Obstructions to the Hasse principle in families

For a family of varieties over a number field, we give conditions under which 100% of members have no Brauer-Manin obstruction to the Hasse principle.Comment: Improvements following referees' comment

Failure of strong approximation on an affine cone

We use the Brauer-Manin obstruction to strong approximation on a punctured affine cone to explain a curious property of coprime integer solutions to a homogeneous Diophantine equation.Comment: Changes following referee's comment

Bad reduction of the Brauer-Manin obstruction

We relate the Brauer group of a smooth variety over a p-adic field to the geometry of the special fibre of a regular model, using the purity theorem in \'etale cohomology. As an illustration, we describe how the Brauer group of a smooth del Pezzo surface is determined by the singularity type of its reduction. We then relate the evaluation of an element of the Brauer group to the existence of points on certain torsors over the special fibre; we use this to describe situations when the evaluation is constant, and situations when the evaluation is surjective. In the latter case, we describe how this surjectivity can be used to prove vanishing of the Brauer-Manin obstruction on varieties over number fields.Comment: 26 pages; minor edit

Brauer groups of singular del Pezzo surfaces

We describe the effect of rational singularities on the Brauer group of a surface, and compute the Brauer groups of all singular del Pezzo surfaces over an algebraically closed field.Comment: 6 page

Modulation of Semiconductor Photoconversion with Surface Modification and Plasmon

Semiconductor devices are the basis of modern technology. Semiconductor-based photoconversion devices that convert light into electrical signals have shown potential for light energy harvesting and conversion, environmental remediation, and sensors for detection of light, chemicals, and biological substances. Despite this potential for use in many applications, semiconductor photoconversion devices need further improvement in the photoconversion performance. This photoconversion improvement may be manifested as increased photoconversion efficiencies for light harvesting devices for power generation such as photovoltaics and photoelectrochemical (PEC) cells or improved photoconversion modulation to increase the sensitivity of semiconductor photoconversion-based sensors. In addition, alternative semiconductor materials to semiconductors that utilize toxic heavy metals such as cadmium and lead must be found for use in certain semiconductor photoconversion devices. In this dissertation, three separate projects related to improving the performance of semiconductor photoconversion devices are presented. In the first project presented, a rutile titanium dioxide (TiO2) nanorod array photoanrode is coated with an ultra-thin porphyrin-based metal-organic framework (MOF) layer to improve the overall photoconversion of the photoelectrode for solar water splitting. The porphyrin-based MOF coated TiO2 nanorod array showed a 2.7x increase in photocurrent versus bare TiO2 nanorod arrays. The porphyrin-based MOF layer suppressed surface states on the rutile TiO2 nanorod array and increased charge separation and extraction from the rutile TiO2 due to the built-in electric field formed by a depleted p-n junction between the porphyrin-based MOF layer and the rutile TiO2 nanorods. In the second project presented, different plasmonic (hot electron injection and plasmon-induced resonant energy transfer (PIRET)) and non-plasmonic photoconversion enhancement mechanisms were tested for modulating photocurrent in PEC-based sensors using Bi3FeMo2O12 (BFMO) thin film semiconductor photoelectrodes and Hg2+ as a proof-of-concept analyte for detection. The possible plasmonic and non-plasmonic photoconversion enhancement mechanisms were controlled by choice of conjugated plasmonic nanoprobe between Au and Au@SiO2 core-shell nanoparticles with the BFMO. The conjugated Au NPs enhanced the BFMO thin film’s PEC performance through a combination of plasmonic hot electron injection, PIRET, Fermi-level equilibration, and a non-plasmonic internal reflection within the BFMO caused by the conjugated Au NPs. The conjugated Au@SiO2 NPs enhanced the BFMO thin film’s PEC performance via PIRET and the non-plasmonic internal reflection within the BFMO caused by the Au@SiO2 NPs. A PEC sensor using the Au NPs as nanoprobes showed sensitivity and selectivity towards Hg2+ showing this PEC sensor design’s potential. In the third project presented, based on the comparison study of plasmonic and non-plasmonic photoconversion enhancement mechanisms with BFMO thin-film photoanodes, a PEC-based immunosensor utilizing PIRET from Au NP-based nanoprobes conjugated to BFMO thin- film photoanodes to modulate photoconversion of the BFMO is synthesized and studied using human immunoglobulin G (IGG) as a proof-of-concept analyte. The plasmonic Au NPs are conjugated in the presence of human IGG via antibody-antigen reactions. The resulting PIRET-based PEC immunosensor shows some sensitivity towards IGG detection. However, the sensitivity of the PIRET-based PEC immunosensor is limited due to the large separation distance (~10 nm) between the plasmonic Au NPs the BFMO thin films from the antibody-antigen sandwich used for Au NP conjugation. As such, further work must focus on improving PIRET between the Au NP based nanoprobes and the BFMO thin film photoanodes

The degraded concept representation system in semantic dementia:damage to pan-modal hub, then visual spoke

The core clinical feature of semantic dementia is a progressive yet selective degradation of conceptual knowledge. Understanding the cognitive and neuroanatomical basis for this deficit is a key challenge for both clinical and basic science. Some researchers attribute the deficit to damage to pan-modal conceptual representations that are independent of any particular sensory-motor modality and are represented in the ventrolateral anterior temporal lobes. Others claim that damage to modality-specific visual feature representations in the occipitotemporal 'ventral stream' is responsible. In the present study, we tested the hypothesis that concept degradation in semantic dementia involves a combination of these pan-modal and modality-specific elements. We investigated factors influencing knowledge of object concepts by analysing 43 sets of picture-naming data from patients with semantic dementia. We found a strong influence of two pan-modal factors: highly familiar and typical items were named more accurately than less familiar/atypical items at all stages of the disorder. Items associated with rich sensory-motor information were also named more successfully at all stages, and this effect was present for sound/motion knowledge and tactile/action knowledge when these modalities were studied separately. However, there was no advantage for items rich in visual colour/form characteristics; instead, this factor had an increasingly negative impact in the later stages of the disorder. We propose that these results are best explained by a combination of (i) degradation of modality-independent conceptual representations, which is present throughout the disorder and is a consequence of atrophy focused on the ventrolateral anterior temporal lobes; and (ii) a later additional deficit for concepts that depend heavily on visual colour/form information, caused by the spreading of atrophy to posterior ventral temporal regions specialized for representing this information. This explanation is consistent with a graded hub-and-spoke model of conceptual knowledge, in which there is a gradual convergence of information along the temporal lobes, with visual attributes represented in the posterior cortex giving way to pan-modal representations in the anterior areas. © 2012 The Author

Evaluating the wild Brauer group

Classifying elements of the Brauer group of a variety X over a p-adic field according to the p-adic accuracy needed to evaluate them gives a filtration on Br X. We relate this filtration to that defined by Kato's Swan conductor. The refined Swan conductor controls how the evaluation maps vary on p-adic discs: this provides a geometric characterisation of the refined Swan conductor. We give applications to rational points on varieties over number fields, including failure of weak approximation for varieties admitting a non-zero global 2-form