'A difficult case' : Pacioli and Cardano on the Chinese Rings

Abstract The Chinese rings puzzle is one of those recreational mathematical problems known for several centuries in the West as well as in Asia. Its origin is diffcult to ascertain but is most likely not Chinese. In this paper we provide an English translation, based on a mathematical analysis of the puzzle, of two sixteenth-century witness accounts. The first is by Luca Pacioli and was previously unpublished. The second is by Girolamo Cardano for which we provide an interpretation considerably different from existing translations. Finally, both treatments of the puzzle are compared, pointing out the presence of an implicit idea of non-numerical recursive algorithms. </jats:p

Ultrafast dynamics of finite Hubbard clusters - a stochastic mean-field approach

Finite lattice models are a prototype for strongly correlated quantum systems and capture essential properties of condensed matter systems. With the dramatic progress in ultracold atoms in optical lattices, finite fermionic Hubbard systems have become directly accessible in experiments, including their ultrafast dynamics far from equilibrium. Here, we present a theoretical approach that is able to treat these dynamics in any dimension and fully includes inhomogeneity effects. The method consists in stochastic sampling of mean-field trajectories and is found to be more accurate and efficient than current nonequilibrium Green functions approaches. This is demonstrated for Hubbard clusters with up to 512 particles in one, two and three dimensions

Energy-aware dynamic pricing model for cloud environments

Energy consumption is a critical operational cost for Cloud providers. However, as commercial providers typically use fixed pricing schemes that are oblivious about the energy costs of running virtual machines, clients are not charged according to their actual energy impact. Some works have proposed energy-aware cost models that are able to capture each client’s real energy usage. However, those models cannot be naturally used for pricing Cloud services, as the energy cost is calculated after the termination of the service, and it depends on decisions taken by the provider, such as the actual placement of the client’s virtual machines. For those reasons, a client cannot estimate in advance how much it will pay. This paper presents a pricing model for virtualized Cloud providers that dynamically derives the energy costs per allocation unit and per work unit for each time period. They account for the energy costs of the provider’s static and dynamic energy consumption by sharing out them according to the virtual resource allocation and the real resource usage of running virtual machines for the corresponding time period. Newly arrived clients during that period can use these costs as a baseline to calculate their expenses in advance as a function of the number of requested allocation and work units. Our results show that providers can get comparable revenue to traditional pricing schemes, while offering to the clients more proportional prices than fixed-price models.Peer ReviewedPostprint (author's final draft

Spectrophotometry with a transmission grating for detecting faint occultations

High-precision spectrophotometry is highly desirable in detecting and characterizing close-in extrasolar planets to learn about their makeup and temperature. For such a goal, a modest-size telescope with a simple low-resolution spectroscopic instrument is potentially as good or better than a complex general purpose spectrograph since calibration and removal of systematic errors is expected to dominate. We use a transmission grating placed in front of an imaging CCD camera on Steward Observatory's Kuiper 1.5 m telescope to provide a high signal-to-noise, low dispersion visible spectrum of the star HD 209458. We attempt to detect the reflected light signal from the extra-solar planet HD 209458b by differencing the signal just before and after secondary occultation. We present a simple data reduction method and explore the limits of ground based low-dispersion spectrophotometry with a diffraction grating. Reflected light detection levels of 0.1% are achievable for 5000-7000A, too coarse for useful limits on ESPs but potentially useful for determining spectra of short-period binary systems with large (Delta m_vis=6) brightness ratios. Limits on the precison are set by variations in atmospheric seeing in the low-resolution spectrum. Calibration of this effect can be carried out by measurement of atmospheric parameters from the observations themselves, which may allow the precision to be limited by the noise due to photon statistics and atmospheric scintillation effects.Comment: 34 pages and 17 figures. Accepted for publication in PAS

Developing a multi-metric habitat index for wadeable streams in Illinois (T-25-P-001), annual segment report to the Illinois Department of Natural Resources.

USFWS through IDNR State Wildlife Grant Grant/Contract No: T-25-P-001INHS Technical Report Prepared for USFWS through IDNR State Wildlife Gran