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

Ueber Farbe Und Durchsichtigkeit Des Ostseewassers: Mit Einer Allgemeinen Theorie Des Zusammenhanges Zwischen Farbe Und Duhchsichtigkeit in Naturlichen Gewassern

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