Uniform Vector Research Articles

Uniform (d + 1)-bundle over the Grassmannian G(d,n)

This paper is dedicated to the classification of uniform vector bundles of rank [Formula: see text] over the Grassmannian [Formula: see text] ([Formula: see text]) over an algebraically closed field in characteristic [Formula: see text]. Specifically, we show that all uniform vector bundles with rank [Formula: see text] over [Formula: see text] are homogeneous.

Improved approximation for two-dimensional vector multiple knapsack

We study the uniform 2-dimensional vector multiple knapsack (2VMK) problem, a natural variant of multiple knapsack arising in real-world applications such as virtual machine placement. The input for 2VMK is a set of items, each associated with a 2-dimensional weight vector and a positive profit, along with m 2-dimensional bins of uniform (unit) capacity in each dimension. The goal is to find an assignment of a subset of the items to the bins, such that the total weight of items assigned to a single bin is at most one in each dimension, and the total profit is maximized.Our main result is a (1−ln⁡22−ε)-approximation algorithm for 2VMK, for every fixed ε>0, thus improving the best known ratio of (1−1e−ε) which follows as a special case from a result of Fleischer et al. (2011) [6].Our algorithm relies on an adaptation of the Round&Approx framework of Bansal et al. (2010) [15], originally designed for set covering problems, to maximization problems. The algorithm uses randomized rounding of a configuration-LP solution to assign items to ≈m⋅ln⁡2≈0.693⋅m of the bins, followed by a reduction to the (1-dimensional) Multiple Knapsack problem for assigning items to the remaining bins.

About one strengthening of the Massera’s existence theorem of periodic solutions of linear differential periodic systems

According to Massera’s theorem, an ordinary differential linear nonhomogeneous periodic system has a periodic solution with a period coinciding with that of the system if and only if this system has a bounded solution. We introduce the class L of vector functions called growing slower than a linear function. This class contains the class B of bounded vector functions in as its own subclass. It has been proved that Massera’s above-mentioned theorem will remain true if in its formulation a bounded solution is replaced by a slower growing solution than a linear function. It is shown that the set B in the metric space (L, distc ), where distc is the uniform convergence metric vector functions on intervals, has Baer’s first category, i. e. almost everything in the sense of the category of space vector functions (L, distc ) are not bounded. This fact shows the significance of the obtained strengthening of Massera’s theorem.

A dual-population-based evolutionary algorithm for multi-objective optimization problems with irregular Pareto fronts

When solving multi-objective optimization problems (MOPs) with irregular Pareto fronts (e.g., disconnected, degenerated, inverted) via evolutionary algorithms, a critical issue is how to obtain a set of well-distributed Pareto optimal solutions. To remedy this issue, we propose a dual-population-based evolutionary algorithm with individual exploitation and weight vector adaptation, named DPEA-IEAW. Specifically, the two populations, termed globPop and locPop, individually evolve by decomposition-based and Pareto dominance-based methods, responsible for global evolution and local evolution, respectively. These two populations collaborate through substantial information exchange, thereby facilitating each other’s evolution. Firstly, the distribution of the two populations is analyzed and an individual exploitation operation is designed for locPop to exploit some promising areas that are undeveloped in globPop. Then, the guide-position is devised for globPop to indicate the optimal point for a subproblem on the Pareto front (PF). By using the guide-position, a strategy for generating uniform weight vectors is proposed to improve the population diversity. Finally, comprehensive experiments on 37 widely used test functions and 2 real-world problems demonstrate that the proposed DPEA-IEAW outperforms comparison algorithms in solving MOPs with various PFs.

