14,331 research outputs found
Gerbes, simplicial forms and invariants for families of foliated bundles
The notion of a gerbe with connection is conveniently reformulated in terms
of the simplicial deRham complex. In particular the usual Chern-Weil and
Chern-Simons theory is well adapted to this framework and rather easily gives
rise to `characteristic gerbes' associated to families of bundles and
connections. In turn this gives invariants for families of foliated bundles. A
special case is the Quillen line bundle associated to families of flat
SU(2)-bundlesComment: 28 page
Integration of simplicial forms and Deligne cohomology
We present two approaches to constructing an integration map for smooth
Deligne cohomology. The first is defined in the simplicial model, where a class
in Deligne cohomology is represented by a simplicial form, and the second in a
related but more combinatorial model.Comment: 28 pages, section on products adde
Normalization of bundle holomorphic contractions and applications to dynamics
We establish a Poincar\'e-Dulac theorem for sequences (G_n)_n of holomorphic
contractions whose differentials d_0 G_n split regularly. The resonant
relations determining the normal forms hold on the moduli of the exponential
rates of contraction. Our results are actually stated in the framework of
bundle maps.
Such sequences of holomorphic contractions appear naturally as iterated
inverse branches of endomorphisms of CP(k). In this context, our normalization
result allows to precisely estimate the distortions of ellipsoids along typical
orbits. As an application, we show how the Lyapunov exponents of the
equilibrium measure are approximated in terms of the multipliers of the
repulsive cycles.Comment: 29 pages, references added, to appear in Ann. Inst. Fourie
Cobordism obstructions to independent vector fields
We define an invariant for the existence of r pointwise linearly independent
sections in the tangent bundle of a closed manifold. For low values of r,
explicit computations of the homotopy groups of certain Thom spectra combined
with classical obstruction theory identifies this invariant as the top
obstruction to the existence of the desired sections. In particular, this shows
that the top obstruction is an invariant of the underlying manifold in these
cases, which is not true in general. The invariant is related to cobordism
theory and this gives rise to an identification of the invariant in terms of
well-known invariants. As a corollary to the computations, we can also compute
low-dimensional homotopy groups of the Thom spectra studied by Galatius,
Tillmann, Madsen, and Weiss.Comment: 46 page
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Statistical Improvements for Ecological Learning about Spatial Processes
Ecological inquiry is rooted fundamentally in understanding population abundance, both to develop theory and improve conservation outcomes. Despite this importance, estimating abundance is difficult due to the imperfect detection of individuals in a sample population. Further, accounting for space can provide more biologically realistic inference, shifting the focus from abundance to density and encouraging the exploration of spatial processes. To address these challenges, Spatial Capture-Recapture (“SCR”) has emerged as the most prominent method for estimating density reliably. The SCR model is conceptually straightforward: it combines a spatial model of detection with a point process model of the spatial distribution of individuals, using data collected on individuals within a spatially referenced sampling design. These data are often coarse in spatial and temporal resolution, though, motivating research into improving the quality of the data available for analysis. Here I explore two related approaches to improve inference from SCR: sampling design and data integration. Chapter 1 describes the context of this thesis in more detail. Chapter 2 presents a framework to improve sampling design for SCR through the development of an algorithmic optimization approach. Compared to pre-existing recommendations, these optimized designs perform just as well but with far more flexibility to account for available resources and challenging sampling scenarios. Chapter 3 presents one of the first methods of integrating an explicit movement model into the SCR model using telemetry data, which provides information at a much finer spatial scale. The integrated model shows significant improvements over the standard model to achieve a specific inferential objective, in this case: the estimation of landscape connectivity. In Chapter 4, I close by providing two broader conclusions about developing statistical methods for ecological inference. First, simulation-based evaluation is integral to this process, but the circularity of its use can, unfortunately, be understated. Second, and often underappreciated: statistical solutions should be as intuitive as possible to facilitate their adoption by a diverse pool of potential users. These novel approaches to sampling design and data integration represent essential steps in advancing SCR and offer intuitive opportunities to advance ecological learning about spatial processes
Cytomegalovirus latency and reactivation: recent insights into an age old problem
Human cytomegalovirus (HCMV) infection remains a major cause of morbidity in patient populations. In certain clinical settings, it is the reactivation of the pre-existing latent infection in the host that poses the health risk. The prevailing view of HCMV latency was that the virus was essentially quiescent in myeloid progenitor cells and that terminal differentiation resulted in the initiation of the lytic lifecycle and reactivation of infectious virus. However, our understanding of HCMV latency and reactivation at the molecular level has been greatly enhanced through recent advancements in systems biology approaches to perform global analyses of both experimental and natural latency. These approaches, in concert with more classical reductionist experimentation, are furnishing researchers with new concepts in cytomegalovirus latency and suggest that latent infection is far more active than first thought. In this review, we will focus on new studies that suggest that distinct sites of cellular latency could exist in the human host, which, when coupled with recent observations that report different transcriptional programmes within cells of the myeloid lineage, argues for multiple latent phenotypes that could impact differently on the biology of this virus in vivo. Finally, we will also consider how the biology of the host cell where the latent infection persists further contributes to the concept of a spectrum of latent phenotypes in multiple cell types that can be exploited by the virus
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