Minimum and maximum against k lies

A neat 1972 result of Pohl asserts that [3n/2]-2 comparisons are sufficient, and also necessary in the worst case, for finding both the minimum and the maximum of an n-element totally ordered set. The set is accessed via an oracle for pairwise comparisons. More recently, the problem has been studied in the context of the Renyi-Ulam liar games, where the oracle may give up to k false answers. For large k, an upper bound due to Aigner shows that (k+O(\sqrt{k}))n comparisons suffice. We improve on this by providing an algorithm with at most (k+1+C)n+O(k^3) comparisons for some constant C. The known lower bounds are of the form (k+1+c_k)n-D, for some constant D, where c_0=0.5, c_1=23/32=0.71875, and c_k=\Omega(2^{-5k/4}) as k goes to infinity.Comment: 11 pages, 3 figure

Use of Nitrapyrin to reduce nitrogen losses in western Canada

Non-Peer ReviewedNitrapyrin is a potent nitrification inhibitor from Dow AgroSciences Canada that keeps more nitrogen in the root zone by delaying the conversion of NH4 to NO3 in the soil. Two formulations of nitrapyrin are now approved for use in Canada: N-Serve ™, an emulsifiable concentrate formulation for use with NH3, and Ntrench™, a water-based micro-encapsulated formulation for use with urea, urea ammonium nitrate (UAN) and liquid manure. In 2013 and 2014, performance of eNtrench and N-Serve in spring preplant applications with urea, UAN or NH3 was evaluated in twenty field research trials conducted in Alberta, Saskatchewan and Manitoba. All treatments were banded or injected into the soil, or broadcast applied and incorporated, prior to planting of spring wheat or canola. Primary assessments were soil nitrogen balance (NH4-N and NO3-N) at depths of 0 to 30 and 30 to 60 cm from samples collected 2, 4 and 6 weeks after crop emergence (WAE). Averaged across trials, application of eNtrench with urea or UAN increased the amount of NH4-N in the soil (0 to 60 cm) by 29, 13 and 12% at 2, 4 and 6 WAE,respectively, relative to application of urea or UAN. In a subset of trials conducted on coarse-textured soils, eNtrench also decreased the amount of NO3-N moving below the root zone to the 30 to 60 cm depth range by 26 and 16% at 4 and 6 WAE, respectively. Application of N-Serve with NH3 increased the amount of NH4-N in the soil (0 to 60 cm) by an average of 21, 59 and 63% at 2, 4 and 6 WAE, respectively, relative to application of NH3. N-Serve also decreased the amount of NO3-N moving below the root zone to the 30 to 60 cm depth range by 32, 30 and 18% at 2, 4 and 6 WAE, respectively. eNtrench and N-Serve will provide Canadian farmers with new tools to optimize crop yield and improve nitrogen use efficiency by keeping more nitrogen in the stable NH4-form and reducing losses associated with NO3 leaching or denitrification. ™ Trademark of The Dow Chemical Company (“Dow”) or an affiliated company of Do

Distributed Minimum Cut Approximation

We study the problem of computing approximate minimum edge cuts by distributed algorithms. We use a standard synchronous message passing model where in each round, $O(\log n)$ bits can be transmitted over each edge (a.k.a. the CONGEST model). We present a distributed algorithm that, for any weighted graph and any $\epsilon \in (0, 1)$, with high probability finds a cut of size at most $O(\epsilon^{-1}\lambda)$ in $O(D) + \tilde{O}(n^{1/2 + \epsilon})$ rounds, where $\lambda$ is the size of the minimum cut. This algorithm is based on a simple approach for analyzing random edge sampling, which we call the random layering technique. In addition, we also present another distributed algorithm, which is based on a centralized algorithm due to Matula [SODA '93], that with high probability computes a cut of size at most $(2+\epsilon)\lambda$ in $\tilde{O}((D+\sqrt{n})/\epsilon^5)$ rounds for any $\epsilon>0$. The time complexities of both of these algorithms almost match the $\tilde{\Omega}(D + \sqrt{n})$ lower bound of Das Sarma et al. [STOC '11], thus leading to an answer to an open question raised by Elkin [SIGACT-News '04] and Das Sarma et al. [STOC '11]. Furthermore, we also strengthen the lower bound of Das Sarma et al. by extending it to unweighted graphs. We show that the same lower bound also holds for unweighted multigraphs (or equivalently for weighted graphs in which $O(w\log n)$ bits can be transmitted in each round over an edge of weight $w$), even if the diameter is $D=O(\log n)$. For unweighted simple graphs, we show that even for networks of diameter $\tilde{O}(\frac{1}{\lambda}\cdot \sqrt{\frac{n}{\alpha\lambda}})$, finding an $\alpha$-approximate minimum cut in networks of edge connectivity $\lambda$ or computing an $\alpha$-approximation of the edge connectivity requires $\tilde{\Omega}(D + \sqrt{\frac{n}{\alpha\lambda}})$ rounds

