3,841 research outputs found
Least-Squares Approximation by Elements from Matrix Orbits Achieved by Gradient Flows on Compact Lie Groups
Let denote the orbit of a complex or real matrix under a certain
equivalence relation such as unitary similarity, unitary equivalence, unitary
congruences etc. Efficient gradient-flow algorithms are constructed to
determine the best approximation of a given matrix by the sum of matrices
in in the sense of finding the Euclidean least-squares
distance
Connections of the results to different pure and applied areas are discussed
Polarization and frequency disentanglement of photons via stochastic polarization mode dispersion
We investigate the quantum decoherence of frequency and polarization
variables of photons via polarization mode dispersion in optical fibers. By
observing the analogy between the propagation equation of the field and the
Schr\"odinger equation, we develop a master equation under Markovian
approximation and analytically solve for the field density matrix. We identify
distinct decay behaviors for the polarization and frequency variables for
single-photon and two-photon states. For the single photon case, purity
functions indicate that complete decoherence for each variable is possible only
for infinite fiber length. For entangled two-photon states passing through
separate fibers, entanglement associated with each variable can be completely
destroyed after characteristic finite propagation distances. In particular, we
show that frequency disentanglement is independent of the initial polarization
status. For propagation of two photons in a common fiber, the evolution of a
polarization singlet state is addressed. We show that while complete
polarization disentanglement occurs at a finite propagation distance, frequency
entanglement could survive at any finite distance for gaussian states.Comment: 2 figure
Cyclin F Is Degraded during G2-M by Mechanisms Fundamentally Different from Other Cyclins
Cyclin F, a cyclin that can form SCF complexes and bind to cyclin B, oscillates in the cell cycle with a pattern similar to cyclin A and cyclin B. Ectopic expression of cyclin F arrests the cell cycle in G2/M. How the level of cyclin F is regulated during the cell cycle is completely obscure. Here we show that, similar to cyclin A, cyclin F is degraded when the spindle assembly checkpoint is activated and accumulates when the DNA damage checkpoint is activated. Cyclin F is a very unstable protein throughout much of the cell cycle. Unlike other cyclins, degradation of cyclin F is independent of ubiquitination and proteasome-mediated pathways. Interestingly, proteolysis of cyclin F is likely to involve metalloproteases. Rapid destruction of cyclin F does not require the N-terminal F-box motif but requires the COOH-terminal PEST sequences. The PEST region alone is sufficient to interfere with the degradation of cyclin F and confer instability when fused to cyclin A. These data show that although cyclin F is degraded at similar time as the mitotic cyclins, the underlying mechanisms are entirely distinct
Relation Between First Arrival Time and Permeability in Self-Affine Fractures with Areas in Contact
We demonstrate that the first arrival time in dispersive processes in
self-affine fractures are governed by the same length scale characterizing the
fractures as that which controls their permeability. In one-dimensional channel
flow this length scale is the aperture of the bottle neck, i.e., the region
having the smallest aperture. In two dimensions, the concept of a bottle neck
is generalized to that of a minimal path normal to the flow. The length scale
is then the average aperture along this path. There is a linear relationship
between the first arrival time and this length scale, even when there is strong
overlap between the fracture surfaces creating areas with zero permeability. We
express the first arrival time directly in terms of the permeability.Comment: EPL (2012)
Least-Squares Approximation by Elements from Matrix Orbits Achieved by Gradient Flows on Compact Lie Groups
Let denote the orbit of a complex or real matrix under a certain
equivalence relation such as unitary similarity, unitary equivalence, unitary
congruences etc. Efficient gradient-flow algorithms are constructed to
determine the best approximation of a given matrix by the sum of matrices
in in the sense of finding the Euclidean least-squares
distance
Connections of the results to different pure and applied areas are discussed
Diffusive Evolution of Stable and Metastable Phases II: Theory of Non-Equilibrium Behaviour in Colloid-Polymer Mixtures
By analytically solving some simple models of phase-ordering kinetics, we
suggest a mechanism for the onset of non-equilibrium behaviour in
colloid-polymer mixtures. These mixtures can function as models of atomic
systems; their physics therefore impinges on many areas of thermodynamics and
phase-ordering. An exact solution is found for the motion of a single, planar
interface separating a growing phase of uniform high density from a
supersaturated low density phase, whose diffusive depletion drives the
interfacial motion. In addition, an approximate solution is found for the
one-dimensional evolution of two interfaces, separated by a slab of a
metastable phase at intermediate density. The theory predicts a critical
supersaturation of the low-density phase, above which the two interfaces become
unbound and the metastable phase grows ad infinitum. The growth of the stable
phase is suppressed in this regime.Comment: 27 pages, Latex, eps
Using Positive Youth Development Constructs to Design a Money Management Curriculum for Junior Secondary School Students in Hong Kong
This paper aims to discuss the relationships between the selected positive youth development constructs and the enhancement of Hong Kong junior secondary school students' money management skills, values, and attitudes. Various issues of money management of adolescents are reviewed. These issues include the need for money management programs for adolescents, the content and coverage of an appropriate money management program, and its relationships with the selected positive youth development constructs. The curriculum units for secondary 3 students are taken as examples to illustrate the design of the program. It is believed that promoting cognitive competence, self-efficacy, and spirituality could be an effective way to enhance students' money management skills, values, and attitudes, thus preparing them better for facing the finance-related issues in life
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