Quasi-Exactly Solvable Potentials on the Line and Orthogonal Polynomials

In this paper we show that a quasi-exactly solvable (normalizable or periodic) one-dimensional Hamiltonian satisfying very mild conditions defines a family of weakly orthogonal polynomials which obey a three-term recursion relation. In particular, we prove that (normalizable) exactly-solvable one-dimensional systems are characterized by the fact that their associated polynomials satisfy a two-term recursion relation. We study the properties of the family of weakly orthogonal polynomials defined by an arbitrary one-dimensional quasi-exactly solvable Hamiltonian, showing in particular that its associated Stieltjes measure is supported on a finite set. From this we deduce that the corresponding moment problem is determined, and that the $k$-th moment grows like the $k$-th power of a constant as $k$ tends to infinity. We also show that the moments satisfy a constant coefficient linear difference equation, and that this property actually characterizes weakly orthogonal polynomial systems.Comment: 22 pages, plain TeX. Please typeset only the file orth.te

Critical behavior of su(1|1) supersymmetric spin chains with long-range interactions

We introduce a general class of su$(1|1)$ supersymmetric spin chains with long-range interactions which includes as particular cases the su$(1|1)$ Inozemtsev (elliptic) and Haldane-Shastry chains, as well as the XX model. We show that this class of models can be fermionized with the help of the algebraic properties of the su$(1|1)$ permutation operator, and take advantage of this fact to analyze their quantum criticality when a chemical potential term is present in the Hamiltonian. We first study the low energy excitations and the low temperature behavior of the free energy, which coincides with that of a $(1+1)$-dimensional conformal field theory (CFT) with central charge $c=1$ when the chemical potential lies in the critical interval $(0,\mathcal E(\pi))$, $\mathcal E(p)$ being the dispersion relation. We also analyze the von Neumann and R\'enyi ground state entanglement entropies, showing that they exhibit the logarithmic scaling with the size of the block of spins characteristic of a one-boson $(1+1)$-dimensional CFT. Our results thus show that the models under study are quantum critical when the chemical potential belongs to the critical interval, with central charge $c=1$. From the analysis of the fermion density at zero temperature, we also conclude that there is a quantum phase transition at both ends of the critical interval. This is further confirmed by the behavior of the fermion density at finite temperature, which is studied analytically (at low temperature), as well as numerically for the su$(1|1)$ elliptic chain.Comment: 13 pages, 6 figures, typeset in REVTe

Generalized isotropic Lipkin-Meshkov-Glick models: ground state entanglement and quantum entropies

We introduce a new class of generalized isotropic Lipkin-Meshkov-Glick models with su$(m+1)$ spin and long-range non-constant interactions, whose non-degenerate ground state is a Dicke state of su$(m+1)$ type. We evaluate in closed form the reduced density matrix of a block of $L$ spins when the whole system is in its ground state, and study the corresponding von Neumann and R\'enyi entanglement entropies in the thermodynamic limit. We show that both of these entropies scale as $a\log L$ when $L$ tends to infinity, where the coefficient $a$ is equal to $(m-k)/2$ in the ground state phase with $k$ vanishing su$(m+1)$ magnon densities. In particular, our results show that none of these generalized Lipkin-Meshkov-Glick models are critical, since when $L\to\infty$ their R\'enyi entropy $R_q$ becomes independent of the parameter $q$. We have also computed the Tsallis entanglement entropy of the ground state of these generalized su$(m+1)$ Lipkin-Meshkov-Glick models, finding that it can be made extensive by an appropriate choice of its parameter only when $m-k\ge3$. Finally, in the su$(3)$ case we construct in detail the phase diagram of the ground state in parameter space, showing that it is determined in a simple way by the weights of the fundamental representation of su$(3)$. This is also true in the su$(m+1)$ case; for instance, we prove that the region for which all the magnon densities are non-vanishing is an $(m+1)$-simplex in $\mathbf R^m$ whose vertices are the weights of the fundamental representation of su$(m+1)$.Comment: Typeset with LaTeX, 32 pages, 3 figures. Final version with corrections and additional reference

Daily physical activity and macronutrient distribution of low-calorie diets jointly affect body fat reduction in obese women.

