286 research outputs found
The Hamilton-Jacobi Formalism for Higher Order Field Theories
We extend the geometric Hamilton-Jacobi formalism for hamiltonian mechanics
to higher order field theories with regular lagrangian density. We also
investigate the dependence of the formalism on the lagrangian density in the
class of those yelding the same Euler-Lagrange equations.Comment: 25 page
Understanding quantization: a hidden variable model
We argue that to solve the foundational problems of quantum theory one has to
first understand what it means to quantize a classical system. We then propose
a quantization method based on replacement of deterministic c-numbers by
stochastically-parameterized c-numbers. Unlike canonical quantization, the
method is free from operator ordering ambiguity and the resulting quantum
system has a straightforward interpretation as statistical modification of
ensemble of classical trajectories. We then develop measurement without wave
function collapse \`a la pilot-wave theory and point out new testable
predictions.Comment: 16 pages, based on a talk given at "Emergent Quantum Mechanics (Heinz
von Foerster Conference 2011)", see http://iopscience.iop.org/1742-6596/361/
Invariant and polynomial identities for higher rank matrices
We exhibit explicit expressions, in terms of components, of discriminants,
determinants, characteristic polynomials and polynomial identities for matrices
of higher rank. We define permutation tensors and in term of them we construct
discriminants and the determinant as the discriminant of order , where
is the dimension of the matrix. The characteristic polynomials and the
Cayley--Hamilton theorem for higher rank matrices are obtained there from
Multi-transmission-line-beam interactive system
We construct here a Lagrangian field formulation for a system consisting of
an electron beam interacting with a slow-wave structure modeled by a possibly
non-uniform multiple transmission line (MTL). In the case of a single line we
recover the linear model of a traveling wave tube (TWT) due to J.R. Pierce.
Since a properly chosen MTL can approximate a real waveguide structure with any
desired accuracy, the proposed model can be used in particular for design
optimization. Furthermore, the Lagrangian formulation provides for: (i) a clear
identification of the mathematical source of amplification, (ii) exact
expressions for the conserved energy and its flux distributions obtained from
the Noether theorem. In the case of uniform MTLs we carry out an exhaustive
analysis of eigenmodes and find sharp conditions on the parameters of the
system to provide for amplifying regimes
The causal structure of spacetime is a parameterized Randers geometry
There is a by now well-established isomorphism between stationary
4-dimensional spacetimes and 3-dimensional purely spatial Randers geometries -
these Randers geometries being a particular case of the more general class of
3-dimensional Finsler geometries. We point out that in stably causal
spacetimes, by using the (time-dependent) ADM decomposition, this result can be
extended to general non-stationary spacetimes - the causal structure (conformal
structure) of the full spacetime is completely encoded in a parameterized
(time-dependent) class of Randers spaces, which can then be used to define a
Fermat principle, and also to reconstruct the null cones and causal structure.Comment: 8 page
Involution and Constrained Dynamics I: The Dirac Approach
We study the theory of systems with constraints from the point of view of the
formal theory of partial differential equations. For finite-dimensional systems
we show that the Dirac algorithm completes the equations of motion to an
involutive system. We discuss the implications of this identification for field
theories and argue that the involution analysis is more general and flexible
than the Dirac approach. We also derive intrinsic expressions for the number of
degrees of freedom.Comment: 28 pages, latex, no figure
Successful outcome of Langerhans cell histiocytosis complicated by therapy-related myelodysplasia and acute myeloid leukemia: a case report
Progress in Classical and Quantum Variational Principles
We review the development and practical uses of a generalized Maupertuis
least action principle in classical mechanics, in which the action is varied
under the constraint of fixed mean energy for the trial trajectory. The
original Maupertuis (Euler-Lagrange) principle constrains the energy at every
point along the trajectory. The generalized Maupertuis principle is equivalent
to Hamilton's principle. Reciprocal principles are also derived for both the
generalized Maupertuis and the Hamilton principles. The Reciprocal Maupertuis
Principle is the classical limit of Schr\"{o}dinger's variational principle of
wave mechanics, and is also very useful to solve practical problems in both
classical and semiclassical mechanics, in complete analogy with the quantum
Rayleigh-Ritz method. Classical, semiclassical and quantum variational
calculations are carried out for a number of systems, and the results are
compared. Pedagogical as well as research problems are used as examples, which
include nonconservative as well as relativistic systems
W-Gravity
The geometric structure of theories with gauge fields of spins two and higher
should involve a higher spin generalisation of Riemannian geometry. Such
geometries are discussed and the case of -gravity is analysed in
detail. While the gauge group for gravity in dimensions is the
diffeomorphism group of the space-time, the gauge group for a certain
-gravity theory (which is -gravity in the case ) is the group
of symplectic diffeomorphisms of the cotangent bundle of the space-time. Gauge
transformations for -gravity gauge fields are given by requiring the
invariance of a generalised line element. Densities exist and can be
constructed from the line element (generalising )
only if or , so that only for can actions be constructed.
These two cases and the corresponding -gravity actions are considered in
detail. In , the gauge group is effectively only a subgroup of the
symplectic diffeomorphism group. Some of the constraints that arise for
are similar to equations arising in the study of self-dual four-dimensional
geometries and can be analysed using twistor methods, allowing contact to be
made with other formulations of -gravity. While the twistor transform for
self-dual spaces with one Killing vector reduces to a Legendre transform, that
for two Killing vectors gives a generalisation of the Legendre transform.Comment: 49 pages, QMW-92-
The Shine-Through Masking Paradigm Is a Potential Endophenotype of Schizophrenia
BACKGROUND: To understand the genetics of schizophrenia, a hunt for so-called intermediate phenotypes or endophenotypes is ongoing. Visual masking has been proposed to be such an endophenotype. However, no systematic study has been conducted yet to prove this claim. Here, we present the first study showing that masking meets the most important criteria for an endophenotype. METHODOLOGY/PRINCIPAL FINDINGS: We tested 62 schizophrenic patients, 39 non-affected first-degree relatives, and 38 healthy controls in the shine-through masking paradigm and, in addition, in the Continuous Performance Test (CPT) and the Wisconsin Card Sorting Test (WCST). Most importantly, masking performance of relatives was significantly in between the one of patients and controls in the shine-through paradigm. Moreover, deficits were stable throughout one year. Using receiver operating characteristics (ROC) methods, we show that the shine-through paradigm distinguishes with high sensitivity and specificity between schizophrenic patients, first-order relatives and healthy controls. CONCLUSIONS/SIGNIFICANCE: The shine-through paradigm is a potential endophenotype
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