15,942 research outputs found
Symmetric Laplacians, Quantum Density Matrices and their Von-Neumann Entropy
We show that the (normalized) symmetric Laplacian of a simple graph can be
obtained from the partial trace over a pure bipartite quantum state that
resides in a bipartite Hilbert space (one part corresponding to the vertices,
the other corresponding to the edges). This suggests an interpretation of the
symmetric Laplacian's Von Neumann entropy as a measure of bipartite
entanglement present between the two parts of the state. We then study extreme
values for a connected graph's generalized R\'enyi- entropy. Specifically,
we show that
(1) the complete graph achieves maximum entropy,
(2) the -regular graph: a) achieves minimum R\'enyi- entropy among all
-regular graphs, b) is within of the minimum R\'enyi- entropy
and of the minimum Von Neumann entropy among all connected
graphs, c) achieves a Von Neumann entropy less than the star graph.
Point contrasts sharply with similar work applied to (normalized)
combinatorial Laplacians, where it has been shown that the star graph almost
always achieves minimum Von Neumann entropy. In this work we find that the star
graph achieves maximum entropy in the limit as the number of vertices grows
without bound.
Keywords: Symmetric; Laplacian; Quantum; Entropy; Bounds; R\'enyi
Broadening of Spectral Lines due to Dynamic Multiple Scattering and the Tully-Fisher Relation
The frequency shift of spectral lines is most often explained by the Doppler
Effect in terms of relative motion, whereas the Doppler broadening of a
particular line mainly depends on the absolute temperature. The Wolf effect on
the other hand deals with the correlation induced spectral change and explains
both the broadening and shift of the spectral lines. In this framework a
relation between the width of the spectral line is related to the redshift z
for the line and hence with the distance. For smaller values of z a relation
similar to the Tully-Fisher relation can be obtained and for larger values of z
a more general relation can be constructed. The derivation of this kind of
relation based on dynamic multiple scattering theory may play a significant
role in explaining the overall spectra of quasi stellar objects. We emphasize
that this mechanism is not applicable for nearby galaxies, .Comment: 18 pages, 5 figures, revised Version has been submitted to Physical
Review A. (2nd author's affiliation corrected
Raised serum transaminases during treatment with pegylated interferon for chronic hepatiti C
Introduction : Serum transaminases rose significantly in 7 patients with chronic hepatitis C, genotypes 2 and 3, who were treated with pegylated interferon and ribavirin.
Methods : 219 patients with chronic hepatitis C, genotypes 2 and 3, were treated between 2005 and 2011 following the same protocol. For the 7 patients presented in this paper, the initial liver screen revealed chronic hepatitis C infection only. The same liver screen was repeated following the transaminase rise during the treatment period and failed to reveal additional comorbidity.
Results : 5 male and 2 female patients with chronic hepatitis C experienced a rise in serum transaminases after commencement on treatment with pegylated interferon and ribavirin. They all achieved rapid and end of treatment virological responses. 3 of the patients achieved sustained virological response and 4 relapsed. There was no evidence to suggest that steatosis, development of autoimmunity or intercurrent illness was the cause of the liver injury. In 3 out of 7 patients, the level of transaminases exhibited a downward trend after pegylated interferon was changed to non pegylated interferon. Additionally, it is evident that in those patients whose treatment was temporarily or permanently aborted, the rise in transaminases rapidly improved and returned to baseline.
Conclusion : Our experience suggests the possibility of a toxic reaction to polyethylene glycol in a small number of patients being treated with pegylated interferon, resulting in an acute hepatitic response which resolved when therapy was stopped or switched to non-pegylated interferon
LMI based Stability and Stabilization of Second-order Linear Repetitive Processes
This paper develops new results on the stability and control of a class of linear repetitive processes described by a second-order matrix discrete or differential equation. These are developed by transformation of the secondorder dynamics to those of an equivalent first-order descriptor state-space model, thus avoiding the need to invert a possibly ill-conditioned leading coefficient matrix in the original model
Rapidly rotating strange stars for a new equation of state of strange quark matter
For a new equation of state of strange quark matter, we construct equilibrium
sequences of rapidly rotating strange stars in general relativity. The
sequences are the normal and supramassive evolutionary sequences of constant
rest mass. We also calculate equilibrium sequences for a constant value of
corresponding to the most rapidly rotating pulsar PSR 1937 + 21. In
addition to this, we calculate the radius of the marginally stable orbit and
its dependence on , relevant for modeling of kilo-Hertz quasi-periodic
oscillations in X-ray binaries.Comment: Two figures, uses psbox.tex and emulateapj5.st
Constitutive modelling of Sandvik 1RK91
A physically based constitutive equation is being developed for the maraging\ud
stainless steel Sandvik 1RK91. The steel is used to make precision parts. These parts are formed through multistage forming operations and heat treatments from cold rolled and annealed sheets. The specific alloy is designed to be thermodynamically unstable, so that deformation even at room temperatures can bring about a change in the phase of face centred cubic austenite to either hexagonal closed packed martensite and/or, body centred cubic martensite. This solid state phase change is a function of the strain path, strain, strain rate and temperature. Thus, the fraction of the new phase formed depends on the state of stress at a given location in the part being formed. Therefore a set of experiments is being conducted in order to quantify the stress-strain behavior of this steel under various stress states, strain, strain rate as well as temperature. A magnetic sensor records the fraction of ferromagnetic martensite formed from paramagnetic austenite. A thermocouple as well as an infra red thermometer is used to log the change in temperature of the steel during a mechanical test. The force-displacement data are converted to stress-strain data after correcting for the changes in strain rate and temperature. These data are then cast into a general form of constitutive equation and the transformation equations are derived from Olson-Cohen type functions
Quantum Transport with Spin Dephasing: A Nonequilibrium Green's Function Approach
A quantum transport model incorporating spin scattering processes is
presented using the non-equilibrium Green's function (NEGF) formalism within
the self-consistent Born approximation. This model offers a unified approach by
capturing the spin-flip scattering and the quantum effects simultaneously. A
numerical implementation of the model is illustrated for magnetic tunnel
junction devices with embedded magnetic impurity layers. The results are
compared with experimental data, revealing the underlying physics of the
coherent and incoherent transport regimes. It is shown that small variations in
magnetic impurity spin-states/concentrations could cause large deviations in
junction magnetoresistances.Comment: NEGF Formalism, Spin Dephasing, Magnetic Tunnel Junctions,
Magnetoresistanc
Hierarchical Nearest-Neighbor Gaussian Process Models for Large Geostatistical Datasets
Spatial process models for analyzing geostatistical data entail computations
that become prohibitive as the number of spatial locations become large. This
manuscript develops a class of highly scalable Nearest Neighbor Gaussian
Process (NNGP) models to provide fully model-based inference for large
geostatistical datasets. We establish that the NNGP is a well-defined spatial
process providing legitimate finite-dimensional Gaussian densities with sparse
precision matrices. We embed the NNGP as a sparsity-inducing prior within a
rich hierarchical modeling framework and outline how computationally efficient
Markov chain Monte Carlo (MCMC) algorithms can be executed without storing or
decomposing large matrices. The floating point operations (flops) per iteration
of this algorithm is linear in the number of spatial locations, thereby
rendering substantial scalability. We illustrate the computational and
inferential benefits of the NNGP over competing methods using simulation
studies and also analyze forest biomass from a massive United States Forest
Inventory dataset at a scale that precludes alternative dimension-reducing
methods
- …