Sparse Matrix Model Research Articles

Super-structured photonic crystal fiber Bragg grating biosensor image model based on sparse matrix

Abstract Fiber grating (FBG) is an important optical device of fiber, which is widely used in optical fiber communication and sensing. At the present stage, the fiber grating is almost prepared in the static state of the fiber, and then the grating is welded into the fiber grating array or network. With the continuous improvement of the application effect of fiber grating, has become one of the most promising, representative and fastest developing fiber passive devices. In this paper, fiber grating is classified according to the refractive index distribution of grating axis. The central wavelength of Bragg fiber grating is modulated by using external parameters (temperature or stress strain). The wave equation of insulating medium is obtained by the reflection characteristic and coupling mode theory of fiber grating. Using sparse matrix model of nerve action potential signal with wavelet decomposition layers, nerve action potential signal reconstruction of the relative error between the value and the original value contrast found that reconstructed and original signals are very close. Good results have been obtained for the sampling reconstruction of the filtered high signal-to-noise ratio neural action potential signal. Researchers have conducted extensive and in-depth research on fiber grating sensing technology, and achieved gratifying results. But with the of the engineering application of technical requirements, they need real-time monitoring. Due to the cross sensitivities of fiber grating, it became the bottleneck of multiple parameter measurement.

Modelling wind power spatial-temporal correlation in multi-interval optimal power flow: A sparse correlation matrix approach

The significantly increasing deployment of wind power necessitates that system operation considers the spatial-temporal correlation of power forecast from different wind power plants. How to model this spatial-temporal correlation in the actual system dispatch is challenging. In this paper, a sparse correlation matrix is utilized to efficiently model the spatial-temporal correlation of wind power forecast in the generation dispatch model. A novel, adjustable, and distributionally-robust chance-constrained multi-interval optimal power flow (ADRCC-MIOPF) model is proposed to obtain reliable economic dispatch (ED) solutions. The spatial-temporal correlation of wind power plants power forecasts is represented by the sparse correlation covariance matrix obtained from historical, time series wind power forecast error data. The chance constraints in the ADRCC-MIOPF model are transformed into a set of second-order-cone (SOC) constraints in which an adjustable coefficient in the chance constraints controls the robustness of the ADRCC-MIOPF model to the wind power forecast errors distribution. Case studies performed on the PJM 5-bus system and IEEE 118-bus system verify the proposed method to improve the system security and reduce the cost especially under the high wind penetration levels. All the cases can be solved within several minutes for both the small and large cases which validates the efficiency of the proposed sparse matrix model. In addition, considering the spatial-temporal correlation of wind power forecast and the distributional robustness of wind power forecast error leads to a more reliable economic dispatch with lower system violations.

Core Module Optimizing PDE Sparse Matrix Models With HPCG Example

This paper introduces a fundamentally new computer architecture for supercomputers. The core module is application compatible with an existing superscalar microprocessor, with minimized energy use, and is optimized for local sparse matrix operations. Optimized sparse matrix manip- ulation is discussed by analyzing the High Performance Conjugate Gradient (HPCG) benchmark speci...cation. This analysis shows how the DRAM memory wall is removed for this benchmark, and for sparse matrix models of partial di¤erential equations (PDEs) for a wide cross section of applications. By giving the programmer improved control over the con...guration of the super- computer, the potential for communication problems is minimized. Application compatibility is achieved while removing the superscalar instruction interpreter and multi-thread controller from the existing microprocessor’s hardware. These are transformed into compile-time utilities. The instruction cache is removed through an innovation in VLIW instruction processing. The data caches are unnecessary and are turned o¤ in order to optimally implement sparse matrix models.

An evolutionary multiobjective method for low-rank and sparse matrix decomposition

This paper addresses the problem of finding the low-rank and sparse components of a given matrix. The problem involves two conflicting objective functions, reducing the rank and sparsity of each part simultaneously. Previous methods combine two objectives into a single objective penalty function to solve with traditional numerical optimization approaches. The main contribution of this paper is to put forward a multiobjective method to decompose the given matrix into low-rank component and sparse part. We optimize two objective functions with an evolutionary multiobjective algorithm MOEA/D. Another contribution of this paper, a modified low-rank and sparse matrix model is proposed, which simplifying the variable of objective functions and improving the efficiency of multiobjective optimization. The proposed method obtains a set of solutions with different trade-off between low-rank and sparse objectives, and decision makers can choose one or more satisfied decomposed results according to different requirements directly. Experiments conducted on artificial datasets and nature images, show that the proposed method always obtains satisfied results, and the convergence, stability and robustness of the proposed method is acceptable.

Matrix Models and Eigenvalue Statistics for Truncations of Classical Ensembles of Random Unitary Matrices

We consider random non-normal matrices constructed by removing one row and column from samples from Dyson's circular ensembles or samples from the classical compact groups. We develop sparse matrix models whose spectral measures match these ensembles. This allows us to compute the joint law of the eigenvalues, which have a natural interpretation as resonances for open quantum systems or as electrostatic charges located in a dielectric medium. Our methods allow us to consider all values of $\beta>0$, not merely $\beta=1,2,4$.

K-mer Sparse matrix model for genetic sequence and its applications in sequence comparison

Based on the k-mer model for genetic sequence, a k-mer sparse matrix representation is proposed to denote the types and sites of k-mers appearing in a genetic sequence, and there exists a one-to-one relationship between a genetic sequence and its associated k-mer sparse matrix. With the singular value decomposition of the k-mer sparse matrix, the k-mer singular value vector is constructed and utilized to numerically quantify the characteristics of a genetic sequence. We investigate and evaluate the optimum value k⁎ chosen for our k-mer sparse matrix model for genetic sequence. To show the usefulness of our k-mer sparse matrix model method, it is applied to the comparison of genetic sequences, and the results obtained fully demonstrate that our proposed method is very powerful in analyzing and determining the relationships of genetic sequences.

Circular β ensembles, CMV representation, characteristic polynomials

In this note we first briefly review some recent progress in the study of the circular β ensemble on the unit circle, where β > 0 is a model parameter. In the special cases β = 1,2 and 4, this ensemble describes the joint probability density of eigenvalues of random orthogonal, unitary and sympletic matrices, respectively. For general β, Killip and Nenciu discovered a five-diagonal sparse matrix model, the CMV representation. This representation is new even in the case β = 2; and it has become a powerful tool for studying the circular β ensemble. We then give an elegant derivation for the moment identities of characteristic polynomials via the link with orthogonal polynomials on the unit circle.