Vectorial Form Research Articles

Vectorial finite element method for neutron transport solving with preconditioning GMRES acceleration

This work proposed a vectorial finite element method (VFEM) for solving neutron transport equation with high accuracy and convergence. The Streamline Upwind Petrov–Galerkin method is used to establish the VFEM for accuracy, and the traditional discrete-ordinate neutron transport equation is organized in vectorial form for high stability and convergence. To further improve the convergence efficiency of VFEM, the preconditioning GMRES is introduced for solving the VFEM linear system, and different preconditioners are imposed, including the Jacobian and Block-Jacobian. Numerical results showed that the proposed VFEM has high accuracy and adaptability for multi-group and multi-dimensional neutron transport simulation. Further performance analyses showed that the proposed VFEM has higher efficiency than the traditional finite element method, while the application of preconditioning GMRESs can further improve the convergence efficiency. This work can provide an innovative and effective unstructured-mesh neutron transport solution format, and provide a valuable reference for further improvement of other numerical methods.

Fractional-Order Vectorial Halanay-Type Inequalities With Applications for Stability and Synchronization Analyses

The Halanay inequality is widely used in various time-delayed dynamical systems analyses and its vectorial form has become available recently. In this article, the integer-order vectorial Halanay-type inequality is further extended to fractional-order ones in both time-invariant and time-varying forms. It is shown that the fractional-order vectorial Halanay-type inequalities hold under the derived conditions in the form of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> -matrices. In addition, the time-invariant inequalities are applied to analyzing the stability and synchronization of fractional-order systems with two numerical examples to substantiate the theoretical results.

ПОЛЯРИЗАЦІЙНО ТА ЧАСТОТНО СЕЛЕКТИВНІ ХАРАКТЕРИСТИКИ ХІРАЛЬНОЇ ПОВЕРХНІ, ЩО СКЛАДАЄТЬСЯ З ПЕРІОДИЧНО РОЗТАШОВАНИХ ДІЕЛЕКТРИЧНИХ КВАДРАТНИХ СПІРАЛЕЙ

Subject and Purpose. The present study is concerned with the linearly polarized electromagnetic wave transmission through a chiral metasurface composed of periodically assembled square dielectric helices. We expect that the metasurface of the kind has a wider range of functional capabilities to transform a polarized wave into a cross-polarized one when compared to a similar metasurface composed of metal helices. Methods and Methodology. To find the scattering coefficients of the considered structure, the well-established method of integral functionals is followed. A set of volume integral equations in the vectorial form is solved for the equivalent electric and magnetic polarization currents of the analyzed periodic layer. A distinctive feature of the method is that the internal electromagnetic fields of the structure are initially found, whence the fields scattered by this structure are sought. The equations are discretized in terms of integral functionals related to the polarization currents and through the use of the double Floquet–Fourier series expansion technique. Results. It has been found that the metasurface transmission coefficients depend critically on the number of bars making the square helical particle. In the case of an even bar number, the chiral metasurface exhibits the same transmission coefficients for co- polarized field components in the event that linearly x- and y-polarized waves are incident. For cross-polarized field components, the transmission coefficients differ and can reach peak values at different frequencies. Finally, transmission coefficients of these polarizers have been investigated versus dimensions of helice-making bars. Conclusion. A wide variety of transmission properties observed in the metasurfaces make them particularly attractive for use in polarization converting and separating devices. The metasurface can feature dichroic asymmetric transmission and be used as a dichroic filter with polarization transformation. It can be put to use in differential phase sections and, also, as an effective dichroic cross-polarization converter (twist polarizer)

Correction, update, and enhancement of vectorial forestry road maps using ALS data, a pathfinder, and seven metrics

