Analytical Vector Research Articles

NOVEL METHODOLOGY FOR DEVELOPING A MACHINE LEARNING-BASED IMAGING TOOL FOR HYBRID VISUALIZATION OF MACROSCOPIC AND MICROSCOPIC DEGENERATIVE CHANGES IN THE INTERVERTEBRAL DISC

BackgroundMagnetic resonance imaging (MRI) algorithm identifies end stage severely degenerated disc as ‘black’, and a moderately degenerate to non-degenerated disc as ‘white’. MRI is based on signal intensity changes that identifies loss of proteoglycans, water, and general radial bulging but lacks association with microscopic features such as fissure, endplate damage, persistent inflammatory catabolism that facilitates proteoglycan loss leading to ultimate collapse of annulus with neo-innervation and vascularization, as an indicator of pain. Thus, we propose a novel machine learning based imaging tool that combines quantifiable microscopic histopathological features with macroscopic signal intensities changes for hybrid assessment of disc degeneration.Methods100-disc tissue were collected from patients undergoing surgeries and cadaveric controls, age range of 35–75 years. MRI Pfirrmann grades were collected in each case, and each disc specimen were processed to identify the 1) region of interest 2) analytical imaging vector 3) data assimilation, grading and scoring pattern 4) identification of machine learning algorithm 5) predictive learning parameters to form an interface between hardware and software operating system.ResultsKernel algorithm defines non-linear data in xy histogram. X,Y values are scored histological spatial variables that signifies loss of proteoglycans, blood vessels ingrowth, and occurrence of tears or fissures in the inner and outer annulus regions mapped with the dampening and graded series of signal intensity changes.ConclusionTo our knowledge this study is the first to propose a machine learning method between microscopic spatial tissue changes and macroscopic signal intensity grades in the intervertebral disc.No conflict of interest declared. Sources of FundingICMR/5/4-5/3/42/Neuro/2022-NCD-1, Dr TMA PAI SMU/ 131/ REG/ TMA PURK/ 164/2020.A part of the above study was presented as an oral paper at the International Society for the Study of Lumbar Spine (ISSLS) meeting held on 1–5th May 2023, Melbourne, Australia.

Analytical Solution to the Steady Navier-Stokes Equation for a Supersonic Cone in the Area of Boundary Layer Behind the Shock Wave by Means Tunnel Mathematics

The means of tunnel mathematics (the theory of functions of a spatial complex variable) allow for an analytical solution to the problem of supersonic flow around a cone in the area of the boundary layer and beyond. The peculiar feature of the Navier-Stokes equations is that they allow for the determination of analytical velocity fields of fluids only for a small number of simple problems. Of course, the problem of the supersonic motion of fluid around a cone is not included in this number. Tunnel mathematics is a method for finding analytical vector velocity fields for steady flows of fluids with axial symmetry. The Navier-Stokes equations are then used to determine pressure and temperature distributions. The main theorem of tunnel mathematics allows for the determination of these distributions for planes z = const (similar to constructing slices of a brain in an MRI procedure). By collecting these “slices,” we can obtain full space distributions of pressure and temperature around a supersonic cone. At this stage of investigation, the conclusions obtained through tunnel mathematics make it possible to qualitatively assess the thickness of the boundary layer on the cone's surface, the shape of the shock wave, and whether the shock wave intersects the boundary layer. First of all, we focused on ensuring that the resulting solutions corresponded to the physical pattern of phenomena. No doubt, solutions obtained through tunnel mathematics must be confirmed experimentally.

Monodromy and Dulac's problem for piecewise analytical planar vector fields

Consider an analytical function f:V⊂R2→R having 0 as its regular value, a switching manifold Σ=f−1(0) and a piecewise analytical vector field X=(X+,X−), i.e. X± are analytical vector fields defined on Σ±={p∈V:±f(p)>0}. We characterize when the vector field X has a monodromic singular point in Σ, called Σ-monodromic singular point. Moreover, under certain conditions, we show that a Σ-monodromic singular point of X has a neighborhood free of limit cycles.

Отклонения от языковой нормы: лингвоэкологический аспект (на материале немецкоязычного микроблога)

The aim of the study is an analytical review of deviations from the language norm in German-language Internet communication based on the texts of the Twitter microblog. The rapid exchange of information with the simultaneous minimization of speech efforts, as well as the self-expression of communicants through the author’s word creation often entail deviations from the language norm. In the course of the study, the author identifies the main types of deviations at various language levels: phonographic, morphophonemic, orthographic, grammatical-syntactic and lexical. The article analyses the causes of deviant phenomena, as well as the features of their functioning. The scientific novelty of the work lies in the fact that for the first time it uses a linguo-ecological approach to the study of language deviations in Internet communication, which allows us to assess the nature and extent of their impact on language development. The obtained results showed that the German microblog is dominated by a tendency to simplify the language, save speech efforts, intentional and unintentional violation of the language norm, which indicates the analytical vector of the German language development at the present stage.

