Kissing numbers and transference theorems from generalized tail bounds

We generalize Banaszczyk's seminal tail bound for the Gaussian mass of a lattice to a wide class of test functions. From this we obtain quite general transference bounds, as well as bounds on the number of lattice points contained in certain bodies. As applications, we bound the lattice kissing number in $\ell_p$ norms by $e^{(n+ o(n))/p}$ for $0 < p \leq 2$, and also give a proof of a new transference bound in the $\ell_1$ norm.Comment: Previous title: "Generalizations of Banaszczyk's transference theorems and tail bound

Smoothening Functions and the Homomorphism Learning Problem

This thesis is an exploration of certain algebraic and geometrical aspects of the Learning With Errors (LWE) problem introduced in Reg05. On the algebraic front, we view it as a Learning Homomorphisms with Noise problem, and provide a generic construction of a public-key cryptosystem based on this generalization. On the geometric front, we explore the importance of the Gaussian distribution for the existing relationships between LWE and lattice problems. We prove that their smoothing properties does not make them special, but rather, the fact that it is infinitely divisible and l2 symmetric are important properties that make the Gaussian unique

EECOLOGY: (pata)physical taoism in e. e. cummings’s poetry

Using an approach rooted in deconstructive close-reading and branching into pataphysics, this thesis studies, with and through the poetry of American modernist E. E. Cummings, ethical cultivations of aesthetics. First, a lover-beloved paradigm is unearthed in Cummings’s poetry, where love, a response to flaws, is the creative actualization of the world, others, and selves. Second, this love is extended (back) into poetry, using Cummings’s figures of birds—his “ornithopoeia,” the double movement of figuring the flesh and enfleshing the figure. Third, the ethico-aesthetic growth of the poet-reader, lover-beloved, and bird-figure is traced to a Taoist responsivity and eecological responsibility, using Cummings’s metaphor of the blossoming flower, or petalody. Cummings’s aversion to the nascent New Criticism allows this thesis to forage for an alternative to New Criticism’s sedentary offspring: namely, deconstruction and ubiquitous contemporary post-structuralist theory. It hybridizes Cummings’s poetry with ecocriticism, ancient and contemporary philosophy of love, ethics and theology, and biology. It holds binaries in suspension through Taoism and bends metaphysics back to physics through pataphysics, a science of exceptions and a poetics of vital matter. It explicates his entire oeuvre from poetry to personal correspondences, its inspirations and aspirations, its inventions and conventions, and its relevance on a still-modernist earth in the oily shadow of ecocatastrophe

Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education

International audienceThis volume contains the Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education (ERME), which took place 9-13 February 2011, at Rzeszñw in Poland

Takin\u27 it to the streets: culture war, rhetorical education, and democratic virtue

The author analyzes the history of rational liberalism, connecting this paradigm with the rhetoric of the culture wars, posing postmodernism as the re-emergence of Classical sophism, and offering a rhetoric pedagogy which draws from neo-Protagorean argumentation and Paolo Freire. Chapter One examines the broad debate as it applies to English Studies, as well as the debate within English Studies, contrasting the epistemological and moral assumptions of rational elitism with those postmodern. The author argues that, as democracy is embodied in rhetorical practice rather than foundational truths, the composition classroom is a natural site for education in the virtues of phronesis . Chapter Two employs an Aristotelian vocabulary to identify the central concern as a tension between moral excellence and political effectiveness. The author argues that the liberal self-concept identifies the individual apart from and in conflict with others and the community and that liberal thinking is undercut by marketplace assumptions which discourage civic participation and provide an inadequate model of inequality, domination, and oppression. Chapter Three examines the assumptions of Euro-western rationalism which underlie liberalism and their implications for democratic practice. The author argues that the dominant paradigm of inquiry misconstrues the Good as an abstract, timeless, and unitary form; misrepresents the practices of reasoning as transcending the oral, the particular, the local, and the timely (Toulmin Cosmopolis 30); and mishandles social institutions by according the misrepresented rationality of individuals. She concludes by raising the specter of the fragmented self, a passive subject, citizen of nowhere, who conflates material acquisition and the right to personal privacy with self-determination and ethical social progress. Chapter Four illustrates the way in which contemporary constructions of the Platonic cardinal virtues are used to silence dissenting voices. The author then proposes a rhetorical way of looking at these virtues which draws its force from the teachings of Protagoras, provisionally resolving the somewhat artificial binary drawn between episteme and doxai , so providing a more democratic vision of rhetorical ethics. Chapter Five offers a view of the classroom in the aftermath of September 11, linking neo-Protagorean argumentation with Freirean pedagogy