Fast computation of Bernoulli, Tangent and Secant numbers

We consider the computation of Bernoulli, Tangent (zag), and Secant (zig or Euler) numbers. In particular, we give asymptotically fast algorithms for computing the first n such numbers in O(n^2.(log n)^(2+o(1))) bit-operations. We also give very short in-place algorithms for computing the first n Tangent or Secant numbers in O(n^2) integer operations. These algorithms are extremely simple, and fast for moderate values of n. They are faster and use less space than the algorithms of Atkinson (for Tangent and Secant numbers) and Akiyama and Tanigawa (for Bernoulli numbers).Comment: 16 pages. To appear in Computational and Analytical Mathematics (associated with the May 2011 workshop in honour of Jonathan Borwein's 60th birthday). For further information, see http://maths.anu.edu.au/~brent/pub/pub242.htm

Efficient Solution of Portfolio Optimization Problems via Dimension Reduction and Sparsification

The Markowitz mean-variance portfolio optimization model aims to balance expected return and risk when investing. However, there is a significant limitation when solving large portfolio optimization problems efficiently: the large and dense covariance matrix. Since portfolio performance can be potentially improved by considering a wider range of investments, it is imperative to be able to solve large portfolio optimization problems efficiently, typically in microseconds. We propose dimension reduction and increased sparsity as remedies for the covariance matrix. The size reduction is based on predictions from machine learning techniques and the solution to a linear programming problem. We find that using the efficient frontier from the linear formulation is much better at predicting the assets on the Markowitz efficient frontier, compared to the predictions from neural networks. Reducing the covariance matrix based on these predictions decreases both runtime and total iterations. We also present a technique to sparsify the covariance matrix such that it preserves positive semi-definiteness, which improves runtime per iteration. The methods we discuss all achieved similar portfolio expected risk and return as we would obtain from a full dense covariance matrix but with improved optimizer performance.Comment: 14 pages, 3 figure

Optimal land conservation decisions for multiple species

Given an allotment of land divided into parcels, government decision-makers, private developers, and conservation biologists can collaborate to select which parcels to protect, in order to accomplish sustainable ecological goals with various constraints. In this paper, we propose a mixed-integer optimization model that considers the presence of multiple species on these parcels, subject to predator-prey relationships and crowding effects.Comment: 10 pages, 4 figures. Proceedings of the 52nd Northeast Decision Sciences Institute (NEDSI) Annual Conference, Washington, D

Decision-Making for Land Conservation: A Derivative-Free Optimization Framework with Nonlinear Inputs

Protected areas (PAs) are designated spaces where human activities are restricted to preserve critical habitats. Decision-makers are challenged with balancing a trade-off of financial feasibility with ecological benefit when establishing PAs. Given the long-term ramifications of these decisions and the constantly shifting environment, it is crucial that PAs are carefully selected with long-term viability in mind. Using AI tools like simulation and optimization is common for designating PAs, but current decision models are primarily linear. In this paper, we propose a derivative-free optimization framework paired with a nonlinear component, population viability analysis (PVA). Formulated as a mixed integer nonlinear programming (MINLP) problem, our model allows for linear and nonlinear inputs. Connectivity, competition, crowding, and other similar concerns are handled by the PVA software, rather than expressed as constraints of the optimization model. In addition, we present numerical results that serve as a proof of concept, showing our models yield PAs with similar expected risk to that of preserving every parcel in a habitat, but at a significantly lower cost. The overall goal is to promote interdisciplinary work by providing a new mathematical programming tool for conservationists that allows for nonlinear inputs and can be paired with existing ecological software.Comment: 8 pages, 2 figure

Charakterisierung von hERG-Kaliumkanalmutationen bei Patienten mit LQT2-Syndrom:Elektrophysiologische Untersuchungen im heterologen Expressionssystem

