Arrival first queueing networks with applications in kanban production systems

In this paper we introduce a new class of queueing networks called {\it arrival first networks}. We characterise its transition rates and derive the relationship between arrival rules, linear partial balance equations, and product form stationary distributions. This model is motivated by production systems operating under a kanban protocol. In contrast with the conventional {\em departure first networks}, where a transition is initiated by service completion of items at the originating nodes that are subsequently routed to the destination nodes (push system), in an arrival first network a transition is initiated by the destination nodes of the items and subsequently those items are processed at and removed from the originating nodes (pull system). These are similar to the push and pull systems in manufacturing systems

Phase space analysis and functional calculus for the linearized Landau and Boltzmann operators

In many works, the linearized non-cutoff Boltzmann operator is considered to behave essentially as a fractional Laplacian. In the present work, we prove that the linearized non-cutoff Boltzmann operator with Maxwellian molecules is exactly equal to a fractional power of the linearized Landau operator which is the sum of the harmonic oscillator and the spherical Laplacian. This result allows to display explicit sharp coercive estimates satisfied by the linearized non-cutoff Boltzmann operator for both Maxwellian and non-Maxwellian molecules.Comment: arXiv admin note: text overlap with arXiv:1111.042

On signal-noise decomposition of timeseries using the continuous wavelet transform: Application to sunspot index

We show that the continuous wavelet transform can provide a unique decomposition of a timeseries in to 'signal-like' and 'noise-like' components: From the overall wavelet spectrum two mutually independent skeleton spectra can be extracted, allowing the separate detection and monitoring in even non-stationary timeseries of the evolution of (a) both stable but also transient, evolving periodicities, such as the output of low dimensional dynamical systems and (b) scale-invariant structures, such as discontinuities, self-similar structures or noise. An indicative application to the monthly-averaged sunspot index reveals, apart from the well-known 11-year periodicity, 3 of its harmonics, the 2-year periodicity (quasi-biennial oscillation, QBO) and several more (some of which detected previously in various solar, earth-solar connection and climate indices), here proposed being just harmonics of the QBO, in all supporting the double-cycle solar magnetic dynamo model (Benevolenskaya, 1998, 2000). The scale maximal spectrum reveals the presence of 1/f fluctuations with timescales up to 1 year in the sunspot number, indicating that the solar magnetic configurations involved in the transient solar activity phenomena with those characteristic timescales are in a self-organized-critical state (SOC), as previously proposed for the solar flare occurence (Lu and Hamilton, 1991).Comment: 22 pages, 2 figure

Unbounded Human Learning: Optimal Scheduling for Spaced Repetition

In the study of human learning, there is broad evidence that our ability to retain information improves with repeated exposure and decays with delay since last exposure. This plays a crucial role in the design of educational software, leading to a trade-off between teaching new material and reviewing what has already been taught. A common way to balance this trade-off is spaced repetition, which uses periodic review of content to improve long-term retention. Though spaced repetition is widely used in practice, e.g., in electronic flashcard software, there is little formal understanding of the design of these systems. Our paper addresses this gap in three ways. First, we mine log data from spaced repetition software to establish the functional dependence of retention on reinforcement and delay. Second, we use this memory model to develop a stochastic model for spaced repetition systems. We propose a queueing network model of the Leitner system for reviewing flashcards, along with a heuristic approximation that admits a tractable optimization problem for review scheduling. Finally, we empirically evaluate our queueing model through a Mechanical Turk experiment, verifying a key qualitative prediction of our model: the existence of a sharp phase transition in learning outcomes upon increasing the rate of new item introductions.Comment: Accepted to the ACM SIGKDD Conference on Knowledge Discovery and Data Mining 201

Dynamic Pricing and Inventory Management with Regular and Expedited Supplies

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/102647/1/poms12047.pd

Newsvendor bounds and heuristics for serial supply chains with regular and expedited shipping

We study an infinite-horizon, N -stage, serial production/inventory system with two transportation modes between stages: regular shipping and expedited shipping. The optimal inventory policy for this system is a top–down echelon base-stock policy, which can be computed through minimizing 2 N nested convex functions recursively (Lawson and Porteus, Oper Res 48 (2000), 878–893). In this article, we first present some structural properties and comparative statics for the parameters of the optimal inventory policies, we then derive simple, newsvendor-type lower and upper bounds for the optimal control parameters. These results are used to develop near optimal heuristic solutions for the echelon base-stock policies. Numerical studies show that the heuristic performs well. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2010Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/64894/1/20388_ftp.pd

Fiber-optic temperature sensor based on interference of selective higher-order modes

A fiber-optic temperature sensor based on the interference of selective higher-order modes in circular optical fibers is described. The authors demonstrate that by coupling the LP01 mode in a standard single-mode fiber to the LP0m modes in a multimode fiber, and utilizing the interference of the higher-order modes, a fiber-optic temperature sensor which has an extremely simple structure and is suitable for high-temperature measurements can be constructed. The sensing principle, temperature measurement experiments, and results are presented

Decays of J/ψJ/\psi and ψ′\psi^\prime into vector and pseudoscalar meson and the pseudoscalar glueball-qqˉq\bar{q} mixing

We introduce a parametrization scheme for $J/\psi(\psi^\prime)\to VP$ where the effects of SU(3) flavor symmetry breaking and doubly OZI-rule violation (DOZI) can be parametrized by certain parameters with explicit physical interpretations. This scheme can be used to clarify the glueball-$q\bar{q}$ mixing within the pseudoscalar mesons. We also include the contributions from the electromagnetic (EM) decays of $J/\psi$ and $\psi^\prime$ via $J/\psi(\psi^\prime)\to \gamma^*\to VP$. Via study of the isospin violated channels, such as $J/\psi(\psi^\prime)\to \rho\eta$, $\rho\eta^\prime$, $\omega\pi^0$ and $\phi\pi^0$, reasonable constraints on the EM decay contributions are obtained. With the up-to-date experimental data for $J/\psi(\psi^\prime)\to VP$, $J/\psi(\psi^\prime)\to \gamma P$ and $P\to \gamma\gamma$, etc, we arrive at a consistent description of the mentioned processes with a minimal set of parameters. As a consequence, we find that there exists an overall suppression of the $\psi^\prime\to 3g$ form factors, which sheds some light on the long-standing "$\rho\pi$ puzzle". By determining the glueball components inside the pseudoscalar $\eta$ and $\eta^\prime$ in three different glueball-$q\bar{q}$ mixing schemes, we deduce that the lowest pseudoscalar glueball, if exists, has rather small $q\bar{q}$ component, and it makes the $\eta(1405)$ a preferable candidate for $0^{-+}$ glueball.Comment: Revised version to appear on J. Phys. G; An error in the code was corrected. There's slight change to the numerical results, while the conclusion is intac