A Pareto dominance relation based on reference vectors for evolutionary many-objective optimization

Pareto dominance based approach is a classical method for solving multi-objective optimization problems (MOPs). However, as the number of objectives increases, the selection pressure drops sharply. Solutions with good convergence and diversity are hardly obtained. To tackle these issues, this paper proposes a Pareto dominance relation based on reference vectors (called PRV-dominance) for evolutionary many-objective optimization. In PRV-dominance, solutions in the population are divided into several subregions according to a set of uniform reference vectors. To enhance the convergence, a new convergence metric based on the ranking of objective function values is designed to determine the dominance relationship between two solutions. Then, the density in different subregions is considered to maintain the diversity. In order to verify the performance of our approach, WFG and MaF benchmark problems with 3, 5, 8, and 15 objectives are utilized. Experimental results demonstrate that the proposed PRV-dominance outperforms eight existing dominance relations in balancing convergence and diversity. An improved NSGA-II is suggested based on the proposed PRV-dominance, which shows the competitive performance when compared with six other state-of-the-art algorithms in solving many-objective optimization problems (MaOPs). The effectiveness of the proposed PRV-dominance is also verified on two other existing many-objective evolutionary algorithms.

Viral Immunogenicity Prediction by Machine Learning Methods.

Since viruses are one of the main causes of infectious illnesses, prophylaxis is essential for efficient disease control. Vaccines play a pivotal role in mitigating the transmission of various viral infections and fortifying our defenses against them. The initial step in modern vaccine design and development involves the identification of potential vaccine targets through computational techniques. Here, using datasets of 1588 known viral immunogens and 468 viral non-immunogens, we apply machine learning algorithms to develop models for the prediction of protective immunogens of viral origin. The datasets are split into training and test sets in a 4:1 ratio. The protein structures are encoded by E-descriptors and transformed into uniform vectors by the auto- and cross-covariance methods. The most relevant descriptors are selected by the gain/ratio technique. The models generated by Random Forest, Multilayer Perceptron, and XGBoost algorithms demonstrate superior predictive performance on the test sets, surpassing predictions made by VaxiJen 2.0-an established gold standard in viral immunogenicity prediction. The key attributes determining immunogenicity in viral proteins are specific fingerprints in hydrophobicity and steric properties.

Delineating postinfarct ventricular tachycardia substrate with dynamic voltage mapping in areas of omnipolar vector disarray

BackgroundDefining post-infarct ventricular arrhythmic substrate is challenging with voltage mapping alone, though may be improved in combination with an activation map. Omnipolar Technology on the EnSite X system displays activation as vectors that can be superimposed onto a voltage map. ObjectiveTo optimise voltage map settings during ventricular tachycardia (VT) ablation, adjusting them dynamically using Omnipolar vectors. MethodsConsecutive patients undergoing substrate mapping were retrospectively studied. We categorised Omni-vectors as “uniform” when pointing in one direction, or in “disarray” when pointing in multiple directions. We superimposed vectors onto voltage maps coloured purple in tissue >1.5mV, and the voltage settings were adjusted so uniform vectors appeared within purple voltages, a process termed “Dynamic Voltage Mapping” (DVM). Vectors in disarray appeared within red-blue lower voltages. Results17 substrate maps were studied in 14 patients (mean age 63±13 years; mean LVEF 35±6%, median 4 (IQR 2-8.5) recent VT episodes). The DVM mean voltage threshold that differentiated tissue supporting uniform vectors from disarray was 0.27mV, ranging between patients from 0.18-0.50mV, with good inter-observer agreement (median difference: 0.00mV). We found that VT isthmus components, as well as sites of latest activation, isochronal crowding, and excellent pace-maps co-located with tissue along the DVM borderzone surrounding areas of disarray. ConclusionDynamic Voltage Mapping, guided by areas of Omnipolar vector disarray, allows for individualised post-infarct ventricular substrate characterisation. Tissue bordering areas of disarray may harbour greater arrhythmogenic potential.

Position-specific evolution in transcription factor binding sites, and a fast likelihood calculation for the F81 model.

