The interplay of classes of algorithmically random objects

We study algorithmically random closed subsets of $2^\omega$, algorithmically random continuous functions from $2^\omega$ to $2^\omega$, and algorithmically random Borel probability measures on $2^\omega$, especially the interplay between these three classes of objects. Our main tools are preservation of randomness and its converse, the no randomness ex nihilo principle, which say together that given an almost-everywhere defined computable map between an effectively compact probability space and an effective Polish space, a real is Martin-L\"of random for the pushforward measure if and only if its preimage is random with respect to the measure on the domain. These tools allow us to prove new facts, some of which answer previously open questions, and reprove some known results more simply. Our main results are the following. First we answer an open question of Barmapalias, Brodhead, Cenzer, Remmel, and Weber by showing that $\mathcal{X}\subseteq2^\omega$ is a random closed set if and only if it is the set of zeros of a random continuous function on $2^\omega$. As a corollary we obtain the result that the collection of random continuous functions on $2^\omega$ is not closed under composition. Next, we construct a computable measure $Q$ on the space of measures on $2^\omega$ such that $\mathcal{X}\subseteq2^\omega$ is a random closed set if and only if $\mathcal{X}$ is the support of a $Q$-random measure. We also establish a correspondence between random closed sets and the random measures studied by Culver in previous work. Lastly, we study the ranges of random continuous functions, showing that the Lebesgue measure of the range of a random continuous function is always contained in $(0,1)$

Age and origin of enigmatic megaherbs from the subantarctic islands

Biogeographic relationships in the southern hemisphere have puzzled biologists for the last two centuries. Once joined to form the supercontinent Gondwana, Africa, Antarctica, Australia, New Zealand and South America are widely separated by the Pacific and Indian oceans. Sir Joseph Hooker was the first to suggest that Antarctica served as a corridor for plant migration not unlike the land-bridges in the northern hemisphere. While the Antarctic flora was largely erased by glaciation during the Pleistocene, at least some of these Antarctic plant communities found refuge on the subantarctic islands. Here we provide support for the hypothesis that giant herbs persisted in the subantactic islands prior to the onset of Pleistocene glaciation, then dispersed northward in response to glacial advance. Our findings provide further evidence that Antarctica has played a pivotal role in shaping southern hemisphere biogeography

When is capital enough to get female microenterprises growing? Evidence from a randomized experiment in Ghana

Standard models of investment predict that credit-constrained firmd should grow rapidly when given additional capital, and that how this capital is provided should not affect decisions to invest in the business or consume the capital. We randomly gave cash and in-kind grants to male- and female- owned microenterprises in urban Ghana. Our findings cast doubt on the ability of caoital alone to stimulate the growth of female microenterprises. First, while the average treatment effects of the in-kind grants are large and positive for both males and females, the gain in profits is almost zerp fpr women with itital profits below the median, suggesting that capital alone is not enough to grow subsistence enterprises owned by women. Second, for women we strongly reject equality of the case and in-kind grants; only in-kind grants lead to growth in business profits. The results for men also suggest a lower impact of cash, but differences between cash and in-kind grants is assoicated more with a lack of self-control than with external pressure. As a result, the manner in which funding is provided affects microenterprise growth.microenterprises; ghana; Conditionality; Asset intergration

Alleviating a form of electric vehicle range anxiety through On-Demand vehicle access

On-demand vehicle access is a method that can be used to reduce types of range anxiety problems related to planned travel for electric vehicle owners. Using ideas from elementary queueing theory, basic QoS metrics are defined to dimension a shared fleet to ensure high levels of vehicle access. Using mobility data from Ireland, it is argued that the potential cost of such a system is very low

Causal Dependence Tree Approximations of Joint Distributions for Multiple Random Processes

