A Birkhoff connection between quantum circuits and linear classical reversible circuits

Birkhoff's theorem tells how any doubly stochastic matrix can be decomposed as a weighted sum of permutation matrices. Similar theorems on unitary matrices reveal a connection between quantum circuits and linear classical reversible circuits. It triggers the question whether a quantum computer can be regarded as a superposition of classical reversible computers

Stochastic velocity motions and processes with random time

The aim of this paper is to analyze a class of random motions which models the motion of a particle on the real line with random velocity and subject to the action of the friction. The speed randomly changes when a Poissonian event occurs. We study the characteristic and the moment generating function of the position reached by the particle at time $t>0$. We are able to derive the explicit probability distributions in few cases for which discuss the connections with the random flights. The moments are also widely analyzed. For the random motions having an explicit density law, further interesting probabilistic interpretations emerge if we deal with them varying up a random time. Essentially, we consider two different type of random times, namely Bessel and Gamma times, which contain, as particular cases, some important probability distributions (e.g. Gaussian, Exponential). In particular, for the random processes built by means of these compositions, we derive the probability distributions fixed the number of Poisson events. Some remarks on the possible extensions to the random motions in higher spaces are proposed. We focus our attention on the persistent planar random motion

Strategies for Developing Sustainable Design Practice for Students and SME Professionals

Designers and engineers seem finally to be awakening to the challenge that sustainable development has given. Educators and students alike are keenly aware of the need to become more effective in the training and practice of their specific disciplines with respect to sustainability. \noindent In the past four years since this research has developed, there has been a marked change in the mass market appeal for sustainable products and services. Implementation of sustainable design practice from both recent graduates and also innovative small and medium enterprises (SMEs) at a local level is slow. One would assume that the consumer drive would push a change in design practice but perhaps the complexities of sustainable design along with the lack of experience in the field are providing barriers to designers and marketers alike. In addition the SME sector alone makes up the bulk of industry within the European Union (EU) varying in some countries from 80-95% of the total numbers of companies (Tukker et al. 2000). These industries by their nature find it difficult to dedicate expertise solely to sustainable development issues. The strategy outlined in this paper intended to introduce concepts of sustainable design thinking and practice to both SMEs and undergraduate students. \noindent This current and ongoing research qualitatively assesses appropriate models for educating for sustainable design thinking with SME employees and undergraduate design students. The sample groups include Industrial Design and Product Design undergraduate students in Ireland at the Institute of Technology, Carlow (IT Carlow), The University of Limerick (UL) and a sample of SMEs in the South East of Ireland, with broad national participation from other students of design and professionals from industry. Current levels of understanding of students and SME professionals of key environmental and social issues are measured

Integrability of Dirac reduced bi-Hamiltonian equations

First, we give a brief review of the theory of the Lenard-Magri scheme for a non-local bi-Poisson structure and of the theory of Dirac reduction. These theories are used in the remainder of the paper to prove integrability of three hierarchies of bi-Hamiltonian PDE's, obtained by Dirac reduction from some generalized Drinfeld-Sokolov hierarchies.Comment: 15 pages. Corrected some typos and added missing equations in Section 5 for g=sl_n, n>

Bose-Einstein Correlations in e+e- -> W+W- at a Linear Collider

We show that the most popular method to simulate Bose-Einstein (BE) interference effects predicts negligible correlations between identical pions originating from the hadronic decay of different W's produced in e+e- -> W+W- -> 4 jets at typical linear collider energies.Comment: 5 pages, 2 eps figures, Proccedings of the Workshop "Physics Studies for a Future Linear Collider", QCD Working Group, 2000, DESY 123

Measuring the W-Boson mass at a hadron collider: a study of phase-space singularity methods

The traditional method to measure the W-Boson mass at a hadron collider (more precisely, its ratio to the Z-mass) utilizes the distributions of three variables in events where the W decays into an electron or a muon: the charged-lepton transverse momentum, the missing transverse energy and the transverse mass of the lepton pair. We study the putative advantages of the additional measurement of a fourth variable: an improved phase-space singularity mass. This variable is statistically optimal, and simultaneously exploits the longitudinal- and transverse-momentum distributions of the charged lepton. Though the process we discuss is one of the simplest realistic ones involving just one unobservable particle, it is fairly non-trivial and constitutes a good "training" example for the scrutiny of phenomena involving invisible objects. Our graphical analysis of the phase space is akin to that of a Dalitz plot, extended to such processes.Comment: 11 pages. 9 figures. Version to be published in JHE

Trigger strategies for SUSY searches at the LHC

Supersymmetry will be searched for in a variety of final states at the LHC. It is crucial that a robust, efficient and unbiased trigger selection for SUSY is implemented from the very early days of data taking. After a brief description of the ATLAS and the CMS trigger systems, and a more in-depth discussion of the ATLAS High-Level Trigger, a triggering strategy is outlined for early SUSY searches at the LHC.Comment: Submitted for the SUSY07 Proceedings, 4 pages, 3 eps figures, LaTe