Random trees between two walls: Exact partition function

We derive the exact partition function for a discrete model of random trees embedded in a one-dimensional space. These trees have vertices labeled by integers representing their position in the target space, with the SOS constraint that adjacent vertices have labels differing by +1 or -1. A non-trivial partition function is obtained whenever the target space is bounded by walls. We concentrate on the two cases where the target space is (i) the half-line bounded by a wall at the origin or (ii) a segment bounded by two walls at a finite distance. The general solution has a soliton-like structure involving elliptic functions. We derive the corresponding continuum scaling limit which takes the remarkable form of the Weierstrass p-function with constrained periods. These results are used to analyze the probability for an evolving population spreading in one dimension to attain the boundary of a given domain with the geometry of the target (i) or (ii). They also translate, via suitable bijections, into generating functions for bounded planar graphs.Comment: 25 pages, 7 figures, tex, harvmac, epsf; accepted version; main modifications in Sect. 5-6 and conclusio

Integrability of graph combinatorics via random walks and heaps of dimers

We investigate the integrability of the discrete non-linear equation governing the dependence on geodesic distance of planar graphs with inner vertices of even valences. This equation follows from a bijection between graphs and blossom trees and is expressed in terms of generating functions for random walks. We construct explicitly an infinite set of conserved quantities for this equation, also involving suitable combinations of random walk generating functions. The proof of their conservation, i.e. their eventual independence on the geodesic distance, relies on the connection between random walks and heaps of dimers. The values of the conserved quantities are identified with generating functions for graphs with fixed numbers of external legs. Alternative equivalent choices for the set of conserved quantities are also discussed and some applications are presented.Comment: 38 pages, 15 figures, uses epsf, lanlmac and hyperbasic

Investigation of peak shapes in the MIBETA experiment calibrations

In calorimetric neutrino mass experiments, where the shape of a beta decay spectrum has to be precisely measured, the understanding of the detector response function is a fundamental issue. In the MIBETA neutrino mass experiment, the X-ray lines measured with external sources did not have Gaussian shapes, but exhibited a pronounced shoulder towards lower energies. If this shoulder were a general feature of the detector response function, it would distort the beta decay spectrum and thus mimic a non-zero neutrino mass. An investigation was performed to understand the origin of the shoulder and its potential influence on the beta spectrum. First, the peaks were fitted with an analytic function in order to determine quantitatively the amount of events contributing to the shoulder, also depending on the energy of the calibration X-rays. In a second step, Montecarlo simulations were performed to reproduce the experimental spectrum and to understand the origin of its shape. We conclude that at least part of the observed shoulder can be attributed to a surface effect

Real-Time Temperature Sensing Using a Ratiometric Dual Fluorescent Protein Biosensor

Accurate temperature control within biological and chemical reaction samples and instrument calibration are essential to the diagnostic, pharmaceutical and chemical industries. This is particularly challenging for microlitre-scale reactions typically used in real-time PCR applications and differential scanning fluorometry. Here, we describe the development of a simple, inexpensive ratiometric dual fluorescent protein temperature biosensor (DFPTB). A combination of cycle three green fluorescent protein and a monomeric red fluorescent protein enabled the quantification of relative temperature changes and the identification of temperature discrepancies across a wide temperature range of 4–70 °C. The maximal sensitivity of 6.7% °C−1 and precision of 0.1 °C were achieved in a biologically relevant temperature range of 25–42 °C in standard phosphate-buffered saline conditions at a pH of 7.2. Good temperature sensitivity was achieved in a variety of biological buffers and pH ranging from 4.8 to 9.1. The DFPTB can be used in either purified or mixed bacteria-encapsulated formats, paving the way for in vitro and in vivo applications for topologically precise temperature measurements

Confluence of geodesic paths and separating loops in large planar quadrangulations

We consider planar quadrangulations with three marked vertices and discuss the geometry of triangles made of three geodesic paths joining them. We also study the geometry of minimal separating loops, i.e. paths of minimal length among all closed paths passing by one of the three vertices and separating the two others in the quadrangulation. We concentrate on the universal scaling limit of large quadrangulations, also known as the Brownian map, where pairs of geodesic paths or minimal separating loops have common parts of non-zero macroscopic length. This is the phenomenon of confluence, which distinguishes the geometry of random quadrangulations from that of smooth surfaces. We characterize the universal probability distribution for the lengths of these common parts.Comment: 48 pages, 33 color figures. Final version, with one concluding paragraph and one reference added, and several other small correction

Policy-based management for body-sensor networks

Accepted versio

Verification of Policy-based Self-Managed Cell Interactions Using Alloy

Abstract—Self-Managed Cells (SMCs) define an infrastruc-ture for building ubiquitous computing applications. An SMC consists of an autonomous administrative domain based on a policy-driven feedback control-loop. SMCs are able to interact with each other and compose with other SMCs to form larger autonomous components. In this paper we present a formal specification of an SMC’s behaviour for the analysis and verification of its operation in collaborations of SMCs. These collaborations typically involve SMCs originated from different administrative authorities, and the definition of a formal model has helped us to verify the correctness of their operation when SMCs are composed or federated. Keywords-policy-based management; self-managed cells; in-teractions; model-checking; I

Comparison of measured and predicted performance of a SIS waveguide mixer at 345 GHz

The measured gain and noise of a SIS waveguide mixer at 345 GHz have been compared with theoretical values, calculated from the quantum mixer theory using a three port model. As a mixing element, we use a series array of two Nb-Al2O3-Nb SIS junctions. The area of each junction is 0.8 sq microns and the normal state resistance is 52 omega. The embedding impedance of the mixer has been determined from the pumped DC-IV curves of the junction and is compared to results from scale model measurements (105 x). Good agreement was obtained. The measured mixer gain, however, is a factor of 0.45 plus or minus 0.5 lower than the theoretical predicted gain. The measured mixer noise temperature is a factor of 4-5 higher than the calculated one. These discrepancies are independent on pump power and are valid for a broad range of tuning conditions