Lyashko-Looijenga morphisms and submaximal factorisations of a Coxeter element

When W is a finite reflection group, the noncrossing partition lattice NCP_W of type W is a rich combinatorial object, extending the notion of noncrossing partitions of an n-gon. A formula (for which the only known proofs are case-by-case) expresses the number of multichains of a given length in NCP_W as a generalised Fuss-Catalan number, depending on the invariant degrees of W. We describe how to understand some specifications of this formula in a case-free way, using an interpretation of the chains of NCP_W as fibers of a Lyashko-Looijenga covering (LL), constructed from the geometry of the discriminant hypersurface of W. We study algebraically the map LL, describing the factorisations of its discriminant and its Jacobian. As byproducts, we generalise a formula stated by K. Saito for real reflection groups, and we deduce new enumeration formulas for certain factorisations of a Coxeter element of W.Comment: 18 pages. Version 2 : corrected typos and improved presentation. Version 3 : corrected typos, added illustrated example. To appear in Journal of Algebraic Combinatoric

Partial wave analysiss of pbar-p -> piminus-piplus, pizero-pizero, eta-eta and eta-etaprime

A partial wave analysis is presented of Crystal Barrel data on pbar-p -> pizero-pizero, eta-eta and eta-etaprime from 600 to 1940 MeV/c, combined with earlier data on d\sigma /d\Omega and P for pbar-p->piminus-piplus. The following s-channel I=0 resonances are identified: (i) J^{PC} = 5^{--} with mass and width (M,\Gamma) at (2295+-30,235^{+65}_{-40}) MeV, (ii) J^{PC} = 4^{++} at (2020+-12, 170+-15) MeV and (2300+-25, 270+-50) MeV, (iii) 3D3 JPC = 3^{--} at (1960+-15, 150+-25) MeV and (2210+-4$, 360+-55) MeV, and a 3G3 state at (2300 ^{+50}_{-80}, 340+-150) MeV, (iv) JPC = 2^{++} at (1910+-30, 260+-40) MeV, (2020+-30, 275+-35) MeV, (2230+-30, 245+-45) MeV, and (2300+-35, 290+-50) MeV, (v) JPC = 1^{--} at (2005+-40, 275+-75) MeV, and (2165+-40, 160 ^{+140}_{-70}) MeV, and (vi) JPC = 0^{++} at (2005+-30, 305+-50) MeV, (2105+-15, 200+-25) MeV, and (2320+-30, 175+-45) MeV. In addition, there is a less well defined 6^{++} resonance at 2485+-40 MeV, with Gamma = 410+-90 MeV. For every JP, almost all these resonances lie on well defined linear trajectories of mass squared v. excitation number. The slope is 1.10+-0.03 Gev^2 per excitation. The f_0(2105) has strong coupling to eta-\eta, but much weaker coupling to pizero-pizero. Its flavour mixing angle between q-qbar and s-sbar is (59-71.6)deg, i.e. dominant decays to s-sbar. Such decays and its strong production in pbar-p interactions strongly suggest exotic character.Comment: Makes available the combined fit to Crystal Barrel data on pbar-p -> 2-body final states. 29 pages, 11 figures. Typo corrected in version

Mapping the Two-Component Atomic Fermi Gas to the Nuclear Shell-Model

The physics of a two-component cold fermi gas is now frequently addressed in laboratories. Usually this is done for large samples of tens to hundreds of thousands of particles. However, it is now possible to produce few-body systems (1-100 particles) in very tight traps where the shell structure of the external potential becomes important. A system of two-species fermionic cold atoms with an attractive zero-range interaction is analogous to a simple model of nucleus in which neutrons and protons interact only through a residual pairing interaction. In this article, we discuss how the problem of a two-component atomic fermi gas in a tight external trap can be mapped to the nuclear shell model so that readily available many-body techniques in nuclear physics, such as the Shell Model Monte Carlo (SMMC) method, can be directly applied to the study of these systems. We demonstrate an application of the SMMC method by estimating the pairing correlations in a small two-component Fermi system with moderate-to-strong short-range two-body interactions in a three-dimensional harmonic external trapping potential.Comment: 13 pages, 3 figures. Final versio

The influence of individual cognitive style on performance in management education

