On Colorful Bin Packing Games

We consider colorful bin packing games in which selfish players control a set of items which are to be packed into a minimum number of unit capacity bins. Each item has one of $m\geq 2$ colors and cannot be packed next to an item of the same color. All bins have the same unitary cost which is shared among the items it contains, so that players are interested in selecting a bin of minimum shared cost. We adopt two standard cost sharing functions: the egalitarian cost function which equally shares the cost of a bin among the items it contains, and the proportional cost function which shares the cost of a bin among the items it contains proportionally to their sizes. Although, under both cost functions, colorful bin packing games do not converge in general to a (pure) Nash equilibrium, we show that Nash equilibria are guaranteed to exist and we design an algorithm for computing a Nash equilibrium whose running time is polynomial under the egalitarian cost function and pseudo-polynomial for a constant number of colors under the proportional one. We also provide a complete characterization of the efficiency of Nash equilibria under both cost functions for general games, by showing that the prices of anarchy and stability are unbounded when $m\geq 3$ while they are equal to 3 for black and white games, where $m=2$. We finally focus on games with uniform sizes (i.e., all items have the same size) for which the two cost functions coincide. We show again a tight characterization of the efficiency of Nash equilibria and design an algorithm which returns Nash equilibria with best achievable performance

Order Selection Problems in Hiring Pipelines

Motivated by hiring pipelines, we study two order selection problems in which applicants for a finite set of positions must be interviewed or made offers sequentially. There is a finite time budget for interviewing or making offers, and a stochastic realization after each decision, leading to computationally-challenging problems. In the first problem we study sequential interviewing, and show that a computationally-tractable, non-adaptive policy that must make offers immediately after interviewing is approximately optimal, assuming offerees always accept their offers. In the second problem, we assume that applicants have already been interviewed but only accept offers with some probability; we develop a computationally-tractable policy that makes offers for the different positions in parallel, which is approximately optimal even relative to a policy that does not need to make parallel offers. Our two results both generalize and improve the guarantees in the work of Purohit et al. on hiring algorithms, from 1/2 and 1/4 to approximation factors that are at least 1-1/e

Food Environment, Built Environment, and Women\u27s BMI: Evidence from Erie County, New York

The authors present the results of a neighborhood-scaled exploratory study that tests the association of the food environment and the built environment with women’s body mass index (BMI) in Erie County, New York. The proximity of women’s homes to a supermarket relative to a convenience store is associated with lower BMI. A diverse land use mix in a neighborhood is positively associated with women’s BMI, especially when restaurants dominate nonresidential land use. The article offers suggestions for how food environments may be improved using planning strategies

Reexamination of silicon effects on rice growth and production under field conditions using a low silicon mutant

Silicon (Si) is a beneficial element for healthy growth and high and sustainable production of rice, but the mode of action of the beneficial effects has not been well understood. We carried out field trials for four years at two different locations to re-examine the effects of Si on the growth and production of rice using a low silicon rice (lsi1) mutant. The mutant accumulated much lower Si at each growth stage compared with the wild-type rice (Oryza sativa L. cv Oochikara), but there was no difference in the accumulation of other nutrients including N, P, and K. Measurements at different growth stages showed that low Si in the mutant hardly affected the tiller number, chlorophyll content (SPAD value), and root growth. The plant height and shoot dry weight of the wild-type rice were slightly higher than those of the mutant at a later growth stage, but the difference was not significant between the two lines. However, grain yield was reduced by 79-98%, depending on year, due to a low Si accumulation in the mutant, which showed the largest effect of Si on rice production among all studies reported so far. Among the yield components, the percentage of filled spikelets was mostly affected, being only 13.9% of the wild-type rice in the mutant. The grain color of the mutant became brown because of excessive transpiration and infection of pathogens. These results indicate that Si increases rice yield mainly by enhancing the fertility of spikelets.</p

Halo bias in the excursion set approach with correlated steps

In the Excursion Set approach, halo abundances and clustering are closely related. This relation is exploited in many modern methods which seek to constrain cosmological parameters on the basis of the observed spatial distribution of clusters. However, to obtain analytic expressions for these quantities, most Excursion Set based predictions ignore the fact that, although different k-modes in the initial Gaussian field are uncorrelated, this is not true in real space: the values of the density field at a given spatial position, when smoothed on different real-space scales, are correlated in a nontrivial way. We show that when the excursion set approach is extended to include such correlations, then one must be careful to account for the fact that the associated prediction for halo bias is explicitly a real-space quantity. Therefore, care must be taken when comparing the predictions of this approach with measurements in simulations, which are typically made in Fourier-space. We show how to correct for this effect, and demonstrate that ignorance of this effect in recent analyses of halo bias has led to incorrect conclusions and biased constraints.Comment: 7 pages, 3 figures; v2 -- minor clarifications, accepted in MNRA

