Analogs of Schur functions for rank two Weyl groups obtained from grid-like posets

In prior work, the authors, along with M. McClard, R. A. Proctor, and N. J. Wildberger, studied certain distributive lattice models for the "Weyl bialternants" (aka "Weyl characters") associated with the rank two root systems/Weyl groups. These distributive lattices were uniformly described as lattices of order ideals taken from certain grid-like posets, although the arguments connecting the lattices to Weyl bialternants were case-by-case depending on the type of the rank two root system. Using this connection with Weyl bialternants, these lattices were shown to be rank symmetric and rank unimodal, and their rank generating functions were shown to have beautiful quotient-of-products expressions. Here, these results are re-derived from scratch using completely uniform and elementary combinatorial reasoning in conjunction with some new combinatorial methodology developed elsewhere by the second listed author.Comment: 15 page

Estimating malaria transmission from humans to mosquitoes in a noisy landscape.

A basic quantitative understanding of malaria transmission requires measuring the probability a mosquito becomes infected after feeding on a human. Parasite prevalence in mosquitoes is highly age-dependent, and the unknown age-structure of fluctuating mosquito populations impedes estimation. Here, we simulate mosquito infection dynamics, where mosquito recruitment is modelled seasonally with fractional Brownian noise, and we develop methods for estimating mosquito infection rates. We find that noise introduces bias, but the magnitude of the bias depends on the 'colour' of the noise. Some of these problems can be overcome by increasing the sampling frequency, but estimates of transmission rates (and estimated reductions in transmission) are most accurate and precise if they combine parity, oocyst rates and sporozoite rates. These studies provide a basis for evaluating the adequacy of various entomological sampling procedures for measuring malaria parasite transmission from humans to mosquitoes and for evaluating the direct transmission-blocking effects of a vaccine

Selection of optimal recording sites for limited lead body surface potential mapping: A sequential selection based approach

BACKGROUND: In this study we propose the development of a new algorithm for selecting optimal recording sites for limited lead body surface potential mapping. The proposed algorithm differs from previously reported methods in that it is based upon a simple and intuitive data driven technique that does not make any presumptions about deterministic characteristics of the data. It uses a forward selection based search technique to find the best combination of electrocardiographic leads. METHODS: The study was conducted using a dataset consisting of body surface potential maps (BSPM) recorded from 116 subjects which included 59 normals and 57 subjects exhibiting evidence of old Myocardial Infarction (MI). The performance of the algorithm was evaluated using spatial RMS voltage error and correlation coefficient to compare original and reconstructed map frames. RESULTS: In all, three configurations of the algorithm were evaluated and it was concluded that there was little difference in the performance of the various configurations. In addition to observing the performance of the selection algorithm, several lead subsets of 32 electrodes as chosen by the various configurations of the algorithm were evaluated. The rationale for choosing this number of recording sites was to allow comparison with a previous study that used a different algorithm, where 32 leads were deemed to provide an acceptable level of reconstruction performance. CONCLUSION: It was observed that although the lead configurations suggested in this study were not identical to that suggested in the previous work, the systems did bear similar characteristics in that recording sites were chosen with greatest density in the precordial region

Creation of a novel peptide with enhanced nuclear localization in prostate and pancreatic cancer cell lines

