Stability of periodic solutions obtained via the averaging method for nonsmooth Lipschitz system

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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.

L’art com a vehicle : la dimensió sagrada de les arts performatives.

Jerzy Grotowski, director de teatre i recercador que va transformar profundament l’escena teatral de la segona meitat del segle vint, l’any 1970 va anunciar que no dirigiria més produccions teatrals. Apocalypsis Cum Figuris, una de les grans produccions escèniques del segle XX, marcaria un punt de transició en la trajectòria de l’investigador polonès obrint nous horitzons de vida creativa. Impulsat per una gran inquietud interior que trobaria la seva culminació en l’allunyament dels límits estrictament teatrals, Grotowski inicia el passatge de l’àmbit de l’Art com a representació, teatre en un sentit clàssic del terme, al domini de l’Art com a vehicle, en el que el mestre polonès recupera un aspecte antic i oblidat de l’art, que el situaria al nivell d’un coneixement superior, esdevenint un vehicle espiritual.

Regulation of Nedd4-2 self-ubiquitination and stability by a PY motif located within its HECT-domain.

Ubiquitin ligases play a pivotal role in substrate recognition and ubiquitin transfer, yet little is known about the regulation of their catalytic activity. Nedd4 (neural-precursor-cell-expressed, developmentally down-regulated 4)-2 is an E3 ubiquitin ligase composed of a C2 domain, four WW domains (protein-protein interaction domains containing two conserved tryptophan residues) that bind PY motifs (L/PPXY) and a ubiquitin ligase HECT (homologous with E6-associated protein C-terminus) domain. In the present paper we show that the WW domains of Nedd4-2 bind (weakly) to a PY motif (LPXY) located within its own HECT domain and inhibit auto-ubiquitination. Pulse-chase experiments demonstrated that mutation of the HECT PY-motif decreases the stability of Nedd4-2, suggesting that it is involved in stabilization of this E3 ligase. Interestingly, the HECT PY-motif mutation does not affect ubiquitination or down-regulation of a known Nedd4-2 substrate, ENaC (epithelial sodium channel). ENaC ubiquitination, in turn, appears to promote Nedd4-2 self-ubiquitination. These results support a model in which the inter- or intra-molecular WW-domain-HECT PY-motif interaction stabilizes Nedd4-2 by preventing self-ubiquitination. Substrate binding disrupts this interaction, allowing self-ubiquitination of Nedd4-2 and subsequent degradation, resulting in down-regulation of Nedd4-2 once it has ubiquitinated its target. These findings also point to a novel mechanism employed by a ubiquitin ligase to regulate itself differentially compared with substrate ubiquitination and stability.

Productive efficiency and regulatory reform: The case of vehicle inspection services

Measuring productive efficiency provides information on the likely effects of regulatory reform. We present a Data Envelopment Analysis (DEA) of a sample of 38 vehicle inspection units under a concession regime, between the years 2000 and 2004. The differences in efficiency scores show the potential technical efficiency benefit of introducing some form of incentive regulation or of progressing towards liberalization. We also compute scale efficiency scores, showing that only units in territories with very low population density operate at a sub-optimal scale. Among those that operate at an optimal scale, there are significant differences in size; the largest ones operate in territories with the highest population density. This suggests that the introduction of new units in the most densely populated territories (a likely effect of some form of liberalization) would not be detrimental in terms of scale efficiency. We also find that inspection units belonging to a large, diversified firm show higher technical efficiency, reflecting economies of scale or scope at the firm level. Finally, we show that between 2002 and 2004, a period of high regulatory uncertainty in the sample’s region, technical change was almost zero. Regulatory reform should take due account of scale and diversification effects, while at the same time avoiding regulatory uncertainty.

Accurate performance of a rat model of schizophrenia in the water maze depends on visual cue availability and stability: a distortion in cognitive mapping abilities?

Rats were treated postnatally (PND 5-16) with BSO (l-buthionine-(S,R)-sulfoximine) in an animal model of schizophrenia based on transient glutathione deficit. The BSO treated rats were impaired in patrolling a maze or a homing table when adult, yet demonstrated preserved escape learning, place discrimination and reversal in a water maze task [37]. In the present work, BSO rats' performance in the water maze was assessed in conditions controlling for the available visual cues. First, in a completely curtained environment with two salient controlled cues, BSO rats showed little accuracy compared to control rats. Secondly, pre-trained BSO rats were impaired in reaching the familiar spatial position when curtains partially occluded different portions of the room environment in successive sessions. The apparently preserved place learning in a classical water maze task thus appears to require the stability and the richness of visual landmarks from the surrounding environment. In other words, the accuracy of BSO rats in place and reversal learning is impaired in a minimal cue condition or when the visual panorama changes between trials. However, if the panorama remains rich and stable between trials, BSO rats are equally efficient in reaching a familiar position or in learning a new one. This suggests that the BSO accurate performance in the water maze does not satisfy all the criteria for a cognitive map based navigation on the integration of polymodal cues. It supports the general hypothesis of a binding deficit in BSO rats.

