Categorification of persistent homology

We redevelop persistent homology (topological persistence) from a categorical point of view. The main objects of study are diagrams, indexed by the poset of real numbers, in some target category. The set of such diagrams has an interleaving distance, which we show generalizes the previously-studied bottleneck distance. To illustrate the utility of this approach, we greatly generalize previous stability results for persistence, extended persistence, and kernel, image and cokernel persistence. We give a natural construction of a category of interleavings of these diagrams, and show that if the target category is abelian, so is this category of interleavings.Comment: 27 pages, v3: minor changes, to appear in Discrete & Computational Geometr

Prospect of Studying Hard X- and Gamma-Rays from Type Ia Supernovae

We perform multi-dimensional, time-dependent radiation transfer simulations for hard X-ray and gamma-ray emissions, following radioactive decays of 56Ni and 56Co, for two-dimensional delayed detonation models of Type Ia supernovae (SNe Ia). The synthetic spectra and light curves are compared with the sensitivities of current and future observatories for an exposure time of 10^6 seconds. The non-detection of the gamma-ray signal from SN 2011fe at 6.4 Mpc by SPI on board INTEGRAL places an upper limit for the mass of 56Ni of \lesssim 1.0 Msun, independently from observations in any other wavelengths. Signals from the newly formed radioactive species have not been convincingly measured yet from any SN Ia, but the future X-ray and gamma-ray missions are expected to deepen the observable horizon to provide the high energy emission data for a significant SN Ia sample. We predict that the hard X-ray detectors on board NuStar (launched in 2012) or ASTRO-H (scheduled for launch in 2014) will reach to SNe Ia at \sim15 Mpc, i.e., one SN every few years. Furthermore, according to the present results, the soft gamma-ray detector on board ASTRO-H will be able to detect the 158 keV line emission up to \sim25 Mpc, i.e., a few SNe Ia per year. Proposed next generation gamma-ray missions, e.g., GRIPS, could reach to SNe Ia at \sim20 - 35 Mpc by MeV observations. Those would provide new diagnostics and strong constraints on explosion models, detecting rather directly the main energy source of supernova light.Comment: 14 pages, 7 figures, 1 table, accepted for publication in Ap

Observation of a 4ΣHe Bound State in the H4e(K−,π−) reaction at 600MeV/c

We have observed a clear peak below the Σ+-production threshold in the 4He(K−,π−) reaction at 600MeV/c and θKπ=4∘. This is confirmation of the existence of the bound state of 4ΣHe, which was reported in the 4He(stoppedK−,π−) reaction. As in the case of stopped kaons, no such peak was found in the 4He(K−,π+) spectrum. Quantitatively reliable parameters for this level have been established. The binding energy and the width of the bound state are 4.4±0.3(stat)±1(syst) MeV and 7.0±0.7(stat)+1.2−0.0(syst) MeV, respectively

Search for the lepton-family-number nonconserving decay \mu -> e + \gamma

The MEGA experiment, which searched for the muon- and electron-number violating decay \mu -> e + \gamma, is described. The spectrometer system, the calibrations, the data taking procedures, the data analysis, and the sensitivity of the experiment are discussed. The most stringent upper limit on the branching ratio of \mu -> e + \gamma) < 1.2 x 10^{-11} was obtained

On the nature of the fourth generation neutrino and its implications

We consider the neutrino sector of a Standard Model with four generations. While the three light neutrinos can obtain their masses from a variety of mechanisms with or without new neutral fermions, fourth-generation neutrinos need at least one new relatively light right-handed neutrino. If lepton number is not conserved this neutrino must have a Majorana mass term whose size depends on the underlying mechanism for lepton number violation. Majorana masses for the fourth generation neutrinos induce relative large two-loop contributions to the light neutrino masses which could be even larger than the cosmological bounds. This sets strong limits on the mass parameters and mixings of the fourth generation neutrinos.Comment: To be published. Few typos corrected, references update

Transverse momentum dependence of semi-inclusive pion production

Cross sections for semi-inclusive electroproduction of charged pions ($\pi^{\pm}$) from both proton and deuteron targets were measured for $0.2<x<0.5$, $2<Q^2<4$ GeV$^2$, $0.3<z<1$, and $P_t^2<0.2$ GeV$^2$. For $P_t<0.1$ GeV, we find the azimuthal dependence to be small, as expected theoretically. For both $\pi^+$ and $\pi^-$, the $P_t$ dependence from the deuteron is found to be slightly weaker than from the proton. In the context of a simple model, this implies that the initial transverse momenta width of $d$ quarks is larger than for $u$ quarks and, contrary to expectations, the transverse momentum width of the favored fragmentation function is larger than the unfavored one.Comment: 15 pages, 4 figures. Fit form changed to include Cahn effect Minor revisions. Added one new figur

