series expansion of the evolution operator and prove the existence of the transfer matrix for V ˆ k as a densely-defined operator acting in C 2 ⊗ L 2 (âˆ' k , k). [ABSTRACT FROM AUTHOR]

We present wave-based signal differentiation with unprecedented fidelity and flexibility by purposefully perturbing overmoded random scattering systems such that zeros of their scattering matrices lie exactly at the desired locations on the real frequency axis. Our technique overcomes limitations of hitherto existing approaches based on few-mode systems, both regarding their extreme vulnerability to fabrication inaccuracies or environmental perturbations and their inability to maintain high fidelity under in-situ adaptability. We demonstrate our technique experimentally by placing a programmable metasurface with hundreds of degrees of freedom inside a 3D disordered metallic box. Regarding the integrability of wave processors, such repurposing of existing enclosures is an enticing alternative to fabricating miniaturized devices. Our over-the-air differentiator can process in parallel multiple signals on distinct carriers and maintains high fidelity when reprogrammed to different carriers. We also perform programmable higher-order differentiation. Conceivable applications include segmentation or compression of communication or radar signals and machine vision. Here, the authors report purposefully perturbed wave chaos that enables analog signal processing with unprecedented fidelity and flexibility. [ABSTRACT FROM AUTHOR]

This work provides a new approach for computing the impedance of a proposed multiband printed fractal antenna for wireless applications. Galerkin's method is applied to deduce the impedance relationship of the proposed structure and then compute the return loss verses frequency by converting the impedance matrix of the proposed antenna [Z] to the scattering matrix [S]. This model is developed in order to study the impedance of the proposed antenna after adding a metamaterial structure in the antenna substrate. The obtained model is able to determine the resonant frequencies and the return loss of the proposed antenna. The model is also able to define the changes in these values when the dimensions of the proposed structure change. The proposed antenna provides multiband wireless applications in the (1–10) GHz frequency band, and the return loss of the proposed fractal antenna has been improved using negative permittivity and negative permeability metamaterial structure. [ABSTRACT FROM AUTHOR]

Due to that the polarization scattering matrices (PSM) of single reflection (SR), double reflection (DR), and single diffraction (SD) at different angles are ignored, the PSM of trihedral corner reflector (TCR) is usually assumed to be [1 0; 0 1], which results in inaccuracy by utilizing its polarization to antijamming. Therefore, this article comprehensively analyzes the PSM of TCR based on high-frequency approximation. First, we separately analyze various reflection components based on the physical optics (PO)-shooting bouncing ray (SBR) model, so as to cure the deficiency that the classification discussion methods are susceptible to changes in target size and shape. Then, the PSMs of SR, DR, triple reflection, and SD are rigorously deduced and demonstrated by combining amplitude/phase information. In this process, we successfully integrate the six kinds of DR by the transforming of polarization base. Subsequently, the PSMs in the 2-D space are extended into the 3-D space, which are more suitable for the polarization characteristics of TCR. Finally, we compare the model in this article with the method of moment (MoM) of Feko software and obviously accelerate the model in this article through compute unified device architecture (CUDA). The conclusion of this article is significant for the polarization analysis of TCR to antijamming. [ABSTRACT FROM AUTHOR]

The Hartman effect refers to the rather paradoxical result that the time spent by a quantum mechanical particle or a photon to tunnel through an opaque potential barrier becomes independent of barrier width for long barriers. Such an effect, which has been observed in different physical settings, raised a lively debate and some controversies, owing to the correct definition and interpretation of tunneling times and the apparent superluminal transmission. A rather open question is whether (and under which conditions) the Hartman effect persists for inelastic scattering, that is, when the potential becomes non‐Hermitian and the scattering matrix is not unitary. Here, tunneling through a heterojunction barrier in the tight‐binding picture is considered, where the barrier consists of a generally non‐Hermitian finite‐sized lattice attached to two semi‐infinite nearest‐neighbor Hermitian lattice leads. A simple and general condition is derived for the persistence of the Hartman effect in non‐Hermitian barriers, showing that it can be found rather generally when non‐Hermiticity arises from nonreciprocal couplings, that is, when the barrier displays the non‐Hermitian skin effect, without any special symmetry in the system. [ABSTRACT FROM AUTHOR]

