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

Health needs of the Roma population in the Czech and Slovak Republics.

In the growing literature on the human rights of Roma people in Central Europe, their relatively poor health status is often mentioned. However, little concrete information exists about the contemporary health status of the Roma in this region. We sought information on the health of the Roma in two of countries with significant Roma minorities, the Czech and Slovak Republics, by means of systematic searches for literature on the health of Roma people published in Czech or Slovak or by authors from the two countries. Published research on health of the Roma population is sparse. The topics that have received attention suggest a focus on concepts of contagion or social Darwinism, indicating a greater concern with the health needs of the majority populations with which they live. What limited evidence exists indicates that the health needs of the Roma population are considerable. With very few exceptions, the health status of Roma is worse than that of non-Roma population in both countries. The burden of communicable disease among Roma is high and diseases associated with poor hygiene seem to be particularly important. Evidence on health care suggests poor communication between Roma and health workers and low uptake of preventative care. The health needs of Roma lack visibility, not only because of the absence of research but also the absence of advocacy on their behalf. Since 1989, Czech and Slovak researchers have largely turned away from health research on particular ethnic groups. This probably reflects a growing sensitivity about stigmatising Roma, but it also makes it difficult to know how their circumstances might be improved. There is a need for further research into the health of Roma people with particular emphasis on non-communicable disease and for interventions that would improve their health

A Robust AFPTAS for Online Bin Packing with Polynomial Migration

In this paper we develop general LP and ILP techniques to find an approximate solution with improved objective value close to an existing solution. The task of improving an approximate solution is closely related to a classical theorem of Cook et al. in the sensitivity analysis for LPs and ILPs. This result is often applied in designing robust algorithms for online problems. We apply our new techniques to the online bin packing problem, where it is allowed to reassign a certain number of items, measured by the migration factor. The migration factor is defined by the total size of reassigned items divided by the size of the arriving item. We obtain a robust asymptotic fully polynomial time approximation scheme (AFPTAS) for the online bin packing problem with migration factor bounded by a polynomial in $\frac{1}{\epsilon}$. This answers an open question stated by Epstein and Levin in the affirmative. As a byproduct we prove an approximate variant of the sensitivity theorem by Cook at el. for linear programs

A PTAS for Bounded-Capacity Vehicle Routing in Planar Graphs

The Capacitated Vehicle Routing problem is to find a minimum-cost set of tours that collectively cover clients in a graph, such that each tour starts and ends at a specified depot and is subject to a capacity bound on the number of clients it can serve. In this paper, we present a polynomial-time approximation scheme (PTAS) for instances in which the input graph is planar and the capacity is bounded. Previously, only a quasipolynomial-time approximation scheme was known for these instances. To obtain this result, we show how to embed planar graphs into bounded-treewidth graphs while preserving, in expectation, the client-to-client distances up to a small additive error proportional to client distances to the depot

Instability and spatiotemporal rheochaos in a shear-thickening fluid model

We model a shear-thickening fluid that combines a tendency to form inhomogeneous, shear-banded flows with a slow relaxational dynamics for fluid microstructure. The interplay between these factors gives rich dynamics, with periodic regimes (oscillating bands, travelling bands, and more complex oscillations) and spatiotemporal rheochaos. These phenomena, arising from constitutive nonlinearity not inertia, can occur even when the steady-state flow curve is monotonic. Our model also shows rheochaos in a low-dimensional truncation where sharply defined shear bands cannot form

Abstract Tensor Systems as Monoidal Categories

The primary contribution of this paper is to give a formal, categorical treatment to Penrose's abstract tensor notation, in the context of traced symmetric monoidal categories. To do so, we introduce a typed, sum-free version of an abstract tensor system and demonstrate the construction of its associated category. We then show that the associated category of the free abstract tensor system is in fact the free traced symmetric monoidal category on a monoidal signature. A notable consequence of this result is a simple proof for the soundness and completeness of the diagrammatic language for traced symmetric monoidal categories.Comment: Dedicated to Joachim Lambek on the occasion of his 90th birthda

