Approximate Decomposition Research Articles

Broadband unidirectional transverse light scattering in a V-shaped silicon nanoantenna

The efficient manipulation of light-matter interactions in subwavelength all-dielectric nanostructures offers a unique opportunity for the design of novel low-loss visible- and telecom-range nanoantennas for light routing applications. Several studies have achieved longitudinal and transverse light scattering with a proper amplitude and phase balance among the multipole moments excited in dielectric nanoantennas. However, they only involve the interaction between electric dipole, magnetic dipole, and up to the electric quadrupole. Here, we extend and demonstrate a unidirectional transverse light scattering in a V-shaped silicon nanoantenna that involves the balance up to the magnetic quadrupole moment. Based on the long-wavelength approximation and exact multipole decomposition analysis, we find the interference conditions needed for near-unity unidirectional transverse light scattering along with near-zero scattering in the opposite direction. These interference conditions involve relative amplitude and phases of the electromagnetic dipoles and quadrupoles supported by the silicon nanoantenna. The conditions can be applied for the development of either polarization- or wavelength- dependent light routing on a V-shaped silicon and plasmonic nanoantennas.

Attentional Factorized Q-Learning for Many-Agent Learning

The difficulty of Multi-Agent Reinforcement Learning (MARL) increases with the growing number of agents in system. The value function decomposition is an effective way to alleviate the curse of dimension. However, the existing methods usually either can only provide the low-order approximate decomposition of no more than the second-order, or need to spend a lot of effort manually designing the high-order interaction among agents according to experience. Therefore, the existing methods either tend to bear large decomposition error or are not convenient to use. In this paper, a high-order approximate value function decomposition method is proposed, which has the following prominent characteristics: the low-rank vector is exploited to represent value function, the low-order and high-order components share the same input (i.e., the embedding vector), the attention mechanism is used to select the agents participating in the high-order interaction, and all agents share the model parameters if the agents are homogeneous. To our knowledge, this is the first MARL method modeling low- and high-order interaction simultaneously among agents that can be trained end-to-end. Extensive experiments on two different multi-agent problems demonstrate the performance gain of our proposed approach in comparison with strong baselines, particularly when there are a large number of agents.

Retracted] Research on the Recommendation Algorithm of Rural Tourism Routes Based on the Fusion Model of Multiple Data Sources

Rural tourism has become an important force in implementing the rural revitalisation strategy and accelerating rural economic development. The hectic pace of life has made more and more city dwellers yearn for rural life, and travelling in the countryside has become their weekend choice. However, the current level of rural tourism informationization is low, the publicity is insufficient, the tourists’ awareness is low, and the source of customers is seriously insufficient. To this end, this paper proposes a relatively novel multidata source fusion tourism recommendation algorithm, which adopts the idea of tensor orthogonal decomposition and fuses multisource data models to predict the target domain’s for rating. The integrated consideration of multiple data sources under the do‐it‐yourself approach assists the target domain to discover the target user neighbourhood users more quickly and to discover the user’s interest degree more accurately. It is worth pointing out that the recommendation algorithm proposed in this paper under the fusion of multiple data sources is not necessarily applicable to data sources with weak correlation, such as travel data sources and music data sources, which are relatively weakly correlated, and the algorithm is slightly weak in making predictions of user preferences.

Signal Models for Changes in Polarimetric SAR Data

Synthetic aperture radar (SAR) polarimetry can improve change detection in terms of detection capabilities. In this work, we are proposing to extend the idea of target decomposition to changes affecting partial targets. This will allow the separation of polarimetric-dependent changes, providing extra information that can be used to better understand the processes affecting the targets. Three models for changes are proposed and compared. The methodologies are based on Lagrangian optimizations of distinct operators built using quadratic forms for a power ratio and a power difference. The optimizations can be accomplished by diagonalizations of specific matrices derived from polarimetric covariance matrices. These are, therefore, spectral decompositions of an appropriate matrix which we define as change matrix. The theoretical validity of the models is assessed using Monte Carlo simulations. Additionally, we perform real data validation exploiting L-band quad-polarimetric data from the E-SAR (DLR) SARTOM 2006 campaign and ALOS PALSAR (JAXA) acquisitions in Morecombe Bay (U.K.). We observed that the two algorithms based on power difference allow to decompose the change into the minimal set of scattering mechanisms (SMs) that have been added or removed from the scene. The two algorithms differ on the initial assumption on the change. On the other hand, the ratio operator provides a better detection performance although the eigenvalues do not correspond to meaningful SMs. A combination of the three methodologies can, therefore, improve detection and classification of changes.