This letter proposes a high isolation two‐element multiple input multiple output (MIMO) antenna by using a wideband pixel neutralization line (NL). The design procedures are simplified as follows: (1) Obtaining the Y‐parameters of the original two‐element antenna with a grid of microstrip stubs, and discrete ports are inserted among microstrip stubs; (2) obtaining the binary codes of the optimum route. Importing Y‐parameters into MATLAB, and using a genetic algorithm to obtain the optimum connection route by design formulas upon scattering matrix which guarantees high isolation; (3) translating the binary codes into the actual connection metallic lines; (4) adding the designed pixel NL and appropriate matching branches into EM simulator to optimize the antenna; (5) obtaining a high isolation two‐element antenna. The original two‐element antenna has poor isolation with the main path coupling, and the pixel NL provides an auxiliary coupling path between two elements. By adjusting pixel NL, the magnitude strengths of two coupling signals realize the same, while the phases are exactly opposite. Therefore, the wideband high isolation between antenna elements is realized. To verify the practicability of the proposed pixel decoupling neutral line, a reference and proposed two‐element MIMO antennas are fabricated and measured. In the experiment, the isolation of the proposed two‐element antenna with an edge‐to‐edge distance of 0.0943λ0 (λ0 is the wavelength in free space at the center frequency) is enhanced by about 17 dB in the working frequency band from 0.975 to 1.025 GHz. Besides, an L‐typed feeding network is added to guarantee a good matching condition. The proposed two‐element antenna has a size of 0.617λ0 × 0.667λ0, and the dimension of each radiation patch is 0.3267λ0 × 0.0725λ0. The proposed GA algorithm‐based decoupling technique has a significant superiority over traditional ones. Efficient, simple, and one‐time EM simulation are its major advantages, which can liberate the RF engineer from the heavy debugging work. [ABSTRACT FROM AUTHOR]

A fast analytical method has been proposed for predicting the shielding effectiveness (SE) and resonances of an apertured enclosure with an interior enclosure. Under the concept of electromagnetic topology, the monitor point and the walls are treated as nodes, and the space between them is treated as tubes. The propagation relationships at tube level and reflection relationships at node level are derived as the propagation matrix. After modeling the front wall of the interior enclosure as a junction between two waveguides, an equivalent circuital model of the enclosures is derived. The front wall and the window structure in front of the adjacent space of the interior enclosure are considered as a three-port scattering matrix. Then we can use the extended BLT equations to calculate the voltage response at each node. Results from the proposed method are compared with those from the numerical method, and the results have a good agreement while it can dramatically save calculation time. [ABSTRACT FROM AUTHOR]

Many extensions of the multivariate normal distribution to heavy-tailed distributions are proposed in the literature, which includes scale Gaussian mixture distribution, elliptical distribution, generalized elliptical distribution and transelliptical distribution. The inferences for each family of distributions are well studied. However, extensions are overlapped or similar to each other, and it is hard to differentiate one extension from the other. For this reason, in practice, researchers simply pick one of many extensions and apply it to the analysis. In this paper, to enlighten practitioners who should conduct statistical procedures not based on their preferences but based on how data look like, we comparatively review various extensions and their estimators. Also, we fully investigate the inclusion and exclusion relations of different extensions by Venn diagrams and examples. Moreover, in the numerical study, we illustrate visual differences of the extensions by bivariate plots and analyze different scatter matrix estimators based on the microarray data. [ABSTRACT FROM AUTHOR]

We evaluate theoretically the interaction of the open bottom and strange systems B ¯ K ¯ , B ¯ ∗ K ¯ , B ¯ K ¯ ∗ and B ¯ ∗ K ¯ ∗ to look for possible bound states which could correspond to exotic non-quark–antiquark mesons since they would contain at least one b and one s quarks. The s-wave scattering matrix is evaluated implementing unitarity by means of the Bethe–Salpeter equation, with the potential kernels obtained from contact and vector meson exchange mechanisms. The vertices needed are supplied from Lagrangians derived from suitable extensions of the hidden gauge symmetry approach to the bottom sector. We find poles below the respective thresholds for isospin 0 interaction and evaluate the widths of the different obtained states by including the main sources of imaginary part, which are the B ∗ → B γ decay in the B ¯ ∗ K ¯ channels, the K ∗ → K π in the channels involving a K ∗ , plus the box diagrams with B ¯ K ¯ and B ¯ ∗ K ¯ intermediate states for the B ¯ ∗ K ¯ ∗ channels. [ABSTRACT FROM AUTHOR]

