The resonance spectrum of the cusp map in the space of analytic functions

We prove that the Frobenius--Perron operator $U$ of the cusp map $F:[-1,1]\to[-1,1]$, $F(x)=1-2\sqrt{|x|}$ (which is an approximation of the Poincar\'e section of the Lorenz attractor) has no analytic eigenfunctions corresponding to eigenvalues different from 0 and 1. We also prove that for any $q\in(0,1)$ the spectrum of $U$ in the Hardy space in the disk \{z\in\C:|z-q|<1+q\} is the union of the segment $[0,1]$ and some finite or countably infinite set of isolated eigenvalues of finite multiplicity.Comment: Submitted to JMP; The description of the spectrum in some Hardy spaces is adde

Processor allocation for partitionable multiprocessor systems

The processor allocation problem in an n-dimensional hypercube multipro-cessor is similar to the conventional memory allocation problem. The main objective is to maximize the utilization of available resources as well as minimize the inherent system fragmentation. In this thesis, a new processor allocation strategy is proposed, and compared with the existing strategies, such as, the Buddy strategy, the Single Gray Code strategy (SGC), the Multiple Gray Code (MGC), and the Maximal Set of Subcubes (MSS). We will show that our proposed processor allocation strategy outperforms the existing strategies, by having the advantage of being able to allocate unused processors to other jobs/algorithms

Quasi Markovian behavior in mixing maps

We consider the time dependent probability distribution of a coarse grained observable Y whose evolution is governed by a discrete time map. If the map is mixing, the time dependent one-step transition probabilities converge in the long time limit to yield an ergodic stochastic matrix. The stationary distribution of this matrix is identical to the asymptotic distribution of Y under the exact dynamics. The nth time iterate of the baker map is explicitly computed and used to compare the time evolution of the occupation probabilities with those of the approximating Markov chain. The convergence is found to be at least exponentially fast for all rectangular partitions with Lebesgue measure. In particular, uniform rectangles form a Markov partition for which we find exact agreement.Comment: 16 pages, 1 figure, uses elsart.sty, to be published in Physica D Special Issue on Predictability: Quantifying Uncertainty in Models of Complex Phenomen

Resonances, Unstable Systems and Irreversibility: Matter Meets Mind

The fundamental time-reversal invariance of dynamical systems can be broken in various ways. One way is based on the presence of resonances and their interactions giving rise to unstable dynamical systems, leading to well-defined time arrows. Associated with these time arrows are semigroups bearing time orientations. Usually, when time symmetry is broken, two time-oriented semigroups result, one directed toward the future and one directed toward the past. If time-reversed states and evolutions are excluded due to resonances, then the status of these states and their associated backwards-in-time oriented semigroups is open to question. One possible role for these latter states and semigroups is as an abstract representation of mental systems as opposed to material systems. The beginnings of this interpretation will be sketched.Comment: 9 pages. Presented at the CFIF Workshop on TimeAsymmetric Quantum Theory: The Theory of Resonances, 23-26 July 2003, Instituto Superior Tecnico, Lisbon, Portugal; and at the Quantum Structures Association Meeting, 7-22 July 2004, University of Denver. Accepted for publication in the Internation Journal of Theoretical Physic

A mixed logit model for the sensitivity analysis of Greek drivers' behaviour towards enforcement for road safety

Traffic violations are among the leading causes of road accidents. In this research, the sensitivity of Greek drivers to a hypothetical intensification of police enforcement for speed violations and improper overtaking is analyzed, using stated preference data. Under the assumption of increased police enforcement, drivers were presented with the option to maintain their unsafe driving patterns (and risk getting fined) or comply with the traffic laws (and experience longer trip duration). A parsimonious mixed logit model has been estimated and sensitivity analysis is performed with respect to the main variables. The model explicitly captures the (unobserved) heterogeneity in the sample, and reflects the fixed random parameter across observations from the same respondent. The behaviour of the surveyed drivers depends on socioeconomic characteristics and trip characteristics. Based on the presented sensitivity analysis, it can be argued that while the “typical” Greek driver may not be particularly riskprone, there are segments of the population that show a tendency to violate traffic laws. This is a useful finding that could be used by policy makers e.g. to develop targeted police enforcement campaigns (or targeted media campaigns, special education initiatives, etc.), aimed at the demographic segments with a higher tendency for traffic violation

Resonances of the cusp family

We study a family of chaotic maps with limit cases the tent map and the cusp map (the cusp family). We discuss the spectral properties of the corresponding Frobenius--Perron operator in different function spaces including spaces of analytic functions. A numerical study of the eigenvalues and eigenfunctions is performed.Comment: 14 pages, 3 figures. Submitted to J.Phys.

Non-trivial stably free modules over crossed products

We consider the class of crossed products of noetherian domains with universal enveloping algebras of Lie algebras. For algebras from this class we give a sufficient condition for the existence of projective non-free modules. This class includes Weyl algebras and universal envelopings of Lie algebras, for which this question, known as noncommutative Serre's problem, was extensively studied before. It turns out that the method of lifting of non-trivial stably free modules from simple Ore extensions can be applied to crossed products after an appropriate choice of filtration. The motivating examples of crossed products are provided by the class of RIT algebras, originating in non-equilibrium physics.Comment: 13 page

Understanding the landscape of shared-e-scooters in North America; Spatiotemporal analysis and policy insights

Shared-e-scooters are being introduced in cities worldwide, with their introduction often being distant from the actual service characteristics understanding, potential benefits, and threats realization. This research explores scooter use by examining approximately nine million scooter trips from five North American cities (Austin; TX, Calgary; AB, Chicago; IL, Louisville; KY, Minneapolis; MN). By investigating the spatiotemporal hourly and daily use, we found that demand patterns tend to be similar in the different cities. Trip characteristics (speed, duration, and distance) are almost empirically consistent across the five cities; however, there is evidence that trip characteristics change over time in the same city. We also examined the impact of exogenous factors on scooter demand, and found that weather (temperature, wind speed, precipitation, and snow), day of the week, infrastructure (bike lanes, sidewalks, and shared bike stations), sociodemographics (gender, age, and income), land use, and accessibility to transit significantly impact demand. Findings highlight the need for evidence-based examination of shared-e-scooters and regulatory processes to guide policy decisions by the different stakeholders

Shared autonomous vehicle services: A comprehensive review

© 2019 Elsevier Ltd The actions of autonomous vehicle manufacturers and related industrial partners, as well as the interest from policy makers and researchers, point towards the likely initial deployment of autonomous vehicles as shared autonomous mobility services. Numerous studies are lately being published regarding Shared Autonomous Vehicle (SAV) applications and hence, it is imperative to have a comprehensive outlook, consolidating the existing knowledge base. This work comprehensively consolidates studies in the rapidly emerging field of SAV. The primary focus is the comprehensive review of the foreseen impacts, which are categorised into seven groups, namely (i) Traffic & Safety, (ii) Travel behaviour, (iii) Economy, (iv) Transport supply, (v) Land–use, (vi) Environment & (vii) Governance. Pertinently, an SAV typology is presented and the components involved in modelling SAV services are described. Issues relating to the expected demand patterns and a required suitable policy framework are explicitly discussed