Transcription factor binding sites (TFBS), like other DNA sequence, evolve via mutation and selection relating to their function. Models of nucleotide evolution describe DNA evolution via single-nucleotide mutation. A stationary vector of such a model is the long-term distribution of nucleotides, unchanging under the model. Neutrally evolving sites may have uniform stationary vectors, but one expects that sites within a TFBS instead have stationary vectors reflective of the fitness of various nucleotides at those positions. We introduce 'position-specific stationary vectors' (PSSVs), the collection of stationary vectors at each site in a TFBS locus, analogous to the position weight matrix (PWM) commonly used to describe TFBS. We infer PSSVs for human TFs using two evolutionary models (Felsenstein 1981 and Hasegawa-Kishino-Yano 1985). We find that PSSVs reflect the nucleotide distribution from PWMs, but with reduced specificity. We infer ancestral nucleotide distributions at individual positions and calculate 'conditional PSSVs' conditioned on specific choices of majority ancestral nucleotide. We find that certain ancestral nucleotides exert a strong evolutionary pressure on neighbouring sequence while others have a negligible effect. Finally, we present a fast likelihood calculation for the F81 model on moderate-sized trees that makes this approach feasible for large-scale studies along these lines.

Decomposition-Based Multiobjective Optimization Algorithms With Adaptively Adjusting Weight Vectors and Neighborhoods

The decomposition-based multi-objective optimization algorithm (MOEA/D) is an effective method of solving a multi-objective optimization problem (MOP). The main idea of MOEA/D is that the objectives are weighted through different vectors to form different subproblems, and an optimal solution set is obtained by co-evolution in a certain neighborhood. However, with the increase of objectives, the number of non-dominated solutions increases exponentially, resulting in the deteriorated capability of searching for optimal solutions. In addition, for an optimization problem with the complex Pareto front(PF), the selection pressure of non-dominated solutions is insufficient. To make evolution more efficient, a decomposition-based multi-objective optimization algorithm with adaptively adjusting weight vectors and neighborhoods (MOEA/D-AAWN) is developed in this paper. Firstly, the evolutionary direction of each subproblem is analyzed and the Sparsity function (Spa) is proposed to measure the population density on the PF. By using Spa, a method of generating uniform vectors is presented to improve the diversity of solutions. Besides, a method of adaptively adjusting neighborhoods is given. It adjusts neighborhoods according to the number of iterations and the Spa value of its corresponding subproblem. In this way, the computational resource can be effectively allocated, leading to the improvement in evolutionary efficiency. The proposed algorithm is applied to solve a series of benchmark optimization instances, and the experimental results show that the proposed algorithm outperforms comparison algorithms in runtime, convergence, and diversity.

Adaptive controller design and disturbance attenuation for minimum phase multiple‐input multiple‐output linear systems with noisy output measurements and with measured disturbances

SummaryIn this paper, we present a systematic procedure for robust adaptive control design for minimum phase uncertain multiple‐input multiple‐output linear systems that are right invertible and can be dynamically extended to a linear system with vector relative degree using a dynamic compensator that is known. For this class of systems, it is always possible to dynamically extend them, and/or integrate a select set of output channels, and/or padding dummy state variables to arrive at a system model that admits uniform vector relative degree and uniform observability indices that is further minimum phase according to Reference 13. We assume that the uniform vector relative degree is known and an upper bound for the uniform observability indices is known. We also assume that the unknown parameter vector lies in a convex compact set such that the high frequency gain matrix remains invertible for any parameter vector value in the set. These are the assumptions that allow for a successful design of a robust adaptive controller. A numerical example is included to fully illustrate the controller design and the effectiveness of the controller.

Multivariate Multiplicative Functions of Uniform Random Vectors in Large Integer Domains

Multivariate Multiplicative Functions of Uniform Random Vectors in Large Integer Domains

A novel residual subsampling method for skew-normal mode regression model with massive data

With the advent of big data, the fields of biomedicine and economics generate massive data with skew characteristics. Numerous methods have been proposed for modeling either skewed or massive data, whereas most existing methods cannot allow a direct handling of massive and skewed data. We first investigate the subsampling algorithms for skew-normal mode regression model, which include uniform subsampling, leverage subsampling, optimal subsampling, and vector mode subsampling. Since the aforementioned algorithms mainly leverage the value of the information module to calculate the sampling probability without accounting for the residuals in the modeling process. This observation motivates us to propose a novel residual subsampling method with applications to massive data. We then employ the signal-to-noise ratio (SNR) to carry out simulation studies to compare the performance of various sampling methods under various information quantities. Finally, a real-data example is provided for illustrative methods.

