103 research outputs found
On the complexity of strongly connected components in directed hypergraphs
We study the complexity of some algorithmic problems on directed hypergraphs
and their strongly connected components (SCCs). The main contribution is an
almost linear time algorithm computing the terminal strongly connected
components (i.e. SCCs which do not reach any components but themselves).
"Almost linear" here means that the complexity of the algorithm is linear in
the size of the hypergraph up to a factor alpha(n), where alpha is the inverse
of Ackermann function, and n is the number of vertices. Our motivation to study
this problem arises from a recent application of directed hypergraphs to
computational tropical geometry.
We also discuss the problem of computing all SCCs. We establish a superlinear
lower bound on the size of the transitive reduction of the reachability
relation in directed hypergraphs, showing that it is combinatorially more
complex than in directed graphs. Besides, we prove a linear time reduction from
the well-studied problem of finding all minimal sets among a given family to
the problem of computing the SCCs. Only subquadratic time algorithms are known
for the former problem. These results strongly suggest that the problem of
computing the SCCs is harder in directed hypergraphs than in directed graphs.Comment: v1: 32 pages, 7 figures; v2: revised version, 34 pages, 7 figure
An adaptive inelastic magnetic mirror for Bose-Einstein condensates
We report the reflection and focussing of a Bose-Einstein condensate by a new
pulsed magnetic mirror. The mirror is adaptive, inelastic, and of extremely
high optical quality. The deviations from specularity are less than 0.5 mrad
rms, making this the best atomic mirror demonstrated to date. We have also used
the mirror to realize the analog of a beam-expander, producing an ultra-cold
collimated fountain of matter wavesComment: 4 pages, 4 figure
Inflation and the Scale Dependent Spectral Index: Prospects and Strategies
We consider the running of the spectral index as a probe of both inflation
itself, and of the overall evolution of the very early universe. Surveying a
collection of simple single field inflationary models, we confirm that the
magnitude of the running is relatively consistent, unlike the tensor amplitude,
which varies by orders of magnitude. Given this target, we confirm that the
running is potentially detectable by future large scale structure or 21 cm
observations, but that only the most futuristic measurements can distinguish
between these models on the basis of their running. For any specified
inflationary scenario, the combination of the running index and unknown
post-inflationary expansion history induces a theoretical uncertainty in the
predicted value of the spectral index. This effect can easily dominate the
statistical uncertainty with which Planck and its successors are expected to
measure the spectral index. More positively, upcoming cosmological experiments
thus provide an intriguing probe of physics between TeV and GUT scales by
constraining the reheating history associated with any specified inflationary
model, opening a window into the "primordial dark age" that follows the end of
inflation.Comment: 32 pages. v2 and v3 Minor reference updates /clarification
Search For Trapped Antihydrogen
We present the results of an experiment to search for trapped antihydrogen
atoms with the ALPHA antihydrogen trap at the CERN Antiproton Decelerator.
Sensitive diagnostics of the temperatures, sizes, and densities of the trapped
antiproton and positron plasmas have been developed, which in turn permitted
development of techniques to precisely and reproducibly control the initial
experimental parameters. The use of a position-sensitive annihilation vertex
detector, together with the capability of controllably quenching the
superconducting magnetic minimum trap, enabled us to carry out a
high-sensitivity and low-background search for trapped synthesised antihydrogen
atoms. We aim to identify the annihilations of antihydrogen atoms held for at
least 130 ms in the trap before being released over ~30 ms. After a three-week
experimental run in 2009 involving mixing of 10^7 antiprotons with 1.3 10^9
positrons to produce 6 10^5 antihydrogen atoms, we have identified six
antiproton annihilation events that are consistent with the release of trapped
antihydrogen. The cosmic ray background, estimated to contribute 0.14 counts,
is incompatible with this observation at a significance of 5.6 sigma. Extensive
simulations predict that an alternative source of annihilations, the escape of
mirror-trapped antiprotons, is highly unlikely, though this possibility has not
yet been ruled out experimentally.Comment: 12 pages, 7 figure
Phenazine cations as anticancer theranostics
The biological properties of two water-soluble organic cations based on polypyridyl structures commonly used as ligands for photoactive transition metal complexes designed to interact with biomolecules are investigated. A cytotoxicity screen employing a small panel of cell lines reveals that both cations show cytotoxicity toward cancer cells but show reduced cytotoxicity to noncancerous HEK293 cells with the more extended system being notably more active. Although it is not a singlet oxygen sensitizer, the more active cation also displayed enhanced potency on irradiation with visible light, making it active at nanomolar concentrations. Using the intrinsic luminescence of the cations, their cellular uptake was investigated in more detail, revealing that the active compound is more readily internalized than its less lipophilic analogue. Colocalization studies with established cell probes reveal that the active cation predominantly localizes within lysosomes and that irradiation leads to the disruption of mitochondrial structure and function. Stimulated emission depletion (STED) nanoscopy and transmission electron microscopy (TEM) imaging reveal that treatment results in distinct lysosomal swelling and extensive cellular vacuolization. Further imaging-based studies confirm that treatment with the active cation induces lysosomal membrane permeabilization, which triggers lysosome-dependent cell-death due to both necrosis and caspase-dependent apoptosis. A preliminary toxicity screen in the Galleria melonella animal model was carried out on both cations and revealed no detectable toxicity up to concentrations of 80 mg/kg. Taken together, these studies indicate that this class of synthetically easy-to-access photoactive compounds offers potential as novel therapeutic leads
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