Super-multiplicativity and a lower bound for the decay of the signature of a path of finite length

For a path of length $L>0$, if for all $n\ge 1$, we multiply the n-th term of the signature by $n!L^{?n}$, we say that the resulting signature is ‘normalised’. It has been established (T. J. Lyons, M. Caruana, T. Lévy, Differential equations driven by rough paths, Springer, 2007) that the norm of the n-th term of the normalised signature of a bounded-variation path is bounded above by 1. In this article, we discuss the super-multiplicativity of the norm of the signature of a path with finite length, and prove by Fekete's lemma the existence of a non-zero limit of the n-th root of the norm of the n-th term in the normalised signature as n approaches infinity.     

Simulation in manufacturing and business: A review

This paper reports the results of a review of simulation applications published within peer-reviewed literature between 1997 and 2006 to provide an up-to-date picture of the role of simulation techniques within manufacturing and business. The review is characterised by three factors: wide coverage, broad scope of the simulation techniques, and a focus on real-world applications. A structured methodology was followed to narrow down the search from around 20,000 papers to 281. Results include interesting trends and patterns. For instance, although discrete event simulation is the most popular technique, it has lower stakeholder engagement than other techniques, such as system dynamics or gaming. This is highly correlated with modelling lead time and purpose. Considering application areas, modelling is mostly used in scheduling. Finally, this review shows an increasing interest in hybrid modelling as an approach to cope with complex enterprise-wide systems.     

Loss tolerance in one-way quantum computation via counterfactual error correction

We introduce a scheme for fault tolerantly dealing with losses (or other "leakage" errors) in cluster state computation that can tolerate up to 50% qubit loss. This is achieved passively using an adaptive strategy of measurement--no coherent measurements or coherent correction is required. Since the scheme relies on inferring information about what would have been the outcome of a measurement had one been able to carry it out, we call this counterfactual error correction.     

The Epistemic Relevance of Morphological Content

Morphological content is information that is implicitly embodied in the standing structure of a cognitive system and is automatically accommodated during cognitive processing without first becoming explicit in consciousness. We maintain that much belief-formation in human cognition is essentially morphological: i.e., it draws heavily on large amounts of morphological content, and must do so in order to tractably accommodate the holistic evidential relevance of background information possessed by the cognitive agent. We also advocate a form of experiential evidentialism concerning epistemic justification—roughly, the view that the justification-status of an agent’s beliefs is fully determined by the character of the agent’s conscious experience. We have previously defended both the thesis that much belief-formation is essentially morphological, and also a version of evidentialism. Here we explain how experiential evidentialism can be smoothly and plausibly combined with the thesis that much of the cognitive processing that generates justified beliefs is essentially morphological. The leading idea is this: even though epistemically relevant morphological content does not become explicit in consciousness during the process of belief-generation, nevertheless such content does affect the overall character of conscious experience in an epistemically significant way: it is implicit in conscious experience, and is implicitly appreciated by the experiencing agent.     

Efficacy of Different Concrete Models for Teaching the Part-Whole Construct for Fractions

The effectiveness of different concrete and pictorial models on students' understanding of the part-whole construct for fractions was investigated. Using interview data from fourth and fifth grade students from three different districts that adopted the Mathematics Trailblazers series, authors identified strengths and limitations of models used. Pattern blocks had limited value in aiding students' construction of mental images for the part-whole model as well as limited value in building meaning for adding and subtracting fractions. A paper fraction chart based on a paper folding model supported students' ability to order fractions with same numerators but was less useful in helping students on estimation tasks. The dot paper model and chips did not support fifth grade students' initial understanding of the algorithm.     

Trace Analysis Using Position-Sensitive Detection in Magnetic Sector Mass Spectrometry

Abstract

A position-sensitive ion detection system for trace analysis with magnetic sector mass spectrometers is described in detail, with particular application to high temperature mass spectrometry. The detection system consists of two stacked microchannel plates (Chevron assembly) backed by a resistive anode encoder and associated electronics. The range of masses simultaneously detectable is m to 1.2m. For electron impact ionization of silver at an electron energy of 10.5 eV, the sensitivity is 1.6 × 10^?7 Pa, and the mass resolution is 260 at mass 80 (valley 10% of the peak height definition). Additional applications for the detection system are discussed.     

Strategic response to pollution taxes in supply chain networks: Dynamic,spatial, and organizational dimensions

This paper presents a model of the strategic behavior of firms operating in a spatial supply chain network. The manufacturing and retailing firms engage in an oligopolistic, noncooperative game by sharing customer demand such that a firm’s decisions impact the product prices, which in turn result in changes in all other firms’ decisions. Each firm’s payoff is to maximize its own profit and we show that, in response to such changes in prices and to exogenous environmental taxes, the manufacturing firms may strategically alter a variety of choices such as ’make-buy’ decisions with respect to intermediate inputs, spatial distribution of production, product shipment patterns and inventory management, environmental tax payment vs recycling decisions, and timing of all such choices to sustainably manage the profit and the environmental regulations. An important implication is that effects of a tax depends on the oligopolistic game structure. With respect to methods, we show that this dynamic game can be represented as a set of differential variational inequalities (DVIs) that motivate a computationally efficient nonlinear complementarity (NCP) approach that enables the full exploitation of above-mentioned salient features. We also provide a numerical example that confirms the utility of our proposed framework and shows substantial strategic reaction can be expected to a tax on pollution stocks.     

Black hole thermodynamics and the factor of 2 problem

We show that the recent tunneling formulas for black hole radiation in static, spherically symmetric spacetimes follow as a consequence of the first law of black hole thermodynamics and the area-entropy relation based on the radiation temperature. A tunneling formula results even if the radiation temperature is different from the one originally derived by Hawking and this is discussed in the context of the recent factor of 2 problem. In particular, it is shown that if the radiation temperature is higher than the Hawking temperature by a factor of two, thermodynamics then leads to a tunneling formula which is exactly the one recently found to be canonically invariant.