Quasi-Exact Solvability and the direct approach to invariant subspaces

We propose a more direct approach to constructing differential operators that preserve polynomial subspaces than the one based on considering elements of the enveloping algebra of sl(2). This approach is used here to construct new exactly solvable and quasi-exactly solvable quantum Hamiltonians on the line which are not Lie-algebraic. It is also applied to generate potentials with multiple algebraic sectors. We discuss two illustrative examples of these two applications: an interesting generalization of the Lam\'e potential which posses four algebraic sectors, and a quasi-exactly solvable deformation of the Morse potential which is not Lie-algebraic.Comment: 17 pages, 3 figure

Effects of alirocumab on types of myocardial infarction: insights from the ODYSSEY OUTCOMES trial

AIMS: The third Universal Definition of Myocardial Infarction (MI) Task Force classified MIs into five types: Type 1, spontaneous; Type 2, related to oxygen supply/demand imbalance; Type 3, fatal without ascertainment of cardiac biomarkers; Type 4, related to percutaneous coronary intervention; and Type 5, related to coronary artery bypass surgery. Low-density lipoprotein cholesterol (LDL-C) reduction with statins and proprotein convertase subtilisin-kexin Type 9 (PCSK9) inhibitors reduces risk of MI, but less is known about effects on types of MI. ODYSSEY OUTCOMES compared the PCSK9 inhibitor alirocumab with placebo in 18 924 patients with recent acute coronary syndrome (ACS) and elevated LDL-C (>/=1.8 mmol/L) despite intensive statin therapy. In a pre-specified analysis, we assessed the effects of alirocumab on types of MI. METHODS AND RESULTS: Median follow-up was 2.8 years. Myocardial infarction types were prospectively adjudicated and classified. Of 1860 total MIs, 1223 (65.8%) were adjudicated as Type 1, 386 (20.8%) as Type 2, and 244 (13.1%) as Type 4. Few events were Type 3 (n = 2) or Type 5 (n = 5). Alirocumab reduced first MIs [hazard ratio (HR) 0.85, 95% confidence interval (CI) 0.77-0.95; P = 0.003], with reductions in both Type 1 (HR 0.87, 95% CI 0.77-0.99; P = 0.032) and Type 2 (0.77, 0.61-0.97; P = 0.025), but not Type 4 MI. CONCLUSION: After ACS, alirocumab added to intensive statin therapy favourably impacted on Type 1 and 2 MIs. The data indicate for the first time that a lipid-lowering therapy can attenuate the risk of Type 2 MI. Low-density lipoprotein cholesterol reduction below levels achievable with statins is an effective preventive strategy for both MI types

Vortices in a Bose-Einstein condensate confined by an optical lattice

We investigate the dynamics of vortices in repulsive Bose-Einstein condensates in the presence of an optical lattice (OL) and a parabolic magnetic trap. The dynamics is sensitive to the phase of the OL potential relative to the magnetic trap, and depends less on the OL strength. For the cosinusoidal OL potential, a local minimum is generated at the trap's center, creating a stable equilibrium for the vortex, while in the case of the sinusoidal potential, the vortex is expelled from the center, demonstrating spiral motion. Cases where the vortex is created far from the trap's center are also studied, revealing slow outward-spiraling drift. Numerical results are explained in an analytical form by means of a variational approximation. Finally, motivated by a discrete model (which is tantamount to the case of the strong OL lattice), we present a novel type of vortex consisting of two pairs of anti-phase solitons.Comment: 10 pages, 6 figure

Leading-effect vs. Risk-taking in Dynamic Tournaments: Evidence from a Real-life Randomized Experiment

Two 'order effects' may emerge in dynamic tournaments with information feedback. First, participants adjust effort across stages, which could advantage the leading participant who faces a larger 'effective prize' after an initial victory (leading-effect). Second, participants lagging behind may increase risk at the final stage as they have 'nothing to lose' (risk-taking). We use a randomized natural experiment in professional two-game soccer tournaments where the treatment (order of a stage-specific advantage) and team characteristics, e.g. ability, are independent. We develop an identification strategy to test for leading-effects controlling for risk-taking. We find no evidence of leading-effects and negligible risk-taking effects

Quantum Mechanics on the cylinder

A new approach to deformation quantization on the cylinder considered as phase space is presented. The method is based on the standard Moyal formalism for R^2 adapted to (S^1 x R) by the Weil--Brezin--Zak transformation. The results are compared with other solutions of this problem presented by Kasperkovitz and Peev (Ann. Phys. vol. 230, 21 (1994)0 and by Plebanski and collaborators (Acta Phys. Pol. vol. B 31}, 561 (2000)). The equivalence of these three methods is proved.Comment: 21 pages, LaTe