Accurate information about forestry roads is a key aspect of forest management in terms of economy (e.g. accessibility, cost, optimal path) and ecology (e.g. wildfire and wildlife protection). In Canada, and in fact, globally, most provincial, state or territory governments maintain vectorial information on the forestry roads under their jurisdiction. However, official maps are not always accurate, may lack road attributes of interest and are not always up-to-date. Airborne Laser Scanning (ALS) has become an established technology to accurately characterize and map broad territories by providing high density 3D point-clouds with, at least, 3 or 4 measurements per square meter. This paper addresses the problem of the automatic updating, fixing, and enhancement of vectorial forestry road maps over large landscapes (¿10000 km 2 ). For this purpose, we developed a production ready, documented and open-source software. From metrics derived from the point-cloud the method produces a raster of road probability. It then uses an existing, inaccurate, map of the road network to define approximate start and end points for each road. Then, a pathfinder retrieves the accurate road shape by computing the least cost path between the two points on the probability raster. Using the accurate road position given by the algorithm, road width and road state are then estimated based the on characteristics of the point-cloud. We demonstrate that our algorithm retrieves the centrelines of roads in a natively vectorial form with an error below 3 m in 95% of the roads using a fully automatic method. The accuracy of the road location allows us to derive other accurate measurements, including the state of the roads. • We accurately relocated roads from governmental database using ALS point-clouds. • We measured the width and estimated the state of each road segment. • The method is natively vectorial and uses pathfinding instead of pixel classification. • The method is open-source, fully packaged, documented, and production-ready.

Shaping fuel utilization by mitochondria

Mitochondria are central to cellular metabolism. They provide intermediate metabolites that are used in biosynthetic pathways and they process diet-derived nutrients into the energy-rich compound ATP. Mitochondrial ATP biosynthesis is a marvel of thermodynamic efficiency. Via the tricarboxylic acid cycle (TCA) and fatty acid β-oxidation, mitochondria extract electrons from dietary carbon compounds and pass them to nucleotides that ultimately deliver them to the respiratory chain complexes located in invaginations in the inner mitochondrial membrane (IMM) known as cristae. The respiratory chain complexes donate electrons in stepwise redox reactions to molecular oxygen and, with the exception of complex II, use the liberated energy to pump protons across the proton-impermeable IMM, generating a proton electrochemical gradient. This gradient is then utilized by the ATP synthase, which, in a rotary mechanism, catalyzes the formation of the high-energy γ-phosphate chemical bond between ADP and inorganic phosphate. The conversion of the chemical energy of carbon compounds into a physical, vectorial form of energy (the electrochemical gradient) maximizes the yield of the ATP biosynthetic process and is perhaps one of the foundations of life as we know it.

VWCluster: Vector-valued optimal transport for network based clustering using multi-omics data in breast cancer.

In this paper, we present a network-based clustering method, called vector Wasserstein clustering (vWCluster), based on the vector-valued Wasserstein distance derived from optimal mass transport (OMT) theory. This approach allows for the natural integration of multi-layer representations of data in a given network from which one derives clusters via a hierarchical clustering approach. In this study, we applied the methodology to multi-omics data from the two largest breast cancer studies. The resultant clusters showed significantly different survival rates in Kaplan-Meier analysis in both datasets. CIBERSORT scores were compared among the identified clusters. Out of the 22 CIBERSORT immune cell types, 9 were commonly significantly different in both datasets, suggesting the difference of tumor immune microenvironment in the clusters. vWCluster can aggregate multi-omics data represented as a vectorial form in a network with multiple layers, taking into account the concordant effect of heterogeneous data, and further identify subgroups of tumors in terms of mortality.

Some applications of Maia's fixed point theorem for Fredholm integral equation systems

"The aim of this paper is to study the existence and uniqueness of solutions for some Fredholm integral equation systems by applying the vectorial form of Maia's fixed point theorem. Some abstract Gronwall lemmas and an abstract comparison lemma are also obtained."

Towards a Vectorial Approach to Predict Beef Farm Performance

Accurate livestock management can be achieved by means of predictive models. Critical factors affecting the welfare of intensive beef cattle husbandry systems can be difficult to be detected, and Machine Learning appears as a promising approach to investigate the hundreds of variables and temporal patterns lying in the data. In this article, we explore the use of Genetic Programming (GP) to build a predictive model for the performance of Piemontese beef cattle farms. In particular, we investigate the use of vectorial GP, a recently developed variant of GP, that is particularly suitable to manage data in a vectorial form. The experiments conducted on the data from 2014 to 2018 confirm that vectorial GP can outperform not only the standard version of GP but also a number of state-of-the-art Machine Learning methods, such as k-Nearest Neighbors, Generalized Linear Models, feed-forward Neural Networks, and long- and short-term memory Recurrent Neural Networks, both in terms of accuracy and generalizability. Moreover, the intrinsic ability of GP in performing an automatic feature selection, while generating interpretable predictive models, allows highlighting the main elements influencing the breeding performance.

