The pre-WDVV ring of physics and its topology

We show how a simplicial complex arising from the WDVV (Witten-Dijkgraaf-Verlinde-Verlinde) equations of string theory is the Whitehouse complex. Using discrete Morse theory, we give an elementary proof that the Whitehouse complex $\Delta_n$ is homotopy equivalent to a wedge of $(n-2)!$ spheres of dimension $n-4$. We also verify the Cohen-Macaulay property. Additionally, recurrences are given for the face enumeration of the complex and the Hilbert series of the associated pre-WDVV ring.Comment: 13 pages, 4 figures, 2 table

Exact Dynamical Correlation Functions of Calogero-Sutherland Model and One-Dimensional Fractional Statistics

One-dimensional model of non-relativistic particles with inverse-square interaction potential known as Calogero-Sutherland Model (CSM) is shown to possess fractional statistics. Using the theory of Jack symmetric polynomial the exact dynamical density-density correlation function and the one-particle Green's function (hole propagator) at any rational interaction coupling constant $\lambda = p/q$ are obtained and used to show clear evidences of the fractional statistics. Motifs representing the eigenstates of the model are also constructed and used to reveal the fractional {\it exclusion} statistics (in the sense of Haldane's ``Generalized Pauli Exclusion Principle''). This model is also endowed with a natural {\it exchange } statistics (1D analog of 2D braiding statistics) compatible with the {\it exclusion} statistics. (Submitted to PRL on April 18, 1994)Comment: Revtex 11 pages, IASSNS-HEP-94/27 (April 18, 1994

INTEGRAL upper limits on gamma-ray emission associated with the gravitational wave event GW150914

Using observations of the INTErnational Gamma-Ray Astrophysics Laboratory (INTEGRAL), we put upper limits on the gamma-ray and hard X-ray prompt emission associated with the gravitational wave event GW150914, discovered by the LIGO/Virgo collaboration. The omni-directional view of the INTEGRAL/SPI-ACS has allowed us to constrain the fraction of energy emitted in the hard X-ray electromagnetic component for the full high-probability sky region of LIGO trigger. Our upper limits on the hard X-ray fluence at the time of the event range from $F_{\gamma}=2 \times 10^{-8}$ erg cm$^{-2}$ to $F_{\gamma}=10^{-6}$ erg cm$^{-2}$ in the 75 keV - 2 MeV energy range for typical spectral models. Our results constrain the ratio of the energy promptly released in gamma-rays in the direction of the observer to the gravitational wave energy E$_\gamma/$E$_\mathrm{GW}<10^{-6}$. We discuss the implication of gamma-ray limits on the characteristics of the gravitational wave source, based on the available predictions for prompt electromagnetic emission.Comment: accepted for publication in ApJ

Light from the Cosmic Frontier: Gamma-Ray Bursts

Gamma-Ray Bursts (GRBs) are the most powerful cosmic explosions since the Big Bang, and thus act as signposts throughout the distant Universe. Over the last 2 decades, these ultra-luminous cosmological explosions have been transformed from a mere curiosity to essential tools for the study of high-redshift stars and galaxies, early structure formation and the evolution of chemical elements. In the future, GRBs will likely provide a powerful probe of the epoch of reionisation of the Universe, constrain the properties of the first generation of stars, and play an important role in the revolution of multi-messenger astronomy by associating neutrinos or gravitational wave (GW) signals with GRBs. Here, we describe the next steps needed to advance the GRB field, as well as the potential of GRBs for studying the Early Universe and their role in the up-coming multi-messenger revolution.Comment: White paper submitted to ESA as a contribution to the deliberations on the science themes for the L2 and L3 mission opportunitie

On Deformations of n-Lie algebras

The aim of this paper is to review the deformation theory of $n$-Lie algebras. We summarize the 1-parameter formal deformation theory and provide a generalized approach using any unital commutative associative algebra as a deformation base. Moreover, we discuss degenerations and quantization of $n$-Lie algebras.Comment: Proceeding of the conference Dakar's Workshop in honor of Pr Amin Kaidi. arXiv admin note: text overlap with arXiv:hep-th/9602016 by other author

Laboratory culture and estimated life span of the Eastern Atlantic squid, Loligo forbesi Steenstrup, 1856 (Mollusca: Cephalopoda)

First culture results are presented from four major experiments (lasting up to 478 days) on the commercially important squid species, Loligo forbesi Steenstrup, Details are provided on eggs, hatching, feeding, growth, survival, behaviour and sexual maturation. Best survival during the critical first 75 days was 15%. The hatchlings (up to 4.9mm mantle length, ML) are the largest among the genus Loligo, and the largest squid grown was a male 155mm ML and 124g. First schooling was observed only 40–50 days post-hatching. Spawning was not achieved although males reached maturity, females had maturing ova and mating was observed. The largest giant axon measured was 425μm in diameter (from a female 130mm ML), a size suitable for most biomedical applications. Laboratory data suggest a 2-year life cycle compared to fishery data which suggest a 1-year cycle