A spatial scan statistic for case event data based on connected components

We propose a new spatial scan statistic based on graph theory as a method for detecting irregularly-shaped clusters of events over space. A graph-based method is proposed for identifying potential clusters in spatial point processes. It relies on linking the events closest than a given distance and thus defining a graph associated to the point process. The set of possible clusters is then restricted to windows including the connected components of the graph. The concentration in each of these possible clusters is measured through classical concentration indices based on likelihood ratio and also through a new concentration index which does not depend on any alternative hypothesis. These graph-based spatial scan tests seem to be very powerful against any arbitrarily-shaped cluster alternative, whatever the dimension of the data. These results have applications in various fields, such as the epidemiological study of rare diseases or the analysis of astrophysical data.     

Prime ideals of ore extensions

For the Ore extension R[t, S,D], where R is a prime ring, we describe prime having zero intersection with R.     

Spin echoes in the charge transport through phosphorus donors in silicon

The electrical detection of spin echoes via echo tomography is used to observe coherent processes associated with the electrical readout of the spin state of phosphorus donor electrons in silicon near a SiO2 interface. Using the Carr-Purcell pulse sequence, an echo decay with a time constant of 1.7+/-0.2 micros is observed and discussed in terms of decoherence and recombination times. Electrical spin echo tomography thus can be used to study the dynamics of the spin-dependent transport processes, e.g., in realistic spin qubit devices for quantum information processing.     

Nanomaterials for electrochemical detection of pollutants in water: A review

The survival of living beings, including humanity, depends on a continuous supply of clean water. However, due to the development of industry, agriculture, and population growth, an increasing number of wastewaters is discarded, and the negative effects of such actions are clear. The first step in solving this situation is the collection and monitoring of pollutants in water bodies to subsequently facilitate their treatment. Nonetheless, traditional sensing techniques are typically laboratory-based, leading to potential diminishment in analysis quality. In this paper, the most recent developments in micro- and nano-electrochemical devices for pollutant detection in wastewater are reviewed. The devices reviewed are based on a variety of electrodes and the sensing of three different categories of pollutants: nutrients and phenolic compounds, heavy metals, and organic matter. From these electrodes, Cu, Co, and Bi showed promise as versatile materials to detect a grand variety of contaminants. Also, the most commonly used material is glassy carbon, present in the detection of all reviewed analytes.     

Reactions with a Metalloid Tin Cluster {Sn10[Si(SiMe3)3]4}2−: Ligand Elimination versus Coordination Chemistry

Chemistry that uses metalloid tin clusters as a starting material is of fundamental interest towards understanding the reactivity of such compounds. Since we identified {Sn₁₀[Si(SiMe₃)₃]₄}^2? 7 as an ideal candidate for such reactions, we present a further step in the understanding of metalloid tin cluster chemistry. In contrast to germanium chemistry, ligand elimination seems to be a major reaction channel, which leads to the more open metalloid cluster {Sn₁₀[Si(SiMe₃)₃]₃}^? 9 , in which the Sn core is only shielded by three Si(SiMe₃)₃ ligands. Compound 9 is obtained through different routes and is crystallised together with two different countercations. Besides the structural characterisation of this novel metalloid tin cluster, the electronic structure is analysed by ¹¹⁹Sn Mössbauer spectroscopy. Additionally, possible reaction pathways are discussed. The presented first step into the chemistry of metalloid tin clusters thus indicates that, with respect to metalloid germanium clusters, more reaction channels are accessible, thereby leading to a more complex reaction system.     

Lowness of higher randomness notions

We study randomness notions given by higher recursion theory, establishing the relationships Π ₁ ¹ -randomness ? Π ₁ ¹ -Martin-Löf randomness ? Δ ₁ ¹ -randomness = Δ ₁ ¹ -Martin-Löf randomness. We characterize the set of reals that are low for Δ ₁ ¹ randomness as precisely those that are Δ ₁ ¹ -traceable. We prove that there is a perfect set of such reals.