Cyclicity versus center problem

We prove that there are one-parameter families of planar differential equations for which the center problem has a trivial solution and on the other hand the cyclicity of the weak focus is arbitrarily high. We illustrate this phenomenon in several examples for which this cyclicity is computed.

Generalization of Vélu’s formulae for isogenies between elliptic curves

Given an elliptic curve E and a finite subgroup G, V ́lu’s formulae concern to a separable isogeny IG : E → E ′ with kernel G. In particular, for a point P ∈ E these formulae express the first elementary symmetric polynomial on the abscissas of the points in the set P + G as the difference between the abscissa of IG (P ) and the first elementary symmetric polynomial on the abscissas of the nontrivial points of the kernel G. On the other hand, they express Weierstraß coefficients of E ′ as polynomials in the coefficients of E and two additional parameters: w0 = t and w1 = w. We generalize this by defining parameters wn for all n ≥ 0 and giving analogous formulae for all the elementary symmetric polynomials and the power sums on the abscissas of the points in P +G. Simultaneously, we obtain an efficient way of performing computations concerning the isogeny when G is a rational group.

Humeral development from neonatal period to skeletal maturity—application in age and sex assessment

The goal of the present study is to examine cross-sectional information on the growth of the humerus based on the analysis of four measurements, namely, diaphyseal length, transversal diameter of the proximal (metaphyseal) end of the shaft, epicondylar breadth and vertical diameter of the head. This analysis was performed in 181 individuals (90 ♂ and 91 ♀) ranging from birth to 25 years of age and belonging to three documented Western European skeletal collections (Coimbra, Lisbon and St. Bride). After testing the homogeneity of the sample, the existence of sexual differences (Student"s t- and Mann-Whitney U-test) and the growth of the variables (polynomial regression) were evaluated. The results showed the presence of sexual differences in epicondylar breadth above 20 years of age and vertical diameter of the head from 15 years of age, thus indicating that these two variables may be of use in determining sex from that age onward. The growth pattern of the variables showed a continuous increase and followed first- and second-degree polynomials. However, growth of the transversal diameter of the proximal end of the shaft followed a fourth-degree polynomial. Strong correlation coefficients were identified between humeral size and age for each of the four metric variables. These results indicate that any of the humeral measurements studied herein is likely to serve as a useful means of estimating sub-adult age in forensic samples.

A parameterization method for the computation of invariant tori and their whiskers in quasi-periodic maps: explorations and mechanisms for the breakdown of hyperbolicity

In two previous papers [J. Differential Equations, 228 (2006), pp. 530 579; Discrete Contin. Dyn. Syst. Ser. B, 6 (2006), pp. 1261 1300] we have developed fast algorithms for the computations of invariant tori in quasi‐periodic systems and developed theorems that assess their accuracy. In this paper, we study the results of implementing these algorithms and study their performance in actual implementations. More importantly, we note that, due to the speed of the algorithms and the theoretical developments about their reliability, we can compute with confidence invariant objects close to the breakdown of their hyperbolicity properties. This allows us to identify a mechanism of loss of hyperbolicity and measure some of its quantitative regularities. We find that some systems lose hyperbolicity because the stable and unstable bundles approach each other but the Lyapunov multipliers remain away from 1. We find empirically that, close to the breakdown, the distances between the invariant bundles and the Lyapunov multipliers which are natural measures of hyperbolicity depend on the parameters, with power laws with universal exponents. We also observe that, even if the rigorous justifications in [J. Differential Equations, 228 (2006), pp. 530-579] are developed only for hyperbolic tori, the algorithms work also for elliptic tori in Hamiltonian systems. We can continue these tori and also compute some bifurcations at resonance which may lead to the existence of hyperbolic tori with nonorientable bundles. We compute manifolds tangent to nonorientable bundles.