Approximate Dynamic Programming Decompositions for Economic Dispatch in Microgrids

Three novel approximate dynamic programming algorithms based on the temporal, spatial, and spatiotemporal decomposition are proposed for the economic dispatch problem (EDP) in a distribution energy system with complex topology and many non-dispatchable renewable energy sources and energy storage systems (ESS). Computational efficiency of the proposed algorithms is compared and convergence to the optimal solution is shown in numeric experiments on the example of the two-day hourly EDP for the IEEE 33bw test network having 200+ consumers, 150+ energy storages, and 1000+ consuming devices.

An Iterative Coordinate Descent Algorithm to Compute Sparse Low-Rank Approximations

In this paper, we describe a new algorithm to build a few sparse principal components from a given data matrix. Our approach does not explicitly create the covariance matrix of the data and can be viewed as an extension of the Kogbetliantz algorithm to build an approximate singular value decomposition for a few principal components. We show the performance of the proposed algorithm to recover sparse principal components on various datasets from the literature and perform dimensionality reduction for classification applications.

ДВУХПАРАМЕТРИЧЕСКИЙ МЕТОД ОПРЕДЕЛЕНИЯ КОЭФФИЦИЕНТА ИНТЕНСИВНОСТИ НАПРЯЖЕНИЙ KI ТРЕЩИНОПОДОБНЫХ ДЕФЕКТОВ МЕТОДОМ ГОЛОГРАФИЧЕСКОЙ ИНТЕРФЕРОМЕТРИИ

A new method has been developed for finding the stress intensity coefficient and the nominal stress σox for a plate with a crack-like (elliptical) defect. As an experimental basis, the patterns of bands of absolute path difference obtained on the basis of the method of holographic interferometry are taken. Using Favre ratios and approximate decomposition of stress components for the plane case, the stress intensity coefficient and the nominal stress σox are determined. The difference of the proposed method is in a more accurate representation of the stress tensor in the vicinity of the vertex of a crack like defect. Such representation allows one to take the geometry of the defect into account. The values of the correction function calculated by the proposed method in the formula for theoretical determining of the intensity factor have been higher than those obtained by previously used methods. This indicates a possible underestimation of the magnitude of the intensity factor when using the previously proposed methods. In addition to using more precise formulas for the stress tensor, the approach implies considering the nominal stress and the intensity factor as independent parameters. Full consideration of the crack geometry and loading features is very difficult from a mathematical point of view; however, this property of the method allows partially compensating for the simplifications of the stress tensor analytic expressions. Also, this method makes it possible to determine the main stresses and the intensity of stresses in the vicinity of the vertex of the defect. The obtained formulas agree well with experimental results.

A Novel Model Based on DA-RNN Network and Skip Gated Recurrent Neural Network for Periodic Time Series Forecasting

Deep learning models are playing an increasingly important role in time series forecasting with their excellent predictive ability and the convenience of not requiring complex feature engineering. However, the existing deep learning models still have shortcomings in dealing with periodic and long-distance dependent sequences, which lead to unsatisfactory forecasting performance on this type of dataset. To handle these two issues better, this paper proposes a novel periodic time series forecasting model based on DA-RNN, called DA-SKIP. Using the idea of task decomposition, the novel model, based on DA-RNN, GRU-SKIP and autoregressive component, breaks down the prediction of periodic time series into three parts: linear forecasting, nonlinear forecasting and periodic forecasting. The results of the experiments on Solar Energy, Electricity Consumption and Air Quality datasets show that the proposed model outperforms the three comparison models in capturing periodicity and long-distance dependence features of sequences.

Learning developmental mode dynamics from single-cell trajectories.

