On the Limiting Vacillating Tableaux for Integer Sequences

A fundamental identity in the representation theory of the partition algeba is $n^k = \sum_{\lambda} f^\lambda m_k^\lambda$ for $n \geq 2k$, where $\lambda$ ranges over integer partitions of $n$, $f^\lambda$ is the number of standard Young tableaux of shape $\lambda$, and $m_k^\lambda$ is the number of vacillating tableaux of shape $\lambda$ and length $2k$. Using a combination of RSK insertion and jeu de taquin, Halverson and Lewandowski constructed a bijection $DI_n^k$ that maps each integer sequence in $[n]^k$ to a pair consisting of a standard Young tableau and a vacillating tableau. In this paper, we show that for a given integer sequence $\boldsymbol{i}$, when $n$ is sufficiently large, the vacillating tableaux determined by $DI_n^k(\boldsymbol{i})$ become stable when $n \rightarrow \infty$; the limit is called the limiting vacillating tableau for $\boldsymbol{i}$. We give a characterization of the set of limiting vacillating tableaux and presents explicit formulas that enumerate those vacillating tableaux

Electric field and tip geometry effects on dielectrophoretic growth of carbon nanotube nanofibrils on scanning probes

Single-wall carbon nanotube (SWNT) nanofibrils were assembled onto a variety of conductive scanning probes including atomic force microscope (AFM) tips and scanning tunnelling microscope (STM) needles using positive dielectrophoresis (DEP). The magnitude of the applied electric field was varied in the range of 1-20 V to investigate its effect on the dimensions of the assembled SWNT nanofibrils. Both length and diameter grew asymptotically as voltage increased from 5 to 18 V. Below 4 V, stable attachment of SWNT nanofibrils could not be achieved due to the relatively weak DEP force versus Brownian motion. At voltages of 20 V and higher, low quality nanofibrils resulted from incorporating large amounts of impurities. For intermediate voltages, optimal nanofibrils were achieved, though pivotal to this assembly is the wetting behaviour upon tip immersion in the SWNT suspension drop. This process was monitored in situ to correlate wetting angle and probe geometry (cone angles and tip height), revealing that probes with narrow cone angles and long shanks are optimal. It is proposed that this results from less wetting of the probe apex, and therefore reduces capillary forces and especially force transients during the nanofibril drawing process. Relatively rigid probes (force constant >= 2 N/m) exhibited no perceivable cantilever bending upon wetting and de-wetting, resulting in the most stable process control

Asteroid taxonomic signatures from photometric phase curves

We explore the correlation between an asteroid's taxonomy and photometric phase curve using the H, G12 photometric phase function, with the shape of the phase function described by the single parameter G12. We explore the usability of G12 in taxonomic classification for individual objects, asteroid families, and dynamical groups. We conclude that the mean values of G12 for the considered taxonomic complexes are statistically different, and also discuss the overall shape of the G12 distribution for each taxonomic complex. Based on the values of G12 for about half a million asteroids, we compute the probabilities of C, S, and X complex membership for each asteroid. For an individual asteroid, these probabilities are rather evenly distributed over all of the complexes, thus preventing meaningful classification. We then present and discuss the G12 distributions for asteroid families, and predict the taxonomic complex preponderance for asteroid families given the distribution of G12 in each family. For certain asteroid families, the probabilistic prediction of taxonomic complex preponderance can clearly be made. The Nysa-Polana family shows two distinct regions in the proper element space with different G12 values dominating in each region. We conclude that the G12-based probabilistic distribution of taxonomic complexes through the main belt agrees with the general view of C complex asteroid proportion increasing towards the outer belt. We conclude that the G12 photometric parameter cannot be used in determining taxonomic complex for individual asteroids, but it can be utilized in the statistical treatment of asteroid families and different regions of the main asteroid belt.Comment: submitted to Icaru

Cardiac involvement in hereditary myopathy with early respiratory failure: A cohort study.

OBJECTIVE: To assess whether hereditary myopathy with early respiratory failure (HMERF) due to the c.951434T>C; (p.Cys31712Arg) TTN missense mutation also includes a cardiac phenotype. METHOD: Clinical cohort study of our HMERF cohort using ECG, 2D echocardiogram, and cross-sectional cardiac imaging with MRI or CT. RESULTS: We studied 22 participants with the c.951434T>C; (p.Cys31712Arg) TTN missense mutation. Three were deceased. Cardiac conduction abnormalities were identified in 7/22 (32%): sustained atrioventricular tachycardia (n = 2), atrial fibrillation (n = 2), nonsustained atrial tachycardia (n = 1), premature supraventricular complexes (n = 1), and unexplained sinus bradycardia (n = 1). In addition, 4/22 (18%) had imaging evidence of otherwise unexplained cardiomyopathy. These findings are supported by histopathologic correlation suggestive of myocardial cytoskeletal remodeling. CONCLUSIONS: Coexisting cardiac and skeletal muscle involvement is not uncommon in patients with HMERF arising due to the c.951434T>C; (p.Cys31712Arg) TTN mutation. All patients with pathogenic or putative pathogenic TTN mutations should be offered periodic cardiac surveillance.Wellcome Trust (101876/Z/13/Z, 096919Z/11/Z), Medical Research Council (UK) (G0601943), Medical Research Council Mitochondrial Biology Unit (MC_UP_1501/2).This is the final version of the article. It first appeared from Wolters Kluwer via http://dx.doi.org/10.1212/WNL.000000000000306