On the relationship between C and N fixation in nodulated alfalfa (Medicago sativa)

Legumes such as alfalfa (Medicago sativa L.) are vital N2-fixing crops accounting for a global N2 fixation of ~35 MtNyear-1. Although enzymatic and molecular mechanisms of nodule N2 fixation are now well documented, some uncertainty remains as to whether N2 fixation is strictly coupled with photosynthetic carbon fixation. That is, the metabolic origin and redistribution of carbon skeletons used to incorporate nitrogen are still relatively undefined. Here, we conducted isotopic labelling with both 15N2 and 13C-depleted CO2 on alfalfa plants grown under controlled conditions and took advantage of isotope ratio mass spectrometry to investigate the relationship between carbon and nitrogen turn-over in respired CO2, total organic matter and amino acids. Our results indicate that CO2 evolved by respiration had an isotopic composition similar to that in organic matter regardless of the organ considered, suggesting that the turn-over of respiratory pools strictly followed photosynthetic input. However, carbon turn-over was nearly three times greater than N turn-over in total organic matter, suggesting that new organic material synthesised was less N-rich than pre-existing organic material (due to progressive nitrogen elemental dilution) or that N remobilisation occurred to sustain growth. This pattern was not consistent with the total commitment into free amino acids where the input of new C and N appeared to be stoichiometric. The labelling pattern in Asn was complex, with contrasted C and N commitments in different organs, suggesting that neosynthesis and redistribution of new Asn molecules required metabolic remobilisation. We conclude that the production of new organic material during alfalfa growth depends on both C and N remobilisation in different organs. At the plant level, this remobilisation is complicated by allocation and metabolism in the different organs. Additional keywords: carbon exchange, carbon isotopes, nitrogen fixation, nitrogen 15 isotope

Postnatal ontogenesis of the tibia. Implications for age and sex estimation

The growth of five variables of the tibia (diaphyseal length, diaphyseal length plus distal epiphysis, condylo-malleolar length, sagittal diameter of the proximal epiphysis, maximum breadth of the distal epiphysis) were analysed using polynomial regression in order to evaluate their significance and capacity for age and sex determination during and after growth. Data were collected from 181 (90♂ and 91♀) individuals ranging from birth to 25 years of age and belonging to three documented collections from Western Europe. Results indicate that all five variables exhibit linear behaviour during growth, which can be expressed by a first-degree polynomial function. Sexual significant differences were observed from age 15 onward in the two epiphysis measurements and condylo-malleolar length, suggesting that these three variables could be useful for sex determination in individuals older than 15 years. Strong correlation coefficients were identified between the five tibial variables and age. These results indicate that any of the studied tibial measurements is likely to serve as a useful source for estimating sub-adult age in both archaeological and forensic samples.

Effect of compressibility in bubble formation in closed systems

We analyze the stability of small bubbles in a closed system with fixed volume, temperature, and number of molecules. We show that there exists a minimum stable size of a bubble. Thus there exists a range of densities where no stable bubbles are allowed and the system has a homogeneous density which is lower than the coexistence density of the liquid. This becomes possible due to the finite liquid compressibility. Capillary analysis within the developed"modified bubble" model illustrates that the existence of the minimum bubble size is associated to the compressibility and it is not possible when the liquid is strictly incompressible. This finding is expected to have very important implications in cavitation and boiling.

The Bonenblust-Hille inequality for homogeneous polynomials is hypercontractive

The Bohnenblust-Hille inequality says that the $\ell^{\frac{2m}{m+1}}$ -norm of the coefficients of an $m$-homogeneous polynomial $P$ on $\Bbb{C}^n$ is bounded by $\| P \|_\infty$ times a constant independent of $n$, where $\|\cdot \|_\infty$ denotes the supremum norm on the polydisc $\mathbb{D}^n$. The main result of this paper is that this inequality is hypercontractive, i.e., the constant can be taken to be $C^m$ for some $C>1$. Combining this improved version of the Bohnenblust-Hille inequality with other results, we obtain the following: The Bohr radius for the polydisc $\mathbb{D}^n$ behaves asymptotically as $\sqrt{(\log n)/n}$ modulo a factor bounded away from 0 and infinity, and the Sidon constant for the set of frequencies $\bigl\{ \log n: n \text{a positive integer} \le N\bigr\}$ is $\sqrt{N}\exp\{(-1/\sqrt{2}+o(1))\sqrt{\log N\log\log N}\}$.

