Linear Vector Research Articles

In-flight validation of the Metis visible-light polarimeter coronagraph on board Solar Orbiter

Context. The Metis coronagraph is one of the remote sensing instruments of the ESA-NASA Solar Orbiter mission. The goal for the instrument is to enable the study of the solar atmosphere and solar wind by simultaneously acquiring images of the solar corona at two different wavelengths: visible light (VL), within a band ranging from 580 nm to 640 nm, and ultraviolet light, in the HI Lyα 121.6 ± 10 nm. The visible-light channel of the coronagraph includes a polarimeter with electro-optically modulating liquid crystal variable retarders to measure the linearly polarized brightness of the K-corona and derive the electron density. Aims. In this paper, we present the first in-flight validation results of the Metis polarimetric channel together with a comparison to the on-ground calibrations. This paper seeks to validate the first use of an electro-optical device, the liquid crystal-based polarimeter, in deep space and within a hard radiation environment. Methods. We used the orientation of the K-corona’s linear polarization vector during the roll maneuvers of the Space Orbiter spacecraft for the in-flight calibration. Results. The Metis coronagraph on board the Solar Orbiter shows good agreement with the on-ground measurements. The in-flight validation confirms the expected performance of the visible-light channel polarimeter. Furthermore, a comparison between the first polarized brightness value obtained by Metis and the polarized brightness values obtained by the space-based coronagraph LASCO and the ground-based coronagraph K-Cor shows the consistency of the Metis calibrated results.

Multiview synthetic aperture radar target recognition method using joint sparse representation and random weight matrix

Multiview synthetic aperture radar (SAR) images could provide richer information for target recognition as reported in previous works. This study exploits multiview SAR images with application to target recognition via the combination of joint sparse representation (JSR) and random weight matrix. First, the multiview SAR images are clustered into several view sets via a coarse clustering algorithm. In this way, the views in each set tend to share high correlations so they can be properly represented with JSR. For the reconstruction errors from different views, they are fused through a random weight matrix, which includes a rich set of linear weight vectors. Afterwards, the fused errors at different choices of weight vectors are analyzed to form a decision value for target recognition, which could better reflect the differences between different classes through multiview SAR images in comparison with traditional JSR-based methods. Therefore, the overall SAR target recognition performance can be effectively enhanced. Experiments are investigated on the moving and stationary target acquisition and recognition dataset under several operating conditions. The results reveal the high effectiveness of the proposed method under standard operating condition and good robustness under typical extended operating conditions including depression angle variance, configuration variants, noise corruption, partial occlusion, and resolution variance.

Spatial Market Integration, Price Transmission and Transaction Costs in Major Onion Markets of India

The price information is one of the prime objectives of marketing strategies, and the farmers are unable to determine the marketing strategies without knowing the price movements of the agricultural commodities. In this context, the study has examined the spatial price integration among four major onion markets using the threshold vector error correction model (TVECM) that takes into account transaction costs in the price adjustment process. Augmented Dickey–Fuller and Phillips–Perron tests for unit root suggest that the time series is I(1). The application of the Johansen cointegration technique supports the presence of long-run price association and equilibrium in all pairs of onion markets. The Granger Causality test unveils that Bengaluru Granger causes all the markets except Kolkata. The Hansen and Seo supreme Lagrange Multiplier ( SupLM) test of linearity suggests that non-linear TVECM with one threshold and two regimes is best fit for the underlying data for three pairs of markets. While the rest of the three pairs, the SupLM test rejects the null of linearity, therefore, linear vector error correction model (VECM) is estimated. Finally, VECM and TVECM results reveal that Mumbai and Bengaluru are dominant markets in price formation in rest of the markets. Against these findings, it is suggested that the prices should be stabilised in the dominant markets so that the price shocks are not transferred to other markets. The threshold parameter, which is analogous to transaction cost, reveals the high transaction costs between the selected markets pairs, especially Mumbai and Delhi. One of the reasons for the high transaction costs may be the inefficiencies in infrastructure and communication. While a more correct explanation for this difference can be attributed to the differences in marketing fees, taxes, commission charges, license fees, etc., across the spatially separated agricultural markets. JEL Codes: Q1, Q13, D4, C22, D23

Adaptive partition of unity interpolation method with moving patches

The adaptive partition of unity interpolation method, introduced by Aiton and Driscoll, using Chebyshev local interpolants, is explored for interpolating functions with sharp gradients representing two-medium problems. For functions that evolve under vector fields, the partition of unity patches (covers) can be shifted and resized to follow the changing dynamics of local profiles. The method is tested for selected 1D and 2D two-medium problems with linear divergence-free vector fields. In those cases, the volume fraction in each patch contributing to volume conservation throughout the domain can be kept in high accuracy down to machine precisions. Applications that could benefit from the method include volume tracking and multiphase flow modeling.

