47 research outputs found
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, for some in a Hilbert space 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 , the Krein--von Neumann extension of the
perturbed Laplacian (in short, the perturbed Krein Laplacian)
defined on , where is measurable, bounded and
nonnegative, in a bounded open set belonging to a
class of nonsmooth domains which contains all convex domains, along with all
domains of class , .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