Integrability and non-integrability of periodic non-autonomous Lyness recurrences

This paper studies non-autonomous Lyness type recurrences of the form x_{n+2}=(a_n+x_n)/x_{n+1}, where a_n is a k-periodic sequence of positive numbers with prime period k. We show that for the cases k in {1,2,3,6} the behavior of the sequence x_n is simple(integrable) while for the remaining cases satisfying k not a multiple of 5 this behavior can be much more complicated(chaotic). The cases k multiple of 5 are studied separately.

Integrability and non-integrability of periodic non-autonomous Lyness recurrences (revised and enlarged version)

This paper studies non-autonomous Lyness type recurrences of the form xn+2 = (an+xn+1)=xn, where fang is a k-periodic sequence of positive numbers with primitive period k. We show that for the cases k 2 f1; 2; 3; 6g the behavior of the sequence fxng is simple (integrable) while for the remaining cases satisfying this behavior can be much more complicated (chaotic). We also show that the cases where k is a multiple of 5 present some di erent features.

Dissemination of periodic mammography and patterns of use, by birth cohort, in Catalonia (Spain)

Background: In Catalonia (Spain) breast cancer mortality has declined since the beginning of the 1990s. The dissemination of early detection by mammography and the introduction of adjuvant treatments are among the possible causes of this decrease, and both were almost coincident in time. Thus, understanding how these procedures were incorporated into use in the general population and in women diagnosed with breast cancer is very important for assessing their contribution to the reduction in breast cancer mortality. In this work we have modeled the dissemination of periodic mammography and described repeat mammography behavior in Catalonia from 1975 to 2006. Methods: Cross-sectional data from three Catalan Health Surveys for the calendar years 1994, 2002 and 2006 was used. The dissemination of mammography by birth cohort was modeled using a mixed effects model and repeat mammography behavior was described by age and survey year. Results: For women born from 1938 to 1952, mammography clearly had a period effect, meaning that they started to have periodic mammograms at the same calendar years but at different ages. The age at which approximately 50% of the women were receiving periodic mammograms went from 57.8 years of age for women born in 1938–1942 to 37.3 years of age for women born in 1963–1967. Women in all age groups experienced an increase in periodic mammography use over time, although women in the 50–69 age group have experienced the highest increase. Currently, the target population of the Catalan Breast Cancer Screening Program, 50–69 years of age, is the group that self-reports the highest utilization of periodic mammograms, followed by the 40–49 age group. A higher proportion of women of all age groups have annual mammograms rather than biennial or irregular ones. Conclusion: Mammography in Catalonia became more widely implemented during the 1990s. We estimated when cohorts initiated periodic mammograms and how frequently women are receiving them. These two pieces of information will be entered into a cost-effectiveness model of early detection in Catalonia.

On the stability of periodic orbits in Rn

We consider an autonomous differential system in Rn with a periodic orbit and we give a new method for computing the characteristic multipliers associated to it. Our method works when the periodic orbit is given by the transversal intersection of n ¡ 1 codimension one hypersurfaces and is an alternative to the use of the first order variational equations. We apply it to study the stability of the periodic orbits in several examples, including a periodic solution found by Steklov studying the rigid body dynamics.

Attenuation of nicotine-induced antinociception, rewarding effects, and dependence in mu-opioid receptor knock-out mice

The involvement of μ-opioid receptors in different behavioral responses elicited by nicotine was explored by using μ-opioid receptor knock-out mice. The acute antinociceptive responses induced by nicotine in the tail-immersion and hot-plate tests were reduced in the mutant mice, whereas no difference between genotypes was observed in the locomotor responses. The rewarding effects induced by nicotine were then investigated using the conditioning place-preference paradigm. Nicotine produced rewarding responses in wild-type mice but failed to produce place preference in knock-out mice, indicating the inability of this drug to induce rewarding effects in the absence of μ-opioid receptors. Finally, the somatic expression of the nicotine withdrawal syndrome, precipitated in dependent mice by the injection of mecamylamine, was evaluated. Nicotine withdrawal was significantly attenuated in knock-out mutants when compared with wild-type mice. In summary, the present results show that μ-opioid receptors are involved in the rewarding responses induced by nicotine and participate in its antinociceptive responses and the expression of nicotine physical dependence.

