Simultaneous diagonalisation of the covariance and complementary covariance matrices in quaternion widely linear signal processing

Recent developments in quaternion-valued widely linear processing have established that the exploitation of complete second-order statistics requires consideration of both the standard covariance and the three complementary covariance matrices. Although such matrices have a tremendous amount of structure and their decomposition is a powerful tool in a variety of applications, the non-commutative nature of the quaternion product has been prohibitive to the development of quaternion uncorrelating transforms. To this end, we introduce novel techniques for a simultaneous decomposition of the covariance and complementary covariance matrices in the quaternion domain, whereby the quaternion version of the Takagi factorisation is explored to diagonalise symmetric quaternion-valued matrices. This gives new insights into the quaternion uncorrelating transform (QUT) and forms a basis for the proposed quaternion approximate uncorrelating transform (QAUT) which simultaneously diagonalises all four covariance matrices associated with improper quaternion signals. The effectiveness of the proposed uncorrelating transforms is validated by simulations on both synthetic and real-world quaternion-valued signals.Comment: 41 pages, single column, 10 figure

Massive MIMO for Internet of Things (IoT) Connectivity

Massive MIMO is considered to be one of the key technologies in the emerging 5G systems, but also a concept applicable to other wireless systems. Exploiting the large number of degrees of freedom (DoFs) of massive MIMO essential for achieving high spectral efficiency, high data rates and extreme spatial multiplexing of densely distributed users. On the one hand, the benefits of applying massive MIMO for broadband communication are well known and there has been a large body of research on designing communication schemes to support high rates. On the other hand, using massive MIMO for Internet-of-Things (IoT) is still a developing topic, as IoT connectivity has requirements and constraints that are significantly different from the broadband connections. In this paper we investigate the applicability of massive MIMO to IoT connectivity. Specifically, we treat the two generic types of IoT connections envisioned in 5G: massive machine-type communication (mMTC) and ultra-reliable low-latency communication (URLLC). This paper fills this important gap by identifying the opportunities and challenges in exploiting massive MIMO for IoT connectivity. We provide insights into the trade-offs that emerge when massive MIMO is applied to mMTC or URLLC and present a number of suitable communication schemes. The discussion continues to the questions of network slicing of the wireless resources and the use of massive MIMO to simultaneously support IoT connections with very heterogeneous requirements. The main conclusion is that massive MIMO can bring benefits to the scenarios with IoT connectivity, but it requires tight integration of the physical-layer techniques with the protocol design.Comment: Submitted for publicatio

Unsupervised discovery of temporal sequences in high-dimensional datasets, with applications to neuroscience.

Identifying low-dimensional features that describe large-scale neural recordings is a major challenge in neuroscience. Repeated temporal patterns (sequences) are thought to be a salient feature of neural dynamics, but are not succinctly captured by traditional dimensionality reduction techniques. Here, we describe a software toolbox-called seqNMF-with new methods for extracting informative, non-redundant, sequences from high-dimensional neural data, testing the significance of these extracted patterns, and assessing the prevalence of sequential structure in data. We test these methods on simulated data under multiple noise conditions, and on several real neural and behavioral datas. In hippocampal data, seqNMF identifies neural sequences that match those calculated manually by reference to behavioral events. In songbird data, seqNMF discovers neural sequences in untutored birds that lack stereotyped songs. Thus, by identifying temporal structure directly from neural data, seqNMF enables dissection of complex neural circuits without relying on temporal references from stimuli or behavioral outputs

Spatial Pyramid Context-Aware Moving Object Detection and Tracking for Full Motion Video and Wide Aerial Motion Imagery

A robust and fast automatic moving object detection and tracking system is essential to characterize target object and extract spatial and temporal information for different functionalities including video surveillance systems, urban traffic monitoring and navigation, robotic. In this dissertation, I present a collaborative Spatial Pyramid Context-aware moving object detection and Tracking system. The proposed visual tracker is composed of one master tracker that usually relies on visual object features and two auxiliary trackers based on object temporal motion information that will be called dynamically to assist master tracker. SPCT utilizes image spatial context at different level to make the video tracking system resistant to occlusion, background noise and improve target localization accuracy and robustness. We chose a pre-selected seven-channel complementary features including RGB color, intensity and spatial pyramid of HoG to encode object color, shape and spatial layout information. We exploit integral histogram as building block to meet the demands of real-time performance. A novel fast algorithm is presented to accurately evaluate spatially weighted local histograms in constant time complexity using an extension of the integral histogram method. Different techniques are explored to efficiently compute integral histogram on GPU architecture and applied for fast spatio-temporal median computations and 3D face reconstruction texturing. We proposed a multi-component framework based on semantic fusion of motion information with projected building footprint map to significantly reduce the false alarm rate in urban scenes with many tall structures. The experiments on extensive VOTC2016 benchmark dataset and aerial video confirm that combining complementary tracking cues in an intelligent fusion framework enables persistent tracking for Full Motion Video and Wide Aerial Motion Imagery.Comment: PhD Dissertation (162 pages

Efficient Transposition of the piggyBac (PB) Transposon in Mammalian Cells and Mice

SummaryTransposable elements have been routinely used for genetic manipulation in lower organisms, including generating transgenic animals and insertional mutagenesis. In contrast, the usage of transposons in mice and other vertebrate systems is still limited due to the lack of an efficient transposition system. We have tested the ability of piggyBac (PB), a DNA transposon from the cabbage looper moth Trichoplusia ni, to transpose in mammalian systems. We show that PB elements carrying multiple genes can efficiently transpose in human and mouse cell lines and also in mice. PB permits the expression of the marker genes it carried. During germline transposition, PB could excise precisely from original insertion sites and transpose into the mouse genome at diverse locations, preferably transcription units. These data provide a first and critical step toward a highly efficient transposon system for a variety of genetic manipulations including transgenesis and insertional mutagenesis in mice and other vertebrates

Graph Kernels

We present a unified framework to study graph kernels, special cases of which include the random walk (Gärtner et al., 2003; Borgwardt et al., 2005) and marginalized (Kashima et al., 2003, 2004; Mahé et al., 2004) graph kernels. Through reduction to a Sylvester equation we improve the time complexity of kernel computation between unlabeled graphs with n vertices from O(n^6) to O(n^3). We find a spectral decomposition approach even more efficient when computing entire kernel matrices. For labeled graphs we develop conjugate gradient and fixed-point methods that take O(dn^3) time per iteration, where d is the size of the label set. By extending the necessary linear algebra to Reproducing Kernel Hilbert Spaces (RKHS) we obtain the same result for d-dimensional edge kernels, and O(n^4) in the infinite-dimensional case; on sparse graphs these algorithms only take O(n^2) time per iteration in all cases. Experiments on graphs from bioinformatics and other application domains show that these techniques can speed up computation of the kernel by an order of magnitude or more. We also show that certain rational kernels (Cortes et al., 2002, 2003, 2004) when specialized to graphs reduce to our random walk graph kernel. Finally, we relate our framework to R-convolution kernels (Haussler, 1999) and provide a kernel that is close to the optimal assignment kernel of Fröhlich et al. (2006) yet provably positive semi-definite