Bionics in architecture and geometric modelling of thin shell surfaces

In the scientific problem of design and calculation of thin elastic shells in the modern world, certain advances have already been made in mathematical and technical theory, based on hypotheses, experimental data, calculation equations and engineering calculations. Only such shells, which are designed based on calculation and used in building and technical constructions, can be referred to a small number of geometric surfaces. When designing thin shells, surfaces of rotation (sphere, torus, paraboloid, ellipsoid of rotation) and transfer surfaces (hyperbolic and elliptic paraboloid, circular transfer surface) are used. Trends in construction and engineering seek to apply complex mathematical models in harmony with environmental policy and the environment. This leads to the necessity of studying the influence of parameters when modeling an object on the parameters and properties of the created construction. Possessing a more complex shape the shells are realized as a result of experiment. As a result of active introduction of information technologies it became possible to introduce cardinally new methods in the application of geometric thin-walled spatial structures for the design of building and technical constructions, a number of machine-building parts. Modern analytical calculation programs and computer-aided design systems (Compass, Autocad, Archicad, etc.) make it possible to create a geometric projection model of a structure on the basis of primitives, to perform structural and static calculations of a project in an elementary manner. The solution of such layout problems is made possible with the support of computer geometry based on descriptive and analytical geometry, linear and vector algebra, mathematical analysis, and differential geometry. Modern bionics and environmental policy relies on the latest methods of mathematical modeling of architectural projects with a wide choice of computational and graphical software for calculation and 3d visualization.

Система колінеарних електрично та магнітно проникних тріщин між двома п’єзоелектромагнітними матеріалами

The plane strain problem for the bimaterial space consisting of two piezoelectromagnetic half-spaces with a finite set of cracks along the material interface is considered. It is assumed that the edges of the crack are electrically and magnetically permeable, and a mixed mechanical load and electric and magnetic fields can be set at infinity. The presentations of electro-magneto-mechanical quantities through a piecewise analytical vector function are constructed with the use of constitutive equations for piezoelectromagnetic materials. By means of these presentations the problem of linear relationship is formulated and solved analytically. Using the obtained solution, all the necessary mechanical, electrical, and magnetic components along the material interface as well as the energy release rate for all crack tips are found analytically. The asymptotic presentations of all fields around the crack tips and the crack closure integral method were used. Numerical results are obtained for different loads, location of the cracks, their number and lengths. A significant increase in energy release rates was demonstrated because of cracks converge, especially for the tips located closest to each other.

A miniaturized multipass cell for measurement of O2 concentration in vials based on TDLAS

Tunable diode laser absorption spectroscopy (TDLAS) is an effective method to inspect possible leakage during filling. However, the sensitivity of TDLAS is confined by the optical path length of the vial headspace. In this letter, the development of a miniaturized multipass cell (MMPC) for improving the sensitivity of laser spectrometer for detecting the O2 content in vial headspaces is presented. Based on analytical vector calculation, a few types of MMPC have been designed and their corresponding beam distributions are derived. The beam spots on the mirrors are compressed in a line-shape parallel with the vial, given the limitation of vial headspace. The simulated configuration with the minimum open path-length is then used for an experimental validating of the MMPC. The horizontal position of the vial has only little influence on the output laser power in the range of -0.5–0.5 mm relative to the optimum one, which is acceptable for practical applications. Wavelength modulation spectroscopy of calibration-free TDLAS was employed to measure the O2 concentration. It is demonstrated that the signal-to-noise ratio improves by 6 times compared to single pass configuration. The R2 of linear fitting the O2 concentration against signal amplitude could reach 0.998 in the range of 0–21% O2. According to the Allan variance analysis, the minimum detection sensitivity of the system is estimated at 0.05% at 141 s.

Exact analytical soliton solutions of N-component coupled nonlinear Schrödinger equationswith arbitrary nonlinear parameters.