High-quality micro/nano structures of 4H-SiC patterning by vector femtosecond laser

High-intensity femtosecond laser processing of hard and brittle materials such as silicon carbide (SiC) has poor surface quality and is prone to micro-cracks, making it difficult to meet the application requirements of silicon carbide microdevices. In this study, a method for fabricating high-quality micro-nanostructures of 4H-SiC using vector polarized light was proposed. The influences of linear polarization and vector polarization on the quality and surface morphology of processed SiC microgrooves were studied, and the micromachined size rule of microgrooves machined under different pulse numbers was summarized. The damage distribution of microstructures machined by linearly polarized light and vector polarized light were characterized by confocal Raman mapping. The study had shown that using vector beam, especially azimuthal polarization beam, can ensure the uniformity of the processing area, effectively reduce micro-cracks and chipping in the processing of hard and brittle materials, and obtain better processing quality. In addition, the vector polarized light can avoid the large microgroove taper during the processing, and ensure good structure size. Finally, a high-quality multi-ring structure was fabricated by an azimuthal polarization beam, which provides an accurate method for preparing microstructures with excellent performance.

Preliminary examination of influence of Chlorophyll, Total Suspended Material, and Turbidity on Satellite Derived-Bathymetry estimation in coastal turbid water

The satellite-Derived Bathymetry (SDB) has been researched for almost the past five decades, but the application of SDB for operational use is still in its initial stages. The higher concentration of suspended material is a major barrier in assessing bathymetry accurately with remote sensing data. The influence of various optically active substances (OAS) needs to be quantified to develop a more robust SDB algorithm. The goal of the study is to improve the accuracy of SDB by understanding the spatial distribution of Chlorophyll (Chl), Total Suspended Material (TSM), and Turbidity in coastal water. A preliminary investigation using the numerical analysis between Landsat-7 & 8 spectral bands, OAS parameters, and bathymetry is presented in this paper. SDB has been derived using three machine learning algorithms; Linear, Random Forest (RF), and Support Vector Machine (SVM) Regression. The resulting SDB residuals have been analyzed in relation to Chlorophyll, Turbidity, and TSM in coastal seawater. The study found that most of the erroneous SDB residuals and extreme values were distributed in high or medium concentrated OAS regions. The result of the study may further enhance SDB estimation accuracy by considering the influence of the above three OAS in coastal waters.

Polarisation of molecular lines in the circumstellar envelope of the post-asymptotic giant branch star OH 17.7–2.0

Context. The role of magnetic field in shaping planetary nebulae (PNe), either directly or indirectly after being enhanced by binary interaction, has long been a topic of debate. Large-scale magnetic fields around pre-PNe have been inferred from polarisation observations of masers. However, because masers probe very specific regions, it is still unclear if the maser results are representative of the intrinsic magnetic field in the circumstellar envelope (CSE). Aims. Molecular line polarisation of non-maser lines can provide important information about the magnetic field. A comparison between the magnetic field morphology determined from maser observations and that observed in the more diffuse CO gas can reveal if the two tracers probe the same magnetic field. Methods. We compared observations taken with the Atacama Large Millimeter/submillimeter Array (ALMA) of molecular line polarisation around the post-asymptotic giant branch (post-AGB) or pre-PN star OH 17.7−2.0 with previous observations of polarisation in the 1612 MHz OH maser region. Earlier mid-infrared observations indicate that OH 17.7−2.0 is a young bipolar pre-PN, with both a torus and bipolar outflow cavities embedded in a remnant AGB envelope. Results. We detect CO J = 2 − 1 molecular line polarisation at a level of ∼4% that displays an ordered linear polarisation structure. We find that, correcting for Faraday rotation of the OH maser linear polarisation vectors, the OH and CO linearly polarised emission trace the same large-scale magnetic field. A structure function analysis of the CO linear polarisation reveals a plane-of-the-sky magnetic field strength of B⊥ ∼ 1 mG in the CO region, consistent with previous OH Zeeman observations. Conclusions. The consistency of the ALMA CO molecular line polarisation observation with maser observations indicate that both can be used to determine the magnetic field strength and morphology in CSEs. The new observations indicate that the magnetic field has a strong toroidal field component projected on the torus structure and a poloidal field component along the outflow cavity. The existence of a strong, ordered, magnetic-field around OH 17.7−2.0 indicates that the magnetic field is likely involved in the formation of this bipolar pre-PN.