Mutationen im human ether-à-go-go related gene (hERG) können zum LQT2-Syndrom mit einer verlängerten QT-Zeit führen, das Arrhythmien bis hin zum Herzstillstand auslösen kann. Mittels voltage clamp wurden Stromamplituden sowie Aktivierungs- u. Inaktivierungsverhalten der Mutationen T623I, G628S, K638Q, Y611X, Q688X und R1055Q im heterologen Expressionssystem Xenopus laevis analysiert. Wildtyp (WT) und alle Coexpressionen zeigten hERG-typische Membranströme, die Mutationen nicht. Keine Coexpression führte zur vollständigen Hemmung des Gesamtstroms. T623I und Y611X zeigten ein rezessives Verhalten. G628S, K638Q, Q688X und R1055Q zeigten mit 70-98% bezogen auf den WT eine gewisse Wiederherstellung der Kanalfunktionalität. Diese Mutationen scheinen mit den WT-Untereinheiten heterotetramere funktionelle Kanäle ausbilden zu können. Es zeigten sich keine Veränderungen der Gleichgewichtsaktivierung; bei einigen Mutationen traten Linksverschiebungen in der Inaktivierung auf, was physiologisch zu einem verringerten Repolarisierungspotential führen würde. R1055Q zeigte keine Veränderung und kann als Polymorphismus eingeordnet werden

Soybean Canopy Gap Influence on Velvetleaf Seed Production

Gaps in the soybean row provide locations for velvetleaf (Abutilon theophrasti) plant growth. Gap width, and velvetleaf plant location within the gap, were investigated for effect on seed production. There was no significant difference in velvetleaf capsule production between plants that grew either centered in a gap or at the western end of a gap in east-west oriented soybean rows. Also, there was no difference in plant survival, emergence through the soybean canopy, flowering, locule number per capsule, or average seed weight of velvetleaf based on gap width. However, there was a difference in capsule production based on gap width. In 1999, seed capsule production increased from approximately 35 capsules plant-1 at 0 cm gap width to 140 capsules plant-1 in the 90 cm gap. In 2000, seed capsule production increased from approximately 9 capsules plant-1 at 0 cm gap width to 98 capsules plant-1 in the 90 cm gap. Seed production ranged from an estimate of 300 to 5900 seeds plant-1. As gap width in the soybean row increases, it becomes more important to monitor and control velvetleaf growth. It is even possible, however, to have significant velvetleaf seed production from plants that emerge in a 30 cm gap in the row

Mars Dust: Characterization of Particle Size and Electrostatic Charge Distribution

Some of the latest pictures of Mars surface sent by NASA's Spirit rover in early January, 2004, show very cohesive, "mud-like" dust layers. Significant amounts of dust clouds are present in the atmosphere of Mars [1-4]. NASA spacecraft missions to Mars confirmed hypotheses from telescopic work that changes observed in the planet's surface markings are caused by wind-driven redistribution of dust. In these dust storms, particles with a wide range of diameters (less than 1 micrometer to 50 micrometers) are a serious problem to solar cells, spacecraft, and spacesuits. Dust storms may cover the entire planet for an extended period of time [5]. It is highly probable that the particles are charged electrostatically by triboelectrification and by UV irradiation

On the Effectiveness of BGP Hijackers That Evade Public Route Collectors

Routing hijack attacks have plagued the Internet for decades. After many failed mitigation attempts, recent Internet-wide BGP monitoring infrastructures relying on distributed route collection systems, called route collectors, give us hope that future monitor systems can quickly detect and ultimately mitigate hijacks. In this paper, we investigate the effectiveness of public route collectors with respect to future attackers deliberately engineering longer hijacks to avoid being recorded by route collectors. Our extensive simulations (and attacks we device) show that monitor-based systems may be unable to observe many carefully crafted hijacks diverting traffic from thousands of ASes. Hijackers could predict whether their attacks would propagate to some BGP feeders (i.e., monitors) of public route collectors. Then, manipulate BGP route propagation so that the attack never reaches those monitors. This observation remains true when considering plausible future Internet topologies, with more IXP links and up to 4 times more monitors peering with route collectors. We then evaluate the feasibility of performing hijacks not observed by route collectors in the real-world. We experiment with two classifiers to predict the monitors that are dangerous to report the attack to route collectors, one based on monitor proximities (i.e., shortest path lengths) and another based on Gao-Rexford routing policies. We show that a proximity-based classifier could be sufficient for the hijacker to identify all dangerous monitors for hijacks announced to peer-to-peer neighbors. For hijacks announced to transit networks, a Gao-Rexford classifier reduces wrong inferences by $\ge 91\%$ without introducing new misclassifications for existing dangerous monitors