Exact analytical soliton solutions play an important role in soliton fields. Soliton solutions were obtained with some special constraints on the nonlinear parameters in nonlinear coupled systems, but they usually do not hold in real physical systems. We successfully release all usual constrain conditions on nonlinear parameters for exact analytical vector soliton solutions in N-component coupled nonlinear Schrödinger equations. The exact soliton solutions and their existence condition are given explicitly. Applications of these results are discussed in several present experimental parameter regimes. The results would motivate experiments to observe more novel vector solitons in nonlinear optical fibers, Bose-Einstein condensates, and other nonlinear coupled systems.

Vector Field based Control of Quadrotor UAVs for Wildfire Boundary Monitoring

Accurate real-time information about an ongoing wildfire event is important for realizing effective and safe wildfire fighting. This paper is intended to solve the problem of guiding Unmanned Air Vehicles (UAVs) equipped with onboard cameras to monitor dynamic wildfire boundaries. According to whether the prior knowledge of the wildfire boundary is available or not, we propose a model-based vector field and a model-free vector field for UAV guidance. By describing the wildfire boundary with a zero level set function, the propagation of the wildfire boundary is modeled with the Hamilton-Jacobi equation. If the prior knowledge of the boundary is available, the typical radial basis function thin-plate spline is adopted to approximate the wildfire boundary and predicts its propagation. Then a 3D analytical vector field is constructed for an implicit function representing the wildfire boundary. If only partial observation of the wildfire boundary within the UAV’s field of view is available, the horizontal error between the UAV and its sensed segment of wildfire boundary and the vertical error between the UAV and the desired altitude are utilized to construct a 3D distance error based vector field, directly. To guide the UAV to converge to and patrol along the advancing wildfire boundary, the complex nonlinear dynamics of the UAV is exploited with differential flatness and incorporated with the above mentioned vector fields to design a nonlinear geometric controller. Computer simulations have been conducted to evaluate the performance of the proposed 3D vector field based controllers with both synthetic and real data, and simulation results demonstrate that the proposed algorithms can be effective methods to monitor the advancing wildfire boundaries.

Predicting the cumulative variation of 3-D mechanical assemblies using an ‘Idea Algebra’ framework

Improving productivity and performance of products require professional tolerance analysis and variation control and, in this context, to make sure the final product will achieve the aimed function, analysing the cumulative effects of component tolerances in an assembly is necessary. Such tolerance analysis generally involves complex and tedious calculations which take time and are susceptible to human error; therefore, for automating this process, computer-aided tolerance (CAT) systems have been used extensively. They are, however, complicated and also require relatively detailed definitions of an assembly (CAD models) before they can be used. In this paper, system topology with highly abstracted geometrical information is translated into an analytical vector model based on a semantic tool in the manner of an ‘idea algebra’. Tolerances may be defined at any level of the system (ranging from the component level to the system-level function), to more readily realise the design intent. This lightweight 3D-capable representation is possible already at an early concept stage, prior to CAD, and persists and is updated throughout the design process. Using a comparative numerical simulation-based study, it was demonstrated that the presented method provides quicker computation with equally accurate output as CAT, while requiring substantially lower complexity of input.

State space construction for continuous time transfer function matrices via Nerode equivalence

AbstractIn this paper, we show that a minimal state space realization in Jordan canonical form for linear multivariable continuous‐time systems described by rational transfer function matrices could be obtained in a natural and basic way by using the concept of Nerode equivalence. While the minimal state space realization is known, the contribution of this note is to provide an alternative realization procedure which is directly introduced in a simple and self‐contained manner. Both scalar and multivariable cases in the continuous‐time setting are discussed. The presentation also provides a concrete construction of rational vector function with preassigned poles to interpolate any 2‐norm bounded analytical vector function in the open left‐half of the complex plane. The basic idea of Nerode equivalence is that the state can be identified with a corresponding equivalence class of inputs. For a linear finite dimensional time‐invariant continuous‐time system, the zero state is identified with the kernel of certain Hankel operator. This characterization via Nerode equivalence class sheds light on the construction of state for general nonlinear input–output systems.

Vector bioprocessing spotlight

Franz Gerner is Chief Technology Officer at Excision BioTherapeutics, a clinical-stage CRISPR company using AAV as transfer vehicle to treat persistent infectious diseases, where he is responsible for CMC and related activities internally and at external contract organizations. Dr Gerner has over 25 years’ experience working in the gene therapy field, in process and analytical development, manufacturing, Quality Control, Quality Assurance and vector development. Prior to joining Excision, he was Vice President of Technical Operations at Axovant/Sio Gene Therapies where he oversaw the activities of CMC activities at contract organizations. Previously, he was one of the early members of Regenxbio, responsible for Process Development, including the establishment and subsequent expansion of in-house capabilities. In addition, he was responsible for new innovative approaches to produce recombinant AAVs. Prior to Regenxbio, he has held increasing positions in the biotech industry. He holds a MS in Chemistry and a PhD in Chemistry with focus on Gene Therapy by the Ludwig-Maximilians-Universität München.

