Blow-up results for semilinear wave equations in the super-conformal case

We consider the semilinear wave equation in higher dimensions with power nonlinearity in the super-conformal range, and its perturbations with lower order terms, including the Klein-Gordon equation. We improve the upper bounds on blow-up solutions previously obtained by Killip, Stovall and Vi\c{s}an [6]. Our proof uses the similarity variables' setting. We consider the equation in that setting as a perturbation of the conformal case, and we handle the extra terms thanks to the ideas we already developed in [5] for perturbations of the pure power case with lower order terms

Art and Otherness: Tragic Visions in Modern Literature

My dissertation is entitled Art and Otherness: Tragic Visions in Modern Literature. The two main subjects of inquiry I take up are the figure of the otherboth as an expression of phenomenological alterity and as a postcolonial subjectand the representation of this figure in modern literature. I investigate the intersections between these two subjects, i.e. whether art is an especially insightful medium or discourse to discuss the subject of otherness in the sense that it represents a disruption within the nature of experience that resembles the encounter with the other. As a basic rationale, my dissertation also accordingly attempts a self-reflexivity grounded in problematizing both the formulation of and interaction between competing conventions of otherness. More succinctly, I attempt herein a methodology that reads across discourses whilst remaining on their margins, with the dual purpose of avoiding the self-confirmation of each ratiocination and finding, specifically in art (and in particular literature), a discursive practice that seeks to avoid, or perhaps transcend, a stable definition of otherness. To effectively probe the various political, psychological, existential and phenomenal aspects of otherness, my project and chapters are organized around these separate but overlapping dimensions. My selected texts are predominantly from the nineteenth, twentieth and twenty-first centuries, with a particular focus on Modernist literature, as the latters anxieties about the nature of art and of the other are particularly useful to probe these and other relevant questions. I focus primarily on fiction by Joseph Conrad, E.M. Forster, Mary Shelley, Virginia Woolf, Salman Rushdie, Anita Desai, Albert Camus, Kamel Daoud, Don DeLillo, Saadat Hasan Manto, Yann Martel and Herman Melville, to which I apply a variety of theoretical lenses. I juxtapose these texts from different literary canons and maintain a correspondingly interdisciplinary critical approach in order to disentangle the figure of the other from various competing ontological and theoretical systems. My premise for this methodology is that pairing and reading these texts in unusual contexts allows for a drawing out of shared symbology, themes and metaphors and opens up a space for a more robust conversation about the relationship between art and otherness

Exploratory Analysis of Effects of Data on Adversarial Perturbations

In recent years, the amount of data being produced has increased tremendously. This data has allowed us to create and train machine learning models that are being used nowadays. Though these models have proven to be very effective in classification and regression problems, they do have a vulnerability. This vulnerability is exploited by adding adversarial perturbations to the original data or in the deployed model. These adversarial attacks are done by making minute changes to the data to confuse the machine learning model. This can lead to models’ misrepresentation and drop the accuracy. For the span of this paper, I have used various statistical and visualization analysis methods to find the effect of adversarial perturbations on the CIFAR10 image data. Some of these methods involved were mean, standard deviation, variance, covariance, the probability distribution of color channels, etc. This paper discusses the insights found during the analysis of the CIFAR10 image dataset and the future work to be expected in this field