First-order Matrix Research Articles

Design and alignment of an all-spherical unobscured four-mirror image relay for an ultra-broadband sub-petawatt laser.

We describe the design and alignment of an unobscured reflective image relay for use in an ultra-broadband half-petawatt laser system in development at the University of Rochester's Laboratory for Laser Energetics. The design consists of four spherical mirrors in an unobscured configuration. We show the theoretical basis for such a four-mirror design using first-order optical matrix methods and nodal aberration theory. We also describe the process of aligning this design in a test bed and show the results of this alignment method. We were able to achieve a diffraction-limited nominal design. Upon aligning the design in our test bed, we were able to successfully align the design to achieve our target wavefront error of less than 0.3 waves peak to valley and 0.07 waves rms at the central laser-operating wavelength of 910 nm.

Differential Mueller matrix imaging of partially depolarizing optically anisotropic biological tissues

Since recently, a number of innovative polarization-based optical imaging modalities have been introduced and extensively used in various biomedical applications, with an ultimate aim to attain the practical tool for the optical biopsy and functional characterization of biological tissues. The techniques utilize polarization properties of light and Mueller matrix mapping of microscopic images of histological sections of biological tissues or polycrystalline films of biological fluids. The main drawback of currently developed laser polarimetry approaches and Mueller matrix mapping techniques is poor reproducibility of experimental data. This is due to azimuthal dependence of polarization and ellipticity values of most matrix elements to sample orientation in respect to incidence light polarization. Current study aims to generalize the methods of laser polarimetry for diagnosis of partially depolarizing optically anisotropic biological tissues. A method of differential Mueller matrix mapping for reconstruction of linear and circular birefringence and dichroism parameter distributions of partially depolarizing layers of biological tissues of different morphological structure is introduced and practically implemented. The coordinate distributions of the value of the first-order differential matrix elements of histological sections of brain tissue with spatially structured, optically anisotropic fibrillar network, as well as of parenchymatous tissue of the rectum wall with an “islet” polycrystalline structure are determined. Within the statistical analysis of polarization reproduced distributions of the averaged parameters of phase and amplitude anisotropy, the significant sensitivity of the statistical moments of the third and fourth orders to changes in the polycrystalline structure of partially depolarizing layers of biological tissue is observed. The differentiation of female reproductive sphere connective tissue is realized with excellent accuracy. The differential Mueller matrix mapping method for reconstruction of distributions of linear and circular birefringence and dichroism parameters of partially depolarizing layers of biological tissues of different morphological structures is proposed and substantiated. Differential diagnostics of changes in the phase (good balanced accuracy) and amplitude (excellent balanced accuracy) of the anisotropy of the partially depolarizing layers of the vagina wall tissue with prolapse of the genitals is realized. The maximum diagnostic efficiency of the first-order differential matrix method was demonstrated in comparison with the traditional methods of polarization and Mueller matrix mapping of histological sections of light-scattering biological tissues.

First-order derivative matrix of a ray: a simple and flexible alternative computation method.

The present group previously proposed a method for determining the first-order derivative matrix (i.e., the Jacobian matrix) of a skew ray by taking all the independent variables of the optical system as the system variable vector, X¯sys. However, many trigonometric function calls, divisions, multiplications and additions were required to determine the ray Jacobian matrix with respect to X¯sys. Accordingly, in the present study, the angular variables in the system variable vector, X¯sys, are replaced with their respective cosine and sine trigonometric functions. The boundary variable vector, X¯i, is similarly redefined such that it includes no angular variables. The proposed method has three main advantages over that previously reported: 1) it is valid for any pose matrix, irrespective of the order in which the rotation and translation motions of a boundary are assigned; 2) it involves only polynomial differentiation, and is thus easily implemented in computer code; and 3) the computation speed of ∂X¯i/∂X¯i ∂X¯sys ∂X¯sys is improved by a factor of approximately ten times.

