Consistent Discretizations for Vanishing Regularization Solutions to Image Processing Problems

A model problem is used to represent a typical image processing problem of reconstructing an unknown in the face of incomplete data. A consistent discretization for a vanishing regularization solution is defined so that, in the absence of noise, limits first with respect to regularization and then with respect to grid refinement agree with a continuum counterpart defined in terms of a saddle point formulation. It is proved and demonstrated computationally for an artificial example and for a realistic example with magnetic resonance images that a mixed finite element discretization is consistent in the sense defined here. On the other hand, it is demonstrated computationally that a standard finite element discretization is not consistent, and the reason for the inconsistency is suggested in terms of theoretical and computational evidence

Evidentiary Power and Propriety of Digital Identifiers and the Impact on Privacy Rights in the United States

Media and network systems capture and store data about electronic activity in new, sometimes unprecedented ways; computational systems make for new means of analysis and knowledge development. These new forms offer new, powerful tactical tools for investigations of electronic malfeasance under traditional legal regulation of state power, particular that of Fourth Amendment limitations on police searches and seizures under the U.S. Constitution. But autonomy, identity and authenticity concerns with electronic data raise issues of public policy, privacy and proper police oversight of civil society. We examine those issues and their implications for digital and computational forensic

Atmospheric potential oxygen: New observations and their implications for some atmospheric and oceanic models

Measurements of atmospheric O2/N2 ratios and CO2 concentrations can be combined into a tracer known as atmospheric potential oxygen (APO ≈ O2/N2 + CO2) that is conservative with respect to terrestrial biological activity. Consequently, APO reflects primarily ocean biogeochemistry and atmospheric circulation. Building on the work of Stephens et al. (1998), we present a set of APO observations for the years 1996-2003 with unprecedented spatial coverage. Combining data from the Princeton and Scripps air sampling programs, the data set includes new observations collected from ships in the low-latitude Pacific. The data show a smaller interhemispheric APO gradient than was observed in past studies, and different structure within the hemispheres. These differences appear to be due primarily to real changes in the APO field over time. The data also show a significant maximum in APO near the equator. Following the approach of Gruber et al. (2001), we compare these observations with predictions of APO generated from ocean O2 and CO2 flux fields and forward models of atmospheric transport. Our model predictions differ from those of earlier modeling studies, reflecting primarily the choice of atmospheric transport model (TM3 in this study). The model predictions show generally good agreement with the observations, matching the size of the interhemispheric gradient, the approximate amplitude and extent of the equatorial maximum, and the amplitude and phasing of the seasonal APO cycle at most stations. Room for improvement remains. The agreement in the interhemispheric gradient appears to be coincidental; over the last decade, the true APO gradient has evolved to a value that is consistent with our time-independent model. In addition, the equatorial maximum is somewhat more pronounced in the data than the model. This may be due to overly vigorous model transport, or insufficient spatial resolution in the air-sea fluxes used in our modeling effort. Finally, the seasonal cycles predicted by the model of atmospheric transport show evidence of an excessive seasonal rectifier in the Aleutian Islands and smaller problems elsewhere. Copyright 2006 by the American Geophysical Union

Public Security & Digital Forensics in the United States: The Continued Need for Expanded Digital Systems for Security

Digital Forensics is one of the latest challenges for the use of forensics in the investigative process in the United States. Some of the challenges are created by conditions and circumstances present for law enforcement around the world. However, many are unique to the United States and created by the standards of evidence within our courts, nature of our law enforcement organizations, and structure of our judicial and prosecutorial systems. It is essential for the preservation of public security and individual safety that competent systems of digital forensics are developed for law enforcement at all levels. The failure to do so will let the guilty avoid responsibility for their criminal actions while possibly subjecting the innocent to unprecedented government intrusion into their private lives

Multi-Scale Force Transmission to and Within the Nucleus.