VCU Stress Relief: Programs and Tools to Ease Student Stress

Examine how VCU can support students who are having trouble, especially in the freshman year, due to economic challenges their families are facing (parent\u27s loss of jobs, parent\u27s loss of home, students tuition debt, etc). Explore ways to address these issues in the classroom or in individual or group settings

Should I and Can I?: a mixed methods study of clinician beliefs and attitudes in the management of lifestyle risk factors in primary health care

BackgroundPrimary health care (PHC) clinicians have an important role to play in addressing lifestyle risk factors for chronic diseases. However they intervene only rarely, despite the opportunities that arise within their routine clinical practice. Beliefs and attitudes have been shown to be associated with risk factor management practices, but little is known about this for PHC clinicians working outside general practice. The aim of this study was to explore the beliefs and attitudes of PHC clinicians about incorporating lifestyle risk factor management into their routine care and to examine whether these varied according to their self reported level of risk factor management.MethodsA cross sectional survey was undertaken with PHC clinicians (n = 59) in three community health teams. Clinicians\u27 beliefs and attitudes were also explored through qualitative interviews with a purposeful sample of 22 clinicians from the teams. Mixed methods analysis was used to compare beliefs and attitudes for those with high and low levels of self reported risk factor management.ResultsRole congruence, perceived client acceptability, beliefs about capabilities, perceived effectiveness and clinicians\u27 own lifestyle were key themes related to risk factor management practices. Those reporting high levels of risk factor screening and intervention had different beliefs and attitudes to those PHC clinicians who reported lower levels.ConclusionPHC clinicians\u27 level of involvement in risk factor management reflects their beliefs and attitudes about it. This provides insights into ways of intervening to improve the integration of behavioural risk factor management into routine practice

Predictive response-relevant clustering of expression data provides insights into disease processes

This article describes and illustrates a novel method of microarray data analysis that couples model-based clustering and binary classification to form clusters of ;response-relevant' genes; that is, genes that are informative when discriminating between the different values of the response. Predictions are subsequently made using an appropriate statistical summary of each gene cluster, which we call the ;meta-covariate' representation of the cluster, in a probit regression model. We first illustrate this method by analysing a leukaemia expression dataset, before focusing closely on the meta-covariate analysis of a renal gene expression dataset in a rat model of salt-sensitive hypertension. We explore the biological insights provided by our analysis of these data. In particular, we identify a highly influential cluster of 13 genes-including three transcription factors (Arntl, Bhlhe41 and Npas2)-that is implicated as being protective against hypertension in response to increased dietary sodium. Functional and canonical pathway analysis of this cluster using Ingenuity Pathway Analysis implicated transcriptional activation and circadian rhythm signalling, respectively. Although we illustrate our method using only expression data, the method is applicable to any high-dimensional datasets

Helping students see eye to eye: Diversifying teaching of sensation and perception in higher education

There is current interest in diversifying teaching curricula across many disciplines in university teaching. Sensation and perception is often considered difficult to diversify. Current challenges include diversity of the topics and teaching tools/materials, and the diversity that characterizes both the student and the teacher populations. We start by describing the diversity present in student and teacher groups, with a UK focus, and discuss how inclusive and diverse teaching materials can impact participation and engagement of broad student groups. We next consider how teaching content can be broadened by teaching on topics that consider differences between participant groups with different characteristics (including gender, ethnicity, disability and culture). Finally, we suggest resources that can be used to diversify sensation and perception teaching. We include example topics where diversity features in perception research, aimed at engaging teachers and students in the process of diversifying the teaching of sensation and perception

N-body models of globular clusters: metallicity, half-light radii and mass-to-light ratios

Size differences of approx. 20% between red (metal-rich) and blue (metal-poor) sub-populations of globular clusters have been observed, generating an ongoing debate as to weather these originate from projection effects or the difference in metallicity. We present direct N-body simulations of metal-rich and metal-poor stellar populations evolved to study the effects of metallicity on cluster evolution. The models start with N = 100000 stars and include primordial binaries. We also take metallicity dependent stellar evolution and an external tidal field into account. We find no significant difference for the half-mass radii of those models, indicating that the clusters are structurally similar. However, utilizing observational tools to fit half-light (or effective) radii confirms that metallicity effects related to stellar evolution combined with dynamical effects such as mass segregation produce an apparent size difference of 17% on average. The metallicity effect on the overall cluster luminosity also leads to higher mass-to-light ratios for metal-rich clusters.Comment: 14 pages, 10 figures, accepted for publication in MNRA