Vector Computers Research Articles

On the computation of ray-velocity vectors for seismic body waves in viscoelastic anisotropic media

Computation of the ray-velocity vector is crucial in seismic ray tracing for the three body waves (qP, qSV, qSH) in viscoelastic anisotropic media. The primary challenge is dealing with the likely cusps or triplications of the qSV wavefronts, which makes it theoretically difficult to track qSV raypaths and the reflection and transmission of these body waves in such media. We review three traditional methods, namely, g-Hamiltonian, p-Hamiltonian, and explicit c-derivative, and then present two new approaches called implicit c-derivative and g*-Hamiltonian to tackle the challenges of seismic ray tracing. We theoretically prove the equivalence of these five methods to calculate the group-velocity vector in a viscoelastic anisotropic medium, apply these methods to some rock samples, and investigate the applicability of each method. Our results indicate that if the body wave is homogeneous (i.e., its propagation and attenuation wavefronts are parallel to each other) or if the body wavefront has no cusps or triplications, then all the methods offer a consistent solution of the ray-velocity vector. If the body wave is inhomogeneous (its propagation and attenuation wavefronts are at different angles or cross each other) and cusps and triplications occur in the wavefronts, then all the methods but the g*-Hamiltonian one fail to give the proper solution of the ray-velocity vector. This work demonstrates that the innovative g*-Hamiltonian method is the only approach to overcome the theoretical difficulty of seismic ray tracing in viscoelastic anisotropic media.

Multiple-base Logarithmic Quantization and Application in Reduced Precision AI Computations

The power of logarithmic quantizations and computations has been recognized as a useful tool in optimizing the performance of large ML models. There are plenty of applications of ML techniques in digital preservation. The accuracy of computations may play a crucial role in the corresponding algorithms. In this article, we provide results that demonstrate significantly better quantization signal-to-noise ratio performance thanks to multiple-base logarithmic number systems (MDLNS) in comparison with the floating point quantizations that use the same number of bits. On a hardware level, we present details about our Xilinx VCU-128 FPGA design for dot product and matrix vector computations. The MDLNS matrix-vector design significantly outperforms equivalent fixed-point binary designs in terms of area (A) and time (T) complexity and power consumption as evidenced by a 4 × scaling of AT 2 metric for VLSI performance, and 57% increase in computational throughput per watt compared to fixed-point arithmetic.

CuGBasis: High-performance CUDA/Python library for efficient computation of quantum chemistry density-based descriptors for larger systems.

CuGBasis is a free and open-source CUDA®/Python library for efficient computation of scalar, vector, and matrix quantities crucial for the post-processing of electronic structure calculations. CuGBasis integrates high-performance Graphical Processing Unit (GPU) computing with the ease and flexibility of Python programming, making it compatible with a vast ecosystem of libraries. We showcase its utility as a Python library and demonstrate its seamless interoperability with existing Python software to gain chemical insight from quantum chemistry calculations. Leveraging GPU-accelerated code, cuGBasis exhibits remarkable performance, making it highly applicable to larger systems or large databases. Our benchmarks reveal a 100-fold performance gain compared to alternative software packages, including serial/multi-threaded Central Processing Unit and GPU implementations. This paper outlines various features and computational strategies that lead to cuGBasis's enhanced performance, guiding developers of GPU-accelerated code.

Actualization of the content of the educational process in the artistic and creative areas of Bachelor's training in terms of the formation of digital competencies

