Global Solutions for the Gravity Water Waves Equation in Dimension 3

We show existence of global solutions for the gravity water waves equation in dimension 3, in the case of small data. The proof combines energy estimates, which yield control of L^2 related norms, with dispersive estimates, which give decay in L^\infty. To obtain these dispersive estimates, we use an analysis in Fourier space; the study of space and time resonances is then the crucial point

Shock conditions and shock wave structures in a steady flow in a dissipative fluid

More precisely, calling xi the reciprocal of the Reynolds number based on the shock wave curvature radius, the xi terms of the first order are systematically taken into account. The most important result is a system of formulas giving a correction of order xi for the various RANKINE-HUGONIOT conditions. The suggested formulas may for instance have to be used instead of the conventional ones to evaluate the loss of the total pressure across the detached shock wave which is found at the nose of a very small probe in supersonic flow

The efficiency of CD4 recruitment to ligand-engaged TCR controls the agonist/partial agonist properties of peptide-MHC molecule ligands.

One hypothesis seeking to explain the signaling and biological properties of T cell receptor for antigen (TCR) partial agonists and antagonists is the coreceptor density/kinetic model, which proposes that the pharmacologic behavior of a TCR ligand is largely determined by the relative rates of (a) dissociation ofligand from an engaged TCR and (b) recruitment oflck-linked coreceptors to this ligand-engaged receptor. Using several approaches to prevent or reduce the association of CD4 with occupied TCR, we demonstrate that consistent with this hypothesis, the biological and biochemical consequence of limiting this interaction is to convert typical agonists into partial agonist stimuli. Thus, adding anti-CD4 antibody to T cells recognizing a wild-type peptide-MHC class II ligand leads to disproportionate inhibition of interleukin-2 (IL-2) relative to IL-3 production, the same pattern seen using a TCR partial agonist/antagonist. In addition, T cells exposed to wild-type ligand in the presence of anti-CD4 antibodies show a pattern of TCR signaling resembling that seen using partial agonists, with predominant accumulation of the p21 tyrosine-phosphorylated form of TCR-zeta, reduced tyrosine phosphorylation of CD3epsilon, and no detectable phosphorylation of ZAP-70. Similar results are obtained when the wild-type ligand is presented by mutant class II MHC molecules unable to bind CD4. Likewise, antibody coligation of CD3 and CD4 results in an agonist-like phosphorylation pattern, whereas bivalent engagement of CD3 alone gives a partial agonist-like pattern. Finally, in accord with data showing that partial agonists often induce T cell anergy, CD4 blockade during antigen exposure renders cloned T cells unable to produce IL-2 upon restimulation. These results demonstrate that the biochemical and functional responses to variant TCR ligands with partial agonist properties can be largely reproduced by inhibiting recruitment of CD4 to a TCR binding a wild-type ligand, consistent with the idea that the relative rates of TCR-ligand disengagement and of association of engaged TCR with CD4 may play a key role in determining the pharmacologic properties of peptide-MHC molecule ligands. Beyond this insight into signaling through the TCR, these results have implications for models of thymocyte selection and the use of anti-coreceptor antibodies in vivo for the establishment ofimmunological tolerance

(Anti)symmetric multivariate trigonometric functions and corresponding Fourier transforms

Four families of special functions, depending on n variables, are studied. We call them symmetric and antisymmetric multivariate sine and cosine functions. They are given as determinants or antideterminants of matrices, whose matrix elements are sine or cosine functions of one variable each. These functions are eigenfunctions of the Laplace operator, satisfying specific conditions at the boundary of a certain domain F of the n-dimensional Euclidean space. Discrete and continuous orthogonality on F of the functions within each family, allows one to introduce symmetrized and antisymmetrized multivariate Fourier-like transforms, involving the symmetric and antisymmetric multivariate sine and cosine functions.Comment: 25 pages, no figures; LaTaX; corrected typo

Hidden Mechanisms of Climate Impacts in Western Forests: Integrating Theory and Observation for Climate Adaptation

