Vector Operations Research Articles

Developing Excel VBA Functions for the Mathematical Modeling of Three-Dimensional Vectors

The current computer support for operations involving three-dimensional vectors is insufficient, even in widely used programs like Excel. These programs lack customised features specifically designed for vector operations. However, this limitation can be overcome by using the options provided by Visual Basic for Applications. By creating user functions, we can effectively calculate various results related to the mathematical application of vectors. These functions include determining the magnitude and absolute value of a vector, calculating the angle between two vectors or the cosine of that angle, finding the scalar product and vector product of two vectors, and evaluating the mixed product of three vectors. By incorporating these custom functions into the spreadsheet program, users can easily perform mathematical calculations pertaining to three-dimensional vectors.

Exploring the lepton flavor violating decay modes b → sμ±τ∓ in SMEFT approach

We perform an analysis of the consequences of various new physics operators on the lepton flavor violating (LFV) decay modes mediated through b→sℓ1ℓ2 transitions. We scrutinize the imprints of the (pseudo)scalar and axial (vector) operators on the exclusive LFV decay channels B(s)→(ϕ,K⁎,K2⁎)ℓ1ℓ2 and Λb→Λℓ1ℓ2, where ℓ1,ℓ2 represent μ or τ. The new physics parameters are constrained by using the upper limits of the branching fractions of the Bs→τμ and B→Kτμ processes, assuming the new physics couplings to be real. We then explore the key observables such as the branching fractions, the forward-backward asymmetries, and the longitudinal polarization fractions of the B→(K⁎,ϕ,K2⁎)τ±μ∓ decays. In addition, we also investigate the impact of the new physics couplings on the baryonic Λb→Λτ±μ∓ decay channels mediated by the b→s quark level transition. With the experimental prospects at LHCb upgrade and Belle II, we also predict the upper limits of the above-discussed observables, which could intrigue the new physics search in these channels.

Sharp Trace and Korn Inequalities for Differential Operators

AbstractWe establish sharp trace and Korn-type inequalities that involve vectorial differential operators, the focus being on situations where global singular integral estimates are not available. Starting from a novel approach to sharp Besov boundary traces by Riesz potentials and oscillations that equally applies to $$p=1$$ p = 1 , a case difficult to be handled by harmonic analysis techniques, we then classify boundary trace- and Korn-type inequalities. For $$p=1$$ p = 1 and so despite the failure of the Calderón-Zygmund theory, we prove that sharp trace estimates can be systematically reduced to full k-th order gradient estimates. Moreover, for $$1<p<\infty $$ 1 < p < ∞ , where sharp trace estimates yield Korn-type inequalities on smooth domains, we show for the basically optimal class of John domains that Korn-type inequalities persist – even though the reduction to global Calderón-Zygmund estimates by extension operators might not be possible.

Exercise preconditioning mitigates brain injury after cerebral ischemia-reperfusion injury in rats by restraining TIMP1.

Cerebral ischemic disease is a common cerebrovascular disease, especially ischemic stroke. Exercise has protective functions on brain tissues following cerebral ischemia-reperfusion injury (CIRI), but its preventive effects and mechanisms in CIRI remain unclear. We aimed to investigate the effects and mechanisms of exercise preconditioning on CIRI. The middle cerebral artery occlusion (MCAO) operation was prepared to establish CIRI rats. All rats were randomized into the MCAO, exercise (exercise preconditioning plus MCAO operation), vector (exercise preconditioning, MCAO operation plus intraventricular injection of empty vector), and tissue inhibitor of metalloprotease 1 overexpression (OE-TIMP1, exercise preconditioning, MCAO operation plus intraventricular injection of OE-TIMP1) groups. The results indicated that exercise preconditioning suppressed approximately 66.67% of neurological deficit scores and 73.79% of TIMP1 mRNA expression in MCAO rats, which were partially offset by OE-TIMP1. The protective effects of exercise against neuron death status and cerebral infarction size in MCAO rats were reversed by OE-TIMP1. It also confirmed that exercise weakened apoptosis and oxidative stress damage, with notable increases of B-cell lymphoma-2, superoxide dismutase, and glutathione peroxidase production, and evident decreases of BCL2-associated X, caspase 3, and malondialdehyde in MCAO rats, while these effects were partially reversed by OE-TIMP1. Additionally, the inhibitory effects of exercise on the protein levels of TIMP1, hypoxia-inducible factor-alpha, vascular endothelial growth factor receptor 2, vascular endothelial growth factor, and neurogenic locus notch homolog protein 1 in MCAO rats were partially reversed by OE-TIMP1. Altogether, exercise preconditioning had protective effects on CIRI by restraining TIMP1, which provided new therapeutic strategies for preventing CIRI.