Granger causality analysis of internal tongue muscles in tongue protrusion from diffusion and tagged MRI

The human tongue is a muscular hydrostat, comprising a group of orthogonally oriented and interdigitated muscles without skeletal support. Key characteristics of the tongue as a muscular hydrostat include that the tongue’s volume is constant, and any decrease in one dimension will be compensated by an increase in another dimension. This work aims to identify causal relationships among internal muscles in protrusive muscle contractions, which is vital to understand their underlying muscle coordination patterns. We investigated four muscles known to contribute to tongue protrusion, including transverse, verticalis, superior longitudinal, and genioglossus muscles. To capture tongue structure and function, we acquired diffusion MRI and tagged MRI to estimate the muscle fiber geometry of the four muscles and the motion patterns of tongue protrusion, respectively. We first computed Lagrangian strains along muscle fiber direction in each voxel, reflecting muscle fiber shortening. Average strain values in each muscle, defined by a vocal tract atlas, were then input into a linear vector autoregression Granger causality model, to investigate their causal relationships. Our findings on the strain patterns over time as well as the pairwise causal relationships were consistent in part with the muscular hydrostat theory, which helps elucidate the tongue muscle coordination patterns.

The Catastrophe of Corruption in the Sustainability of Foreign aid: A Prediction of Artificial Neural Network Method in Indonesia

The rising corruption levels in Indonesia are becoming a cause for concern and raise doubts about their impact on the stability of foreign aid in the country. Therefore, this study aims to predict the long-term viability of foreign aid in Indonesia based on international perceptions of corruption and corruption cases in the country. Data were obtained from World Governance Indicators, the Indonesian Ministry of Finance, and the World Bank, and the study used a backpropagation artificial neural network (ANN) for prediction. The results from ANN are compared to linear models and vector autoregression (VAR). The finding shows that ANN outperforms the other models based on the coefficient of determination and MSE values. Furthermore, it highlights the strong relationship between corruption perception and foreign aid sustainability with an R-value of 0.991. According to the ANN estimation, gratification has a significant impact on foreign aid. In response to this finding, the study recommends the Indonesian government take action to combat corruption in maintaining the international trust and ensuring the stability of foreign aid.

Inherent color symmetry in quantum Yang-Mills theory

We present the basic non-perturbative structure of the space of classical dynamical solutions and corresponding one particle quantum states in SU(3) Yang-Mills theory. It has been demonstrated that the Weyl group of su(3) algebra plays an important role in constructing non-perturbative solutions and leads to profound changes in the structure of the classical and quantum Yang-Mills theory. We show that the Weyl group as a non-trivial color subgroup of SU(3) admits singlet irreducible representations on a space of classical dynamical solutions which lead to strict concepts of one particle quantum states for gluons and quarks. The Yang-Mills theory is a non-linear theory and, in general, it is not possible to construct a Hilbert space of classical solutions and quantum states as a linear vector space, so, usually, a perturbative approach is applied. We propose a non-perturbative approach based on Weyl symmetric solutions to full non-linear equations of motion and construct a full space of dynamical solutions representing an infinite but countable solution space classified by a finite set of integer numbers. It has been proved that the Weyl singlet structure of classical solutions provides the existence of a stable non-degenerate vacuum which serves as a main precondition of the color confinement phenomenon. Some physical implications in quantum chromodynamics are considered.

