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"Gerard, Patrick"
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Lectures on integrable equations of Benjamin–Ono type
These lectures are devoted to two integrable PDE on the line enjoying similar structures: the Benjamin–Ono equation and the Calogero–Moser derivative nonlinear Schrödinger equation. For both equations, a Lax pair of operators is introduced on the Hardy space of the upper-half plane, and is used to prove conservation laws and explicit formulae, and to study soliton and multisoliton solutions. In the special case of the Benjamin–Ono equation, the small dispersion limit with general initial data is proved to exist and is identified. These lectures were presented at the 2024 PDE Days, Centre Paul Langevin, Aussois, France.
Journal Article
Dynamic oceanography determines fine scale foraging behavior of Masked Boobies in the Gulf of Mexico
During breeding, foraging marine birds are under biological, geographic, and temporal constraints. These contraints require foraging birds to efficiently process environmental cues derived from physical habitat features that occur at nested spatial scales. Mesoscale oceanography in particular may change rapidly within and between breeding seasons, and findings from well-studied systems that relate oceanography to seabird foraging may transfer poorly to regions with substantially different oceanographic conditions. Our objective was to examine foraging behavior of a pan-tropical seabird, the Masked Booby (Sula dactylatra), in the understudied Caribbean province, a moderately productive region driven by highly dynamic currents and fronts. We tracked 135 individuals with GPS units during May 2013, November 2013, and December 2014 at a regionally important breeding colony in the southern Gulf of Mexico. We measured foraging behavior using characteristics of foraging trips and used area restricted search as a proxy for foraging events. Among individual attributes, nest stage contributed to differences in foraging behavior whereas sex did not. Birds searched for prey at nested hierarchical scales ranging from 200 m-35 km. Large-scale coastal and shelf-slope fronts shifted position between sampling periods and overlapped geographically with overall foraging locations. At small scales (at the prey patch level), the specific relationship between environmental variables and foraging behavior was highly variable among individuals but general patterns emerged. Sea surface height anomaly and velocity of water were the strongest predictors of area restricted search behavior in random forest models, a finding that is consistent with the characterization of the Gulf of Mexico as an energetic system strongly influenced by currents and eddies. Our data may be combined with tracking efforts in the Caribbean province and across tropical regions to advance understanding of seabird sensing of the environment and serve as a baseline for anthropogenic based threats such as development, pollution, and commercial fisheries.
Journal Article
An inverse problem for Hankel operators and turbulent solutions of the cubic Szegő equation on the line
We construct inverse spectral theory for finite rank Hankel operators acting on the Hardy space of the upper half-plane. A particular feature of our theory is that we completely characterise the set of spectral data. As an application of this theory, we prove the genericity of turbulent solutions of the cubic Szegő equation on the real line.
Journal Article
Exchange of polar lipids from adults to neonates in Daphnia magna: Perturbations in sphingomyelin allocation by dietary lipids and environmental toxicants
Because xenosensing nuclear receptors are also lipid sensors that regulate lipid allocation, we hypothesized that toxicant-induced modulation of HR96 activity would alter lipid profiles and the balance between adult survival and neonate production following exposure in Daphnia magna. Adult daphnids were exposed to unsaturated fatty acid- and toxicant- activators or inhibitors of HR96 and later starved to test whether chemical exposure altered allocation toward survival or reproduction. The HR96 activators, linoleic acid and atrazine, decreased reproduction as expected with concomitant changes in the expression of HR96 regulated genes such as magro. The HR96 inhibitors, docosahexaenoic acid (DHA) and triclosan, increased reproduction or neonate starvation survival, respectively. However, pre-exposure to triclosan increased in neonate survival at the expense of reproductive maturation. Lipidomic analysis revealed that sphingomyelins (SM) are predominantly found in neonates and therefore we propose are important in development. DHA and triclosan increased neonatal SM, consistent with HR96's regulation of Niemann-Pick genes. While DHA altered expression of magro, Niemann-Pick 1b, mannosidase, and other HR96-regulated genes as expected, triclosan primarily perturbed sphingomyelinase and mannosidase expression indicating different but potentially overlapping mechanisms for perturbing SM. Overall, SM appears to be a key lipid in Daphnia maturation and further support was provided by carmofur, which inhibits sphingomyelin/ceramide metabolism and in turn severely represses Daphnia maturation and initial brood production. In conclusion, toxicants can perturb lipid allocation and in turn impair development and reproduction.
Journal Article
Lunapark stabilizes nascent three-way junctions in the endoplasmic reticulum
The endoplasmic reticulum (ER) consists of a polygonal network of sheets and tubules interconnected by three-way junctions. This network undergoes continual remodeling through competing processes: the branching and fusion of tubules forms new three-way junctions and new polygons, and junction sliding and ring closure leads to polygon loss. However, little is known about the machinery required to generate and maintain junctions. We previously reported that yeast Lnp1 localizes to ER junctions, and that loss of Lnp1 leads to a collapsed, densely reticulated ER network. In mammalian cells, only approximately half the junctions contain Lnp1. Here we use live cell imaging to show that mammalian Lnp1 (mLnp1) affects ER junction mobility and hence network dynamics. Three-way junctions with mLnp1 are less mobile than junctions without mLnp1. Newly formed junctions that acquire mLnp1 remain stable within the ER network, whereas nascent junctions that fail to acquire mLnp1 undergo rapid ring closure. These findings imply that mLnp1 plays a key role in stabilizing nascent three-way ER junctions.
Significance In this study, we have identified an important role of mammalian Lnp1 (mLnp1) in stabilizing nascent three-way ER junctions. When new junctions acquire mLnp1, they tend to remain stable within the ER network, whereas the nascent junctions that fail to acquire mLnp1 preferentially undergo ring closure. Our findings provide insights into the function of mLnp1.
Journal Article