66,724 research outputs found
Syzygies, Betti numbers and regularity of cover ideals of certain multipartite graphs
Let be a finite simple graph on vertices. Let be the cover ideal of . In this article, we obtain syzygies,
Betti numbers and Castelnuovo-Mumford regularity of for all
for certain classes of graphs .Comment: Title and other minor change
A Stochastic model for dynamics of FtsZ filaments and the formation of Z-ring
Understanding the mechanisms responsible for the formation and growth of FtsZ
polymers and their subsequent formation of the -ring is important for
gaining insight into the cell division in prokaryotic cells. In this work, we
present a minimal stochastic model that qualitatively reproduces {\it in vitro}
observations of polymerization, formation of dynamic contractile ring that is
stable for a long time and depolymerization shown by FtsZ polymer filaments. In
this stochastic model, we explore different mechanisms for ring breaking and
hydrolysis. In addition to hydrolysis, which is known to regulate the dynamics
of other tubulin polymers like microtubules, we find that the presence of the
ring allows for an additional mechanism for regulating the dynamics of FtsZ
polymers. Ring breaking dynamics in the presence of hydrolysis naturally induce
rescue and catastrophe events in this model irrespective of the mechanism of
hydrolysis.Comment: Replaced with published versio
Birefringence analysis of multilayer leaky cladding optical fibre
We analyse a multilayer leaky cladding (MLC) fibre using the finite element
method and study the effect of the MLC on the bending loss and birefringence of
two types of structures: (i) a circular core large-mode-area structure and (ii)
an elliptical-small-core structure. In a large-mode-area structure, we verify
that the multilayer leaky cladding strongly discriminates against higher order
modes to achieve single-mode operation, the fibre shows negligible
birefringence, and the bending loss of the fibre is low for bending radii
larger than 10 cm. In the elliptical-small-core structure we show that the MLC
reduces the birefringence of the fibre. This prevents the structure from
becoming birefringent in case of any departures from circular geometry. The
study should be useful in the designs of MLC fibres for various applications
including high power amplifiers, gain flattening of fibre amplifiers and
dispersion compensation.Comment: 18 page
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