A Spoonful of Math Helps the Medicine Go Down: An Illustration of How Healthcare can Benefit from Mathematical Modeling and Analysis

<p>Abstract</p> <p>Objectives</p> <p>A recent joint report from the Institute of Medicine and the National Academy of Engineering, highlights the benefits of--indeed, the need for--mathematical analysis of healthcare delivery. Tools for such analysis have been developed over decades by researchers in Operations Research (OR). An OR perspective typically frames a complex problem in terms of its essential mathematical structure. This article illustrates the use and value of the tools of operations research in healthcare. It reviews one OR tool, queueing theory, and provides an illustration involving a hypothetical drug treatment facility.</p> <p>Method</p> <p>Queueing Theory (QT) is the study of waiting lines. The theory is useful in that it provides solutions to problems of waiting and its relationship to key characteristics of healthcare systems. More generally, it illustrates the strengths of modeling in healthcare and service delivery.</p> <p>Queueing theory offers insights that initially may be hidden. For example, a queueing model allows one to incorporate randomness, which is inherent in the actual system, into the mathematical analysis. As a result of this randomness, these systems often perform much worse than one might have guessed based on deterministic conditions. Poor performance is reflected in longer lines, longer waits, and lower levels of server utilization.</p> <p>As an illustration, we specify a queueing model of a representative drug treatment facility. The analysis of this model provides mathematical expressions for some of the key performance measures, such as average waiting time for admission.</p> <p>Results</p> <p>We calculate average occupancy in the facility and its relationship to system characteristics. For example, when the facility has 28 beds, the average wait for admission is 4 days. We also explore the relationship between arrival rate at the facility, the capacity of the facility, and waiting times.</p> <p>Conclusions</p> <p>One key aspect of the healthcare system is its complexity, and policy makers want to design and reform the system in a way that affects competing goals. OR methodologies, particularly queueing theory, can be very useful in gaining deeper understanding of this complexity and exploring the potential effects of proposed changes on the system without making any actual changes.</p

Genes targeted by the estrogen and progesterone receptors in the human endometrial cell lines HEC1A and RL95-2

<p>Abstract</p> <p>Background</p> <p>When the steroid hormones estrogen and progesterone bind to nuclear receptors, they have transcriptional impact on target genes in the human endometrium. These transcriptional changes have a critical function in preparing the endometrium for embryo implantation.</p> <p>Methods</p> <p>382 genes were selected, differentially expressed in the receptive endometrium, to study their responsiveness of estrogen and progesterone. The endometrial cell lines HEC1A and RL95-2 were used as experimental models for the non-receptive and receptive endometrium, respectively. Putative targets for activated steroid hormone receptors were investigated by chromatin immunoprecipitation (ChIP) using receptor-specific antibodies. Promoter occupancy of the selected genes by steroid receptors was detected in ChIP-purified DNA by quantitative PCR (qPCR). Expression analysis by reverse transcriptase (RT)-PCR was used to further investigate hormone dependent mRNA expression regulation of a subset of genes.</p> <p>Results</p> <p>ChIP-qPCR analysis demonstrated that each steroid hormone receptor had distinct group of target genes in the endometrial cell lines. After estradiol treatment, expression of estrogen receptor target genes predominated in HEC1A cells (n = 137) compared to RL95-2 cells (n = 35). In contrast, expression of progesterone receptor target genes was higher in RL95-2 cells (n = 83) than in HEC1A cells (n = 7) after progesterone treatment. RT-PCR analysis of 20 genes demonstrated transcriptional changes after estradiol or progesterone treatment of the cell lines.</p> <p>Conclusions</p> <p>Combined results from ChIP-qPCR and RT-PCR analysis showed different patterns of steroid hormone receptor occupancy at target genes, corresponding to activation or suppression of gene expression after hormone treatment of HEC1A and RL95-2 cell lines.</p

X-ray emission from the Sombrero galaxy: discrete sources

We present a study of discrete X-ray sources in and around the bulge-dominated, massive Sa galaxy, Sombrero (M104), based on new and archival Chandra observations with a total exposure of ~200 ks. With a detection limit of L_X = 1E37 erg/s and a field of view covering a galactocentric radius of ~30 kpc (11.5 arcminute), 383 sources are detected. Cross-correlation with Spitler et al.'s catalogue of Sombrero globular clusters (GCs) identified from HST/ACS observations reveals 41 X-rays sources in GCs, presumably low-mass X-ray binaries (LMXBs). We quantify the differential luminosity functions (LFs) for both the detected GC and field LMXBs, whose power-low indices (~1.1 for the GC-LF and ~1.6 for field-LF) are consistent with previous studies for elliptical galaxies. With precise sky positions of the GCs without a detected X-ray source, we further quantify, through a fluctuation analysis, the GC LF at fainter luminosities down to 1E35 erg/s. The derived index rules out a faint-end slope flatter than 1.1 at a 2 sigma significance, contrary to recent findings in several elliptical galaxies and the bulge of M31. On the other hand, the 2-6 keV unresolved emission places a tight constraint on the field LF, implying a flattened index of ~1.0 below 1E37 erg/s. We also detect 101 sources in the halo of Sombrero. The presence of these sources cannot be interpreted as galactic LMXBs whose spatial distribution empirically follows the starlight. Their number is also higher than the expected number of cosmic AGNs (52+/-11 [1 sigma]) whose surface density is constrained by deep X-ray surveys. We suggest that either the cosmic X-ray background is unusually high in the direction of Sombrero, or a distinct population of X-ray sources is present in the halo of Sombrero.Comment: 11 figures, 5 tables, ApJ in pres

