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

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

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

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

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

A rare presentation of the Klinefelter's syndrome

A 16 years old boy with Chronic Renal Failure (CRF) was not suspected of having Klinefelter's syndrome until he complained of painful gynecomastia. He was under haemodialysis for 2 years. At first, he was in an approximately full pubertal development (P5, G5), but he had a small and a firm testis (length 2.2cm) and some degree of facial male pattern hair. He also had a decreased upper to lower body segment ratio and despite having chronic renal failure, he was taller than his parents and siblings. His laboratory tests showed high levels of FSH and normal levels of LH and testosterone. With regards to all these findings, we suspected that there might be an occult Klinefelter's syndrome. So, we made his karyotype that showed a 47XXY pattern. Because there are only a few number of cases that have occult Klinefelter's syndrome in the basis of chronic renal failure, we decided to report this case

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

Clinically relevant enhancement of human sperm motility using compounds with reported phosphodiesterase inhibitor activity

STUDY QUESTION: Can we identify compound(s) with reported phosphodiesterase inhibitor (PDEI) activity that could be added to human spermatozoa in vitro to enhance their motility without compromising other sperm functions? SUMMARY ANSWER: We have identified several compounds that produce robust and effective stimulation of sperm motility and, importantly, have a positive response on patient samples. WHAT IS KNOWN ALREADY: For >20 years, the use of non-selective PDEIs, such as pentoxifylline, has been known to influence the motility of human spermatozoa; however, conflicting results have been obtained. It is now clear that human sperm express several different phosphodiesterases and these are compartmentalized at different regions of the cells. By using type-specific PDEIs, differential modulation of sperm motility may be achieved without adversely affecting other functions such as the acrosome reaction (AR). STUDY DESIGN, SIZE, DURATION: This was a basic medical research study examining sperm samples from normozoospermic donors and subfertile patients attending the Assisted Conception Unit (ACU), Ninewells Hospital Dundee for diagnostic semen analysis, IVF and ICSI. Phase 1 screened 43 commercially available compounds with reported PDEI activity to identify lead compounds that stimulate sperm motility. Samples were exposed (20 min) to three concentrations (1, 10 and 100 µM) of compound, and selected candidates (n = 6) progressed to Phase 2, which provided a more comprehensive assessment using a battery of in vitro sperm function tests.  PARTICIPANTS/MATERIALS, SETTING, METHODS: All healthy donors and subfertile patients were recruited at the Medical Research Institute, University of Dundee and ACU, Ninewells Hospital Dundee (ethical approval 08/S1402/6). In Phase 1, poor motility cells recovered from the 40% interface of the discontinuous density gradient were used as surrogates for patient samples. Pooled samples from three to four different donors were utilized in order to reduce variability and increase the number of cells available for simultaneous examination of multiple compounds. During Phase 2 testing, semen samples from 23 patients attending for either routine diagnostic andrology assessment or IVF/ICSI were prepared and exposed to selected compounds. Additionally, 48 aliquots of prepared samples, surplus to clinical use, were examined from IVF (n = 32) and ICSI (n = 16) patients to further determine the effects of selected compounds under clinical conditions of treatment. Effects of compounds on sperm motility were assessed by computer-assisted sperm analysis. A modified Kremer test using methyl cellulose was used to assess sperm functional ability to penetrate into viscous media. Sperm acrosome integrity and induction of apoptosis were assessed using the acrosomal content marker PSA-FITC and annexin V kit, respectively. MAIN RESULTS AND THE ROLE OF CHANCE: In Phase 1, six compounds were found to have a strong effect on poor motility samples with a magnitude of response of ≥60% increase in percentage total motility. Under capacitating and non-capacitating conditions, these compounds significantly (P ≤ 0.05) increased the percentage of total and progressive motility. Furthermore, these compounds enhanced penetration into a cervical mucus substitute (P ≤ 0.05). Finally, the AR was not significantly induced and these compounds did not significantly increase the externalization of phosphatidylserine (P = 0.6, respectively). In general, the six compounds maintained the stimulation of motility over long periods of time (180 min) and their effects were still observed after their removal. In examinations of clinical samples, there was a general observation of a more significant stimulation of sperm motility in samples with lower baseline motility. In ICSI samples, compounds #26, #37 and #38 were the most effective at significantly increasing total motility (88, 81 and 79% of samples, respectively) and progressive motility (94, 93 and 81% of samples, respectively). In conclusion, using a two-phased drug discovery screening approach including the examination of clinical samples, 3/43 compounds were identified as promising candidates for further study. LIMITATIONS, REASONS FOR CAUTION: This is an in vitro study and caution must be taken when extrapolating the results. Data for patients were from one assessment and thus the robustness of responses needs to be established. The n values for ICSI samples were relatively small. WIDER IMPLICATIONS OF THE FINDINGS: We have systematically screened and identified several compounds that have robust and effective stimulation (i.e. functional significance with longevity and no toxicity) of total and progressive motility under clinical conditions of treatment. These compounds could be clinical candidates with possibilities in terms of assisted reproductive technology options for current or future patients affected by asthenozoospermia or oligoasthenozoospermia

Nonlinear Differential Equations Satisfied by Certain Classical Modular Forms

A unified treatment is given of low-weight modular forms on \Gamma_0(N), N=2,3,4, that have Eisenstein series representations. For each N, certain weight-1 forms are shown to satisfy a coupled system of nonlinear differential equations, which yields a single nonlinear third-order equation, called a generalized Chazy equation. As byproducts, a table of divisor function and theta identities is generated by means of q-expansions, and a transformation law under \Gamma_0(4) for the second complete elliptic integral is derived. More generally, it is shown how Picard-Fuchs equations of triangle subgroups of PSL(2,R) which are hypergeometric equations, yield systems of nonlinear equations for weight-1 forms, and generalized Chazy equations. Each triangle group commensurable with \Gamma(1) is treated.Comment: 40 pages, final version, accepted by Manuscripta Mathematic

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