On Necessary and Sufficient Number of Cops in the Game of Cops and Robber in Multidimensional Grids

We theoretically analyze the Cops and Robber Game for the first time in a multidimensional grid. It is shown that for an $n$-dimensional grid, at least $n$ cops are necessary to ensure capture of the robber. We also present a set of cop strategies for which $n$ cops are provably sufficient to catch the robber. Further, for two-dimensional grid, we provide an efficient cop strategy for which the robber is caught even by a single cop under certain conditions.Comment: This is a revised and extended version of the poster paper with the same title that has been presented in the 8th Asian Symposium on Computer Mathematics (ASCM), December 15-17, 2007, Singapor

O(αs3){\cal O}(\alpha_s^3) analysis of inclusive jet and di-jet production in heavy ion reactions at the Large Hadron Collider

Jets physics in heavy ion reactions is an important new area of active research at the Relativistic Heavy Ion Collider (RHIC) and at the Large Hadron Collider (LHC) that paves the way for novel tests of QCD multi-parton dynamics in dense nuclear matter. At present, perturbative QCD calculations of hard probes in elementary nucleon-nucleon reactions can be consistently combined with the effects of the nuclear medium up to ${\cal O}(\alpha_s^3)$. While such accuracy is desirable but not necessary for leading particle tomography, it is absolutely essential for the new jet observables. With this motivation, we present first results and predictions to ${\cal O}(\alpha_s^3)$ for the recent LHC lead-lead (Pb+Pb) run at a center-of-mass energy of 2.76 TeV per nucleon-nucleon pair. Specifically, we focus on the suppression of the single and double inclusive jet cross sections. Our analysis includes not only final-state inelastic parton interactions in the QGP, but also initial-state cold nuclear matter effects and an estimate of the non-perturbative hadronization corrections. We demonstrate how an enhanced di-jet asymmetry in central Pb+Pb reactions at the LHC, recently measured by the ATLAS and CMS experiments, can be derived from these results. We show quantitatively that a fraction of this enhancement may be related to the ambiguity in the separation between the jet and the soft background medium and/or the diffusion of the parton shower energy away from the jet axis through collisional processes. We point to a suite of measurements that can help build a consistent picture of parton shower modification in heavy ion collisions at the LHC.Comment: 10 pages, 9.eps figures; revised version accepted for publication in PL

3-Neutrino Mass Spectrum from Combining Seesaw and Radiative Neutrino Mass Mechanisms

We extend the Standard Model by adding a second Higgs doublet and a right-handed neutrino singlet with a heavy Majorana mass term. In this model, there are one heavy and three light Majorana neutrinos with a mass hierarchy m_3 >> m_2 >> m_1 such that that only m_3 is non-zero at the tree level and light because of the seesaw mechanism, m_2 is generated at the one-loop and m_1 at the two-loop level. We show that the atmospheric neutrino oscillations and large mixing MSW solar neutrino transitions with $\Delta m^2_\mathrm{atm} \simeq m_3^2$ and $\Delta m^2_\mathrm{solar} \simeq m_2^2$, respectively, are naturally accommodated in this model without employing any symmetry.Comment: 9 pages, Revtex, no figures; misprints correcte

To Treat or Not To Treat—From Guidelines to Individualized Patient Management

Immune thrombocytopenia (ITP) is a rare disorder. Evidence-based guidelines provide important information for hematologists, as well as diagnostic and therapeutic recommendations to other physicians with limited expertise in the field. However, guidelines in pediatric and adult ITP do not answer some imperative questions: which patient is at risk of severe bleeding and requires pharmacologic treatment? Who will recover spontaneously? Is splenectomy still an appropriate second-line treatment for all chronic or persistent ITP patients? This review summarizes the current approach to these important issues, the patients’ perspective, and how we can improve individual patient managemen