Radial basis function-based vector field algorithm for wildfire boundary tracking with UAVs

This paper tackles the problem of dynamic wildfire boundary tracking with UAVs. Wildfire boundary is treated as the zero-level set curve of an implicit function and is approximated with radial basis functions. Its propagation is modeled with the Hamilton–Jacobi equation with an arbitrary initial boundary as the input. To navigate UAVs to the wildfire boundary, an analytical velocity vector field, whose integral curves converge to the wildfire boundary, is constructed on the basis of the typical radial basis function thin-plate spline. Computer simulations with a single UAV and multiple UAVs have been conducted for the evaluation of the proposed solution, and numerical results show that the proposed algorithm can ensure the successful tracking of an arbitrarily shaped wildfire boundary.

Remaining Service Life (RSL ) Assessment of Engine Oil in Rock Excavators

The quality of lubricant oil plays a central role in the performance of machineries. Aggressive working environment of industry, particularly in mining industry, remains a dominant point in faster rate of degradation. The colossal consumption of oil is a factor to an inflated maintenance cost which can be averted by optimizing the lubricant oil consumption using scientific and methodical approaches. At present the schedule drain-off interval is accomplished at a regular interval of operation hour recommended by manufacturers. This is a conservative approach and results in loss of useful life. This work aims to determine the Remaining Service life (RSL) of the engine oil in Excavators. The oil properties are measured at regular intervals. Kinematic Viscosity, Viscosity Index (VI), Total Acid Number (TAN) and Total Base Number (TBN) are measured. The measured values suggest the degradation level of oil before filling fresh oil. The remaining service life (RSL) is determined by juxtaposing Parameter Profile Approach (PPA), Analytical Hierarchy Process (AHP) and Vector Projection Approach (VPA). The approach will be a precursor to the excavator maintenance personnel to drain-off the oil at right time despite of manufacturer’s recommendation.

High-dimensional vector solitons for a variable-coefficient partially nonlocal coupled Gross–Pitaevskii equation in a harmonic potential

A (3+1)-dimensional variable-coefficient partially nonlocal coupled Gross–Pitaevskii equation trapped in a harmonic potential becomes a focus of this paper. A counterpart of this variable-coefficient coupled equation is found as a (2+1)-dimensional constant-coefficient single nonlinear Schrödinger equation via the reduction procedure. By solutions of constant-coefficient single equation via the Hirota method, and from this counterpart, analytical high-dimensional vector soliton solutions with the Hermite–Gaussian envelope of the variable-coefficient coupled equation are deduced. Expanded behaviors of high-dimensional vector solitons emerge in the exponential diffraction decreasing system.

Flexible control for power‐sharing in the CHB‐based SST under voltage unbalance conditions

AbstractSolid‐state transformers (SSTs) have flexible capabilities to improve the power quality issues. These improvements impose disturbances into the SST converters that require proper control algorithms. In this paper, the problems of the unequal active power flow in different phases of the SST due to the grid voltage unbalance conditions and the negative sequence current injection are discussed, and an effective method is proposed to equally sharing the active powers between the SST clusters by creating an optimum zero sequence current. Based on the power dependencies, an analytical vector for the zero‐sequence current is proposed, which can equally share the power among the SST clusters and balance the HVDC‐link voltages. Also, the proposed control strategy by using PIR controllers can achieve the zero‐sequence current based on a direct current control method. The provided equal power‐sharing among the clusters is kept in the considerable unbalanced voltage of the grid and prevents the SST outage during faults. The simulation and experimental results confirm the proposed control method to equalise the power‐sharing among the SST clusters and voltage equalisation of the HVDC‐links while the SST tries to improve the grid voltage unbalance and in the fault conditions of the grid.