Thermodynamic behavior and flotation kinetics of an ionic liquid microemulsion collector for coal flotation

To develop a new type of coal slime collector, an ionic liquid microemulsion was prepared using 1-alkyl-3-methylimidazolium chloride ([Cnmim]Cl, where n = 12, 14, or 16) as a surfactant, n-alcohol (n-butanol, n-pentanol or n-hexanol) as a cosurfactant, and n-dodecane as the oil phase, and the interfacial composition and thermodynamic changes of these systems were investigated using Schulman’s titration. Therefore, the [C16mimCl]/n-dodecane/n-pentanol/water microemulsion system was chosen as the microemulsion collector. Moreover, the droplet size and polydispersity index (PDI) of the microemulsion collector were determined, and the average droplet radius of the microemulsion was about 32 nm and the PDI was less than 0.06. The average droplet radius was found to range from 30 to 50 nm by transmission electron microscopy analysis. Furthermore, the coal slime flotation experiments and flotation kinetics analysis showed that the microemulsion collector applied for coal slime flotation yielded the same behavior as that of n-dodecane, but the collector dose can be reduced by about 43% and the cost is only 71% without the need for a frother. And, of the four kinetic models tested, the flotation process using the microemulsion collector was consistent with the first-order matrix distribution model.

Exact Solutions for Buckling and Second-Order Effect of Shear Deformable Timoshenko Beam–Columns Based on Matrix Structural Analysis

Shear deformable beams have been widely used in engineering applications. Based on the matrix structural analysis (MSA), this paper presents a method for the buckling and second-order solutions of shear deformable beams, which allows the use of one element per member for the exact solution. To develop the second-order MSA method, this paper develops the element stability stiffness matrix of axial-loaded Timoshenko beam–columns, which relates the element-end deformations (translation and rotation angle) and corresponding forces (shear force and bending moment). First, an equilibrium analysis of an axial-loaded Timoshenko beam–column is conducted, and the element flexural deformations and forces are solved exactly from the governing differential equation. The element stability stiffness matrix is derived with a focus on the element-end deformations and the corresponding forces. Then, a matrix structural analysis approach for the elastic buckling analysis of Timoshenko beam–columns is established and demonstrated using classical application examples. Discussions on the errors of a previous simplified expression of the stability stiffness matrix is presented by comparing with the derived exact expression. In addition, the asymptotic behavior of the stability stiffness matrix to the first-order stiffness matrix is noted.

Design of Terminal Sliding Mode Controllers for Disturbed Non-Linear Systems Described by Matrix Differential Equations of the Second and First Orders

This paper describes a design scheme for terminal sliding mode controllers of certain types of non-linear dynamical systems. Two classes of such systems are considered: the dynamic behavior of the first class of systems is described by non-linear second-order matrix differential equations, and the other class is described by non-linear first-order matrix differential equations. These two classes of non-linear systems are not completely disjointed, and are, therefore, investigated together; however, they are certainly not equivalent. In both cases, the systems experience unknown disturbances which are considered bounded. Sliding surfaces are defined by equations combining the state of the system and the expected trajectory. The control laws are drawn to force the system trajectory from an initial condition to the defined sliding surface in finite time. After reaching the sliding surface, the system trajectory remains on it. The effectiveness of the approaches proposed is verified by a few computer simulation examples.

On the reduction of 2-D polynomial systems into first order equivalent models

In this paper we propose a novel approach for the reduction of a 2-D rectangular polynomial matrix of arbitrary degree, to first-order matrix pencils of the form $$sE_{1}+zE_{2}+A$$, utilizing the framework of zero coprime equivalence (ZC-E). The proposed approach is in turn employed to derive a series of ZC-E matrix pencils, which can be obtained “by inspection” of the coefficients of the original bivariate polynomial matrix. Improving similar constructions of first order pencils available in the literature, our approach results in matrix pencils whose size increases linearly with the degrees of the indeterminates of the original polynomial matrix. From a system-theoretic point of view, the proposed method, provides the algebraic tools to transform a high order bivariate linear system, into a zero coprime system equivalent first order representation. Notably, one of the proposed transformation techniques gives rise to generalized 2$$-D$$ Roesser models.

