On maximal green sequences for type $$\mathbb {}$$ quivers

Given a framed quiver, i.e., one with a frozen vertex associated with each mutable vertex, there is a concept of green mutation, as introduced by Keller. Maximal sequences of such mutations, known as maximal green sequences, are important in representation theory and physics as they have numerous applications, including the computations of spectrums of BPS states, Donaldson–Thomas invariants, tilting of hearts in derived categories, and quantum dilogarithm identities. In this paper, we study such sequences and construct a maximal green sequence for every quiver mutation equivalent to an orientation of a type \(\mathbb {A}\) Dynkin diagram.     

Synthesis of cytotoxic cyanobactin,Wewakazole B

We report herein the synthesis of cytotoxic cyanobactin, Wewakazole B through an efficient solution-phase approach. The key steps of the synthesis are the macrocyclic lactamization of linear dodecapeptide and construction of two hexapeptides with three different substituted oxazole rings.     

Expedient Lewis acid catalyzed synthesis of a 3-substituted 5-arylidene-1-methyl-2-thiohydantoin Library

An efficient and rapid solution phase combinatorial synthesis of a 3-substituted 5-arylidene-1-methyl-2-thiohydantoin library was developed. The salient feature for this library production procedure is the addition of the Lewis acid catalyst, indium(III) trifluoromethanesulfonate, which serves to facilitate the direct condensation of aldehydes with 3-substituted 1-methyl-2-thiohydantoins. Use of this Lewis acid catalyst has resulted in faster reaction times, higher conversions and better purity profiles for these condensation reactions as compared to traditional uncatalyzed reactions. The resulting 315 member library of 3-substituted 5-arylidene-1-methyl-2-thiohydantoin is described.     

Dynamic pH barrage junction focusing of amino acids,peptides, and digested monoclonal antibodies in capillary electrophoresis–mass spectrometry

Dynamic pH barrage junction focusing in CE enables effective signal enhancement, quantitative capture efficiencies, and straightforward optimization. The method is a technical variant of dynamic pH junction focusing. CE separation with dynamic pH barrage junction focusing is compatible with both optical and mass spectrometric detection. We developed a CE–MS/MS method using hydrophilic polyethyleneimine-coated capillaries and validated it for the qualitative analysis of amino acids, peptides, and tryptic peptides of digested monoclonal antibodies. The S/N of extracted ion electropherograms of zwitterionic analytes were enhanced by approximately two orders of magnitude with a tradeoff of a shortened separation window. Online focusing improved the MS signal intensity of a diluted antibody digest, enabling more precursor ions to be analyzed with subsequent tandem mass spectrometric identification. It also broadened the concentration range of protein digest samples for which adequate sequence coverage data can be obtained. With only 0.9 ng of digested infliximab sample loaded into the capillary, 76% and 100% sequence coverage was realized for antibody heavy and light chains, respectively, after online focusing. Full coverage was achieved with 9 ng of injected digest.     

Maternal meddling in neonatal sharks: implications for interpreting stable isotopes in young animals

Stable isotopes of neonatal vertebrates reflect those of their mother's diet and foraging location. Evaluating feeding strategies and habitat use of neonates is consequently complicated by the maternal isotopic signal and its subsequent elimination with growth. Thus, methods that measure the loss of the maternal signal, i.e. when the isotopic signal of a neonate reflects its own diet, are needed. Values of δ¹³C and δ¹⁵N were measured in liver and muscle tissues of <1 year old bull (Carcharhinus leucas) and Atlantic sharpnose (Rhizoprionodon terraenovae) sharks and related to age using, total length, date sampled and umbilical scar stage (USS). We observed a decline in δ¹³C and δ¹⁵N values with age that was different among species, similar among isotopes, and greater in liver than in muscle; highlighting that retention of the maternal signal is dependent on species‐specific life history and tissue characteristics. USS was most effective for assessing the loss of the maternal isotopic signal in the faster growing Atlantic sharpnose shark, but was less effective for the slower growing bull shark. Total length and date sampled were overall less effective and may be more informative for slower growing species when coupled with USS, as variable size at birth and misclassification of animals >1 year old, which remain in nursery habitats, increase the variability of the isotopic values. Consideration of the maternal signal and measuring its loss are thus necessary when analyzing the stable isotopes of young animals, as there is potential to misinterpret feeding strategies, over‐estimate trophic position and incorrectly assign carbon source. Copyright © 2011 John Wiley & Sons, Ltd.     