Embryogenesis is a multiscale process during which developmental symmetry breaking transitions give rise to complex multicellular organisms. Recent advances in high-resolution live-cell microscopy provide unprecedented insights into the collective cell dynamics at various stages of embryonic development. This rapid experimental progress poses the theoretical challenge of translating high-dimensional imaging data into predictive low-dimensional models that capture the essential ordering principles governing developmental cell migration in complex geometries. Here, we combine mode decomposition ideas that have proved successful in condensed matter physics and turbulence theory with recent advances in sparse dynamical systems inference to realize a computational framework for learning quantitative continuum models from single-cell imaging data. Considering pan-embryo cell migration during early gastrulation in zebrafish as a widely studied example, we show how cell trajectory data on a curved surface can be coarse-grained and compressed with suitable harmonic basis functions. The resulting low-dimensional representation of the collective cell dynamics enables a compact characterization of developmental symmetry breaking and the direct inference of an interpretable hydrodynamic model, which reveals similarities between pan-embryo cell migration and active Brownian particle dynamics on curved surfaces. Due to its generic conceptual foundation, we expect that mode-based model learning can help advance the quantitative biophysical understanding of a wide range of developmental structure formation processes.

Power Quality Disturbance Signal Denoising Based on Overcomplete Representation

A denoising method for power quality (PQ) disturbance signal based on optimized decomposition of overcomplete dictionary is proposed. First, based on the idea of sparse decomposition, an overcomplete synthesis dictionary matching the time‐frequency characteristics of PQ disturbance signal is constructed. Then, the matching pursuit (MP) algorithm is used to search the disturbance parameters in Gabor dictionary, and the improved particle swarm optimization (PSO) algorithm is combined with the improved Nelder–Mead simplex extremum algorithm to improve the search speed and accuracy. Finally, the obtained disturbance parameters and the overcomplete synthesis dictionary are used to extract the disturbance characteristic waveform, and then the noise is separated. This method is used to reduce the noisy PQ signals and compared with the results of wavelet and other noise reduction methods, the results show that the method can effectively denoise PQ signal, and better retain the original characteristics of PQ disturbances. © 2021 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

Fractional cycle decompositions in hypergraphs

AbstractWe prove that for any integer and , there is an integer such that any k‐uniform hypergraph on n vertices with minimum codegree at least has a fractional decomposition into (tight) cycles of length (‐cycles for short) whenever and n is large in terms of . This is essentially tight. This immediately yields also approximate integral decompositions for these hypergraphs into ‐cycles. Moreover, for graphs this even guarantees integral decompositions into ‐cycles and solves a problem posed by Glock, Kühn, and Osthus. For our proof, we introduce a new method for finding a set of ‐cycles such that every edge is contained in roughly the same number of ‐cycles from this set by exploiting that certain Markov chains are rapidly mixing.

A Semianalytic Method for Vibration Analysis of a Sandwich FGP Doubly Curved Shell with Arbitrary Boundary Conditions

Due to the excellent mechanical properties of doubly curved structure and functionally graded porous (FGP) material, the study of their vibration characteristics has attracted wide attention. The main aim of this research is to establish a formulation for free and forced vibration analysis of a new Sandwich FGP doubly curved structure. Four models of Sandwich materials are considered. The potential energy and kinetic energy functions are obtained on the foundation of the first-order shear deformation theory (FSDT). The idea of domain energy decomposition is applied to the theoretical modeling, where the structure is segmented along the generatrix direction. The continuity conditions for the interfaces between adjacent segments are balanced by the weighted parameters. For each segment, the displacement functions are selected as the Jacobi orthogonal polynomials and trigonometric series. The boundary conditions of the structure are obtained by the boundary spring simulation technique. The solution is obtained by the variational operation of the structural functional. The convergence performance and correctness of the theoretical model are examined by several numerical examples. Finally, some novel results are given, where free and forced vibration characteristics of Sandwich FGP doubly curved structures are examined in detail.