Predicting the pathological response to chemoradiotherapy of non-mucinous rectal cancer using pretreatment texture features based on intravoxel incoherent motion diffusion-weighted imaging

ObjectivesTo investigate the performance of the mean parametric values and texture features based on intravoxel incoherent motion diffusion-weighted imaging (IVIM-DWI) on identifying pathological complete response (pCR) to neoadjuvant chemoradiotherapy (nCRT) in locally advanced rectal cancer (LARC).MethodsPretreatment IVIM-DWI was performed on 41 LARC patients receiving nCRT in this prospective study. The values of IVIM-DWI parameters (apparent diffusion coefficient, ADC; pure diffusion coefficient, D; pseudo-diffusion coefficient, D* and perfusion fraction, f), the first-order, and gray-level co-occurrence matrix (GLCM) texture features were compared between the pCR (n = 9) and non-pathological responder (non-pCR, n = 32) groups. Receiver operating characteristic (ROC) curves in univariate and multivariate logistic regression analysis were generated to determine the efficiency for identifying pCR.ResultsThe values of IVIM-DWI parameters and first-order texture features did not show significant differences between the pCR and non-pCR groups. The pCR group had lower Contrast and DifVarnc values extracted from the ADC, D, and D* maps, respectively, as well as lower CorrelatD value. Higher CorrelatD*, Correlatf, SumAvergADC, and SumAvergD values were observed in the pCR group. The area under the ROC curve (AUC) values for the individual predictors in univariate analysis ranged from 0.698 to 0.837, with sensitivities from 43.75% to 87.50% and specificities from 66.67 to 100.00%. In multivariate analysis, CorrelatD* (P < 0.001), DifVarncADC (P = 0.024), and DifVarncD (P < 0.001) were the independent predictors to pCR, with an AUC of 0.986, a sensitivity of 93.75%, and a specificity of 100.00%.ConclusionPretreatment GLCM analysis based on IVIM-DWI may be a potential approach to identify the pathological response of LARC.

Emergent Behavior of a Second-Order Lohe Matrix Model on the Unitary Group

We study a second-order extension to the first-order Lohe matrix model on the unitary group which can be reduced to the second-order Kuramoto model with inertia as a special case. For the proposed second-order model, we present several sufficient frameworks leading to the emergence of the complete and practical synchronizations in terms of the initial data and the system parameters. For the identical hamiltonians, we show that the complete synchronization emerges asymptotically. In contrast, for the non-identical hamiltonians, the practical synchronization occurs for some class of initial data when the product of the coupling strength and inertia is sufficiently small.

An Alternative PML Implementation for Arbitrary Media

An efficient implementation of the complex frequency-shifted perfectly matched layer (PML) is proposed to terminate the finite-difference time domain (FDTD) lattices. The proposal is based on the matrix exponential algorithm originally used for modeling frequency dispersive media. As the equations of describing $E (D)$ fields, $H (B)$ fields, and auxiliary variables associated with PML are formulated as a compact first-order differential matrix form, no convolution operations, variable substitutions, or equations rearrangements are needed in its mathematical derivations. Via the concept of generalized material-independent PML, this new implementation can also be used to truncate arbitrary media. Furthermore, since its iteration forms are similar to those of the convolutional PML (CPML) that has been widely used in FDTD simulations, the proposal can be directly applied to existing codes with only minor changes. Meanwhile, it can achieve better absorption effect than CPML. Through a numerical example in terms of the printed F antenna and corresponding analyses of performance and efficiency, we find that the proposal works well as absorbing boundary condition.

TEMPORAL-SPATIAL CHARACTERISTICS AND KEY INFLUENCING FACTORS OF PM2.5 CONCENTRATIONS IN CHINA BASED ON STIRPAT MODEL AND KUZNETS CURVE