This paper reports the outcomes of an empirical study undertaken to explore the possibility that cognitive style may be an important factor influencing performance on certain types of task in management education. Four hundred and twelve final-year undergraduate degree students studying management and business administration were tested using the Allinson-Hayes Cognitive Style Index. Their cognitive styles were then compared with assessment grades achieved for academic modules, the task categories of which were deemed to be consonant with either the wholist/intuitive or the analytic style of working. Overall ability defined by final degree grades was also tested against individuals’ cognitive styles. As expected, students whose dominant cognitive styles were analytic attained higher grades for long term solitary tasks involving careful planning and analysis of information. However, contrary to expectations, performance on tasks believed to be more suited to the wholist/intuitive style was also higher for analytic individuals, as was overall ability defined by final degree grades. The results were discussed in terms of the nature of the tasks and the need for methods of performance assessment that are independent of an orientation bias. Without this, it is argued, employment selection criteria may favour the wrong type of candidate in some circumstances

Classification of a supersolid: Trial wavefunctions, Symmetry breakings and Excitation spectra

A state of matter is characterized by its symmetry breaking and elementary excitations. A supersolid is a state which breaks both translational symmetry and internal $U(1)$ symmetry. Here, we review some past and recent works in phenomenological Ginsburg-Landau theories, ground state trial wavefunctions and microscopic numerical calculations. We also write down a new effective supersolid Hamiltonian on a lattice. The eigenstates of the Hamiltonian contains both the ground state wavefunction and all the excited states (supersolidon) wavefunctions. We contrast various kinds of supersolids in both continuous systems and on lattices, both condensed matter and cold atom systems. We provide additional new insights in studying their order parameters, symmetry breaking patterns, the excitation spectra and detection methods.Comment: REVTEX4, 19 pages, 3 figure

Regression Error Characteristic Optimisation of Non-Linear Models.

Copyright © 2006 Springer-Verlag Berlin Heidelberg. The final publication is available at link.springer.comBook title: Multi-Objective Machine LearningIn this chapter recent research in the area of multi-objective optimisation of regression models is presented and combined. Evolutionary multi-objective optimisation techniques are described for training a population of regression models to optimise the recently defined Regression Error Characteristic Curves (REC). A method which meaningfully compares across regressors and against benchmark models (i.e. ‘random walk’ and maximum a posteriori approaches) for varying error rates. Through bootstrapping training data, degrees of confident out-performance are also highlighted

Identification of cardiac MRI thresholds for risk stratification in pulmonary arterial hypertension

Rationale: Pulmonary arterial hypertension (PAH) is a life-shortening condition. The European Society of Cardiology and European Respiratory Society and the REVEAL (North American Registry to Evaluate Early and Long-Term PAH Disease Management) risk score calculator (REVEAL 2.0) identify thresholds to predict 1-year mortality. Objectives: This study evaluates whether cardiac magnetic resonance imaging (MRI) thresholds can be identified and used to aid risk stratification and facilitate decision-making. Methods: Consecutive patients with PAH (n = 438) undergoing cardiac MRI were identified from the ASPIRE (Assessing the Spectrum of Pulmonary Hypertension Identified at a Referral Center) MRI database. Thresholds were identified from a discovery cohort and evaluated in a test cohort. Measurements and Main Results: A percentage-predicted right ventricular end-systolic volume index threshold of 227% or a left ventricular end-diastolic volume index of 58 ml/m2 identified patients at low (10%) risk of 1-year mortality. These metrics respectively identified 63% and 34% of patients as low risk. Right ventricular ejection fraction >54%, 37–54%, and <37% identified 21%, 43%, and 36% of patients at low, intermediate, and high risk, respectively, of 1-year mortality. At follow-up cardiac MRI, patients who improved to or were maintained in a low-risk group had a 1-year mortality <5%. Percentage-predicted right ventricular end-systolic volume index independently predicted outcome and, when used in conjunction with the REVEAL 2.0 risk score calculator or a modified French Pulmonary Hypertension Registry approach, improved risk stratification for 1-year mortality. Conclusions: Cardiac MRI can be used to risk stratify patients with PAH using a threshold approach. Percentage-predicted right ventricular end-systolic volume index can identify a high percentage of patients at low-risk of 1-year mortality and, when used in conjunction with current risk stratification approaches, can improve risk stratification. This study supports further evaluation of cardiac MRI in risk stratification in PAH