Measuring the Effect of Off-Balancing Vectors on the Delivery of High-Quality CPR during Ambulance Transport: A Proof of Concept Study

Aim This study aims to demonstrate the feasibility of quantifying the off-balancing vectors experienced during ambulance transport and comparing them to high-quality cardiopulmonary resuscitation (HQ-CPR) metrics. Methods Ten participants completed a total of 20 evolutions of compression-only HQ-CPR in an ambulance driven in a manner that minimized or increased linear and angular off-balancing vectors. Linear and angular velocity, linear and angular acceleration, and linear jerk were recorded. HQ-CPR variables measured were compression fraction and proportion of compressions with depth >5 cm (depth%), rate 100–120 (rate%), full chest recoil (recoil%), and hand position (hand%). A composite score was calculated: [(depth% + rate% + recoil% + hand%)/4) * compression fraction]. Difficulty of HQ-CPR performance was measured with the Borg rating of perceived exertion (RPE) Scale. A series of mixed effects models were fitted regressing each HQ-CPR metric on each off-balancing vector. Results HQ-CPR data and vector quantity data were successfully recorded in all evolutions. Rate% was negatively associated with increasing linear velocity (slope = −3.82, standard error [SE] 1.12, p = 0.005), linear acceleration (slope = −5.52, SE 1.93, p = 0.013), linear jerk (slope = −17.60, SE 5.78, p = 0.007), angular velocity (slope = −75.74, SE 22.72, p = 0.004), and angular acceleration (slope = −152.53, SE 59.60, p = 0.022). Compression fraction was negatively associated with increasing linear velocity (slope = −1.35, SE 0.37, p = 0.004), linear acceleration (slope = −1.67, SE 0.48, p = 0.003), linear jerk (slope = −4.90, SE 1.86, p = 0.018), angular velocity (slope = −25.66, SE 6.49, p = 0.001), and angular acceleration (slope = −45.35, SE 18.91, p = 0.031). Recoil% was negatively associated with increasing linear velocity (slope = −5.80, SE 2.21, p = 0.023) and angular velocity (slope = −116.96, SE 44.24, p = 0.019)). Composite score was negatively associated with increasing linear velocity (slope = −4.49, SE 1.45, p = 0.009) and angular velocity (slope = −86.13, SE 31.24, p = 0.014) and approached a negative association with increasing magnitudes of linear acceleration (slope −5.54, SE 2.93, p = 0.075), linear jerk (slope = −17.43, SE 8.80, p = 0.064), and angular acceleration (slope = −170.43, SE 80.73, p = 0.051). Borg RPE scale was positively associated with all off-balancing vectors. Depth%, hand%, mean compression depth, and mean compression rate were not correlated with any off-balancing vector. Conclusion Off-balancing vector data can be successfully quantified during ambulance transport and compared with HQ-CPR performance parameters. Increasing off-balancing vectors experienced during ambulance transport are associated with worse HQ-CPR metrics and increased perceived physical exertion. These data may help guide future drive styles, ambulance design, or use of mechanical CPR devices to improve HQ-CPR delivery during selected patient transport scenarios.

Price discovery in equity markets: A state-dependent analysis of spot and futures markets

This paper investigates the potentially time-varying importance of spot and futures markets in the price discovery process of financial assets. For this purpose, we generalize the concept of component shares and information shares to allow for state-dependent relevance of different markets over time. Instead of using a linear vector error correction model (VECM) to construct the component shares and information shares as it is common in the literature, we employ a Markov-switching VECM with time-varying adjustment behaviour and state-dependent covariance matrices. Simulation results confirm that state-dependent component shares and information shares can be estimated consistently within this framework. We apply our approach to spot and futures prices for different stock indices such as EuroStoxx50, FTSE100, Nikkei225, and SP500. We find a clear state probability pattern over the trading day that closely resembles the well-studied volatility smile and might be related to the presence of heterogeneous agents in those markets.

