The odd primary order of the commutator on low rank Lie groups

Let $G$ be a simply-connected, compact, simple Lie group of low rank relative to a fixed prime $p$. After localization at $p$, there is a space $A$ which "generates" $G$ in a certain sense. Assuming $G$ satisfies a homotopy nilpotency condition relative to $p$, we show that the Samelson product $\langle Id_G, Id_G\rangle$ of the identity of $G$ equals the order of the Samelson product $\langle\imath,\imath\rangle$ of the inclusion $\imath:A\to G$. Applying this result, we calculate the orders of $\langle Id_G,Id_G\rangle$ for all $p$-regular Lie groups and give bounds on the orders of $\langle Id_G,Id_G\rangle$ for certain quasi-$p$-regular Lie groups.Comment: 18 pages; Accepted by Topology and its Application

The acquisition of Cantonese classifiers by preschool children in Hong Kong

The Cantonese language has a complex classifier system and young learners need to pay attention to both the semantics and syntax of classifiers. This study investigated the repertoire of classifiers produced by 492 Cantonese-speaking preschoolers in three age groups (3 ;0, 4 ;0 and 5 ;0). Spontaneous utterances produced in 30-mmute toy-play contexts were collected and transcribed. Analyses identified a productive repertoire of 73 classifiers in the utterances, which could be appropriately classified into the typology proposed in the present study. An age-related increase in the number of classifier types per child as well as the repertoire size of each group was found. g03 (CL) was widely used as the general classifier by the young children. It was also discovered that the three-year-olds were already showing signs of grasping the basic syntax of classifiers. Cognitive, linguistic and contextual influences presumed to shape the evidence are discussed. © 2007 Cambridge University Press.published_or_final_versio

Asking for action or information? Crosslinguistic comparison of interrogative functions in early child Cantonese and Mandarin

Request for information (RfI) is believed to be the universally dominant function of young children’s questioning, whereas request for action (RfA) has been reported to be the leading interrogative form used in early child Cantonese. The possibility of crosslinguistic variability prompts further research and comparison with additional languages. This study compares the interrogatives elicited from two early Chinese language corpora: Early Childhood Cantonese Corpus (ECCC) and Early Childhood Mandarin (ECMC). Altogether, 1214 and 942 question types were elicited from ECCC and ECMC, respectively. Analyses indicated that: (1) all the interrogative functions identified in an earlier study of Cantonese were also observed in the early Mandarin interrrogatives; and (2) both RfA (49.9%) and RfI (45.5%) were the most frequently observed functions of early child Chinese interrogatives. This crosslinguistic evidence suggests that follow-up studies are needed to further explore the possible influences of language, culture and communication tasks on children’s uses of interrogative forms.postprin

Lupus nephritis in Chinese children--a territory-wide cohort study in Hong Kong

We report a multicenter study of Chinese children in Hong Kong with systemic lupus erythematosus (SLE) nephritis. Children were included if: they fulfilled the ACR criteria, had significant proteinuria or casturia, were Chinese and younger than 19 years and had been diagnosed with SLE between January 1990 and December 2003. Investigators in each center retrieved data on clinical features, biopsy reports, treatment and outcome of these patients. There were 128 patients (eight boys, 120 girls; mean age: 11.9+/-2.8 years). About 50% presented with multisystem illness and 40% with nephritic/nephrotic symptoms. Negative anti-dsDNA antibodies were found in 6% of the patients. Renal biopsy revealed WHO Class II, III, IV and V nephritis in 13 (10%), 22 (17%), 69 (54%) and 13 (10%) patients, respectively. The clinical severity of the nephritis did not accurately predict renal biopsy findings. The follow-up period ranged from 1 to 16.5 years (mean+/-SD: 5.76+/-3.61 years). During the study five patients died (two from lupus flare, one from cardiomyopathy, two from infections). Four patients had endstage renal failure (ESRF) (one died during a lupus flare). All deaths and end-stage renal failure occurred in the Class IV nephritis group. Chronic organ damage was infrequent in the survivors. The actuarial patient survival rates at 5, 10 and 15 years of age were 95.3, 91.8, and 91.8%, respectively. For Class IV nephritis patients, the survival rates without ESRF at 5, 10, and 15 years were 91.5, 82.3 and 76%, respectively. The survival and chronic morbidity rates of the Chinese SLE children in the present study are comparable to those of other published studies.postprin