Introduction. Currently, almost all spheres of society life activities are developing in terms of progressive digitalization, therefore it is required to promptly transform existing approaches to organizing the student learning process. The purpose of research: to determine digital competencies relevant to the field of professional activity of graduates of artistic and creative areas of training and to actualize the content of the educational process in accordance with the results obtained. Materials and methods. The study was conducted during 2021 – 2023 on the basis of the Department of Design, Art Education and Technology of Yelets State University named after I.A. Bunin. The target group included 157 respondents with experience in conducting creative activities using modern digital technologies. Empirical test methods for data collection were implemented in two ways: during direct communication and remotely using Yandex Forms. Quantitative statistical analysis was carried out using LibreOffice Calc. Results. 6 enlarged groups of digital competencies of graduates of artistic and creative areas of training, currently in demand by society and the labor market, have been identified. Based on the opinions of the respondents, they were ranked according to the degree of importance: have the skills and abilities to work with raster (16.6%) and vector (12.1%) computer graphics, design and edit pages or sites on the Internet (13.3%) , develop multimedia content (5.7%), create and edit 3D models (23.6%), use specialized programs according to the training profile (28.7%). Conclusions. The empirically obtained results were integrated into the curriculum for undergraduate training in the direction 54.03.01 Design, specialty (profile) “Design and Contemporary Digital Art”, in terms of the proportional distribution of study time between disciplines and modules focused on the development of digital competencies. The optimal sequence of developing skills in mastering specialized digital tools has been identified, which is the key to the effective outcome of the educational process. Promising vectors for the development of artistic and creative education of students have been identified, which include: design of mobile applications, creation of elements of augmented and virtual reality, development of conceptual digital games.

Vector-Based Advanced Computation for Photovoltaic Devices and Arrays: Numerical Reproduction of Unusual Behaviors of Curved Photovoltaic Devices

Most equations and models for photovoltaics are based on the assumption that photovoltaic (PV) devices are flat. Therefore, the actual performance of nonplanar PV devices should be investigated and developed. In this study, two algorithms were developed and defined using vector computations to describe a curved surface based on differential geometry and the interaction with non-uniform solar irradiance (i.e., non-uniform shading distribution in the sky). To validate the computational model, the power output from a commercial curved solar panel for the Toyota Prius 40 series was monitored at four orientation angles and in various climates. Then, these were compared with the calculation results obtained using the developed algorithm. The conventional calculation used for flat PV devices showed an overestimated performance due to ignorance of inherent errors due to curved surfaces. However, the new algorithms matched the measured trends, particularly on clear-sky days. The validated computation method for curved PV devices is advantageous for vehicle-integrated photovoltaic devices and PVs including building-integrated photovoltaics (BIPVs), drones, and agriphotovoltaics.

Unravelling the spatial directionality of urban mobility.

As it is central to sustainable urban development, urban mobility has primarily been scrutinised for its scaling and hierarchical properties. However, traditional analyses frequently overlook spatial directionality, a critical factor in city centre congestion and suburban development. Here, we apply vector computation to unravel the spatial directionality of urban mobility, introducing a two-dimensional anisotropy-centripetality metric. Utilising travel data from 90 million mobile users across 60 Chinese cities, we effectively quantify mobility patterns through this metric, distinguishing between strong monocentric, weak monocentric, and polycentric patterns. Our findings highlight a notable difference: residents in monocentric cities face increasing commuting distances as cities expand, in contrast to the consistent commuting patterns observed in polycentric cities. Notably, mobility anisotropy intensifies in the outskirts of monocentric cities, whereas it remains uniform in polycentric settings. Additionally, centripetality wanes as one moves from the urban core, with a steeper decline observed in polycentric cities. Finally, we reveal that employment attraction strength and commuting distance scaling are key to explaining these divergent urban mobility patterns. These insights are important for shaping effective policies aimed at alleviating congestion and guiding suburban housing development.

