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Polarization of a vacuum as well as of dispersive and dissipative dielectric media with piece-wise and smooth inhomogeneities is studied with the goal to clarify the question of renormalizability of diverging electromagnetic stress-energy tensor. First, the stress tensor is computed with the Lifshitz approach to London forces in the non-retarded limit, which after the substraction of the leading free space ultraviolet divergencies still retains the divergencies associated with the presence of sharp boundaries between piece-wise inhomogeneities. We call these contributions finite because they become renormalized after a sharp interface is replaced with a dielectric permittivity changing according to a smooth function of spatial coordinates. In addition, such a smoothed out interface exhibits new subleading ultraviolet divergencies that appear due to its internal structure. To systematically deal with the polarization of inhomogeneous media, the Hadamard expansion is applied to single out both finite and subleading contributions and to unequivocally demonstrate incomplete renormalizability of the Lifshitz theory. The above approach also allows us to reveal the nature of surface tension, which proves to be purely quantum mechanical. The deduced theory of surface tension and its calculations for real dielectric media are favorably compared to the available experimental data. While the sharp interface limit recovers the classical boundary conditions for the electric field and uncovers the origin of the apparent local divergencies of the renormalized stresses in the sharp interface formulation previously pointed out in the literature, the problem of surface tension proves to be of a distinguished limit type because the sharp interface formulation loses the information about the internal structure of an interface and hence cannot explain the origin of surface tension. Comment: 62 pages, 7 figures

Real spherical designs and real and complex projective designs have been shown by Delsarte, Goethals, and Seidel to give rise to association schemes when the strength of the design is high compared to its degree as a code. In contrast, designs on the complex unit sphere remain relatively uninvestigated, despite their importance in numerous applications. In this paper we develop the notion of a complex spherical design and show how many such designs carry the structure of an association scheme. In contrast with the real spherical designs and the real and complex projective designs, these association schemes are nonsymmetric. Comment: 45 pages, no figures

Avec l’accélération de la production narrative au vingt-et-unième siècle, ainsi que les tentatives d’appropriation des moyens de production et des mythes collectifs par le marché, il y a lieu de questionner l’effet des nouveaux mythes sur la psyché humaine. L’ingestion persistante et soutenue de récits infusés de symboles capitalistes produit une mutation de la subjectivité humaine, dans un mouvement vers une certaine homogénéité. Par une relecture de la Poétique d’Aristote, la première section de cette thèse propose une vision politique de la catharsis, qui théorise le récepteur de toute narration comme programmable et pouvant être guidé vers des attitudes et des postures. Cette conception mène directement à une définition machinique du récit et la notion d’asservissement machinique, qui conçoit la subjectivité humaine comme engagée dans des processus de connectivité où elle perd certains fragments de son unicité. La troisième foulée de cette thèse théorise la société de contrôle de Deleuze et ses héritiers conceptuels, le capitalisme de surveillance et l’ectosubjectivité. Ces deux notions tentent de percevoir le régime de pouvoir du vingt-et-unième siècle, fondé sur les données personnelles et la standardisation de la psyché humaine. Finalement, le quatrième et dernier chapitre de cette recherche se penche sur la notion de vérité telle que décrite par Michel Foucault dans Le Courage de la Vérité. Dans la notion Grecque, et particulièrement son développement platonicien, de parrhēsia, Foucault identifie l’homogénéité d’une vérité basée sur une hiérarchie éthique, et son renversement par les Cyniques en animalité assumée qui ouvre de nouveaux territoires d’existence et de vérité. En somme, ce renversement nous permet de concevoir ce que serait une existence libre, hors d’un régime de vérité qui désubjective et rend homogène. With the acceleration of narrative production in the twenty-first century, as well as the attempted appropriation of means of production and collective myths by market economy, there is an increasing need to question the effect of these new myths on the human psyche. The persistent and sustained ingestion of narratives infused with capitalist symbols produces a transformation of subjectivity, which mutates from unicity to increased standardization. Through a rereading of Aristotle’s Poetics, the first section of this thesis offers a political conception of catharsis that theorizes the receiver of narratives as programmable and guidable towards attitudes and postures. This conception leads directly to a machinic definition of the narrative and the concept of machinic enslavement. These concepts conceive of human subjectivity as engaged in processes of networking where it loses fragments of its unicity. The third chapter of this thesis theorizes Deleuze's society of control and its conceptual successors, surveillance capitalism and ectosubjectivity. Both these concepts attempt to theorize the reigning regime of power of the twenty-first century, based on personal data and the standardization of the human psyche. Finally, the fourth and final chapter of this research analyzes the notion of truth as described by Michel Foucault in The Courage of Truth. In the Greek notion of parrhēsia, and especially in its platonic development, Foucault identifies the homogeneity of a truth system based on a hierarchization of ethics. The reversal of this system by the Cynics into an assumed bestiality is crucial to this thesis as it opens new territories of existence and truth. In sum, the Cynic reversal permits us to conceive of a free existence, outside of a regime of truth that desubjectivates and homogenizes.

Proceedings of the European Conference on Artificial Intelligence, 1996, Budapest, Hungary

We study the prime number race for elliptic curves over the function field of a proper, smooth and geometrically connected curve over a finite field. This constitutes a function field analogue of prior work by Mazur, Sarnak and the second author. In this geometric setting we can prove unconditional results whose counterparts in the number field case are conditional on a Riemann Hypothesis and a linear independence hypothesis on the zeros of the implied L-functions. Notably we show that in certain natural families of elliptic curves, the bias generically dissipates as the conductor grows. This is achieved by proving a central limit theorem and combining it with generic linear independence results that will appear in a separate paper. Also we study in detail a particular family of elliptic curves that have been considered by Ulmer. In contrast to the generic case we show that the race exhibits very diverse outcomes, some of which are believed to be impossible in the number field setting. Such behaviors are possible in the function field case because the zeros of Hasse-Weil L-functions for those elliptic curves can be proven to be highly dependent among themselves, which is a very non generic situation.

We propose the existence of an infinite-parameter family of solutions in AdS that oscillate on any number of non-commensurate frequencies. Some of these solutions appear stable when perturbed, and we suggest that they can be used to map out the AdS "islands of stability". By numerically constructing two-frequency solutions and exploring their parameter space, we find that both collapse and non-collapse are generic scenarios near AdS. Unlike other approaches, our results are valid on any timescale and do not rely on perturbation theory.

Recent shifts in wildfire activity in regions of boreal North America indicate decreased resiliency of carbon pools and forest state. Here, I quantify the initial response and long-term recovery of belowground carbon pools to wildfire across various vegetation trajectories in ~140,000km2 area of the Northwest Territories, Canada, across 502 stands ranging from 1-100 years post-fire. Recovery of soil organic carbon depth and stocks post-fire are regulated primarily by time, moisture level, and their interaction. Hydric sites store more carbon than mesic and dry sites, and rates of post-fire soil carbon accumulation are slower in wetter stands than in mesic or dry stands. My results also suggest that shifts in vegetation state are likely to reduce soil organic carbon depth and stocks during the fire-free period. By modelling across gradients of fire history, hydrology, and vegetation dominance, we can predict the short- and long-term consequences of wildfire for ecosystem carbon behaviour. This research was funded by Northern Science Training Program (NSTP), Northern Water Futures, NASA, and was in kind partnership with the Government of the Northwest Territories.