Strong Decays of Strange Quarkonia

In this paper we evaluate strong decay amplitudes and partial widths of strange mesons (strangeonia and kaonia) in the 3P0 decay model. We give numerical results for all energetically allowed open-flavor two-body decay modes of all nsbar and ssbar strange mesons in the 1S, 2S, 3S, 1P, 2P, 1D and 1F multiplets, comprising strong decays of a total of 43 resonances into 525 two-body modes, with 891 numerically evaluated amplitudes. This set of resonances includes all strange qqbar states with allowed strong decays expected in the quark model up to ca. 2.2 GeV. We use standard nonrelativistic quark model SHO wavefunctions to evaluate these amplitudes, and quote numerical results for all amplitudes present in each decay mode. We also discuss the status of the associated experimental candidates, and note which states and decay modes would be especially interesting for future experimental study at hadronic, e+e- and photoproduction facilities. These results should also be useful in distinguishing conventional quark model mesons from exotica such as glueballs and hybrids through their strong decays.Comment: 69 pages, 5 figures, 39 table

Committed Global Warming Risks Triggering Multiple Climate Tipping Points

Many scenarios for limiting global warming to 1.5°C assume planetary-scale carbon dioxide removal sufficient to exceed anthropogenic emissions, resulting in radiative forcing falling and temperatures stabilizing. However, such removal technology may prove unfeasible for technical, environmental, political, or economic reasons, resulting in continuing greenhouse gas emissions from hard-to-mitigate sectors. This may lead to constant concentration scenarios, where net anthropogenic emissions remain non-zero but small, and are roughly balanced by natural carbon sinks. Such a situation would keep atmospheric radiative forcing roughly constant. Fixed radiative forcing creates an equilibrium “committed” warming, captured in the concept of “equilibrium climate sensitivity.” This scenario is rarely analyzed as a potential extension to transient climate scenarios. Here, we aim to understand the planetary response to such fixed concentration commitments, with an emphasis on assessing the resulting likelihood of exceeding temperature thresholds that trigger climate tipping points. We explore transients followed by respective equilibrium committed warming initiated under low to high emission scenarios. We find that the likelihood of crossing the 1.5°C threshold and the 2.0°C threshold is 83% and 55%, respectively, if today's radiative forcing is maintained until achieving equilibrium global warming. Under the scenario that best matches current national commitments (RCP4.5), we estimate that in the transient stage, two tipping points will be crossed. If radiative forcing is then held fixed after the year 2100, a further six tipping point thresholds are crossed. Achieving a trajectory similar to RCP2.6 requires reaching net-zero emissions rapidly, which would greatly reduce the likelihood of tipping events

IGF-1 does not moderate the time-dependent transcriptional patterns of key homeostatic genes induced by sustained compression of bovine cartilage

Objective To determine changes in chondrocyte transcription of a range of anabolic, catabolic and signaling genes following simultaneous treatment of cartilage with Insulin-like growth factor-1 (IGF-1) and ramp-and-hold mechanical compression, and compare with effects on biosynthesis. Methods Explant disks of bovine calf cartilage were slowly compressed (unconfined) over 3-min to their 1 mm cut-thickness (0%-compression) or to 50%-compression with or without 300 ng/ml IGF-1. Expression of 24 genes involved in cartilage homeostasis was measured using qPCR at 2, 8, 24, 32, 48 h after compression ±IGF-1. Clustering analysis was used to identify groups of co-expressed genes to further elucidate mechanistic pathways. Results IGF-1 alone stimulated gene expression of aggrecan and collagen II, but simultaneous 24h compression suppressed this effect. Compression alone up-regulated expression of matrix metalloproteinase (MMP)-3, MMP-13, a disintegrin and metalloproteinase with thrombospondin motif (ADAMTS)-5 and transforming growth factor (TGF)-β, an effect not reversed by simultaneous IGF-1 treatment. Temporal changes in expression following IGF-1 treatment were generally slower than that following compression. Clustering analysis revealed five distinct groups within which the pairings, tissue inhibitor of metalloproteinase (TIMP)-3 and ADAMTS-5, MMP-1 and IGF-2, and IGF-1 and Collagen II, were all robustly co-expressed, suggesting inherent regulation and feedback in chondrocyte gene expression. While aggrecan synthesis was transcriptionally regulated by IGF-1, inhibition of aggrecan synthesis by sustained compression appeared post-transcriptionally regulated. Conclusion Sustained compression markedly altered the effects of IGF-1 on expression of genes involved in cartilage homeostasis, while IGF-1 was largely unable to moderate the transcriptional effects of compression alone. The demonstrated co-expressed gene pairings suggest a balance of anabolic and catabolic activity following simultaneous mechanical and growth factor stimuli.National Institutes of Health (U.S.) (grant R01-AR33236)National Institutes of Health (U.S.) (grant R01-HG003352)National Institutes of Health (U.S.) (grant P42-ES04699)National Institutes of Health (U.S.) (grant T32-EB006348