First Records for \u3ci\u3eAeshna Sitchensis\u3c/i\u3e (Odonata: Aeshnidae) and \u3ci\u3eEnallagma Clausum\u3c/i\u3e (Odonata: Coenagrionidae), and a Northwestern Record for the State-Endangered \u3ci\u3eSomatochlora Incurvata\u3c/i\u3e (Odonata: Corduliidae) in Wisconsin

While surveying for Odonata in coastal peatlands and associated shoreline areas adjacent to Lake Superior in Wisconsin, we documented populations of two new state record species, the zig-zag darner (Aeshna sitchensis Hagen) and the alkali bluet (Enallagma clausum Morse). We also located a robust population of the state-endangered incurvate emerald (Somatochlora incurvata Walker) at the northwestern edge of the known range of this species. Adults and exuviae of A. sitchensis and S. incurvata were found at an insular fen on Stockton Island, Ashland County, within the Apostle Islands National Lakeshore (AINL). Breeding of both species had occurred in areas of the fen where small pools had dried by summer. Additionally, a single adult male A. sitchensis was collected in the City of Superior in Douglas County. Adult E. clausum were found at two sites: on the Lake Superior beach near the mouth of the Sand River within the AINL in Bayfield County, and along the northeast shore of Allouez Bay in the City of Superior in Douglas County

Factors Affecting the Corporate Decision-Making Process of Air Transport Manufacturers

Fuel economy is a pivotal question influencing the future sale and utilization of commercial aircraft. The NASA Aircraft Energy Efficiency (ACEE) Program Office has a program intended to accelerate the readiness of advanced technologies for energy efficient aircraft. Because the decision to develop a new airframe or engine is a major financial hazard for manufacturers, it is important to know what factors influence the decision making process. A method is described for identifying and ranking individuals and organizations involved at each stage of commercial air transport development, and the barriers that must be overcome in adopting new technologies

Submodular Maximization Meets Streaming: Matchings, Matroids, and More

We study the problem of finding a maximum matching in a graph given by an input stream listing its edges in some arbitrary order, where the quantity to be maximized is given by a monotone submodular function on subsets of edges. This problem, which we call maximum submodular-function matching (MSM), is a natural generalization of maximum weight matching (MWM), which is in turn a generalization of maximum cardinality matching (MCM). We give two incomparable algorithms for this problem with space usage falling in the semi-streaming range---they store only $O(n)$ edges, using $O(n\log n)$ working memory---that achieve approximation ratios of $7.75$ in a single pass and $(3+\epsilon)$ in $O(\epsilon^{-3})$ passes respectively. The operations of these algorithms mimic those of Zelke's and McGregor's respective algorithms for MWM; the novelty lies in the analysis for the MSM setting. In fact we identify a general framework for MWM algorithms that allows this kind of adaptation to the broader setting of MSM. In the sequel, we give generalizations of these results where the maximization is over "independent sets" in a very general sense. This generalization captures hypermatchings in hypergraphs as well as independence in the intersection of multiple matroids.Comment: 18 page

Polarization and readout of coupled single spins in diamond

We study the coupling of a single nitrogen-vacancy center in diamond to a nearby single nitrogen defect at room temperature. The magnetic dipolar coupling leads to a splitting in the electron spin resonance frequency of the nitrogen-vacancy center, allowing readout of the state of a single nitrogen electron spin. At magnetic fields where the spin splitting of the two centers is the same we observe a strong polarization of the nitrogen electron spin. The amount of polarization can be controlled by the optical excitation power. We combine the polarization and the readout in time-resolved pump-probe measurements to determine the spin relaxation time of a single nitrogen electron spin. Finally, we discuss indications for hyperfine-induced polarization of the nitrogen nuclear spin