New characterization of two-state normal distribution

In this article we give a purely noncommutative criterion for the characterization of two-state normal distribution. We prove that families of two-state normal distribution can be described by relations which is similar to the conditional expectation in free probability, but has no classical analogue. We also show a generalization of Bozejko, Leinert and Speicher's formula (relating moments and noncommutative cumulants).Comment: 19 pages, 2 figures, accepted for publication by Infinite Dimensional Analysis, Quantum Probability and Related Topic

The New Normal

On September 19, 2013 an individual wielding a military-grade assault rifle fired sixteen bullets into a Chicago park harming thirteen individuals, among them a 3-year old named Deonta Howard who was shot in the cheek. On September 16, 2013 a man by the name of Aaron Alexis opened fire on the cafeteria at the Navy Yard in Washington D.C. Thirteen people died, and eight others were injured. On December 14, 2012 Adam Lanza shot twenty-six people—twenty of whom were children between the ages of 6 and 7—in Newtown, Connecticut. Barack Obama called it the “worst day of [his] presidency.” On July 20, 2012, twelve people died and seventy others were injured at the hands of James Egan Holmes who entered a movie theater in Aurora, Colorado and proceeded to launch tear gas grenades and shoot from multiple firearms into the crowd. Investigators called it “a scene straight out of a horror film.” [excerpt

Are Lower Private Equity Returns the New Normal?

U.S. private equity fundraising had its best year ever in 2015 -- raising $185 billion. But is the enthusiasm of investors warranted? Do PE buyout funds deliver outsized returns to investors and will they do so in the future? This report answers this question by reviewing the most recent empirical evidence on buyout fund performance; the answer is no. While median private equity buyout funds once beat the S&P 500, they have not done so since 2006 -- despite industry claims to the contrary

A new catalogue of ISM content of normal galaxies

We have compiled a catalogue of the gas content for a sample of 1916 galaxies, considered to be a fair representation of `normality'. The definition of 'normal' galaxy adopted in this work implies that we have purposely excluded from the catalogue galaxies having distorted morphology (such as interaction bridges, tails or lopsidedness) and/or any signature of peculiar kinematics (such as polar rings, counterrotating disks or other decoupled components). In contrast, we have included systems hosting active galactic nuclei (AGN) in the catalogue. This catalogue revises previous compendia on the ISM content of galaxies, and compiles data available in the literature from several small samples of galaxies. Masses for warm dust, atomic and molecular gas, as well as X-ray luminosities have been converted to a uniform distance scale taken from the Catalogue of Principal Galaxies (PGC). We have used two different normalization factors to explore the variation of the gas content along the Hubble sequence: the blue luminosity and the square of linear diameter. Our catalogue significantly improves the statistics of previous reference catalogues and can be used in future studies to define a template ISM content for 'normal' galaxies along the Hubble sequence. The catalogue can be accessed on-line at http://dipastro.pd.astro.it/galletta/ismcat/Comment: 12 pages. 4 figures, 6 tables - A&A accepte