Spectral properties of the gradient operator with nonconstant coefficients

In mathematical physics, the gradient operator with nonconstant coefficients encompasses various models, including Fourier’s law for heat propagation and Fick’s first law, that relates the diffusive flux to the gradient of the concentration. Specifically, consider n≥3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n\\ge 3$$\\end{document} orthogonal unit vectors e1,…,en∈Rn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$e_1,\\ldots ,e_n\\in {\\mathbb {R}}^n$$\\end{document}, and let Ω⊆Rn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Omega \\subseteq {\\mathbb {R}}^n$$\\end{document} be some (in general unbounded) Lipschitz domain. This paper investigates the spectral properties of the gradient operator T=∑i=1neiai(x)∂∂xi\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T=\\sum _{i=1}^ne_ia_i(x)\\frac{\\partial }{\\partial x_i}$$\\end{document} with nonconstant positive coefficients ai:Ω¯→(0,∞)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$a_i:{\\overline{\\Omega }}\\rightarrow (0,\\infty )$$\\end{document}. Under certain regularity and growth conditions on the ai\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$a_i$$\\end{document}, we identify bisectorial or strip-type regions that belong to the S-resolvent set of T. Moreover, we obtain suitable estimates of the associated resolvent operator. Our focus lies in the spectral theory on the S-spectrum, designed to study the operators acting in Clifford modules V over the Clifford algebra Rn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb {R}}_n$$\\end{document}, with vector operators being a specific crucial subclass. The spectral properties related to the S-spectrum of T are linked to the inversion of the operator Qs(T):=T2-2s0T+|s|2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Q_s(T):=T^2-2s_0T+|s|^2$$\\end{document}, where s∈Rn+1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$s\\in {\\mathbb {R}}^{n+1}$$\\end{document} is a paravector, i.e., it is of the form s=s0+s1e1+⋯+snen\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$s=s_0+s_1e_1+\\cdots +s_ne_n$$\\end{document}. This spectral problem is substantially different from the complex one, since it allows to associate general boundary conditions to Qs(T)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Q_s(T)$$\\end{document}, i.e., to the squared operator T2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T^2$$\\end{document}.

Flat space spinning massive amplitudes from momentum space CFT

We discuss the flat space limit of AdS using the momentum space representation of CFT correlators. The flat space limit involves sending the AdS radius and the dimensions of operators dual to massive fields to infinity while also scaling appropriately the sources of the dual operators. In this limit, d-dimensional CFT correlators become (d + 1)-dimensional scattering amplitudes. We exemplify our discussion with the computation of the flat-space limit of the CFT 3-point function of a conserved current, a non-conserved charged vector operator and its conjugate. The flat-space limit should yield the scattering amplitude of an Abelian gauge field with two massive vector fields. This scattering amplitude computes the electromagnetic form factors of the electromagnetic current in a spin-1 state, and these form factors encode the electromagnetic properties of the massive vector field (charge, magnetic moment and quadruple moment). In terms of the CFT, the flat-space limit amounts to zooming in the infrared region of the triple-K integrals that determine the 3-point function, while also scaling to infinity the order of (some of) the Bessel functions that feature in the triple-K integrals. In this limit the triple-K integral becomes proportional to the energy-preserving delta function, and the flat space limit correctly yields the corresponding flat space scattering amplitude in complete detail.

Efficient Hyperdimensional Computing With Spiking Phasors.

Hyperdimensional (HD) computing (also referred to as vector symbolic architectures, VSAs) offers a method for encoding symbols into vectors, allowing for those symbols to be combined in different ways to form other vectors in the same vector space. The vectors and operators form a compositional algebra, such that composite vectors can be decomposed back to their constituent vectors. Many useful algorithms have implementations in HD computing, such as classification, spatial navigation, language modeling, and logic. In this letter, we propose a spiking implementation of Fourier holographic reduced representation (FHRR), one of the most versatile VSAs. The phase of each complex number of an FHRR vector is encoded as a spike time within a cycle. Neuron models derived from these spiking phasors can perform the requisite vector operations to implement an FHRR. We demonstrate the power and versatility of our spiking networks in a number of foundational problem domains, including symbol binding and unbinding, spatial representation, function representation, function integration, and memory (i.e., signal delay).