PhD Theses.The mechanical state of cells, controlled primarily by cytoskeletal (CSK) networks (actin, microtubules and intermediate filaments) is a critical component of maintaining healthy function. Forces transmitted through the cytoskeleton influence the organisation and state of nuclear material, leading to changes in gene expression. This thesis aims to increase our understanding of the role of the CSK networks, specifically the intermediate filament keratin, and their interplay in integrating mechanical forces. We primarily use immunofluorescence imaging of the CSK networks and the nucleus, supported by Atomic Force Microscopy. We work in human epidermal keratinocytes (HEKs), as they are rich in keratin, whose role in cytoskeletal force transmission is under-studied. Since drugs to disrupt keratin are scarce, we first established that Withaferin-A, a compound previously used to disrupt vimentin intermediate filaments, can disrupt keratin at non cyto-toxic doses; impacting cell mechanics and migration. Following from this, Withaferin-A was used alongside established cyto-modulatory drugs to disrupt CSK networks, quantifying a range of properties describing their organisation. These data were fitted to nuclear parameters that described opposing functions on the nuclear state of HEKs for keratin and tubulin, with keratin protecting the nucleus from mechanical force. Finally, machine and deep learning techniques were used to expand the mathematical modelling of data. By training networks to predict nuclear location from only CSK images, a causative relationship between CSK organisation and nuclear location can be derived. In addition, we develop new models to rapidly analyse Atomic Force Microscopy curves and generate synthetic cell images. These results demonstrate the important role of keratin in protecting the nucleus from mechanical force and that deep learning techniques can be used in the study of cell mechanics to gain new insights

Redesigning a sustainable English capstone course through a virtual student-faculty partnership

This collaborative essay between undergraduate students and a faculty member illustrates the importance of partnerships between students and faculty when redesigning courses. We ground this partnering in Students as Partner (SaP) praxis. SaP reinvigorates the faculty and student relationship as one in which both students and faculty serve as active agents in curriculum development, redesign, and assessment. In this essay, we introduce our partnership, locally ground our partnership, and highlight how we redesigned a sustainable English Department capstone course to include a cumulative, integrative assignment. Our partnership was not designed to lead to a quantifiable direct output (i.e., a publication or even a redesigned class); instead, our goal was to build community, to support each other, to learn, to write for ourselves and each other. We conclude by offering brief qualitative data on the effectiveness of our redesign efforts and how our approach may work as a model for redesigning courses in different contexts/institutions

Rapid simulation of spatial epidemics : a spectral method

Spatial structure and hence the spatial position of host populations plays a vital role in the spread of infection. In the majority of situations, it is only possible to predict the spatial spread of infection using simulation models, which can be computationally demanding especially for large population sizes. Here we develop an approximation method that vastly reduces this computational burden. We assume that the transmission rates between individuals or sub-populations are determined by a spatial transmission kernel. This kernel is assumed to be isotropic, such that the transmission rate is simply a function of the distance between susceptible and infectious individuals; as such this provides the ideal mechanism for modelling localised transmission in a spatial environment. We show that the spatial force of infection acting on all susceptibles can be represented as a spatial convolution between the transmission kernel and a spatially extended ‘image’ of the infection state. This representation allows the rapid calculation of stochastic rates of infection using fast-Fourier transform (FFT) routines, which greatly improves the computational efficiency of spatial simulations. We demonstrate the efficiency and accuracy of this fast spectral rate recalculation (FSR) method with two examples: an idealised scenario simulating an SIR-type epidemic outbreak amongst N habitats distributed across a two-dimensional plane; the spread of infection between US cattle farms, illustrating that the FSR method makes continental-scale outbreak forecasting feasible with desktop processing power. The latter model demonstrates which areas of the US are at consistently high risk for cattle-infections, although predictions of epidemic size are highly dependent on assumptions about the tail of the transmission kernel

British Liberal Internationalism in Retreat: the Channel Tunnel Controversy and the Naval Defence Act, 1880-1894

