Invariants of Collective Neutrino Oscillations

We consider the flavor evolution of a dense neutrino gas by taking into account both vacuum oscillations and self interactions of neutrinos. We examine the system from a many-body perspective as well as from the point of view of an effective one-body description formulated in terms of the neutrino polarization vectors. We show that, in the single angle approximation, both the many-body picture and the effective one-particle picture possess several constants of motion. We write down these constants of motion explicitly in terms of the neutrino isospin operators for the many-body case and in terms of the polarization vectors for the effective one-body case. The existence of these constants of motion is a direct consequence of the fact that the collective neutrino oscillation Hamiltonian belongs to the class of Gaudin Hamiltonians. This class of Hamiltonians also includes the (reduced) BCS pairing Hamiltonian describing superconductivity. We point out the similarity between the collective neutrino oscillation Hamiltonian and the BCS pairing Hamiltonian. The constants of motion manifest the exact solvability of the system. Borrowing the well established techniques of calculating the exact BCS spectrum, we present exact eigenstates and eigenvalues of both the many-body and the effective one-particle Hamiltonians describing the collective neutrino oscillations. For the effective one-body case, we show that spectral splits of neutrinos can be understood in terms of the adiabatic evolution of some quasi-particle degrees of freedom from a high density region where they coincide with flavor eigenstates to the vacuum where they coincide with mass eigenstates. We write down the most general consistency equations which should be satisfied by the effective one-body eigenstates and show that they reduce to the spectral split consistency equations for the appropriate initial conditions.Comment: 26 pages with one figure. Published versio

Lacunary statistical cluster points of sequences

In this note we introduce the concept of a lacunary statistical cluster (l.s.c.) point and prove some of its properties in finite dimensional Banach spaces. We develop the method suggested by S. Pehlivan and M.A. Mamedov [20] where it was proved that under some conditions optimal paths have the same unique stationary limit point and stationary cluster point. We also show that the set $Gamma_x^{theta}$ of l.s.c. points is nonempty and compact

Exactly Solvable Pairing Model Using an Extension of Richardson-Gaudin Approach

We introduce a new class of exactly solvable boson pairing models using the technique of Richardson and Gaudin. Analytical expressions for all energy eigenvalues and first few energy eigenstates are given. In addition, another solution to Gaudin's equation is also mentioned. A relation with the Calogero-Sutherland model is suggested.Comment: 9 pages of Latex. In the proceedings of Blueprints for the Nucleus: From First Principles to Collective Motion: A Festschrift in Honor of Professor Bruce Barrett, Istanbul, Turkey, 17-23 May 200

Interpolation of SUSY quantum mechanics

Interpolation of two adjacent Hamiltonians in SUSY quantum mechanics $H_s=(1-s)A^{\dagger}A + sAA^{\dagger}$, $0\le s\le 1$ is discussed together with related operators. For a wide variety of shape-invariant degree one quantum mechanics and their `discrete' counterparts, the interpolation Hamiltonian is also shape-invariant, that is it takes the same form as the original Hamiltonian with shifted coupling constant(s).Comment: 18 page

Spectra and Symmetry in Nuclear Pairing

We apply the algebraic Bethe ansatz technique to the nuclear pairing problem with orbit dependent coupling constants and degenerate single particle energy levels. We find the exact energies and eigenstates. We show that for a given shell, there are degeneracies between the states corresponding to less and more than half full shell. We also provide a technique to solve the equations of Bethe ansatz.Comment: 15 pages of REVTEX with 2 eps figure

The neutrino signal at HALO: learning about the primary supernova neutrino fluxes and neutrino properties

Core-collapse supernova neutrinos undergo a variety of phenomena when they travel from the high neutrino density region and large matter densities to the Earth. We perform analytical calculations of the supernova neutrino fluxes including collective effects due to the neutrino-neutrino interactions, the Mikheev-Smirnov-Wolfenstein (MSW) effect due to the neutrino interactions with the background matter and decoherence of the wave packets as they propagate in space. We predict the numbers of one- and two-neutron charged and neutral-current electron-neutrino scattering on lead events. We show that, due to the energy thresholds, the ratios of one- to two-neutron events are sensitive to the pinching parameters of neutrino fluxes at the neutrinosphere, almost independently of the presently unknown neutrino properties. Besides, such events have an interesting sensitivity to the spectral split features that depend upon the presence/absence of energy equipartition among neutrino flavors. Our calculations show that a lead-based observatory like the Helium And Lead Observatory (HALO) has the potential to pin down important characteristics of the neutrino fluxes at the neutrinosphere, and provide us with information on the neutrino transport in the supernova core.Comment: 30 pages, 12 figures, 6 tables, minor correction

History of the rare cancer network and past research.

Approximately, twenty years ago, the Rare Cancer Network (RCN) was formed in Lausanne, Switzerland, to support the study of rare malignancies. The RCN has grown over the years and now includes 130 investigators from twenty-four nations on six continents. The network held its first international symposium in Nice, France, on March 21-22, 2014. The proceedings of that meeting are presented in two companion papers. This manuscript reviews the history of the growth of the RCN and contains the abstracts of fourteen oral presentations made at the meeting of prior RCN studies. From 1993 to 2014, 74 RCN studies have been initiated, of which 54 were completed, 10 are in progress or under analysis, and 9 were stopped due to poor accrual. Forty-four peer reviewed publications have been written on behalf of the RCN

Endothelial nitric oxide synthase gene polymorphisms associated with periodontal diseases in Turkish adults

Endothelial nitric oxide synthase (NOS3) is involved in key steps of immune response. Genetic factors predispose individuals to periodontal disease. This study's aim was to explore the association between NOS3 gene polymorphisms and clinical parameters in patients with periodontal disease. Genomic DNA was obtained from the peripheral blood of 23 subjects with aggressive periodontitis (AgP), 26 with chronic periodontitis (CP), 31 with gingivitis (G) and 50 healthy controls. Probing depth (PD), clinical attachment loss (CAL), plaque index (PI) and gingival index (GI) were recorded as clinical parameters. We genotyped NOS3 polymorphisms using the PCR and/or PCR-RFLP method. Genotype frequencies differed significantly among periodontal diseases and controls for these polymorphisms. A significant association was detected between NOS3 +894 polymorphism and PD and CAL in the CP and AgP patient groups; whereas NOS VNTR analysis detected no associations with clinical parameters in theCP and AgP groups. However, a significant association was detected between the AA genotype and both PI and GI in patients with gingivitis; and a significant association was shown between the BB genotype and PI. The present study shows that two common polymorphisms of the NOS3 gene cluster are significantly associated with the occurrence of periodontal diseases