Revisiting Database Indexing for Parallel and Accelerated Computing: A Comprehensive Study and Novel Approaches

While the importance of indexing strategies for optimizing query performance in database systems is widely acknowledged, the impact of rapidly evolving hardware architectures on indexing techniques has been an underexplored area. As modern computing systems increasingly leverage parallel processing capabilities, multi-core CPUs, and specialized hardware accelerators, traditional indexing approaches may not fully capitalize on these advancements. This comprehensive experimental study investigates the effects of hardware-conscious indexing strategies tailored for contemporary and emerging hardware platforms. Through rigorous experimentation on a real-world database environment using the industry-standard TPC-H benchmark, this research evaluates the performance implications of indexing techniques specifically designed to exploit parallelism, vectorization, and hardware-accelerated operations. By examining approaches such as cache-conscious B-Tree variants, SIMD-optimized hash indexes, and GPU-accelerated spatial indexing, the study provides valuable insights into the potential performance gains and trade-offs associated with these hardware-aware indexing methods. The findings reveal that hardware-conscious indexing strategies can significantly outperform their traditional counterparts, particularly in data-intensive workloads and large-scale database deployments. Our experiments show improvements ranging from 32.4% to 48.6% in query execution time, depending on the specific technique and hardware configuration. However, the study also highlights the complexity of implementing and tuning these techniques, as they often require intricate code optimizations and a deep understanding of the underlying hardware architecture. Additionally, this research explores the potential of machine learning-based indexing approaches, including reinforcement learning for index selection and neural network-based index advisors. While these techniques show promise, with performance improvements of up to 48.6% in certain scenarios, their effectiveness varies across different query types and data distributions. By offering a comprehensive analysis and practical recommendations, this research contributes to the ongoing pursuit of database performance optimization in the era of heterogeneous computing. The findings inform database administrators, developers, and system architects on effective indexing practices tailored for modern hardware, while also paving the way for future research into adaptive indexing techniques that can dynamically leverage hardware capabilities based on workload characteristics and resource availability.

Students’ understanding of vector operations: With and without physics education technology simulation

This study aims to investigate the influence of technology integration (physics education technology simulation) in physics learning. A quantitative method with a quasi-experimental post-test-only design was applied to reveal the differences in students’ abilities to operate vectors between the group that learned and tested using simulation and the group that learned using graphics only. The test consisted of 16 questions on the addition and subtraction of two vectors divided into one and two dimensions. Student response data were analyzed using descriptive statistics and Kruskal-Wallis test. The analysis results show that the vector operation score for experimental group 1, which learned vector operations through graphic learning using simulation and tested with the same simulation (86.15), is higher than experimental group 2, which learned vector operations through graphic learning using simulation (76.59), and the control group, which learned vector operations through graphic learning without simulation assistance (71.81). All three groups have higher average scores for one-dimensional than two-dimensional vector operations. They also have higher average scores for vector addition compared to vector subtraction operations. Kruskal-Wallis test results indicate a significant difference in the average vector operation scores for the three groups (ρ=0.021). This suggests that integrating technology in the learning and testing processes leads to a significant difference. Moreover, the difference is significant for one-dimensional vector operations (ρ=0.004) and not significant for two-dimensional vector operations (ρ=0.107). These findings could support the implementation of similar approaches at the university and high school levels, especially for vector-related topics, in both learning and testing processes.

Learning solid dynamics with graph neural network

Deep learning has shown great promise in solid physic dynamic simulation. By incorporating physical laws, recent works have further improved performance. However, existing methods rarely conform to macrophysics and incur computational costs. Furthermore, the velocity direction features of the current model have not been decomposed, forcing the model to learn vector operations. To address the aforementioned problems, we propose a Solid-Graph Network (Solid-GN), designed for more accurate and efficient learning of solid dynamics. Firstly, we design a novel and cost-effective symmetric direction encoding system that achieves macroscopic equivariance in 2D space by representing same relative directional relationships among particle pairs and their flipping version. Secondly, we propose a message-passing mechanism incorporated with the contact process, facilitating an accurate description of interactions through the decomposition of normal and tangential effects. Lastly, four novel datasets for solid dynamics with non-uniform radius particles are released, thereby enabling more complex and realistic physical simulations. Experimental evaluations conducted on five datasets demonstrate our model's performance concerning predictive accuracy, macroscopic equivariance, and computational cost over the state-of-the-art ones.

Hyperseed: Unsupervised Learning With Vector Symbolic Architectures.