Fire, insects, and disease are necessary components of forest ecosystems. Yet, climate change is intensifying these tree stressors and creating new interactions that threaten forest survival. This dissertation combined field observations with statistical predictions of changing disturbances in western forests to identify 1) how conventional models may underestimate future forest loss, and 2) how positive relationships between trees may be exploited by managers to prevent forest loss. In Chapter II, I tested whether increasingly extreme weather with climate change increases Pacific yew extinction risk. I found that conventional modeling methods underestimated local extinction risk because trees were adapted to a range in average conditions, but had limited tolerance of extreme drought. In Chapter III, I predicted whether future climate change will alter the strength of competition between species (heterospecifics) versus within species (conspecifics). I found that heterospecific competition is more sensitive to drought than conspecific competition, leading to higher tree mortality during drought than is currently expected. In Chapter IV, I looked at sugar pine tree rings to measure how pines respond to three centuries of fire exclusion, drought, fire, and a bark beetle outbreak. I found that fire suppression led to higher competitive stress, which decreased pines’ resilience to fire, and consequently, decreased pines’ survival during a subsequent bark beetle outbreak. Woody species diversity, however, was able to increase pine survival following fire and bark beetles by allowing higher pine growth and defenses. In Chapter V, I tested whether beneficial relationships between trees and mutualistic fungi could help trees survive across regional differences in climate, environmental conditions, and disturbances. I found that woody species diversity increased large-diameter tree resistance to insects and disease, but only if those species shared a mycorrhizal network. Large trees comprising 17 common western species across three canonical forest types showed this pattern –– despite residing in different topographic positions and climatological contexts. I identified how biodiversity can increase forest resistance and resilience to disturbances, but also found climate change to be weakening the processes responsible for maintaining biodiversity. Managers must take a more active approach to cultivating and preserving forest tree biodiversity to ensure forests are able to continue provisioning essential services, such as carbon storage, in the future. These four long-term studies of spatially explicit, cause-specific tree mortality provided useful insights into tree survival and forest change that will improve vegetation model accuracy and inform management of mature forests in western North America

Cervical Cancer-Associated Human Papillomavirus 16 E7 Oncoprotein Inhibits Induction of Anti-Cancer Immunity by a CD4+ T Cell Dependent Mechanism

Attempts to develop therapeutic vaccines against cervical cancer have been proven difficult. One of the major causes of the failure is due to the use of the wrong mouse models based on transplantable tumours in testing the efficacy of vaccines. Now that a transgenic epithelial mouse model has been developed to closely mimic cervical cancer, the mechanisms needed to eliminate this type of cancer could be studied. The E7 oncoprotein of Human Papillomavirus (HPV) is the most expressed HPV protein in cervical cancers and its continuous production is essential to maintain the cancerous state and therefore the obvious target in the development of vaccines. Skin grafts expressing the HPV 16 E7 protein (E7 autografts) are not spontaneously rejected from an MHC matched immunocompetent host. Interestingly, simultaneous placement of an MHC mismatched skin (allograft) next to an E7 autograft results in the E7 autograft rejection. However when the allograft also expresses E7, the E7 autograft is rejected more slowly. Autograft rejection requires CD8+ T cells, and is accelerated by removal of CD4+ T cells after placement of the E7 expressing allograft, suggesting induction of an E7 specific CD4+ regulatory T cell population by the E7 expressing allograft. This observation may have implications in designing effective vaccines and immunotherapy against cervical cancers in women

Tuning of antigen sensitivity by T cell receptor-dependent negative feedback controls T cell effector function inflammed tissues

Activated T cells must mediate effector responses sufficient to clear pathogens while avoiding excessive tissue damage. Here we have combined dynamic intravital microscopy with ex vivo assessments of T cell cytokine responses to generate a detailed spatiotemporal picture of CD4+ T cell effector regulation in the skin. In response to antigen, effector T cells arrested transiently on antigen presenting cells, briefly producing cytokine and then resuming migration. Antigen recognition led to PD-1 upregulation of the programmed death-1 (PD-1) glycoprotein by T cells and blocking its canonical ligand, programmed death-ligand 1 (PD-L1), lengthened the duration of migration arrest and cytokine production, showing that PD-1 interaction with PD-L1 is a major negative feedback regulator of antigen responsiveness. We speculate that the immune system employs a mechanism involving T cell recruitment, transient activation, and rapid desensitization, allowing the T cell response to rapidly adjust to changes in antigen presentation and minimize collateral injury to the host

Continuous volumetric imaging via an optical phase-locked ultrasound lens

In vivo imaging at high spatiotemporal resolution is key to the understanding of complex biological systems. We integrated an optical phase-locked ultrasound lens into a two-photon fluorescence microscope and achieved microsecond-scale axial scanning, thus enabling volumetric imaging at tens of hertz. We applied this system to multicolor volumetric imaging of processes sensitive to motion artifacts, including calcium dynamics in behaving mouse brain and transient morphology changes and trafficking of immune cells

Scattering for the Zakharov system in 3 dimensions

We prove global existence and scattering for small localized solutions of the Cauchy problem for the Zakharov system in 3 space dimensions. The wave component is shown to decay pointwise at the optimal rate of t^{-1}, whereas the Schr\"odinger component decays almost at a rate of t^{-7/6}.Comment: Minor changes and referee's comments include