Inadequate dietary patterns and sedentary lifestyles are believed to be important factors in predisposing people to obesity. This study analyzed the potential interaction between habitual physical activity and the carbohydrate (CHO)-fat distribution in 2 hypocaloric diets and the impact of such interplay on body composition changes. Forty healthy obese women, 20–50 years old, were randomly assigned to a high- or low-CHO energy-restricted diet, which was low or high in fat, respectively, during 10 weeks. Baseline and final measurements were performed to assess dietary habits, resting metabolic rate, and body composition changes. Physical activity was measured with a triaxial accelerometer and with a questionnaire. There were no significant differences in anthropometric and metabolic variables between both dietary groups at baseline. However, there was a positive correlation between total free-living physical activity and arm muscle preservation after 10 weeks (r = 0.371; p = 0.024). Interestingly, an interaction between macronutrient (CHO–fat distribution) intake and physical activity was found, since less-active subjects with a high-CHO–low-fat diet showed a greater fat loss than those more active with a lower-CHO–high-fat diet, whereas more-active subjects with a high-CHO–low-fat diet showed a smaller fat loss than those receiving a low-CHO–high-fat diet. Physical activity and the macronutrient content of energyrestricted diets, when designed to promote body fat mass reduction, should be considered together to better predict the outcome

Induction of auxin biosynthesis and WOX5 repression mediate changes in root development in Arabidopsis exposed to chitosan

[EN] Chitosan is a natural polymer with applications in agriculture, which causes plasma membrane permeabilisation and induction of intracellular reactive oxygen species (ROS) in plants. Chitosan has been mostly applied in the phylloplane to control plant diseases and to enhance plant defences, but has also been considered for controlling root pests. However, the effect of chitosan on roots is virtually unknown. In this work, we show that chitosan interfered with auxin homeostasis in Arabidopsis roots, promoting a 2-3 fold accumulation of indole acetic acid (IAA). We observed chitosan dose-dependent alterations of auxin synthesis, transport and signalling in Arabidopsis roots. As a consequence, high doses of chitosan reduce WOX5 expression in the root apical meristem and arrest root growth. Chitosan also propitiates accumulation of salicylic (SA) and jasmonic (JA) acids in Arabidopsis roots by induction of genes involved in their biosynthesis and signalling. In addition, high-dose chitosan irrigation of tomato and barley plants also arrests root development. Tomato root apices treated with chitosan showed isodiametric cells respect to rectangular cells in the controls. We found that chitosan causes strong alterations in root cell morphology. Our results highlight the importance of considering chitosan dose during agronomical applications to the rhizosphere.This work was supported by AGL 2015 66833-R Grant from the Spanish Ministry of Economy and Competitiveness Grant AGL 2015. We would like to thank Drs Isabel Lopez-Diaz and Esther Carrera for plant hormone quantitation (IBMCP, Valencia, Spain). Part of this work was filed for a patent (P201431399) by L. V. Lopez-Llorca, F. Lopez-Moya and N. Escudero as inventors. We would like to thank Dr Michael Kershaw (University of Exeter) for his English revision and critical comments of the manuscript. 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Co-expression of inducible nitric oxide synthase and arginases in different human monocyte subsets. Apoptosis regulated by endogenous NO

Human monocyte subsets, isolated from cultures of mononuclear cells, or freshly obtained from patients with multiple sclerosis, Graves' disease or pemphigus vulgaris, differed in phenotype, apoptotic features, mRNA levels of arginase II (A-II) and the inducible form of nitric oxide synthase (iNOS). Liver-type arginase I mRNA was present in all subsets. Apoptosis was followed by the expression of T cell intracellular antigen (TIA) and the simultaneous detection of DNA stainability by propidium iodine and annexin V binding. Apoptosis was practically absent both in activated CD14(++)CD33(++)DR(++)CD25(++)CD69(++)CD71(++/+) CD16(-) cells, expressing A-II mRNA and having arginase activity, but not iNOS mRNA, and in not fully mature large CD14(++)CD16(+)CD23(+)DR(++) monocytes, expressing simultaneously both mRNAs and having both enzyme activities. However, differentiated small CD14(+/++)CD16(+)CD69(+)CD25(+/-)CD71(++)CD23(+) DR(++) monocytes, expressing high levels of iNOS mRNA, exhibited apoptotic signs. Amounts of NO synthesised by monocytes co-expressing iNOS and arginase changed with the addition of arginine or an iNOS inhibitor; in that case a correlation of NO production and apoptotic features was observed. Data suggest a regulatory role for endogenous NO in apoptosis of stimulated and differentiated monocytes, and also that iNOS and A-II, when simultaneously present, could control the production of NO as a consequence of their competition for arginine