Motivated by recent innovations in biologically inspired neuromorphic hardware, this article presents a novel unsupervised machine learning algorithm named Hyperseed that draws on the principles of vector symbolic architectures (VSAs) for fast learning of a topology preserving feature map of unlabeled data. It relies on two major operations of VSA, binding and bundling. The algorithmic part of Hyperseed is expressed within the Fourier holographic reduced representations (FHRR) model, which is specifically suited for implementation on spiking neuromorphic hardware. The two primary contributions of the Hyperseed algorithm are few-shot learning and a learning rule based on single vector operation. These properties are empirically evaluated on synthetic datasets and on illustrative benchmark use cases, IRIS classification, and a language identification task using the n -gram statistics. The results of these experiments confirm the capabilities of Hyperseed and its applications in neuromorphic hardware.

SKHASH: A Python Package for Computing Earthquake Focal Mechanisms

Abstract We introduce a Python package for computing focal mechanism solutions. This algorithm, which we refer to as SKHASH, is largely based on the HASH algorithm originally written in Fortran over 20 yr ago. HASH innovated the use of suites of solutions, spanning the expected errors in polarities and takeoff angles, to estimate focal mechanism uncertainty. SKHASH benefits from new features with flexible input formats and allows users to take advantage of recent advances in constraining focal mechanisms for small magnitude or poorly recorded earthquakes. The 3D locations of earthquakes and the velocity models used are varied when finding acceptable solutions. As a result, source–receiver azimuths are reflective of errors from the earthquake locations and velocity models, in addition to the takeoff angles. Users can consider weighted P-wave first-motion polarities derived from traditional or machine-learning picks, cross-correlation consensus, and/or imputation techniques using SKHASH. Focal mechanism solutions can also be further constrained using traditional, machine learning, and/or cross-correlation consensus S/P amplitude ratios. With improved reporting of individual and collective P polarity and S/P amplitude misfits, users can better evaluate the success of the solutions and the quality of the measurements. The reporting also makes it easier to identify potential issues with metadata, including incorrectly reported station polarity reversals. In addition, by leveraging vectorized operations, taking advantage of an efficient backend Python C Application Programming Interface, and the use of a parallel environment, the Python SKHASH routine may compute mechanisms quicker than the HASH routine.

Direction-of-Arrival Estimation via Sparse Bayesian Learning Exploiting Hierarchical Priors with Low Complexity.

For direction-of-arrival (DOA) estimation problems in a sparse domain, sparse Bayesian learning (SBL) is highly favored by researchers owing to its excellent estimation performance. However, traditional SBL-based methods always assign Gaussian priors to parameters to be solved, leading to moderate sparse signal recovery (SSR) effects. The reason is Gaussian priors play a similar role to l2 regularization in sparsity constraint. Therefore, numerous methods are developed by adopting hierarchical priors that are used to perform better than Gaussian priors. However, these methods are in straitened circumstances when multiple measurement vector (MMV) data are adopted. On this basis, a block-sparse SBL method (named BSBL) is developed to handle DOA estimation problems in MMV models. The novelty of BSBL is the combination of hierarchical priors and block-sparse model originating from MMV data. Therefore, on the one hand, BSBL transfers the MMV model to a block-sparse model by vectorization so that Bayesian learning is directly performed, regardless of the prior independent assumption of different measurement vectors and the inconvenience caused by the solution of matrix form. On the other hand, BSBL inherited the advantage of hierarchical priors for better SSR ability. Despite the benefit, BSBL still has the disadvantage of relatively large computation complexity caused by high dimensional matrix operations. In view of this, two operations are implemented for low complexity. One is reducing the matrix dimension of BSBL by approximation, generating a method named BSBL-APPR, and the other is embedding the generalized approximate message passing (GAMB) technique into BSBL so as to decompose matrix operations into vector or scale operations, named BSBL-GAMP. Moreover, BSBL is able to suppress temporal correlation and handle wideband sources easily. Extensive simulation results are presented to prove the superiority of BSBL over other state-of-the-art algorithms.

