Connection between type B (or C) and F factorizations and construction of algebras

In a recent paper (Del Sol Mesa A and Quesne C 2000 J. Phys. A: Math. Gen. 33 4059), we started a systematic study of the connections among different factorization types, suggested by Infeld and Hull, and of their consequences for the construction of algebras. We devised a general procedure for constructing satellite algebras for all the Hamiltonians admitting a type E factorization by using the relationship between type A and E factorizations. Here we complete our analysis by showing that for Hamiltonians admitting a type F factorization, a similar method, starting from either type B or type C ones, leads to other types of algebras. We therefore conclude that the existence of satellite algebras is a characteristic property of type E factorizable Hamiltonians. Our results are illustrated with the detailed discussion of the Coulomb problem.Comment: minor changes, 1 additional reference, final form to be published in JP

Cardiovascular risk assessment using carotid ultrasonography: The Rotterdam Study

Atherosclerosis is the main cause of coronary heart disease, stroke and peripheral arterial disease. These cardiovascular diseases are the most important cause of morbidity and responsible for 50% of all mortality in the United States, Europe and much of Asia. l Since atherosclerosis and cardiovascular diseases are most prominently present in the elderly and the number of elderly people will increase in the coming decades, atherosclerosis-related diseases will put a heavy burden on our health care systems

Tool-path effect on the geometric deviations in the machining of UNS A92024 aeronautic skins

Traditionally, aeronautics skins are being machined by chemical milling, a high-pollutant process. An efficient alternative to this technology is conventional machining. However, to ensure the parts machined with this process keeps the industrial quality controls, the effect of tool-path might be characterized, specially analyzing final thickness and roughness. In this paper, five different tool-paths have been applied under the same machining parameters in the dry milling of Al-Cu UNS A92024 thin plates. Machining time, final thickness and roughness have been evaluated. Most roughness and thickness results are under the industrial quality limits stablished for this type of parts.This work has received financial support from Spanish Goverment (Project DPI2015-71448-R), TECNALIA Research & Innovation and the University of Cadiz (University training plan UCA/REC01VI/2016)

Single-cell analysis of cardiogenesis reveals basis for organ-level developmental defects.

Organogenesis involves integration of diverse cell types; dysregulation of cell-type-specific gene networks results in birth defects, which affect 5% of live births. Congenital heart defects are the most common malformations, and result from disruption of discrete subsets of cardiac progenitor cells1, but the transcriptional changes in individual progenitors that lead to organ-level defects remain unknown. Here we used single-cell RNA sequencing to interrogate early cardiac progenitor cells as they become specified during normal and abnormal cardiogenesis, revealing how dysregulation of specific cellular subpopulations has catastrophic consequences. A network-based computational method for single-cell RNA-sequencing analysis that predicts lineage-specifying transcription factors2,3 identified Hand2 as a specifier of outflow tract cells but not right ventricular cells, despite the failure of right ventricular formation in Hand2-null mice4. Temporal single-cell-transcriptome analysis of Hand2-null embryos revealed failure of outflow tract myocardium specification, whereas right ventricular myocardium was specified but failed to properly differentiate and migrate. Loss of Hand2 also led to dysregulation of retinoic acid signalling and disruption of anterior-posterior patterning of cardiac progenitors. This work reveals transcriptional determinants that specify fate and differentiation in individual cardiac progenitor cells, and exposes mechanisms of disrupted cardiac development at single-cell resolution, providing a framework for investigating congenital heart defects

Satellite potentials for hypergeometric Natanzon potentials

As a result of the so(2,1) of the hypergeometric Natanzon potential a set of potentials related to the given one is determined. The set arises as a result of the action of the so(2,1) generators.Comment: 9 page

Connection Between Type A and E Factorizations and Construction of Satellite Algebras

Recently, we introduced a new class of symmetry algebras, called satellite algebras, which connect with one another wavefunctions belonging to different potentials of a given family, and corresponding to different energy eigenvalues. Here the role of the factorization method in the construction of such algebras is investigated. A general procedure for determining an so(2,2) or so(2,1) satellite algebra for all the Hamiltonians that admit a type E factorization is proposed. Such a procedure is based on the known relationship between type A and E factorizations, combined with an algebraization similar to that used in the construction of potential algebras. It is illustrated with the examples of the generalized Morse potential, the Rosen-Morse potential, the Kepler problem in a space of constant negative curvature, and, in each case, the conserved quantity is identified. It should be stressed that the method proposed is fairly general since the other factorization types may be considered as limiting cases of type A or E factorizations.Comment: 20 pages, LaTeX, no figure, to be published in J. Phys.

