Deep Quaternion Networks

The field of deep learning has seen significant advancement in recent years. However, much of the existing work has been focused on real-valued numbers. Recent work has shown that a deep learning system using the complex numbers can be deeper for a fixed parameter budget compared to its real-valued counterpart. In this work, we explore the benefits of generalizing one step further into the hyper-complex numbers, quaternions specifically, and provide the architecture components needed to build deep quaternion networks. We develop the theoretical basis by reviewing quaternion convolutions, developing a novel quaternion weight initialization scheme, and developing novel algorithms for quaternion batch-normalization. These pieces are tested in a classification model by end-to-end training on the CIFAR-10 and CIFAR-100 data sets and a segmentation model by end-to-end training on the KITTI Road Segmentation data set. These quaternion networks show improved convergence compared to real-valued and complex-valued networks, especially on the segmentation task, while having fewer parametersComment: IJCNN 2018, 8 pages, 1 figur

Vertical Integration, Foreclosure and Profits in the Presence of Double Marginalisation

Whether vertical integration between a downstrean oligopolist and an upstream oligopolist is profitable for an integrated pair of firms is shown to depend on how one formulates the questions, on the number of firms in each oligopoly and on the type of interaction which is assumed between firms that are integrated and firms that are not. In particular, it is shown that if no restriction is put on trade between integrated and non integrated firms, integrated firms may continue to purchase inputs from the non integrated upstream firms, with the goal of raising their downstream rival's costs. Furthermore, even though firms are identical, asymmetric equilibria, where integrated and non integrated firms coexist, may actually arise as an outcome of the integration game. La rentabilité de l'intégration verticale entre une firme à l'amont et une firme à l'aval dépend de la manière de poser la question, du nombre de firmes et du type d'interaction entre les firmes intégrées et les firmes non-intégrées. Si l'on n'impose aucune contrainte sur les transactions entre les firmes intégrées et les firmes non-intégrées, alors les premières peuvent continuer à acheter l'input produit par les firmes non-intégrées à l'amont afin de hausser les coûts des firmes non-intégrées à l'aval. On montre que, même dans le cas où les firmes sont identiques, il y a des équilibres asymétriques dans le jeu d'intégration.Integration vertical, integration game, asymmetric equilibria, Intégration verticale, jeu d'intégration, équilibre asymétrique

Deficient Cholesterol Esterification in Plasma of apoc2 Knockout Zebrafish and Familial Chylomicronemia Patients.

Hypertriglyceridemia is an independent risk factor for cardiovascular disease. Apolipoprotein C-II (APOC2) is an obligatory cofactor for lipoprotein lipase (LPL), the major enzyme catalyzing plasma triglyceride hydrolysis. We have created an apoc2 knockout zebrafish model, which mimics the familial chylomicronemia syndrome (FCS) in human patients with a defect in the APOC2 or LPL gene. In this study, we measured plasma levels of free cholesterol (FC) and cholesterol esters (CE) and found that apoc2 mutant zebrafish have a significantly higher FC to CE ratio (FC/CE), when compared to the wild type. Feeding apoc2 mutant zebrafish a low-fat diet reduced triglyceride levels but not the FC/CE ratio. In situ hybridization and qPCR results demonstrated that the hepatic expression of lecithin-cholesterol acyltransferase (lcat), the enzyme responsible for esterifying plasma FC to CE, and of apolipoprotein A-I, a major protein component of HDL, were dramatically decreased in apoc2 mutants. Furthermore, the FC/CE ratio was significantly increased in the whole plasma and in a chylomicron-depleted fraction of human FCS patients. The FCS plasma LCAT activity was significantly lower than that of healthy controls. In summary, this study, using a zebrafish model and human patient samples, reports for the first time the defect in plasma cholesterol esterification associated with LPL deficiency