On Conceptually Simple Algorithms for Variants of Online Bipartite Matching

We present a series of results regarding conceptually simple algorithms for bipartite matching in various online and related models. We first consider a deterministic adversarial model. The best approximation ratio possible for a one-pass deterministic online algorithm is $1/2$, which is achieved by any greedy algorithm. D\"urr et al. recently presented a $2$-pass algorithm called Category-Advice that achieves approximation ratio $3/5$. We extend their algorithm to multiple passes. We prove the exact approximation ratio for the $k$-pass Category-Advice algorithm for all $k \ge 1$, and show that the approximation ratio converges to the inverse of the golden ratio $2/(1+\sqrt{5}) \approx 0.618$ as $k$ goes to infinity. The convergence is extremely fast --- the $5$-pass Category-Advice algorithm is already within $0.01\%$ of the inverse of the golden ratio. We then consider a natural greedy algorithm in the online stochastic IID model---MinDegree. This algorithm is an online version of a well-known and extensively studied offline algorithm MinGreedy. We show that MinDegree cannot achieve an approximation ratio better than $1-1/e$, which is guaranteed by any consistent greedy algorithm in the known IID model. Finally, following the work in Besser and Poloczek, we depart from an adversarial or stochastic ordering and investigate a natural randomized algorithm (MinRanking) in the priority model. Although the priority model allows the algorithm to choose the input ordering in a general but well defined way, this natural algorithm cannot obtain the approximation of the Ranking algorithm in the ROM model

Magnetopause stand-off distance in dependence on the magnetosheath and solar wind parameters

International audienceA model of the magnetosheath structure proposed in a recent paper from the authors is extended to estimate the magnetopause stand-off distance from solar wind data. For this purpose, the relationship of the magnetopause location to the magnetosheath and solar wind parameters is studied. It is shown that magnetopause erosion may be explained in terms of the magnetosheath magnetic field penetration into the magnetosphere. The coefficient of penetration (the ratio of the magnetospheric magnetic field depression to the intensity of the magnetosheath magnetic field Bm?z=?Bmsin2?/2, is estimated and found approximately to equal 1. It is shown that having combined a magnetosheath model presented in an earlier paper and the magnetosheath field penetration model presented in this paper, it is possible to predict the magnetopause stand-off distance from solar wind parameters

Test-retest reliability of temporal and spatial gait characteristics measured with an instrumented walkway system (GAITRite(®))

BACKGROUND: The purpose of this study was to determine the test-retest reliability of temporal and spatial gait measurements over a one-week period as measured using an instrumented walkway system (GAITRite(®)). METHODS: Subjects were tested on two occasions one week apart. Measurements were made at preferred and fast walking speeds using the GAITRite(® )system. Measurements tested included walking speed, step length, stride length, base of support, step time, stride time, swing time, stance time, single and double support times, and toe in-toe out angle. RESULTS: Twenty-one healthy subjects participated in this study. The group consisted of 12 men and 9 women, with an average age of 34 years (range: 19 – 59 years). At preferred walking speed, all gait measurements had ICC's of 0.92 and higher, except base of support which had an ICC of 0.80. At fast walking speed all gait measurements had ICC's above 0.89 except base of support (ICC = 0.79), CONCLUSIONS: Spatial-temporal gait measurements demonstrate good to excellent test-retest reliability over a one-week time span

Laser structuring of NMC 811 high energy electrodes in battery production for enhancing the electrochemical performance for xEV energy storage systems

