On the Existence of Solutions to the Muskat Problem With Surface Tension

We consider the Muskat Problem with surface tension in two dimensions over the real line, with $H^{s}$ initial data and allowing the two fluids to have different constant densities and viscosities. We take the angle between the interface and the horizontal, and derive an evolution equation for it. We use energy methods to prove that a solution $\theta$ exists locally and can be continued while $||\theta||_{s}$ remains bounded and the arc chord condition holds. Furthermore, the resulting solution is unique, and depends continuously on the initial data. Additionally, when both fluids have the same viscosity and the initial data is sufficiently small, we show the energy is non-increasing, and that the solution $\theta$ exists globally in time

Spatial two tissue compartment model for DCE-MRI

In the quantitative analysis of Dynamic Contrast-Enhanced Magnetic Resonance Imaging (DCE-MRI) compartment models allow to describe the uptake of contrast medium with biological meaningful kinetic parameters. As simple models often fail to adequately describe the observed uptake behavior, more complex compartment models have been proposed. However, the nonlinear regression problem arising from more complex compartment models often suffers from parameter redundancy. In this paper, we incorporate spatial smoothness on the kinetic parameters of a two tissue compartment model by imposing Gaussian Markov random field priors on them. We analyse to what extent this spatial regularisation helps to avoid parameter redundancy and to obtain stable parameter estimates. Choosing a full Bayesian approach, we obtain posteriors and point estimates running Markov Chain Monte Carlo simulations. The proposed approach is evaluated for simulated concentration time curves as well as for in vivo data from a breast cancer study

On the assembly of a grassland plant community

The species pool for a site is defined as that set of species which have a non-zero probability of maintaining viable populations under the prevailing environmental conditions. it may contain many more species than are actually present in the community of the site. The science of community assembly attempts to understand how particular communities arise from the welter of possible species combinations. The assembly of a grassland plant community from the local species pool was examined in a phylogenetically corrected trait-based study. Competition theory suggests coexisting species should be less similar than expected by chance, whilst environmental sorting theory suggests they should be more similar. This work suggests that, at the whole community scale, species tend to be more similar and that their likelihood of occurrence in communities can to an extent be predicted from their traits. Experimental studies revealed a complicated picture. Species naturally occurring in the community did not show convincing signs of outperforming their absent congeners. Community composition appears to depend in considerable measure upon chance events such as seed dispersal coinciding with the availability of vacant microsites in the community, rather than just a sorting process in which the best suited species are invariably present. These findings suggest that it modelling community assembly is possible, but that it is unlikely ever to be an exact science because it is influenced to a large extent by unpredictable events

Estimate of vascular permeability and cerebral blood volume using Gd-DTPA contrast enhancement and dynamic T2*-weighted MRI

Purpose To develop a numerical approach for estimation of vascular permeability from dynamic T2*-weighted imaging, a technique routinely used to measure cerebral blood volume (CBV) and flow in gliomas. Materials and Methods This study describes a process for estimating both the gadolinium diethylenetriamine pentaacetic acid (Gd-DTPA) transvascular transfer constant and CBV from dynamic T2*-weighted images. The algorithm was applied to data from the brains of 12 patients with grade IV gliomas. The stability of the method was assessed. Estimates of CBV by this technique were compared to those of the conventional method. Results The algorithm was found to be insensitive to noise and to generate stable voxel-by-voxel estimates of permeability and CBV. Conclusion Using a single imaging acquisition, the three most important vascular properties, CBV, cerebral blood flow (CBF), and permeability, can be estimated. This approach may have potential in clinical evaluation of patients with brain tumor or acute ischemic stroke. J. Magn. Reson. Imaging 2006. © 2006 Wiley-Liss, Inc.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/55796/1/20634_ftp.pd

Talking with images: using private photographs from the Imperial War Museums’ Photograph Archive to explore the experiences and intergenerational memories of Holocaust victims, survivors and their families

This thesis examines photographs from private collections of Holocaust survivors which were copied and displayed by Imperial War Museums (IWM) in the period from the mid-1990s to 2021. It explores the collections within, and between the families of Holocaust survivors, IWM’s Photograph Archive and IWM’s two permanent exhibitions: The Holocaust Exhibition and The Holocaust Galleries, which opened in 2000 and 2021 respectively. It responds to growing interest in pertinent fields of academic research in studying private collections of photographs to further understand Jewish experiences and memories of life prior to, during and following the Holocaust. It responds to three main concerns related to the study and use of private photographs. The first is that private photographs are a problematic source in historical and biographical research, the second that they appear as ‘banal’ and stylised reflections on the world and the third, how do private photographs help connect or engender empathy in those who did not experience the Holocaust with those who did. The first four chapters each focus on one Holocaust survivor and their private collection. Each chapter examines individual and familial memory and, the family’s public engagement with memorial cultures and IWM. They employ a transgenerational approach to understand how different generations understand, construct, and then communicate the past through private photographs, testimony, photo narratives and testimony. The first chapter focuses on the collection of Ruth Locke’s childhood in Dachau, Germany. The second chapter examines the collection of Esther Brunstein who grew up in Łódź, Poland. The third focuses on that of Lea Goodman from Kraków, Poland. The fourth chapter examines Jan Imich’s collection who also grew up in Kraków. Although these four chapters highlight very different experiences and memories, they all emphasise that private photographs’ meanings can be fluid, opaque, surprising and sometimes paradoxical. The fifth chapter focuses on IWM’s Holocaust Galleries and the ways that curators have collected and displayed private photographs and testimonies. By doing so it highlights the opportunities, challenges and limitations of transforming familial memory into a museum archive and exhibition. This thesis emphasises the complexity of using private photographs as historical sources and museum objects and, in doing so, encourages rather than deters, others from investigating this rich and under-studied visual source