Validation of metabolic syndrome using medical records in the SUN cohort

The objective of this study was to evaluate the validity of self reported criteria of Metabolic Syndrome (MS) in the SUN (Seguimiento Universidad de Navarra) cohort using their medical records as the gold standard. METHODS: We selected 336 participants and we obtained MS related data according to Adult Treatment Panel III (ATP III) and International Diabetes Federation (IDF). Then we compared information on the self reported diagnosis of MS and MS diagnosed in their medical records. We calculated the proportion of confirmed MS, the proportion of confirmed non-MS and the intraclass correlation coefficients for each component of the MS. RESULTS: From those 336 selected participants, we obtained sufficient data in 172 participants to confirm or reject MS using ATP III criteria. The proportion of confirmed MS was 91.2% (95% CI: 80.7- 97.1) and the proportion of confirmed non-MS was 92.2% (95% CI: 85.7-96.4) using ATP III criteria. The proportion of confirmed MS using IDF criteria was 100% (95% CI: 87.2-100) and the proportion of confirmed non-MS was 97.1% (95% CI: 85.1-99.9). Kappa Index was 0.82 in the group diagnosed by ATP III criteria and 0.97 in the group diagnosed by IDF criteria. Intraclass correlation coefficients for the different component of MS were: 0.93 (IC 95%:0.91- 0.95) for BMI; 0.96 (IC 95%: 0.93-0.98) for waist circumference; 0.75 (IC 95%: 0.66-0.82) for fasting glucose; 0.50 (IC 95%:0.35-0.639) for HDL cholesterol; 0.78 (IC 95%: 0.70-0.84) for triglycerides; 0.49 (IC 95%:0.34-0.61) for systolic blood pressure and 0.55 (IC 95%: 0.41-0.65) for diastolic blood pressure. CONCLUSIONS: Self-reported MS based on self reported components of the SM in a Spanish cohort of university graduates was sufficiently valid as to be used in epidemiological studies

Distributed acoustic sensing for seismic activity monitoring

Continuous, real-time monitoring of surface seismic activity around the globe is of great interest for acquiring new insight into global tomography analyses and for recognition of seismic patterns leading to potentially hazardous situations. The already-existing telecommunication fiber optic network arises as an ideal solution for this application, owing to its ubiquity and the capacity of optical fibers to perform distributed, highly sensitive monitoring of vibrations at relatively low cost (ultra-high density of point sensors available with minimal deployment of new equipment). This perspective article discusses early approaches on the application of fiber-optic distributed acoustic sensors (DASs) for seismic activity monitoring. The benefits and potential impact of DAS technology in these kinds of applications are here illustrated with new experimental results on teleseism monitoring based on a specific approach: the so-called chirped-pulse DAS. This technology offers promising prospects for the field of seismic tomography due to its appealing properties in terms of simplicity, consistent sensitivity across sensing channels, and robustness. Furthermore, we also report on several signal processing techniques readily applicable to chirped-pulse DAS recordings for extracting relevant seismic information from ambient acoustic noise. The outcome presented here may serve as a foundation for a novel conception for ubiquitous seismic monitoring with minimal investment

Polarisation pulling in Brillouin optical time-domain analysers

The impact of Brillouin scattering on the polarisation of pump and probe in a Brillouin optical-time domain analyser is investigated. Experimental results indicate that the Brillouin interaction integrated along the entire sensing fibre produces a polarisation pulling force that changes the pump polarisation. Although this force can be compensated to first order by dual-sideband probes, the Brillouin gain/loss experienced by probe bands induce a net pulling that leads to uncompensated polarisation fading and reduced signal-to-noise ratio. While the use of two simultaneous orthogonally-polarised probes alleviates fading issues, spectral distortions originate from the coupling between Brillouin gain and polarisation pulling