An Efficient Code-Embedding-Based Vulnerability Detection Model for Ethereum Smart Contracts

Efficient and convenient vulnerability detection for smart contracts is a key issue in the field of smart contracts. The earlier vulnerability detection for smart contracts mainly relies on static symbol analysis, which has high accuracy but low efficiency and is prone to path explosion. In this paper, the authors propose a static method for vulnerability detection based on deep learning. It first disassembles Ethereum smart contracts into opcode sequences and then converts the vulnerability detection problem into a natural language text classification problem. The word vector method is employed to map each opcode to a uniform vector space, and the opcode sequence matrix is trained by the TextCNN method to detect vulnerabilities. Furthermore, a code obfuscation method is given to enhance and balance the dataset, while three different opcode sequence generation methods are proposed to construct features. The experimental results verify that the average prediction accuracy of each smart contract exceeds 96%, and the average detection time is less than 0.1 s.

A Statistical Comparison of Call Volume Uniformity Due to Mailing Strategy

Abstract For operations such as a decennial census, the U.S. Census Bureau sends mail to potential respondents inviting a self-response. It is suspected that the mailing strategy affects the distribution of call volumes to the U.S. Census Bureau's telephone helplines. For staffing purposes, more uniform call volumes throughout the week are desirable. In this work, we formulate tests and confidence intervals to compare uniformity of call volumes resulting from competing mailing strategies. Regarding the data as multinomial observations, we compare pairs of call volume observations to determine whether one mailing strategy has multinomial cell probabilities closer to the uniform probability vector compared to another strategy. A motivating illustration is provided by call volume data recorded in three studies which were carried out in advance of the 2020 Decennial Census.

Decoupled Fault-Tolerant Model Predictive Current Control for Dual Three-Phase PMSMs With Harmonic Compensation

This article proposes a decoupled fault-tolerant model predictive current control for a dual three-phase permanent magnet synchronous motor with harmonic compensation. The harmonics caused by nonsinusoidal back electromotive force can be well controlled under the open-circuit fault scenario by designing a harmonic closed-loop scheme. First, a decoupled predictive model and fault-tolerant voltage vectors are deduced based on a reduced-dimension matrix, which can eliminate the coupling issues between the harmonic and fundamental subspaces. Afterward, a uniform harmonic-free virtual vector is constructed by rearranging the irregular voltage vectors. More importantly, a virtual null vector is designed in the scheme, where the virtual null vector is effective in the harmonic subspace and has no components in the fundamental subspace. So, the harmonics can be further controlled without affecting torque and flux generation. Extensive experimental results verify the effectiveness of the proposed method.

Differential behavior of magnetic field and magnetic vector potential in an optically pumped Rb atomic magnetometer

Although vector potentials are more intrinsic physical quantities than magnetic and electric fields, measuring them macroscopically is difficult. A double-nested Helmholtz-type vector potential coil, consisting of an elongated solenoid coil wound around a cylinder, and producing a uniform magnetic vector potential, was developed in this study. The coil is carefully designed to reduce the influence of the leakage magnetic field and the scalar potential generated by the coil’s electrical resistance on the measurement. It has the ability to toggle between vector potential and magnetic field generation. We adapted the coil for use in an optically pumped atomic magnetometer. We also developed an optically pumping Rb atomic magnetometer that can calibrate in a zero magnetic field and applied a time-varying magnetic vector potential. We found that the output signal changed with the vector potential even when there was virtually no magnetic field. With increasing frequency, the output voltage decreases for the magnetic signal and increases for the magnetic vector potential signal. The results revealed that the atomic magnetometer is influenced not only by the magnetic field but also by the magnetic vector potential and that the frequency responses are opposite.

