Donaldson invariants of product ruled surfaces and two-dimensional gauge theories

Using the u-plane integral of Moore and Witten, we derive a simple expression for the Donaldson invariants of $\Sigma_g \times S^2$, where $\Sigma_g$ is a Riemann surface of genus g. This expression generalizes a theorem of Morgan and Szabo for g=1 to any genus g. We give two applications of our results: (1) We derive Thaddeus' formulae for the intersection pairings on the moduli space of rank two stable bundles over a Riemann surface. (2) We derive the eigenvalue spectrum of the Fukaya-Floer cohomology of $\Sigma_g \times S^1$.Comment: 39 pages, harvmac b mod

Antimagic Labelings of Caterpillars

A $k$-antimagic labeling of a graph $G$ is an injection from $E(G)$ to $\{1,2,\dots,|E(G)|+k\}$ such that all vertex sums are pairwise distinct, where the vertex sum at vertex $u$ is the sum of the labels assigned to edges incident to $u$. We call a graph $k$-antimagic when it has a $k$-antimagic labeling, and antimagic when it is 0-antimagic. Hartsfield and Ringel conjectured that every simple connected graph other than $K_2$ is antimagic, but the conjecture is still open even for trees. Here we study $k$-antimagic labelings of caterpillars, which are defined as trees the removal of whose leaves produces a path, called its spine. As a general result, we use constructive techniques to prove that any caterpillar of order $n$ is $(\lfloor (n-1)/2 \rfloor - 2)$-antimagic. Furthermore, if $C$ is a caterpillar with a spine of order $s$, we prove that when $C$ has at least $\lfloor (3s+1)/2 \rfloor$ leaves or $\lfloor (s-1)/2 \rfloor$ consecutive vertices of degree at most 2 at one end of a longest path, then $C$ is antimagic. As a consequence of a result by Wong and Zhu, we also prove that if $p$ is a prime number, any caterpillar with a spine of order $p$, $p-1$ or $p-2$ is $1$-antimagic.Comment: 13 pages, 4 figure

Entropy and Adjoint Methods

Aerodynamic drag can be partially approximated by the entropy flux across fluid domain boundaries with a formula due to Oswatitsch. In this paper, we build the adjoint solution that corresponds to this representation of the drag and investigate its relation to the entropy variables, which are linked to the integrated residual of the entropy transport equation. For inviscid isentropic flows, the resulting adjoint variables are identical to the entropy variables, an observation originally due to Fidkowski and Roe, while for non-isentropic flows there is a significant difference that is explicitly demonstrated with analytic solutions in the shocked quasi-1D case. Both approaches are also investigated for viscous and inviscid flows in two and three dimensions, where the adjoint equations and boundary conditions are derived. The application of both approaches to mesh adaptation is investigated, with especial emphasis on inviscid flows with shocks.Comment: This is a postprint (accepted version) of an article published in the Journal of Scientific Computing. The published version may differ from this postprint and is available at: Lozano, C. "Entropy and Adjoint Methods". J Sci Comput (2019). https://doi.org/10.1007/s10915-019-01092-

Dynamics of ingress, hatch dates, growth, and feeding of Atlantic menhaden, Brevoortia tyrannus, larvae at the Chesapeake Bay mouth

Recruitment of Atlantic menhaden to Chesapeake Bay declined in the late 1980s. Although reasons are not understood, a decline in larval supply to the Bay is one hypothesized explanation. The objective of this thesis was to evaluate levels and variability in larval ingress by conducting 18 ichthyoplankton cruises at the Bay mouth during three years at monthly intervals from fall through spring (2005-06, 2006-07, and 2007-08). The concentrations of ingressing larvae were estimated for each year and also for months within each year. Larval spatial and temporal distributions at the Bay mouth were evaluated with respect to tides and day-night differences. Age, growth rates and hatch dates were determined from otolith-aged larvae and compared among years and months. Larvae were most abundant in 2007-08, but grew fastest in 2006-07. Most ingressing larvae hatched in the November to December period. Copepods were the dominant prey in diets of larval menhaden

