Analysis of airplane boarding via space-time geometry and random matrix theory

We show that airplane boarding can be asymptotically modeled by 2-dimensional Lorentzian geometry. Boarding time is given by the maximal proper time among curves in the model. Discrepancies between the model and simulation results are closely related to random matrix theory. We then show how such models can be used to explain why some commonly practiced airline boarding policies are ineffective and even detrimental.Comment: 4 page

Discrete charging of metallic grains: Statistics of addition spectra

We analyze the statistics of electrostatic energies (and their differences) for a quantum dot system composed of a finite number $K$ of electron islands (metallic grains) with random capacitance-inductance matrix $C$, for which the total charge is discrete, $Q=Ne$ (where $e$ is the charge of an electron and $N$ is an integer). The analysis is based on a generalized charging model, where the electrons are distributed among the grains such that the electrostatic energy E(N) is minimal. Its second difference (inverse compressibility) $\chi_{N}=E(N+1)-2 E(N)+E(N-1)$ represents the spacing between adjacent Coulomb blockade peaks appearing when the conductance of the quantum dot is plotted against gate voltage. The statistics of this quantity has been the focus of experimental and theoretical investigations during the last two decades. We provide an algorithm for calculating the distribution function corresponding to $\chi_{N}$ and show that this function is piecewise polynomial.Comment: 21 pages, no figures, mathematical nomenclature (except for Abstract and Introduction

Approaches for improving cutting processes and machine too in re-contouring

Re-contouring in the repair process of aircraft engine blades and vanes is a crucial task. Highest demands are made on the geometrical accuracy as well as on the machined surface of the part. Complexity rises even more due to the unique part characteristic originating from the operation and repair history. This requires well-designed processes and machine tool technologies. In this paper, approaches for coping with these challenges and improving the re-contouring process are described and discussed. This includes an advanced process simulation with its capabilities to accurately depict different material areas and predict process forces. Beyond, experimental investigations on workpiece-tooldeflection are presented. Finally, a machine tool prototype with a novel electromagnetic guiding system is introduced and the benefits of this technology in the field of repair are outlined.DFG/CRC/87

Ergodicity, Decisions, and Partial Information

In the simplest sequential decision problem for an ergodic stochastic process X, at each time n a decision u_n is made as a function of past observations X_0,...,X_{n-1}, and a loss l(u_n,X_n) is incurred. In this setting, it is known that one may choose (under a mild integrability assumption) a decision strategy whose pathwise time-average loss is asymptotically smaller than that of any other strategy. The corresponding problem in the case of partial information proves to be much more delicate, however: if the process X is not observable, but decisions must be based on the observation of a different process Y, the existence of pathwise optimal strategies is not guaranteed. The aim of this paper is to exhibit connections between pathwise optimal strategies and notions from ergodic theory. The sequential decision problem is developed in the general setting of an ergodic dynamical system (\Omega,B,P,T) with partial information Y\subseteq B. The existence of pathwise optimal strategies grounded in two basic properties: the conditional ergodic theory of the dynamical system, and the complexity of the loss function. When the loss function is not too complex, a general sufficient condition for the existence of pathwise optimal strategies is that the dynamical system is a conditional K-automorphism relative to the past observations \bigvee_n T^n Y. If the conditional ergodicity assumption is strengthened, the complexity assumption can be weakened. Several examples demonstrate the interplay between complexity and ergodicity, which does not arise in the case of full information. Our results also yield a decision-theoretic characterization of weak mixing in ergodic theory, and establish pathwise optimality of ergodic nonlinear filters.Comment: 45 page

Demand-Driven Scheduling of Movies in a Multiplex

This paper describes a model that generates weekly movie schedules in a multiplex movie theater. A movie schedule specifies within each day of the week, on which screen(s) different movies will be played, and at which time(s). The model consists of two parts: (i) conditional forecasts of the number of visitors per show for any possible starting time; and (ii) an optimization procedure that quickly finds an almost optimal schedule (which can be demonstrated to be close to the optimal schedule). To generate this schedule we formulate the so-called movie scheduling problem as a generalized set partitioning problem. The latter is solved with an algorithm based on column generation techniques. We have applied this combined demand forecasting /schedule optimization procedure to a multiplex in Amsterdam where we supported the scheduling of fourteen movie weeks. The proposed model not 2 only makes movie scheduling easier and less time consuming, but also generates schedules that would attract more visitors than the current ‘intuition-based’ schedules

