Geometric information in eight dimensions vs. quantum information

Complementary idempotent paravectors and their ordered compositions, are used to represent multivector basis elements of geometric Clifford algebra for 3D Euclidean space as the states of a geometric byte in a given frame of reference. Two layers of information, available in real numbers, are distinguished. The first layer is a continuous one. It is used to identify spatial orientations of similar geometric objects in the same computational basis. The second layer is a binary one. It is used to manipulate with 8D structure elements inside the computational basis itself. An oriented unit cube representation, rather than a matrix one, is used to visualize an inner structure of basis multivectors. Both layers of information are used to describe unitary operations -- reflections and rotations -- in Euclidian and Hilbert spaces. The results are compared with ones for quantum gates. Some consequences for quantum and classical information technologies are discussed.Comment: 14 pages, presented at International Symposium "Quantum Informatics 2007", October 3rd - 5th, 2007, Moscow Zvenigorod, Russi

Autoresonance in a Dissipative System

We study the autoresonant solution of Duffing's equation in the presence of dissipation. This solution is proved to be an attracting set. We evaluate the maximal amplitude of the autoresonant solution and the time of transition from autoresonant growth of the amplitude to the mode of fast oscillations. Analytical results are illustrated by numerical simulations.Comment: 22 pages, 3 figure

A Survey on the Krein-von Neumann Extension, the corresponding Abstract Buckling Problem, and Weyl-Type Spectral Asymptotics for Perturbed Krein Laplacians in Nonsmooth Domains

In the first (and abstract) part of this survey we prove the unitary equivalence of the inverse of the Krein--von Neumann extension (on the orthogonal complement of its kernel) of a densely defined, closed, strictly positive operator, $S\geq \varepsilon I_{\mathcal{H}}$ for some $\varepsilon >0$ in a Hilbert space $\mathcal{H}$ to an abstract buckling problem operator. This establishes the Krein extension as a natural object in elasticity theory (in analogy to the Friedrichs extension, which found natural applications in quantum mechanics, elasticity, etc.). In the second, and principal part of this survey, we study spectral properties for $H_{K,\Omega}$, the Krein--von Neumann extension of the perturbed Laplacian $-\Delta+V$ (in short, the perturbed Krein Laplacian) defined on $C^\infty_0(\Omega)$, where $V$ is measurable, bounded and nonnegative, in a bounded open set $\Omega\subset\mathbb{R}^n$ belonging to a class of nonsmooth domains which contains all convex domains, along with all domains of class $C^{1,r}$, $r>1/2$.Comment: 68 pages. arXiv admin note: extreme text overlap with arXiv:0907.144

A Yersinia Effector with Enhanced Inhibitory Activity on the NF-κB Pathway Activates the NLRP3/ASC/Caspase-1 Inflammasome in Macrophages

A type III secretion system (T3SS) in pathogenic Yersinia species functions to translocate Yop effectors, which modulate cytokine production and regulate cell death in macrophages. Distinct pathways of T3SS-dependent cell death and caspase-1 activation occur in Yersinia-infected macrophages. One pathway of cell death and caspase-1 activation in macrophages requires the effector YopJ. YopJ is an acetyltransferase that inactivates MAPK kinases and IKKβ to cause TLR4-dependent apoptosis in naïve macrophages. A YopJ isoform in Y. pestis KIM (YopJKIM) has two amino acid substitutions, F177L and K206E, not present in YopJ proteins of Y. pseudotuberculosis and Y. pestis CO92. As compared to other YopJ isoforms, YopJKIM causes increased apoptosis, caspase-1 activation, and secretion of IL-1β in Yersinia-infected macrophages. The molecular basis for increased apoptosis and activation of caspase-1 by YopJKIM in Yersinia-infected macrophages was studied. Site directed mutagenesis showed that the F177L and K206E substitutions in YopJKIM were important for enhanced apoptosis, caspase-1 activation, and IL-1β secretion. As compared to YopJCO92, YopJKIM displayed an enhanced capacity to inhibit phosphorylation of IκB-α in macrophages and to bind IKKβ in vitro. YopJKIM also showed a moderately increased ability to inhibit phosphorylation of MAPKs. Increased caspase-1 cleavage and IL-1β secretion occurred in IKKβ-deficient macrophages infected with Y. pestis expressing YopJCO92, confirming that the NF-κB pathway can negatively regulate inflammasome activation. K+ efflux, NLRP3 and ASC were important for secretion of IL-1β in response to Y. pestis KIM infection as shown using macrophages lacking inflammasome components or by the addition of exogenous KCl. These data show that caspase-1 is activated in naïve macrophages in response to infection with a pathogen that inhibits IKKβ and MAPK kinases and induces TLR4-dependent apoptosis. This pro-inflammatory form of apoptosis may represent an early innate immune response to highly virulent pathogens such as Y. pestis KIM that have evolved an enhanced ability to inhibit host signaling pathways

Properties of field functionals and characterization of local functionals

Functionals (i.e. functions of functions) are widely used in quantum field theory and solid-state physics. In this paper, functionals are given a rigorous mathematical framework and their main properties are described. The choice of the proper space of test functions (smooth functions) and of the relevant concept of differential (Bastiani differential) are discussed. The relation between the multiple derivatives of a functional and the corresponding distributions is described in detail. It is proved that, in a neighborhood of every test function, the support of a smooth functional is uniformly compactly supported and the order of the corresponding distribution is uniformly bounded. Relying on a recent work by Yoann Dabrowski, several spaces of functionals are furnished with a complete and nuclear topology. In view of physical applications, it is shown that most formal manipulations can be given a rigorous meaning. A new concept of local functionals is proposed and two characterizations of them are given: the first one uses the additivity (or Hammerstein) property, the second one is a variant of Peetre's theorem. Finally, the first step of a cohomological approach to quantum field theory is carried out by proving a global Poincar\'e lemma and defining multi-vector fields and graded functionals within our framework.Comment: 32 pages, no figur