Almost Optimal Streaming Algorithms for Coverage Problems

Maximum coverage and minimum set cover problems --collectively called coverage problems-- have been studied extensively in streaming models. However, previous research not only achieve sub-optimal approximation factors and space complexities, but also study a restricted set arrival model which makes an explicit or implicit assumption on oracle access to the sets, ignoring the complexity of reading and storing the whole set at once. In this paper, we address the above shortcomings, and present algorithms with improved approximation factor and improved space complexity, and prove that our results are almost tight. Moreover, unlike most of previous work, our results hold on a more general edge arrival model. More specifically, we present (almost) optimal approximation algorithms for maximum coverage and minimum set cover problems in the streaming model with an (almost) optimal space complexity of $\tilde{O}(n)$, i.e., the space is {\em independent of the size of the sets or the size of the ground set of elements}. These results not only improve over the best known algorithms for the set arrival model, but also are the first such algorithms for the more powerful {\em edge arrival} model. In order to achieve the above results, we introduce a new general sketching technique for coverage functions: This sketching scheme can be applied to convert an $\alpha$-approximation algorithm for a coverage problem to a (1-\eps)\alpha-approximation algorithm for the same problem in streaming, or RAM models. We show the significance of our sketching technique by ruling out the possibility of solving coverage problems via accessing (as a black box) a (1 \pm \eps)-approximate oracle (e.g., a sketch function) that estimates the coverage function on any subfamily of the sets

Semi-Streaming Set Cover

This paper studies the set cover problem under the semi-streaming model. The underlying set system is formalized in terms of a hypergraph $G = (V, E)$ whose edges arrive one-by-one and the goal is to construct an edge cover $F \subseteq E$ with the objective of minimizing the cardinality (or cost in the weighted case) of $F$. We consider a parameterized relaxation of this problem, where given some $0 \leq \epsilon < 1$, the goal is to construct an edge $(1 - \epsilon)$-cover, namely, a subset of edges incident to all but an $\epsilon$-fraction of the vertices (or their benefit in the weighted case). The key limitation imposed on the algorithm is that its space is limited to (poly)logarithmically many bits per vertex. Our main result is an asymptotically tight trade-off between $\epsilon$ and the approximation ratio: We design a semi-streaming algorithm that on input graph $G$, constructs a succinct data structure $\mathcal{D}$ such that for every $0 \leq \epsilon < 1$, an edge $(1 - \epsilon)$-cover that approximates the optimal edge \mbox{($1$-)cover} within a factor of $f(\epsilon, n)$ can be extracted from $\mathcal{D}$ (efficiently and with no additional space requirements), where $$f(\epsilon, n) = \left\{ \begin{array}{ll} O (1 / \epsilon), & \text{if } \epsilon > 1 / \sqrt{n} \\ O (\sqrt{n}), & \text{otherwise} \end{array} \right. \, .$$ In particular for the traditional set cover problem we obtain an $O(\sqrt{n})$-approximation. This algorithm is proved to be best possible by establishing a family (parameterized by $\epsilon$) of matching lower bounds.Comment: Full version of the extended abstract that will appear in Proceedings of ICALP 2014 track

Longitudinal Monitoring of SARS-CoV-2 IgM and IgG Seropositivity to Detect COVID-19.

BackgroundSevere acute respiratory syndrome coronavirus 2 (SARS-CoV-2), is a novel beta-coronavirus that has recently emerged as the cause of the 2019 coronavirus pandemic (COVID-19). Polymerase chain reaction (PCR) based tests are optimal and recommended for the diagnosis of an acute SARS-CoV-2 infection. Serology tests for viral antibodies provide an important tool to diagnose previous exposure to the virus. Here we evaluate the analytical performance parameters of the Diazyme SARS-CoV-2 IgM/IgG serology assays and describe the kinetics of IgM and IgG seroconversion observed in patients with PCR-confirmed COVID-19 who were admitted to our hospital.MethodsWe validated the performance of the Diazyme assay in 235 presumed SARS-CoV-2 negative subjects to determine specificity. Subsequently, we evaluated the SARS-CoV-2 IgM and IgG seroconversion of 54 PCR-confirmed COVID-19 patients and determined sensitivity of the assay at three different timeframes.ResultSensitivity and specificity for detecting seropositivity at ≥15 days following a positive SARS-CoV-2 PCR result, was 100.0% and 98.7% when assaying for the panel of IgM and IgG. The median time to seropositivity observed for a reactive IgM and IgG result from the date of a positive PCR was 5 days (IQR: 2.75-9 days) and 4 days (IQR: 2.75-6.75 days), respectively.ConclusionsOur data demonstrate that the Diazyme IgM/IgG assays are suited for the purpose of detecting SARS-CoV-2 IgG and IgM in patients with suspected SARS-CoV-2 infections. For the first time, we report longitudinal data showing the evolution of seroconversion for both IgG and IgM in a cohort of acutely ill patients in the United States. We also demonstrate a low false positive rate in patients who were presumed to be disease free

