Sublinear Estimation of Weighted Matchings in Dynamic Data Streams

This paper presents an algorithm for estimating the weight of a maximum weighted matching by augmenting any estimation routine for the size of an unweighted matching. The algorithm is implementable in any streaming model including dynamic graph streams. We also give the first constant estimation for the maximum matching size in a dynamic graph stream for planar graphs (or any graph with bounded arboricity) using $\tilde{O}(n^{4/5})$ space which also extends to weighted matching. Using previous results by Kapralov, Khanna, and Sudan (2014) we obtain a $\mathrm{polylog}(n)$ approximation for general graphs using $\mathrm{polylog}(n)$ space in random order streams, respectively. In addition, we give a space lower bound of $\Omega(n^{1-\varepsilon})$ for any randomized algorithm estimating the size of a maximum matching up to a $1+O(\varepsilon)$ factor for adversarial streams

A survey of the economics and management of gummy ewes

The purpose of this survey was to investigate the practice of running gummy ewes. Their management, production and costing factors were analysed. The information was gathered from fifty farmers in the Canterbury, Otago and Southland areas by a personal interview survey. The questionnaire covered the above aspects and aimed to gain farmer opinion on the practice of running these ewes. It is evident from this survey that a decrease in wool weight can be expected; 47 percent of the farmers stated that they expected the drop to be approximately 1 kg compared with their mixed aged ewes. Furthermore, 67 percent of the farmers have found that slightly higher losses could be expected. These losses are significantly offset by a gain in lambing percentage of between 10 and 15 percent compared with mixed aged flocks on the same farms. Gross margin analyses showed that a five year breeding own replacements system gave highest returns when the cull ewe and lamb prices were similar but as the difference between these two became larger, the two year flock system of buying gummy ewes was the more profitable. For the majority of the surveyed farms this latter policy has proven the most profitable over recent years

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

Maximum Matching in Turnstile Streams

We consider the unweighted bipartite maximum matching problem in the one-pass turnstile streaming model where the input stream consists of edge insertions and deletions. In the insertion-only model, a one-pass $2$-approximation streaming algorithm can be easily obtained with space $O(n \log n)$, where $n$ denotes the number of vertices of the input graph. We show that no such result is possible if edge deletions are allowed, even if space $O(n^{3/2-\delta})$ is granted, for every $\delta > 0$. Specifically, for every $0 \le \epsilon \le 1$, we show that in the one-pass turnstile streaming model, in order to compute a $O(n^{\epsilon})$-approximation, space $\Omega(n^{3/2 - 4\epsilon})$ is required for constant error randomized algorithms, and, up to logarithmic factors, space $O( n^{2-2\epsilon} )$ is sufficient. Our lower bound result is proved in the simultaneous message model of communication and may be of independent interest

Buyback Problem - Approximate matroid intersection with cancellation costs

In the buyback problem, an algorithm observes a sequence of bids and must decide whether to accept each bid at the moment it arrives, subject to some constraints on the set of accepted bids. Decisions to reject bids are irrevocable, whereas decisions to accept bids may be canceled at a cost that is a fixed fraction of the bid value. Previous to our work, deterministic and randomized algorithms were known when the constraint is a matroid constraint. We extend this and give a deterministic algorithm for the case when the constraint is an intersection of $k$ matroid constraints. We further prove a matching lower bound on the competitive ratio for this problem and extend our results to arbitrary downward closed set systems. This problem has applications to banner advertisement, semi-streaming, routing, load balancing and other problems where preemption or cancellation of previous allocations is allowed

Susceptibility to apoptosis is differentially regulated by c-myc and mutated Ha-ras oncogenes and is associated with endonuclease availability.