Finite Algebras for Solid Modeling using Julia’s Sparse Arrays

An early research in solid modeling led by Herbert Voelcker at the University of Rochester and later at Cornell suggested that every solid representation scheme corresponds to an algebra, where the elements of the algebra are solid representations constructed and edited using operations in the algebra. For example, every CSG representation describes an element in a finite Boolean algebra of closed regular sets, whereas every boundary representation describes an element of a vector space of 2-chains in an algebraic topological chain complex. In this paper, we elucidate the precise relationships (functors) between all algebras used for CSG and boundary representations of solids. Based on these properties, we show that many solid modeling operations, including boundary evaluation, reduce to straightforward algebraic operations or application of identified functors that are efficiently implemented using point membership tests and sparse matrix operations. To fully exploit the efficacy of the new algebraic approach to solid modeling, all algorithms are fully implemented in Julia, the modern language of choice for numerical and scientific computing. • New research direction in solid modeling. • Algebraic relationships between CSG and boundary representations of PL solids. • Arrangements are isomorphic to the finite Boolean algebra of regularized sets. • This algebra is isomorphic to a linear vector space of 3-chains. • Operations on CSG and b-reps reduce to composition of algebraic operations. operations.

Comparison of Regression Algorithms to Predict Average Air Temperature

Regression algorithms are statistical techniques used to predict the value of a dependent variable, based on one or more independent variables. These algorithms are commonly used in fields such as economics, finance, and engineering. Temperature prediction is a specific application of regression analysis. In this case, the dependent variable is temperature and the independent variables include factors such as humidity, speed of the wind, direction of the wind, and precipitation. There are many different types of regression algorithms, each with its strengths and weaknesses. The study compares the performance of multiple regression models in predicting the average air temperature, using one month's weather data for the Beşiktaş district of Istanbul. A total of 6 different regression models, including ridge, lasso, linear, polynomial, random forest (RF), and support vector (SV) regressions, were included in the study. Among the regression models trained and tested on two different data sets, the three most successful models in predicting average air temperature were lasso, RF, and polynomial regressions (PRs), respectively.

Study of the Hypergeometric Equation via Data Driven Koopman-EDMD Theory

We consider a data-driven method, which combines Koopman operator theory with Extended Dynamic Mode Decomposition. We apply this method to the hypergeometric equation which is the Fuchsian equation with three regular singular points. The space of solutions at any of its singular points is a two-dimensional linear vector space on the field of reals when the independent variable is restricted to take values in the real axis and the unknown function is restricted to be a real-valued function of a real variable. A basis of the linear vector space of solutions is spanned by the hypergeometric function and its products with appropriate powers of the independent variable or the logarithmic function depending on the roots of the indicial equation of the hypergeometric equation. With our work, we obtain a new representation of the fundamental solutions of the hypergeometric equation and relate them to the spectral analysis of the finite approximation of the Koopman operator associated with the hypergeometric equation. We expect that the usefulness of our results will come more to the fore when we extend our study into the complex domain.

Direction of dependence analysis for pre-post assessments using non-Gaussian methods: a tutorial

Objective We introduced methods for solving causal direction of dependence between variables observed in pre- and post-psychotherapy assessments, showing how to apply them and investigate their properties via simulations. In addition, we investigated whether changes in depressive symptoms drive changes in social and occupational functioning as suggested by the phase model of psychotherapy or vice versa, or neither. Method As a Gaussian (normal-distribution) model is unidentifiable here, we used an identifiable linear non-Gaussian structural vector autoregression model, conceptualizing instantaneous effects as during-psychotherapy causation and lagged effects as pre-treatment predictors of change. We tested six alternative estimators in six simulation settings that captured different real-world scenarios, and used real psychotherapy data from 1428 adult patients (Finnish Psychotherapy Quality Registry; assessments on Patient Health Questionnaire-9 and Social and Occupational Functioning Assessment Schedule). Results The methodology was successful in identifying causal directions in simulated data. The real-data results provided no evidence for single direction of dependence, suggesting shared or reciprocal causation. Conclusions A powerful new tool was presented to investigate the process of psychotherapy using observational data. Application to patient data suggested that depression symptoms and functioning may reciprocate or reflect third variables instead of one predominantly driving the other during psychotherapy.

