Chaos induced by turbulent and erratic functions

Let (X, d) be a compact metric space and f: X → X a continuous function and consider the hyperspace (K(X), H) of all nonempty compact subsets of X endowed with the Hausdorff metric induced by d. Let f̄: K(X) → K (X) be defined by f̄(A) = {f(a)/a ∈ A} the natural extension of f to K(X), then the aim of this work is to study the dynamics of f when f is turbulent (erratic, respectively) and its relationships.

The Lamination of Infinitely Renormalizable Dissipative Gap Maps: Analyticity, Holonomies and Conjugacies

Motivated by return maps near saddles for three-dimensional flows and also by return maps in the torus associated to Cherry flows, we study gap maps with derivative positive and smaller than one outside the discontinuity point. We prove that the lamination of infinitely renormalizable maps (or else maps with irrational rotation numbers) has analytic leaves in a natural subset of a Banach space of analytic maps of this kind. With maps having Hölder continuous derivative and derivative bounded away from zero, we also prove Hölder continuity of holonomies of the lamination and also of conjugacies between maps having the same combinatorics. © 2011 Springer Basel AG.

Reproductive biology of two macrourid fish, Nezumia aequalis and Coelorinchus mediterraneus, inhabiting the NW Mediterranean continental margin (400-2000m)

Nezumia aequalis and Coelorinchus mediterraneus are abundant species on the upper and lower continental slopes, respectively, in the Mediterranean Sea. A study on the reproductive strategy of the two species was conducted on the Catalan margin (NW Mediterranean). The reproductive cycle of both species was investigated using visual analyses of gonads and histological screening. The shallower species, N. aequalis, showed continuous reproduction with a peak of spawning females in winter months. In contrast, the deeper-living species, C. mediterraneus, showed semi-continuous reproduction with a regression period during the spring. Juveniles of N. aequalis were present in all seasons, but most abundant in the spring. Only two juveniles of C. mediterraneus were found. Both species had asynchronous oocyte development. The average fecundity of N. aequalis was 10,630 oocytes per individual, lower than known for the same species in the Atlantic Ocean. The fecundity of C. mediterraneus was measured for the first time in this study, with an average of 7693 oocytes per individual. Males of both species appear to have semi-cystic spermatogenesis. © 2013 Elsevier Ltd.

Sharp comparison and maximum principles via horizontal normal mapping in the Heisenberg group

In this paper we solve a problem raised by Gutiérrez and Montanari about comparison principles for H−convex functions on subdomains of Heisenberg groups. Our approach is based on the notion of the sub-Riemannian horizontal normal mapping and uses degree theory for set-valued maps. The statement of the comparison principle combined with a Harnack inequality is applied to prove the Aleksandrov-type maximum principle, describing the correct boundary behavior of continuous H−convex functions vanishing at the boundary of horizontally bounded subdomains of Heisenberg groups. This result answers a question by Garofalo and Tournier. The sharpness of our results are illustrated by examples.

Multiple imputation for missing continuous and dichotomous data: The effects of patterns of missingness and variable correlations on type I error with small samples

The purpose of this study is to investigate the effects of predictor variable correlations and patterns of missingness with dichotomous and/or continuous data in small samples when missing data is multiply imputed. Missing data of predictor variables is multiply imputed under three different multivariate models: the multivariate normal model for continuous data, the multinomial model for dichotomous data and the general location model for mixed dichotomous and continuous data. Subsequent to the multiple imputation process, Type I error rates of the regression coefficients obtained with logistic regression analysis are estimated under various conditions of correlation structure, sample size, type of data and patterns of missing data. The distributional properties of average mean, variance and correlations among the predictor variables are assessed after the multiple imputation process. ^ For continuous predictor data under the multivariate normal model, Type I error rates are generally within the nominal values with samples of size n = 100. Smaller samples of size n = 50 resulted in more conservative estimates (i.e., lower than the nominal value). Correlation and variance estimates of the original data are retained after multiple imputation with less than 50% missing continuous predictor data. For dichotomous predictor data under the multinomial model, Type I error rates are generally conservative, which in part is due to the sparseness of the data. The correlation structure for the predictor variables is not well retained on multiply-imputed data from small samples with more than 50% missing data with this model. For mixed continuous and dichotomous predictor data, the results are similar to those found under the multivariate normal model for continuous data and under the multinomial model for dichotomous data. With all data types, a fully-observed variable included with variables subject to missingness in the multiple imputation process and subsequent statistical analysis provided liberal (larger than nominal values) Type I error rates under a specific pattern of missing data. It is suggested that future studies focus on the effects of multiple imputation in multivariate settings with more realistic data characteristics and a variety of multivariate analyses, assessing both Type I error and power. ^