Two-stage stochastic minimum s − t cut problems: Formulations, complexity and decomposition algorithms

We introduce the two‐stage stochastic minimum s − t cut problem. Based on a classical linear 0‐1 programming model for the deterministic minimum s − t cut problem, we provide a mathematical programming formulation for the proposed stochastic extension. We show that its constraint matrix loses the total unimodularity property, however, preserves it if the considered graph is a tree. This fact turns out to be not surprising as we prove that the considered problem is NP-hard in general, but admits a linear time solution algorithm when the graph is a tree. We exploit the special structure of the problem and propose a tailored Benders decomposition algorithm. We evaluate the computational efficiency of this algorithm by solving the Benders dual subproblems as max-flow problems. For many tested instances, we outperform a standard Benders decomposition by two orders of magnitude with the Benders decomposition exploiting the max-flow structure of the subproblems

Non-Coexistence of Infinite Clusters in Two-Dimensional Dependent Site Percolation

This paper presents three results on dependent site percolation on the square lattice. First, there exists no positively associated probability measure on {0,1}^{Z^2} with the following properties: a) a single infinite 0cluster exists almost surely, b) at most one infinite 1*cluster exists almost surely, c) some probabilities regarding 1*clusters are bounded away from zero. Second, we show that coexistence of an infinite 1*cluster and an infinite 0cluster is almost surely impossible when the underlying probability measure is ergodic with respect to translations, positively associated, and satisfies the finite energy condition. The third result analyses the typical structure of infinite clusters of both types in the absence of positive association. Namely, under a slightly sharpened finite energy condition, the existence of infinitely many disjoint infinite self-avoiding 1*paths follows from the existence of an infinite 1*cluster. The same holds with respect to 0paths and 0clusters.Comment: 17 pages, 1 figur

Notions of Connectivity in Overlay Networks

International audience" How well connected is the network? " This is one of the most fundamental questions one would ask when facing the challenge of designing a communication network. Three major notions of connectivity have been considered in the literature, but in the context of traditional (single-layer) networks, they turn out to be equivalent. This paper introduces a model for studying the three notions of connectivity in multi-layer networks. Using this model, it is easy to demonstrate that in multi-layer networks the three notions may differ dramatically. Unfortunately, in contrast to the single-layer case, where the values of the three connectivity notions can be computed efficiently, it has been recently shown in the context of WDM networks (results that can be easily translated to our model) that the values of two of these notions of connectivity are hard to compute or even approximate in multi-layer networks. The current paper shed some positive light into the multi-layer connectivity topic: we show that the value of the third connectivity notion can be computed in polynomial time and develop an approximation for the construction of well connected overlay networks

A Tale of Two Fractals: The Hofstadter Butterfly and The Integral Apollonian Gaskets

This paper unveils a mapping between a quantum fractal that describes a physical phenomena, and an abstract geometrical fractal. The quantum fractal is the Hofstadter butterfly discovered in 1976 in an iconic condensed matter problem of electrons moving in a two-dimensional lattice in a transverse magnetic field. The geometric fractal is the integer Apollonian gasket characterized in terms of a 300 BC problem of mutually tangent circles. Both of these fractals are made up of integers. In the Hofstadter butterfly, these integers encode the topological quantum numbers of quantum Hall conductivity. In the Apollonian gaskets an infinite number of mutually tangent circles are nested inside each other, where each circle has integer curvature. The mapping between these two fractals reveals a hidden threefold symmetry embedded in the kaleidoscopic images that describe the asymptotic scaling properties of the butterfly. This paper also serves as a mini review of these fractals, emphasizing their hierarchical aspects in terms of Farey fractions

Searching for Radio Pulsars in 3EG Sources at Urumqi Observatory

Since mid-2005, a pulsar searching system has been operating at 18 cm on the 25-m radio telescope of Urumqi Observatory. Test observations on known pulsars show that the system can perform the intended task. The prospect of using this system to observe 3EG sources and other target searching tasks is discussed.Comment: a training project about MSc thesi