Overview of Constrained PARAFAC Models

In this paper, we present an overview of constrained PARAFAC models where the constraints model linear dependencies among columns of the factor matrices of the tensor decomposition, or alternatively, the pattern of interactions between different modes of the tensor which are captured by the equivalent core tensor. Some tensor prerequisites with a particular emphasis on mode combination using Kronecker products of canonical vectors that makes easier matricization operations, are first introduced. This Kronecker product based approach is also formulated in terms of the index notation, which provides an original and concise formalism for both matricizing tensors and writing tensor models. Then, after a brief reminder of PARAFAC and Tucker models, two families of constrained tensor models, the co-called PARALIND/CONFAC and PARATUCK models, are described in a unified framework, for $N^{th}$ order tensors. New tensor models, called nested Tucker models and block PARALIND/CONFAC models, are also introduced. A link between PARATUCK models and constrained PARAFAC models is then established. Finally, new uniqueness properties of PARATUCK models are deduced from sufficient conditions for essential uniqueness of their associated constrained PARAFAC models

Distributed Large-Scale Tensor Decomposition

International audienceCanonical Polyadic Decomposition (CPD), also known as PARAFAC, is a useful tool for tensor factorization. It has found application in several domains including signal processing and data mining. With the deluge of data faced in our societies, large-scale matrix and tensor factorizations become a crucial issue. Few works have been devoted to large-scale tensor factorizations. In this paper, we introduce a fully distributed method to compute the CPD of a large-scale data tensor across a network of machines with limited computation resources. The proposed approach is based on collaboration between the machines in the network across the three modes of the data tensor. Such a multi-modal collaboration allows an essentially unique reconstruction of the factor matrices in an efficient way. We provide an analysis of the computation and communication cost of the proposed scheme and address the problem of minimizing communication costs while maximizing the use of available computation resources

Energy efficiency of mmWave massive MIMO precoding with low-resolution DACs

With the congestion of the sub-6 GHz spectrum, the interest in massive multiple-input multiple-output (MIMO) systems operating on millimeter wave spectrum grows. In order to reduce the power consumption of such massive MIMO systems, hybrid analog/digital transceivers and application of low-resolution digital-to-analog/analog-to-digital converters have been recently proposed. In this work, we investigate the energy efficiency of quantized hybrid transmitters equipped with a fully/partially-connected phase-shifting network composed of active/passive phase-shifters and compare it to that of quantized digital precoders. We introduce a quantized single-user MIMO system model based on an additive quantization noise approximation considering realistic power consumption and loss models to evaluate the spectral and energy efficiencies of the transmit precoding methods. Simulation results show that partially-connected hybrid precoders can be more energy-efficient compared to digital precoders, while fully-connected hybrid precoders exhibit poor energy efficiency in general. Also, the topology of phase-shifting components offers an energy-spectral efficiency trade-off: active phase-shifters provide higher data rates, while passive phase-shifters maintain better energy efficiency.Comment: Published in IEEE Journal of Selected Topics in Signal Processin

Culex quinquefasciatus vitellogenesis: morphological and biochemical aspects

The vitellogenic process in Culex quinquefasciatus, which is triggered by a blood meal, involves the synthesis, distribution and storage of the nutrients necessary for embryo development. The fat body of an adult female Cx. quinquefasciatus revealed two cell types: large trophocytes and small, eosinophilic, "oenocyte-like" cells, which show no morphological changes throughout the gonotrophic cycle. Trophocytes, which only begin to synthesise vitellogenin (Vg) 12 h post-blood meal (PBM), undergo a series of morphological changes following engorgement. These changes include the expansion of the rough endoplasmic reticulum (RER) and Golgi complex, which are later destroyed by autophagosomes. At 84 h PBM, trophocytes return to their pre-engorgement morphology. The ovarian follicles of non-blood-fed Cx. quinquefasciatus contain a cluster of eight undifferentiated cells surrounded by follicular epithelium. After engorgement, the oocyte membrane facing the perioocytic space increases its absorptive surface by microvilli development; large amounts of Vg and lipids are stored between 24 and 48 h PBM. Along with yolk storage in the oocyte, follicular cells exhibit the development of RER cisternae and electron-dense granules begin to fill the perioocytic space, possibly giving rise to endochorion. Later in the gonotrophic cycle, electron-dense vesicles, which are possible exochorion precursors, fuse at the apical membrane of follicular cells. This fusion is followed by follicular cell degeneration.FAPESPCoordenacao de Aperfeicoamento de Pessoal de Nivel Superior (CAPES