Full jet tomography of high-energy nuclear collisions

Parton energy loss in the hot QCD medium will manifest itself not only in leading hadron spectra but also in reconstructed jet productions in high-energy nucleus-nucleus collisions. In this paper we report on recent theoretical efforts in studying full jet observables in relativistic heavy-ion collisions by discussing the modifications of jet shapes, inclusive jet cross section and the vector boson accompanied jet production in the presence of the QGP-induced jet quenching.Comment: Plenary talk at Hard Probe 2010, October 10-15, 2010, Eilat, Israel. 8 pages, 6 figure

Probing Shadowed Nuclear Sea with Massive Gauge Bosons in the Future Heavy-Ion Collisions

The production of the massive bosons $Z^0$ and $W^{\pm}$ could provide an excellent tool to study cold nuclear matter effects and the modifications of nuclear parton distribution functions (nPDFs) relative to parton distribution functions (PDFs) of a free proton in high energy nuclear reactions at the LHC as well as in heavy-ion collisions (HIC) with much higher center-of mass energies available in the future colliders. In this paper we calculate the rapidity and transverse momentum distributions of the vector boson and their nuclear modification factors in p+Pb collisions at $\sqrt{s_{NN}}=63$TeV and in Pb+Pb collisions at $\sqrt{s_{NN}}=39$TeV in the framework of perturbative QCD by utilizing three parametrization sets of nPDFs: EPS09, DSSZ and nCTEQ. It is found that in heavy-ion collisions at such high colliding energies, both the rapidity distribution and the transverse momentum spectrum of vector bosons are considerably suppressed in wide kinematic regions with respect to p+p reactions due to large nuclear shadowing effect. We demonstrate that in the massive vector boson productions processes with sea quarks in the initial-state may give more contributions than those with valence quarks in the initial-state, therefore in future heavy-ion collisions the isospin effect is less pronounced and the charge asymmetry of W boson will be reduced significantly as compared to that at the LHC. Large difference between results with nCTEQ and results with EPS09 and DSSZ is observed in nuclear modifications of both rapidity and $p_T$ distributions of $Z^0$ and $W$ in the future HIC.Comment: 13 pages, 21 figures, version accepted for publication in Eur. Phys. J.

Prospective longitudinal study of coagulation profiles in children with hypoplastic left heart syndrome from stage I through Fontan completion

ObjectiveThe risk for thrombosis is increased after the Fontan operation. It is unknown whether children with univentricular heart disease have an intrinsic coagulation anomaly or acquire a defect in coagulation during the course of the staged repair. This prospective, longitudinal study evaluated changes in coagulation profiles in a cohort of patients with hypoplastic left heart syndrome from stage I palliation through completion of the Fontan operation.MethodsThirty-seven patients with hypoplastic left heart syndrome were enrolled prospectively, and the concentration of factors II, V, VII, VIII, IX, X, proteins C and S, fibrinogen, antithrombin, serum albumin, and liver enzymes were measured before stage I palliation (mean age 4 ± 2 days), before bidirectional Glenn (mean age 5.9 ± 1.8 months), before the Fontan procedure (mean age 27.1 ± 6.6 months), and after the Fontan procedure (mean age 49 ± 17.6months). Healthy children were used as age-matched controls for coagulation factors. Demographic, hemodynamic variables, and elapsed time after the Fontan procedure were evaluated as possible predictors of coagulation abnormalities.ResultsSignificantly lower levels of both procoagulation and anticoagulation factors were demonstrated through to completion of the Fontan procedure. After the Fontan procedure, there was a significantly higher factor VIII level (P < .005) but no correlation with hemodynamic variables or liver function.ConclusionThis longitudinal study in patients with identical cardiac disease and staged surgical procedures confirms the increase in factor VIII level after the Fontan procedure. This is an acquired defect, and although the cause remains to be determined, monitoring factor VIII levels after the Fontan operation could indicate a subset of patients at risk for thrombosis

Prospective longitudinal study of coagulation profiles in children with hypoplastic left heart syndrome from stage I through Fontan completion