FRF-based probabilistic modal parameter identification of structures with known seismic input

In this study, an FRF based Bayesian approach is presented for modal identification of civil structures with known seismic input. The proposed method utilizes the statistical properties of frequency response function (FRF) of the observed structure which is obtained from the acceleration response (output) and the seismic input recorded at the base level. In this context, first, the joint pdf of prediction error term and seismic input is derived. Then, applying a linear vector transformation, the output term in the derived joint pdf is defined as depending on the FRF and the seismic input. Finally, the marginal probability of FRF is obtained as a complex ratio distribution from the transformed joint pdf. The posterior probability function for modal parameters is obtained by using Bayes’ theorem. The modal parameters are obtained by maximum likelihood estimation of the constructed probability density function. Finally, the posterior uncertainties for modal parameters are calculated. Two numerical and two real data examples are presented to illustrate the computational efficiency of the proposed methodology against input–output and output only techniques.

PTA-Sync: Packet-Train-Aided Time Synchronization for Underwater Acoustic Applications

In underwater acoustic applications, time synchronization errors accumulate severely with time, owing to the unpredictable propagation delay change induced by mobility and low sound propagation speed. In previously reported schemes, error accumulation during underwater acoustic time synchronization occurred, decreasing their performance and affecting their applicability. To overcome this limitation, we propose packet-train-aided time synchronization (PTA-Sync) for underwater acoustic application. The proposed PTA-Sync adaptively tracks one-way travel time (OWTT) change using three-dimensional linear velocity vector, the transmit time difference and arrival time difference of two adjacent packets in a packet train, and the position information of a mobile reference node. Thus, this scheme enables us to reduce the synchronization error accumulation rate by estimating the propagation delay change more accurately. Simulation results show PTA-Sync achieves higher accuracy than existing OWTT-based synchronization schemes. Thus, PTA-Sync can be effectively used in underwater exploratory activities because it can successfully reduce time synchronization errors.

Fredholm boundary-value problem for the system of fractional differential equations.

This paper deals with the study of Fredholm boundary-value problem for the system of fractional differential equations with Caputo derivative. The boundary-value problem is specified by linear vector functional such that the number of it components does not coincide with the dimension of the system of fractional differential equations. We first considered the general solution of the system of fractional differential equations that consist with the general solution of the associated homogeneous system and the arbitrary particular solution of the inhomogeneous system. The particular solution we found is a solution of the system of linear Volterra integral equations of the second kind with weakly singular kernels. Further, by using the theory of pseudo-inverse matrices, we established conditions that should be imposed on the coefficients of the original problem to guarantee that the indicated boundary conditions are satisfied. Moreover, a family of linearly independent solutions of this boundary-value problem is constructed. The specific examples are provided to verify the effectiveness of the proposed approach.

Nonequilibrium diffusion processes via non-Hermitian electromagnetic quantum mechanics with application to the statistics of entropy production in the Brownian gyrator.

The nonequilibrium Fokker-Planck dynamics in an arbitrary force field f[over ⃗](x[over ⃗]) in dimension N is revisited via the correspondence with the non-Hermitian quantum mechanics in a real scalar potential V(x[over ⃗]) and in a purely imaginary vector potential [-iA[over ⃗](x[over ⃗])] of real amplitude A[over ⃗](x[over ⃗]). The relevant parameters of irreversibility are then the N(N-1)/2 magnetic matrix elements B_{nm}(x[over ⃗])=-B_{mn}(x[over ⃗])=∂_{n}A_{m}(x[over ⃗])-∂_{m}A_{n}(x[over ⃗]), while it is enlightening to explore the corresponding gauge transformations of the vector potential A[over ⃗](x[over ⃗]). This quantum interpretation is even more fruitful to study the statistics of all the time-additive observables of the stochastic trajectories, since their generating functions correspond to the same quantum problem with additional scalar and/or vector potentials. Our main conclusion is that the analysis of their large deviations properties and the construction of the corresponding Doob conditioned processes can be drastically simplified via the choice of an appropriate gauge for each purpose. This general framework is then applied to the special time-additive observables of Ornstein-Uhlenbeck trajectories in dimension N, whose generating functions correspond to quantum propagators involving quadratic scalar potentials and linear vector potentials, i.e., to quantum harmonic oscillators in constant magnetic matrices. As simple illustrative example, we finally focus on the Brownian gyrator in dimension N=2 to compute the large deviations properties of the entropy production of its stochastic trajectories and to construct the corresponding conditioned processes having a given value of the entropy production per unit time.