Toeplitz Inverse Covariance-Based Clustering of Multivariate Time Series Data

Subsequence clustering of multivariate time series is a useful tool for discovering repeated patterns in temporal data. Once these patterns have been discovered, seemingly complicated datasets can be interpreted as a temporal sequence of only a small number of states, or clusters. For example, raw sensor data from a fitness-tracking application can be expressed as a timeline of a select few actions (i.e., walking, sitting, running). However, discovering these patterns is challenging because it requires simultaneous segmentation and clustering of the time series. Furthermore, interpreting the resulting clusters is difficult, especially when the data is high-dimensional. Here we propose a new method of model-based clustering, which we call Toeplitz Inverse Covariance-based Clustering (TICC). Each cluster in the TICC method is defined by a correlation network, or Markov random field (MRF), characterizing the interdependencies between different observations in a typical subsequence of that cluster. Based on this graphical representation, TICC simultaneously segments and clusters the time series data. We solve the TICC problem through alternating minimization, using a variation of the expectation maximization (EM) algorithm. We derive closed-form solutions to efficiently solve the two resulting subproblems in a scalable way, through dynamic programming and the alternating direction method of multipliers (ADMM), respectively. We validate our approach by comparing TICC to several state-of-the-art baselines in a series of synthetic experiments, and we then demonstrate on an automobile sensor dataset how TICC can be used to learn interpretable clusters in real-world scenarios.Comment: This revised version fixes two small typos in the published versio

Integrated-light Two Micron All Sky Survey infrared photometry of Galactic globular clusters

We have mosaicked Two Micron All Sky Survey (2MASS) images to derive surface brightness profiles in J, H, and K_s for 104 Galactic globular clusters. We fit these with King profiles and show that the core radii are identical to within the errors for each of these IR colors and are identical to the core radii at V in essentially all cases. We derive integrated-light colors V-J, V-H, V-K_s, J-H, and J-Ks for these globular clusters. Each color shows a reasonably tight relation between the dereddened colors and metallicity. Fits to these are given for each color. The IR-IR colors have very small errors, due largely to the all-sky photometric calibration of the 2MASS survey, while the V-IR colors have substantially larger uncertainties. We find fairly good agreement with measurements of integrated-light colors for a smaller sample of Galactic globular clusters by M. Aaronson, M. Malkan, and D. Kleinmann from 1977. Our results provide a calibration for the integrated light of distant single-burst old stellar populations from very low to solar metallicities. A comparison of our dereddened measured colors with predictions from several models of the integrated light of single-burst old populations shows good agreement in the low-metallicity domain for V-K_s colors but also shows an offset at a fixed [Fe/H] of ~0.1 mag in J-K_s, which we ascribe to photometric system transformation issues. Some of the models fail to reproduce the behavior of the integrated-light colors of the Galactic globular clusters near solar metallicity

An upper limit for the water outgassing rate of the main-belt comet 176P/LINEAR observed with Herschel/HIFI

176P/LINEAR is a member of the new cometary class known as main-belt comets (MBCs). It displayed cometary activity shortly during its 2005 perihelion passage that may be driven by the sublimation of sub-surface ices. We have therefore searched for emission of the H2O 110-101 ground state rotational line at 557 GHz toward 176P/LINEAR with the Heterodyne Instrument for the Far Infrared (HIFI) on board the Herschel Space Observatory on UT 8.78 August 2011, about 40 days after its most recent perihelion passage, when the object was at a heliocentric distance of 2.58 AU. No H2O line emission was detected in our observations, from which we derive sensitive 3-sigma upper limits for the water production rate and column density of < 4e25 molec/s and of < 3e10 cm^{-2}, respectively. From the peak brightness measured during the object's active period in 2005, this upper limit is lower than predicted by the relation between production rates and visual magnitudes observed for a sample of comets by Jorda et al. (2008) at this heliocentric distance. Thus, 176P/LINEAR was likely less active at the time of our observation than during its previous perihelion passage. The retrieved upper limit is lower than most values derived for the H2O production rate from the spectroscopic search for CN emission in MBCs.Comment: 5 pages, 2 figures. Minor changes to match published versio

