Uniform Vector Research Articles

On training non-uniform fuzzy partitions for function approximation using differential evolution: A study on fuzzy transform and fuzzy projection

This paper focuses on the use of differential evolution to improve the approximation properties of function approximation models based on fuzzy partitions. Two cases are considered: Fuzzy transform and Fuzzy projection, and the design of hybrid evolutionary fuzzy systems, is studied. Even though function approximation techniques based on fuzzy partitions have been well studied, few papers consider the problem of centroid selection of the basis functions. Thus, in most cases uniform fuzzy partitions are considered. By using an evolutionary algorithm a systematic approach on the selection of the partition, is provided. The optimisation problem involves the determination of the model parameters, which in our case are the fuzzy partition’s membership functions’ locations. The proposed method is tested on the scattered data approximation problem, in a regression sense, that is given a set of sparse data the latent function is approximated. Numerical studies on one and two-dimensional test functions demonstrate that the evolutionary algorithm based fuzzy projection displays high performance in terms of approximation error. Moreover, the proposed approach shows high approximation capabilities with a small number of basis functions. Comparison results, with uniform fuzzy partition models, neural networks and support vector machines, are provided.

Pseudorandom vector generation using elliptic curves and applications to Wiener processes

In this paper we present, using the arithmetic of elliptic curves over finite fields, an algorithm for the efficient generation of a sequence of uniform pseudorandom vectors in high dimensions, that simulates a sample of a sequence of i.i.d. random variables, with values in the hypercube [0,1]d with uniform distribution. As an application, we obtain, in the discrete time simulation, an efficient algorithm to simulate, uniformly distributed sample path sequence of a sequence of independent standard Wiener processes. This could be employed for use, in the full history recursive multi-level Picard approximation method, for numerically solving the class of semilinear parabolic partial differential equations of the Kolmogorov type.

Real-time high quality font generation with Conditional Font GAN

Designing and generating novels fonts manually is a laborious and time-consuming process owing to the large number and complexity of characters in the majority of language systems. Recent advancements in generative adversarial networks (GANs) have significantly improved font generation. These GAN-based approaches either handle the font generation as a vanilla GAN problem (that is, by synthesizing characters from a uniform latent vector) or an image-to-image translation problem. While the former approach has no limitation in generating diverse font styles, the generated fonts contain artifacts and can operate only on low-resolution images, thus impairing their usability. The latter approach generates high-quality font images for previously observed fonts, but the quality degrades during the inference phase while designing novel fonts. Furthermore, additional fine-tuning steps are required to achieve photorealistic results, which is computationally expensive and time-consuming. To address the shortcomings of these approaches, we propose a font generation method that employs the vanilla GAN approach to generate an infinite number of font styles but focuses on the real-time generation of photo-realistic font images. Additionally, we strive to create high-resolution images that can be used in practical applications. To accomplish this, we propose a conditional font GAN (CFGAN) with a sophisticated network architecture that is designed to generate novel style-consistent diverse font character sets. We control the generated characters in the proposed network using a non-trainable fixed character vector, while the style variation sampled from a Gaussian distribution is fused at all blocks of the generator through adaptive instance normalization (AdaIN) operation. Thus, the generator architecture can simultaneously generate an infinite number of font styles with style consistency and diversity during inference. We conducted various quantitative and qualitative experiments to demonstrate the effectiveness of the proposed model in terms of both image quality and computational cost.

Symmetry Reduction to Optimize a Graph-based Polynomial From Queueing Theory

For given integers $n$ and $d$, both at least 2, we consider a homogeneous multivariate polynomial $f_d$ of degree $d$ in variables indexed by the edges of the complete graph on $n$ vertices and coefficients depending on cardinalities of certain unions of edges. Cardinaels, Borst and Van Leeuwaarden (arXiv:2111.05777, 2021) asked whether $f_d$, which arises in a model of job-occupancy in redundancy scheduling, attains its minimum over the standard simplex at the uniform probability vector. Brosch, Laurent and Steenkamp [SIAM J. Optim. 31 (2021), 2227--2254] proved that $f_d$ is convex over the standard simplex if $d=2$ and $d=3$, implying the desired result for these $d$. We give a symmetry reduction to show that for fixed $d$, the polynomial is convex over the standard simplex (for all $n\geq 2$) if a constant number of constant matrices (with size and coefficients independent of $n$) are positive semidefinite. This result is then used in combination with a computer-assisted verification to show that the polynomial $f_d$ is convex for $d\leq 9$.

