Prophet Inequalities with Limited Information

In the classical prophet inequality, a gambler observes a sequence of stochastic rewards $V_1,...,V_n$ and must decide, for each reward $V_i$, whether to keep it and stop the game or to forfeit the reward forever and reveal the next value $V_i$. The gambler's goal is to obtain a constant fraction of the expected reward that the optimal offline algorithm would get. Recently, prophet inequalities have been generalized to settings where the gambler can choose $k$ items, and, more generally, where he can choose any independent set in a matroid. However, all the existing algorithms require the gambler to know the distribution from which the rewards $V_1,...,V_n$ are drawn. The assumption that the gambler knows the distribution from which $V_1,...,V_n$ are drawn is very strong. Instead, we work with the much simpler assumption that the gambler only knows a few samples from this distribution. We construct the first single-sample prophet inequalities for many settings of interest, whose guarantees all match the best possible asymptotically, \emph{even with full knowledge of the distribution}. Specifically, we provide a novel single-sample algorithm when the gambler can choose any $k$ elements whose analysis is based on random walks with limited correlation. In addition, we provide a black-box method for converting specific types of solutions to the related \emph{secretary problem} to single-sample prophet inequalities, and apply it to several existing algorithms. Finally, we provide a constant-sample prophet inequality for constant-degree bipartite matchings. We apply these results to design the first posted-price and multi-dimensional auction mechanisms with limited information in settings with asymmetric bidders

El Paso/Yslete schools Get-Away Special Space Shuttle student projects

Student projects for the Get Away Special (GAS) space shuttle program were summarized. Experimental topics included: seed germination, shrimp growth, liquid lasers, planaria regeneration, fluid dynamics (wicking), soil molds, antibiotics, crystallization, the symbiosis of yeast and fungi, and the performance of electronic chips. A brief experimental design is included for each project

Imaging Techniques for Detecting Breast Cancer: Survey and Perspectives

Breast cancer is the most commonly diagnosed cancer and the second leading cause of cancer death among women in America. A few years ago, the odds of developing breast cancer were reported as 1 in 13. Now the chance is 1 in 9. The only way today to find out for sure if a breast lump or abnormal tissue is cancer, is by having a biopsy: A suspicious tissue is removed by a surgical excision or needle biopsy and is examined under a microscope by a pathologist who makes the diagnosis. Imaging techniques of the breast are therefore vital since they will allow early detection of cancer, and localization of the suspicious lesion in the breast for a biopsy procedure

Multiattribute Decision-Making: Use of Three Scoring Methods to Compare the Performance of Imaging Techniques for Breast Cancer Detection

Multiple Attribute Decision Making (MADM) involves making preference decisions (such as evaluation, prioritization, selection) over the available alternatives that are characterized by multiple, usually conflicting, attributes . The problems of MADM are diverse, and can be found in virtually any topic. In this paper, we use three different scoring methods for evaluating the performance of different imaging techniques used to detect cancers in the female breast. The need for such a decision support system arises from the fact that each of the several techniques which helps diagnose breast cancer today, has its own specific characteristics, advantages and drawbacks. These characteristics or attributes are generally conflicting. The goal is to detect as many malignant lesions in the breast as is possible, while identifying the maximum number of benign lesions. The four imaging techniques that are compared here are Magnetic Resonance Imaging (MRI), Mammography, Ultrasonography, and Nuclear Medicine. The three different multiattribute scoring methods are the Simple Additive Weighting method (SAW), the Weighted Product Method (WPM), and the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). The three methods are described in detail, and then used to rank the four imaging techniques. The results are analyzed and the validity and robustness of the methods are tested using post-evaluation analysis

The effect of worry and rumination on cognitive abilities with considering role of mediating role of emotional intelligence

