The Absolute Line Quadric and Camera Autocalibration

We introduce a geometrical object providing the same information as the absolute conic: the absolute line quadric (ALQ). After the introduction of the necessary exterior algebra and Grassmannian geometry tools, we analyze the Grassmannian of lines of P^3 from both the projective and Euclidean points of view. The exterior algebra setting allows then to introduce the ALQ as a quadric arising very naturally from the dual absolute quadric. We fully characterize the ALQ and provide clean relationships to solve the inverse problem, i.e., recovering the Euclidean structure of space from the ALQ. Finally we show how the ALQ turns out to be particularly suitable to address the Euclidean autocalibration of a set of cameras with square pixels and otherwise varying intrinsic parameters, providing new linear and non-linear algorithms for this problem. We also provide experimental results showing the good performance of the techniques

A Grassmann integral equation

The present study introduces and investigates a new type of equation which is called Grassmann integral equation in analogy to integral equations studied in real analysis. A Grassmann integral equation is an equation which involves Grassmann integrations and which is to be obeyed by an unknown function over a (finite-dimensional) Grassmann algebra G_m. A particular type of Grassmann integral equations is explicitly studied for certain low-dimensional Grassmann algebras. The choice of the equation under investigation is motivated by the effective action formalism of (lattice) quantum field theory. In a very general setting, for the Grassmann algebras G_2n, n = 2,3,4, the finite-dimensional analogues of the generating functionals of the Green functions are worked out explicitly by solving a coupled system of nonlinear matrix equations. Finally, by imposing the condition G[{\bar\Psi},{\Psi}] = G_0[{\lambda\bar\Psi}, {\lambda\Psi}] + const., 0<\lambda\in R (\bar\Psi_k, \Psi_k, k=1,...,n, are the generators of the Grassmann algebra G_2n), between the finite-dimensional analogues G_0 and G of the (``classical'') action and effective action functionals, respectively, a special Grassmann integral equation is being established and solved which also is equivalent to a coupled system of nonlinear matrix equations. If \lambda \not= 1, solutions to this Grassmann integral equation exist for n=2 (and consequently, also for any even value of n, specifically, for n=4) but not for n=3. If \lambda=1, the considered Grassmann integral equation has always a solution which corresponds to a Gaussian integral, but remarkably in the case n=4 a further solution is found which corresponds to a non-Gaussian integral. The investigation sheds light on the structures to be met for Grassmann algebras G_2n with arbitrarily chosen n.Comment: 58 pages LaTeX (v2: mainly, minor updates and corrections to the reference section; v3: references [4], [17]-[21], [39], [46], [49]-[54], [61], [64], [139] added

Chromatin lipids and their possible role in gene expression. A study in normal and neoplastic cells.

Certain phospholipids are associated with the nonhistone chromosomal proteins extracted from normal B- and chronic lymphocytic leukemia lymphocytes. The ratio of phospholipids to nonhistone chromosomal proteins was constant with the different methods used for isolating nuclei and extracting the chromatin, although the various methods allowed a different recovery of total lipids from chromatin. Three phospholipids were extractable from the nonhistone protein fraction, but their respective ratios varied in chronic lymphocytic leukemia compared to normal B-lymphocytes. The most significant variation concerns the reduction of sphingomyelin content in leukemic lymphocytes, since this prospholipid in vitro affects both DNA stability and transcription

Nuclear lipid-dependent signal transduction in human osteosarcoma cells.

The enzymes and substrates involved in phosphoinositide signal transduction which have been detected in the nucleus of several cell types have been demonstrated to be responsive to agonists. The complexity of this aspect of inositide function has been previously analyzed in some cell models characterized by a mitogenic or differentiating response to specific factors. An interesting experimental model is represented by human derived osteosarcoma Saos-2 cells, characterized by the expression of high affinity receptors for interleukin 1 alpha (IL-1 alpha), which is one of the most potent stimulators of bone resorption. In particular, we investigated the earliest intracellular events following the binding of IL-1 alpha to its receptor, involving the inositide signal transduction pathway. Saos-2 cells present a partitioning of the phosphoinositidase (PLC) isoforms; in fact, the nucleus contains both PLC beta 1 and gamma 1, while the cytoplasm contains almost exclusively the gamma 1 isoform. IL-1 alpha evokes a rapid and transient increase of the PLC beta 1 activity in the nucleus, which causes the hydrolysis of phosphatidylinositol mono- and bis-phosphate. In response to IL-1 alpha, not only the canonical inositol lipid pathway appears to be involved; also the 3'-phosphorylated lipids generated by phosphatidylinositol 3-kinase (PI 3-K), which may act as second messengers, appear to be affected. In fact, Saos-2 cells present a nuclear PI 3-K activity which can be enhanced by the IL-1 alpha treatment. Among the possible targets of the second messengers released by the nuclear PLC beta 1 activation, we found that some protein kinase C isoforms, namely the epsilon and zeta, which are present within the nucleus, are activated after IL-1 alpha exposure. These activated PKC isoforms, in turn, could modulate the activity of the transcription factor NFkB, which, 5 min after IL-1 alpha treatment, has already translocated to the nucleus and bound to DNA to promote gene activation. The actual role of the inositide pathway in the Saos-2 cell function has also been investigated by utilizing cell clones transfected with the mouse sequence of the PLC beta 1