En kvantitativ genetisk studie av andel hannfisk hos tilapia

Early sexual maturation is one the main constraints in Tilapia farming since early breeding causes stunted growth and large size variability. To circumvent this problem all-male populations are used commercially, and production of all male fry with use of hormones is the industry standard for Nile tilapia. To evaluate alternatives for production of all male fry, variation of male proportion of different strains and among strains combinations of Nile tilapia were studied. Additionally, to evaluate the feasibility of selection for increased male proportion, genetic parameters for male proportion were studied in Nile tilapia and hybrids between Nile and blue tilapias. None of the eight purebred Nile tilapia strain and strain crosses evaluated in Paper I showed a male proportion (MP) close to the desired commercial threshold (above 95% males). Additive genetic variation for male proportion was estimated within a synthetic population of Nile tilapia. Moderate to low heritabilities were obtained, but estimates may be biased upwards due to effects of the major genetic sex determination factors. Selection for increased male proportion will be very difficult to implement since it likely will result in an increased proportion of masculinized XX sires, which will counteract the response to selection. If selection is to be implemented, use of hormones will be needed to reproduce the population. Identification of genetic sex through the use of genetic markers could provide more reliable estimates of the genetic parameters for MP. Genetic variation was also estimated among hybrids of Nile tilapia females and blue tilapia males. Heritability estimates were moderate to high. Since only one generation of data was evaluated there can still be some level of confounding between the additive genetic effects and the other effects common to full-sibs due to shallow pedigrees. Crossbreeding (hybrid production) may be a good way to increase male proportion in places where cold winters affect production since hybrids between these two species show high male proportion and increased low temperature tolerance as compared to pure Nile tilapia. To make the Nile x blue tilapia hybrid of interest also in a tropical environment the growth of the blue tilapia must be improved through selection.Tidlig kjønnsmodning representerer en av de viktigste begrensningene i tilapiaoppdrett, siden tidlig reproduksjon medfører betydelig redusert vekst og stor variasjon i størrelse. For å omga dette problemet er kommersiell produksjon som regel basert på bruk av ”all male” populasjoner (dvs. kun hannfisk). I oppdrett av Nil tilapia (Oreochromis niloticus), som dominerer verdens tilapiaproduksjon, er kjønnsreversering av yngel ved hjelp av hormoner tilsatt i fôret i dag industristandarden. I dette arbeidet er alternative metoder for etablering av ”all male” populasjoner basert på utnyttelse av naturlig variasjon i andel hannfisk mellom ulike stammer og stammekombinasjoner vurdert. I tillegg er det estimert genetiske parametre for andel hannfisk hos Nil tilapia og hos hybrider mellom Nil tilapia og bla tilapia (O. aureus). Hos Nil tilapia undersøkt i et diallell krysningseksperiment gjennomført i GIFT prosjektet viste resultatene lave, men statistisk signifikante, additiv genetisk, heterosis og resiproke krysningseffekter for andel hannfisk. Av disse hadde de resiproke effektene størst betydning, og for å oppnå en økt andel av hanndyr bor derfor krysningene med høyest innslag av hanndyr benyttes. Basert på størrelsen på disse effektene synes det imidlertid klart at dette neppe vil vare tilstrekkelig til å oppnå minimum 95% hanndyr, noe som kreves for at denne strategien kan være et reelt alternativ til konvensjonelle metoder som i dag benyttes for produksjon av ”all male” populasjoner. Genetisk variasjon for andel hanndyr ble estimert i en syntetisk populasjon av Nil tilapia. Den beregnede arvegraden for egenskapen var lav til moderat, men estimatet kan likevel være overestimert på grunn av samspill med kjønnskromosomer. Seleksjon for økt andel hanndyr vil være svært krevende, fordi det, mest sannsynlig, vil resultere i en økt andel maskuliniserte XX fedre, noe som vil motvirke den ønskede seleksjonsresponsen i neste generasjon. Dersom seleksjon for økt andel hanndyr gjennomføres, vil bruk av hormoner være nødvendig for å få reprodusert populasjonen, og YY hanndyr og XY hunndyr kan dermed selekteres. Genetiske markører for kjønn eller avkomsgranskning av foreldre vil kunne øke effektiviteten av en slik seleksjonsstrategi. Genetisk variasjon for andel hanndyr ble også estimert for hybrider av Nil tilapia hunner og bla tilapia hanner. Arvegradsestimatene var moderate til høye. Siden det analyserte datasettet var begrenset til en enkelt årgang kan de additive genetiske effektene potensielt være sammenblandet med andre effekter felles for fullsøsken. På grunn av høyere toleranse for lave temperaturer hos bla tilapia kan slik hybridproduksjon være en god strategi i omrader der lave vintertemperaturer påvirker produksjonen. For at denne hybriden skal være kommersielt interessant i tropiske områder må tilveksten hos bla tilapia forbedres gjennom seleksjon.Akvaforsk Genetics Center (AFGC