Permutation Tests for Equality of Distributions of Functional Data

Economic data are often generated by stochastic processes that take place in continuous time, though observations may occur only at discrete times. For example, electricity and gas consumption take place in continuous time. Data generated by a continuous time stochastic process are called functional data. This paper is concerned with comparing two or more stochastic processes that generate functional data. The data may be produced by a randomized experiment in which there are multiple treatments. The paper presents a method for testing the hypothesis that the same stochastic process generates all the functional data. The test described here applies to both functional data and multiple treatments. It is implemented as a combination of two permutation tests. This ensures that in finite samples, the true and nominal probabilities that each test rejects a correct null hypothesis are equal. The paper presents upper and lower bounds on the asymptotic power of the test under alternative hypotheses. The results of Monte Carlo experiments and an application to an experiment on billing and pricing of natural gas illustrate the usefulness of the test.Comment: 47 pages, 6 figures, 3 table

Exact results for a noise-induced bistable system

A stochastic system where bistability is caused by noise has been recently investigated by Biancalani et al. (PRL 112:038101, 2014). They have computed the mean switching time for such a system using a continuous Fokker-Planck equation derived from the Taylor expansion of the Master equation to estimate the parameter of such a system from experiment. In this article, we provide the exact solution for the full discrete system without resorting to continuous approximation and obtain the expression for the mean switching time. We further extend this investigation by solving exactly the Master equation and obtaining the expression of other quantities of interests such as the dynamics of the moments and the equilibrium time

A Comment on "Cycles and Instability in a Rock-Paper-Scissors Population Game: A Continuous Time Experiment"

The authors (Cason, Friedman and Hopkins, Reviews of Economics Studies, 2014) claimed a result that the treatments (using simultaneous matching in discrete time) replicate previous results that exhibit weak or no cycles. After correct two mathematical mistakes in their cycles tripwire algorithm, we research the cycles by scanning the tripwire in the full strategy space of the games and we find significant cycles missed by the authors. So we suggest that, all of the treatments (using simultaneous matching in discrete time) exhibit significant cycles.Comment: 2 pages, Keywords: experiments, cycles, mixed equilibrium, discrete time. JEL numbers: C72, C73, C92, D8

Time Horizon and Cooperation in Continuous Time

When subjects interact in continuous time, their ability to cooperate may dramatically increase. In an experiment, we study the impact of different time horizons on cooperation in (quasi) continuous time prisoner's dilemmas. We find that cooperation levels are similar or higher when the horizon is deterministic rather than stochastic. Moreover, a deterministic duration generates different aggregate patterns and individual strategies than a stochastic one. For instance, under a deterministic horizon subjects show high initial cooperation and a strong end-of-period reversal to defection. Moreover, they do not learn to apply backward induction but to postpone defection closer to the end.

Entanglement dynamics in open two-qubit systems via diffusive quantum trajectories

We use quantum diffusive trajectories to prove that the time evolution of two-qubit entanglement under spontaneous emission can be fully characterized by optimal continuous monitoring. We analytically determine this optimal unraveling and derive a deterministic evolution equation for the system's concurrence. Furthermore, we propose an experiment to monitor the entanglement dynamics in bipartite two-level systems and to determine the disentanglement time from a single trajectory.Comment: 4 pages, 2 figures, changed title, abstract and fig. 2, corrected typo

Aging in Financial Market

We analyze the data of the Italian and U.S. futures on the stock markets and we test the validity of the Continuous Time Random Walk assumption for the survival probability of the returns time series via a renewal aging experiment. We also study the survival probability of returns sign and apply a coarse graining procedure to reveal the renewal aspects of the process underlying its dynamics.Comment: To appear in special issue of Chaos, Solitons and Fractal

Observation of Spin Flips with a Single Trapped Proton

Radio-frequency induced spin transitions of one individual proton are observed for the first time. The spin quantum jumps are detected via the continuous Stern-Gerlach effect, which is used in an experiment with a single proton stored in a cryogenic Penning trap. This is an important milestone towards a direct high-precision measurement of the magnetic moment of the proton and a new test of the matter-antimatter symmetry in the baryon sector

Spectra of ultrabroadband squeezed pulses and the finite-time Unruh-Davies effect

We study spectral properties of quantum radiation of ultimately short duration. In particular, we introduce a continuous multimode squeezing operator for the description of subcycle pulses of entangled photons generated by a coherent-field driving in a thin nonlinear crystal with second order susceptibility. We find the ultrabroadband spectra of the emitted quantum radiation perturbatively in the strength of the driving field. These spectra can be related to the spectra expected in an Unruh-Davies experiment with a finite time of acceleration. In the time domain, we describe the corresponding behavior of the normally ordered electric field variance.Comment: 11 pages, 5 figure

Decoherence and the Quantum Zeno Effect

The experiment of Etano et al which demonstrated the quantum Zeno effect (QZE) in an optical experiment was explained by Frerichs and Schenzle without invoking the wave function collapse. In this report it is proposed that the collapse does occur, and it can be explained by the `environment induced decoherence' theory. The environment here consists of the completely quantized field vacuum modes. The spontaneous emission life time of the atom sets a fundamental limit on the requirement of `continuous measurements' for QZE. This limit turns out to be related to the time-energy uncertainty relation discussed by Ghirardi et al.Comment: Based on a poster presented at the "Workshop on Advanced Laser Spectroscopy", I.I.T. Kanpur, India, 25-28 February 1995. RevTeX, one page, two uunecoded post-script figures appended