Decision-makers across many professions are often required to make multi-objective decisions over increasingly larger volumes of data with several competing criteria. Data visualization is a powerful tool for exploring these complex ‘solution spaces’, but there is limited research on its ability to support multi-objective decisions. In this article, we explore the effects of chart complexity and data volume on decision quality in multi-objective scenarios with complex trade-offs. We look at the impact of four common multidimensional chart types (scatter plot matrices, parallel coordinates plots, heat maps, radar charts), the number of options and dimensions and participant chart usage experience on decision time and accuracy when selecting the ‘optimal option’. As objectively evaluating the quality of multi-objective decisions and the trade-offs involved is challenging, we employ rank- and score-based accuracy metrics. While heat maps demonstrate a time advantage, our findings show no strong performance benefit for one chart type over another for accuracy. We find mixed evidence for the impact of chart complexity on performance, with our results suggesting the existence of a ‘ceiling’ in the number of dimensions considered by participants. This points to a potential limit to data complexity that is useful for decision making. Lastly, participants who use charts frequently performed better, suggesting that users can potentially be trained to effectively use complex visualizations in their decision-making. [ABSTRACT FROM AUTHOR]

Big data has the traits such as "the curse of dimensionality," high storage cost, and heavy computation burden. Self-representation-based feature extraction methods cannot effectively deal with the image-level structural noise in the data, so how to character a better relationship of reconstruction representation is very important. Recently, sparse representation with smoothed matrix multivariate elliptical distribution (SMED) using structural information to handle low-rank error images caused by illumination or occlusion has been proposed. Based on SMED, we present a new method named SMEDP for feature extraction. SMEDP firstly utilizes SMED to automatically construct an adjacency graph and then obtains an optimal projection matrix by maximizing the ratio of the local scatter matrix and the total scatter matrix in the PCA subspace. Experiments on the COIL-20 object database, ORL face database, and CMU PIE face database prove that SMEDP works well and can achieve considerable visual and recognition performance than the relevant methods. [ABSTRACT FROM AUTHOR]

We consider the inverse resonance problem in scattering theory. In one-dimensional setting, the scattering matrix consists of 2 × 2 entries of meromorphic functions. The resonances are defined as the poles of the meromorphic determinant. For the compactly supported perturbation, we are able to quantitatively estimate the zeros and poles of each meromorphic entry. The size of potential support is connected to the zero density of scattered wave field due to the form of Fourier transform. We will investigate certain properties of Fourier transforms in scattering theory and derive the inverse uniqueness on scattering source given certain knowledge on the perturbation and all the given resonances. [ABSTRACT FROM AUTHOR]

Arrays fed by substrate-integrated waveguides (SIWs) are a current topic of interest. However, most designers have to rely on general-purpose commercial software, usually inefficient for multiple full-wave simulations in a design process. This work proposes a new fast full-wave strategy, with very low iteration times, based on the simultaneous use of addition theorems for spherical and cylindrical modes. After a domain decomposition of the array into fixed or modifiable (to be optimized) sections, each section is analyzed using a finite-element/modal analysis to obtain its general scattering matrix. Fixed sections are only once coupled at the beginning, while each optimization iteration is calculated with full-wave precision by adding the interactions with the modifiable sections. A complete design process of a novel 16-slot progressive-wave SIW-fed array is performed to validate the strategy usefulness. 112800 iterations, with 47 optimization variables, are calculated in under 4 h (speed-up factor of over 2000 compared to general-purpose commercial software). The designed device is manufactured and experimentally characterized, measuring a 1.05 GHz $\vert S_{11} \vert $ bandwidth under −10 dB and a maximum gain of 15.6 dBi at $\theta =-11^\circ $ in the array plane. [ABSTRACT FROM AUTHOR]