Extended Endoscopic Endonasal Approaches for Cerebral Aneurysms: Anatomical, Virtual Reality and Morphometric Study

Introduction. The purpose of the present contribution is to perform a detailed anatomic and virtual reality three-dimensional stereoscopic study in order to test the effectiveness of the extended endoscopic endonasal approaches for selected anterior and posterior circulation aneurysms. Methods. The study was divided in two main steps: (1) simulation step, using a dedicated Virtual Reality System (Dextroscope, Volume Interactions); (2) dissection step, in which the feasibility to reach specific vascular territory via the nose was verified in the anatomical laboratory. Results. Good visualization and proximal and distal vascular control of the main midline anterior and posterior circulation territory were achieved during the simulation step as well as in the dissection step (anterior communicating complex, internal carotid, ophthalmic, superior hypophyseal, posterior cerebral and posterior communicating, basilar, superior cerebellar, anterior inferior cerebellar, vertebral, and posterior inferior cerebellar arteries). Conclusion. The present contribution is intended as strictly anatomic study in which we highlighted some specific anterior and posterior circulation aneurysms that can be reached via the nose. For clinical applications of these approaches, some relevant complications, mainly related to the endonasal route, such as proximal and distal vascular control, major arterial bleeding, postoperative cerebrospinal fluid leak, and olfactory disturbances must be considered

Anàlisis dels immunofenotips dels NKR de les cèl·lules Natural Killer en pacients amb Esclerosi Múltiple (MS).

La MS és una malaltia autoimmunitària les causes de la qual són encara desconegudes. Entre altres efectes, els pacients d’aquesta malaltia veuen reduït el nombre de limfòcits, així com el percentatge d’aquests ocupats pel compartiment NK. Tot i que molts estudis es centren en investigar aquesta malaltia, el motiu d’aquesta reducció, continua essent un misteri. En el present estudi s’ha plantejat una hipòtesi, la qual apunta a què aquesta reducció, pugui venir causada pel fet que les cèl·lules NK s’hagin vist eliminades de la circulació; a la qual cosa s’esperaria trobar una població de NK més joves per aquells pacients que tinguessin en un percentatge menor de NK, ja que aquesta pèrdua s’hauria hagut de compensar amb cèl·lules NK de nova formació. Per tal de determinar l’antiguitat de les cèl·lules NK s’analitzen els receptors ILT2 (present en cèl·lules més antigues, ja que s’acumula amb el temps), NKG2A (molt present en cèl·lules NK joves), i en la subpoblació CD56bright, (estat de maduració precoç, ja que aquestes amb el temps esdevindran CD56dim). Després de molts anàlisis, s’ha pogut comprovar com la presència de CMV influeix en els receptors de les cèl·lules NK, igual que també influeix la presència de tractament amb immunomoduladors. Però a part d’aquestes influències les quals ja s’havien descrit en altres estudis previs, s’ha pogut trobar que aquells pacients CMV- sense tractament, presenten una correlació significativament negativa entre el percentatge de les cèl·lules CD56bright respecte al total del compartiment NK, la qual al no estar sota la influència de CMV ni de tractament, està causada per algun factor estrictament lligat a la malaltia, fet del qual no se’n havien presentat evidències significatives fins ara. Tot i que aquests resultats, a la vegada de ser molt interessants, recolzen la hipòtesi base, no s’han trobat resultats significatius per a NKG2A i els resultats per a ILT2 són significatius però no concloents. Igualment però, aquests resultats són molt prometedors, i pensem que seria interesant continuar treballant en aquestes troballes.

Pubic growth study: applicability in sexual and age diagnostic.

