226 research outputs found
Converting between quadrilateral and standard solution sets in normal surface theory
The enumeration of normal surfaces is a crucial but very slow operation in
algorithmic 3-manifold topology. At the heart of this operation is a polytope
vertex enumeration in a high-dimensional space (standard coordinates).
Tollefson's Q-theory speeds up this operation by using a much smaller space
(quadrilateral coordinates), at the cost of a reduced solution set that might
not always be sufficient for our needs. In this paper we present algorithms for
converting between solution sets in quadrilateral and standard coordinates. As
a consequence we obtain a new algorithm for enumerating all standard vertex
normal surfaces, yielding both the speed of quadrilateral coordinates and the
wider applicability of standard coordinates. Experimentation with the software
package Regina shows this new algorithm to be extremely fast in practice,
improving speed for large cases by factors from thousands up to millions.Comment: 55 pages, 10 figures; v2: minor fixes only, plus a reformat for the
journal styl
Linear -positive sets and their polar subspaces
In this paper, we define a Banach SNL space to be a Banach space with a
certain kind of linear map from it into its dual, and we develop the theory of
linear -positive subsets of Banach SNL spaces with Banach SNL dual spaces.
We use this theory to give simplified proofs of some recent results of
Bauschke, Borwein, Wang and Yao, and also of the classical Brezis-Browder
theorem.Comment: 11 pages. Notational changes since version
Necessary and sufficient condition on global optimality without convexity and second order differentiability
The main goal of this paper is to give a necessary and sufficient condition
of global optimality for unconstrained optimization problems, when the objective
function is not necessarily convex. We use GĂąteaux differentiability of the objective
function and its bidual (the latter is known from convex analysis)
Quantum Sign Permutation Polytopes
Convex polytopes are convex hulls of point sets in the -dimensional space
\E^n that generalize 2-dimensional convex polygons and 3-dimensional convex
polyhedra. We concentrate on the class of -dimensional polytopes in \E^n
called sign permutation polytopes. We characterize sign permutation polytopes
before relating their construction to constructions over the space of quantum
density matrices. Finally, we consider the problem of state identification and
show how sign permutation polytopes may be useful in addressing issues of
robustness
An additive subfamily of enlargements of a maximally monotone operator
We introduce a subfamily of additive enlargements of a maximally monotone
operator. Our definition is inspired by the early work of Simon Fitzpatrick.
These enlargements constitute a subfamily of the family of enlargements
introduced by Svaiter. When the operator under consideration is the
subdifferential of a convex lower semicontinuous proper function, we prove that
some members of the subfamily are smaller than the classical
-subdifferential enlargement widely used in convex analysis. We also
recover the epsilon-subdifferential within the subfamily. Since they are all
additive, the enlargements in our subfamily can be seen as structurally closer
to the -subdifferential enlargement
Excited States of Proton-bound DNA/RNA Base Homo-dimers: Pyrimidines
We are presenting the electronic photo fragment spectra of the protonated
pyrimidine DNA bases homo-dimers. Only the thymine dimer exhibits a well
structured vibrational progression, while protonated monomer shows broad
vibrational bands. This shows that proton bonding can block some non radiative
processes present in the monomer.Comment: We acknowledge the use of the computing facility cluster GMPCS of the
LUMAT federation (FR LUMAT 2764
Action spectroscopy of the isolated red Kaede fluorescent protein chromophore
Incorporation of fluorescent proteins into biochemical systems has revolutionized the field of bioimaging. In a bottom-up approach, understanding the photophysics of fluorescent proteins requires detailed investigations of the light-absorbing chromophore, which can be achieved by studying the chromophore in isolation. This paper reports a photodissociation action spectroscopy study on the deprotonated anion of the red Kaede fluorescent protein chromophore, demonstrating that at least three isomersâassigned to deprotomersâare generated in the gas phase. Deprotomer-selected action spectra are recorded over the S1 â S0 band using an instrument with differential mobility spectrometry coupled with photodissociation spectroscopy. The spectrum for the principal phenoxide deprotomer spans the 480â660 nm range with a maximum response at â610 nm. The imidazolate deprotomer has a blue-shifted action spectrum with a maximum response at â545 nm. The action spectra are consistent with excited state coupled-cluster calculations of excitation wavelengths for the deprotomers. A third gas-phase species with a distinct action spectrum is tentatively assigned to an imidazole tautomer of the principal phenoxide deprotomer. This study highlights the need for isomer-selective methods when studying the photophysics of biochromophores possessing several deprotonation sites
The regeneration capacity of the flatworm Macrostomum lignanoâon repeated regeneration, rejuvenation, and the minimal size needed for regeneration
The lionâs share of studies on regeneration in Plathelminthes (flatworms) has been so far carried out on a derived taxon of rhabditophorans, the freshwater planarians (Tricladida), and has shown this groupâs outstanding regeneration capabilities in detail. Sharing a likely totipotent stem cell system, many other flatworm taxa are capable of regeneration as well. In this paper, we present the regeneration capacity of Macrostomum lignano, a representative of the Macrostomorpha, the basal-most taxon of rhabditophoran flatworms and one of the most basal extant bilaterian protostomes. Amputated or incised transversally, obliquely, and longitudinally at various cutting levels, M. lignano is able to regenerate the anterior-most body part (the rostrum) and any part posterior of the pharynx, but cannot regenerate a head. Repeated regeneration was observed for 29 successive amputations over a period of almost 12Â months. Besides adults, also first-day hatchlings and older juveniles were shown to regenerate after transversal cutting. The minimum number of cells required for regeneration in adults (with a total of 25,000 cells) is 4,000, including 160 neoblasts. In hatchlings only 1,500 cells, including 50 neoblasts, are needed for regeneration. The life span of untreated M. lignano was determined to be about 10Â months
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