Neural axiom network for knowledge graph reasoning

Knowledge graph reasoning (KGR) aims to infer new knowledge or detect noises, which is essential for improving the quality of knowledge graphs. Recently, various KGR techniques, such as symbolic- and embedding-based methods, have been proposed and shown strong reasoning ability. Symbolic-based reasoning methods infer missing triples according to predefined rules or ontologies. Although rules and axioms have proven effective, it is difficult to obtain them. Embedding-based reasoning methods represent entities and relations as vectors, and complete KGs via vector computation. However, they mainly rely on structural information and ignore implicit axiom information not predefined in KGs but can be reflected in data. That is, each correct triple is also a logically consistent triple and satisfies all axioms. In this paper, we propose a novel NeuRal Axiom Network (NeuRAN) framework that combines explicit structural and implicit axiom information without introducing additional ontologies. Specifically, the framework consists of a KG embedding module that preserves the semantics of triples and five axiom modules that encode five kinds of implicit axioms. These axioms correspond to five typical object property expression axioms defined in OWL2, including ObjectPropertyDomain, ObjectPropertyRange, DisjointObjectProperties, IrreflexiveObjectProperty and AsymmetricObjectProperty. The KG embedding module and axiom modules compute the scores that the triple conforms to the semantics and the corresponding axioms, respectively. Compared with KG embedding models and CKRL, our method achieves comparable performance on noise detection and triple classification and achieves significant performance on link prediction. Compared with TransE and TransH, our method improves the link prediction performance on the Hits@1 metric by 22.0% and 20.8% on WN18RR-10% dataset, respectively.

Lie Symmetries of the Wave Equation on the Sphere Using Geometry

A semilinear quadratic equation of the form Aij(x)uij=Bi(x,u)ui+F(x,u) defines a metric Aij; therefore, it is possible to relate the Lie point symmetries of the equation with the symmetries of this metric. The Lie symmetry conditions break into two sets: one set containing the Lie derivative of the metric wrt the Lie symmetry generator, and the other set containing the quantities Bi(x,u),F(x,u). From the first set, it follows that the generators of Lie point symmetries are elements of the conformal algebra of the metric Aij, while the second set serves as constraint equations, which select elements from the conformal algebra of Aij. Therefore, it is possible to determine the Lie point symmetries using a geometric approach based on the computation of the conformal Killing vectors of the metric Aij. In the present article, the nonlinear Poisson equation Δgu−f(u)=0 is studied. The metric defined by this equation is 1 + 2 decomposable along the gradient Killing vector ∂t. It is a conformally flat metric, which admits 10 conformal Killing vectors. We determine the conformal Killing vectors of this metric using a general geometric method, which computes the conformal Killing vectors of a general 1+(n−1) decomposable metric in a systematic way. It is found that the nonlinear Poisson equation Δgu−f(u)=0 admits Lie point symmetries only when f(u)=ku, and in this case, only the Killing vectors are admitted. It is shown that the Noether point symmetries coincide with the Lie point symmetries. This approach/method can be used to study the Lie point symmetries of more complex equations and with more degrees of freedom.

Modelling permanent magnet excited uniform fields with rational approximations

PurposeA novel method for modelling permanent magnets is investigated based on numerical approximations with rational functions. This study aims to introduce the AAA algorithm and other recently developed, cutting-edge mathematical tools, which provide outstandingly fast and accurate numerical computation of potentials and vector fields.Design/methodology/approachFirst, the AAA algorithm is briefly introduced along with its main variants and other advanced mathematical tools involved in the modelling. Then, the analysis of a circular Halbach array with a one-pole pair is carried out by means of the AAA-least squares method, focusing on vector potential and flux density in the bore and validating results by means of classic finite element software. Finally, the investigation is completed by a finite difference analysis.FindingsAAA methods for field analysis prove to be strikingly fast and accurate. Results are in excellent agreement with those provided by the finite element model, and the very good agreement with those from finite differences suggests future improvements. They are also easy programming; the MATLAB code is less than 200 lines. This indicates they can provide an effective tool for rapid analysis.Research limitations/implicationsAAA methods in magnetostatics are novel, but their extension to analogous physical problems seems straightforward. Being a meshless method, it is unlikely that local non-linearities can be considered. An aspect of particular interest, left for future research, is the capability of handling inhomogeneous domains, i.e. solving general interface problems.Originality/valueThe authors use cutting-edge mathematical tools for the modelling of complex physical objects in magnetostatics.

