Approximation Algorithms for Correlated Knapsacks and Non-Martingale Bandits

In the stochastic knapsack problem, we are given a knapsack of size B, and a set of jobs whose sizes and rewards are drawn from a known probability distribution. However, we know the actual size and reward only when the job completes. How should we schedule jobs to maximize the expected total reward? We know O(1)-approximations when we assume that (i) rewards and sizes are independent random variables, and (ii) we cannot prematurely cancel jobs. What can we say when either or both of these assumptions are changed? The stochastic knapsack problem is of interest in its own right, but techniques developed for it are applicable to other stochastic packing problems. Indeed, ideas for this problem have been useful for budgeted learning problems, where one is given several arms which evolve in a specified stochastic fashion with each pull, and the goal is to pull the arms a total of B times to maximize the reward obtained. Much recent work on this problem focus on the case when the evolution of the arms follows a martingale, i.e., when the expected reward from the future is the same as the reward at the current state. What can we say when the rewards do not form a martingale? In this paper, we give constant-factor approximation algorithms for the stochastic knapsack problem with correlations and/or cancellations, and also for budgeted learning problems where the martingale condition is not satisfied. Indeed, we can show that previously proposed LP relaxations have large integrality gaps. We propose new time-indexed LP relaxations, and convert the fractional solutions into distributions over strategies, and then use the LP values and the time ordering information from these strategies to devise a randomized adaptive scheduling algorithm. We hope our LP formulation and decomposition methods may provide a new way to address other correlated bandit problems with more general contexts

The Brownian Web: Characterization and Convergence

The Brownian Web (BW) is the random network formally consisting of the paths of coalescing one-dimensional Brownian motions starting from every space-time point in ${\mathbb R}\times{\mathbb R}$. We extend the earlier work of Arratia and of T\'oth and Werner by providing characterization and convergence results for the BW distribution, including convergence of the system of all coalescing random walkssktop/brownian web/finale/arXiv submits/bweb.tex to the BW under diffusive space-time scaling. We also provide characterization and convergence results for the Double Brownian Web, which combines the BW with its dual process of coalescing Brownian motions moving backwards in time, with forward and backward paths ``reflecting'' off each other. For the BW, deterministic space-time points are almost surely of ``type'' $(0,1)$ -- {\em zero} paths into the point from the past and exactly {\em one} path out of the point to the future; we determine the Hausdorff dimension for all types that actually occur: dimension 2 for type $(0,1)$, 3/2 for $(1,1)$ and $(0,2)$, 1 for $(1,2)$, and 0 for $(2,1)$ and $(0,3)$.Comment: 52 pages with 4 figure

Antimicrobial efficacy of plant essential oils and extracts against Escherichia coli

The efficacies of 11 plant-derived antimicrobials were evaluated against Escherichia coli in vitro in solution at room temperature. These included lemongrass, cinnamon, and oregano essential oils and their active components (citral, cinnamaldehyde, and carvacrol, respectively). Allspice and clove bud oils and olive, green tea, and grape seed extracts were also studied. The efficacies of the antimicrobials were both concentration- and exposure time-dependent. The essential oils and their active components demonstrated statistically significant >5.0-log10 reductions within 1-10 min. The plant extracts were less effective; green tea and grape seed extracts required 24 h before significant reductions were observed (1.93-log10 and 5.05-log10, respectively). Nevertheless, olive extract exhibited a reduction of ∼5-log10 within 30 min. Most of these plant-derived compounds exhibited strong bactericidal activity and can potentially be applied as alternatives to chemicals for foods/food contact surfaces since they are generally recognized as safe (GRAS) for human consumption. They may also be useful in applications in which other antimicrobials have reduced efficacy (e.g., in the presence of organics) or used with sensitive populations that are unable to tolerate exposure to harsher chemicals (e.g., elderly care facilities). These compounds could be used alone, in combination, or with fast-acting antimicrobials to provide a long-lasting residual.United States Department of Agriculture [2010-51300-21760]12 month embargo; published online: 1 March 2019This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

Mango Breeding in India - Past and Future

The mango (Mangifera indica L.) is one of the most important tropical fruits of India in which improvement has been attempted since the early 20th Century. The species, M. indica, having originated in India, has a large diversity within the country. Extensive surveys have located several wild species of importance, many of them figuring in the IUCN Red List. Conservation and evaluation of these species, as well as the large seedling diversity, needs attention as these could be a source for important traits. Strategies of in situ, ex situ and 'onfarm' conservation should from a priority at this juncture. Hybridization has resulted in several hybrids. Widening of genetic base in polyembryonic varieties and identification of zygotic embryos through markers is the need of the hour for utilization in breeding programmes. Although several of these have not become popular, they can be very well used as pre-breeding lines. Use of molecular markers for selection will greatly reduce time taken for developing improved varieties. Strategies other than hybridization, viz., selection among open-pollinated progenies, should be adopted for identifying better recombinants, as, a large number of progenies are available in this method