On the Cost of Essentially Fair Clusterings

Clustering is a fundamental tool in data mining. It partitions points into groups (clusters) and may be used to make decisions for each point based on its group. However, this process may harm protected (minority) classes if the clustering algorithm does not adequately represent them in desirable clusters -- especially if the data is already biased. At NIPS 2017, Chierichetti et al. proposed a model for fair clustering requiring the representation in each cluster to (approximately) preserve the global fraction of each protected class. Restricting to two protected classes, they developed both a 4-approximation for the fair $k$-center problem and a $O(t)$-approximation for the fair $k$-median problem, where $t$ is a parameter for the fairness model. For multiple protected classes, the best known result is a 14-approximation for fair $k$-center. We extend and improve the known results. Firstly, we give a 5-approximation for the fair $k$-center problem with multiple protected classes. Secondly, we propose a relaxed fairness notion under which we can give bicriteria constant-factor approximations for all of the classical clustering objectives $k$-center, $k$-supplier, $k$-median, $k$-means and facility location. The latter approximations are achieved by a framework that takes an arbitrary existing unfair (integral) solution and a fair (fractional) LP solution and combines them into an essentially fair clustering with a weakly supervised rounding scheme. In this way, a fair clustering can be established belatedly, in a situation where the centers are already fixed

A Constant Approximation for Colorful k-Center

In this paper, we consider the colorful k-center problem, which is a generalization of the well-known k-center problem. Here, we are given red and blue points in a metric space, and a coverage requirement for each color. The goal is to find the smallest radius rho, such that with k balls of radius rho, the desired number of points of each color can be covered. We obtain a constant approximation for this problem in the Euclidean plane. We obtain this result by combining a "pseudo-approximation" algorithm that works in any metric space, and an approximation algorithm that works for a special class of instances in the plane. The latter algorithm uses a novel connection to a certain matching problem in graphs

Evaluation of Hungarian Wines for Resveratrol by Overpressured Layer Chromatography

A method, including solid phase extraction sample preparation, overpressured layer chromatographic separation and subsequent densitometric evaluation, was developed for measurement of total resveratrol (cis- and trans-isomers) content of wine. The amount of resveratrol was determined in wine samples from different winemaking regions of Hungary. The total resveratrol was high in Hungarian red wines (3.6–11 mg/L), and much lower in white ones (0.04–1.5 mg/L)

Prepare for the Expected Worst: Algorithms for Reconfigurable Resources Under Uncertainty

In this paper we study how to optimally balance cheap inflexible resources with more expensive, reconfigurable resources despite uncertainty in the input problem. Specifically, we introduce the MinEMax model to study "build versus rent" problems. In our model different scenarios appear independently. Before knowing which scenarios appear, we may build rigid resources that cannot be changed for different scenarios. Once we know which scenarios appear, we are allowed to rent reconfigurable but expensive resources to use across scenarios. Although computing the objective in our model might seem to require enumerating exponentially-many possibilities, we show it is well estimated by a surrogate objective which is representable by a polynomial-size LP. In this surrogate objective we pay for each scenario only to the extent that it exceeds a certain threshold. Using this objective we design algorithms that approximately-optimally balance inflexible and reconfigurable resources for several NP-hard covering problems. For example, we study variants of minimum spanning and Steiner trees, minimum cuts, and facility location. Up to constants, our approximation guarantees match those of previously-studied algorithms for demand-robust and stochastic two-stage models. Lastly, we demonstrate that our problem is sufficiently general to smoothly interpolate between previous demand-robust and stochastic two-stage problems

Application of STARFLEET Velocimetry in the NASA Langley 0.3-Meter Transonic Cryogenic Tunnel

Selective two-photon absorptive resonance femtosecond laser electronic excitation tagging (STARFLEET) velocimetry is demonstrated for the first time in a NASA Langley wind tunnel with high repetition-rate and single-shot imaging. Experiments performed in the 0.3-meter Transonic Cryogenic Tunnel (TCT) allowed for testing at 300 K over a range of pressures (124 to 517 kPa) and Mach numbers (0.2-0.8) for freestream conditions and flow behind a cylindrical model. Measurement precision and accuracy are determined for the current set of experiments, as are signal intensity and lifetime. Precisions of 3-5 m/s (based on one standard deviation) were typical in the experiment; precisions better than 2% of the mean velocity were obtained for some of the highest velocity conditions. Agreement within a mean error of 3 m/s between STARFLEET freestream velocity measurements and facility DAS readings is demonstrated. STARFLEET is also shown to return spatially-resolved velocity profiles, though some binning of the signal is required

Probing dense QCD matter in the laboratory: The CBM experiment at FAIR

The Facility for Antiproton and Ion Research (FAIR) in Darmstadt will provide unique research opportunities for the investigation of fundamental open questions related to nuclear physics and astrophysics, including the exploration of QCD matter under extreme conditions, which governs the structure and dynamics of cosmic objects and phenomena like neutron stars, supernova explosions, and neutron star mergers. The physics program of the Compressed Baryonic Matter (CBM) experiment is devoted to the production and investigation of dense nuclear matter, with a focus on the high-density equation-of-state (EOS), and signatures for new phases of dense QCD matter. According to the present schedule, the CBM experiment will receive the first beams from the FAIR accelerators in 2025. This article reviews promising observables, outlines the CBM detector system, and presents results of physics performance studies.Comment: 16 pages, 13 figures. Physica Scripta 202