Birkhoff’s Decomposition Revisited: Sparse Scheduling for High-Speed Circuit Switches

Data centers are increasingly using high-speed circuit switches to cope with the growing demand and reduce operational costs. One of the fundamental tasks of circuit switches is to compute a sparse collection of switching configurations to support a traffic demand matrix. Such a problem has been addressed in the literature with variations of the approach proposed by Birkhoff in 1946 to decompose a doubly stochastic matrix exactly. However, the existing methods are heuristic and do not have theoretical guarantees on how well a collection of switching configurations (i.e., permutations) can approximate a traffic matrix (i.e., a scaled doubly stochastic matrix). In this paper, we revisit Birkhoff's approach and make three contributions. First, we establish the first theoretical bound on the sparsity of Birkhoff's algorithm (i.e., the number of switching configurations necessary to approximate a traffic matrix). In particular, we show that by using a subset of the admissible permutation matrices, Birkhoff's algorithm obtains an $\epsilon$-approximate decomposition with at most $O( \log(1 / \epsilon))$ permutations. Second, we propose a new algorithm, Birkhoff+, which combines the wealth of Frank-Wolfe with Birkhoff's approach to obtain sparse decompositions in a fast manner. And third, we evaluate the performance of the proposed algorithm numerically and study how this affects the performance of a circuit switch. Our results show that Birkhoff+ is superior to previous algorithms in terms of throughput, running time, and number of switching configurations.

How do we teach and learn with cases?

AbstractIn this article, we review the literature on learning and teaching with cases drawing from several applied professions (e.g., education, business, medicine). First, we summarize the learning philosophies and concepts that ground case‐centered teaching and learning. This section touches on views of professional practice, important and relevant theories and concepts, and the value of decomposition of professional practice. Then, we use the idea of decomposition of professional practice to illuminate for readers how the learning philosophies and concepts that ground case‐centered teaching might show up in evaluation classrooms. This discussion necessarily focuses on instructional design, types of cases, issues to consider in selecting cases, developing meaningful questions, and cultivating the type of learning environment case‐centered teaching and learning demands. Implications for evaluation educators and research on evaluation are noted.

Multi-Modal Image Fusion Based on Matrix Product State of Tensor.

Multi-modal image fusion integrates different images of the same scene collected by different sensors into one image, making the fused image recognizable by the computer and perceived by human vision easily. The traditional tensor decomposition is an approximate decomposition method and has been applied to image fusion. In this way, the image details may be lost in the process of fusion image reconstruction. To preserve the fine information of the images, an image fusion method based on tensor matrix product decomposition is proposed to fuse multi-modal images in this article. First, each source image is initialized into a separate third-order tensor. Then, the tensor is decomposed into a matrix product form by using singular value decomposition (SVD), and the Sigmoid function is used to fuse the features extracted in the decomposition process. Finally, the fused image is reconstructed by multiplying all the fused tensor components. Since the algorithm is based on a series of singular value decomposition, a stable closed solution can be obtained and the calculation is also simple. The experimental results show that the fusion image quality obtained by this algorithm is superior to other algorithms in both objective evaluation metrics and subjective evaluation.

Multilevel Picard iterations for solving smooth semilinear parabolic heat equations

We introduce a new family of numerical algorithms for approximating solutions of general high-dimensional semilinear parabolic partial differential equations at single space-time points. The algorithm is obtained through a delicate combination of the Feynman–Kac and the Bismut–Elworthy–Li formulas, and an approximate decomposition of the Picard fixed-point iteration with multilevel accuracy. The algorithm has been tested on a variety of semilinear partial differential equations that arise in physics and finance, with satisfactory results. Analytical tools needed for the analysis of such algorithms, including a semilinear Feynman–Kac formula, a new class of seminorms and their recursive inequalities, are also introduced. They allow us to prove for semilinear heat equations with gradient-independent nonlinearities that the computational complexity of the proposed algorithm is bounded by O(d,{varepsilon }^{-(4+delta )}) for any delta in (0,infty ) under suitable assumptions, where din {{mathbb {N}}} is the dimensionality of the problem and {varepsilon }in (0,infty ) is the prescribed accuracy. Moreover, the introduced class of numerical algorithms is also powerful for proving high-dimensional approximation capacities for deep neural networks.