Masking Floating-Point Number Multiplication and Addition of Falcon

In this paper, we provide the first masking scheme for floating-point number multiplication and addition to defend against recent side-channel attacks on Falcon’s pre-image vector computation. Our approach involves a masked nonzero check gadget that securely identifies whether a shared value is zero. This gadget can be utilized for various computations such as rounding the mantissa, computing the sticky bit, checking the equality of two values, and normalizing a number. To support the masked floating-point number addition, we also developed a masked shift and a masked normalization gadget. Our masking design provides both first- and higherorder mask protection, and we demonstrate the theoretical security by proving the (Strong)-Non-Interference properties in the probing model. To evaluate the performance of our approach, we implemented unmasked, first-order, and second-order algorithms on an Arm Cortex-M4 processor, providing cycle counts and the number of random bytes used. We also report the time for one complete signing process with our countermeasure on an Intel-Core CPU. In addition, we assessed the practical security of our approach by conducting the test vector leakage assessment (TVLA) to validate the effectiveness of our protection. Specifically, our TVLA experiment results for second-order masking passed the test in 100,000 measured traces.

Financial Risk Assessment Model Based on Fuzzy Logic

In the rapidly evolving landscape of business operations, establishing a robust security domain prevention system in the Middle Office is of utmost importance. To achieve this, the integration of Choquet expectation-based methodologies offers a powerful approach. The Middle Office acts as a critical hub for various business processes, including risk management, compliance, and data protection. With the implementation of Choquet expectation theory, which encompasses the combination of multiple criteria and preferences, businesses can effectively assess and optimize their security domain prevention system. The establishment and optimization of a security domain prevention system based on Choquet’s expectations provide businesses with a comprehensive and tailored approach to protect their critical assets, maintain operational continuity, and safeguard sensitive data from emerging threats in the Middle Office environment. This paper constructed a Fuzzy Optimization Membership Estimation (FOME) for the computation of the feature vector. The proposed FOME model uses the Flemingo Optimization model for the evaluation of the feature vector in the business middle office. The FOME model effectively computes the Choquet expectation features for the analysis of the risk management of the feature vector in the middle office. Through the membership estimation with the FOME model, the model significantly computes the different attacks in the middle office. The analysis of the proposed FOME is evaluated for the conventional CICIDS dataset for the attack analysis. The simulation analysis stated that the proposed FOME model achieves a higher classification accuracy of 99.89% for attack detection.

Lagrange Points and the James Webb Space Telescope

This article guides the reader through Lagrange’s famous solution to the so-called “three-body problem” and shows its application to the recently launched James Webb Space Telescope. Lagrange’s original equations are presented in his original notation, supplemented by modern vector computations. The entire work is accomplished with mathematics typically taught at the college freshman and sophomore levels.

A portable coding strategy to exploit vectorization on combustion simulations

The complexity of combustion simulations demands the latest high-performance computing tools to accelerate its time-to-solution results. A current trend on HPC systems is the utilization of CPUs with SIMD or vector extensions to exploit data parallelism. Our work proposes a strategy to improve the automatic vectorization of finite-element-based scientific codes. The approach applies a parametric configuration to the data structures to help the compiler detect the block of codes that can take advantage of vector computation while maintaining the code portable. A detailed analysis of the computational impact of this methodology on the different stages of a CFD solver is studied on the PRECCINSTA burner simulation. Our parametric implementation has proven to help the compiler generate more vector instructions in the assembly operation: this results in a reduction of up to 9.39× of the total executed instruction maintaining constant the Instructions Per Cycle and the CPU frequency. The proposed strategy improves the performance of the CFD case under study up to 4.67× on the MareNostrum 4 supercomputer.

