Some Properties of the Calogero-Sutherland Model with Reflections

We prove that the Calogero-Sutherland Model with reflections (the BC_N model) possesses a property of duality relating the eigenfunctions of two Hamiltonians with different coupling constants. We obtain a generating function for their polynomial eigenfunctions, the generalized Jacobi polynomials. The symmetry of the wave-functions for certain particular cases (associated to the root systems of the classical Lie groups B_N, C_N and D_N) is also discussed.Comment: 16 pages, harvmac.te

Quantum Calogero-Moser Models: Integrability for all Root Systems

The issues related to the integrability of quantum Calogero-Moser models based on any root systems are addressed. For the models with degenerate potentials, i.e. the rational with/without the harmonic confining force, the hyperbolic and the trigonometric, we demonstrate the following for all the root systems: (i) Construction of a complete set of quantum conserved quantities in terms of a total sum of the Lax matrix (L), i.e. (\sum_{\mu,\nu\in{\cal R}}(L^n)_{\mu\nu}), in which ({\cal R}) is a representation space of the Coxeter group. (ii) Proof of Liouville integrability. (iii) Triangularity of the quantum Hamiltonian and the entire discrete spectrum. Generalised Jack polynomials are defined for all root systems as unique eigenfunctions of the Hamiltonian. (iv) Equivalence of the Lax operator and the Dunkl operator. (v) Algebraic construction of all excited states in terms of creation operators. These are mainly generalisations of the results known for the models based on the (A) series, i.e. (su(N)) type, root systems.Comment: 45 pages, LaTeX2e, no figure

Explicit solution of the quantum three-body Calogero-Sutherland model

Quantum integrable systems generalizing Calogero-Sutherland systems were introduced by Olshanetsky and Perelomov (1977). Recently, it was proved that for systems with trigonometric potential, the series in the product of two wave functions is a deformation of the Clebsch-Gordan series. This yields recursion relations for the wave functions of those systems. In this note, this approach is used to compute the explicit expressions for the three-body Calogero-Sutherland wave functions, which are the Jack polynomials. We conjecture that similar results are also valid for the more general two-parameters deformation introduced by Macdonald.Comment: 10 page

Multi-decadal shoreline changes in Eastern Ghana—natural dynamics versus human interventions

Human infrastructures, such as dams, seawalls, and ports, can affect both the sedimentary budget and nearshore hydrodynamics, enhancing and accelerating the loss or gain of coastal sediments. Understanding the processes and factors controlling beach morphodynamics is essential for implementing adequate adaptation strategies in coastal areas, particularly in those regions where coastal protection measures are scarce. This study analyzes shoreline changes in the Keta Municipal District, located in southeastern Ghana (West Africa). This area is characterized by the sedimentary input of the Volta River, forming a river delta situated to the west, i.e., updrift, of our study site. Following the construction of two dams (Akosombo and Kpong) on the Volta River in 1965 and 1982, groins and revetments have been built along the coast between 2005 and 2015 to reduce the high rates of coastal erosion in this area. Here, we explore the influence of these dams and the hard protection constructions on beach morphodynamics using historical maps and satellite images complemented by a shoreline survey undertaken with a differential GNSS in 2015. The multi-decadal evolution between 1913 and 2015 reconstructed for 90 km of shoreline suggests that local erosion rates in the region predate the construction of the two dams on the Volta River, indicating that these structures might not be the primary driver of coastal erosion in this area, as previously suggested. We emphasize that delta dynamics under conditions of high-energy longshore drift, modified by anthropogenic drivers such as sand mining, play a key role in the long-term evolution of this coast. Our results also show that the infrastructures built to halt coastal erosion result in localized erosion and accretion down-current along the coastline towards the border with Togo, highlighting the need for a transnational perspective in addressing the problems caused by coastal erosion

Telomere lengths in human oocytes, cleavage stage embryos and blastocysts

Telomeres are repeated sequences that protect the ends of chromosomes and harbour DNA-repair proteins. Telomeres shorten during each cell division in the absence of telomerase. When telomere length becomes critically short, cell senescence occurs. Telomere length therefore reflects both cellular ageing and capacity for division. We have measured telomere length in human germinal vesicle (GV) oocytes and pre-implantation embryos, by quantitative fluorescence in-situ hybridisation (Q-FISH), providing baseline data towards our hypothesis that telomere length is a marker of embryo quality. The numbers of fluorescent foci suggest that extensive clustering of telomeres occurs in mature GV stage oocytes, and in pre-implantation embryos. When calculating average telomere length by assuming that each signal presents one telomere, the calculated telomere length decreased from the oocyte to the cleavage stages, and increased between the cleavage stages and the blastocyst (11.12 vs 8.43 vs 12.22kb respectively, p<0.001). Other methods of calculation, based upon expected maximum and minimum numbers of telomeres, confirm that telomere length in blastocysts is significantly longer than cleavage stages. Individual blastomeres within an embryo showed substantial variation in calculated average telomere length. This study implies that telomere length changes according to the stage of pre-implantation embryo development