Delocalization and re-entrant localization of flat-band states in non-Hermitian disordered lattice models with flat bands

Abstract We present a numerical study of Anderson localization in disordered non-Hermitian lattice models with flat bands. Specifically, we consider 1D stub and 2D kagome lattices that have a random scalar potential and a uniform imaginary vector potential and calculate the spectra of the complex energy, the participation ratio, and the winding number as a function of the strength of the imaginary vector potential, h. The flat-band states are found to show a double transition from localized to delocalized and back to localized states with h, in contrast to the dispersive-band states going through a single delocalization transition. When h is sufficiently small, all flat-band states are localized. As h increases above a certain critical value h1, some pairs of flat-band states become delocalized. The participation ratio associated with them increases substantially and their winding numbers become nonzero. As h increases further, more and more flat-band states get delocalized until the fraction of the delocalized states reaches a maximum. For larger h values, a re-entrant localization takes place and, at another critical value h2, all flat-band states return to compact localized states with very small participation ratios and zero winding numbers. This re-entrant localization transition, which is due to the interplay among disorder, non-hermiticity, and the flat band, is a phenomenon occurring in many models having an imaginary vector potential and a flat band simultaneously. We explore the spatial characteristics of the flat-band states by calculating the local density distribution.

A Rough-to-Fine Evolutionary Multiobjective Optimization Algorithm.

This article presents a rough-to-fine evolutionary multiobjective optimization algorithm based on the decomposition for solving problems in which the solutions are initially far from the Pareto-optimal set. Subsequently, a tree is constructed by a modified k -means algorithm on N uniform weight vectors, and each node of the tree contains a weight vector. Each node is associated with a subproblem with the help of its weight vector. Consequently, a subproblem tree can be established. It is easy to find that the descendant subproblems are refinements of their ancestor subproblems. The proposed algorithm approaches the Pareto front (PF) by solving a few subproblems in the first few levels to obtain a rough PF and gradually refining the PF by involving the subproblems level-by-level. This strategy is highly favorable for solving problems in which the solutions are initially far from the Pareto set. Moreover, the proposed algorithm has lower time complexity. Theoretical analysis shows the complexity of dealing with a new candidate solution is O(M logN) , where M is the number of objectives. Empirical studies demonstrate the efficacy of the proposed algorithm.

Vector bundles on flag varieties

AbstractWe study vector bundles on flag varieties over an algebraically closed field k. In the first part, we suppose to be the Grassmannian parameterizing linear subspaces of dimension d in , where k is an algebraically closed field of characteristic . Let E be a uniform vector bundle over G of rank . We show that E is either a direct sum of line bundles or a twist of the pullback of the universal subbundle or its dual by a series of absolute Frobenius maps. In the second part, splitting properties of vector bundles on general flag varieties in characteristic zero are considered. We prove a structure theorem for bundles over flag varieties which are uniform with respect to the ith component of the manifold of lines in . Furthermore, we generalize the Grauert–Mlich–Barth theorem to flag varieties. As a corollary, we show that any strongly uniform i‐semistable bundle over the complete flag variety splits as a direct sum of special line bundles.

Multi-Function Reflective Vector Light Fields Generated by All-Dielectric Encoding Metasurface.

Traditional optics usually studies the uniform polarization state of light. Compared with uniform vector beams, non-uniform vector beams have more polarization information. Most of the research on generating cylindrical vector beams using metasurfaces focuses on generating transmitted beams using the geometric phase. However, the geometric phase requires the incident light to be circularly polarized, which limits the design freedom. Here, an all-dielectric reflective metasurface is designed to generate different output light according to the different polarization states of the incident light. By combining the two encoding arrangements of the dynamic phase and the geometric phase, the output light is a radial vector beam when the linearly polarized light is incident along the x-direction. Under the incidence of linearly polarized light along the y-direction, the generated output light is an azimuthal vector beam. Under the incidence of left-handed circularly polarized light, the generated output light is a vortex beam with a topological charge of -1. Under the incidence of right-handed circularly polarized light, the generated output light is a vortex beam with a topological charge of +1. The proposed reflective metasurface has potential applications in generating vector beams with high integration.