Circulating dengue virus serotypes and vertical transmission in Aedes larvae during outbreak and inter-outbreak seasons in a high dengue risk area of Sri Lanka

BackgroundSpatial and temporal changes in the dengue incidence are associated with multiple factors, such as climate, immunity among a population against dengue viruses (DENV), circulating DENV serotypes and vertical transmission (VT) of DENV in an area at a given time. The level of VT in a specific location has epidemiological implications in terms of viral maintenance in vectors. Identification of the circulating DENV serotypes in both patients and Aedes mosquito larvae in an area may be useful for the early detection of outbreaks. We report here the results of a prospective descriptive study that was conducted to detect the levels of VT in Aedes mosquito larvae and circulating DENV serotypes in patients and Aedes mosquito larvae from December 2015 to March 2017 in an area of Sri Lanka at high risk for dengue.MethodsA total of 200 patients with clinically suspected dengue who had been admitted to a tertiary care hospital during a dengue outbreak (3 study periods: December 2015–January 2016, June–August 2016, December 2016–January 2017) and in the inter-outbreak periods (February–May 2016 and September–November 2016) were investigated. Blood samples were drawn from the study participants to test for DENV. The houses of the study participants were visited within 7 days of admission to the hospital, and Aedes larvae were also collected within a radius of 400 m from the houses. The larvae were separately identified to species and then pooled according to each patient’s identification number. Patients’ sera and the Aedes larvae were tested to identify the infecting DENV serotypes using a reverse transcription PCR (RT-PCR) method. Levels of VT in Aedes mosquito larvae were also identified.ResultsAll four DENV serotypes (DENV-1 to -4) were identified in the study area. In the early part of the study (December 2015–February 2016), DENV-3 was predominant and from April 2016 to March 2017, DENV-2 became the most predominant type. Four cases of DENV co-infections were noted during the study period in patients. Interestingly, all four DENV serotypes were detected in Aedes albopictus larvae, which was the prominent immature vectorial form identified throughout the study period in the area, showing 9.8% VT of DENV. With the exception of DENV-4, the other three DENV serotypes were identified in Aedes aegypti larvae with a VT of 8.1%.ConclusionComparatively high rates of VT of DENV was detected in Ae. albopictus and Ae. aegypti larvae. A shift in the predominant DENV serotype with simultaneous circulation of all four DENV serotypes was identified in the study area from December 2015 to March 2017.Graphical

Vectorial integer bootstrapping: flexible integer estimation with application to GNSS

In this contribution, we extend the principle of integer bootstrapping (IB) to a vectorial form (VIB). The mathematical definition of the class of VIB-estimators is introduced together with their pull-in regions and other properties such as probability bounds and success rate approximations. The vectorial formulation allows sequential block-by-block processing of the ambiguities based on a user-chosen partitioning. In this way, flexibility is created, where for specific choices of partitioning, tailored VIB-estimators can be designed. This wide range of possibilities is discussed, supported by numerical simulations and analytical examples. Further guidelines are provided, as well as the possible extension to other classes of estimators.

An Efficient CNN and BI-LSTM Model for Abnormal Event Detection in Video Surveillance

Abnormal event detection plays a complex and important task in intelligent transportation and Computer vision. At present, the existing abnormal event detection models based on deep learning mainly focus on data represented by a vectorial form, which pay little attention to the impact of the internal structure characteristics of feature vector. In order to address the above issues, we propose an abnormal event detection hybrid modulation method via feature extraction calibrating classification in video surveillance scenes in this paper. Our main contribution is to calibrate the classification of an abnormal event by constructing feature expectation subgraphs. First, we employ convolutional neural network and long short-term memory models to extract the spatiotemporal features of video frame, and then construct the feature expectation subgraph for each key frame of every video, which could be used to capture the internal sequential and topological relational characteristics of structured feature vector. This model included a pre-trained CNN for extracting spatio-temporal features from each individual frame selected from a series of frames, which is then passed to multi-layer Bi-directional Long Short-term Memory (BD-LSTM) that possesses the capability of accurately classifying the abnormal events in complex surveillance scenes of the road. Finally, the experiments and performance of frame level and pixel level values on a common UMN dataset are estimated and evaluated.