In the atmosphere, the dust shapes are various, and a single model is difficult to represent the complex shapes of dust. We proposed a tunable model to represent dust with various shapes. Two tunable parameters were used to represent the effects of the erosion degree and binding forces from the mass center, respectively. Thus, the model can represent various dust shapes by adjusting the tunable parameters. To evaluate the applicability of the single spheroid model in calculating the optical properties of single dust with irregular shapes, the aspect ratios of spheroids were retrieved by best fitting the phase function of dust with irregular shapes. In this work, the optical properties and polarimetric characteristics of irregular dust with a diameter range of 0.2–2.0 µm were investigated. Our findings show that the dust shapes have a substantial impact on the scattering matrix, and sometimes the sign of elements of the scattering matrix could be modified by changing the tunable parameters. The applicability of the spheroid model is significantly affected by the erosion degree and binding forces, and substantial deviations could be observed when the dust diameter is in the range of 0.8–2.0 µm. The F11 relative differences of approximately 100 % between dust with irregular shapes and best-fitted spheroids could be observed in certain scattering angles. The maximum differences in other elements between irregular dust particles and best-fitted spheroids can reach approximately 0.3–0.8. Besides, the signs of F12/F11 , F33/F11 , F34/F11 and F44/F11 can be modified from negative to positive at some scattering angles if substituting the irregular dust with best-fitted spheroids. As the binding force is small, the deviation of extinction or scattering cross-section generally increases with the erosion degree, and the relative differences between dust with irregular shapes and spheroids can reach approximately 30 % when the erosion degree is large, while the differences are mitigated with the binding force increasing. Besides, with the binding force increasing, the aspect ratio is closer to 1:1. The deviations of the spheroid model in estimating the polarized light were also investigated using the successive-order-of-scattering (SOS) vector radiative transfer (VRT) model. With a diameter (dp) of 0.2 µm , the relative difference of normalized radiance does not exceed 3 %, and the absolute values of the deviation of the polarized bidirectional reflectance factor (PBRF) and the ratio of radiance to polarized intensity (DoLP) are below 0.005 and 0.02, respectively. However, with the particle size increasing, the difference becomes much more substantial. The relative difference of the normalized radiance can exceed 10 %, and the deviations of the PBRF and DoLP can vary in the ranges of -0.015 to 0.025 and -0.05 to 0.15, respectively. Thus, the single spheroid model may lead to non-negligible deviations for estimating the polarimetric characteristics of single dust particles with more complex shapes. In this work, only the optical properties of single particles were considered. In the future, the applicability of an ensemble of spheroidal particles for reproducing the scattering properties and polarimetric characteristics of an ensemble of irregularly shaped dust particles should be further investigated. [ABSTRACT FROM AUTHOR]

The internal meanflow with nonuniform distributions of velocity and temperature is a major challenge for acoustic analysis of a muffler in the frequency domain. On the other hand, the three-dimensional time-domain numerical method is well suited for solving the influence of meanflow on the muffler, but it is time-consuming, especially for calculating the transfer matrix that requires two sets of boundary conditions. We proposed a more efficient time-domain method to calculate the scattering matrix (SM) of an actual engine muffler using a numerical model with only one set of boundary conditions. The reciprocity, as a basic property of waves, was for the first time demonstrated in such a complex muffler with hot nonuniform flow exhausted from the engine and used to reduce the procedures for calculating the SM. The reciprocal relationship was not only expressed in the modules of the transmission coefficients in the SM but also corrected in the phases using the time delay between the incident and transmitted waves observed with the time-domain method. At last, the SM was adopted to obtain the performance of the muffler, which was validated with the measurement. The proposed method shall make the time-domain method more efficient for calculating the characterizing matrix of a muffler without or with meanflow. [ABSTRACT FROM AUTHOR]