Privacy Preserving Image Retrieval Using Multi-Key Random Projection Encryption and Machine Learning Decryption

Homomorphic Encryption (HE), Multiparty Computation (MPC), Differential Privacy (DP) and Random Projection (RP) have been used in privacy preserving computing. The main benefit of the random projection approach is the lighter time and space complexity compared to the other available techniques. However, RP is typically used in a symmetric encryption mode, with one random projection matrix single key, making it vulnerable to attacks. An enhanced multi-key RP approach is proposed in this paper where a set of N random matrices are used as projection keys. Moreover, a randomly chosen one is used for each new query. Machine learning models are trained to perform specific vector operations on the randomly projected vectors and produce another randomly projected results vector. Another machine learning model is trained to decrypt the final result at the user’s side. The proposed system is shown to offer privacy against known plaintext and cipher-only attacks while preserving Euclidean distance calculations accuracy in the randomly projected domain which are demonstrated on the COREL 1K image retrieval task. Results show that the cyphertext space took sixteen times less than the ciphertext done with homomorphic encryption, and the computation of distance using random projection was 8 times faster than homomorphic encryption distance calculation.

Fast knowledge graph completion using graphics processing units

Knowledge graphs can be used in many areas related to data semantics such as question-answering systems, knowledge based systems. However, the currently constructed knowledge graphs need to be complemented for better knowledge in terms of relations. It is called knowledge graph completion. To add new relations to the existing knowledge graph by using knowledge graph embedding models, we have to evaluate N×N×R vector operations, where N is the number of entities and R is the number of relation types. It is very costly.In this paper, we provide an efficient knowledge graph completion framework on GPUs to get new relations using knowledge graph embedding vectors. In the proposed framework, we first define transformable to a metric space and then provide a method to transform the knowledge graph completion problem into the similarity join problem for a model which is transformable to a metric space. After that, to efficiently process the similarity join problem, we derive formulas using the properties of a metric space. Based on the formulas, we develop a fast knowledge graph completion algorithm. Finally, we experimentally show that our framework can efficiently process the knowledge graph completion problem.

Enhanced HAR using Dynamic STGAT

Action recognition has seen significant advancements with the integration of spatio-temporal representations, particularly leveraging skeleton-based models and cross-modal data fusion techniques. However, existing approaches face challenges in capturing long- range dependencies within the human body skeleton and effectively balancing features from diverse modalities. To address these limitations, a novel framework, the Dynamic Spatio-Temporal Graph Attention Transformer (D-STGAT), is proposed, which seamlessly integrates the strengths of dynamic graph attention mechanisms and transformer architectures for enhanced action recognition. The framework builds upon recent innovations in graph attention networks (GAT) and transformer models. First, the Spatial-Temporal Dynamic Graph Attention Network (ST-DGAT) is introduced, extending traditional GAT by incorporating a dynamic attention mechanism to capture spatial- temporal patterns within skeleton sequences. By reordering the weighted vector operations in GAT, the approach achieves a global approximate attention function, significantly enhancing its expressivity and capturing long-distance dependencies more effectively than static attention mechanisms. Furthermore, to address the challenges of cross-modal feature representation and fusion, the spatio-temporal Cross Attention Transformer (ST-CAT) is introduced. This model efficiently integrates spatio-temporal information from both video frames and skeleton sequences by employing a combination of full spatio-temporal attention (FAttn), zigzag spatio-temporal attention (ZAttn), and binary spatio-temporal attention (BAttn) modules. Through the proper arrangement of these modules within the transformer encoder and decoder, ST-CAT learns a multi-feature representation that effectively captures the intricate spatiotemporal dynamics inherent in action recognition tasks. Experimental results on the Penn- Action, NTU-RGB+D 60, and 120 datasets showcase the efficacy of the approach, yielding promising performance improvements over previous state-of-the-art methods. In summary, the proposed D-STGAT and ST-CAT frameworks offer novel solutions for action recognition tasks by leveraging dynamic graph attention mechanisms and transformer architectures to effectively capture and fuse spatiotemporal features from diverse modalities, leading to superior performance compared to existing approaches.

Analysis of anomalies using weak effective Hamiltonian with complex couplings and their impact on various physical observables