Applications of quark-hadron duality in F2 structure function

Inclusive electron-proton and electron-deuteron inelastic cross sections have been measured at Jefferson Lab (JLab) in the resonance region, at large Bjorken x, up to 0.92, and four-momentum transfer squared Q2 up to 7.5 GeV2 in the experiment E00-116. These measurements are used to extend to larger x and Q2 precision, quantitative, studies of the phenomenon of quark-hadron duality. Our analysis confirms, both globally and locally, the apparent violation of quark-hadron duality previously observed at a Q2 of 3.5 GeV2 when resonance data are compared to structure function data created from CTEQ6M and MRST2004 parton distribution functions (PDFs). More importantly, our new data show that this discrepancy saturates by Q2 ~ 4 Gev2, becoming Q2 independent. This suggests only small violations of Q2 evolution by contributions from the higher-twist terms in the resonance region which is confirmed by our comparisons to ALEKHIN and ALLM97.We conclude that the unconstrained strength of the CTEQ6M and MRST2004 PDFs at large x is the major source of the disagreement between data and these parameterizations in the kinematic regime we study and that, in view of quark-hadron duality, properly averaged resonance region data could be used in global QCD fits to reduce PDF uncertainties at large x.Comment: 35 page

The Onset of Quark-Hadron Duality in Pion Electroproduction

A large data set of charged-pion electroproduction from both hydrogen and deuterium targets has been obtained spanning the low-energy residual-mass region. These data conclusively show the onset of the quark-hadron duality phenomenon, as predicted for high-energy hadron electroproduction. We construct several ratios from these data to exhibit the relation of this phenomenon to the high-energy factorization ansatz of electron-quark scattering and subsequent quark-to- pion production mechanisms.Comment: 11 pages, 3 figures, accepted in Phys. Rev. Lett. Tables adde

Domain formation in DODAB–cholesterol mixed systems monitored via nile red anisotropy

The effect of the cholesterol (Ch) on liposomes composed of the cationic lipid dioctadecyldimethylammonium bromide (DODAB) was assessed by studying both the steady-state and time-resolved fluorescence anisotropy of the dye Nile Red. The information obtained combined with analysis of the steady-state emission and luorescence lifetime of Nile Red (NR) for different cholesterol concentrations (5–50%) elucidated the presence of “condensed complexes” and cholesterol-rich domains in these mixed systems. The steady-state fluorescence spectra were decomposed into the sum of two lognormal emissions, emanating from two different states, and the effect of temperature on the anisotropy decay of Nile Red for different cholesterol concentrations was observed. At room temperature, the time-resolved anisotropy decays are indicative of NR being relatively immobile (manifest by a high r∞ value). At higher temperature, rotational times ca. 1 ns were obtained throughout and a trend in increasing hindrance was seen with increase of Ch content

The repulsive lattice gas, the independent-set polynomial, and the Lov\'asz local lemma

We elucidate the close connection between the repulsive lattice gas in equilibrium statistical mechanics and the Lovasz local lemma in probabilistic combinatorics. We show that the conclusion of the Lovasz local lemma holds for dependency graph G and probabilities {p_x} if and only if the independent-set polynomial for G is nonvanishing in the polydisc of radii {p_x}. Furthermore, we show that the usual proof of the Lovasz local lemma -- which provides a sufficient condition for this to occur -- corresponds to a simple inductive argument for the nonvanishing of the independent-set polynomial in a polydisc, which was discovered implicitly by Shearer and explicitly by Dobrushin. We also present some refinements and extensions of both arguments, including a generalization of the Lovasz local lemma that allows for "soft" dependencies. In addition, we prove some general properties of the partition function of a repulsive lattice gas, most of which are consequences of the alternating-sign property for the Mayer coefficients. We conclude with a brief discussion of the repulsive lattice gas on countably infinite graphs.Comment: LaTex2e, 97 pages. Version 2 makes slight changes to improve clarity. To be published in J. Stat. Phy