Department of Mathematical Sciences Articles
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Item Filling Jars to Measure Time(Sciendo, 10-2021) Le, Tiffany-Chau; Sarkar, Jyotirmoy; Mathematical Sciences, School of ScienceIf water is flowing at the same constant rate through each of H>3 hoses, so that any one hose will fill any one of J>2 available jars in exactly one hour, then what are the fillable fractions of a jar, and what are the measurable fractions of an hour? Learning to systematically answer such questions will not only equip readers to fluently use fractions, but also introduce or reintroduce them gently to the Queen of Mathematics – Number Theory.Item Rotation sets for unimodal maps of the interval(American Institute of Mathematical Sciences, 2003-02) Cleveland, Christopher; Mathematical Sciences, School of ScienceWe relate the rotation interval ρ(f) of a unimodal map f of the interval with its kneading invariant K(f). In particular, we show that for any μ∈(0,12), there are kneading invariants νμ and νμ,hom such that ρ(f)=[μ,12] if and only if νμ⪯K(f)⪯νμ,hom.Item Intermittency in local field potentials recorded from the thalamus of patients with essential tremor(Springer (Biomed Central Ltd.), 2007-07-06) Sen, Asok; Kane, Abdoul; Hutchison, William D; Lozano, Andres M; Hodaie, Mojgan; Dostrovsky, Jonathan O; Department of Mathematical Sciences, School of ScienceItem A semiparametric modeling framework for potential biomarker discovery and the development of metabonomic profiles(BioMed Central, 2008-01-23) Ghosh, Samiran; Grant, David F.; Dey, Dipak K.; Hill, Dennis W.; Mathematical Sciences, School of ScienceBackground The discovery of biomarkers is an important step towards the development of criteria for early diagnosis of disease status. Recently electrospray ionization (ESI) and matrix assisted laser desorption (MALDI) time-of-flight (TOF) mass spectrometry have been used to identify biomarkers both in proteomics and metabonomics studies. Data sets generated from such studies are generally very large in size and thus require the use of sophisticated statistical techniques to glean useful information. Most recent attempts to process these types of data model each compound's intensity either discretely by positional (mass to charge ratio) clustering or through each compounds' own intensity distribution. Traditionally data processing steps such as noise removal, background elimination and m/z alignment, are generally carried out separately resulting in unsatisfactory propagation of signals in the final model. Results In the present study a novel semi-parametric approach has been developed to distinguish urinary metabolic profiles in a group of traumatic patients from those of a control group consisting of normal individuals. Data sets obtained from the replicates of a single subject were used to develop a functional profile through Dirichlet mixture of beta distribution. This functional profile is flexible enough to accommodate variability of the instrument and the inherent variability of each individual, thus simultaneously addressing different sources of systematic error. To address instrument variability, all data sets were analyzed in replicate, an important issue ignored by most studies in the past. Different model comparisons were performed to select the best model for each subject. The m/z values in the window of the irregular pattern are then further recommended for possible biomarker discovery. Conclusion To the best of our knowledge this is the very first attempt to model the physical process behind the time-of flight mass spectrometry. Most of the state of the art techniques does not take these physical principles in consideration while modeling such data. The proposed modeling process will apply as long as the basic physical principle presented in this paper is valid. Notably we have confined our present work mostly within the modeling aspect. Nevertheless clinical validation of our recommended list of potential biomarkers will be required. Hence, we have termed our modeling approach as a "framework" for further work.Item Recurrence Plots for Diesel Engine Variability Tests(De Gruyter, 2009-02-20) Longwic, Rafał; Litak, Grzegorz; Sen, Asok K.; Mathematical Sciences, School of ScienceCycle-to-cycle variations of maximum pressure in a diesel engine are studied by using the methods of recurrence plots and recurrence quantification analysis. The pressure variations are found to exhibit strong periodicities in low frequency bands and intermittent oscillations at higher frequencies. The results are confirmed by wavelet analysis.Item A Note on Dirac Operators on the Quantum Punctured Disk(National Academy of Science of Ukraine, 2010-07-16) Klimek, Slawomir; McBride, Matt; Mathematical Sciences, School of ScienceWe study quantum analogs of the Dirac type operator −2z¯¯¯∂∂z¯¯¯ on the punctured disk, subject to the Atiyah–Patodi–Singer boundary conditions. We construct a parametrix of the quantum operator and show that it is bounded outside of the zero mode.Item Fine temporal structure of beta-band synchronization in Parkinson’s disease: experiments, models and mechanisms(Springer Nature, 2010-07-20) Rubchinsky, Leonid L.; Park, Choongseok; Worth, Robert M.; Mathematical Sciences, School of ScienceItem An interlocked oscillator model for firing of the mesencephalic dopaminergic neuron(Springer Nature, 2010-07-20) Ha, Joon; Kuznetsov, Alexey; Mathematical Sciences, School of ScienceItem Modulation of thalamocortical relay by basal ganglia in Parkinson’s disease and dystonia(Springer Nature, 2011-07-18) Guo, Yixin; Park, Choongseok; Rong, Min; Worth, Robert M.; Rubchinsky, Leonid L.; Mathematical Sciences, School of ScienceItem Possible mechanisms underlying intermittent synchronous activity in the networks of excitatory and inhibitory bursting neurons(Springer Nature, 2011-07-18) Park, Choongseok; Rubchinsky, Leonid L.; Mathematical Sciences, School of Science