We propose a stable and efficient approach to extract the frequency-dependent parasitic effects of any computer-aided design (CAD) model with the finite element method (FEM). An equivalent circuit (EC) of the parasitics for use in transient circuit simulations is generated by applying vector fitting to the result of a full-wave simulation on the one hand and to a magnetoquasistatic (MQS) simulation result on the other hand. The circuit generated from the magnetoquasistatic results is combined with capacitances computed in an electrostatic (ES) simulation. This separate consideration of resistive and inductive, and capacitive effects ensures stability also at low frequencies by avoiding impedance or scattering matrices that otherwise would become ill-conditioned when approaching the dc point. A comparison of measurement and simulation results for the example of a common mode (CM) choke validates the method. [ABSTRACT FROM AUTHOR]

The paper considers an infinite two-dimensional ultra-wideband two-section antenna array in which the first section is made in the form of an isolated block connected to the second section via a special transition. Based on an approximate solution of a boundary value problem, an analytical model of the transition, making it possible to calculate its scattering matrix, is constructed. The scattering and transfer matrices of the first and second sections of the array in the quasi-periodic excitation mode are found in the approximation of the theory of microwave transmission lines. The total transfer matrix of the entire array is determined by multiplying the transfer matrices of its components. The numerically constructed analytical model of the array makes it possible to calculate its scattering matrix in the scan mode and has a high computational efficiency. The results of calculations by the proposed approximate model are compared with the results given by rigorous full-wave methods. [ABSTRACT FROM AUTHOR]

For a unitary unramified genuine principal series representation of a covering group of a simply-connected group, we studied in a previous paper a conjectural formula relating its R-group to the dimension of the Whittaker space of the irreducible constituents. In this paper, the formula is refined and also verified for several important cases. [ABSTRACT FROM AUTHOR]

The photonic spin Hall effect (PSHE), featured by a spin-dependent shift driven by its polarization handedness, is proposed to facilitate the applications in precision metrology and quantum information processing. Here, due to the magnetoelectric coupling of the chirality, the PSHE is accompanied with Goos–Hänchen and Imbert–Fedorov effects. Taking advantage of this superiority, the transverse shift (TS) and longitudinal shift (LS) can be applied simultaneously. Rearranging the PT-symmetric scattering matrix, the responsive PSHE near the exceptional points and their basic physical mechanisms are discussed in detail in the case of complex chirality κ. Re[κ] and Im[κ] regulated the rich (at multi-angle), gaint (reach upper limit) and tunable (magnitude and direction) TS and LS, respectively. Based on the chirality-modulated PSHE, the novel applications in binary code conversion and barcode encryption are proposed systematically. By incorporating the quantum weak measurement technology, our applications provide new mechanisms to realize optoelectronic communication. [ABSTRACT FROM AUTHOR]

We demonstrate a concept for the giant enhancement of the transverse magneto-optical Kerr effect (TMOKE) using bulk plasmon polariton (BPP) modes in non-magnetic multilayer hyperbolic metamaterials (HMMs). Since the BPP modes are excited through the attenuated total reflection (ATR) mechanism, using a Si-based prism-coupler, we considered a single dielectric magneto-optical (MO) spacer between the prism and the HMM. The working wavelength was estimated, using the effective medium approach for a semi-infinite dielectric-plasmonic multilayer, considering the region where the system exhibits type II HMM dispersion relations. Analytical results, by means of the scattering matrix method (SMM), were used to explain the physical principle behind our concept. Numerical results for giant TMOKE values (close to their maximum theoretical values, ± 1 ) were obtained using the finite element method (FEM), applying the commercial software COMSOL Multiphysics. Our proposal comprises a simple and experimentally feasible structure that enables the study of MO phenomena in HMMs, which may find application in future nanostructured magnetoplasmonic metamaterials for active nanophotonic devices. [ABSTRACT FROM AUTHOR]

This communication presents a novel technique for obtaining bistatic radar cross sections (RCSs) extracted from a monostatic scattering field dataset using a discrete scattering center model and basis pursuit denoising (BPDN) algorithm, which is compressive sensing (CS) technique. With the high-frequency assumption, a complex vector of independent point sources is formulated in a monostatic configuration for a geometrical relationship among the transmitter, receiver, and equivalent scatterers. A matrix equation for the scattering problem of an underdetermined form is effectively calculated by an iterative BPDN solver. Then, compensating the phase difference in the bistatic condition can derive the bistatic RCS at specific frequency points and observation angles. The accuracy of the proposed method for extracting bistatic results is verified using two numerical examples, and the performance of the method in terms of measurement efficiency and data resolution in frequency and angle domains is compared with that of conventional method. [ABSTRACT FROM AUTHOR]