PartialHD: Toward Efficient Hyperdimensional Computing by Partial Processing

Hyperdimensional (HD) computing is a brain inspired learning method that is widely employed in resource-constrained applications such as the internet of things (IoT) regarding its lightweight computation. Although HD computing has high efficiency in the IoT applications, it suffers from high computation due to the large vector size. Thus, several studies are proposed to speedup and increase the efficiency of HD computing. In this work, we propose a method to process HD computing called PartialHD. Our method divides a long hypervector into multiple partial vectors, and process each vector separately. In the retraining phase, this method improves accuracy up to 1.93%. Moreover, by employing our proposed method in the retraining and inference, only a few partial vectors participate and this causes the computational overhead reduces in these phases. The evaluation shows that our method processes on average 22.2% and 36.23% of the entire hypervectors with negligible accuracy loss in inference and retraining, respectively. Furthermore, we propose two general architectures (light-weight and high-speed), which accelerate partial vector computations on different FPGA platforms. The result shows that the light-weight architecture can accelerate HD computing on resource-constrained FPGAs such as Artix while the high-speed architecture has 4.72× higher throughput than light-weight architecture.

Optimum Vector Information Technologies Based on the Multidimensional Combinatorial Configurations

Paper devoiced to optimum vector information technologies based on the multi-dimensional combinatorial configurations, such as Ideal Ring Bundles (IRBs). One-dimensional IRBs are ring ordered positive integers that form finite set of integers from 1 to S using both these numbers and all its consecutive terms. Two- and multi-dimensional IRBs make available to configure intelligent information and telecommunication systems providing generate the maximum number of distinct vector sums of consecutive terms in the combinatorial configuration. Applications profiting from optimum vector information technologies based on the multi-dimensional combinatorial theory provide for example data mining technologies and big vector data processing, data analysis and system security, signal compression and reconstruction, vector computing and telecommunications, and other branches of sciences and advanced information technologies.

Coherent chord computation and cross ratio for accurate ellipse detection

This paper presents a new method for detecting ellipses in images, which has many applications in pattern recognition and robotic tasks. Previous approaches typically use sophisticated arc grouping strategies or calculate differential such as tangents, and thereby they are less efficient or more sensitive to noise. In this work, we present a novel ellipse detector, based on the simple yet effective chord computation, and on the projective invariant cross ratio, which achieves promising performance in both accuracy and efficiency. First, elliptical arcs are extracted by fast vector computations along with the removal of straight segments to speed up detection. Then, arcs from the same ellipse are grouped together according to the relative location and the intersecting chord constraints, both are on coherent chord computation without differential. Additionally, an efficient additive principle is applied to further accelerate the grouping process. Finally, a novel and robust verification by area-deduced cross ratio is introduced to pick out salient ellipses. Compared with predecessor methods, cross ratio is not only simple for computation, but also has invariant properties (used to discriminate ellipses). Extensive experiments on seven public datasets (including synthetic and real-world images) are implemented. The results highlight the salient advantages of the proposed method compared to state-of-the-art detectors: Easier to implementation, more robust against occlusion and noise, as well as attaining higher F-measure.

Vector-logic computing for faults-as-address deductive simulation

The aim of the research is to create logic-free vector computing, leveraging read-write transactions in memory, to solve the problems of modeling and simulation stuck-at-fault combinations for complex logic elements and digital structures. At the same time, the problem of creating smart data structures based on logical vectors, truth tables, and deductive matrices is considered to simplify algorithms for parallel stuck-at-fault simulation. Vector computing is a computational process based on read-write transactions on bits of a binary vector of functionality, where the input data and faults are the addresses of the bits. A method for the synthesis of deductive vectors for propagating input fault lists is proposed, which has a quadratic computational complexity of read-write transactions. Deductive vectors, combined into a quadratic matrix, represent explicit data structures for parallel simulation of single and multiple stuck-at-faults. The initial information for constructing a deductive matrix is a logical vector and a bit-recoding matrix. Matrix is easily obtained using a recursive procedure based on the combinatorial properties of the truth table. Considering emerging trends, focused on in-memory computing, an algorithm for fault, as addresses, simulation is proposed, using logical and deductive vectors placed in memory. The simulation algorithm is proposed not to use commands of powerful processors.