China's tremendous economic developments are achieved at the expense of environmental deterioration. In recent years, PM2.5 pollution has become increasingly serious in China, attracting widespread attention from the citizens and the government. This study aims to investigate the temporal spatial characteristics of PM2.5 in China in 1998 2012, fully considering the potential influencing factors of PM2.5. The satellite remote sensing data compensate for the deficiency of surface monitoring data in China, such as minimising bias from data contamination, broad coverage and representing long-term temporal spatial resolution data. A largely expanded list of potential impacting factors is selected based on environmental Kuznets curve (EKC) theory and Stochastic Impacts by Regression on Population, Affluence and Technology (STIRPAT) framework. Moran s I tests are used to examine the spatial correlation of PM2.5, and the pooled regression, spatial lag and time-fixed effects spatial lag models are used and compared to explore the influencing factors of PM2.5. The thresholded first-order inverse distance spatial weight matrix can measure the spatial spillover effect of PM2.5 more accurately by fully considering the effect of distance on spatial influence level. Several important findings are derived. Firstly, China s PM2.5 shows a distinct positive spatial correlation. The local Moran s I test shows that the significant high high PM2.5 agglomeration regions include Beijing Tianjin Hebei region, Yangtze River Delta and central China, connecting the two economic urban agglomerations. Secondly, the regression results of the time-fixed effects spatial lag model indicate that that PM2.5 of a given region increases by 0.362% if the PM2.5 of its ambient region increases by 1%. Thirdly, factors from all perspectives of STIRPAT model are very effective in explaining PM2.5. Fourthly, no inverted U shape EKC is found between the overall economic development level and the PM2.5 concentration in China in 1998-2012.

Klasifikasi Citra X-Ray Diagnosis Tuberkulosis Berbasis Fitur Statistis

Tuberkulosis merupakan salah satu penyebab kematian manusia. Hasil pemeriksaan x-ray diagnosis tuberkulosis dapat dijadikan objek pada proses ekstraksi ciri yang merupakan suatu tahapan dalam mengekstrak ciri/ informasi dari objek yang terdapat pada suatu citra diagnosis tuberkulosis. Pada penelitian ini digunakan metode ekstraksi ciri citra berbasis tekstur statistis orde satu (histogram), orde kedua berbasis Gray-Level Co-occurrence Matrix (GLCM), serta Principle Component Analysis (PCA). Data penelitian diperoleh dari RS Dr. Sardjito Yogyakarta sebanyak 33 citra digital x-ray pasien diagnosis tuberkulosis Tahun 2012 masing-masing 6 citra PA (Postero-Anterior) normal, 19 citra abnormal, 4 citra AP (Antero-Posterior) normal, dan 4 citra AP abnormal. Penelitian ini bertujuan mencari ciri terbaik yang terkandung pada citra x-ray diagnosis tuberkulosis menggunakan analisis tekstur statistis yang diperoleh dari fitur ciri yang terdapat pada metode ekstraksi ciri berbasis tekstur. Fitur ciri yang teridentifikasi antara lain: varians, std deviasi, skewness, kurtosis, contrast dan energy. Klasifikasi menggunakan data input berupa 33 data uji yang dibangun dengan metode Multi Layer Perceptron (MLP), sedang output berupa citra normal dan citra abnormal. Hasil penelitian menunjukkan bahwa akurasi klasifikasi menggunakan metode Histogram (81,81%), metode GLCM (96,96%), metode PCA (81,82%), dan metode kombinasi Histogram GLCM (100%).

Photonic Floquet media with a complex time-periodic permittivity

We study the exceptional point (EP) phenomena in a photonic medium with a complex time-periodic permiitivity, i.e., $\epsilon(t)=\epsilon_o+\epsilon_r*sin(\Omega t+\phi)$. We formulate the Maxwell's equations in a form of first-order non-Hermitian Floquet Hamiltonian matrix and solve it analytically for the Floquet band structures. In the case when $\epsilon_r$ is real, to the first order in $\epsilon_r$, the band structures show a phase transition from an exact phase with real quasienergies to a broken phase with complex quasienergies inside a region of wave vector space, the so-called k-gap. We show that the two EPs at the upper and lower edges of the k-gap have opposite chiralities in the stroboscopic sense. Thus, by picking up the mode with a positive imaginary quasienergy, the wave propagation inside the k-gap can grow exponentially. In three dimensions, such pairs of EPs span two concentric spherical surfaces in the $\vec{k}$ space and repeat themselves periodically in the quasienergy space with Omega as the period. However, in the case when $\epsilon_r$ is pure imaginary, the k-gap disappears and gaps in the quasienergy space are opened. Our analytical results agree well with the finite difference time domain (FDTD) simulations. To the second order in $\epsilon_r$, additional EP pairs are found for both the cases of real and imaginary $\epsilon_r$.