Oncogenes and oncosuppressors can deregulate cell replication in tumours, and recently have been shown to influence the probability of apoptosis. The effects of human c-myc and mutated (T24) Ha-ras oncogenes on susceptibility to apoptosis were investigated by introducing them into immortalised rat fibroblasts. The resulting family of transfectants showed closely similar measures of proliferation, but widely divergent rates of apoptosis, differing by up to fifteen-fold, that correlated inversely with population expansion rates in vitro. T24-ras transfectants with moderate or high p21ras expression showed reduced apoptosis, and this was reversed by pharmacological inhibition of membrane localisation of p21ras by mevinolin. In contrast, c-myc stimulated apoptosis, and this was further enhanced by serum deprivation. Inducibility of effector proteins represents one possible mechanism of genetic control of the susceptibility to apoptosis, and its investigation showed that c-myc was associated with expression by viable cells of latent calcium/magnesium sensitive endonuclease activity characteristic of apoptosis. In contrast, endonuclease activity was not detected in viable cells of a T24-ras transfectant expressing high levels of p21ras. Thus, there appeared to be differential regulation of susceptibility to apoptosis, positively by c-myc and negatively by activated ras, and this was associated with availability of endonuclease activity. Genetic modulation of apoptosis in human neoplasms is likely to influence net growth rate, retention of cells acquiring new mutations and response to certain chemotherapeutic agents

A joint role for forced and internally-driven variability in the decadal modulation of global warming

Despite the observed monotonic increase in greenhouse-gas concentrations, global mean temperature displays important decadal fluctuations typically attributed to both external forcing and internal variability. Here, we provide a robust quantification of the relative contributions of anthropogenic, natural, and internally-driven decadal variability of global mean sea surface temperature (GMSST) by using a unique dataset consisting of 30-member large initial-condition ensembles with five Earth System Models (ESM-LE). We present evidence that a large fraction (~29–53%) of the simulated decadal-scale variance in individual timeseries of GMSST over 1950–2010 is externally forced and largely linked to the representation of volcanic aerosols. Comparison with the future (2010–2070) period suggests that external forcing provides a source of additional decadal-scale variability in the historical period. Given the unpredictable nature of future volcanic aerosol forcing, it is suggested that a large portion of decadal GMSST variability might not be predictable

The Black Hole Mass of NGC 4151. II. Stellar Dynamical Measurement from Near-Infrared Integral Field Spectroscopy

We present a revised measurement of the mass of the central black hole (Mbh) in the Seyfert 1 galaxy NGC 4151. The new stellar dynamical mass measurement is derived by applying an axisymmetric orbit-superposition code to near-infrared integral field data obtained using adaptive optics with the Gemini NIFS spectrograph. When our models attempt to fit both the NIFS kinematics and additional low spatial resolution kinematics, our results depend sensitively on how chi-squared is computed--probably a consequence of complex bar kinematics that manifest immediately outside the nuclear region. The most robust results are obtained when only the high spatial resolution kinematic constraints in the nuclear region are included in the fit. Our best estimates for the BH mass and H-band mass-to-light ratio are Mbh~(3.76+/-1.15)E7 Msun (1-sigma error) and M/L(H-band)~0.34+/-0.03 Msun/Lsun (3-sigma error), respectively (the quoted errors reflect the model uncertainties). Our BH mass measurement is consistent with estimates from both reverberation mapping (3.57[+0.45/-0.37]E7 Msun) and gas kinematics (3.0[+0.75/-2.2]E7 Msun; 1-sigma errors), and our best-fit mass-to-light ratio is consistent with the photometric estimate of M/L(H-band)=0.4+/-0.2 Msun/Lsun. The NIFS kinematics give a central bulge velocity dispersion sigma_c=116+/-3 km/s, bringing this object slightly closer to the M-sigma relation for quiescent galaxies. Although NGC 4151 is one of only a few Seyfert 1 galaxies in which it is possible to obtain a direct dynamical BH mass measurement--and thus, an independent calibration of the reverberation mapping mass scale--the complex bar kinematics makes it less than ideally suited for this purpose.Comment: 21 pages, 15 figures. Accepted for publication in Ap