A novel femtosecond-laser formation of CdS nanocrystallites in zirconia matrices

A novel method for direct laser writing of two-dimensional cadmium sulfide (CdS) semiconductor nanoparticle microstructures is reported. A two photon or a higher-order multiphoton absorption process, originating from femtosecond laser pulses, was used to decompose CdS precursors dispersed in a zirconia thin film previously dip-coated on a glass substrate. The kinetics of nanoparticle formation as a function of laser power were monitored in situ by photoluminescence spectroscopy. Raman spectroscopy was also performed to characterize the structural changes of the zirconia matrix under irradiation and to verify the formation of CdS nanoparticles. Results show that CdS nanoparticles were formed by two-photon absorption (TPA) with or without the help of an additional carbazole photoinitiator.     

Monotone {sigma}-Complete RC-Groups

An RC-group is a unital group G with a distinguished compressionbase with respect to which G satisfies the Rickart projectionand general comparison properties. We prove that a monotone-complete RC-group is a union of subgroups each of which isa lattice-ordered Dedekind -complete RC-group.     

ClcR-based biosensing system in the detection of cis-dihydroxylated (chloro-)biphenyls

Polychlorinated biphenyls (PCBs) are a group of organic pollutants that are persistent when released into the environment. Among the metabolites of PCBs, dihydroxylated PCBs are also considered as toxic compounds. Various studies have shown that dihydroxylated PCBs affect the reproductive, immune, nervous, and endocrine systems. Detection of these chemicals in environmental and biological samples could provide first-hand information about their levels and lead to a better understanding of their role in toxicity. To that end, we developed a sensing system for the detection of dihydroxylated PCBs based on the clc operon. The Pseudomonas putida clc operon encodes a catabolic pathway for degradation of chlorocatechols, which are major metabolites of a large number of chlorinated compounds. In P. putida, the expression of these genes is regulated by a protein encoded by the gene clcR located upstream from the clcABD genes. We demonstrate here for the first time that dihydroxy PCBs can also induce the clc operon. Our sensing system employs P. putida bacteria harboring a plasmid in which the reporter gene, lacZ, is under the control of the regulatory protein ClcR. Consequently, when exposed to dihydroxy PCBs, the bacteria express β-galactosidase in an amount related to the concentration of the corresponding dihydroxy PCB. Various dihydroxylated PCBs, differing in the number and position of chlorines and in the position of hydroxyls, were tested for their ability to induce expression of β-galactosidase. Detection limits as low as 1×10⁻⁶ mol L⁻¹ were obtained for various dihydroxylated PCBs. Electronic Supplementary Material Supplementary material is available for this article at and is accessible for authorized users.     

Type-Decomposition of an Effect Algebra

Effect algebras (EAs), play a significant role in quantum logic, are featured in the theory of partially ordered Abelian groups, and generalize orthoalgebras, MV-algebras, orthomodular posets, orthomodular lattices, modular ortholattices, and boolean algebras. We study centrally orthocomplete effect algebras (COEAs), i.e., EAs satisfying the condition that every family of elements that is dominated by an orthogonal family of central elements has a supremum. For COEAs, we introduce a general notion of decomposition into types; prove that a COEA factors uniquely as a direct sum of types I, II, and III; and obtain a generalization for COEAs of Ramsay’s fourfold decomposition of a complete orthomodular lattice.     

Finding small somatic structural variants in exome sequencing data: a machine learning approach

Genetic variation forms the basis for diversity but can as well be harmful and cause diseases, such as tumors. Structural variants (SV) are an example of complex genetic variations that comprise of many nucleotides ranging up to several megabases. Based on recent developments in sequencing technology it has become feasable to elucidate the genetic state of a person’s genes (i.e. the exome) or even the complete genome. Here, a machine learning approach is presented to find small disease-related SVs with the help of sequencing data. The method uses differences in characteristics of mapping patterns between tumor and normal samples at a genomic locus. This way, the method aims to be directly applicable for exome sequencing data to improve detection of SVs since specific SV detection methods are currently lacking. The method has been evaluated based on a simulation study as well as with exome data of patients with acute myeloid leukemia. An implementation of the algorithm is available at https://github.com/lenz99-/svmod.     

Projections in a Synaptic Algebra

A synaptic algebra is an abstract version of the partially ordered Jordan algebra of all bounded Hermitian operators on a Hilbert space. We review the basic features of a synaptic algebra and then focus on the interaction between a synaptic algebra and its orthomodular lattice of projections. Each element in a synaptic algebra determines and is determined by a one-parameter family of projections—its spectral resolution. We observe that a synaptic algebra is commutative if and only if its projection lattice is boolean, and we prove that any commutative synaptic algebra is isomorphic to a subalgebra of the Banach algebra of all continuous functions on the Stone space of its boolean algebra of projections. We study the so-called range-closed elements of a synaptic algebra, prove that (von Neumann) regular elements are range-closed, relate certain range-closed elements to modular pairs of projections, show that the projections in a synaptic algebra form an M-symmetric orthomodular lattice, and give several sufficient conditions for modularity of the projection lattice.     

Properties of Quasi-Hermitian Operators Inherited from Self-Adjoint Operators

We study a generalized effect algebra of unbounded linear operators in an infinite-dimensional complex Hilbert space. This algebra equipped with a certain kind of topology allows us to show that unbounded quasi-Hermitian operators can be expressed as a difference of two infinite sums of bounded quasi-Hermitian operators.