ObjectiveThe risk for thrombosis is increased after the Fontan operation. It is unknown whether children with univentricular heart disease have an intrinsic coagulation anomaly or acquire a defect in coagulation during the course of the staged repair. This prospective, longitudinal study evaluated changes in coagulation profiles in a cohort of patients with hypoplastic left heart syndrome from stage I palliation through completion of the Fontan operation.MethodsThirty-seven patients with hypoplastic left heart syndrome were enrolled prospectively, and the concentration of factors II, V, VII, VIII, IX, X, proteins C and S, fibrinogen, antithrombin, serum albumin, and liver enzymes were measured before stage I palliation (mean age 4 ± 2 days), before bidirectional Glenn (mean age 5.9 ± 1.8 months), before the Fontan procedure (mean age 27.1 ± 6.6 months), and after the Fontan procedure (mean age 49 ± 17.6months). Healthy children were used as age-matched controls for coagulation factors. Demographic, hemodynamic variables, and elapsed time after the Fontan procedure were evaluated as possible predictors of coagulation abnormalities.ResultsSignificantly lower levels of both procoagulation and anticoagulation factors were demonstrated through to completion of the Fontan procedure. After the Fontan procedure, there was a significantly higher factor VIII level (P < .005) but no correlation with hemodynamic variables or liver function.ConclusionThis longitudinal study in patients with identical cardiac disease and staged surgical procedures confirms the increase in factor VIII level after the Fontan procedure. This is an acquired defect, and although the cause remains to be determined, monitoring factor VIII levels after the Fontan operation could indicate a subset of patients at risk for thrombosis

Estimating and interpreting individual patients' pharmacokinetic profiles in persons with Hemophilia A or B using a population pharmacokinetic approach: communication from the SSC of the ISTH

The ISTH SSC on Factor VIII/IX has previously issued guidelines for studies assessing the pharmacokinetics (PK) of factor concentrates [1,2]. They suggested drawing 10 or 11 blood samples over a period of 32-48h or 50-72h, after infusing 25-50 or 50-75 IU/kg, respectively for factor VIII (FVIII) or factor IX (FIX), in cohorts of 12-15 patients with a crossover design. Such PK studies are not ideal for tailoring the treatment of individual patients, mostly for the requirement of several blood samples. Due to broad inter-individual variation, the individual disposition of FVIII and FIX cannot be predicted from morphometric characteristics and average PK parameters, but requires empirical assessment in each individual [3–6]. Previous guidance of this ISTH SSC described the PK methodology for the prediction of individual trough levels of FVIII [7]. The present communication, building on recent advancements in the population PK (PopPK) of FVIII and FIX [8], adds to the former documents

Cold Nuclear Matter Effects on Dijet Productions in Relativistic Heavy-ion Reactions at LHC

We investigate the cold nuclear matter(CNM) effects on dijet productions in high-energy nuclear collisions at LHC with the next-to-leading order perturbative QCD. The nuclear modifications for dijet angular distributions, dijet invariant mass spectra, dijet transverse momentum spectra and dijet momentum imbalance due to CNM effects are calculated by incorporating EPS, EKS, HKN and DS param-etrization sets of parton distributions in nucleus . It is found that dijet angular distributions and dijet momentum imbalance are insensitive to the initial-state CNM effects and thus provide optimal tools to study the final-state hot QGP effects such as jet quenching. On the other hand, the invariant mass spectra and the transverse momentum spectra of dijet are generally enhanced in a wide region of the invariant mass or transverse momentum due to CNM effects with a feature opposite to the expected suppression because of the final-state parton energy loss effect in the QGP. The difference of EPS, EKS, HKN and DS parametrization sets of nuclear parton distribution functions is appreciable for dijet invariant mass spectra and transverse momentum spectra at p+Pb collisions, and becomes more pronounced for those at Pb+Pb reactions.Comment: 10 pages, 11 figure