An Efficient Hybrid Algorithm for the Separable Convex Quadratic Knapsack Problem

This article considers the problem of minimizing a convex, separable quadratic function subject to a knapsack constraint and a box constraint. An algorithm called NAPHEAP has been developed to solve this problem. The algorithm solves the Karush-Kuhn-Tucker system using a starting guess to the optimal Lagrange multiplier and updating the guess monotonically in the direction of the solution. The starting guess is computed using the variable fixing method or is supplied by the user. A key innovation in our algorithm is the implementation of a heap data structure for storing the break points of the dual function and computing the solution of the dual problem. Also, a new version of the variable fixing algorithm is developed that is convergent even when the objective Hessian is not strictly positive definite. The hybrid algorithm NAPHEAP that uses a Newton-type method (variable fixing method, secant method, or Newton's method) to bracket a root, followed by a heap-based monotone break point search, can be faster than a Newton-type method by itself, as demonstrated in the numerical experiments

Multiple-rank modifications of a sparse Cholesky factorization.

Given a sparse symmetric positive definite matrix AA T and an associated sparse Cholesky factorization LDL T or LL T , we develop sparse techniques for updating the factorization after either adding a collection of columns to A or deleting a collection of columns from A. Our techniques are based on an analysis and manipulation of the underlying graph structure, using the framework developed in an earlier paper on rank-1 modifications [T. A. Davis and W. W. Hager, SIAM J. Matrix Anal. Appl., 20 (1999), pp. 606-627]. Computationally, the multiple-rank update has better memory traffic and executes much faster than an equivalent series of rank-1 updates since the multiple-rank update makes one pass through L computing the new entries, while a series of rank-1 updates requires multiple passes through L

Isolation and Characterization of Rhizophydiales (Chytridiomycota), Obligate Parasites of Planktothrix agardhii in a Laurentian Great Lakes Embayment

Planktothrix agardhii dominates the cyanobacterial harmful algal bloom community in Sandusky Bay, Lake Erie (USA), from May through September. This filamentous cyanobacterium is host to a known obligate parasite, the chytrid Rhizophydium sp. During the 2018 bloom season, by utilizing dilution and single-filament isolation techniques, 7 chytrid and 12 P. agardhii strains were isolated from Sandusky Bay. These 7 chytrids and a selection of P. agardhii hosts were then characterized with respect to infection rates. Infections by the isolated chytrids were specific to Planktothrix planktonic species and were not found on other filamentous cyanobacterial taxa present in the bay (Aphanizomenon sp. and Cuspidothrix sp.). Even among the potential P. agardhii host strains, individual chytrid isolates had different degrees of infectivity and showed preferences for different host isolates, suggesting possible ecological partitioning even within the same sample population. When mechanisms of chytrid pathogenesis were examined, the zoospores displayed a swarming pattern to attack and fracture the host filament and create new infection sites at the trichome termini. Infections by these parasitic chytrids also led to a release of intracellular microcystin toxins from the hosts. Additionally, infections were dependent on medium type, highlighting the importance of medium choice for experimental outcomes. Media in which chytrid swarming was observed closely matched the ionic strength of the natural environment. Understanding pathogenesis by fungal parasites will assist future efforts to determine environmental factors favoring loss mechanisms for Planktothrix agardhii-dominated blooms. IMPORTANCE Whereas many studies have focused on the factors contributing to the establishment and persistence of cyanobacterial harmful algal blooms (cHABs), few studies have examined bloom pathogenesis. Chytrid fungi infect cyanobacteria and stimulate food web interactions through manipulation of previously hard-to-digest filaments and the release of nutrients to support heterotrophic microbes. Specifically, chytrids infective for filamentous Planktothrix agardhii exhibit a species-specific infection that fragments trichomes into shorter units that can be consumed more easily by grazers. Chytrid zoospores also serve as a high-quality food source for the lower food web. Understanding host-pathogen relationships and mechanisms of pathogenesis on cyanobacteria will be necessary to effectively model the ecology of cHABs

Environmental factors affecting chytrid (Chytridiomycota) infection rates on Planktothrix agardhii

Planktothrix agardhii dominates the cyanobacterial harmful algal bloom biomass in Sandusky Bay, Lake Erie (USA) from May until September. This filamentous cyanobacterium known parasites including the chytrid fungal species Rhizophydium sp. C02, which was previously isolated from this region. The purpose of our work has been to establish how parasitic interactions affect Planktothrix population dynamics during a bloom event. Samples analyzed from the 2015 to 2019 bloom seasons using quantitative PCR investigate the spatial and temporal prevalence of chytrid infections. Abiotic factors examined in lab include manipulating temperature (17-31°C), conductivity (0.226-1.225 mS/cm) and turbulence. Planktothrix-specific chytrids are present throughout the bloom period and are occasionally at high enough densities to exert parasitic pressure on their hosts. Temperatures above 27.1°C in lab can inhibit chytrid infection, indicating the presence of a possible upper thermal refuge for the host. Data suggest that chytrids can survive conductivity spikes in lab at levels three-fold above Sandusky Bay waters if given sufficient time (7-12 days), whereas increased turbulence in lab severely inhibits chytrid infections, perhaps due to disruption of chemical signaling. Overall, these data provide insights into the environmental conditions that inhibit chytrid infections during Planktothrix-dominated blooms in temperate waters

Modeling of gold circular sub-wavelength apertures on a fiber endface for refractive index sensing

A finite-difference time-domain approach was used to investigate the excitation of surface plasmons of the circular sub-wavelength apertures on an optical fiber endface. This phenomenon provided the basis of a sensitive liquid refractive index sensor. The proposed sensor is compact and has the potential to be used in biomedical applications, having a sensitivity of (373 ± 16) nm per refractive index unit (RIU) as found through the variation of a reflection minimum with the wavelength

Energy transfer in pendant perylene diimide copolymers

We report the synthesis, characterisation and polymerisation of two novel asymmetric perylene diimide acrylate monomers. The novel monomers form a sensitiser–acceptor pair capable of undergoing Förster resonance energy transfer, and were incorporated as copolymers with tert-butyl acrylate. The tert-butyl acrylate units act as spacers along the polymer chain allowing high concentrations of dye while mitigating aggregate quenching, leading to persistent fluorescence in the solid state at high concentrations of up to 0.3 M. Analysis of fluorescence kinetics showed efficient energy transfer between the optically dense sensitiser and the lower concentration acceptor luminophores within the polymer. This reduced reabsorption within the material demonstrates that the copolymer-scaffold energy transfer system has potential for use in luminescent solar concentrators