Enhanced non-perturbative effects through the collinear anomaly

We show that non-perturbative effects are logarithmically enhanced for transverse-momentum-dependent observables such as q_T-spectra of electroweak bosons in hadronic collisions and jet broadening at e^+e^- colliders. This enhancement arises from the collinear anomaly, a mechanism characteristic for transverse observables, which induces logarithmic dependence on the hard scale in the product of the soft and collinear matrix elements. Our analysis is based on an operator product expansion and provides, for the first time, a systematic, model-independent way to study non-perturbative effects for this class of observables. For the case of jet broadening, we relate the leading correction to the non-perturbative shift of the thrust distribution.Comment: 5 pages, 2 figures. v2: Minor changes, references added. Journal versio

A C*-algebra of geometric operators on self-similar CW-complexes. Novikov-Shubin and L^2-Betti numbers

A class of CW-complexes, called self-similar complexes, is introduced, together with C*-algebras A_j of operators, endowed with a finite trace, acting on square-summable cellular j-chains. Since the Laplacian Delta_j belongs to A_j, L^2-Betti numbers and Novikov-Shubin numbers are defined for such complexes in terms of the trace. In particular a relation involving the Euler-Poincare' characteristic is proved. L^2-Betti and Novikov-Shubin numbers are computed for some self-similar complexes arising from self-similar fractals.Comment: 30 pages, 7 figure

Large deviation rule for Anosov flows

The volume contraction in dissipative reversible transitive Anosov flows obeys a large deviation rule (fluctuation theorem).Comment: See instruction at the beginning of the tex file, in order to obatin the (two) postscript figures. The file is in Plain Te

Mathematics in the work of Spinoza and Guarini

During the seventeenth century mathematics and the exact sciences brought about a scientific revolution, and seemed to be involved in all novel social developments of the time. To give just a few examples, Newton (1643-1727) used mathematical principles to explain the philosophy of nature in his Principia, and, prior to that, Descartes (1569-1650) used mathematics as a model for his metaphysics, his main concern for many years. His greatest legacy, for the purposes and framing of this paper, has to do with moving classical geometry within the reach of algebra, putting into connection Euclid's and Vitruvius’s theories. This has great relevance within the field of architecture, translating these theories to the building experience of that period. Baroque architecture indeed shares with mathematics a spatial structure which combines the arts and the sciences. Space is controlled by the possible variations of mathematical laws — which is the cause of the way in which architects struggle to work within pre-established rules.The aim of this paper, intended as research from a history of architectural points of view, is to find relations between the idea of mathematics used by Spinoza (Ethics) and Guarini (Placita philosophica; Architettura civile) in their metaphysics, and the outcomes they had in architecture. In addition, if it is difficult to establish whether Spinoza had any influence on Guarini — their most relevant texts were published posthumously — the role of mathematics in the work of these two figures, whose similarities and differences are worth enumerating, is particularly interesting when related to the architectural period of Baroque, a period when the use of mathematics in architecture might be said to have reached a peak.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Status of Neutrino Masses and Mixing in 2010

We present a short summary of our present knowledge and understanding of neutrino masses and mixing.Comment: 15 pages, 2 figures. Talk given at the Quarks, Strings and the Cosmos - Hector Rubinstein Memorial Symposium, August 09-11, 2010, AlbaNova, Stockholm, Swede

Essay: Developing Appropriate Standards for Achieving Diversity in Faculty Appointments

I am writing today to talk about diversity within law school faculties. And when I say “diversity,” I mean all sorts of diversities, not just the ones that most of those who address the issue tend to focus on. I have, for many years, been thinking about the different types of diversities that seem crucial to a law school, and the appropriate ways of achieving them. Part I lists the categories of diversity that I think are important to considering diversity within law school faculties. It then indicates a problem that inheres with this list. Part II suggests how different schools may view the appropriateness of achieving some of these diversities. And finally, in Part III, I will come to the main thesis of this piece and propose how schools can achieve the diversities they deem desirable

Two Conceptions of Logical Form

In this paper a brief presentation of Wittgenstein"s picture theory of language is provided, as it is put forth in the Tractatus Logico-Philosophicus. Then some conclusions are drawn with reference to the notion of logical form; in particular, two different conceptions of logical form are expounded, and one of them is shown to be untenable. Two are the features of the picture theory which interest us here. The first is the automatism of sense, i.e. the idea that, once the referents of the names occurring in a proposition are fixed, then the sense of the proposition is automatically determined. That also means that when we know what the names occurring in a proposition refer to, we automatically grasp the sense of the proposition itself: no other piece of information is required