AI is a viable alternative to high throughput screening: a 318-target study

: High throughput screening (HTS) is routinely used to identify bioactive small molecules. This requires physical compounds, which limits coverage of accessible chemical space. Computational approaches combined with vast on-demand chemical libraries can access far greater chemical space, provided that the predictive accuracy is sufficient to identify useful molecules. Through the largest and most diverse virtual HTS campaign reported to date, comprising 318 individual projects, we demonstrate that our AtomNet® convolutional neural network successfully finds novel hits across every major therapeutic area and protein class. We address historical limitations of computational screening by demonstrating success for target proteins without known binders, high-quality X-ray crystal structures, or manual cherry-picking of compounds. We show that the molecules selected by the AtomNet® model are novel drug-like scaffolds rather than minor modifications to known bioactive compounds. Our empirical results suggest that computational methods can substantially replace HTS as the first step of small-molecule drug discovery

Robust estimation of bacterial cell count from optical density

Optical density (OD) is widely used to estimate the density of cells in liquid culture, but cannot be compared between instruments without a standardized calibration protocol and is challenging to relate to actual cell count. We address this with an interlaboratory study comparing three simple, low-cost, and highly accessible OD calibration protocols across 244 laboratories, applied to eight strains of constitutive GFP-expressing E. coli. Based on our results, we recommend calibrating OD to estimated cell count using serial dilution of silica microspheres, which produces highly precise calibration (95.5% of residuals <1.2-fold), is easily assessed for quality control, also assesses instrument effective linear range, and can be combined with fluorescence calibration to obtain units of Molecules of Equivalent Fluorescein (MEFL) per cell, allowing direct comparison and data fusion with flow cytometry measurements: in our study, fluorescence per cell measurements showed only a 1.07-fold mean difference between plate reader and flow cytometry data

Guidelines for the use and interpretation of assays for monitoring autophagy (4th edition)1.

In 2008, we published the first set of guidelines for standardizing research in autophagy. Since then, this topic has received increasing attention, and many scientists have entered the field. Our knowledge base and relevant new technologies have also been expanding. Thus, it is important to formulate on a regular basis updated guidelines for monitoring autophagy in different organisms. Despite numerous reviews, there continues to be confusion regarding acceptable methods to evaluate autophagy, especially in multicellular eukaryotes. Here, we present a set of guidelines for investigators to select and interpret methods to examine autophagy and related processes, and for reviewers to provide realistic and reasonable critiques of reports that are focused on these processes. These guidelines are not meant to be a dogmatic set of rules, because the appropriateness of any assay largely depends on the question being asked and the system being used. Moreover, no individual assay is perfect for every situation, calling for the use of multiple techniques to properly monitor autophagy in each experimental setting. Finally, several core components of the autophagy machinery have been implicated in distinct autophagic processes (canonical and noncanonical autophagy), implying that genetic approaches to block autophagy should rely on targeting two or more autophagy-related genes that ideally participate in distinct steps of the pathway. Along similar lines, because multiple proteins involved in autophagy also regulate other cellular pathways including apoptosis, not all of them can be used as a specific marker for bona fide autophagic responses. Here, we critically discuss current methods of assessing autophagy and the information they can, or cannot, provide. Our ultimate goal is to encourage intellectual and technical innovation in the field

Homotopy types of SU(n)-gauge groups over non-spin 4-manifolds

Let M be an orientable, simply-connected, closed, non-spin 4-manifold and let Gk(M) be the gauge group of the principal G-bundle over M with second Chern class k∈Z. It is known that the homotopy type of Gk(M) is determined by the homotopy type of Gk(CP2). In this paper we investigate properties of Gk(CP2) when G=SU(n) that partly classify the homotopy types of the gauge groups

Homotopy theory of gauge groups over 4-manifolds

Given a principal G-bundle P over a space X, the gauge group G(P) of P is the topological group of G-equivariant automorphisms of P which fix X. The study of gauge groups has a deep connection to topics in algebraic geometry and the topology of 4-manifolds. Topologists have been studying the topology of gauge groups of principal G-bundles over 4-manifolds for a long time. In this thesis, we investigate the homotopy types of gauge groups when X is an orientable, connected, closed 4-manifold. In particular, we study the homotopy types of gauge groups when X is a non-simply-connected 4-manifold or a simply-connected non-spin 4-manifold. Furthermore, we calculate the orders of the Samelson products on low rank Lie groups, which help determine the classification of gauge groups over S4.<br/

The suspension of a 4-manifold and its applications

Let M be a smooth, orientable, closed, connected 4-manifold and suppose that H_1(M;Z) is finitely generated and has no 2-torsion. We give a homotopy decomposition of the suspension of M in terms of spheres, Moore spaces and the suspension of the complex projective plane. This is used to calculate any reduced generalized cohomology theory of M as a group and to determine the homotopy types of certain current groups and gauge groups