Integrated Light 2MASS IR Photometry of Galactic Globular Clusters

We have mosaiced 2MASS images to derive surface brightness profiles in JHK for 104 Galactic globular clusters. We fit these with King profiles, and show that the core radii are identical to within the errors for each of these IR colors, and are identical to the core radii at V in essentially all cases. We derive integrated light colors V-J, V-H, V-K_s, J-H and J-K_s for these globular clusters. Each color shows a reasonably tight relation between the dereddened colors and metallicity. Fits to these are given for each color. The IR--IR colors have very small errors due largely to the all-sky photometric calibration of the 2MASS survey, while the V-IR colors have substantially larger uncertainties. We find fairly good agreement with measurements of integrated light colors for a smaller sample of Galactic globular clusters by Aaronson, Malkan & Kleinmann from 1977. Our results provide a calibration for the integrated light of distant single burst old stellar populations from very low to Solar metallicities. A comparison of our dereddened measured colors with predictions from several models of the integrated light of single burst old populations shows good agreement in the low metallicity domain for V-K_s colors, but an offset at a fixed [Fe/H] of ~0.1 mag in J-K_s, which we ascribe to photometric system transformation issues. Some of the models fail to reproduce the behavior of the integrated light colors of the Galactic globular clusters near Solar metallicity.Comment: Accepted for publication in the A

The quantum dynamic capacity formula of a quantum channel

The dynamic capacity theorem characterizes the reliable communication rates of a quantum channel when combined with the noiseless resources of classical communication, quantum communication, and entanglement. In prior work, we proved the converse part of this theorem by making contact with many previous results in the quantum Shannon theory literature. In this work, we prove the theorem with an "ab initio" approach, using only the most basic tools in the quantum information theorist's toolkit: the Alicki-Fannes' inequality, the chain rule for quantum mutual information, elementary properties of quantum entropy, and the quantum data processing inequality. The result is a simplified proof of the theorem that should be more accessible to those unfamiliar with the quantum Shannon theory literature. We also demonstrate that the "quantum dynamic capacity formula" characterizes the Pareto optimal trade-off surface for the full dynamic capacity region. Additivity of this formula simplifies the computation of the trade-off surface, and we prove that its additivity holds for the quantum Hadamard channels and the quantum erasure channel. We then determine exact expressions for and plot the dynamic capacity region of the quantum dephasing channel, an example from the Hadamard class, and the quantum erasure channel.Comment: 24 pages, 3 figures; v2 has improved structure and minor corrections; v3 has correction regarding the optimizatio

Observational and Dynamical Characterization of Main-Belt Comet P/2010 R2 (La Sagra)

We present observations of comet-like main-belt object P/2010 R2 (La Sagra) obtained by Pan-STARRS 1 and the Faulkes Telescope-North on Haleakala in Hawaii, the University of Hawaii 2.2 m, Gemini-North, and Keck I telescopes on Mauna Kea, the Danish 1.54 m telescope at La Silla, and the Isaac Newton Telescope on La Palma. An antisolar dust tail is observed from August 2010 through February 2011, while a dust trail aligned with the object's orbit plane is also observed from December 2010 through August 2011. Assuming typical phase darkening behavior, P/La Sagra is seen to increase in brightness by >1 mag between August 2010 and December 2010, suggesting that dust production is ongoing over this period. These results strongly suggest that the observed activity is cometary in nature (i.e., driven by the sublimation of volatile material), and that P/La Sagra is therefore the most recent main-belt comet to be discovered. We find an approximate absolute magnitude for the nucleus of H_R=17.9+/-0.2 mag, corresponding to a nucleus radius of ~0.7 km, assuming an albedo of p=0.05. Using optical spectroscopy, we find no evidence of sublimation products (i.e., gas emission), finding an upper limit CN production rate of Q_CN<6x10^23 mol/s, from which we infer an H2O production rate of Q_H2O<10^26 mol/s. Numerical simulations indicate that P/La Sagra is dynamically stable for >100 Myr, suggesting that it is likely native to its current location and that its composition is likely representative of other objects in the same region of the main belt, though the relatively close proximity of the 13:6 mean-motion resonance with Jupiter and the (3,-2,-1) three-body mean-motion resonance with Jupiter and Saturn mean that dynamical instability on larger timescales cannot be ruled out.Comment: 23 pages, 13 figures, accepted for publication in A

Involving users in OPAC interface design: Perspective from a UK study

This is the post-print versoin of the Article. The official published version can be accessed from the link below - Copyright @ 2007 SpringerThe purpose of this study was to determine user suggestions for a typical OPAC (Online Public Library Catalogue) application’s functionality and features. An experiment was undertaken to find out the type of interactions features that users prefer to have in an OPAC. The study revealed that regardless of users’ Information Technology (IT) backgrounds, their functionality expectations of OPACs are the same. However, based on users’ previous experiences with OPACs, their requirements with respect to specific features may change. Users should be involved early in the OPAC development cycle process in order to ensure usable and functional interface