Background and aims: The cognitive abilities were included functions such as planning, attention, response inhibition, problem solving and cognitive flexibility. The aim of the present study was to investigate effects of worry and rumination on cognitive abilities based on emotional intelligence. Methods: The present study was a correlational and cross-sectional research. For this purpose, from the statistical population of the urmia University students, 340 were selected by multi-stage cluster random sampling. Then, the worry, rumination, emotional intelligence and cognitive abilities questionnaire were distributed among research participants to respond. Collected data were analyzed by using descriptive and correlational indicators, and structural equation modeling. Results: Results indicated that there is a significant negative correlation between worry and rumination and a positive correlation between emotional intelligence with cognitive abilities. Also, path analysis model indicated mediating role of emotional intelligence between worry and rumination with cognitive abilities. Conclusion: The results support the hypothesis that worry and rumination lead to disruption of cognitive abilities and high emotional intelligence can have a moderating role in this regard

Online Makespan Minimization with Parallel Schedules

In online makespan minimization a sequence of jobs $\sigma = J_1,..., J_n$ has to be scheduled on $m$ identical parallel machines so as to minimize the maximum completion time of any job. We investigate the problem with an essentially new model of resource augmentation. Here, an online algorithm is allowed to build several schedules in parallel while processing $\sigma$. At the end of the scheduling process the best schedule is selected. This model can be viewed as providing an online algorithm with extra space, which is invested to maintain multiple solutions. The setting is of particular interest in parallel processing environments where each processor can maintain a single or a small set of solutions. We develop a (4/3+\eps)-competitive algorithm, for any 0<\eps\leq 1, that uses a number of 1/\eps^{O(\log (1/\eps))} schedules. We also give a (1+\eps)-competitive algorithm, for any 0<\eps\leq 1, that builds a polynomial number of (m/\eps)^{O(\log (1/\eps) / \eps)} schedules. This value depends on $m$ but is independent of the input $\sigma$. The performance guarantees are nearly best possible. We show that any algorithm that achieves a competitiveness smaller than 4/3 must construct $\Omega(m)$ schedules. Our algorithms make use of novel guessing schemes that (1) predict the optimum makespan of a job sequence $\sigma$ to within a factor of 1+\eps and (2) guess the job processing times and their frequencies in $\sigma$. In (2) we have to sparsify the universe of all guesses so as to reduce the number of schedules to a constant. The competitive ratios achieved using parallel schedules are considerably smaller than those in the standard problem without resource augmentation

Increasing gland number and red pigments in St. John’s wort in vitro

In order to develop a protocol for increasing the gland number and red pigments of Hypericum perforatum, this study was carried out to evaluate the effect of hydrolyzed casein (0.0 and 500 mg l-1), mannitol (0.0, 5 and10 g l-1) and sucrose (20 and 30 g l-1) on the synthesis of these pigments and glands on the produced leaves. Leaf discs of in vitro plantlets, were prepared and cultured on MS medium with 0.5 mg l-1 BAP to induce the shoot. All the cultures were incubated in the dark at 25 ± 2°C for 1 month. In all of the treatments, callus and shoot induction were observed. Percentage of calli and leaves containing red pigments, number of glands and percentage of leaves containing gland were noted as indicating the presence of hypericin and pseudohypericin pigments. Percentage of calli and leaves containing red pigments were significantly influenced by different concentrations of the hydrolyzed casein, mannitol and sucrose. The highest percentage of calli containing red pigments was observed in the culture medium which had 500 or 0.0 mg l-1 hydrolyzed casein and 20 g l-1 sucrose, without mannitol. Glands were observed on all the produced leaves. Number of glands and percentage of leaves containing gland were significantly influenced by the different concentrations of mannitol and sucrose and their interaction. The highest number of gland and percentage of leaves containing gland was achieved when explants were cultured in medium that included 30 g l-1 sucrose with 5 or 10 g l-1 mannitol and in medium containing 20 g l-1 sucrose, with 5 g l-1 mannitol. Morphological changes induced by carbon source and hydrolyzed casein were observed and described in detail. The obtained results will be applied in experimental botany and in the technology of H. perforatum cultivation for pharmaceutical applications.Key words: Hydrolyzed casein, hypericin, Hypericum perforatum, mannitol, pseudohypericin, sucrose