410 research outputs found
Projective Ring Line Encompassing Two-Qubits
The projective line over the (non-commutative) ring of two-by-two matrices
with coefficients in GF(2) is found to fully accommodate the algebra of 15
operators - generalized Pauli matrices - characterizing two-qubit systems. The
relevant sub-configuration consists of 15 points each of which is either
simultaneously distant or simultaneously neighbor to (any) two given distant
points of the line. The operators can be identified with the points in such a
one-to-one manner that their commutation relations are exactly reproduced by
the underlying geometry of the points, with the ring geometrical notions of
neighbor/distant answering, respectively, to the operational ones of
commuting/non-commuting. This remarkable configuration can be viewed in two
principally different ways accounting, respectively, for the basic 9+6 and 10+5
factorizations of the algebra of the observables. First, as a disjoint union of
the projective line over GF(2) x GF(2) (the "Mermin" part) and two lines over
GF(4) passing through the two selected points, the latter omitted. Second, as
the generalized quadrangle of order two, with its ovoids and/or spreads
standing for (maximum) sets of five mutually non-commuting operators and/or
groups of five maximally commuting subsets of three operators each. These
findings open up rather unexpected vistas for an algebraic geometrical
modelling of finite-dimensional quantum systems and give their numerous
applications a wholly new perspective.Comment: 8 pages, three tables; Version 2 - a few typos and one discrepancy
corrected; Version 3: substantial extension of the paper - two-qubits are
generalized quadrangles of order two; Version 4: self-dual picture completed;
Version 5: intriguing triality found -- three kinds of geometric hyperplanes
within GQ and three distinguished subsets of Pauli operator
On Invariant Notions of Segre Varieties in Binary Projective Spaces
Invariant notions of a class of Segre varieties \Segrem(2) of PG(2^m - 1,
2) that are direct products of copies of PG(1, 2), being any positive
integer, are established and studied. We first demonstrate that there exists a
hyperbolic quadric that contains \Segrem(2) and is invariant under its
projective stabiliser group \Stab{m}{2}. By embedding PG(2^m - 1, 2) into
\PG(2^m - 1, 4), a basis of the latter space is constructed that is invariant
under \Stab{m}{2} as well. Such a basis can be split into two subsets whose
spans are either real or complex-conjugate subspaces according as is even
or odd. In the latter case, these spans can, in addition, be viewed as
indicator sets of a \Stab{m}{2}-invariant geometric spread of lines of PG(2^m
- 1, 2). This spread is also related with a \Stab{m}{2}-invariant
non-singular Hermitian variety. The case is examined in detail to
illustrate the theory. Here, the lines of the invariant spread are found to
fall into four distinct orbits under \Stab{3}{2}, while the points of PG(7,
2) form five orbits.Comment: 18 pages, 1 figure; v2 - version accepted in Designs, Codes and
Cryptograph
Time-dependent spectral-feature variations of stars displaying the B[e] phenomenon; I. V2028 Cyg
We present results of nearly six years of spectroscopic observations of the
B[e] star V2028 Cyg. The presence of the cold-type absorption lines combined
with a hot-type spectrum indicate the binarity of this object. Since B[e] stars
are embedded in an extended envelope, the usage of common stellar atmosphere
models for the analysis is quite inappropriate. Therefore, we focus on the
analysis of the long-term spectral line variations in order to determine the
nature of this object. We present the time dependences of the equivalent width
and radial velocities of the H alpha line, [O I] 6300 A, Fe II 6427, 6433, and
6456 A lines. The bisector variations and line intensities are shown for the H
alpha line. The radial velocities are also measured for the absorption lines of
the K component. No periodic variation is found. The observed data show
correlations between the measured quantities, which can be used in future
modelling
A novel stepwise integrative analysis pipeline reveals distinct microbiota-host interactions and link to symptoms in irritable bowel syndrome
Although incompletely understood, microbiota-host interactions are assumed to be altered in irritable bowel syndrome (IBS). We, therefore, aimed to develop a novel analysis pipeline tailored for the integrative analysis of microbiota-host interactions and association to symptoms and prove its utility in a pilot cohort. A multilayer stepwise integrative analysis pipeline was developed to visualize complex variable associations. Application of the pipeline was demonstrated on a dataset of IBS patients and healthy controls (HC), using the R software package to analyze colonic host mRNA and mucosal microbiota (16S rRNA gene sequencing), as well as gastrointestinal (GI) and psychological symptoms. In total, 42 IBS patients (57% female, mean age 33.6 (range 18–58)) and 20 HC (60% female, mean age 26.8 (range 23–41)) were included. Only in IBS patients, mRNA expression of Toll-like receptor 4 and genes associated with barrier function (PAR2, OCLN, TJP1) intercorrelated closely, suggesting potential functional relationships. This host genes-based “permeability cluster” was associated to mucosa-adjacent Chlamydiae and Lentisphaerae, and furthermore associated to satiety as well as to anxiety, depression and fatigue. In both IBS patients and HC, chromogranins, secretogranins and TLRs clustered together. In IBS patients, this host genes-based “immune-enteroendocrine cluster” was associated to specific members of Firmicutes, and to depression and fatigue, whereas in HC no significant association to microbiota was identified. We have developed a stepwise integrative analysis pipeline that allowed identification of unique host-microbiota intercorrelation patterns and association to symptoms in IBS patients. This analysis pipeline may aid in advancing the understanding of complex variable associations in health and disease