A novel approach based on the use of a resistor-loaded meta-surface (RL-MS) with optimized resistor values is proposed for scattering control in wideband conformal phased arrays. Specifically, the resistance of the loaded resistor in each RL-MS element is varied. As a result, the proposed RL-MS structure not only absorbs incident EM waves but also scatters the remainders away from threatening directions. To accelerate the design process, the scattering matrix approach is used to calculate the scattering patterns efficiently. Proper resistor element distribution can be achieved by optimizing the scattering characteristics. The RL-MS structure is used as the cover layer of a wideband conformal array. By loading the optimized resistors, scattering in the proposed array is reduced to a relatively low level with little degradation of radiation performances. The final designed array achieves 3:1 impedance bandwidth with scanning up to $\pm 60^{\circ }/\pm 45^{\circ }$ in the E-/H-plane. Remarkably, a monostatic scattering reduction of approximately 30 dB is observed throughout the X-band in the simulated results of the optimized array. To demonstrate the effectiveness of this design, prototype arrays are fabricated and measured. The measured results are in reasonable agreement with the simulated results. [ABSTRACT FROM AUTHOR]

All elements of the scattering matrix have been numerically studied for particles of irregular shapes whose size is much larger than incident wavelength. The calculations are performed in the physical optics approximation for a particle size of 20 μm at a wavelength of 0.532 μm. Here the scattered intensity reveals the backscattering coherent peak. It is shown that the polarization elements of the matrix reveal the surges within the backscattering peak. The angular width of the surges does not practically depend on particle shape, but depends on the particle size. It is shown that these surges are created by interference between the conjugate scattered waves propagating in the inverse directions. The results obtained are of interest for interpretation of lidar measurements in cirrus clouds. [ABSTRACT FROM AUTHOR]

This paper presents a model to predict the shielding effectiveness (SE) and resonant modes of cylindrical enclosure with apertures or dielectric substrate. In this model, the Robinson equivalent circuit model (RECM) is introduced to deal with aperture impedance, and the extended form of the Baum–Liu–Tesche equation is deduced to calculate the induced voltage in the enclosure. The electromagnetic topology (EMT) model is established to analyze the process of energy transmission inside the enclosure. The energy propagation coefficient matrix and the scattering coefficient matrix are calculated to deal with the SE results of the observation point. To quantify the efficiency of the proposed model, the calculation results are compared with the full-wave transmission line matrix method (TLM) and RECM through the Fréchet distance. The comparison results show that the accuracy of the proposed model is better over a wide frequency range compared with RECM, and meanwhile, it consumes less run time and fewer CPU resources than traditional numerical methods. The validity of the presented model is verified by TLM. [ABSTRACT FROM AUTHOR]

Current research is dedicated to the development of new theoretical model for guide polarization converter with irises. New created model is derived based on the equivalent circuits and transmission line representations. Specific feature of the model consists in the possibility of account of irises thickness in the simulations by approximate single-mode method. Using equivalent lumped elements of the circuits we obtained general scattering matrices of the polarization transformer for fundamental modes of vertical and horizontal linear polarizations. Besides, numerical simulations and optimization of the device were carried out by finite elements method. Good agreement of obtained optimal sizes and polarization characteristics is observed. Provided by the polarizer phase difference between two orthogonal polarizations falls within range 90°±5° in the operating Ku-band. Calculated ellipticity coefficient is better than 1.5 dB. Developed model can be applied for designing of new waveguide polarization converters, filters and other waveguide components with irises. [ABSTRACT FROM AUTHOR]

The presented method describes reflection and transmission of electromagnetic waves at multiple closely stacked metal grids using multimodal S-parameter propagation. For that, the periodic surface admittance curve of every metal layer was determined through a novel semianalytic approach that uses simple Fourier transformations instead of solving an integral equation. The modal components of this surface admittance were used to express the generalized scattering matrices of the individual grids. By applying multimodal propagation techniques to the resulting scattering parameters, it was possible to model the electromagnetic interactions within a multilayer stack of periodic impedance sheets. Resulting reflection and transmission parameters perfectly matched the corresponding full-wave simulations even above the grating lobe regime. In the end, the universal mode propagation method enabled modeling of a layer stack, connected to lumped components. [ABSTRACT FROM AUTHOR]

