72 research outputs found
A simple construction of complex equiangular lines
A set of vectors of equal norm in represents equiangular lines
if the magnitudes of the inner product of every pair of distinct vectors in the
set are equal. The maximum size of such a set is , and it is conjectured
that sets of this maximum size exist in for every . We
describe a new construction for maximum-sized sets of equiangular lines,
exposing a previously unrecognized connection with Hadamard matrices. The
construction produces a maximum-sized set of equiangular lines in dimensions 2,
3 and 8.Comment: 11 pages; minor revisions and comments added in section 1 describing
a link to previously known results; correction to Theorem 1 and updates to
reference
Algebro-geometric approach in the theory of integrable hydrodynamic type systems
The algebro-geometric approach for integrability of semi-Hamiltonian
hydrodynamic type systems is presented. This method is significantly simplified
for so-called symmetric hydrodynamic type systems. Plenty interesting and
physically motivated examples are investigated
Equivalence problem for the orthogonal webs on the sphere
We solve the equivalence problem for the orthogonally separable webs on the
three-sphere under the action of the isometry group. This continues a classical
project initiated by Olevsky in which he solved the corresponding canonical
forms problem. The solution to the equivalence problem together with the
results by Olevsky forms a complete solution to the problem of orthogonal
separation of variables to the Hamilton-Jacobi equation defined on the
three-sphere via orthogonal separation of variables. It is based on invariant
properties of the characteristic Killing two-tensors in addition to properties
of the corresponding algebraic curvature tensor and the associated Ricci
tensor. The result is illustrated by a non-trivial application to a natural
Hamiltonian defined on the three-sphere.Comment: 32 page
Hamiltonian systems of hydrodynamic type in 2 + 1 dimensions
We investigate multi-dimensional Hamiltonian systems associated with constant
Poisson brackets of hydrodynamic type. A complete list of two- and
three-component integrable Hamiltonians is obtained. All our examples possess
dispersionless Lax pairs and an infinity of hydrodynamic reductions.Comment: 34 page
Strict selection alone of patients undergoing liver transplantation for hilar cholangiocarcinoma is associated with improved survival
Liver transplantation for hilar cholangiocarcinoma (hCCA) has regained attention since the Mayo Clinic reported their favorable results with the use of a neo-adjuvant chemoradiation protocol. However, debate remains whether the success of the protocol should be attributed to the neo-adjuvant therapy or to the strict selection criteria that are being applied. The aim of this study was to investigate the value of patient selection alone on the outcome of liver transplantation for hCCA. In this retrospective study, patients that were transplanted for hCCA between1990 and 2010 in Europe were identified using the European Liver Transplant Registry (ELTR). Twenty-one centers reported 173 patients (69%) of a total of 249 patients in the ELTR. Twenty-six patients were wrongly coded, resulting in a study group of 147 patients. We identified 28 patients (19%) who met the strict selection criteria of the Mayo Clinic protocol, but had not undergone neo-adjuvant chemoradiation therapy. Five-year survival in this subgroup was 59%, which is comparable to patients with pretreatment pathological confirmed hCCA that were transplanted after completion of the chemoradiation protocol at the Mayo Clinic. In conclusion, although the results should be cautiously interpreted, this study suggests that with strict selection alone, improved survival after transplantation can be achieved, approaching the Mayo Clinic experience
The Nontriviality of Trivial General Covariance: How Electrons Restrict 'Time' Coordinates, Spinors (Almost) Fit into Tensor Calculus, and 7/16 of a Tetrad Is Surplus Structure
It is a commonplace that any theory can be written in any coordinates via
tensor calculus. But it is claimed that spinors as such cannot be represented
in coordinates in a curved space-time. What general covariance means for
theories with fermions is thus unclear. In fact both commonplaces are wrong.
Though it is not widely known, Ogievetsky and Polubarinov (OP) constructed
spinors in coordinates in 1965, helping to spawn nonlinear group
representations. Locally, these spinors resemble the orthonormal basis or
"tetrad" formalism in the symmetric gauge, but they are conceptually
self-sufficient. The tetrad formalism is de-Ockhamized, with 6 extra fields and
6 compensating gauge symmetries. OP spinors, as developed nonperturbatively by
Bilyalov, admit any coordinates at a point, but "time" must be listed first:
the product of the metric components and the matrix diag(-1,1,1,1) must have no
negative eigenvalues to yield a real symmetric square root function of the
metric. Thus the admissible coordinates depend on the types and values of the
fields. Apart from coordinate order and spinorial two-valuedness, OP spinors
form, with the metric, a nonlinear geometric object, with Lie and covariant
derivatives. Such spinors avoid a spurious absolute object in the
Anderson-Friedman analysis of substantive general covariance. They also permit
the gauge-invariant localization of the infinite-component gravitational energy
in GR. Density-weighted spinors exploit the conformal invariance of the
massless Dirac equation to show that the volume element is absent. Thus instead
of a matrix with 16 components, one can use weighted OP spinors coupled to the
9-component symmetric unimodular square root of the conformal metric density.
The surprising mildness of the restrictions on coordinates for the
Schwarzschild solution is exhibited. (edited)Comment: Forthcoming in \textit{Studies in History and Philosophy of Modern
Physics
Gauging the spacetime metric -- looking back and forth a century later
H. Weyl's proposal of 1918 for generalizing Riemannian geometry by local
scale gauge (later called {\em Weyl geometry}) was motivated by mathematical,
philosophical and physical considerations. It was the starting point of his
unified field theory of electromagnetism and gravity. After getting
disillusioned with this research program and after the rise of a convincing
alternative for the gauge idea by translating it to the phase of wave functions
and spinor fields in quantum mechanics, Weyl no longer considered the original
scale gauge as physically relevant.
About the middle of the last century the question of conformal and/or local
scale gauge transformation were reconsidered by different authors in high
energy physics (Bopp, Wess, et al.) and, independently, in gravitation theory
(Jordan, Fierz, Brans, Dicke). In this context Weyl geometry attracted new
interest among different groups of physicists (Omote/Utiyama/Kugo,
Dirac/Canuto/Maeder, Ehlers/Pirani/Schild and others), often by hypothesizing a
new scalar field linked to gravity and/or high energy physics. Although not
crowned by immediate success, this ``retake'' of Weyl geometrical methods lives
on and has been extended a century after Weyl's first proposal of his basic
geometrical structure. It finds new interest in present day studies of
elementary particle physics, cosmology, and philosophy of physics.Comment: 56 pages, contribution to Workshop Hundred Years of Gauge Theory Bad
Honnef, July 30 - August 3, 201
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