770 research outputs found

### The Extended Fock Basis of Clifford Algebra

We investigate the properties of the Extended Fock Basis (EFB) of Clifford
algebras introduced in [1]. We show that a Clifford algebra can be seen as a
direct sum of multiple spinor subspaces that are characterized as being left
eigenvectors of \Gamma. We also show that a simple spinor, expressed in Fock
basis, can have a maximum number of non zero coordinates that equals the size
of the maximal totally null plane (with the notable exception of vectorial
spaces with 6 dimensions).Comment: Minimal corrections to the published versio

### Complex structures and the Elie Cartan approach to the theory of spinors

Each isometric complex structure on a 2$\ell$-dimensional euclidean space $E$
corresponds to an identification of the Clifford algebra of $E$ with the
canonical anticommutation relation algebra for $\ell$ ( fermionic) degrees of
freedom. The simple spinors in the terminology of E.~Cartan or the pure spinors
in the one of C. Chevalley are the associated vacua. The corresponding states
are the Fock states (i.e. pure free states), therefore, none of the above
terminologies is very good.Comment: 10

### On Spinors Transformations

We begin showing that for even dimensional vector spaces $V$ all
automorphisms of their Clifford algebras are inner. So all orthogonal
transformations of $V$ are restrictions to $V$ of inner automorphisms of the
algebra. Thus under orthogonal transformations $P$ and $T$ - space and time
reversal - all algebra elements, including vectors $v$ and spinors $\varphi$,
transform as $v \to x v x^{-1}$ and $\varphi \to x \varphi x^{-1}$ for some
algebra element $x$. We show that while under combined $PT$ spinor $\varphi \to
x \varphi x^{-1}$ remain in its spinor space, under $P$ or $T$ separately
$\varphi$ goes to a 'different' spinor space and may have opposite chirality.
We conclude with a preliminary characterization of inner automorphisms with
respect to their property to change, or not, spinor spaces.Comment: Minor changes to propositions 1 and

### On Computational Complexity of Clifford Algebra

After a brief discussion of the computational complexity of Clifford
algebras, we present a new basis for even Clifford algebra Cl(2m) that
simplifies greatly the actual calculations and, without resorting to the
conventional matrix isomorphism formulation, obtains the same complexity. In
the last part we apply these results to the Clifford algebra formulation of the
NP-complete problem of the maximum clique of a graph introduced in a previous
paper.Comment: 13 page

### Warped metrics for location-scale models

This paper argues that a class of Riemannian metrics, called warped metrics,
plays a fundamental role in statistical problems involving location-scale
models. The paper reports three new results : i) the Rao-Fisher metric of any
location-scale model is a warped metric, provided that this model satisfies a
natural invariance condition, ii) the analytic expression of the sectional
curvature of this metric, iii) the exact analytic solution of the geodesic
equation of this metric. The paper applies these new results to several
examples of interest, where it shows that warped metrics turn location-scale
models into complete Riemannian manifolds of negative sectional curvature. This
is a very suitable situation for developing algorithms which solve problems of
classification and on-line estimation. Thus, by revealing the connection
between warped metrics and location-scale models, the present paper paves the
way to the introduction of new efficient statistical algorithms.Comment: preprint of a submission to GSI 2017 conferenc

### Serre Theorem for involutory Hopf algebras

We call a monoidal category ${\mathcal C}$ a Serre category if for any $C$,
$D \in {\mathcal C}$ such that C\ot D is semisimple, $C$ and $D$ are
semisimple objects in ${\mathcal C}$. Let $H$ be an involutory Hopf algebra,
$M$, $N$ two $H$-(co)modules such that $M \otimes N$ is (co)semisimple as a
$H$-(co)module. If $N$ (resp. $M$) is a finitely generated projective
$k$-module with invertible Hattory-Stallings rank in $k$ then $M$ (resp. $N$)
is (co)semisimple as a $H$-(co)module. In particular, the full subcategory of
all finite dimensional modules, comodules or Yetter-Drinfel'd modules over $H$
the dimension of which is invertible in $k$ are Serre categories.Comment: a new version: 8 page

### Reconstructing the geometric structure of a Riemannian symmetric space from its Satake diagram

The local geometry of a Riemannian symmetric space is described completely by
the Riemannian metric and the Riemannian curvature tensor of the space. In the
present article I describe how to compute these tensors for any Riemannian
symmetric space from the Satake diagram, in a way that is suited for the use
with computer algebra systems. As an example application, the totally geodesic
submanifolds of the Riemannian symmetric space SU(3)/SO(3) are classified.
The submission also contains an example implementation of the algorithms and
formulas of the paper as a package for Maple 10, the technical documentation
for this implementation, and a worksheet carrying out the computations for the
space SU(3)/SO(3) used in the proof of Proposition 6.1 of the paper.Comment: 23 pages, also contains two Maple worksheets and technical
documentatio

### Dramatic post-cardiotomy outcome, due to severe anaphylactic reaction to protamine

Immunologic reactions to protamine sulfate during cardiac surgery are very rare. The frequency and outcome of such adverse reactions is unclear. We report a case of lethal anaphylactic reaction to protamine that occurred in a non-diabetic patient following the uneventful replacement of the ascending aorta. We also briefly review the mechanisms of this adverse reaction and emit some considerations on the management of this situatio

### Free Differential Algebras: Their Use in Field Theory and Dual Formulation

The gauging of free differential algebras (FDA's) produces gauge field
theories containing antisymmetric tensors. The FDA's extend the Cartan-Maurer
equations of ordinary Lie algebras by incorporating p-form potentials ($p >
1$). We study here the algebra of FDA transformations. To every p-form in the
FDA we associate an extended Lie derivative $\ell$ generating a corresponding
``gauge" transformation. The field theory based on the FDA is invariant under
these new transformations. This gives geometrical meaning to the antisymmetric
tensors. The algebra of Lie derivatives is shown to close and provides the dual
formulation of FDA's.Comment: 10 pages, latex, no figures. Talk presented at the 4-th Colloquium on
"Quantum Groups and Integrable Sysytems", Prague, June 199

### Inhibition of Membrane-Bound BAFF by the Anti-BAFF Antibody Belimumab.

B cell activating factor of the TNF family (BAFF, also known as BLyS), a cytokine that regulates homeostasis of peripheral B cells, is elevated in the circulation of patients with autoimmune diseases such as systemic lupus erythematosus (SLE). BAFF is synthetized as a membrane-bound protein that can be processed to a soluble form after cleavage at a furin consensus sequence, a site that in principle can be recognized by any of the several proteases of the pro-protein convertase family. Belimumab is a human antibody approved for the treatment of SLE, often cited as specific for the soluble form of BAFF. Here we show in different experimental systems, including in a monocytic cell line (U937) that naturally expresses BAFF, that belimumab binds to membrane-bound BAFF with similar EC50 as the positive control atacicept, which is a decoy receptor for both BAFF and the related cytokine APRIL (a proliferation inducing ligand). In U937 cells, binding of both reagents was only detectable in furin-deficient U937 cells, showing that furin is the main BAFF processing protease in these cells. In CHO cells expressing membrane-bound BAFF lacking the stalk region, belimumab inhibited the activity of membrane-bound BAFF less efficiently than atacicept, while in furin-deficient U937 cells, belimumab inhibited membrane-bound BAFF and residual soluble BAFF as efficiently as atacicept. These reagents did not activate complement or antibody-dependent cell cytotoxicity upon binding to membrane-bound BAFF in vitro. In conclusion, our data show that belimumab can inhibit membrane-bound BAFF, and that BAFF in U937 cells is processed by furin

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