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]

War of hormones over resource allocation to seeds: strategies and counter-strategies of offspring and maternal parent

It is suggested that maternal parent and offspring have conflicting interests over the extent of resource allocation to developing seeds. While maternal parent would be selected to allocate her resources optimally among her offspring, the latter would be selected to demand more. In animals, offspring are known to demand additional resources either visibly (through intense vocal calls) or subtly through the production of hormones. In plants though parent offspring conflict over resource allocation has been invoked, the mechanism through which the parent and offspring interact in regulating resource allocation into developing seeds is not yet clear. In this paper, we propose that the strategies and counter-strategies of the offspring and mother during the development of seeds might be manifested through the production of appropriate growth hormones. Accordingly, we predict (i) hormones that mobilize resources into seeds (e.g. auxins and gibberellic acid) shall be synthesized exclusively by the offspring tissue and (ii) hormones that inhibit resource flow in to seeds (e.g. abscisic acid) be produced exclusively by the maternal tissue. We show that these predictions are supported by existing literature on the temporal dynamics and source of production of growth hormones during seed development. Finally, we suggest that such analysis viewing the production of different hormones during early seed development, as strategies and counter-strategies of mother and offspring tissue, helps ofer a meaningful interpretation of the otherwise complex dynamics of hormone fluxes

Varate Giduga (Acc. No. 21067; IC No. 418238) : A unique mango (Mangifera indica L.) variety

Varate Giduga is one of the unique variety from Sirsi region of Karnataka. The tree is Semi-circular shaped with dense foliage, leaves about 25cm long; dark green in colour with wavy margin. It is a very consistent and heavy producer. The fruit of this tree matures by mid-April and fruit has a distinctive yellow skin color on fruit exposed to the sun. The fruit shape is round, fruit weight ranged from 350-400 g, fruit length was 9.8 cm, fruit diameter was 9.2 cm, fruit thickness was 8.0cm and bisexual flowers were 16.53%. Biochemical constituents such as the total phenols (317.50 mg/100 g), flavonoids (5.79 mg/100g), carotenoids (1.46 mg/100 g) and acidity (0.19%) were recorded which suggests that these characters are unique as compared to other varieties. The fruit skin is rough and glossy in appearance and the fruit has little or no fiber. It is very delicious in taste with high pulp percentage (74.0%) and high TSS (23.4º B). The flesh color is orange. The fruits have deep orange firm pulp and very sweet with pleasant flavor. Besides,several other traits have drawn special attention to this mango variety as it has large sized fruits (Fig-1), late variety with very good taste, fruit can be cut into two halves by retaining the stone in one half, regular bearer and fruit fly resistant genotype because of its thick peel and high phenolic content in pulp (317.50 mg/100 g)

Effect of pretreatment with chromium picolinate on haematological parameters during dengue virus infection in mice

Background & objectives: Dengue virus (DV) has caused severe epidemics of dengue fever (DF) and dengue haemorrhagic fever (DHF) and is endemic all over India. We have earlier reported that exposure of mice to hexavalent chromium [Cr(VI)] compounds increased the severity of dengue virus infection. Trivalent chromium picolinate (CrP) is used worldwide as micronutrient and nutritional supplement. The present study was therefore, carried out to investigate the effects of CrP on various haematological parameters during DV infection of mice. Methods: The Swiss Albino smice were inoculated with dengue virus (1000 LD50, intracerebrally) and fed with chromium picolinate (CrP) in drinking water (100 and 250 mg/l) for 24 wk. Peripheral blood leucocytes and other haematological parameters, and spleens were studied on days 4 and 8 after virus inoculations and the findings were compared with those given only CrP and the normal control age matched mice. Results: CrP in drinking water for 24 wk had no significant effects on peripheral blood cells of mice. On the other hand, there was significant decrease in different haematological parameters following inoculation of normal mice with DV. In CrP fed mice the effects of DV infection were abolished on most of the haematological parameters. Interpretation & conclusions: The findings of present study showed that the adverse effects of DV infection, specially on platelets and leucocytes, were abrogated by pretreatment of mice with CrP. The therapeutic utility of CrP in viral infections including dengue needs to be studied in depth