This thesis considers the decline of idealistic 'liberal internationalism' within British politics between the Liberal election victory of 1880 and the final resignation of William Gladstone as Prime Minister in 1894. It argues that by this latter date British political attitudes towards international relations had dramatically changed. Where once policymaking was directed with reference to British power and the progress of peace, by the 1890s government decisions were driven by an assumption of British weakness and foreign strength, with sudden, unprovoked and unforeseen war a constant concern. In its conclusion, the thesis explains how this changed environment eventually forced the unrepentant optimist Gladstone out of office by his refusal to endorse Britain's continuing involvement in the European arms race. In charting these developments the thesis identifies a trinity of themes which brought about the liberal internationalist collapse. These were (1) the anxieties about British vulnerability here termed 'defence pessimism'; (2) the politicisation of the armed forces' officer corps; (3) the manipulation of 'public opinion'. Building on the work of military, naval, social and intellectual historians, the thesis deconstructs many of the foundations upon which the narrative of British defence and foreign policy during this period has been built. British vulnerability is shown to have been largely a myth, generated by 'alarmists' within the British armed forces themselves, in their quest for a larger defence budget; meanwhile assumptions about popular support for the 'anti-internationalist' policy shift of the 1890s are challenged with an analysis which argues that public opinion was misrepresented or ignored in favour of the alarmists. Throughout, these three themes are contrasted with the inability of the liberal internationalists to respond to the anti-internationalist attacks, with the conclusion that the defeat of the former ideology was reflective of a wider malaise within contemporary liberal thought and organisation. These themes are examined in detail in the two case studies which make up the bulk of the thesis. The first is a study of the 1882 Channel Tunnel attempt, which was cancelled after the War Office whipped up a media 'scare' over fears of French invasion. Unlike previous histories of the nineteenth-century Tunnel this study provides a balanced account of the pro-Tunnel case, framing its defeat not simply as a victory for Francophobic defence pessimism but also as a decisive defeat for liberal internationalism. In the first in-depth look at the state of 'public opinion', the study, challenges the established narrative of overwhelming and popular opposition to the Tunnel borne of British 'insularity', revealing substantial support especially among working class organisations. The second study looks at the genesis and passage of the 1889 Naval Defence Act, which formally established the Royal Navy's 'two-power standard'. It is commonly believed that the Act was the result of a popular 'navalist' campaign for naval increases and that it enjoyed widespread support both in and out of Parliament. This study completely rejects that assessment, and instead shows how the navalists' success relied not on public support, but on pessimistic hyperbole, a misrepresentation of the strength of the Navy and a lacklustre political response. In a long analysis of the Bill's parliamentary passage the thesis dramatically reverses our understanding of the Liberal Party's attitude to the Act, revealing that, although disorganised, the Party voted repeatedly against the programme, which was framed by the Conservative government as an explicitly 'anti-internationalist' policy. This new understanding is then applied to Gladstone's 1894 resignation, showing how he became a victim of the 'transformed' politics of national defence

Aggregation dynamics explain vegetation patch-size distributions

Vegetation patch-size distributions have been an intense area of study for theoreticians and applied ecologists alike in recent years. Of particular interest is the seemingly ubiquitous nature of power-law patch-size distributions emerging in a number of diverse ecosystems. The leading explanation of the emergence of these power-laws is due to local facilitative mechanisms. There is also a common transition from power law to exponential distribution when a system is under global pressure, such as grazing or lack of rainfall. These phenomena require a simple mechanistic explanation. Here, we study vegetation patches from a spatially implicit, patch dynamic viewpoint. We show that under minimal assumptions a power-law patch-size distribution appears as a natural consequence of aggregation. A linear death term also leads to an exponential term in the distribution for any non-zero death rate. This work shows the origin of the breakdown of the power-law under increasing pressure and shows that in general, we expect to observe a power law with an exponential cutoff (rather than pure power laws). The estimated parameters of this distribution also provide insight into the underlying ecological mechanisms of aggregation and death