Abstract Recently, the experimental measurements of the branching ratios and different polarization asymmetries for processes occurring through flavor-changing-charged current transitions by BABAR, Belle, and LHCb have revealed some significant differences from the corresponding Standard Model (SM) predictions. This has triggered an interest to search for physics beyond the SM in the context of various new physics (NP) models and using the model-independent weak effective Hamiltonian (WEH). Assuming left-handed neutrinos, we add the dimension-six vector, (pseudo-)scalar, and tensor operators with complex Wilson coefficients (WCs) to the SM WEH. Using 60%, 30%, and 10% constraints resulting from the branching ratio of , we reassess the parametric space of these new physics WCs accommodating the current anomalies based on the most recent HFLAV data of and and Belle data of and . We find that the allowed parametric region of left-handed scalar couplings strongly depends on the constraints of the branching ratio, and the maximum pull from the SM predictions results from the <60% branching ratio limit. Also, the parametric region changes significantly if we extend the analysis by adding LHCb data of and . Furthermore, due to the large uncertainties in the measurements of and , we derive the sum rules which complement them with and . Using the best-fit points of the new complex WCs along with the latest measurements of , we predict the numerical values of the observable , , and from the sum rules. The simultaneous dependence of abovementioned physical observables on the NP WCs is established by plotting their correlation with and , which are useful to discriminate between various NP scenarios. We find that the most significant impact of NP results from the WC . Finally, we study the impact of these NP couplings on various angular and triple product asymmetries that could be measured in some ongoing and future experiments. The precise measurements of these observables are important to check the SM and extract the possible NP.

Optimizing CNN Hardware Acceleration with Configurable Vector Units and Feature Layout Strategies

Convolutional neural network (CNN) hardware acceleration is critical to improve the performance and facilitate the deployment of CNNs in edge applications. Due to its efficiency and simplicity, channel group parallelism has become a popular method for CNN hardware acceleration. However, when processing data involving small channels, there will be a mismatch between feature data and computing units, resulting in a low utilization of the computing units. When processing the middle layer of the convolutional neural network, the mismatch between the feature-usage order and the feature-loading order leads to a low input feature cache hit rate. To address these challenges, this paper proposes an innovative method inspired by data reordering technology, aiming to achieve CNN hardware acceleration that reuses the same multiplier resources. This method focuses on transforming the hardware acceleration process into feature organization, feature block scheduling and allocation, and feature calculation subtasks to ensure the efficient mapping of continuous loading and the calculation of feature data. Specifically, this paper introduces a convolutional algorithm mapping strategy and a configurable vector operation unit to enhance multiplier utilization for different feature map sizes and channel numbers. In addition, an off-chip address mapping and on-chip cache management mechanism is proposed to effectively improve the feature access efficiency and on-chip feature cache hit rate. Furthermore, a configurable feature block scheduling policy is proposed to strike a balance between weight reuse and feature writeback pressure. Experimental results demonstrate the effectiveness of this method. When using 512 multipliers and accelerating VGG16 at 100 MHz, the actual computing performance reaches 102.3 giga operations per second (GOPS). Compared with other CNN hardware acceleration methods, the average computing array utilization is as high as 99.88% and the computing density is higher.

Multi-agent system consistency-based cooperative scheduling strategy of regional integrated energy system

This article presents a multi-agent system (MAS)-consistency-based cooperative scheduling strategy for regional integrated energy system to address the real-time economic scheduling problem with high penetration of multiple flexible loads. First, the MAS-based hierarchical optimal operation framework is developed to perform the real-time scheduling, where the framework with distributed control is further developed into the hierarchical framework with low-dimensional adjacency matrix. Furthermore, the economic scheduling optimization models corresponding to hierarchical distributed control mode and distributed control mode are established. The optimal objective of the proposed control structure is to 1) minimize the total operation cost, 2) optimize the electrical and heat power of all dispatchable units in balancing energy supply-demand. The operational rule of following heat load for hierarchical distributed control mode and a hill-climbing search model for distributed control mode are proposed to achieve the consistency of agents, so as to realize the cooperative optimal dispatch of electricity and heat vectors. Simulation results validate the effectiveness of the proposed MAS-based strategy in optimizing the cooperative operation of electricity-heat vectors. The real-time energy generation and load demand can be accurately balanced. The proposed strategy can perform efficient real-time economic scheduling and has satisfied adaptive capability for random variations of flexible loads.

Vector Accelerator Unit for Caravel

Caravel is an open-source project developed by Efabless for creating custom System-on-Chips (SoCs). It includes the design of a configurable chip, development tools, and documentation. The Caravel SoC includes a RISC-V with the Instruction Set Architecture RV32I. One of the key features of Caravel is its open-source nature. In this article, the Vector Accelerator Unit for the Caravel SoC template is presented to increase the RISC-V capabilities, allowing parallel data processing through 14 vector operations. The accelerator is based on 4 Arithmetic Logic Units connected directly to the RISC-V through Logic Analyzer port and the General-Purpose Input/Output (GPIO) port. The total area of this accelerator is less than 20% of the User Project Wrapper area allowing the user to implement their custom designs in 8.4256 mm.