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The maximum of Brownian motion minus a parabola

We derive a simple integral representation for the distribution of the maximum of Brownian motion minus a parabola, which can be used for computing the density and moments of the distribution, both for one-sided and two-sided Brownian motion.Comment: 7 pages, 4 figures, to appear in the Electronic Journal of Probabilit

Principales colaboradores

Esta sección ofrece un currículum resumido de los principales colaboradores de esta obra.

Large-angle Polarization of the Cosmic Microwave Background Radiation and Reionization

We discuss the effect of matter reionization on the large-angular-scale anisotropy and polarization of the cosmic microwave background radiation (CMBR) in the standard CDM model. We separate three cases in which the anisotropy is induced by pure scalar, pure tensor, and mixed metric perturbations respectively. It is found that, if reionization occurs early enough, the polarization can reach a detectable level of sequentially $6\%$, $9\%$, and $6.5\%$ of the anisotropy. In general, a higher degree of polarization implies a dominant contribution from the tensor mode or reionization at high redshift. Since early reionization will suppress small-scale CMBR anisotropies and polarizations significantly, measuring the polarization on few degree scales can be a direct probe of the reionization history of the early universe.Comment: Changes in the revised version: 1. Below Eq. (2), we demonstrate the method of our numerical work, by adding the evolution equations for the Legendre coefficents for both the scalar and tensor mode pertubations. 2. Below Eq. (9), we added a paragraph on discussing the basis we employed in computing the polarization correlation function. 3. In Sec. 4, we have rewritten the first and second paragraphs, where we illustrate how to the explain the discrepancies with the previous wor

Instanton Floer homology and the Alexander polynomial

The instanton Floer homology of a knot in the three-sphere is a vector space with a canonical mod 2 grading. It carries a distinguished endomorphism of even degree,arising from the 2-dimensional homology class represented by a Seifert surface. The Floer homology decomposes as a direct sum of the generalized eigenspaces of this endomorphism. We show that the Euler characteristics of these generalized eigenspaces are the coefficients of the Alexander polynomial of the knot. Among other applications, we deduce that instanton homology detects fibered knots.Comment: 25 pages, 6 figures. Revised version, correcting errors concerning mod 2 gradings in the skein sequenc

Enfoques contemporáneos sobre la cuenta corriente

En esta sección se incluyen los ensayos “¿Importa la cuenta corriente? El punto de vista tradicional y el moderno” de Max Corden y “Un marco de análisis teórico para el ‘problema’ de la cuenta corriente” de Raúl Aníbal Feliz, así como un comentario general de Jacques Polak, que se presentaron en el seminario sobre la relevancia de la cuenta corriente, que organizó la revista Economía Mexicana. Nueva Época en la sexagésima segunda Conferencia Anual de la Southern Economic Association en la ciudad de Washington, D.C., en noviembre de 1992.

New Results in Light-Front Phenomenology

The light-front quantization of gauge theories such as QCD in light-cone gauge provides a frame-independent wavefunction representation of relativistic bound states, simple forms for current matrix elements, explicit unitarity, and a trivial vacuum. The freedom to choose the light-like quantization four-vector provides an explicitly covariant formulation of light-front quantization and can be used to determine the analytic structure of light-front wave functions and to define a kinematical definition of angular momentum. The AdS/CFT correspondence of large $N_C$ supergravity theory in higher-dimensional anti-de Sitter space with supersymmetric QCD in 4-dimensional space-time has interesting implications for hadron phenomenology in the conformal limit, including an all-orders demonstration of counting rules for exclusive processes. String/gauge duality also predicts the QCD power-law behavior of light-front Fock-state hadronic wavefunctions with arbitrary orbital angular momentum at high momentum transfer. The form of these near-conformal wavefunctions can be used as an initial ansatz for a variational treatment of the light-front QCD Hamiltonian. I also briefly review recent analyses which shows that some leading-twist phenomena such as the diffractive component of deep inelastic scattering, single-spin asymmetries, nuclear shadowing and antishadowing cannot be computed from the LFWFs of hadrons in isolation.Comment: Presented at LightCone 2004, Amsterdam, The Netherlands, 16-20 August 200

On a Problem of Harary and Schwenk on Graphs with Distinct Eigenvalues

Harary and Schwenk posed the problem forty years ago: Which graphs have distinct adjacency eigenvalues? In this paper, we obtain a necessary and sufficient condition for an Hermitian matrix with simple spectral radius and distinct eigenvalues. As its application, we give an algebraic characterization to the Harary-Schwenk's problem. As an extension of their problem, we also obtain a necessary and sufficient condition for a positive semidefinite matrix with simple least eigenvalue and distinct eigenvalues, which can provide an algebraic characterization to their problem with respect to the (normalized) Laplacian matrix.Comment: 11 page

Rethinking the Social Construction of Technology Through 'Following the Actors': A Reappraisal of Technological Frames

In this paper, I summarize case study research on an information system called Connected Kids. This case study was guided by an approach to technology studies called the \'Social construction of technology\' or SCOT Bijker (1984). In discussing Connected Kids, I illustrate many of SCOT\'s main tenents, e.g. the various social interactions that surround and influence technology design. As the paper progresses, however, I focus on one concept in particular, i.e. SCOT\'s notion of a \'technological frame,\' which is used as a catch-all concept for handling the structural influences in technology design. My discussion and illustration of this concept shows that – whilst technological frames help an analyst understand, in general terms, the role structure(s) play in shaping technology – the \'heterogeneity\' of technological frames can cloak the more obvious, and potentially most influential, forces at work in technology design. In the case of Connected kids, the role of resources, and which actors had access to these resources, was critical in pointing Connected Kids down a particular trajectory. Further, this discovery emerged from listening carefully to respondents\' comments on the role of resources in their community. These comments, and my own observations on how resource-access propelled certain actors into a leadership position, led to my developing an alternative method for analyzing technological frames. The implications of this analysis are then discussed within the context of SCOT and technology studies more generally.Social Construction of Technology, Technological Frames, Information Technology

Safe Schedulability of Bounded-Rate Multi-Mode Systems

Bounded-rate multi-mode systems (BMMS) are hybrid systems that can switch freely among a finite set of modes, and whose dynamics is specified by a finite number of real-valued variables with mode-dependent rates that can vary within given bounded sets. The schedulability problem for BMMS is defined as an infinite-round game between two players---the scheduler and the environment---where in each round the scheduler proposes a time and a mode while the environment chooses an allowable rate for that mode, and the state of the system changes linearly in the direction of the rate vector. The goal of the scheduler is to keep the state of the system within a pre-specified safe set using a non-Zeno schedule, while the goal of the environment is the opposite. Green scheduling under uncertainty is a paradigmatic example of BMMS where a winning strategy of the scheduler corresponds to a robust energy-optimal policy. We present an algorithm to decide whether the scheduler has a winning strategy from an arbitrary starting state, and give an algorithm to compute such a winning strategy, if it exists. We show that the schedulability problem for BMMS is co-NP complete in general, but for two variables it is in PTIME. We also study the discrete schedulability problem where the environment has only finitely many choices of rate vectors in each mode and the scheduler can make decisions only at multiples of a given clock period, and show it to be EXPTIME-complete.Comment: Technical report for a paper presented at HSCC 201