1,907 research outputs found
Duality and canonical extensions for stably compact spaces
We construct a canonical extension for strong proximity lattices in order to
give an algebraic, point-free description of a finitary duality for stably
compact spaces. In this setting not only morphisms, but also objects may have
distinct pi- and sigma-extensions.Comment: 29 pages, 1 figur
A view of canonical extension
This is a short survey illustrating some of the essential aspects of the
theory of canonical extensions. In addition some topological results about
canonical extensions of lattices with additional operations in finitely
generated varieties are given. In particular, they are doubly algebraic
lattices and their interval topologies agree with their double Scott topologies
and make them Priestley topological algebras.Comment: 24 pages, 2 figures. Presented at the Eighth International Tbilisi
Symposium on Language, Logic and Computation Bakuriani, Georgia, September
21-25 200
Assessing the efficiency of first-principles basin-hopping sampling
We present a systematic performance analysis of first-principles
basin-hopping (BH) runs, with the target to identify all low-energy isomers of
small Si and Cu clusters described within density-functional theory. As
representative and widely employed move classes we focus on single-particle and
collective moves, in which one or all atoms in the cluster at once are
displaced in a random direction by some prescribed move distance, respectively.
The analysis provides detailed insights into the bottlenecks and governing
factors for the sampling efficiency, as well as simple rules-of-thumb for
near-optimum move settings, that are intriguingly independent of the distinctly
different chemistry of Si and Cu. At corresponding settings, the observed
performance of the BH algorithm employing two simple, general-purpose move
classes is already very good, and for the small systems studied essentially
limited by frequent revisits to a few dominant isomers.Comment: 11 pages including 8 figures; related publications can be found at
http://www.fhi-berlin.mpg.de/th/th.htm
Sheaf representations of MV-algebras and lattice-ordered abelian groups via duality
We study representations of MV-algebras -- equivalently, unital
lattice-ordered abelian groups -- through the lens of Stone-Priestley duality,
using canonical extensions as an essential tool. Specifically, the theory of
canonical extensions implies that the (Stone-Priestley) dual spaces of
MV-algebras carry the structure of topological partial commutative ordered
semigroups. We use this structure to obtain two different decompositions of
such spaces, one indexed over the prime MV-spectrum, the other over the maximal
MV-spectrum. These decompositions yield sheaf representations of MV-algebras,
using a new and purely duality-theoretic result that relates certain sheaf
representations of distributive lattices to decompositions of their dual
spaces. Importantly, the proofs of the MV-algebraic representation theorems
that we obtain in this way are distinguished from the existing work on this
topic by the following features: (1) we use only basic algebraic facts about
MV-algebras; (2) we show that the two aforementioned sheaf representations are
special cases of a common result, with potential for generalizations; and (3)
we show that these results are strongly related to the structure of the
Stone-Priestley duals of MV-algebras. In addition, using our analysis of these
decompositions, we prove that MV-algebras with isomorphic underlying lattices
have homeomorphic maximal MV-spectra. This result is an MV-algebraic
generalization of a classical theorem by Kaplansky stating that two compact
Hausdorff spaces are homeomorphic if, and only if, the lattices of continuous
[0, 1]-valued functions on the spaces are isomorphic.Comment: 36 pages, 1 tabl
Awareness Matters: Improving Healthcare Workers’ Self-Efficacy, Knowledge, Skills and Attitudes Related to Mental Illness and Suicide Prevention
Problem Description: Healthcare workers’ (HCWs) lack of knowledge impacts the care received by patients with mental illness and suicidal ideations.
Rationale: Increasing knowledge has been linked to patients seeking care and achieving optimal health outcomes.
Intervention: Participants attended training and received interactive emails over a six-week period.
Results: 73 HCWs attended training and responded to eight of the twelve emails. A paired t-test demonstrated a statistically significant change in both survey instruments when participants attended training and answered 5 or more emails (p=0.01 & p=0.02).
Conclusion: Raising awareness through training and emails impacted HCWs\u27 knowledge which led to better identification of patients in need
Hiding Private Locations by Anonymizing Data
Researchers explore ways of masking private locations in the interest of making useful data publicly available
Nature of Ar bonding to small Co_n^+ clusters and its effect on the structure determination by far-infrared absorption spectroscopy
Far-infrared vibrational spectroscopy by multiple photon dissociation has
proven to be a very useful technique for the structural fingerprinting of small
metal clusters. Contrary to previous studies on cationic V, Nb and Ta clusters,
measured vibrational spectra of small cationic cobalt clusters show a strong
dependence on the number of adsorbed Ar probe atoms, which increases with
decreasing cluster size. Focusing on the series Co_4^+ to Co_8^+ we therefore
use density-functional theory to analyze the nature of the Ar-Co_n^+ bond and
its role for the vibrational spectra. In a first step, energetically low-lying
isomer structures are identified through first-principles basin-hopping
sampling runs and their vibrational spectra computed for a varying number of
adsorbed Ar atoms. A comparison of these fingerprints with the experimental
data enables in some cases a unique assignment of the cluster structure.
Independent of the specific low-lying isomer, we obtain a pronounced increase
of the Ar binding energy for the smallest cluster sizes, which correlates
nicely with the observed increased influence of the Ar probe atoms on the IR
spectra. Further analysis of the electronic structure motivates a simple
electrostatic picture that not only explains this binding energy trend, but
also why the influence of the rare-gas atom is much stronger than in the
previously studied systems.Comment: 12 pages including 10 figures; related publications can be found at
http://www.fhi-berlin.mpg.de/th/th.htm
Application of Electron-Attachment Reactions to Enhance Selectivity of Electron-Capture Detector for Nitroaromatic Explosives
The differences in the extent of electron-attachment reactions between thermal electrons and selected classes of organic molecules with high electron affinities were investigated. the investigations showed that interactions of thermal electrons with nitroaromatic compounds lead to the formation of neutral products with very low electron affinities. by contrast, a number of other analytes with high electron affinities such as polyhalogenated organic compounds, lead to products with high electron affinities. This difference was exploited to differentiate between nitroaromatic and polychlorinated organic compounds with a tandem arrangement consisting of two electron-capture detectors connected in series with an electron-attachment reactor
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