Abstract 2955: A radiomic-based MRI phenotype is uniquely associated with hypermutated genotype in gliomas

Abstract INTRODUCTION Hypermutation is the excessive accumulation of DNA mutation in cancer cells. This specific hypermutated genotype has been reported in low and high grade gliomas, specifically post-temozolomide treatment and is associated with treatment-resistance. Herein, we sought to identify an imaging-based signature for hypermutated gliomas using a radiomics-based approach. MATERIALS AND METHODS In this IRB-approved retrospective study, we analyzed a total of 101 patients with primary gliomas from the University of Texas MD Anderson Cancer Center. Next generation sequencing (NGS) platforms (T200 and Foundation 1) were used to determine the Mutation burden status in post-biopsy (stereotactic/excisional). Patients were dichotomized based on their mutation burden; 77 hypomutated (&amp;lt;30 mutations) and 24 hypermutated (&amp;gt;=30 mutations or &amp;lt;30 with MMR gene or POLE/POLD gene mutations). Radiomic analysis was performed on the conventional MR images (FLAIR and T1 post-contrast) obtained prior to tumor tissue surgical sampling; and a total of 2480 rotation-invariant radiomic features were extracted using: (i) the first-order histogram and (ii) grey level co-occurrence matrix. The Maximum Relevance Minimum Redundancy technique was used to select the most relevant radiomic features. ROC analysis and leave-one-out cross-validation (LOOCV) were used to assess the performance of the Support Vector Machine (SVM) classifier as and AUC, Sensitivity, Specificity, and p-value were obtained. RESULTS We found 100 radiomic features that can discriminate between hypermutated versus hypomutated gliomas, AUC 96.3% (CI: 90.2%-98.9%), Sensitivity 100%, Specificity 95%, p-value=3.769e-6. CONCLUSION Hypermutated gliomas has a unique radiomic quantitative signature that can be used to predict mutation burden regardless of tumor grade or histopathology. Citation Format: Islam Hassan, Aikaterini Kotrotsou, Carlos Kamiya Matsuoka, Kristin D. Alfaro-Munoz, Nabil Elshafeey, Nancy El Shafei, Pascal O. Zinn, John F. de Groot, Rivka R. Colen. A radiomic-based MRI phenotype is uniquely associated with hypermutated genotype in gliomas [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2018; 2018 Apr 14-18; Chicago, IL. Philadelphia (PA): AACR; Cancer Res 2018;78(13 Suppl):Abstract nr 2955.

Dynamic Analysis of Flexible Structures Under The Influence of Moving Multiple Vehicles

Bu çalışmada, esnek yapılardan çoklu taşıt geçmesi durumunda dinamik davranışa etki eden parametreler detaylı şekilde incelenmiştir. Çalışmada esnek yapı olarak; Euler-Bernoulli ince kiriş teorisine göre modellenen basit mesnetli köprü kirişi göz önüne alınmıştır. Köprü kirişi ile üzerinden geçen taşıtların temasıyla oluşan hareket denklemleri; sistemin kinetik ve potansiyel enerjisi çıkarıldıktan sonra Lagrange denklemi kullanılarak elde edilmiştir. Sistemin hareketini ifade eden ikinci dereceden diferansiyel denklemler çalışmada belirtilen durum değişkenlerini kullanarak; birinci derece durum uzay formuna dönüştürülmüştür. Diferansiyel denklem sistemi; zamana göre dördüncü dereceden Runge-Kutta algoritması ile MATLAB ticari yazılımında hazırlanan program kullanılarak yüksek hassasiyetle çözülmüştür.

An Improved Process Discovery Approach Based on the Markov Transition Matrix

Process mining has been widely used to discover the predefined process model from an event log. The discovered model either shows the connection of reality and original model, or indicates the conformance of the process and the event log, which can be used to discover, monitor and improve the original process.The paperaims to enhance the flexibility and adaptability of the process discovery algorithm. The paperfirst analyses the process patterns using hierarchical structure, then proposes an improved multi-step process discovery approach based on the first-order Markov transition matrix. Finally, this paper verifies the feasibility and applicability of the improved approach through a simulation example.

