Local versus Global Search in Channel Graphs

Previous studies of search in channel graphs has assumed that the search is global; that is, that the status of any link can be probed by the search algorithm at any time. We consider for the first time local search, for which only links to which an idle path from the source has already been established may be probed. We show that some well known channel graphs may require exponentially more probes, on the average, when search must be local than when it may be global.Comment: i+13 pages, 2 figure

The economic and social benefits of increasing Indigenous employment

Using the latest available data and research, this paper provides estimates of the likely economic and social benefits of increasing Indigenous employment to the same level as in the non-Indigenous population. Introduction Relatively low rates of employment are one of the reasons for many of the poor economic and social outcomes experienced by Indigenous Australians. Increases in the rate of Indigenous employment would result in significant economic gains to the individuals who move into employment, and their families and communities, to the government who would receive higher tax revenues and have lower social security outlays, and the economy as a whole via the increases in the effective labour supply. The existing research also finds that there are health and social benefits that flow from paid employment. This paper, using the latest available data and research, provides estimates of the likely economic and social benefits of increasing Indigenous employment to the same level as in the non-Indigenous population (i.e. closing the employment gap). It was commissioned by the Department of the Prime Minister and Cabinet to help inform the work of the Indigenous Jobs and Training Review chaired by Andrew Forrest

On thermalization in the SYK and supersymmetric SYK models

The eigenstate thermalization hypothesis is a compelling conjecture which strives to explain the apparent thermal behavior of generic observables in closed quantum systems. Although we are far from a complete analytic understanding, quantum chaos is often seen as a strong indication that the ansatz holds true. In this paper, we address the thermalization of energy eigenstates in the Sachdev-Ye-Kitaev model, a maximally chaotic model of strongly-interacting Majorana fermions. We numerically investigate eigenstate thermalization for specific few-body operators in the original SYK model as well as its $\mathcal{N}=1$ supersymmetric extension and find evidence that these models satisfy ETH. We discuss the implications of ETH for a gravitational dual and the quantum information-theoretic properties of SYK it suggests.Comment: Published versio

Bright Ultraviolet Regions and Star Formation Characteristics in Nearby Dwarf Galaxies

We compare star formation in the inner and outer disks of 11 dwarf Irregular galaxies (dIm) within 3.6 Mpc. The regions are identified on GALEX near-UV images, and modeled with UV, optical, and near-IR colors to determine masses and ages. A few galaxies have made 10^5-10^6 Msun complexes in a starburst phase, while others have not formed clusters in the last 50 Myrs. The maximum region mass correlates with the number of regions as expected from the size-of-sample effect. We find no radial gradients in region masses and ages, even beyond the realm of Halpha emission, although there is an exponential decrease in the luminosity density and number density of the regions with radius. Halpha is apparently lacking in the outer parts only because nebular emission around massive stars is too faint to see. The outermost regions for the 5 galaxies with HI data formed at average gas surface densities of 1.9-5.9 Msun/pc2. These low average densities imply either that local gas densities are high or sub-threshold star formation is possible. The distribution of regions on a log Mass - log age plot is is usually uniform along log age for equal intervals of log Mass. This uniformity results from either an individual region mass that varies as 1/age or a region disruption probability that varies as 1/age. A correlation between fading-corrected surface brightness and age suggests the former.Comment: Astronomical Journal, in press for November 2009. 34 pages, 18 figures, 5 table

Chaos, Complexity, and Random Matrices

Chaos and complexity entail an entropic and computational obstruction to describing a system, and thus are intrinsically difficult to characterize. In this paper, we consider time evolution by Gaussian Unitary Ensemble (GUE) Hamiltonians and analytically compute out-of-time-ordered correlation functions (OTOCs) and frame potentials to quantify scrambling, Haar-randomness, and circuit complexity. While our random matrix analysis gives a qualitatively correct prediction of the late-time behavior of chaotic systems, we find unphysical behavior at early times including an $\mathcal{O}(1)$ scrambling time and the apparent breakdown of spatial and temporal locality. The salient feature of GUE Hamiltonians which gives us computational traction is the Haar-invariance of the ensemble, meaning that the ensemble-averaged dynamics look the same in any basis. Motivated by this property of the GUE, we introduce $k$-invariance as a precise definition of what it means for the dynamics of a quantum system to be described by random matrix theory. We envision that the dynamical onset of approximate $k$-invariance will be a useful tool for capturing the transition from early-time chaos, as seen by OTOCs, to late-time chaos, as seen by random matrix theory.Comment: 61 pages, 14 figures; v2: references added, typos fixe