Fluctuations of the Magnetization in the Block Potts Model

In this note we study the block spin mean-field Potts model, in which the spins are divided into s blocks and can take qge 2 different values (colors). Each block is allowed to contain a different proportion of vertices and behaves itself like a mean-field Ising/Potts model which also interacts with other blocks according to different temperatures. Of particular interest is the behavior of the magnetization, which counts the number of colors appearing in the distinct blocks. We prove central limit theorems for the magnetization in the generalized high-temperature regime and provide a moderate deviation principle for its fluctuations on lower scalings. More precisely, the magnetization concentrates around the uniform vector of all colors with an explicit, but singular, Gaussian distribution. In order to remove the singular component, we will also consider a rotated magnetization, which enables us to compare our results to various related models.

Conditional transport of geometrical flamelet statistics in planar freely propagating turbulent premixed flames

The geometrical flamelet statistics in a turbulent premixed flame are represented by c ¯ , Σ f , 〈 n 〉 f , 〈 ∇ · n 〉 f and 〈 | ∇ · n | 〉 f which are respectively mean reaction progress variable, flame surface density, mean orientation vector, mean curvature and mean absolute curvature. New conditional transport equations are derived for the listed geometrical statistics of successively higher orders in terms of net normal flame motion from the equation of the reaction progress variable. They are simpler and allow easier closure than the unconditionally averaged formulations involving the tangential velocity component and the turbulent flux term involving countergradient diffusion. Balance is checked for all component terms of those transport equations in two freely propagating, constant density DNS flames in statistical steadiness. Results show that the mean orientation vector and the mean absolute curvature remain approximately uniform in local equilibrium with negligible spatial transport except near the edges of a flame brush . A simple closure strategy is suggested with the flame surface density given in terms of uniform mean absolute curvature and mean orientation vectors, 〈 n x 〉 f and 〈 n x 〉 K , given as the conditional averages weighted by Σ f ′ ( = ∂ c / ∂ n ) and ∂ 2 c / ∂ n 2 respectively. The governing equations and closure models are expected to be valid in planar freely propagating turbulent premixed flames of either constant or variable density with heat release. The suggested closure requires prior knowledge on the magnitude of the mean orientation vector and the mean absolute curvature given as the ratio of laminar and turbulent flame speeds and the inverse characteristic wrinkling scale through a flame brush. Good agreement is shown against DNS results of two constant density flames for closure models of the conditional velocities, 〈 u 〉 f and 〈 S d 〉 f , and for the predicted profiles of c ¯ and Σ f except for minor deviation near the edges. The suggested closure scheme may be extended to general turbulent premixed flames, while further work may be required for proper closure relationships under the given circumstances.

Attributed multiplex graph clustering: A heuristic clustering-aware network embedding approach

Attributed multiplex graph clustering, which partitions graph nodes from different relationships into different clusters with each cluster retaining structure closeness and attribute homogeneity simultaneously, is a fundamental graph data analysis task. Although network embedding has shown to be useful in a variety of graph analysis tasks, research dedicated to the attributed multiplex graph clustering, an important aspect of graph network analysis, is limited. Some efforts have been made for multiplex graph networks with network embedding techniques. However, most of this work has overlooked the clustering-aware information, which has not been fully explored. To solve these issues, we propose a fast method with sequenced-based network embedding for attributed multiplex graph clustering, namely NEAMC, to efficiently capture the clustering-aware information between nodes and different relationships and place them into a uniform vector space. A novel and heuristic clustering-aware across multi-relationship random walk node sampling strategy is proposed, which can not only select the relationship to proceed according to the information level of each relationship to retain the clustering-aware relationship and interaction among different relationships, but also leverage the node similarity to sample node sequences to retain the clustering-aware interactive information between nodes. Therefore, NEAMC can improve the attributed multiplex graph clustering to maintain the structure closeness and attribute homogeneity of the cluster. NEAMC is evaluated on five datasets, and the results demonstrate that it outperforms existing competitive baselines.

