On the Arithmetic Fundamental Lemma in the minuscule case

The arithmetic fundamental lemma conjecture of the third author connects the derivative of an orbital integral on a symmetric space with an intersection number on a formal moduli space of $p$-divisible groups of Picard type. It arises in the relative trace formula approach to the arithmetic Gan-Gross-Prasad conjecture. We prove this conjecture in the minuscule case.Comment: Referee's comments incorporated; in particular, the existence of frames for using the theory of displays in the proofs of Theorems 9.4 and 9.5 is clarified. To appear in Compositio Mat

Characterizing Far-infrared Laser Emissions and the Measurement of Their Frequencies

The generation and subsequent measurement of far-infrared radiation has found numerous applications in high-resolution spectroscopy, radioastronomy, and Terahertz imaging. For about 45 years, the generation of coherent, far-infrared radiation has been accomplished using the optically pumped molecular laser. Once far-infrared laser radiation is detected, the frequencies of these laser emissions are measured using a three-laser heterodyne technique. With this technique, the unknown frequency from the optically pumped molecular laser is mixed with the difference frequency between two stabilized, infrared reference frequencies. These reference frequencies are generated by independent carbon dioxide lasers, each stabilized using the fluorescence signal from an external, low pressure reference cell. The resulting beat between the known and unknown laser frequencies is monitored by a metal-insulator-metal point contact diode detector whose output is observed on a spectrum analyzer. The beat frequency between these laser emissions is subsequently measured and combined with the known reference frequencies to extrapolate the unknown far-infrared laser frequency. The resulting one-sigma fractional uncertainty for laser frequencies measured with this technique is ± 5 parts in 107. Accurately determining the frequency of far-infrared laser emissions is critical as they are often used as a reference for other measurements, as in the high-resolution spectroscopic investigations of free radicals using laser magnetic resonance. As part of this investigation, difluoromethane, CH2F2, was used as the far-infrared laser medium. In all, eight far-infrared laser frequencies were measured for the first time with frequencies ranging from 0.359 to 1.273 THz. Three of these laser emissions were discovered during this investigation and are reported with their optimal operating pressure, polarization with respect to the CO2 pump laser, and strength

Assessing the fidelity of COTS 802.11 sniffers

Proceedings of: 2009 IEEE INFOCOM, 19 – 25 April 2009, Rio de Janeiro, BrazilRecent measurement studies have analyzed WLAN performance by means of wireless sniffers that passively capture transmitted frames. Also, for relatively large (enterprise) WLAN scenarios, previous work has investigated multi-sniffer deployments with devices placed far apart in order to capture all traffic in the network (even frames transmitted simultaneously by different nodes at non-interfering locations). However, for both these single- and multi-sniffer scenarios, little attention has been given to the fidelity of an individual device, i.e., the ability of a given sniffer to capture all frames that could have been captured by a more faithful device. We assess this fidelity (a term we make precise in this paper) by running controlled experiments inside an anechoic chamber and analyzing the similarities and differences between the trace file from the device under study and those of additional "shadow" devices placed in its close proximity. Our results show that fidelity varies significantly across sniffers, both quantitatively and qualitatively, and that performance may also depend on the nature of the experiment under study and on slight changes of the sniffer position.European Community's Seventh Framework ProgramThis work was funded in part by the National Science Foundation under grants, EEC-0313747 001, ANI-0325868, and EIA-0080119, and by the Ministry of Education and Science of Spain, under a José Castillejo grant, and POSEIDON project (TSI2006-12507-C03-01)Publicad

On the p-adic uniformization of unitary Shimura curves

We prove $p$-adic uniformization for Shimura curves attached to the group of unitary similitudes of certain binary skew hermitian spaces $V$ with respect to an arbitrary CM field $K$ with maximal totally real subfield $F$. For a place $v|p$ of $F$ that is not split in $K$ and for which $V_v$ is anisotropic, let $\nu$ be an extension of $v$ to the reflex field $E$. We define an integral model of the corresponding Shimura curve over ${\rm Spec}\, O_{E, (\nu)}$ by means of a moduli problem for abelian schemes with suitable polarization and level structure prime to $p$. The formulation of the moduli problem involves a Kottwitz condition, an Eisenstein condition, and an adjusted invariant. The first two conditions are conditions on the Lie algebra of the abelian varieties; the last condition is a condition on the Riemann form of the polarization. The uniformization of the formal completion of this model along its special fiber is given in terms of the formal Drinfeld upper half plane for $F_v$. The proof relies on the construction of the contracting functor which relates a relative Rapoport-Zink space for strict formal $O_{F_v}$-modules with a Rapoport-Zink space of $p$-divisible groups which arise from the moduli problem, where the $O_{F_v}$-action is usually not strict when $F_v\ne \mathbb {Q}_p$. Our main tool is the theory of displays, in particular the Ahsendorf functor.Comment: 145 page