Методы моделирования и идентификация параметров неоднородных анормальных неврологических движений многокомпонентных нейробиосистемах с когнитивными обратными связями

Разработаны основы математического моделирования и идентификации параметров неоднородных анормальных неврологических движений (АНР) в многокомпонентных нейробиосистемах с обратными когнитивными связями. На основе развитых авторами методов интегральных превращений и спектрального анализа для неоднородных сред предложен новый подход к построению гибридных моделей распространения волнового сигнала, описывающего нежелательные дрожания конечности руки пациента (Т-объекта) в результате самопроизвольного сокращения скелетных мышц. за счет когнитивных воздействий отдельной группы нейронных узлов коры головного мозга (КГМ). Разработана гибридная модель нейробиосистемы, описывающая состояние и поведение Т-объектов, а именно посегментное описание 3D-элементов траекторий АНР Т-объекта с учетом матрицы когнитивных воздействий групп нейроузлов КГМ. На основе гибридных интегральных преобразований Фурье получено высокоскоростное аналитическое векторное решение модели, описывающей элементы траекторий на каждом АНР-сегменте. Предложена новая методика вычисления гибридной спектральной функции, спектральных значений и матрицы когнитивных воздействий нейроузлов КГМ, определяющих гибридное интегральное преобразование построения решения. Сформулированы и решены новые неклассические задачи многопараметрической идентификации нейросистем с обратной связью в неоднородных средах на основе минимизации функционала-невязки между траекториями наблюдения и их модельными аналогами. Построены высокопроизводительные алгоритмы идентификации амплитудно-частотных характеристик систем обратной связи для компонентной оценки влияния когнитивных обратных связей, позволяющих распараллелировать вычисления для многоядерных компьютеров. Выполнено компьютерное моделирование и идентификацию АНР-траекторий нейросистем обратной связи.

Симетрія коливальних станів та електронних π-орбі-талей молекули бензену C6H6. Тонка структура спінза-лежних розщеплень

Iз застосуванням оператора проектування на елементи матриць незвiдних представлень точкової групи симетрiї 6/mmm (D6ℎ) молекули бензену C6H6 побудовано аналiтичнi вирази та векторнi зображення форм всiх її нормальних коливань, у тому числi двократно вироджених. Знайдено характери представлень, що вiдповiдають симетрiї п-електронних орбiталей молекули бензену без урахування спiну електрона та проективних представлень її спiнорних п′-орбiталей. Представлення спiнорних п′-орбiталей молекули бензену C6H6 належать проективному класу K1 та описують тонку структуру вперше встановлених спiнзалежних при врахуваннi спiну електрона розщеплень станiв, вироджених без врахування спiну п-орбiталей.

Assessment of Landscape Retention Water Capacity and Hydrological Balance in Traditional Agricultural Landscape (Model Area Liptovská Teplička Settlements, Slovakia)

The hydration potential of a landscape is an increasingly important attribute in a time of advancing climate change, making its assessment also a matter of some urgency. This study used the landscape ecological approach involving the hydrological balance, in which the soil water retention capacity (SWRC) and landscape water retention capacity (LWRC) are evaluated. To support our assessment of the water retention capacity in the landscape (LWRC), we used a synthetic interconnection of analytical vector layers of selected physical parameters of soil subtypes and secondary landscape structure (SLS) to create homogeneous polygons in the GIS Arc/Map10 computing environment. Selected abiotic and biotic attributes were assigned coefficients using a simple algorithm according to the authors, which were projected into landscape ecological complexes (LEC) in the GIS computer program in the Arc/Map10 program. We used hydrological balance calculations to specify the volumes of water retained in the landscape. The aim is to spatially estimate the retention capacity of the landscape, taking into account the current land use, including historical anti-erosion measures to reduce unwanted water runoff and soil erosion. Using zonal statistics, we achieved the following results. The part of the model area with very low or low LWCR represents 39.91% of the agricultural land used. We recorded a high LWCR on 17.69% of the area, with a predominance of meadows and cultizol cambis and cultizol fluvials. The calculation of the hydrological balance, which represents only 22.9% of atmospheric precipitation, also made a significant contribution to our knowledge of the LWRC.

Implementation of the toroidal absorption cell with multi-layer patterns by a single ring surface.

We developed a type of toroidal multi-pass cell with multi-layer patterns based on the off-axis model. The effective path length of the original toroidal multi-pass cell is extended several roundtrips in comparison with the single-layer pattern, since the inner surface of the toroidal multi-pass cell is more efficiently utilized. The light pattern has been achieved by using the simple ring surface, which is easy to fabricate. The exact analytical equations for the design of the toroidal multi-pass cell were derived based on analytical vector calculations. A series of numerical ray tracing simulations is presented, and the maximum theoretical optical path length that can be reached is 30 m with a setup of 5 cm column radius. Furthermore, two practical spot patterns are demonstrated with a path length of 8.3 m for a two-layer pattern and 10 m for a three-layer pattern, with respective effective volumes of 63 mL and 94 mL. Furthermore, the fringe effect is substantially reduced to less than 0.5% by the usage of our designed mask.