We investigate approximating joint distributions of random processes with causal dependence tree distributions. Such distributions are particularly useful in providing parsimonious representation when there exists causal dynamics among processes. By extending the results by Chow and Liu on dependence tree approximations, we show that the best causal dependence tree approximation is the one which maximizes the sum of directed informations on its edges, where best is defined in terms of minimizing the KL-divergence between the original and the approximate distribution. Moreover, we describe a low-complexity algorithm to efficiently pick this approximate distribution.Comment: 9 pages, 15 figure

Directed Information Graphs

We propose a graphical model for representing networks of stochastic processes, the minimal generative model graph. It is based on reduced factorizations of the joint distribution over time. We show that under appropriate conditions, it is unique and consistent with another type of graphical model, the directed information graph, which is based on a generalization of Granger causality. We demonstrate how directed information quantifies Granger causality in a particular sequential prediction setting. We also develop efficient methods to estimate the topological structure from data that obviate estimating the joint statistics. One algorithm assumes upper-bounds on the degrees and uses the minimal dimension statistics necessary. In the event that the upper-bounds are not valid, the resulting graph is nonetheless an optimal approximation. Another algorithm uses near-minimal dimension statistics when no bounds are known but the distribution satisfies a certain criterion. Analogous to how structure learning algorithms for undirected graphical models use mutual information estimates, these algorithms use directed information estimates. We characterize the sample-complexity of two plug-in directed information estimators and obtain confidence intervals. For the setting when point estimates are unreliable, we propose an algorithm that uses confidence intervals to identify the best approximation that is robust to estimation error. Lastly, we demonstrate the effectiveness of the proposed algorithms through analysis of both synthetic data and real data from the Twitter network. In the latter case, we identify which news sources influence users in the network by merely analyzing tweet times.Comment: 41 pages, 15 figure

A controlled study of community-based exercise training in patients with moderate COPD.

BackgroundThe effectiveness of clinic-based pulmonary rehabilitation in advanced COPD is well established, but few data exist for less severe patients treated in alternative settings. The purpose of this study was to investigate whether a novel, community-based exercise program (CBE) was feasible and effective for patients with moderate COPD.MethodsNineteen patients with moderate COPD (mean FEV1 62%) and self-reported exercise impairment were randomized to 12-weeks of progressive endurance and strength training at a local health club under the guidance of a certified personal trainer, or to continuation of unsupervised habitual physical activity. Outcomes assessed at baseline and 12 weeks included session compliance, intensity adherence, treadmill endurance time, muscle strength, dyspnea, and health status.ResultsCompliance was 94% and adherence was 83%. Comparisons between CBE and control groups yielded the following mean (SEM) differences in favor of CBE: endurance time 134 (74) seconds versus -59 (49) seconds (P=0.041) and TDI 5.1 (0.8) versus -0.2 (0.5) (P<0.001). The CBE group increased muscle strength (weight lifted) by 11.8 kilograms per subject per week of training (P<0.001). SGRQ was not significantly changed.ConclusionsWe demonstrated the feasibility and effectiveness of a novel community-based exercise program involving health clubs and personal trainers for patients with moderate COPD.Trial registrationClinicalTrials.gov Identifier NCT01985529

An Advanced, Three-Dimensional Plotting Library for Astronomy

We present a new, three-dimensional (3D) plotting library with advanced features, and support for standard and enhanced display devices. The library - S2PLOT - is written in C and can be used by C, C++ and FORTRAN programs on GNU/Linux and Apple/OSX systems. S2PLOT draws objects in a 3D (x,y,z) Cartesian space and the user interactively controls how this space is rendered at run time. With a PGPLOT inspired interface, S2PLOT provides astronomers with elegant techniques for displaying and exploring 3D data sets directly from their program code, and the potential to use stereoscopic and dome display devices. The S2PLOT architecture supports dynamic geometry and can be used to plot time-evolving data sets, such as might be produced by simulation codes. In this paper, we introduce S2PLOT to the astronomical community, describe its potential applications, and present some example uses of the library.Comment: 12 pages, 10 eps figures (higher resolution versions available from http://astronomy.swin.edu.au/s2plot/paperfigures). The S2PLOT library is available for download from http://astronomy.swin.edu.au/s2plo