The concept of digital twins (DTs) for reflectarray (RA) unit cells (UCs) is discussed and implemented by exploiting electromagnetic-driven machine learning (ML) techniques. Toward this end, several open challenges are addressed, such as the reliability and the effectiveness of using surrogates for modeling different, in terms of descriptors and complexity, UCs, the accuracy in predicting the scattering matrix entries of both single- and dual-polarization elements, the implementation of effective and efficient strategies for the setup of the training set, and the definition of generalized and robust guidelines for the use of popular ML techniques to the problem at hand. Representative results of an extensive numerical validation are presented to assess the performance and the potentialities of DTs when dealing with different RA modeling problems and training sets. [ABSTRACT FROM AUTHOR]

In this paper, we propose a Regge-pole model with a Gaussian potential to study hadron scattering at high energies. In the diffraction approximation, considering the consequences of the analyticity and unitarity of the scattering amplitude, expressions are obtained for the matrix of the scattering amplitude, the cross section, and the slope of the diffraction cone for reactions a + A → B + b. The resulting expressions are applied to p-p scattering. The results obtained show that the model describes well the slope coefficient of the diffraction cone at energies below 102 GeV. To obtain agreement with the experiment at high energies, the parameters should be adjusted. [ABSTRACT FROM AUTHOR]

This article presents a robust method for detecting multiple outliers from multidimensional data using robust Mahalanobis distance. Initial scatter matrix for robust Mahalanobis distance is constructed using a robust estimator of covariance ( S n C o v ) established from a robust scale estimator Sn and casewise median are chosen to be the location vector. The performance of the proposed method is evaluated using the results of simulated samples. This outlier detection method is compared with some well-known methods available in the current literature. The application of the proposed method in real-life data is also executed in this article. [ABSTRACT FROM AUTHOR]

Based on the chemical reaction model proposed by Park, the 'blackout' of a reentry vehicle is studied in this paper. The temperature, pressure and electron density distribution characteristics around the reentry vehicle were simulated at various flight speeds and altitudes by USim. Subsequently, the scattering matrix method was used to study the transmission characteristics of terahertz waves in 'blackout'. The simulation results show that the temperature around the aircraft is mainly affected by speed, the pressure is mainly affected by the altitude and electron density is affected by both of these factors. The calculation results show that the transmission characteristics of terahertz waves in plasma are mainly affected by electron density, while the effects of temperature and pressure cannot be ignored either. [ABSTRACT FROM AUTHOR]

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The influence of the geometry of a TEM horn being a part of the infinite cophased array of irregular horns with the metallized interhorn space on the matching band of the array is investigated. The frequency dependences of the reflection coefficient are analyzed within the framework of the smooth transition in the Floquet channel for different laws of the change of the wave impedance. This analysis is performed with the use of the following two methods of the waveguide theory: the cross-section method and the scattering matrix method. In addition, the numerical modeling with the use of the finite element method is applied. [ABSTRACT FROM AUTHOR]

With the continuous development of China's economy and society and the gradual reform of various industries, the modern folk opera performance art has received more and more attention, and through the excavation of features in the folk opera performance art, the modern folk opera performance level can be promoted. This paper proposes a generalised principal component analysis (PCA) feature extraction method, which first reorganizes the image matrix, constructs the overall scatter matrix based on the reorganized image matrix, and then finds the best projection vector for feature extraction. The proposed method is a further extension of the 2DPCA module, which can build a scatter matrix of arbitrary dimensions and obtain a projection vector of arbitrary dimensions. The results show that the best feature extraction is achieved by optimising the SVM with a principal component contribution of 50% and using the grid search algorithm. The smaller the dimension of the scatter matrix, the stronger the feature extraction ability of the generalised principal component analysis and the faster the feature extraction speed. [ABSTRACT FROM AUTHOR]