Welding of gold nanoparticles on graphitic templates for chemical sensing

Controlled self-assembly of zero-dimensional gold nanoparticles and construction of complex gold nanostructures from these building blocks could significantly extend their applications in many fields. Carbon nanotubes are one of the most promising inorganic templates for this strategy because of their unique physical, chemical, and mechanical properties, which translate into numerous potential applications. Here we report the bottom-up synthesis of gold nanowires in aqueous solution through self-assembly of gold nanoparticles on single-walled carbon nanotubes followed by thermal-heating-induced nanowelding. We investigate the mechanism of this process by exploring different graphitic templates. The experimental work is assisted by computational studies that provide additional insight into the self-assembly and nanowelding mechanism. We also demonstrate the chemical sensitivity of the nanomaterial to parts-per-billion concentrations of hydrogen sulfide with potential applications in industrial safety and personal healthcare.     

Palladium-catalyzed direct arylation of imidazolone N-oxides with aryl bromides and its application in the synthesis of GSK2137305

The palladium-catalyzed direct arylation of imidazolone N-oxides with aryl bromides to afford the corresponding 4-aryl imidazolone N-oxides is described. This method has been successfully used for the synthesis of GSK2137305.     

Hazard function estimation with cause-of-death data missing at random

Hazard function estimation is an important part of survival analysis. Interest often centers on estimating the hazard function associated with a particular cause of death. We propose three nonparametric kernel estimators for the hazard function, all of which are appropriate when death times are subject to random censorship and censoring indicators can be missing at random. Specifically, we present a regression surrogate estimator, an imputation estimator, and an inverse probability weighted estimator. All three estimators are uniformly strongly consistent and asymptotically normal. We derive asymptotic representations of the mean squared error and the mean integrated squared error for these estimators and we discuss a data-driven bandwidth selection method. A simulation study, conducted to assess finite sample behavior, demonstrates that the proposed hazard estimators perform relatively well. We illustrate our methods with an analysis of some vascular disease data.     

The critical groups of a family of graphs and elliptic curves over finite fields

Let q be a power of a prime, and E be an elliptic curve defined over  . Such curves have a classical group structure, and one can form an infinite tower of groups by considering E over field extensions for all k≥1. The critical group of a graph may be defined as the cokernel of L(G), the Laplacian matrix of G. In this paper, we compare elliptic curve groups with the critical groups of a certain family of graphs. This collection of critical groups also decomposes into towers of subgroups, and we highlight additional comparisons by using the Frobenius map of E over  . This work was partially supported by the NSF, grant DMS-0500557 during the author’s graduate school at the University of California, San Diego, and partially supported by an NSF Postdoctoral Fellowship.     

The relationship between magnetic and electrophysiological responses to complex tactile stimuli

Background  

Magnetoencephalography (MEG) has become an increasingly popular technique for non-invasively characterizing neuromagnetic field changes in the brain at a high temporal resolution. To examine the reliability of the MEG signal, we compared magnetic and electrophysiological responses to complex natural stimuli from the same animals. We examined changes in neuromagnetic fields, local field potentials (LFP) and multi-unit activity (MUA) in macaque monkey primary somatosensory cortex that were induced by varying the rate of mechanical stimulation. Stimuli were applied to the fingertips with three inter-stimulus intervals (ISIs): 0.33s, 1s and 2s.