On uniform flag bundles on Fano manifolds

As a natural extension of the theory of uniform vector bundles on Fano manifolds, we consider uniform principal bundles, and study them by means of the associated flag bundles, as their natural projective geometric realizations. In this paper, we develop the necessary background and prove some theorems that are flag bundle counterparts of some of the central results in the theory of uniform vector bundles.

Models of federalism in Switzerland and Germany: a comparative analysis

The article is the first to structure the concept of “model of federalism”. According to the author, it includes such essential elements as the initial factors that influenced the formation of the state, the stages of its development and the essential components of the model, namely, historical-typological and genesis ones features of federalism and the vector of development. Based on the use of historical and state literature, constitutional and legal materials, and the results of a recently published international political science project, the author examines the models of federalism of neighboring countries-Switzerland and Germany, formed in the middle of the XIX century, proposes its graphic description. These states vary in territorial extent and state dynamics, but are still similar at the initial stages of the formation of a federal model, namely the transition to a federal form from a confederal one. Also, the Swiss and German models were radically different from the point of view of their essence and their genesis, but they had a uniform centripetal vector, which in modern globalization conditions is characterized by a strengthening of the management center and a decrease in the autonomy of the subjects.

An All-in-One Geometric Algorithm for Cutting, Tearing, and Drilling Deformable Models

Conformal geometric algebra (CGA) is a framework that allows the representation of objects, such as points, planes and spheres, and deformations, such as translations, rotations and dilations as uniform vectors, called multivectors. In this work, we demonstrate the merits of multivector usage with a novel, integrated rigged character simulation framework based on CGA. In such a framework, and for the first time, one may perform real-time cuts and tears as well as drill holes on a rigged 3D model. These operations can be performed before and/or after model animation, while maintaining deformation topology. Moreover, our framework permits generation of intermediate keyframes on-the-fly based on user input, apart from the frames provided in the model data. We are motivated to use CGA as it is the lowest-dimension extension of dual-quaternion algebra that amends the shortcomings of the majority of existing animation and deformation techniques. Specifically, we no longer need to maintain objects of multiple algebras and constantly transmute between them, such as matrices, quaternions and dual-quaternions, and we can effortlessly apply dilations. Using such an all-in-one geometric framework allows for better maintenance and optimization and enables easier interpolation and application of all native deformations. Furthermore, we present these three novel algorithms in a single CGA representation which enables cutting, tearing and drilling of the input rigged model, where the output model can be further re-deformed in interactive frame rates. These close to real-time cut,tear and drill algorithms can enable a new suite of applications, especially under the scope of a medical VR simulation.

Laser-Material Interactions of High-Quality Ultrashort Pulsed Vector Vortex Beams.

Diffractive multi-beams based on 1 × 5 and 2 × 2 binary Dammann gratings applied to a spatial light modulator (SLM) combined with a nanostructured S-wave plate have been used to generate uniform multiple cylindrical vector beams with radial and azimuthal polarizations. The vector quality factor (concurrence) of the single vector vortex beam was found to be C = 0.95 ± 0.02, hence showing a high degree of vector purity. The multi-beams have been used to ablate polished metal samples (Ti-6Al-4V) with laser-induced periodic surface structures (LIPSS), which confirm the polarization states unambiguously. The measured ablation thresholds of the ring mode radial and azimuthal polarizations are close to those of a Gaussian mode when allowance is made for the expected absolute intensity distribution of a ring beam generated from a Gaussian. In addition, ring mode vortex beams with varying orbital angular momentum (OAM) exhibit the same ablation threshold on titanium alloy. Beam scanning with ring modes for surface LIPSS formation can increase micro-structuring throughput by optimizing fluence over a larger effective beam diameter. The comparison of each machined spot was analysed with a machine learning method—cosine similarity—which confirmed the degree of spatial uniformity achieved, reaching cosθ > 0.96 and 0.92 for the 1 × 5 and 2 × 2 arrays, respectively. Scanning electron microscopy (SEM), optical microscopy and white light surface profiling were used to characterize and quantify the effects of surface modification.