Parameters Sensitivity Analysis of Position-Based Impedance Control for Bionic Legged Robots’ HDU

For the hydraulic drive unit (HDU) on the joints of bionic legged robots, this paper proposes the position-based impedance control method. Then, the impedance control performance is tested by a HDU performance test platform. Further, the method of first-order sensitivity matrix is proposed to analyze the dynamic sensitivity of four main control parameters under four working conditions. To research the parameter sensitivity quantificationally, two sensitivity indexes are defined, and the sensitivity analysis results are verified by experiments. The results of the experiments show that, when combined with corresponding optimization strategies, the dynamic compliance composition theory and the results from sensitivity analysis can compensate for the control parameters and optimize the control performance in different working conditions.

Three-band k.p Hamiltonian of monolayer MoS2 based on the group theory and infinitesimal basis transformations approach

In this work, we present the matrix representation of three-band low-energy k.p Hamiltonian of monolayer MoS2 (ML-MDS) based on the group theory and infinitesimal basis transformations approach. We have derived the matrix representation of k.p Hamiltonian up to the second-order of perturbation at the Γ point of the Brillouin zone. Due to the symmetries of doubly degenerate conduction band (CB), namely the CB+1 and (CB+1)', the optical transitions from these bands to valance band (VB) are allowed. Therefore, we have chosen three bands to describe the dynamics of ML-MDS around the Γ point. We have obtained three main 3 × 3 matrices including a zero-order matrix describing the edge band energies, a first-order matrix describing the coupling of VB, CB + 1, and (CB + 1)' away from the Γ point, and a second-order matrix which is itself consisted of three matrices as a free-electron energy matrix, an isotropic diagonal matrix and a anisotropic matrix. The whole matrix definitely show the isotropic and parabolic properties of VB and the anisotropy property of two degenerate CB + 1 and (CB + 1)'.

Uncertain reduced-order modeling for unsteady aerodynamics with interval parameters and its application on robust flutter boundary prediction

Computational fluid dynamics based unsteady aerodynamic reduced-order models can significantly improve the efficiency of transonic aeroelastic analysis. In this paper, the concept of the conventional model reduction method based on the system identification theory is extended to aerodynamic subsystems with the consideration of computational fluid dynamics-induced interval uncertainties in simulation to get the aerodynamic reduced-order model as uncertain as the original aerodynamic subsystem. The interval estimation of identified coefficients involved in the uncertain reduced-order model is obtained by utilizing the first-order interval perturbation method. The stability problem of the interval aeroelastic state-space model formulated based on the constructed uncertain aerodynamic reduced-order model is equivalently transformed into a standard interval eigenvalue problem associated with a real non-symmetric interval matrix in which the interval bounds of eigenvalues are evaluated by virtue of the first-order interval matrix perturbation algorithm. A new stability criterion for the interval aeroelastic state matrix is defined to predict the robust flutter boundary of the concerned uncertain aeroelastic system. Two numerical examples with respect to the uncertain aerodynamic ROM constructions and robust flutter boundary predictions of the two-dimensional Isogai wing and the three-dimensional AGARD 445.6 wing in transonic regime are implemented to assess the validity and accuracy of the presented approach. The obtained results are also compared with Monte Carlo simulation solutions as well as numerical and experimental results in the literatures indicating that the proposed method can provide a more robust and conservative prediction on the flutter boundary of an aeroelastic system compared with conventional deterministic aeroelastic analysis approaches.

Impacts of neighboring countries on military expenditures

Using the latest spatial econometric techniques and data pertaining to 144 countries over the period 1993–2007, this article tests and compares four frequently used spatial econometric models and eight matrices describing the mutual relationships among the countries, all within a common framework, which helps clarify the impact of neighboring countries on military expenditures. Furthermore, it utilizes two different data sources. Due to this setup, it provides one of the most thorough spatial analyses of military expenditures so far. Furthermore, it confirms but also challenges the results of several previous studies. Military spending measured as a ratio of GDP in one country indeed depends primarily on the spending of other countries, but in a limited number of cases, it also depends on control variables that can be observed in other countries, among which are the level of GDP, the occurrence of international wars, and the political regime. The most likely specification of the matrix describing the relationships among countries is the first-order binary contiguity matrix based on land or maritime borders, extended to include two-sided relationships among the five countries that are permanent members of the UN Security Council and one-sided relationships to all other countries. Finally, cross-sectional approaches are rejected in favor of dynamic spatial panel data approaches due to their controls for habit persistence, country, and time-period fixed effects.