411 research outputs found

    Exact Algorithms and Lower Bounds for Stable Instances of Euclidean k-Means

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    We investigate the complexity of solving stable or perturbation-resilient instances of k-Means and k-Median clustering in fixed dimension Euclidean metrics (or more generally doubling metrics). The notion of stable or perturbation resilient instances was introduced by Bilu and Linial [2010] and Awasthi et al. [2012]. In our context we say a k-Means instance is \alpha-stable if there is a unique OPT solution which remains unchanged if distances are (non-uniformly) stretched by a factor of at most \alpha. Stable clustering instances have been studied to explain why heuristics such as Lloyd's algorithm perform well in practice. In this work we show that for any fixed \epsilon>0, (1+\epsilon)-stable instances of k-Means in doubling metrics can be solved in polynomial time. More precisely we show a natural multiswap local search algorithm in fact finds the OPT solution for (1+\epsilon)-stable instances of k-Means and k-Median in a polynomial number of iterations. We complement this result by showing that under a plausible PCP hypothesis this is essentially tight: that when the dimension d is part of the input, there is a fixed \epsilon_0>0 s.t. there is not even a PTAS for (1+\epsilon_0)-stable k-Means in R^d unless NP=RP. To do this, we consider a robust property of CSPs; call an instance stable if there is a unique optimum solution x^* and for any other solution x', the number of unsatisfied clauses is proportional to the Hamming distance between x^* and x'. Dinur et al. have already shown stable QSAT is hard to approximate for some constant Q, our hypothesis is simply that stable QSAT with bounded variable occurrence is also hard. Given this hypothesis, we consider "stability-preserving" reductions to prove our hardness for stable k-Means. Such reductions seem to be more fragile than standard L-reductions and may be of further use to demonstrate other stable optimization problems are hard.Comment: 29 page

    Observations of Peak Strength Behavior in CSA Cement Mortars

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    The purpose of this study was to assess the mechanical property performance behavior of calcium sulfoaluminate (CSA) cement mortar when cured at ambient laboratory temperature of ~23°C (73°F) and constant 50% relative humidity for an extended period of time. Four CSA cement mortars were tested. Three CSA cement mortars contained equivalent mass amounts of calcium sulfate; whereas, the fourth mortar contained double the amount of calcium sulfate. The three CSA cement mortars containing constant mass amounts of calcium sulfate differed as the specific type of calcium sulfate varied across the three formulations—one mortar containing solely anhydrite, one mortar contained half anhydrite and half gypsum while the other mortar solely contained gypsum. The fourth mortar contained double the amount of calcium sulfate when compared with the others while having a 1/1 blend of anhydrite and gypsum. Specific mortars were either tested for direct tensile strength according to ASTM C307 or for compressive strength according to ASTM C109. All tested mortars displayed statistically significant strength loss trends versus time when cured at constant 50% relative humidity. Cement paste samples were analyzed with TGA/SDT and XRD in an effort to identify microstructure changes corresponding to observed strength loss. Cement paste analysis suggests strength loss within the tested CSA cement mortars occurred as a result of ettringite decomposition

    Averting the legacy of kidney disease: focus on childhood

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    World Kidney Day 2016 focuses on kidney disease in childhood and the antecedents of adult kidney disease that can begin in earliest childhood. Chronic kidney disease (CKD) in childhood differs from that in adults, as the largest diagnostic group among children includes congenital anomalies and inherited disorders, with glomerulopathies and kidney disease in the setting of diabetes being relatively uncommon. In addition, many children with acute kidney injury will ultimately develop sequelae that may lead to hypertension and CKD in later childhood or in adult life. Children born early or who are small-for date newborns have relatively increased risk for the development of CKD later in life. Persons with a high-risk birth and early childhood history should be watched closely in order to help detect early signs of kidney disease in time to provide effective prevention or treatment. Successful therapy is feasible for advanced CKD in childhood; there is evidence that children fare better than adults, if they receive kidney replacement therapy including dialysis and transplantation, while only a minority of children may require this ultimate intervention Because there are disparities in access to care, effort is needed so that those children with kidney disease, wherever they live, may be treated effectively, irrespective of their geographic or economic circumstances. Our hope is that World Kidney Day will inform the general public, policy makers and caregivers about the needs and possibilities surrounding kidney disease in childhood

    Treatment of Iron-deficiency Anemia in Patients with Subclinical Hypothyroidism

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    Subclinical hypothyroidism is a health state that is associated with hypercholesterolemia, infertility, iron-deficiency anemia, and poor obstetric outcome. This article summarizes the results of a prospective clinical investigation of whether treatment of subclinical hypothyroidism and iron-deficiency anemia with a combination of levothyroxine plus iron salt would be superior to each treatment alone

    A Comparison between Recombinant Activated Factor VII (Aryoseven) and Novoseven in Patients with Congenital Factor VII Deficiency

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    In order to establish the efficacy and biosimilar nature of AryoSeven to NovoSeven in the treatment of congenital factor VII (FVII) deficiency, patients received either agent at 30 1/4g/kg, intravenously per week for 4 weeks, in a randomized fashion. The primary aim was to compare FVII:coagulation activity (FVII:C), 20 minutes after recombinant activated FVII (rFVIIa) injection, in the 2 groups. A secondary measure was self-reported bleeding. The median interquartile baseline range of the plasma level of activated FVII (FVIIa) activity in the 2 groups was 1.6 (1.1-14.0) IU/dL and 5.0 (1.1-25.5) IU/dL. All patients achieved levels of FVIIa (FVII:C) >30 IU/dL, 20 minutes after the injection of rFVIIa. Bleeding was similar between the 2 groups, with a comparable decrease in severity and frequency compared to the last month prior to treatment. AryoSeven is similar to NovoSeven in increasing postinjection FVIIa activity as well as in clinical safety and efficacy. © The Author(s) 2014

    The College News, 1965-11-19, Vol. 52, No. 08

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    Bryn Mawr College student newspaper. Merged with The Haverford News in 1968 to form the Bi-college News (with various titles from 1968 on). Published weekly (except holidays) during the academic year

    Scheduling Problems over Network of Machines

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    We consider scheduling problems in which jobs need to be processed through a (shared) network of machines. The network is given in the form of a graph the edges of which represent the machines. We are also given a set of jobs, each specified by its processing time and a path in the graph. Every job needs to be processed in the order of edges specified by its path. We assume that jobs can wait between machines and preemption is not allowed; that is, once a job is started being processed on a machine, it must be completed without interruption. Every machine can only process one job at a time. The makespan of a schedule is the earliest time by which all the jobs have finished processing. The flow time (a.k.a. the completion time) of a job in a schedule is the difference in time between when it finishes processing on its last machine and when the it begins processing on its first machine. The total flow time (or the sum of completion times) is the sum of flow times (or completion times) of all jobs. Our focus is on finding schedules with the minimum sum of completion times or minimum makespan. In this paper, we develop several algorithms (both approximate and exact) for the problem both on general graphs and when the underlying graph of machines is a tree. Even in the very special case when the underlying network is a simple star, the problem is very interesting as it models a biprocessor scheduling with applications to data migration
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