Double-Shift: A Low-Power DNN Weights Storage and Access Framework based on Approximate Decomposition and Quantization

One major challenge in deploying Deep Neural Network (DNN) in resource-constrained applications, such as edge nodes, mobile embedded systems, and IoT devices, is its high energy cost. The emerging approximate computing methodology can effectively reduce the energy consumption during the computing process in DNN. However, a recent study shows that the weight storage and access operations can dominate DNN's energy consumption due to the fact that the huge size of DNN weights must be stored in the high-energy-cost DRAM. In this paper, we propose Double-Shift, a low-power DNN weight storage and access framework, to solve this problem. Enabled by approximate decomposition and quantization, Double-Shift can reduce the data size of the weights effectively. By designing a novel weight storage allocation strategy, Double-Shift can boost the energy efficiency by trading the energy consuming weight storage and access operations for low-energy-cost computations. Our experimental results show that Double-Shift can reduce DNN weights to 3.96%–6.38% of the original size and achieve an energy saving of 86.47%–93.62%, while introducing a DNN classification error within 2%.

GENERAL ASSESSMENT OF THE PROSPECTS FOR THE APPLICATION OF THE BIG DATA PARADIGM IN SOCIO-ECONOMIC SYSTEMS

The paper assesses the prospects for the application of the big data paradigm in socio-economic systems through the analysis of factors that distinguish it from the well-known scientific ideas of data synthesis and decomposition. The idea of extracting knowledge directly from big data is analyzed. The article compares approaches to extracting knowledge from big data: algebraic and multidimensional data analysis used in OLAP-systems (OnLine Analytical Processing). An intermediate conclusion is made about the advisability of dividing systems for working with big data into two main classes: automatic and non-automatic. To assess the result of extracting knowledge from big data, it is proposed to use well-known scientific criteria: reliability and efficiency. It is proposed to consider two components of reliability: methodical and instrumental. The main goals of knowledge extraction in socio-economic systems are highlighted: forecasting and support for making management decisions. The factors that distinguish big data are analyzed: volume, variety, velocity, as applied to the study of socio-economic systems. The expediency of introducing a universe into systems for processing big data, which provides a description of the variety of big data and source protocols, is analyzed. The impact of the properties of sample populations from big data: incompleteness, heterogeneity, and non-representativeness, the choice of mathematical methods for processing big data is analyzed. The conclusion is made about the need for a systemic, comprehensive, cautious approach to the development of fundamental decisions of a socio-economic nature when using the big data paradigm in the study of individual socio-economic subsystems.

Estimates for solutions of systems of linear equations with circulant matrices

In the present paper we consider the problem to estimate a solution of the system of equations with a circulant matrix in uniform norm. We give the estimate for circulant matrices with diagonal dominance. The estimate is sharp. Based on this result and an idea of decomposition of the matrix into a product of matrices associated with factorization of the characteristic polynomial, we propose an estimate for any circulant matrix.

Devising methods for planning a multifactorial multilevel experiment with high dimensionality

This paper considers the task of planning a multifactorial multilevel experiment for problems with high dimensionality. Planning an experiment is a combinatorial task. At the same time, the catastrophically rapid growth in the number of possible variants of experiment plans with an increase in the dimensionality of the problem excludes the possibility of solving it using accurate algorithms. On the other hand, approximate methods of finding the optimal plan have fundamental drawbacks. Of these, the main one is the lack of the capability to assess the proximity of the resulting solution to the optimal one. In these circumstances, searching for methods to obtain an accurate solution to the problem remains a relevant task. Two different approaches to obtaining the optimal plan for a multifactorial multilevel experiment have been considered. The first of these is based on the idea of decomposition. In this case, the initial problem with high dimensionality is reduced to a sequence of problems of smaller dimensionality, solving each of which is possible by using precise algorithms. The decomposition procedure, which is usually implemented empirically, in the considered problem of planning the experiment is solved by employing a strictly formally justified technique. The exact solutions to the problems obtained during the decomposition are combined into the desired solution to the original problem. The second approach directly leads to an accurate solution to the task of planning a multifactorial multilevel experiment for an important special case where the costs of implementing the experiment plan are proportional to the total number of single-level transitions performed by all factors. At the same time, it has been proven that the proposed procedure for forming a route that implements the experiment plan minimizes the total number of one-level changes in the values of factors. Examples of problem solving are given