Structure-Aware Sampling: Flexible and Accurate Summarization

In processing large quantities of data, a fundamental problem is to obtain a summary which supports approximate query answering. Random sampling yields flexible summaries which naturally support subset-sum queries with unbiased estimators and well-understood confidence bounds. Classic sample-based summaries, however, are designed for arbitrary subset queries and are oblivious to the structure in the set of keys. The particular structure, such as hierarchy, order, or product space (multi-dimensional), makes range queries much more relevant for most analysis of the data. Dedicated summarization algorithms for range-sum queries have also been extensively studied. They can outperform existing sampling schemes in terms of accuracy on range queries per summary size. Their accuracy, however, rapidly degrades when, as is often the case, the query spans multiple ranges. They are also less flexible - being targeted for range sum queries alone - and are often quite costly to build and use. In this paper we propose and evaluate variance optimal sampling schemes that are structure-aware. These summaries improve over the accuracy of existing structure-oblivious sampling schemes on range queries while retaining the benefits of sample-based summaries: flexible summaries, with high accuracy on both range queries and arbitrary subset queries

On the tradeoff between stability and fit

In computing, as in many aspects of life, changes incur cost. Many optimization problems are formulated as a one-time instance starting from scratch. However, a common case that arises is when we already have a set of prior assignments and must decide how to respond to a new set of constraints, given that each change from the current assignment comes at a price. That is, we would like to maximize the fitness or efficiency of our system, but we need to balance it with the changeout cost from the previous state. We provide a precise formulation for this tradeoff and analyze the resulting stable extensions of some fundamental problems in measurement and analytics. Our main technical contribution is a stable extension of Probability Proportional to Size (PPS) weighted random sampling, with applications to monitoring and anomaly detection problems. We also provide a general framework that applies to top-k, minimum spanning tree, and assignment. In both cases, we are able to provide exact solutions and discuss efficient incremental algorithms that can find new solutions as the input changes

Torsion in Milnor fiber homology

In a recent paper, Dimca and Nemethi pose the problem of finding a homogeneous polynomial f such that the homology of the complement of the hypersurface defined by f is torsion-free, but the homology of the Milnor fiber of f has torsion. We prove that this is indeed possible, and show by construction that, for each prime p, there is a polynomial with p-torsion in the homology of the Milnor fiber. The techniques make use of properties of characteristic varieties of hyperplane arrangements.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-16.abs.htm

Impacts of Unattended Train Operations (UTO) on Productivity and Efficiency in Metropolitan Railways

Urban metro subway systems (metros) around the world are choosing increasing levels of automation for new and existing lines: the global length of metro lines capable of unattended train operation (UTO) is predicted to triple in the next 10 years. Despite significant investment in this technology, empirical evidence for the financial and service quality impacts of UTO in metros remains scarce. This study used questionnaires and semistructured interviews with the Community of Metros and Nova Group benchmarking groups to assemble emerging evidence of how automation affected costs, staffing, service capacity, and reliability. The results from an analysis of data from 23 lines suggested that UTO could reduce staff numbers by 30% to 70%, with the amount of wage cost reduction depending on whether staff on UTO lines were paid more. On the basis of the experience of seven metros, the capital costs of lines capable of UTO were higher, but the internal rate of return had been estimated by two metros at 10% to 15%. Automated lines were capable of operating at the highest service frequencies of up to 42 trains per hour, and the limited available data suggested that automated lines were more reliable. The findings indicated that UTO was a means to a more flexible and reliable operating model that could increase metro productivity and efficiency. The study identified important work needed to understand the impacts of UTO and identify where statistical analyses would add value once sufficiently large data sets became available

Lasing and cooling in a hot cavity

We present a microscopic laser model for many atoms coupled to a single cavity mode, including the light forces resulting from atom-field momentum exchange. Within a semiclassical description, we solve the equations for atomic motion and internal dynamics to obtain analytic expressions for the optical potential and friction force seen by each atom. When optical gain is maximum at frequencies where the light field extracts kinetic energy from the atomic motion, the dynamics combines optical lasing and motional cooling. From the corresponding momentum diffusion coefficient we predict sub-Doppler temperatures in the stationary state. This generalizes the theory of cavity enhanced laser cooling to active cavity systems. We identify the gain induced reduction of the effective resonator linewidth as key origin for the faster cooling and lower temperatures, which implys that a bad cavity with a gain medium can replace a high-Q cavity. In addition, this shows the importance of light forces for gas lasers in the low-temperature limit, where atoms can arrange in a periodic pattern maximizing gain and counteracting spatial hole burning. Ultimately, in the low temperature limit, such a setup should allow to combine optical lasing and atom lasing in single device.Comment: 11 pages, 6 figure

An explicit height bound for the classical modular polynomial

For a prime m, let Phi_m be the classical modular polynomial, and let h(Phi_m) denote its logarithmic height. By specializing a theorem of Cohen, we prove that h(Phi_m) <= 6 m log m + 16 m + 14 sqrt m log m. As a corollary, we find that h(Phi_m) <= 6 m log m + 18 m also holds. A table of h(Phi_m) values is provided for m <= 3607.Comment: Minor correction to the constants in Theorem 1 and Corollary 9. To appear in the Ramanujan Journal. 17 pages