Notice of Removal: Practical Simulation Method on Multimode-No-Core-Multimode Fiber Structure Based on the Mode Expansion

In this paper, a simplified simulation method for multimode-no-core-multimode (MNM) fiber structures is developed and demonstrated. The method is based on the mode expansion in the vectorial form, taking account of a complete set of guided modes. The simulated results are in good agreement with the experimental results. Also, it is shown that mode distribution of an input multimode fiber (MMF) is an influence on multimode interference(MMI) in the MNM fiber structure and can be controlled by using a single mode fiber(SMF) segment coupled to it. The proposed method provides an effective way for the designs of multimode-interference(MMI)-based fiber devices, which particularly contain a lot of modes.

Petrov–Galerkin method for the band structure computation of anisotropic and piezoelectric phononic crystals

In this paper, the Petrov-Galerkin finite element interface method is modified to the vectorial form and applied to compute the band structure of phononic crystals with complicated scatterer geometry. Value-periodic subspace and projective grid are employed in this method. Complete mathematical model together with the continuity and equilibrium conditions on the scatterer interface as well as the Bloch-periodic boundary conditions on the unit cell are presented for these systems. We then apply this method to compute the band structure of three kinds of special phononic crystals: phononic crystal with anisotropic inclusions, phononic crystal containing piezoelectric materials and phononic crystal containing nano-piezoelectric materials. Taking advantage of asymmetric basis functions and non-body-fitted meshes, our method is suitable for the calculation and analysis of phononic crystals with complicated scatterer geometries. With plenty of numerical experiments, the accuracy and convergency of the proposed method is demonstrated. The influences of the rotation angle of anisotropic inclusion, complicated scatterer shape, filling fraction of the scatterers, and the rotation angle of the scatterers to the band structure of these three kinds of phononic crystals are investigated. This will provide a new perspective for the design and manufacture of phononic crystals with specific band structures.

Existence and uniqueness of the solution for a general system of Fredholm integral equations

The aim of this paper is to present existence and uniqueness results for the solution of a general system of Fredholm integral equations by applying the vectorial form of Maia's fixed‐point theorem. A Gronwall‐type lemma and comparison theorems are also obtained.

Distance geometry and data science

Data are often represented as graphs. Many common tasks in data science are based on distances between entities. While some data science methodologies natively take graphs as their input, there are many more that take their input in vectorial form. In this survey, we discuss the fundamental problem of mapping graphs to vectors, and its relation with mathematical programming. We discuss applications, solution methods, dimensional reduction techniques, and some of their limits. We then present an application of some of these ideas to neural networks, showing that distance geometry techniques can give competitive performance with respect to more traditional graph-to-vector mappings.

Lunar close encounters compete with the circumterrestrial Lidov–Kozai effect

Luna 3 (or Lunik 3 in Russian sources) was the first spacecraft to perform a flyby of the Moon. Launched in October 1959 on a translunar trajectory with large semi-major axis and eccentricity, it collided with the Earth in late March 1960. The short, 6-month dynamical lifetime has often been explained through an increase in eccentricity due to the Lidov-Kozai effect. However, the classical Lidov-Kozai solution is only valid in the limit of small semi-major axis ratio, a condition that is satisfied only for solar (but not for lunar) perturbations. We undertook a study of the dynamics of Luna 3 with the aim of assessing the principal mechanisms affecting its evolution. We analyze the Luna 3 trajectory by generating accurate osculating solutions, and by comparing them to integrations of singly- and doubly-averaged equations of motion in vectorial form. Lunar close encounters, which cannot be reproduced in an averaging approach, decisively affect the trajectory and break the doubly-averaged dynamics. Solar perturbations induce oscillations of intermediate period that affect the geometry of the close encounters and cause the singly-averaged and osculating inclinations to change quadrants (the orbital plane ``flips''). We find that the peculiar evolution of Luna 3 can only be explained by taking into account lunar close encounters and intermediate-period terms; such terms are averaged out in the Lidov-Kozai solution, which is not adequate to describe translunar or cislunar trajectories. Understanding the limits of the Lidov-Kozai solution is of particular significance for the motion of objects in the Earth-Moon environment and of exoplanetary systems.

