On supersymmetric quantum mechanics

This paper constitutes a review on N=2 fractional supersymmetric Quantum Mechanics of order k. The presentation is based on the introduction of a generalized Weyl-Heisenberg algebra W_k. It is shown how a general Hamiltonian can be associated with the algebra W_k. This general Hamiltonian covers various supersymmetrical versions of dynamical systems (Morse system, Poschl-Teller system, fractional supersymmetric oscillator of order k, etc.). The case of ordinary supersymmetric Quantum Mechanics corresponds to k=2. A connection between fractional supersymmetric Quantum Mechanics and ordinary supersymmetric Quantum Mechanics is briefly described. A realization of the algebra W_k, of the N=2 supercharges and of the corresponding Hamiltonian is given in terms of deformed-bosons and k-fermions as well as in terms of differential operators.Comment: Review paper (31 pages) to be published in: Fundamental World of Quantum Chemistry, A Tribute to the Memory of Per-Olov Lowdin, Volume 3, E. Brandas and E.S. Kryachko (Eds.), Springer-Verlag, Berlin, 200

Quantum Spacetime Phenomenology

I review the current status of phenomenological programs inspired by quantum-spacetime research. I stress in particular the significance of results establishing that certain data analyses provide sensitivity to effects introduced genuinely at the Planck scale. And my main focus is on phenomenological programs that managed to affect the directions taken by studies of quantum-spacetime theories.Comment: 125 pages, LaTex. This V2 is updated and more detailed than the V1, particularly for quantum-spacetime phenomenology. The main text of this V2 is about 25% more than the main text of the V1. Reference list roughly double

Genetic correlation between multiple myeloma and chronic lymphocytic leukaemia provides evidence for shared aetiology

The clustering of different types of B-cell malignancies in families raises the possibility of shared aetiology. To examine this, we performed cross-trait linkage disequilibrium (LD)-score regression of multiple myeloma (MM) and chronic lymphocytic leukaemia (CLL) genome-wide association study (GWAS) data sets, totalling 11,734 cases and 29,468 controls. A significant genetic correlation between these two B-cell malignancies was shown (Rg = 0.4, P = 0.0046). Furthermore, four of the 45 known CLL risk loci were shown to associate with MM risk and five of the 23 known MM risk loci associate with CLL risk. By integrating eQTL, Hi-C and ChIP-seq data, we show that these pleiotropic risk loci are enriched for B-cell regulatory elements and implicate B-cell developmental genes. These data identify shared biological pathways influencing the development of CLL and, MM and further our understanding of the aetiological basis of these B-cell malignancies