Quantum algorithm for MUSIC-based DOA estimation in hybrid MIMO systems

The multiple signal classification (MUSIC) algorithm is a well-established method to evaluate the direction of arrival (DOA) of signals. However, the construction and eigen-decomposition of the sample covariance matrix (SCM) are computationally costly for MUSIC in hybrid multiple input multiple output (MIMO) systems, which limits the application and advancement of the algorithm. In this paper, we present a novel quantum method for MUSIC in hybrid MIMO systems. Our scheme makes the following three contributions. First, the quantum subroutine for constructing the approximate SCM is designed, along with the quantum circuit for the steering vector and a proposal for quantum singular vector transformation. Second, the variational density matrix eigensolver is proposed to determine the signal and noise subspaces utilizing the destructive swap test. As a proof of principle, we conduct two numerical experiments using a quantum simulator. Finally, the quantum labelling procedure is explored to determine the DOA. The proposed quantum method can potentially achieve exponential speedup on certain parameters and polynomial speedup on others under specific moderate circumstances, compared with their classical counterparts.

Prefrontal, striatal, and VTA subnetwork dynamics during novelty and exploration

Multiple distinct brain areas have been implicated in memory including the prefrontal cortex (PFC), striatum (STR), and ventral tegmental area (VTA). Information-exchange across these widespread networks requires flexible coordination at a fine time-scale. In the present study, we collected high-density recordings from the PFC, STR, and VTA of male rats during baseline, encoding, consolidation, and retrieval stages of memory formation. Novel sub-regional clustering analyses identified patterns of spatially restricted, temporally coherent, and frequency specific signals that were reproducible across days and were modulated by behavioral states. Clustering identified miniscule patches of neural tissue. Generalized eigen decomposition (GED) reduced each cluster to a single time series. Amplitude envelope correlation of the cluster time series was used to assess functional connectivity between clusters. Dense intra- and inter regional functional connectivity characterized the baseline period, with delta oscillations playing an outsized role. There was a dramatic pruning of network connectivity during encoding. Connectivity rebounded during consolidation, but connections in the theta band became stronger, and those in the delta band were weaker. Finally, during retrieval, connections were not as severely reduced as they had been during encoding, and specifically theta and higher-frequency connections were stronger. Underlying these connectivity changes, the anatomical extent of clusters observed in the gamma band in the PFC and in both the gamma and delta bands in the VTA changed markedly across behavioral conditions. These results demonstrate the brain's ability to reorganize functionally at both the intra- and inter-regional levels during different stages of memory processing.

A Multi-Marker Test for Analyzing Paired Genetic Data in Transplantation

Emerging evidence suggests that donor/recipient matching in non-HLA (human leukocyte antigen) regions of the genome may impact transplant outcomes and recognizing these matching effects may increase the power of transplant genetics studies. Most available matching scores account for either single-nucleotide polymorphism (SNP) matching only or sum these SNP matching scores across multiple gene-coding regions, which makes it challenging to interpret the association findings. We propose a multi-marker Joint Score Test (JST) to jointly test for association between recipient genotype SNP effects and a gene-based matching score with transplant outcomes. This method utilizes Eigen decomposition as a dimension reduction technique to potentially increase statistical power by decreasing the degrees of freedom for the test. In addition, JST allows for the matching effect and the recipient genotype effect to follow different biological mechanisms, which is not the case for other multi-marker methods. Extensive simulation studies show that JST is competitive when compared with existing methods, such as the sequence kernel association test (SKAT), especially under scenarios where associated SNPs are in low linkage disequilibrium with non-associated SNPs or in gene regions containing a large number of SNPs. Applying the method to paired donor/recipient genetic data from kidney transplant studies yields various gene regions that are potentially associated with incidence of acute rejection after transplant.