Intertwining symmetry algebras of quantum superintegrable systems on the hyperboloid

A class of quantum superintegrable Hamiltonians defined on a two-dimensional hyperboloid is considered together with a set of intertwining operators connecting them. It is shown that such intertwining operators close a su(2,1) Lie algebra and determine the Hamiltonians through the Casimir operators. By means of discrete symmetries a broader set of operators is obtained closing a so(4,2) algebra. The physical states corresponding to the discrete spectrum of bound states as well as the degeneration are characterized in terms of unitary representations of su(2,1) and so(4,2).Comment: 11 pages, 5 figure

Predictive value of noninvasive measures of atherosclerosis for incident myocardial infarction: the Rotterdam Study.

BACKGROUND: Several noninvasive methods are available to investigate the severity of extracoronary atherosclerotic disease. No population-based study has yet examined whether differences exist between these measures with regard to their predictive value for myocardial infarction (MI) or whether a given measure of atherosclerosis has predictive value independently of the other measures. METHODS AND RESULTS: At the baseline (1990-1993) examination of the Rotterdam Study, a population-based cohort study among subjects age > or =55 years, carotid plaques and intima-media thickness (IMT) were measured by ultrasound, abdominal aortic atherosclerosis by x-ray, and lower-extremity atherosclerosis by computation of the ankle-arm index. In the present study, 6389 subjects were included; 258 cases of incident MI occurred before January 1, 2000. All 4 measures of atherosclerosis were good predictors of MI independently of traditional cardiovascular risk factors. Hazard ratios were equally high for carotid plaques (1.83 [1.27 to 2.62], severe versus no atherosclerosis), carotid IMT (1.95 [1.19 to 3.19]), and aortic atherosclerosis (1.94 [1.30 to 2.90]) and slightly lower for lower-extremity atherosclerosis (1.59 [1.05 to 2.39]), although differences were small. The hazard ratio for MI for subjects with severe atherosclerosis according to a composite atherosclerosis score was 2.77 (1.70 to 4.52) compared with subjects with no atherosclerosis. The predictive value of MI for a given measure of atherosclerosis was independent of the other atherosclerosis measures. CONCLUSIONS: Noninvasive measures of extracoronary atherosclerosis are strong predictors of MI. The relatively crude measures directly assessing plaques in the carotid artery and abdominal aorta predict MI equally well as the more precisely measured carotid IMT

Deformations of the Boson sp(4,R)sp(4,R) Representation and its Subalgebras

The boson representation of the sp(4,R) algebra and two distinct deformations of it, are considered, as well as the compact and noncompact subalgebras of each. The initial as well as the deformed representations act in the same Fock space. One of the deformed representation is based on the standard q-deformation of the boson creation and annihilation operators. The subalgebras of sp(4,R) (compact u(2) and three representations of the noncompact u(1,1) are also deformed and are contained in this deformed algebra. They are reducible in the action spaces of sp(4,R) and decompose into irreducible representations. The other deformed representation, is realized by means of a transformation of the q-deformed bosons into q-tensors (spinor-like) with respect to the standard deformed su(2). All of its generators are deformed and have expressions in terms of tensor products of spinor-like operators. In this case, an other deformation of su(2) appears in a natural way as a subalgebra and can be interpreted as a deformation of the angular momentum algebra so(3). Its representation is reducible and decomposes into irreducible ones that yields a complete description of the same

Computational Prediction of Heme-Binding Residues by Exploiting Residue Interaction Network

Computational identification of heme-binding residues is beneficial for predicting and designing novel heme proteins. Here we proposed a novel method for heme-binding residue prediction by exploiting topological properties of these residues in the residue interaction networks derived from three-dimensional structures. Comprehensive analysis showed that key residues located in heme-binding regions are generally associated with the nodes with higher degree, closeness and betweenness, but lower clustering coefficient in the network. HemeNet, a support vector machine (SVM) based predictor, was developed to identify heme-binding residues by combining topological features with existing sequence and structural features. The results showed that incorporation of network-based features significantly improved the prediction performance. We also compared the residue interaction networks of heme proteins before and after heme binding and found that the topological features can well characterize the heme-binding sites of apo structures as well as those of holo structures, which led to reliable performance improvement as we applied HemeNet to predicting the binding residues of proteins in the heme-free state. HemeNet web server is freely accessible at http://mleg.cse.sc.edu/hemeNet/