Association of combined PD- L1 expression and tumour- infiltrating lymphocyte features with survival and treatment outcomes in patients with metastatic melanoma

BackgroundRecent advances obtained with immune checkpoint inhibitors (ICIs) targeting the programmed cell death- 1 (PD- 1) protein have significantly improved the outcome of patients with metastatic melanoma. The PD- L1 expression in tumour cells as detected by immunohistochemistry is a predictive biomarker in some solid tumours, but appears insufficient as prognostic or predictive factor of response to ICIs in metastatic melanomas.ObjectivesWe investigated whether the presence and the features of pretreatment CD8+tumour- infiltrating T lymphocytes (TILs) could be a complementary prognostic or predictive biomarker in patients with metastatic melanoma.MethodsIn this retrospective study, we evaluated the association of PD- L1 expression - ¥5% of tumour cells combined with TIL features (CD8, CD28, Ki67) with the overall survival (OS) among 51 patients treated with ICIs and 54 patients treated with other treatment options (non- ICIs).ResultsPD- L1 positivity was observed in 33% and 39% of primary melanomas and matched metastases, respectively, with, however, poor concordance between the primary and the matched metastatic site (κ = 0.283). No significant association was noted between PD- L1 expression and CD8+TIL profile analysed as single markers and OS or response to immunotherapy. Instead, their combined analysis in primary melanoma samples showed that the PD- L1- /CD8+status was significantly associated with prolonged OS in the whole population (P = 0.04) and in the subgroup treated with non- ICIs (P = 0.009). Conversely, the PD- L1+/CD8+ status was a good prognostic factor in patients treated with ICIs (P = 0.022), whereas was significantly associated with poor prognosis in patients treated with non- ICIs (P = 0.014). While the expression of CD28 was not related to outcome, the Ki67 expression was significantly associated with poor OS in the subgroup CD8+TIL+/PD- L1- (P = 0.02).ConclusionsThe pretreatment combination of PD- L1 expression with the level of CD8+TILs could better assess OS and predict therapeutic response of patients with metastatic melanoma treated by either immunotherapy or other treatment regimens.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/155478/1/jdv16016_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/155478/2/jdv16016.pd

Bacterial microevolution and the Pangenome

The comparison of multiple genome sequences sampled from a bacterial population reveals considerable diversity in both the core and the accessory parts of the pangenome. This diversity can be analysed in terms of microevolutionary events that took place since the genomes shared a common ancestor, especially deletion, duplication, and recombination. We review the basic modelling ingredients used implicitly or explicitly when performing such a pangenome analysis. In particular, we describe a basic neutral phylogenetic framework of bacterial pangenome microevolution, which is not incompatible with evaluating the role of natural selection. We survey the different ways in which pangenome data is summarised in order to be included in microevolutionary models, as well as the main methodological approaches that have been proposed to reconstruct pangenome microevolutionary history

Precision measurements of the top quark mass from the Tevatron in the pre-LHC era

The top quark is the heaviest of the six quarks of the Standard Model. Precise knowledge of its mass is important for imposing constraints on a number of physics processes, including interactions of the as yet unobserved Higgs boson. The Higgs boson is the only missing particle of the Standard Model, central to the electroweak symmetry breaking mechanism and generation of particle masses. In this Review, experimental measurements of the top quark mass accomplished at the Tevatron, a proton-antiproton collider located at the Fermi National Accelerator Laboratory, are described. Topologies of top quark events and methods used to separate signal events from background sources are discussed. Data analysis techniques used to extract information about the top mass value are reviewed. The combination of several most precise measurements performed with the two Tevatron particle detectors, CDF and \D0, yields a value of \Mt = 173.2 \pm 0.9 GeV/$c^2$.Comment: This version contains the most up-to-date top quark mass averag

Genetic analysis of variation in human meiotic recombination

The number of recombination events per meiosis varies extensively among individuals. This recombination phenotype differs between female and male, and also among individuals of each gender. In this study, we used high-density SNP genotypes of over 2,300 individuals and their offspring in two datasets to characterize recombination landscape and to map the genetic variants that contribute to variation in recombination phenotypes. We found six genetic loci that are associated with recombination phenotypes. Two of these (RNF212 and an inversion on chromosome 17q21.31) were previously reported in the Icelandic population, and this is the first replication in any other population. Of the four newly identified loci (KIAA1462, PDZK1, UGCG, NUB1), results from expression studies provide support for their roles in meiosis. Each of the variants that we identified explains only a small fraction of the individual variation in recombination. Notably, we found different sequence variants associated with female and male recombination phenotypes, suggesting that they are regulated by different genes. Characterization of genetic variants that influence natural variation in meiotic recombination will lead to a better understanding of normal meiotic events as well as of non-disjunction, the primary cause of pregnancy loss. © 2009 Chowdhury et al