SR 33557, a Novel Calcium Entry Blocker. I. In Vitro Isolated Tissue Studies1
ABSTRACT The effects of SR 33557 on isolated cardiovascular preparations were compared to those of nifedipine, verapamil and diltiazem
Potentiation of the glutamatergic synaptic input to rat locus coeruleus neurons by P2X7 receptors
Locus coeruleus (LC) neurons in a rat brain slice preparation were superfused with a Mg2+-free and bicuculline-containing external medium. Under these conditions, glutamatergic spontaneous excitatory postsynaptic currents (sEPSCs) were recorded by means of the whole-cell patch-clamp method. ATP, as well as its structural analogue 2-methylthio ATP (2-MeSATP), both caused transient inward currents, which were outlasted by an increase in the frequency but not the amplitude of the sEPSCs. PPADS, but not suramin or reactive blue 2 counteracted both effects of 2-MeSATP. By contrast, α,β-methylene ATP (α,β-meATP), UTP and BzATP did not cause an inward current response. Of these latter agonists, only BzATP slightly facilitated the sEPSC amplitude and strongly potentiated its frequency. PPADS and Brilliant Blue G, as well as fluorocitric acid and aminoadipic acid prevented the activity of BzATP. Furthermore, BzATP caused a similar facilitation of the miniature (m)EPSC (recorded in the presence of tetrodotoxin) and sEPSC frequencies (recorded in its absence). Eventually, capsaicin augmented the frequency of the sEPSCs in a capsazepine-, but not PPADS-antagonizable, manner. In conclusion, the stimulation of astrocytic P2X7 receptors appears to lead to the outflow of a signalling molecule, which presynaptically increases the spontaneous release of glutamate onto LC neurons from their afferent fibre tracts. It is suggested, that the two algogenic compounds ATP and capsaicin utilise separate receptor systems to potentiate the release of glutamate and in consequence to increase the excitability of LC neurons. © 2010 Springer Science+Business Media B.V
Constraining Antimatter Domains in the Early Universe with Big Bang Nucleosynthesis
We consider the effect of a small-scale matter-antimatter domain structure on
big bang nucleosynthesis and place upper limits on the amount of antimatter in
the early universe. For small domains, which annihilate before nucleosynthesis,
this limit comes from underproduction of He-4. For larger domains, the limit
comes from He-3 overproduction. Most of the He-3 from antiproton-helium
annihilation is annihilated also. The main source of He-3 is
photodisintegration of He-4 by the electromagnetic cascades initiated by the
annihilation.Comment: 4 pages, 2 figures, revtex, (slightly shortened
Isospin Physics in Heavy-Ion Collisions at Intermediate Energies
In nuclear collisions induced by stable or radioactive neutron-rich nuclei a
transient state of nuclear matter with an appreciable isospin asymmetry as well
as thermal and compressional excitation can be created. This offers the
possibility to study the properties of nuclear matter in the region between
symmetric nuclear matter and pure neutron matter. In this review, we discuss
recent theoretical studies of the equation of state of isospin-asymmetric
nuclear matter and its relations to the properties of neutron stars and
radioactive nuclei. Chemical and mechanical instabilities as well as the
liquid-gas phase transition in asymmetric nuclear matter are investigated. The
in-medium nucleon-nucleon cross sections at different isospin states are
reviewed as they affect significantly the dynamics of heavy ion collisions
induced by radioactive beams. We then discuss an isospin-dependent transport
model, which includes different mean-field potentials and cross sections for
the proton and neutron, and its application to these reactions. Furthermore, we
review the comparisons between theoretical predictions and available
experimental data. In particular, we discuss the study of nuclear stopping in
terms of isospin equilibration, the dependence of nuclear collective flow and
balance energy on the isospin-dependent nuclear equation of state and cross
sections, the isospin dependence of total nuclear reaction cross sections, and
the role of isospin in preequilibrium nucleon emissions and subthreshold pion
production.Comment: 101 pages with embedded epsf figures, review article for
"International Journal of Modern Physics E: Nuclear Physics". Send request
for a hard copy to 1/author
Black Hole Entropy and Finite Geometry
It is shown that the symmetric entropy formula describing black
holes and black strings in D=5 is intimately tied to the geometry of the
generalized quadrangle GQ with automorphism group the Weyl group
. The 27 charges correspond to the points and the 45 terms in the
entropy formula to the lines of GQ. Different truncations with
and 9 charges are represented by three distinguished subconfigurations of
GQ, well-known to finite geometers; these are the "doily" (i. e.
GQ) with 15, the "perp-set" of a point with 11, and the "grid" (i. e.
GQ) with 9 points, respectively. In order to obtain the correct signs
for the terms in the entropy formula, we use a non- commutative labelling for
the points of GQ. For the 40 different possible truncations with 9
charges this labelling yields 120 Mermin squares -- objects well-known from
studies concerning Bell-Kochen-Specker-like theorems. These results are
connected to our previous ones obtained for the symmetric entropy
formula in D=4 by observing that the structure of GQ is linked to a
particular kind of geometric hyperplane of the split Cayley hexagon of order
two, featuring 27 points located on 9 pairwise disjoint lines (a
distance-3-spread). We conjecture that the different possibilities of
describing the D=5 entropy formula using Jordan algebras, qubits and/or qutrits
correspond to employing different coordinates for an underlying non-commutative
geometric structure based on GQ.Comment: 17 pages, 3 figures, v2 a new paragraph added, typos correcte
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