Nonsingular recursion formulas for third-body perturbations in mean vectorial elements

The description of the long-term dynamics of highly elliptic orbits under third-body perturbations may require an expansion of the disturbing function in series of the semi-major axes ratio up to higher orders. To avoid dealing with long series in trigonometric functions, we refer the motion to the apsidal frame and efficiently remove the short-period effects of this expansion in vectorial form up to an arbitrary order. We then provide the variation equations of the two fundamental vectors of the Keplerian motion by analogous vectorial recurrences, which are free from singularities and take a compact form useful for the numerical propagation of the flow in mean elements.

Abnormal Event Detection via Feature Expectation Subgraph Calibrating Classification in Video Surveillance Scenes

At present, the existing abnormal event detection models based on deep learning mainly focus on data represented by a vectorial form, which pay little attention to the impact of the internal structure characteristics of feature vector. In addition, a single classifier is difficult to ensure the accuracy of classification. In order to address the above issues, we propose an abnormal event detection hybrid modulation method via feature expectation subgraph calibrating classification in video surveillance scenes in this paper. Our main contribution is to calibrate the classification of a single classifier by constructing feature expectation subgraphs. First, we employ convolutional neural network and long short-term memory models to extract the spatiotemporal features of video frame, and then construct the feature expectation subgraph for each key frame of every video, which could be used to capture the internal sequential and topological relational characteristics of structured feature vector. Second, we project expectation subgraphs on the sparse vector to combine with a support vector classifier to calibrate the results of a linear support vector classifier. Finally, the experiments on a common dataset named UCSDped1 and a coal mining video dataset in comparison with some existing works demonstrate that the performance of the proposed method is better than several the state-of-the-art approaches.

Vibration Control of Truck Cabins With the Adaptive Vectorial Backstepping Design of Electromagnetic Active Suspension System

The active suspension system is an important equipment that isolates the vibrations that may come from outside in a land vehicle. In heavy vehicles, the active suspension system can be used to dampen vibrations in the driver’s cabin. The electromagnetic actuator is used as an active element in suspension system. Traditionally, the use of active suspension systems is mainly on automobiles and the studies related to heavy vehicles like trucks lack enough interest. In this study, dynamic modeling of a three-axle heavy vehicle cabin is performed with a half-car approach and it is aimed to suppress the disruptive effects coming from the road with active electromagnetic actuators. Lyapunov based backstepping control design is expressed in vectorial form for the heavy vehicle system, which is a multi-input multi-output system. To demonstrate the performance of the designed controller, a comparison has been made for the active and passive states for the truck cabin suspension system. The main feature of the applied control method is that it does not require knowing the actuator parameters, the adaptive term can handle the estimate of the actuator parameter. The stability of the proposed system has been proven via Lyapunov based arguments and given simulation works. The results obtained are important to suppress vibration, consequently, decreases the vibration exposure for truck drivers in terms of occupational health and safety aspects.

Vector-Coupled Flight Controller Design Based on Multivariable Backstepping Sliding Mode

This study aims to address the issues of the simultaneous control of the angle of attack, sideslip angle, and airspeed of a flight in a vectorial form. A vector controller, with a symmetry structure, is developed to transform the attitude and speed control problem into a space-vector tracking problem. We first establish flight vector-coupled dynamics, i.e., describe velocity and angular-velocity vectors in a body-fixed frame, and then propose a multivariable backstepping sliding mode control algorithm along with nonlinear disturbance observers for the vectorial dynamics. The theoretical analysis ensures that the states of the system can be enforced to reach a small neighborhood of the desired sliding manifold. The results of the numerical simulation illustrate the effectiveness and robustness of the combined vector-control scheme.