Multivariate radial symmetry of copula functions: finite sample comparison in the i.i.d case

Abstract Given a d-dimensional random vector X = (X 1, . . ., X d ), if the standard uniform vector U obtained by the component-wise probability integral transform (PIT) of X has the same distribution of its point reflection through the center of the unit hypercube, then X is said to have copula radial symmetry. We generalize to higher dimensions the bivariate test introduced in [11], using three different possibilities for estimating copula derivatives under the null. In a comprehensive simulation study, we assess the finite-sample properties of the resulting tests, comparing them with the finite-sample performance of the multivariate competitors introduced in [17] and [1].

Development of a system based on aerial images for the morphological patterns classification using support vector machine

Oil palm cultivation is one of the major agricultural activities in Colombia. Production performance is related to the good practices in the plantation, mainly regarding the management of phytosanitary conditions. Bud rot disease is the one with the greatest impact in Colombia. The most commonly used technique for its detection is from routine visual inspection on each palm, being costly and inefficient. For this reason, the aim of this study is the development of a classification algorithm based on binary support vector machines for the detection of Bud Rot. The model was obtained from 798 aerial images acquired by unmanned aerial vehicles. Each image was tagged by an expert palm grower based on the presence or absence of the disease. These images were described by 531 morphological features extracted using the concatenation of uniform binary local pattern vectors. Bootstrapping was used to balance the classes, obtaining 507 observations per class. To evaluate the performance metrics of the classifier, an 8-fold Monte Carlo cross-validation was implemented by randomly splitting the data set into training (80%), validation (10%), and test (10%) sets with balanced classes. Finally, the model achieved a performance greater than 96.0%. This indicates that the model developed could be a great technique to automate bud rot detection with high reliability, increasing the efficiency in the recognition. All these thanks to the fusion of Machine Learning techniques with the phenomena of optical physics.

КОНСТРУЮВАННЯ ДИСКРЕТНИХ СІТОК ТА ПОВЕРХОНЬ НА ОСНОВІ ІЗОТРОПНИХ В-СПЛАЙНІВ

Modeling geometric objects in isotropic space allows us to simplify a number of calculations related to the calculation of differential characteristics. To create the ability to control the curved contours of objects, it is advisable to apply parametric curves based on characteristic polygons. For each type of such curves, there are limitations to the calculation of coordinates and lengths in isotropic space. Studies on modeling isotropic B-splines and based on them grids and surfaces are local in nature and require more detailed consideration. The paper proposes to model isotropic B-splines based on the recursive Cox de Boer formulas. The coordinates of the points for the spline are calculated based on the equal to zero side lengths of the characteristic polygons. Examples of constructed splines for different types of nodal vectors are given. It is shown that some types of nodal vectors do not allow the curve to pass through the start and end points of polygons. In this case, it is necessary to carry out adjustments to the nodal vector. The authors of the work developed an algorithm for modeling discrete grids and surfaces based on B-splines. All calculations are made in a complex space. When displaying geometric objects, the selection of the real part and the transition to the real space are carried out. As an example, visualization of the grid and surface based on an open uniform nodal vector is given. To research isotropic discrete curves, grids and surfaces based on B-splines, C # software was created for the .Net Core platform. Further research is related to the study of the influence of nodal vectors on the basis of an isotropic B-spline and surfaces. Keywords: isotropic curve, B-spline, discrete grids, discrete surfaces based on isotropic splines.

Two-stage MUSIC with reduced spectrum search for spherical arrays

The multiple signal classification (MUSIC) algorithm is widely used in direction of arrival (DOA) estimation. Conventional MUSIC-like algorithms suffer from the heavy computational burden imposed by the two-dimensional (2-D) angle search and an exhaustive spectral search. We propose a two-stage unitary spherical harmonics MUSIC (TSU-SHMUSIC) that converts 2-D MUSIC into two new one-dimensional (1-D) MUSICs. The spherical harmonic steering vector is expressed in two forms, the linear weight of a uniform phase vector and the linear weight of a vector constructed by associated Legendre functions. These two expressions are used conjunction with Lagrange multiplier method to obtain two new corresponding search functions for the elevation and azimuth. We exploit the characteristics of real-valued spherical harmonics to construct virtual signals from the mirror directions of signal sources. A new noise subspace is computed from the covariance matrices of the virtual and real signals. We use this noise subspace to reduce the angle search ranges to half of the total angular field of view. The proposed methods have a considerably lower computational complexity than U-SHMUSIC. Numerical simulations demonstrate that the proposed methods provide perform better than the two-stage decoupled approach (TSDA).

