U.S. coins: forecasting change

Our next article talks about change-as in coins. Every year, the government produces about 70 new coins for every man, woman, and child. But the economy's need for coins can vary from year to year. So how do the U.S. Mint, which makes the coins, and the Federal Reserve, which distributes them, decide how many coins the economy needs? In "U.S. Coins: Forecasting Change," Dean Croushore highlights some facts about coins and describes how demand for change is forecast.Coinage

An Improved Distributed Algorithm for Maximal Independent Set

The Maximal Independent Set (MIS) problem is one of the basics in the study of locality in distributed graph algorithms. This paper presents an extremely simple randomized algorithm providing a near-optimal local complexity for this problem, which incidentally, when combined with some recent techniques, also leads to a near-optimal global complexity. Classical algorithms of Luby [STOC'85] and Alon, Babai and Itai [JALG'86] provide the global complexity guarantee that, with high probability, all nodes terminate after $O(\log n)$ rounds. In contrast, our initial focus is on the local complexity, and our main contribution is to provide a very simple algorithm guaranteeing that each particular node $v$ terminates after $O(\log \mathsf{deg}(v)+\log 1/\epsilon)$ rounds, with probability at least $1-\epsilon$. The guarantee holds even if the randomness outside $2$-hops neighborhood of $v$ is determined adversarially. This degree-dependency is optimal, due to a lower bound of Kuhn, Moscibroda, and Wattenhofer [PODC'04]. Interestingly, this local complexity smoothly transitions to a global complexity: by adding techniques of Barenboim, Elkin, Pettie, and Schneider [FOCS'12, arXiv: 1202.1983v3], we get a randomized MIS algorithm with a high probability global complexity of $O(\log \Delta) + 2^{O(\sqrt{\log \log n})}$, where $\Delta$ denotes the maximum degree. This improves over the $O(\log^2 \Delta) + 2^{O(\sqrt{\log \log n})}$ result of Barenboim et al., and gets close to the $\Omega(\min\{\log \Delta, \sqrt{\log n}\})$ lower bound of Kuhn et al. Corollaries include improved algorithms for MIS in graphs of upper-bounded arboricity, or lower-bounded girth, for Ruling Sets, for MIS in the Local Computation Algorithms (LCA) model, and a faster distributed algorithm for the Lov\'asz Local Lemma

What If (Dublin)

Raby developed three ‘What If...’ exhibitions with Dunne (RCA), asking what role design can play in imagining possible futures and raising social, cultural and ethical questions, building on 20 years’ practice in Critical Design theorised inter alia in Dunne and Raby’s Design Noir (2001), Hertzian Tales (2005) and Speculative Everything (2013). Raby’s research included concept development, extended collaboration with exhibitors to develop their contributions, and devising the engagement strategy: all three required localised approaches to audiences, circumstances and commissioning hosts. Extensive investigation was needed in synthetic biology, nanotechnology, surveillance technologies and the domestication of natural phenomena, working with scientific partners at Imperial College and Cambridge University. ‘What If…’ Dublin (2009) comprised 29 projects envisioning hypothetical futures and was reviewed in Irish broadsheets (Examiner, Times, Independent), Wired and New Scientist: ‘the exhibits…address questions on scientific or medical ethics that must be asked in our bio-technological age’ (http://www.newscientist.com/blogs/culturelab/2009/12/post-2.html). Exhibits were also shown at the Art Institute of Chicago, Israel Museum, MoMA and Ars Electronica Center. About 1.8 million people pass the windows of the Wellcome Trust building in London annually, making them an important means of science communication. Wellcome commissioned a changing ‘What If…’ exhibition of 15 themes over 15 months (February 2010 – March 2011). Raby reconceived the design strategy with exhibits engaging at different distances, from passing buses to close-up study. The third exhibition, for the Beijing International Design Triennial (2011), explored the impact on future life of novel technologies through 58 projects in 130 exhibits from 36 designers (12 from China), for a diverse audience. The exhibition and related symposium at Tsinghua University were supported by the British Council. The Triennial was visited by approximately 500,000 visitors and featured widely, e.g. China Central Television, People's Daily, New York Times (all 2011) and Zhuangshi journal (2011 and 2012)

Learning Markov Decision Processes for Model Checking

Constructing an accurate system model for formal model verification can be both resource demanding and time-consuming. To alleviate this shortcoming, algorithms have been proposed for automatically learning system models based on observed system behaviors. In this paper we extend the algorithm on learning probabilistic automata to reactive systems, where the observed system behavior is in the form of alternating sequences of inputs and outputs. We propose an algorithm for automatically learning a deterministic labeled Markov decision process model from the observed behavior of a reactive system. The proposed learning algorithm is adapted from algorithms for learning deterministic probabilistic finite automata, and extended to include both probabilistic and nondeterministic transitions. The algorithm is empirically analyzed and evaluated by learning system models of slot machines. The evaluation is performed by analyzing the probabilistic linear temporal logic properties of the system as well as by analyzing the schedulers, in particular the optimal schedulers, induced by the learned models.Comment: In Proceedings QFM 2012, arXiv:1212.345

Forecasting coin demand.

Shortages of coins in 1999 and 2000 motivated the authors to develop models for forecasting coin demand. A variety of models were developed, tested, and used in realtime forecasting. This paper describes the models that were developed and examines the forecast errors from the models both in quasi-ex-ante forecasting exercises and in realtime use. Tests for forecast efficiency are run on each model. Real-time forecasts are examined. The authors conclude with suggestions for further refinements of the models.Coinage

Spartan Daily, November 14, 1950

Volume 39, Issue 34https://scholarworks.sjsu.edu/spartandaily/11455/thumbnail.jp

Free Fibonacci Sequences

This paper describes a class of sequences that are in many ways similar to Fibonacci sequences: given n, sum the previous two terms and divide them by the largest possible power of n. The behavior of such sequences depends on n. We analyze these sequences for small n: 2, 3, 4, and 5. Surprisingly these behaviors are very different. We also talk about any n. Many statements about these sequences are difficult or impossible to prove, but they can be supported by probabilistic arguments, we have plenty of those in this paper. We also introduce ten new sequences. Most of the new sequences are also related to Fibonacci numbers proper, not just free Fibonacci numbers.Comment: 18 page