Stability of Growth Models with Generalised Lag Structures

This paper considers the lag structures of dynamic models in economics, arguing that the standard approach is too simple to capture the complexity of actual lag structures arising, for example, from production and investment decisions. It is argued that recent (1990s) developments in the the theory of functional differential equations provide a means to analyse models with generalised lag structures. The stability and asymptotic stability of two growth models with generalised lag structures are analysed. The paper concludes with some speculative discussion of time-varying parameters.

Nominal Stability and Financial Globalization

Over the past four decades, advanced economies experienced a large growth in gross external portfolio positions. This phenomenon has been described as Financial Globalization. Over roughly the same time frame, most of these countries also saw a substantial fall in the level and variability of inflation. Many economists have conjectured that financial globalization contributed to the improved performance in the level and predictability of inflation. In this paper, we explore the causal link running in the opposite direction. We show that a monetary policy rule which reduces inflation variability leads to an increase in the size of gross external positions, both in equity and bond portfolios. This appears to be a robust prediction of open economy macro models with endogenous portfolio choice. It holds across different modeling specifications and parameterizations. We also present preliminary empirical evidence which shows a negative relationship between inflation volatility and the size of gross external positions.

The thermal stability of yellow fever vaccines

The assessment of yellow fever vaccine thermostability both in lyophilized form and after reconstitution were analyzed. Two commercial yellow fever vaccines were assayed for their thermal stability. Vaccines were exposed to test temperatures in the range of 8 (graus) C to 45 (graus) C. Residual infectivity was measured by a plaque assay using Vero cells. The titre values were used in an accelerated degradation test that follows the Arrhenius equation and the minimum immunizing dose was assumed to be 10 (ao cubo) particles forming unit (pfu)/dose. Some of the most relevant results include that (i) regular culture medium show the same degradation pattern of a reconstituted 17D-204 vaccine; (ii) reconstituted YF-17D-204 showed a predictable half life of more than six days if kept at 0 (graus) C; (iii) there are differences in thermostability between different products that are probably due to both presence of stabilizers in the preparation and the modernization in the vaccine production; (iv) it is important to establish a proper correlation between the mouse infectivity test and the plaque assay since the last appears to be more simple, economical, and practical for small laboratories to assess the potency of the vaccine, and (v) the accelerated degradation test appears to be the best procedure to quantify the thermostability of biological products.

Stability of isoenzyme and kinetoplast DNA (k-DNA) patterns in successively cloned Trypanosoma cruzi populations

Four Trypanosoma cruzi strains from zymodermes A, B, C and D were successively clonedon BHI-LIT-agar-blood BLAB). Twenty clones from the first generation (F1), 10 from The second (F2) and 4 from the third (F3) from the strains A138, B147 and C23 were isolated. The D150 strain provied 29 F1 and F2 clones. The strains and clones had their isoenzyme and K-DNA patterns determined. The clones from A138, Bl47 and C231 strains presented isoemzyme and K-DNA patterns identical between thewmselves and their respective parental strains. Therefore showing the homogenety and stability of isoenzyme and K-DNA patterns after successive cloning. The Dl50 strain from zymodeme D (ZD) showed heterogeneity. Twenty-eight out of 29 clones of the first generation were of zymodeme A and only one was of zymodeme C, confirming previous reports that ZD strains consisted of ZA and ZC parasite populations. The only D150 strain clone of zymodeme C showed a K-DNA pattern identical to its parental strain. The remining clones although similar among themselves were different from the parental strain. Thus the T. cruzi strains had either homonogeneus or heterogeneous populations. The clones produced by successive cloning provided genetically homonogeous populations. Their experimental use will make future results more reliable and reproducible.

Three-dimensional slope stability analysis of South Peak, Crowsnest Pass, Alberta, Canada

South Peak is a 7-Mm3 potentially unstable rock mass located adjacent to the 1903 Frank Slide on Turtle Mountain, Alberta. This paper presents three-dimensional numerical rock slope stability models and compares them with a previous conceptual slope instability model based on discontinuity surfaces identified using an airborne LiDAR digital elevation model (DEM). Rock mass conditions at South Peak are described using the Geological Strength Index and point load tests, whilst the mean discontinuity set orientations and characteristics are based on approximately 500 field measurements. A kinematic analysis was first conducted to evaluate probable simple discontinuity-controlled failure modes. The potential for wedge failure was further assessed by considering the orientation of wedge intersections over the airborne LiDAR DEM and through a limit equilibrium combination analysis. Block theory was used to evaluate the finiteness and removability of blocks in the rock mass. Finally, the complex interaction between discontinuity sets and the topography within South Peak was investigated through three-dimensional distinct element models using the code 3DEC. The influence of individual discontinuity sets, scale effects, friction angle and the persistence along the discontinuity surfaces on the slope stability conditions were all investigated using this code.