An optimised one-way wave migration method for complex media with arbitrarily varying velocity based on eigen-decomposition

The classical one-way generalised screen propagator (GSP) and Fourier finite-difference (FFD) schemes have limitations in imaging large angles in complex media with substantial lateral variations in wave velocity. Some improvements to the classical one-way wave scheme have been proposed with optimised methods. However, the performance of these methods in imaging complex media remains unsatisfying. To overcome this issue, a new strategy for wavefield extrapolation based on the eigenvalue and eigenvector decomposition of the Helmholtz operator is presented herein. In this method, the square root operator is calculated after the decomposition of the Helmholtz operator at the product of the eigenvalues and eigenvectors. Then, Euler transformation is applied using the best polynomial approximation of the trigonometric function based on the infinite norm, and the propagator for one-way wave migration is calculated. According to this scheme, a one-way operator can be computed more accurately with a lower-order expansion. The imaging performance of this scheme was compared with that of the classical GSP, FFD and the recently developed full-wave-equation depth migration (FWDM) schemes. The impulse responses in media with arbitrary velocity inhomogeneity demonstrate that the proposed migration scheme performs better at large angles than the classical GSP scheme. The wavefronts calculated in the dipping and salt dome models illustrate that this scheme can provide a precise wavefield calculation. The applications of the Marmousi model further demonstrate that the proposed approach can achieve better-migrated results in imaging small-scale and complex structures, especially in media with steep-dipping faults.

Key Validity Using the Multiple-Parameter Fractional Fourier Transform for Image Encryption

As a symmetric encryption algorithm, multiple-parameter fractional Fourier transform (MPFRFT) is proposed and applied to image encryption. The MPFRFT with two vector parameters has better security, which becomes the main technical means to protect information security. However, our study found that many keys of the MPFRFT are invalid, which greatly reduces its security. In this paper, we propose a new reformulation of MPFRFT and analyze it using eigen-decomposition-type fractional Fourier transform (FRFT) and weighted-type FRFT as basis functions, respectively. The results show that the effective keys are extremely limited. Furthermore, we analyze the extended encryption methods based on MPFRFT, which also have the security risk of key invalidation. Theoretical analysis and numerical simulation verify our point of view. Our discovery has important reference value for a class of generalized FRFT image encryption methods.

Gradient Eigen-decomposition Invariance Biogeography-based Optimization for Mobile Robot Path Planning

The path planning for mobile robots has attracted extensive attention, and evolutionary algorithms have been applied to this problem increas-ingly. In this paper, we propose a novel gradient eigen-decomposition invariance biogeography-based optimization (GEI-BBO) for mobile robot path planning, which has the merits of high rotation invariance and excel-lent search performance. In GEI-BBO, we design an eigen-decomposition mechanism for migration operation, which can reduce the dependence of biogeography-based optimization (BBO) on the coordinate system, improve the rotation invariance and share the information between eigen solutions more effectively. Meanwhile, to find the local opti-mal solution better, gradient descent is added, and the system search strategy can reduce the occurrence of local trapping phenomenon. In addition, combining the GEI-BBO with cubic spline interpola-tion will solve the problem of mobile robot path planning through a defined coding method and fitness function. A series of experiments are implemented on benchmark functions, whose results indicated that the optimization performance of GEI-BBO is superior to other algo-rithms. And the successful application of GEI-BBO for path planning in different environments confirms its effectiveness and practicability.

AF-vapeR: A multivariate genome scan for detecting parallel evolution using allele frequency change vectors

The repeatability of evolution at the genetic level has been demonstrated to vary along a continuum from complete parallelism to divergence. In order to better understand why this continuum exists within and among systems, hypotheses must be tested using high-confidence sets of candidate loci for repeatability. Despite this, few methods have been developed to scan SNP data for signatures specifically associated with repeatability, as opposed to local adaptation. Here we present AF-vapeR (Allele Frequency Vector Analysis of Parallel Evolutionary Responses), an approach designed to identify genome regions exhibiting highly correlated allele frequency changes within haplotypes and among replicated allele frequency change vectors. The method divides the genome into windows of an equivalent number of SNPs, and within each window performs eigen decomposition over normalised allele frequency change vectors (AFV), each derived from a replicated pair of populations/species. Properties of the resulting eigenvalue distribution can be used to compare regions of the genome for those exhibiting strong parallelism, and can also be compared against a null distribution derived from randomly permuted AFV. We demonstrate the utility of this approach to detect different modes of parallel evolution using simulations, and also demonstrate a reduction in error rate compared with intersecting FST outliers. Lastly, we apply AF-vapeR to three previously published datasets (stickleback, guppies, and Galapagos finches) which comprise a range of sampling and sequencing strategies, and lineage ages. We highlight known parallel regions whilst also identifying novel candidates. The main benefits of this approach include a reduced false-negative rate under many conditions, an emphasis on signals associated specifically with repeatable evolution as opposed to local adaptation, and an opportunity to identify different modes of parallel evolution at the first instance.