Polymorphisms of pyrimidine pathway enzymes encoding genes and HLA-B*4001 carriage in stavudine-associated lipodystrophy in HIV-infected patients.

: To assess in a cohort of Caucasian patients exposed to stavudine (d4T) the association of polymorphisms in pyrimidine pathway enzymes and HLA-B*4001 carriage with HIV lipodystrophy syndrome (HALS). 336 patients, 187 with HALS and 149 without HALS, and 72 controls were recruited. HALS was associated with the presence of a low expression, thymidylate synthase (TS) genotype polymorphism. Methylene-tetrahydrofolate reductase (MTHFR) gene polymorphisms and HLA-B*4001 carriage were not associated with HALS or d4T-TP intracellular levels. In conclusion HALS is associated with combined low-expression TS and MTHFR associated with high activity polymorphisms but not with HLA-B*4001 carriage.

Experiments of periodic forcing of Saffman-Taylor fingers

We report on an experimental study of long normal Saffman-Taylor fingers subject to periodic forcing. The sides of the finger develop a low amplitude, long wavelength instability. We discuss the finger response in stationary and nonstationary situations, as well as the dynamics towards the stationary states. The response frequency of the instability increases with forcing frequency at low forcing frequencies, while, remarkably, it becomes independent of forcing frequency at large forcing frequencies. This implies a process of wavelength selection. These observations are in good agreement with previous numerical results reported in [Ledesma-Aguilar et al., Phys. Rev. E 71, 016312 (2005)]. We also study the average value of the finger width, and its fluctuations, as a function of forcing frequency. The average finger width is always smaller than the width of the steady-state finger. Fluctuations have a nonmonotonic behavior with a maximum at a particular frequency.

Different effects of hyperlipidic diets in human lactation and adulthood: growth versus the development of obesity

After birth, the body shifts from glucose as primary energy substrate to milk-derived fats, with sugars from lactose taking a secondary place. At weaning, glucose recovers its primogeniture and dietary fat role decreases. In spite of human temporary adaptation to a high-fat (and sugars and protein) diet during lactation, the ability to thrive on this type of diet is lost irreversibly after weaning. We could not revert too the lactating period metabolic setting because of different proportions of brain/muscle metabolism in the total energy budget, lower thermogenesis needs and capabilities, and absence of significant growth in adults. A key reason for change was the limited availability of foods with high energy content at weaning and during the whole adult life of our ancestors, which physiological adaptations remain practically unchanged in our present-day bodies. Humans have evolved to survive with relatively poor diets interspersed by bouts of scarcity and abundance. Today diets in many societies are largely made up from choice foods, responding to our deeply ingrained desire for fats, protein, sugars, salt etc. Consequently our diets are not well adjusted to our physiological needs/adaptations but mainly to our tastes (another adaptation to periodic scarcity), and thus are rich in energy roughly comparable to milk. However, most adult humans cannot process the food ingested in excess because our cortical-derived craving overrides the mechanisms controlling appetite. This is produced not because we lack the biochemical mechanisms to use this energy, but because we are unprepared for excess, and wholly adapted to survive scarcity. The thrifty mechanisms compound the effects of excess nutrients and damage the control of energy metabolism, developing a pathologic state. As a consequence, an overflow of energy is generated and the disease of plenty develops.