Performance of CMS muon reconstruction in pp collision events at sqrt(s) = 7 TeV

The performance of muon reconstruction, identification, and triggering in CMS has been studied using 40 inverse picobarns of data collected in pp collisions at sqrt(s) = 7 TeV at the LHC in 2010. A few benchmark sets of selection criteria covering a wide range of physics analysis needs have been examined. For all considered selections, the efficiency to reconstruct and identify a muon with a transverse momentum pT larger than a few GeV is above 95% over the whole region of pseudorapidity covered by the CMS muon system, abs(eta) < 2.4, while the probability to misidentify a hadron as a muon is well below 1%. The efficiency to trigger on single muons with pT above a few GeV is higher than 90% over the full eta range, and typically substantially better. The overall momentum scale is measured to a precision of 0.2% with muons from Z decays. The transverse momentum resolution varies from 1% to 6% depending on pseudorapidity for muons with pT below 100 GeV and, using cosmic rays, it is shown to be better than 10% in the central region up to pT = 1 TeV. Observed distributions of all quantities are well reproduced by the Monte Carlo simulation.Comment: Replaced with published version. Added journal reference and DO

Performance of CMS muon reconstruction in pp collision events at sqrt(s) = 7 TeV

The performance of muon reconstruction, identification, and triggering in CMS has been studied using 40 inverse picobarns of data collected in pp collisions at sqrt(s) = 7 TeV at the LHC in 2010. A few benchmark sets of selection criteria covering a wide range of physics analysis needs have been examined. For all considered selections, the efficiency to reconstruct and identify a muon with a transverse momentum pT larger than a few GeV is above 95% over the whole region of pseudorapidity covered by the CMS muon system, abs(eta) < 2.4, while the probability to misidentify a hadron as a muon is well below 1%. The efficiency to trigger on single muons with pT above a few GeV is higher than 90% over the full eta range, and typically substantially better. The overall momentum scale is measured to a precision of 0.2% with muons from Z decays. The transverse momentum resolution varies from 1% to 6% depending on pseudorapidity for muons with pT below 100 GeV and, using cosmic rays, it is shown to be better than 10% in the central region up to pT = 1 TeV. Observed distributions of all quantities are well reproduced by the Monte Carlo simulation.Comment: Replaced with published version. Added journal reference and DO

Azimuthal anisotropy of charged particles at high transverse momenta in PbPb collisions at sqrt(s[NN]) = 2.76 TeV

The azimuthal anisotropy of charged particles in PbPb collisions at nucleon-nucleon center-of-mass energy of 2.76 TeV is measured with the CMS detector at the LHC over an extended transverse momentum (pt) range up to approximately 60 GeV. The data cover both the low-pt region associated with hydrodynamic flow phenomena and the high-pt region where the anisotropies may reflect the path-length dependence of parton energy loss in the created medium. The anisotropy parameter (v2) of the particles is extracted by correlating charged tracks with respect to the event-plane reconstructed by using the energy deposited in forward-angle calorimeters. For the six bins of collision centrality studied, spanning the range of 0-60% most-central events, the observed v2 values are found to first increase with pt, reaching a maximum around pt = 3 GeV, and then to gradually decrease to almost zero, with the decline persisting up to at least pt = 40 GeV over the full centrality range measured.Comment: Replaced with published version. Added journal reference and DO

Search for new physics with same-sign isolated dilepton events with jets and missing transverse energy

A search for new physics is performed in events with two same-sign isolated leptons, hadronic jets, and missing transverse energy in the final state. The analysis is based on a data sample corresponding to an integrated luminosity of 4.98 inverse femtobarns produced in pp collisions at a center-of-mass energy of 7 TeV collected by the CMS experiment at the LHC. This constitutes a factor of 140 increase in integrated luminosity over previously published results. The observed yields agree with the standard model predictions and thus no evidence for new physics is found. The observations are used to set upper limits on possible new physics contributions and to constrain supersymmetric models. To facilitate the interpretation of the data in a broader range of new physics scenarios, information on the event selection, detector response, and efficiencies is provided.Comment: Published in Physical Review Letter

Compressed representation of a partially defined integer function over multiple arguments

In OLAP (OnLine Analitical Processing) data are analysed in an n-dimensional cube. The cube may be represented as a partially defined function over n arguments. Considering that often the function is not defined everywhere, we ask: is there a known way of representing the function or the points in which it is defined, in a more compact manner than the trivial one