Gamma-ray emission from massive young stellar objects

Massive stars form in dense and massive molecular cores. The exact formation mechanism is unclear, but it is possible that some massive stars are formed by processes similar to those that produce the low-mass stars, with accretion/ejection phenomena occurring at some point of the evolution of the protostar. This picture seems to be supported by the detection of a collimated stellar wind emanating from the massive protostar IRAS 16547-4247. A triple radio source is associated with the protostar: a compact core and two radio lobes. The emission of the southern lobe is clearly non-thermal. Such emission is interpreted as synchrotron radiation produced by relativistic electrons locally accelerated at the termination point of a thermal jet. Since the ambient medium is determined by the properties of the molecular cloud in which the whole system is embedded, we can expect high densities of particles and infrared photons. Because of the confirmed presence of relativistic electrons, inverse Compton and relativistic Bremsstrahlung interactions are unavoidable. Proton-proton collision should also occur, producing an injection of neutral pions. In this paper we aim at making quantitative predictions of the spectral energy distribution of the non-thermal spots generated by massive young stellar objects, with emphasis on the particular case of IRAS 16547-4247. We present spectral energy distributions for the southern lobe of this source, for a variety of conditions. We show that high-energy emission might be detectable from this object in the gamma-ray domain (MeV to TeV). The source may also be detectable at X-rays through long exposures with current X-ray instruments.Comment: 8 pages, 6 figures, accepted for publication in A&

Hydroxyurea derivatives of irofulven with improved antitumor efficacy.

Irofulven is a semi-synthetic derivative of Illudin S, a toxic sesquiterpene isolated from the mushroom Omphalotus illudens. Irofulven has displayed significant antitumor activity in various clinical trials but displayed a limited therapeutic index. A new derivative of irofulven was prepared by reacting hydroxyurea with irofulven under acidic conditions. Acetylation of this new compound with acetic anhydride produced a second derivative. Both of these new derivatives displayed significant antitumor activity in vitro and in vivo comparable to or exceeding that of irofulven

Make Research Data Public? -- Not Always so Simple: A Dialogue for Statisticians and Science Editors

Putting data into the public domain is not the same thing as making those data accessible for intelligent analysis. A distinguished group of editors and experts who were already engaged in one way or another with the issues inherent in making research data public came together with statisticians to initiate a dialogue about policies and practicalities of requiring published research to be accompanied by publication of the research data. This dialogue carried beyond the broad issues of the advisability, the intellectual integrity, the scientific exigencies to the relevance of these issues to statistics as a discipline and the relevance of statistics, from inference to modeling to data exploration, to science and social science policies on these issues.Comment: Published in at http://dx.doi.org/10.1214/10-STS320 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Distributed Edge Connectivity in Sublinear Time

