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To date, parallel simulation algorithms for spiking neural P (SNP) systems are based on a matrix representation. This way, the simulation is implemented with linear algebra operations, which can be easily parallelized on high performance computing platforms such as GPUs. Although it has been convenient for the first generation of GPU-based simulators, such as CuSNP, there are some bottlenecks to sort out. For example, the proposed matrix representations of SNP systems lead to very sparse matrices, where the majority of values are zero. It is known that sparse matrices can compromise the performance of algorithms since they involve a waste of memory and time. This problem has been extensively studied in the literature of parallel computing. In this paper, we analyze some of these ideas and apply them to represent some variants of SNP systems. We also provide a new simulation algorithm based on a novel compressed representation for sparse matrices. We also conclude which SNP system variant better suits our new compressed matrix representation.

In this study, the authors discuss the topic of joint angle and Doppler frequency estimation in a monostatic multiple-input–multiple-output radar and a compressed sensing parallel factor (CS-PARAFAC) analysis-based algorithm is proposed. In this algorithm, the joint estimation problem is firstly linked to the compressed sensing trilinear model, then the estimated compressed matrix can be derived through trilinear alternating least square method and the angle and Doppler frequency are jointly estimated with sparsity from the compressed matrices. The proposed CS-PARAFAC algorithm, which can obtain automatically paired angle and Doppler frequency estimation, has very close estimation performance to the conventional parallel factor analysis algorithm. When compared to the conventional subspace-based algorithm, such as estimation of signal parameters via rotational invariance techniques, it can achieve much better joint angle and Doppler frequency estimation performance. As the compression, the proposed algorithm has much lower computational complexity and smaller memory capacity meanwhile. Numerical simulations verify the efficiency and illustrate performance improvement of the proposed algorithm.

Methods of spatiotemporal characterization of nonequilibrated polymer based matrices are still immature and imperfect. The purpose of the study was to develop the methodology for the spatiotemporal characterization of water transport and properties in alginate tablets under hydration. The regions of low water content were spatially and temporally sampled using Karl Fisher and Differential Scanning Callorimetry (spatial distribution of freezing/nonfreezing water) with spatial resolution of 1 mm. In the regions of high water content, where sampling was infeasible due to gel/sol consistency, magnetic resonance imaging (MRI) enabled characterization with an order of magnitude higher spatial resolution. The minimally hydrated layer (MHL), infiltration layer (IL) and fully hydrated layer (FHL) were identified in the unilaterally hydrated matrices. The MHL gained water from the first hour of incubation (5–10% w/w) and at 4 h total water content was 29–39% with nonfreezing pool of 28–29%. The water content in the IL was 45–47% and at 4 h it reached ~50% with the nonfreezing pool of 28% and T2 relaxation time < 10 ms. The FHL consisted of gel and sol layer with water content of 85–86% with a nonfreezing pool of 11% at 4 h and T2 in the range 20–200 ms. Hybrid destructive/nondestructive analysis of alginate matrices under hydration was proposed. It allowed assessing the temporal changes of water distribution, its mobility and interaction with matrices in identified layers.

Testing covariance structure is of significant interest in many areas of statistical analysis and construction of compressed sensing matrices is an important problem in signal processing. Motivated by these applications, we study in this paper the limiting laws of the coherence of an n × p random matrix in the high-dimensional setting where p can be much larger than n. Both the law of large numbers and the limiting distribution are derived. We then consider testing the bandedness of the covariance matrix of a high-dimensional Gaussian distribution which includes testing for independence as a special case. The limiting laws of the coherence of the data matrix play a critical role in the construction of the test. We also apply the asymptotic results to the construction of compressed sensing matrices.

In this paper, we make study on the compressed matrices in the compressed sensing trilinear model-based angle estimation algorithm, whose complexity is lower than conventional trilinear decomposition-based method, due to the use of compressed matrices. And we take the problem of angle estimation for bistatic multiple-input multiple-output (MIMO) radar as an example. Simulation results can provide reference for the choice of compressed matrices.

A technique is presented that reduces the required memory of neural networks through improving weight storage. In contrast to traditional methods, which have an exponential memory overhead with the increase in network size, the proposed method stores only the number of connections between neurons. The proposed method is evaluated on feedforward networks and demonstrates memory saving capabilities of up to almost 80% while also being more efficient, especially with larger architectures.

As an emerging sampling technique, Compressed Sensing provides a quite masterly approach to data acquisition. Compared with the traditional method, how to conquer the Shannon/Nyquist sampling theorem has been fundamentally resolved. In this paper, first, we provide deterministic constructions of sensing matrices based on vector spaces over finite fields. Second, we analyze two kinds of attributes of sensing matrices. One is the recovery performance with respect to compressing and recovering signals in terms of restricted isometry property. In particular, we obtain a series of binary sensing matrices with sparsity level that are quite better than some existing ones. In order to save the storage space and accelerate the recovery process of signals, another character sparsity of matrices has been taken into account. Third, we merge our binary matrices with some matrices owning low coherence in terms of an embedding manipulation to obtain the improved matrices still having low coherence. Finally, compared with the quintessential binary matrices, the improved matrices possess better character of compressing and recovering signals. The favorable performance of our binary and improved matrices have been demonstrated by numerical simulations.

To cope with the huge expenditure associated with the fast growing sampling rate, compressed sensing (CS) is proposed as an effective technique of signal processing. In this paper, first, we construct a type of CS matrix to process signals based on singular linear spaces over finite fields. Second, we analyze two kinds of attributes of sensing matrices. One is the recovery performance corresponding to compressing and recovering signals. In particular, we apply two types of criteria, error-correcting pooling designs (PD) and restricted isometry property (RIP), to investigate this attribute. Another is the sparsity corresponding to storage and transmission signals. Third, in order to improve the ability associated with our matrices, we use an embedding approach to merge our binary matrices with some other matrices owing low coherence. At last, we compare our matrices with other existing ones via numerical simulations and the results show that ours outperform others.

A valuable opportunity is provided by compressed sensing (CS) to accomplish the tasks of high speed sampling, the transmission of large volumes of data, and storage in signal processing. To some extent, CS has brought tremendous changes in the information technologies that we use in our daily lives. However, the construction of compressed sensing matrices still can pose substantial problems. In this paper, we provide a kind of deterministic construction of sensing matrices based on singular linear spaces over finite fields. In particular, by choosing appropriate parameters, we constructed binary sensing matrices that are superior to existing matrices, and they outperform DeVore’s matrices. In addition, we used an embedding manipulation to merge our binary matrices with matrices that had low coherence, thereby improving such matrices. Compared with the quintessential binary matrices, the improved matrices possess better ability to compress and recover signals. The favorable performance of our binary and improved matrices was demonstrated by numerical simulations.

A matrix is called totally positive if all its minors are positive. If a totally positive matrix A is partitioned as$A = (A_{ij})$$i,j=1,2,\\ldots,k$ , in which each block$A_{ij}$is n x n, we show that the k x k compressed matrix given by$(\\det A_{ij})$is also totally positive and that the determinant of the compressed matrix exceeds A when k=2,3. An extension that allows for overlapping blocks is also presented when k=2,3. For$k \\geq 4$we verify, by example, that the k x k compressed matrix of a totally positive matrix need not be totally positive.