The growth of five variables of the ischiopubic area was analyzed from bone material from birth to old age. The main purpose was to evaluate its significance and capacity for age and sex determination during and after growth. The material used consisted of 327 specimens from four documented Western European collections. Growth curves were calculated by polynomial regression for two classical variables of the ischiopubic area (pubis length and ischiopubic index) and three new variables of the pubic acetabular area (horizontal and vertical diameter of the pubic acetabular area and the pubic acetabular index). None of the curves showed lineal growth, with the exception of the ischiopubic index and the masculine vertical diameter of the pubis acetabular area. Pubis length has the most complicated growth, expressed by a five-degree polynomial. All the variables are useful for adult sex determination, except the pubic acetabular index. The ischopubic index, vertical diameter of the pubic acetabular area and the pubic acetabular index seem to be good variables for sub-adult sex determination. For age estimation the best variables, in both archaeological and forensic remains, are the absolute measurements (pubic length, vertical and horizontal diameter of the pubis). However, pubis length is the best variable for age estimation because it can be applied until 25 years of age.

Analyzing lifelong learning student behavior in a progressive degree

Peer-reviewed

Fragmentation of massive dense cores down to <~ 1000 AU: relation between fragmentation and density structure

In order to shed light on the main physical processes controlling fragmentation of massive dense cores, we present a uniform study of the density structure of 19 massive dense cores, selected to be at similar evolutionary stages, for which their relative fragmentation level was assessed in a previous work. We inferred the density structure of the 19 cores through a simultaneous fit of the radial intensity profiles at 450 and 850 μm (or 1.2 mm in two cases) and the spectral energy distribution, assuming spherical symmetry and that the density and temperature of the cores decrease with radius following power-laws. Even though the estimated fragmentation level is strictly speaking a lower limit, its relative value is significant and several trends could be explored with our data. We find a weak (inverse) trend of fragmentation level and density power-law index, with steeper density profiles tending to show lower fragmentation, and vice versa. In addition, we find a trend of fragmentation increasing with density within a given radius, which arises from a combination of flat density profile and high central density and is consistent with Jeans fragmentation. We considered the effects of rotational-to-gravitational energy ratio, non-thermal velocity dispersion, and turbulence mode on the density structure of the cores, and found that compressive turbulence seems to yield higher central densities. Finally, a possible explanation for the origin of cores with concentrated density profiles, which are the cores showing no fragmentation, could be related with a strong magnetic field, consistent with the outcome of radiation magnetohydrodynamic simulations.

On the Connectivity of the Julia sets of meromorphic functions

We prove that every transcendental meromorphic map $f$ with disconnected Julia set has a weakly repelling fixed point. This implies that the Julia set of Newton's method for finding zeroes of an entire map is connected. Moreover, extending a result of Cowen for holomorphic self-maps of the disc, we show the existence of absorbing domains for holomorphic self-maps of hyperbolic regions, whose iterates tend to a boundary point. In particular, the results imply that periodic Baker domains of Newton's method for entire maps are simply connected, which solves a well-known open question.

G+: Enhanced Traffic Grooming in WDM Mesh Networks using Lighttours

In this article, a new technique for grooming low-speed traffic demands into high-speed optical routes is proposed. This enhancement allows a transparent wavelength-routing switch (WRS) to aggregate traffic en route over existing optical routes without incurring expensive optical-electrical-optical (OEO) conversions. This implies that: a) an optical route may be considered as having more than one ingress node (all inline) and, b) traffic demands can partially use optical routes to reach their destination. The proposed optical routes are named "lighttours" since the traffic originating from different sources can be forwarded together in a single optical route, i.e., as taking a "tour" over different sources towards the same destination. The possibility of creating lighttours is the consequence of a novel WRS architecture proposed in this article, named "enhanced grooming" (G+). The ability to groom more traffic in the middle of a lighttour is achieved with the support of a simple optical device named lambda-monitor (previously introduced in the RingO project). In this article, we present the new WRS architecture and its advantages. To compare the advantages of lighttours with respect to classical lightpaths, an integer linear programming (ILP) model is proposed for the well-known multilayer problem: traffic grooming, routing and wavelength assignment The ILP model may be used for several objectives. However, this article focuses on two objectives: maximizing the network throughput, and minimizing the number of optical-electro-optical conversions used. Experiments show that G+ can route all the traffic using only half of the total OEO conversions needed by classical grooming. An heuristic is also proposed, aiming at achieving near optimal results in polynomial time