Layered oxide cathodes, especially thick-film electrodes like lithium nickel manganese cobalt oxide, NMC, are under continuously investigation to meet the ambitious requirements, e.g. 700 Wh/l, for future Li-ion batteries in electric drive applications. The objective of the most current studies is to reduce the Co content with a concurrent increasing Ni-content in the NMC cathodes such as NMC 811 [1]. It must not leave the fact out of consideration, that NMC cathodes suffer from low high rate capability and corresponding low capacity retention at high C-rates. In particular, the negative impact is even higher for thick-film high energy cathodes. To counteract the negative effect, high repetition ultrafast laser ablation is applied to create appropriate 3D electrode designs [2]. New Li+-diffusion pathways, applied by the laser structuring process, shell enhance electrolyte wettability and reduce overpotentials at high C-rates. It is attempted to integrate the laser structuring into a continuous roll-to-roll electrode production process. In this way, the positive properties achieved through 3D structuring can also be obtained for Li-ion batteries that are produced on a large scale. By using this novel production technology, future NMC batteries can be produced with improved performance characteristics for xEV applications. Furthermore, this technology can also be applied for other generation 3b battery cells. This work is performed under the frame of the RealLi! project, in which the following aspects are covered: a) Development of thick film NMC811 electrodes with high areal capacity b) Passivation approach to improve cycle stability and lifetime c) Cell Assembly and electrochemical characterization d) Holistic evaluation of the potential environmental impact of the NMC811 cells via life cycle assessment e) An experimentally validated electrochemical model to describe electrode structures and their optimization. f) Improved electrochemical performance of NMC811 electrodes on a laboratory scale by using 3D laser structuring. g) Scale up of the 3D laser structuring process and corresponding improved electrochemical performance of NMC811 electrodes in pouch cell format by using 3D laser ablation

Bone stress injury of the ankle in professional ballet dancers seen on MRI

<p>Abstract</p> <p>Background</p> <p>Ballet Dancers have been shown to have a relatively high incidence of stress fractures of the foot and ankle. It was our objective to examine MR imaging patterns of bone marrow edema (BME) in the ankles of high performance professional ballet dancers, to evaluate clinical relevance.</p> <p>Methods</p> <p>MR Imaging was performed on 12 ankles of 11 active professional ballet dancers (6 female, 5 male; mean age 24 years, range 19 to 32). Individuals were imaged on a 0.2 T or 1.5 T MRI units. Images were evaluated by two musculoskeletal radiologists and one orthopaedic surgeon in consensus for location and pattern of bone marrow edema. In order to control for recognized sources of bone marrow edema, images were also reviewed for presence of osseous, ligamentous, tendinous and cartilage injuries. Statistical analysis was performed to assess the strength of the correlation between bone marrow edema and ankle pain.</p> <p>Results</p> <p>Bone marrow edema was seen only in the talus, and was a common finding, observed in nine of the twelve ankles imaged (75%) and was associated with pain in all cases. On fluid-sensitive sequences, bone marrow edema was ill-defined and centered in the talar neck or body, although in three cases it extended to the talar dome. No apparent gender predilection was noted. No occult stress fracture could be diagnosed. A moderately strong correlation (phi = 0.77, p= 0.0054) was found between edema and pain in the study population.</p> <p>Conclusion</p> <p>Bone marrow edema seems to be a specific MRI finding in the talus of professional ballet dancers, likely related to biomechanical stress reactions, due to their frequently performed unique maneuvers. Clinically, this condition may indicate a sign of a bone stress injury of the ankle.</p

Phase transitions for PP-adic Potts model on the Cayley tree of order three

In the present paper, we study a phase transition problem for the $q$-state $p$-adic Potts model over the Cayley tree of order three. We consider a more general notion of $p$-adic Gibbs measure which depends on parameter \rho\in\bq_p. Such a measure is called {\it generalized $p$-adic quasi Gibbs measure}. When $\rho$ equals to $p$-adic exponent, then it coincides with the $p$-adic Gibbs measure. When $\rho=p$, then it coincides with $p$-adic quasi Gibbs measure. Therefore, we investigate two regimes with respect to the value of $|\rho|_p$. Namely, in the first regime, one takes $\rho=\exp_p(J)$ for some J\in\bq_p, in the second one $|\rho|_p<1$. In each regime, we first find conditions for the existence of generalized $p$-adic quasi Gibbs measures. Furthermore, in the first regime, we establish the existence of the phase transition under some conditions. In the second regime, when $|\r|_p,|q|_p\leq p^{-2}$ we prove the existence of a quasi phase transition. It turns out that if $|\r|_p<|q-1|_p^2<1$ and \sqrt{-3}\in\bq_p, then one finds the existence of the strong phase transition.Comment: 27 page