<p>Abstract</p> <p>Background</p> <p>For improved uptake of oligonucleotide-based therapy, the oligonucleotides often are coupled to peptides that facilitate entry into cells. To this end, novel cell-penetrating peptides (CPPs) were designed for mediating intracellular uptake of oligonucleotide-based therapeutics. The novel peptides were based on taking advantage of the nuclear localization properties of transcription factors in combination with a peptide that would bind putatively to cell surfaces. It was observed that adding a glutamate peptide to the N-terminus of the nuclear localization signal (NLS) of the Oct6 transcription factor resulted in a novel CPP with better uptake and better nuclear colocalization than any other peptide tested.</p> <p>Results</p> <p>Uptake of the novel peptide Glu-Oct6 by cancer cell lines was rapid (in less than 1 hr, more than 60% of DU-145 cells were positive for FITC), complete (by 4 hr, 99% of cells were positive for FITC), concentration-dependent, temperature-dependent, and inhibited by sodium azide (NaN₃). Substitution of Phe, Tyr, or Asn moieties for the glutamate portion of the novel peptide resulted in abrogation of novel CPP uptake; however none of the substituted peptides inhibited uptake of the novel CPP when coincubated with cells. Live-cell imaging and analysis by imaging flow cytometry revealed that the novel CPP accumulated in nuclei. Finally, the novel CPP was coupled to a carboxyfluorescein-labeled synthetic oligonucleotide, to see if the peptide could ferry a therapeutic payload into cells.</p> <p>Conclusions</p> <p>These studies document the creation of a novel CPP consisting of a glutamate peptide coupled to the N-terminus of the Oct6 NLS; the novel CPP exhibited nuclear colocalization as well as uptake by prostate and pancreatic cancer cell lines.</p

Distributive Lattices Defined for Representations of Rank Two Semisimple Lie Algebras

For a rank two root system and a pair of nonnegative integers, using only elementary combinatorics we construct two posets. The constructions are uniform across the root systems A1+A1, A2, C2, and G2. Examples appear in Figures 3.2 and 3.3. We then form the distributive lattices of order ideals of these posets. Corollary 5.4 gives elegant quotient-of-products expressions for the rank generating functions of these lattices (thereby providing answers to a 1979 question of Stanley). Also, Theorem 5.3 describes how these lattices provide a new combinatorial setting for the Weyl characters of representations of rank two semisimple Lie algebras. Most of these lattices are new; the rest of them (or related structures) have arisen in work of Stanley, Kashiwara, Nakashima, Littelmann, and Molev. In a future paper, one author shows that the posets constructed here form a Dynkin diagram-indexed answer to a combinatorially posed classification question. In a companion paper, some of these lattices are used to explicitly construct some representations of rank two semisimple Lie algebras. This implies that these lattices are strongly Sperner

Impact of climate change on New York City’s coastal flood hazard: Increasing flood heights from the preindustrial to 2300 CE

The flood hazard in New York City depends on both storm surges and rising sea levels. We combine modeled storm surges with probabilistic sea-level rise projections to assess future coastal inundation in New York City from the preindustrial era through 2300 CE. The storm surges are derived from large sets of synthetic tropical cyclones, downscaled from RCP8.5 simulations from three CMIP5 models. The sea-level rise projections account for potential partial collapse of the Antarctic ice sheet in assessing future coastal inundation. CMIP5 models indicate that there will be minimal change in storm-surge heights from 2010 to 2100 or 2300, because the predicted strengthening of the strongest storms will be compensated by storm tracks moving offshore at the latitude of New York City. However, projected sea-level rise causes overall flood heights associated with tropical cyclones in New York City in coming centuries to increase greatly compared with preindustrial or modern flood heights. For the various sea-level rise scenarios we consider, the 1-in-500-y flood event increases from 3.4 m above mean tidal level during 1970–2005 to 4.0–5.1 m above mean tidal level by 2080–2100 and ranges from 5.0–15.4 m above mean tidal level by 2280–2300. Further, we find that the return period of a 2.25-m flood has decreased from ∼500 y before 1800 to ∼25 y during 1970–2005 and further decreases to ∼5 y by 2030–2045 in 95% of our simulations. The 2.25-m flood height is permanently exceeded by 2280–2300 for scenarios that include Antarctica’s potential partial collapse

A candidate fusion engineering material, WC-FeCr

A new candidate fusion engineering material, WC-FeCr, has been irradiated with He ions at 25 and 500 °C. Ions were injected at 6 keV to a dose of ~15 dpa and 50 at. % He, simulating direct helium injection from the plasma. The microstructural evolution was continuously characterised in situ using transmission electron microscopy. In the FeCr phase, a coarse array of 3–6 nm bubbles formed. In the WC, bubbles were less prominent and smaller (~2 nm). Spherical-cap bubbles formed at hetero-phase interfaces of tertiary precipitates, indicating that enhanced processing routes to minimise precipitation could further improve irradiation tolerance