Task-driven assessment of experimental designs in diffusion MRI: A computational framework

This paper proposes a task-driven computational framework for assessing diffusion MRI experimental designs which, rather than relying on parameter-estimation metrics, directly measures quantitative task performance. Traditional computational experimental design (CED) methods may be ill-suited to experimental tasks, such as clinical classification, where outcome does not depend on parameter-estimation accuracy or precision alone. Current assessment metrics evaluate experiments’ ability to faithfully recover microstructural parameters rather than their task performance. The method we propose addresses this shortcoming. For a given MRI experimental design (protocol, parameter-estimation method, model, etc.), experiments are simulated start-to-finish and task performance is computed from receiver operating characteristic (ROC) curves and associated summary metrics (e.g. area under the curve (AUC)). Two experiments were performed: first, a validation of the pipeline’s task performance predictions against clinical results, comparing in-silico predictions to real-world ROC/AUC; and second, a demonstration of the pipeline’s advantages over traditional CED approaches, using two simulated clinical classification tasks. Comparison with clinical datasets validates our method’s predictions of (a) the qualitative form of ROC curves, (b) the relative task performance of different experimental designs, and (c) the absolute performance (AUC) of each experimental design. Furthermore, we show that our method outperforms traditional task-agnostic assessment methods, enabling improved, more useful experimental design. Our pipeline produces accurate, quantitative predictions of real-world task performance. Compared to current approaches, such task-driven assessment is more likely to identify experimental designs that perform well in practice. Our method is not limited to diffusion MRI; the pipeline generalises to any task-based quantitative MRI application, and provides the foundation for developing future task-driven end-to end CED frameworks

Identification of Maize Silicon Influx Transporters

Maize (Zea mays L.) shows a high accumulation of silicon (Si), but transporters involved in the uptake and distribution have not been identified. In the present study, we isolated two genes (ZmLsi1 and ZmLsi6), which are homologous to rice influx Si transporter OsLsi1. Heterologous expression in Xenopus laevis oocytes showed that both ZmLsi1 and ZmLsi6 are permeable to silicic acid. ZmLsi1 was mainly expressed in the roots. By contrast, ZmLsi6 was expressed more in the leaf sheaths and blades. Different from OsLsi1, the expression level of both ZmLsi1 and ZmLsi6 was unaffected by Si supply. Immunostaining showed that ZmLsi1 was localized on the plasma membrane of the distal side of root epidermal and hypodermal cells in the seminal and crown roots, and also in cortex cells in lateral roots. In the shoots, ZmLsi6 was found in the xylem parenchyma cells that are adjacent to the vessels in both leaf sheaths and leaf blades. ZmLsi6 in the leaf sheaths and blades also exhibited polar localization on the side facing towards the vessel. Taken together, it can be concluded that ZmLsi1 is an influx transporter of Si, which is responsible for the transport of Si from the external solution to the root cells and that ZmLsi6 mainly functions as a Si transporter for xylem unloading

Remarks on the naturality of quantization

Hamiltonian quantization of an integral compact symplectic manifold M depends on a choice of compatible almost complex structure J. For open sets U in the set of compatible almost complex structures and small enough values of Planck's constant, the Hilbert spaces of the quantization form a bundle over U with a natural connection. In this paper we examine the dependence of the Hilbert spaces on the choice of J, by computing the semi-classical limit of the curvature of this connection. We also show that parallel transport provides a link between the action of the group Symp(M) of symplectomorphisms of M and the Schrodinger equation.Comment: 20 page

Postprocessing for quantum random number generators: entropy evaluation and randomness extraction

Quantum random-number generators (QRNGs) can offer a means to generate information-theoretically provable random numbers, in principle. In practice, unfortunately, the quantum randomness is inevitably mixed with classical randomness due to classical noises. To distill this quantum randomness, one needs to quantify the randomness of the source and apply a randomness extractor. Here, we propose a generic framework for evaluating quantum randomness of real-life QRNGs by min-entropy, and apply it to two different existing quantum random-number systems in the literature. Moreover, we provide a guideline of QRNG data postprocessing for which we implement two information-theoretically provable randomness extractors: Toeplitz-hashing extractor and Trevisan's extractor.Comment: 13 pages, 2 figure