Validation of a Biomechanical Injury and Disease Assessment Platform Applying an Inertial-Based Biosensor and Axis Vector Computation.

Inertial kinetics and kinematics have substantial influences on human biomechanical function. A new algorithm for Inertial Measurement Unit (IMU)-based motion tracking is presented in this work. The primary aims of this paper are to combine recent developments in improved biosensor technology with mainstream motion-tracking hardware to measure the overall performance of human movement based on joint axis-angle representations of limb rotation. This work describes an alternative approach to representing three-dimensional rotations using a normalized vector around which an identified joint angle defines the overall rotation, rather than a traditional Euler angle approach. Furthermore, IMUs allow for the direct measurement of joint angular velocities, offering the opportunity to increase the accuracy of instantaneous axis of rotation estimations. Although the axis-angle representation requires vector quotient algebra (quaternions) to define rotation, this approach may be preferred for many graphics, vision, and virtual reality software applications. The analytical method was validated with laboratory data gathered from an infant dummy leg's flexion and extension knee movements and applied to a living subject's upper limb movement. The results showed that the novel approach could reasonably handle a simple case and provide a detailed analysis of axis-angle migration. The described algorithm could play a notable role in the biomechanical analysis of human joints and offers a harbinger of IMU-based biosensors that may detect pathological patterns of joint disease and injury.

Орнамент как основа формирования алгоритмических умений будущих бакалавров изобразительного и прикладных видов искусств

Ornamental compositions open up significant opportunities for the formation of algorithmic skills among bachelors of fine and applied arts. Geometric ornament is a good training material for the construction and analysis of digital art models with a flexible level of complexity. Descriptive geometry is considered as an applied tool for analyzing and creating an ornamental composition. The analysis of the ornament allows you to read architectural and artistic forms more professionally. The integration of descriptive geometry and computer graphics disciplines takes the content to a qualitatively new level. Geometric constructions in ornamental compositions are functionally convenient for creating digital models when studying vector graphic editors. The article reveals the problem of the formation of algorithmic skills among future bachelors of art as an important component of algorithmic culture and computational thinking. The descriptive geometry language and digital tools of vector computer graphics were chosen as the language of the algorithm description in solving ornamental compositions. The article presents a generalized algorithm for constructing a digital model of ornamental compositions, consisting of analytical, search, constructive, reproductive, reflexive, evaluative stages, including action and auxiliary questions for finding a solution to a graphical problem. An example of a particular algorithm for constructing the rose of Amiens Cathedral, performed by a student in the framework of studying the discipline "Modern Information Technologies", is given. The search for solutions at each stage is carried out with the help of auxiliary questions of the generalized algorithm. Special attention is paid to such stages of the algorithm as reflection of the finished digital model to investigate the possibility of using it in a given material.

Vector relation acquisition and scene knowledge for solving arithmetic word problems

This paper presents a vector relation-centric algorithm for solving arithmetic word problems (AWPs), which uses vector relation acquisition and scene knowledge to ensure the performances of problem understanding and symbolic solver correspondingly. The vector relation acquisition procedure builds on the synergy of the vector syntax-semantics method and the deep neural miner. Compared with the syntax-semantics method, the vector syntax-semantics method decreases not only the number of models but also semantic ambiguities and computational costs. For the scene knowledge, this paper proposes a scene-aware symbolic solver which infers relations obeying scene rules to decrease the occurrences of unwanted operations. Experimental results show that the proposed algorithm is superior to the high-performance baseline algorithm in both accuracy and computational cost. In accuracy, the proposed algorithm increased the accuracy by 3.9% on the sum of the three scene subsets due to the use of the scene knowledge and vector computing; as a result, it increased the accuracy by 0.5% on the sum of six authoritative datasets. In computational cost, the proposed algorithm decreased the computing cost by more than 50%. Thus, this paper makes a significant contribution to developing instruments for solving AWPs.