Theorie ohne Praxis? Die Kontrapunktlehre in italienischen Traktaten aus der zweiten Hälfte des 17. und zu Beginn des 18. Jahrhunderts

Im Gebiet des heutigen Italien entstehen in der zweiten Hälfte des 17. und zu Beginn des 18. Jahrhunderts zahlreiche musiktheoretische Traktate, darunter ein gutes Dutzend Schriften, die auch die Kontrapunktlehre behandeln. Diese wirken, gemessen an der gleichzeitigen kompositorischen Praxis und an den Schriften des 16. Jahrhunderts, merkwürdig konservativ. Die vorliegende Studie untersucht die in den Traktaten dargelegte Kontrapunktlehre auf ihre Inhalte, die spezifische Art ihrer Darstellung und die Traditionszusammenhänge von beiden. Anhand sozial- und kulturgeschichtlicher Überlegungen zu den Entstehungsumständen der Schriften wird außerdem eine Erklärung ihres konservativen Charakters versucht. Dass die Traktate - trotz ihren quantitativ überwiegenden traditionellen Lehrinhalten - nicht lediglich Dokumente musikspezifischer Sozialgeschichte sind, sondern ebenso in ihren besten und modernsten Partien Quellen historisch-informierter Analyse und Satzlehre, erweist die abschließende Analyse ausgewählter Literaturbeispiele

Watch Global, Cache Local: YouTube Network Traffic at a Campus Network - Measurements and Implications

User Generated Content has become very popular since the birth of web services such as YouTube allowing the distribution of such user-produced media content in an easy manner. YouTube-like services are different from existing traditional VoD services because the service provider has only limited control over the creation of new content. We analyze how the content distribution in YouTube is realized and then conduct a measurement study of YouTube traffic in a large university campus network. The analysis of the traffic shows that: (1) No strong correlation is observed between global and local popularity; (2) neither time scale nor user population has an impact on the local popularity distribution; (3) video clips of local interest have a high local popularity. Using our measurement data to drive trace-driven simulations, we also demonstrate the implications of alternative distribution infrastructures on the performance of a YouTube-like VoD service. The results of these simulations show that client-based local caching, P2P-based distribution, and proxy caching can reduce network traffic significantly and allow faster access to video clips

Uncovering Design: Translating the Past Can Enhance the Design Process

Throughout the late 20th century, urban buildings around the world have repeatedly lost their unique reason for being. The phenomenon of diminished value, while tragic at the time, provides extraordinary opportunities for future use, by offering an authentic narrative to build upon, and overcoming the "blank slate" approach of traditional design thinking. A current generation of designers is recognizing the potential value in these deteriorated and neglected structures and districts. However, we should look critically and creatively at the past to understand the causes of displacement, before attempting to design for the future. War, deindustrialization, tourism, gentrification, white-flight, and economic instability are some of the principal forces responsible for the emptying our downtown communities. By establishing proper analytical and imaginative lenses through which to examine unique developments around the world, we can better see how to reconstitute value in these derelict buildings, thus achieving a more sustainable future. This thesis applies a framework for interjecting creativity and considerations into the regeneration process. I will use a district of abandoned building in the Portland neighborhood of downtown Louisville, Kentucky, to depict these ideas at a variety of scales. This process will develop and utilize appropriate design principles and proposals, to illustrate how architecture can revitalize and reoccupy abandoned buildings, while bringing neighborhoods and communities back to life. In utilizing neglected but rediscovered space, urban infrastructure and buildings within the urban fabric, opportunities are created through the understanding and appreciation of existing contexts, combined with the integration of innovative approaches. The process of uncovering and providing alternative interventions strategies is not linear and blurs the edge between re-search and design. This thesis reveals how architects, by uncovering the past, can fuel a creative process and lead the transformation of a lost community