Electronic structure and magnetic interactions of the spin-chain compounds Ca2CuO3 and Sr2CuO3

The results are presented of a combined periodic and cluster model approach to the electronic structure and magnetic interactions in the spin-chain compounds Ca2CuO3 and Sr2CuO3. An extended t-J model is presented that includes in-chain and interchain hopping and magnetic interaction processes with parameters extracted from ab initio calculations. For both compounds, the in-chain magnetic interaction is found to be around -240 meV, larger than in any of the other cuprates reported in the literature. The interchain magnetic coupling is found to be weakly antiferromagnetic, -1 meV. The effective in-chain hopping parameters are estimated to be ~650 meV for both compounds, whereas the value of the interchain hopping parameter is 30 meV for Sr2CuO3 and 40 meV for Ca2CuO3, in line with the larger interchain distance in the former compound. These effective parameters are shown to be consistent with expressions recently suggested for the Néel temperature and the magnetic moments, and with relations that emerge from the t-J model Hamiltonian. Next, we investigate the physical nature of the band gap. Periodic calculations indicate that an interpretation in terms of a charge-transfer insulator is the most appropriate one, in contrast to the suggestion of a covalent correlated insulator recently reported in the literature.

Families of periodic orbits for the spatial isosceles 3-body problem

We study the families of periodic orbits of the spatial isosceles 3-body problem (for small enough values of the mass lying on the symmetry axis) coming via the analytic continuation method from periodic orbits of the circular Sitnikov problem. Using the first integral of the angular momentum, we reduce the dimension of the phase space of the problem by two units. Since periodic orbits of the reduced isosceles problem generate invariant two-dimensional tori of the nonreduced problem, the analytic continuation of periodic orbits of the (reduced) circular Sitnikov problem at this level becomes the continuation of invariant two-dimensional tori from the circular Sitnikov problem to the nonreduced isosceles problem, each one filled with periodic or quasi-periodic orbits. These tori are not KAM tori but just isotropic, since we are dealing with a three-degrees-of-freedom system. The continuation of periodic orbits is done in two different ways, the first going directly from the reduced circular Sitnikov problem to the reduced isosceles problem, and the second one using two steps: first we continue the periodic orbits from the reduced circular Sitnikov problem to the reduced elliptic Sitnikov problem, and then we continue those periodic orbits of the reduced elliptic Sitnikov problem to the reduced isosceles problem. The continuation in one or two steps produces different results. This work is merely analytic and uses the variational equations in order to apply Poincar´e’s continuation method.

Modulation in Wistar rats of blood corticosterone compartmentation by sex and prior exposure to a cafeteria diet

In the metabolic syndrome, glucocorticoid activity is increased, but circulating levels show little change. Most of blood glucocorticoids are bound to corticosteroid-binding globulin (CBG), which liver expression and circulating levels are higher in females than in males. Since blood hormones are also bound to blood cells, and the size of this compartment is considerable for androgens and estrogens, we analyzed whether sex or eating a cafeteria diet altered the compartmentation of corticosterone in rat blood. The main corticosterone compartment in rat blood is that specifically bound to plasma proteins, with smaller compartments bound to blood cells or free. Cafeteria diet increased the expression of liver CBG gene, binding plasma capacity and the proportion of blood cell-bound corticosterone. There were marked sex differences in blood corticosterone compartmentation in rats, which were unrelated to testosterone. The use of a monoclonal antibody ELISA and a polyclonal Western blot for plasma CBG compared with both specific plasma binding of corticosterone and CBG gene expression suggested the existence of different forms of CBG, with varying affinities for corticosterone in males and females, since ELISA data showed higher plasma CBG for males, but binding and Western blot analyses (plus liver gene expression) and higher physiological effectiveness for females. Good cross- reactivity to the antigen for polyclonal CBG antibody suggests that in all cases we were measuring CBG.The different immunoreactivity and binding affinity may help explain the marked sex-related differences in plasma hormone binding as sex-linked different proportions of CBG forms.

Families of periodic horseshoe orbits in the restricted three-body problem

We compute families of symmetric periodic horseshoe orbits in the restricted three-body problem. Both the planar and three-dimensional cases are considered and several families are found.We describe how these families are organized as well as the behavior along and among the families of parameters such as the Jacobi constant or the eccentricity. We also determine the stability properties of individual orbits along the families. Interestingly, we find stable horseshoe-shaped orbit up to the quite high inclination of 17◦