We present the first sublinear-time algorithm for a distributed message-passing network sto compute its edge connectivity $\lambda$ exactly in the CONGEST model, as long as there are no parallel edges. Our algorithm takes $\tilde O(n^{1-1/353}D^{1/353}+n^{1-1/706})$ time to compute $\lambda$ and a cut of cardinality $\lambda$ with high probability, where $n$ and $D$ are the number of nodes and the diameter of the network, respectively, and $\tilde O$ hides polylogarithmic factors. This running time is sublinear in $n$ (i.e. $\tilde O(n^{1-\epsilon})$) whenever $D$ is. Previous sublinear-time distributed algorithms can solve this problem either (i) exactly only when $\lambda=O(n^{1/8-\epsilon})$ [Thurimella PODC'95; Pritchard, Thurimella, ACM Trans. Algorithms'11; Nanongkai, Su, DISC'14] or (ii) approximately [Ghaffari, Kuhn, DISC'13; Nanongkai, Su, DISC'14]. To achieve this we develop and combine several new techniques. First, we design the first distributed algorithm that can compute a $k$-edge connectivity certificate for any $k=O(n^{1-\epsilon})$ in time $\tilde O(\sqrt{nk}+D)$. Second, we show that by combining the recent distributed expander decomposition technique of [Chang, Pettie, Zhang, SODA'19] with techniques from the sequential deterministic edge connectivity algorithm of [Kawarabayashi, Thorup, STOC'15], we can decompose the network into a sublinear number of clusters with small average diameter and without any mincut separating a cluster (except the `trivial' ones). Finally, by extending the tree packing technique from [Karger STOC'96], we can find the minimum cut in time proportional to the number of components. As a byproduct of this technique, we obtain an $\tilde O(n)$-time algorithm for computing exact minimum cut for weighted graphs.Comment: Accepted at 51st ACM Symposium on Theory of Computing (STOC 2019

Detection of nonthermal emission from the bow shock of a massive runaway star

The environs of massive, early-type stars have been inspected in recent years in the search for sites where particles can be accelerated up to relativistic energies. Wind regions of massive binaries that collide have already been established as sources of high-energy emission; however, there is a different scenario for massive stars where strong shocks can also be produced: the bow-shaped region of matter piled up by the action of the stellar strong wind of a runaway star interacting with the interstellar medium. We study the bow-shock region produced by a very massive runaway star, BD+43 3654, to look for nonthermal radio emission as evidence of a relativistic particle population. We observed the field of BD+43 3654 at two frequencies, 1.42 and 4.86 GHz, with the Very Large Array (VLA), and obtained a spectral index map of the radio emission. We have detected, for the first time, nonthermal radio emission from the bow shock of a massive runaway star. After analyzing the radiative mechanisms that can be at work, we conclude that the region under study could produce enough relativistic particles whose radiation might be detectable by forthcoming gamma-ray instruments, like CTA North.Comment: Accepted in Astronomy and Astrophysics Letter

The Portrayal of Complementary and Alternative Medicine in Mass Print Magazines Since 1980

Objectives: The objectives of this study were to examine and describe the portrayal of complementary and alternative medicine (CAM) in mass print media magazines. Design: The sample included all 37 articles found in magazines with circulation rates of greater than 1 million published in the United States and Canada from 1980 to 2005. The analysis was quantitative and qualitative and included investigation of both manifest and latent magazine story messages. Results: Manifest analysis noted that CAM was largely represented as a treatment for a patient with a medically diagnosed illness or specific symptoms. Discussions used biomedical terms such as patient rather than consumer and disease rather than wellness. Latent analysis revealed three themes: (1) CAMs were described as good but not good enough; (2) individualism and consumerism were venerated; and (3) questions of costs were raised in the context of confusion and ambivalence

Massive protostars as gamma-ray sources

Massive protostars have associated bipolar outflows with velocities of hundreds of km s$^{-1}$. Such outflows can produce strong shocks when interact with the ambient medium leading to regions of non-thermal radio emission. We aim at exploring under which conditions relativistic particles are accelerated at the terminal shocks of the protostellar jets and can produce significant gamma-ray emission. We estimate the conditions necessary for particle acceleration up to very high energies and gamma-ray production in the non-thermal hot spots of jets associated with massive protostars embedded in dense molecular clouds. We show that relativistic Bremsstrahlung and proton-proton collisions can make molecular clouds with massive young stellar objects detectable by the {\it Fermi}{} satellite at MeV-GeV energies and by Cherenkov telescope arrays in the GeV-TeV range. Gamma-ray astronomy can be used to probe the physical conditions in star forming regions and particle acceleration processes in the complex environment of massive molecular clouds.Comment: 10 pages, 5 figures, 2 tables, accepted for publication in Astronomy and Astrophysic