Wave decay in the asymptotically flat stationary setting

The current work considers solutions to the wave equation on asymptotically flat, stationary, Lorentzian spacetimes in (1+3) dimensions. We investigate the relationship between the rate at which the geometry tends to flat and the pointwise decay rate of solutions. Tataru 2013 studied the case where the spacetime tends toward flat at a rate of $|x|^{-1}$ and obtained a $t^{-3}$ pointwise decay rate. Here we extend the result to geometries tending toward flat at a rate of $|x|^{-\kappa}$ and establish a pointwise decay rate of $t^{-\kappa-2}$ for $\kappa \in \N$ with $\kappa \ge 2$. A weak local energy decay estimate is assumed to hold, which restricts the geodesic trapping allowed to occur on the underlying geometry. We use the resolvent to connect the time Fourier Transform of a solution to the Cauchy data. The resolvent is initially well-defined in the lower half plane, and once we extend it to the real axis we are able to invert the Fourier Transform to obtain decay. The final decay rate is obtained via analysis of the zero resolvent, whose behavior depends on the rate at which the geometry tends to flat.Doctor of Philosoph

Understanding Charles Bonnet syndrome: mechanisms and intervention

Ph. D. Thesis.Background: Charles Bonnet Syndrome (CBS) is defined by the occurrence of vivid, recurring visual hallucinations (VH) secondary to visual impairment in the absence of psychiatric illness or cognitive impairment. Previous research has proposed that deafferentation, due to loss of sensory input from the eyes, leads to spontaneous hyperexcitability in the visual cortex resulting in VH. Approximately one-third of people with CBS report distress and disruption to daily functioning as a consequence of VH, however there are currently no effective treatments and a lack of research into the aetiology of VH has hindered their development. Aims: 1) To investigate the role of visual cortical activity in the production of VH in CBS, compared to non-hallucinating controls, to better understand why VH occur in some patients but not others. 2) To investigate whether inhibitory non-invasive transcranial direct current stimulation (tDCS) could be used to remediate VH by reducing cortical excitability in CBS. Methods: Study 1: A comparison study consisting of people with CBS (n=19) and nonhallucinating sight-matched controls (n=18) was performed utilising transcranial magnetic stimulation, functional magnetic resonance imaging, and magnetic resonance spectroscopy to compare differences in visual cortical activity between groups. Study 2: Informed by a pilot study in continuous CBS hallucinators, sixteen members of the CBS group received 4- consecutive days of active and sham inhibitory tDCS over the primary visual cortex, comparing visual cortical activity and VH ratings before and after stimulation between active and sham weeks. Results: Study 1: Comparable visual cortical excitability was observed in both groups, although greater excitability was associated with more severe VH in the CBS group. Functional activation of the visual cortex was observed to be lower in the CBS group than controls during an eye movement task, with greater functional activation associated with lower visual cortical excitability. Study 2: Active cathodal tDCS of the primary visual cortex resulted in a significant decrease to VH frequency and intrusiveness compared to sham stimulation. No significant changes to cortical activity were observed following stimulation. Conclusions: This thesis constitutes the largest neurophysiological comparison and treatment study performed in CBS to date. These data support the role of changes to visual cortical activity in the production of VH following sight loss, providing a basis for further study. Furthermore, tDCS was observed to present a potential effective new treatment option for CBS, however further study is needed to understand underlying mechanisms.The Macular Society, Esme’s Umbrella, Fight for Sight, the National Eye Research Centre, and the Thomas Pocklington Trus

Outcome of revision total knee arthroplasty with bone allograft in 30 cases

Revision Total Knee Arthroplasty is often complicated by large bone defects in the distal femur and proximal tibia. These defects can be managed in a variety of ways including the use of allograft bone. The purpose of this study was to retrospectively evaluate the clinical outcome of revision total knee arthroplasty cases where allograft bone was used. Thirty revision TKA's (27 patients) performed between 1994 and 2009 were followed for a mean of 5 years (1- 14 years). Preoperative bone defects were classified using the Anderson Orthopaedic Research Institute classification system. Patient follow-up entailed calculation of the Knee Society Score and radiological assessment of the revision joint replacement in addition to review of complications. Kaplan Meier analysis predicted survivorship at 5 years as 93%, with further revision surgery as end point. The average Knee Society Score was 76.4, with 19 (63%) of knees scoring "excellent" results, 4 (14%) "good", 1 (3%) "fair" and 6 (20%) were "poor". The overall complication rate was 23.3%. Radiological lucency was demonstrated on recent radiographs for one patient. Three knees were re-revised at 1 year, 6 years and 8 years respectively. Our study demonstrates promising short to medium term results with the use of allograft bone in revision total knee replacement presenting with significant bone loss

Total dose hardness of TiN/HfOx/TiN resistive random access memory

Resistive random access memory based on TiN/HfOx/TiN has been fabricated, with the stoichiometry of the HfOx layer altered through control of atomic layer deposition (ALD) temperature. Sweep and pulsed electrical characteristics were extracted before and after 60Co gamma irradiation. Monoclinic HfOx deposited at 400°C did not result in resistive switching. Deposition at 300°C and 350°C resulted in cubic HfOx which switched successfully. Both stoichiometric HfO2 and sub-oxides HfO2-x result in similar memory characteristics. All devices are shown to be radiation hard up to 10 Mrad(Si), independent of stoichiometry

Microglia promote anti-tumor immunity and suppress breast cancer brain metastasis

Breast cancer brain metastasis (BCBM) is a lethal disease with no effective treatments. Prior work has shown that brain cancers and metastases are densely infiltrated with anti-inflammatory, protumorigenic tumor associated macrophages (TAMs), but the role of brain resident microglia remains controversial because they are challenging to discriminate from other TAMs. Using single-cell RNA-sequencing (scRNA-seq), genetic, and humanized mouse models, we specifically identify microglia and find that they play a distinct pro-inflammatory and tumor suppressive role in BCBM. Animals lacking microglia show increased metastasis, decreased survival, and reduced NK and T cell responses, showing that microglia are critical to promote antitumor immunity to suppress BCBM. We find that the pro-inflammatory response is conserved in human microglia, and markers of their response are associated with better prognosis in BCBM patients. These findings establish an important role for microglia in anti-tumor immunity and highlight them as a potential immunotherapy target for brain metastasis