Особенности процесса трещинообразования в массиве при управлении его газодинамикой

Исследован процесс сдерживания перехода угля из потенциально устойчивого состояния в стадию бурного разрушения. Ей, как правило, предшествует некоторый промежуток времени относительного затишья. Особенно важно улавливать этот момент среди массы различных откликов массива на ведение горных работ. Одним из вариантов управления развитием и релаксацией системы трещин может служить физико-химическая обработка.The inhibition process of coal transition from the potentially stable state in the stage of stormy destruction is investigation. As a rule, to it is preceded some interval of relative time calm. It is especially important to catch this moment among mass of different responses of array on the conduct of mountain works. Physical and chemical treatment can serve as one of control variants the development and relaxation of the cracks system

Kick stability in groups and dynamical systems

We consider a general construction of ``kicked systems''. Let G be a group of measure preserving transformations of a probability space. Given its one-parameter/cyclic subgroup (the flow), and any sequence of elements (the kicks) we define the kicked dynamics on the space by alternately flowing with given period, then applying a kick. Our main finding is the following stability phenomenon: the kicked system often inherits recurrence properties of the original flow. We present three main examples. 1) G is the torus. We show that for generic linear flows, and any sequence of kicks, the trajectories of the kicked system are uniformly distributed for almost all periods. 2) G is a discrete subgroup of PSL(2,R) acting on the unit tangent bundle of a Riemann surface. The flow is generated by a single element of G, and we take any bounded sequence of elements of G as our kicks. We prove that the kicked system is mixing for all sufficiently large periods if and only if the generator is of infinite order and is not conjugate to its inverse in G. 3) G is the group of Hamiltonian diffeomorphisms of a closed symplectic manifold. We assume that the flow is rapidly growing in the sense of Hofer's norm, and the kicks are bounded. We prove that for a positive proportion of the periods the kicked system inherits a kind of energy conservation law and is thus superrecurrent. We use tools of geometric group theory and symplectic topology.Comment: Latex, 40 pages, revised versio

Autonomous quantum machines and the finite sized Quasi-Ideal clock

Processes such as quantum computation, or the evolution of quantum cellular automata are typically described by a unitary operation implemented by an external observer. In particular, an interaction is generally turned on for a precise amount of time, using a classical clock. A fully quantum mechanical description of such a device would include a quantum description of the clock whose state is generally disturbed because of the back-reaction on it. Such a description is needed if we wish to consider finite sized autonomous quantum machines requiring no external control. The extent of the back-reaction has implications on how small the device can be, on the length of time the device can run, and is required if we want to understand what a fully quantum mechanical treatment of an observer would look like. Here, we consider the implementation of a unitary by a finite sized device which we call the "Quasi-Ideal clock", and show that the back-reaction on it can be made exponentially small in the device's dimension with only a linear increase in energy. As a result, an autonomous quantum machine need only be of modest size and or energy. We are also able to solve a long-standing open problem by using a finite sized quantum clock to approximate the continuous evolution of an Idealised clock. The result has implications on the equivalence of different paradigms of quantum thermodynamics, some which allow external control and some which only allow autonomous thermal machines.Comment: Main text: 9 + 53 pages. V4: Close to the published version, J. Annales Henri Poincar\'e (2018) [Communicated by David P\'erez-Garc\'ia

Developmental perspectives on Europe

The crisis of 2008–2009 has ended, stockmarkets skyrocketed in 2012–2013, while growth of the real sector remained sluggish in Europe. This article attempts to explain the latter puzzle. Analyzing long term factors, the costs of short-termism in crisis management become obvious. The limitations of EU as a growth engine are highlighted