Gamma Ray Bursts as Probes of Quantum Gravity

Gamma ray bursts (GRBs) are short and intense pulses of $\gamma$-rays arriving from random directions in the sky. Several years ago Amelino-Camelia et al. pointed out that a comparison of time of arrival of photons at different energies from a GRB could be used to measure (or obtain a limit on) possible deviations from a constant speed of light at high photons energies. I review here our current understanding of GRBs and reconsider the possibility of performing these observations.Comment: Lectures given at the 40th winter school of theretical physics: Quantum Gravity and Phenomenology, Feb. 2004 Polan

Regularity Properties and Pathologies of Position-Space Renormalization-Group Transformations

We reconsider the conceptual foundations of the renormalization-group (RG) formalism, and prove some rigorous theorems on the regularity properties and possible pathologies of the RG map. Regarding regularity, we show that the RG map, defined on a suitable space of interactions (= formal Hamiltonians), is always single-valued and Lipschitz continuous on its domain of definition. This rules out a recently proposed scenario for the RG description of first-order phase transitions. On the pathological side, we make rigorous some arguments of Griffiths, Pearce and Israel, and prove in several cases that the renormalized measure is not a Gibbs measure for any reasonable interaction. This means that the RG map is ill-defined, and that the conventional RG description of first-order phase transitions is not universally valid. For decimation or Kadanoff transformations applied to the Ising model in dimension $d \ge 3$, these pathologies occur in a full neighborhood $\{ \beta > \beta_0 ,\, |h| < \epsilon(\beta) \}$ of the low-temperature part of the first-order phase-transition surface. For block-averaging transformations applied to the Ising model in dimension $d \ge 2$, the pathologies occur at low temperatures for arbitrary magnetic-field strength. Pathologies may also occur in the critical region for Ising models in dimension $d \ge 4$. We discuss in detail the distinction between Gibbsian and non-Gibbsian measures, and give a rather complete catalogue of the known examples. Finally, we discuss the heuristic and numerical evidence on RG pathologies in the light of our rigorous theorems.Comment: 273 pages including 14 figures, Postscript, See also ftp.scri.fsu.edu:hep-lat/papers/9210/9210032.ps.

Distributionally chaotic families of operators on Fréchet spaces

This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Communications on Pure and Applied Analysis (CPAA) following peer review. The definitive publisher-authenticated version Conejero, J. A., Kostić, M., Miana, P. J., & Murillo-Arcila, M. (2016). Distributionally chaotic families of operators on Fréchet spaces.Communications on Pure and Applied Analysis, 2016, vol. 15, no 5, p. 1915-1939, is available online at: http://dx.doi.org/10.3934/cpaa.2016022The existence of distributional chaos and distributional irregular vectors has been recently considered in the study of linear dynamics of operators and C-0-semigroups. In this paper we extend some previous results on both notions to sequences of operators, C-0-semigroups, C-regularized semigroups, and alpha-timesintegrated semigroups on Frechet spaces. We also add a study of rescaled distributionally chaotic C-0-semigroups. Some examples are provided to illustrate all these results.The first and fourth authors are supported in part by MEC Project MTM2010-14909, MTM2013-47093-P, and Programa de Investigacion y Desarrollo de la UPV, Ref. SP20120700. The second author is partially supported by grant 174024 of Ministry of Science and Technological Development, Republic of Serbia. The third author has been partially supported by Project MTM2013-42105-P, DGI-FEDER, of the MCYTS; Project E-64, D.G. Aragon, and Project UZCUD2014-CIE-09, Universidad de Zaragoza. The fourth author is supported by a grant of the FPU Program of Ministry of education of Spain.Conejero, JA.; Kostic, M.; Miana Sanz, PJ.; Murillo Arcila, M. (2016). Distributionally chaotic families of operators on Fréchet spaces. Communications on Pure and Applied Analysis. 15(5):1915-1939. https://doi.org/10.3934/cpaa.2016022S1915193915

Oncogenic driver mutations predict outcome in a cohort of head and neck squamous cell carcinoma (HNSCC) patients within a clinical trial

234 diagnostic formalin-fixed paraffin-embedded (FFPE) blocks from homogeneously treated patients with locally advanced head and neck squamous cell carcinoma (HNSCC) within a multicentre phase III clinical trial were characterised. The mutational spectrum was examined by next generation sequencing in the 26 most frequent oncogenic drivers in cancer and correlated with treatment response and survival. Human papillomavirus (HPV) status was measured by p16INK4a immunohistochemistry in oropharyngeal tumours. Clinicopathological features and response to treatment were measured and compared with the sequencing results. The results indicated TP53 as the most mutated gene in locally advanced HNSCC. HPV-positive oropharyngeal tumours were less mutated than HPV-negative tumours in TP53 (p < 0.01). Mutational and HPV status influences patient survival, being mutated or HPV-negative tumours associated with poor overall survival (p < 0.05). No association was found between mutations and clinicopathological features. This study confirmed and expanded previously published genomic characterization data in HNSCC. Survival analysis showed that non-mutated HNSCC tumours associated with better prognosis and lack of mutations can be identified as an important biomarker in HNSCC. Frequent alterations in PI3K pathway in HPV-positive HNSCC could define a promising pathway for pharmacological intervention in this group of tumours