Decomposition and Dominance Relation Based Many-objective Evolutionary Algorithm

In recent year, the Many-objective Optimization Problems (MaOPs) have become an increasingly hot research area in evolutionary computation. However, it is still a difficult problem to achieve a good balance between convergence and diversity on solving various kinds of MaOPs. To alleviate this issue mentioned above, a Decomposition and dominance relation based many-objective Evolutionary Algorithm(DdrEA) is proposed in this paper. Firstly, the population is decomposed into numbers of sub-populations by using a set of uniform weight vectors, in which they are optimized in a cooperative manner. Then, the fitness value of solution in each sub-population is calculated by angle dominance relation and angle. Finally, elite selection strategy is performed according to its corresponding fitness value. That is, in each subspace, the solution with the smallest fitness value is selected as the elite solution to enter the next generation. Comparing with several high-dimensional and multi-objective evolutionary algorithms (NSGA-II/AD, RVEA, MOMBI-II), the experimental results show that the performance of the proposed algorithm DdrEA is better than that of the comparison algorithm, and the convergence and diversity of the population can be effectively balanced.

Constraint on vector coherent oscillation dark matter with kinetic function

A spatially uniform vector condensate can be formed during inflation if the vector boson is coupled to the inflaton through nontrivial kinetic function. The coherent oscillation of such a massive vector boson is a dark matter candidate. In this paper we show that the curvature/isocurvature perturbation gives stringent constraint on this scenario and no consistent parameter space is found in a minimal setup.

A new self-starting drainage method for slope stabilization and its application

Drainage is a cost-effective way to stabilize slopes. However, clogging has always been a factor that decreases the sustainability and efficiency of the drainage method in slope stabilization. A new drainage method utilizing the hydraulic principle is presented in this paper. A deterministic method, which is performed by integrated software, for evaluating the factor of safety (FOS) under the action of a given self-starting drainage design is proposed correspondingly. A framework for the optimized design of self-starting drainage is established, and the following steps are mainly included: The optimal dip angles of the inclined boreholes are determined by a plotting method; the optimal lengths of the permeable section of the inclined boreholes are determined based on uniform design and support vector machine; the concept of Pareto front is introduced to determine the most preferred design in design space considering multiple objectives including safety, cost, and drain effectiveness. The entire process is illustrated with a case study, the Qili landslide in Zhejiang Province, China.

Hybrid Beamforming in MU-MIMO Using Partial Interfering Beam Feedback

We propose a hybrid beamforming scheme with partial interfering beam feedback for a codebook-based multi-user multiple-input multiple-output (MU-MIMO) system, where users feed back information only about the top- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula> transmit beams. For the analog part of the precoding, we consider two codebooks, the conventional Discrete Fourier Transform (DFT) codebook with uniform amplitude beamforming vectors and the Taylor codebook with non-uniform amplitude beamforming vectors. For the digital precoding part, the effective channel matrix is approximated and used for zero-forcing (ZF). We also propose a beam pairing algorithm that results in reduced inter-beam interference and simplifies beam and user selection in MU-MIMO. When <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula> is equal to the number of beams in the transmit codebook, the proposed scheme includes an existing scheme with full effective channel matrix feedback as a special case. Numerical results show that the proposed hybrid beamforming performs better than an existing hybrid precoding scheme based on channel reconstruction.

Archimedean non-vanishing, cohomological test vectors, and standard L-functions of GL2n: Complex case

The purpose of this paper is to study the local zeta integrals of Friedberg-Jacquet at complex place and to establish similar results to the recent work [4] joint with C. Chen and D. Jiang. In this paper, we will (1) give a necessary and sufficient condition on an irreducible essentially tempered cohomological representation π of GL2n(C) with a non-zero Shalika model; (2) construct a new twisted linear period Λs,χ and give a different expression of the linear model for π; (3) give a necessary and sufficient condition on the character χ such that there exists a uniform cohomological test vector v∈Vπ (which we construct explicitly) for Λs,χ. As a consequence, we obtain the non-vanishing of local Friedberg-Jacquet integral at complex place. All of the above are essential preparations for attacking a global period relation problem in the forthcoming paper ([11]).