Effect of conservation tillage on soil physical properties, in-situ rainwater harvesting, and erosion control in arid and semi-arid regions

La escasez del agua en las regiones áridas y semiáridas se debe a la escasez de precipitaciones y la distribución desigual en toda la temporada, lo que hace de la agricultura de secano una empresa precaria. Un enfoque para mejorar y estabilizar el agua disponible para la producción de cultivos en estas regiones es el uso de tecnologías de captación de agua de lluvia in situ y su conservación. La adopción de los sistemas de conservación de la humedad del suelo in situ, tales como la labranza de conservación, es una de las estrategias para mejorar la gestión de la agricultura en zonas áridas y semiáridas. El objetivo general de esta tesis ha sido desarrollar una metodología de aplicación de labranza de depósito e investigar los efectos a corto plazo sobre las propiedades físicas del suelo de las diferentes prácticas de cultivo que incluyen labranza de depósito: (reservoir tillage, RT), la laboreo mínimo: (minimum tillage, MT), la no laboreo: (zero tillage, ZT) y laboreo convencional: (conventional tillage, CT) Así como, la retención de agua del suelo y el control de la erosión del suelo en las zonas áridas y semiáridas. Como una primera aproximación, se ha realizado una revisión profunda del estado de la técnica, después de la cual, se encontró que la labranza de depósito es un sistema eficaz de cosecha del agua de lluvia y conservación del suelo, pero que no ha sido evaluada científicamente tanto como otros sistemas de labranza. Los trabajos experimentales cubrieron tres condiciones diferentes: experimentos en laboratorio, experimentos de campo en una región árida, y experimentos de campo en una región semiárida. Para investigar y cuantificar el almacenamiento de agua a temperatura ambiente y la forma en que podría adaptarse para mejorar la infiltración del agua de lluvia recolectada y reducir la erosión del suelo, se ha desarrollado un simulador de lluvia a escala de laboratorio. Las características de las lluvias, entre ellas la intensidad de las precipitaciones, la uniformidad espacial y tamaño de la gota de lluvia, confirmaron que las condiciones naturales de precipitación son simuladas con suficiente precisión. El simulador fue controlado automáticamente mediante una válvula de solenoide y tres boquillas de presión que se usaron para rociar agua correspondiente a diferentes intensidades de lluvia. Con el fin de evaluar el método de RT bajo diferentes pendientes de superficie, se utilizaron diferentes dispositivos de pala de suelo para sacar un volumen idéntico para hacer depresiones. Estas depresiones se compararon con una superficie de suelo control sin depresión, y los resultados mostraron que la RT fue capaz de reducir la erosión del suelo y la escorrentía superficial y aumentar significativamente la infiltración. Luego, basándonos en estos resultados, y después de identificar la forma adecuada de las depresiones, se ha diseñado una herramienta combinada (sistema integrado de labranza de depósito (RT)) compuesto por un arado de una sola línea de chisel, una sola línea de grada en diente de pico, sembradora modificada, y rodillo de púas. El equipo fue construido y se utiliza para comparación con MT y CT en un ambiente árido en Egipto. El estudio se realizó para evaluar el impacto de diferentes prácticas de labranza y sus parámetros de funcionamiento a diferentes profundidades de labranza y con distintas velocidades de avance sobre las propiedades físicas del suelo, así como, la pérdida de suelo, régimen de humedad, la eficiencia de recolección de agua, y la productividad de trigo de invierno. Los resultados indicaron que la RT aumentó drásticamente la infiltración, produciendo una tasa que era 47.51% más alta que MT y 64.56% mayor que la CT. Además, los resultados mostraron que los valores más bajos de la escorrentía y pérdidas de suelos 4.91 mm y 0.65 t ha-1, respectivamente, se registraron en la RT, mientras que los valores más altos, 11.36 mm y 1.66 t ha-1, respectivamente, se produjeron en el marco del CT. Además, otros dos experimentos de campo se llevaron a cabo en ambiente semiárido en Madrid con la cebada y el maíz como los principales cultivos. También ha sido estudiado el potencial de la tecnología inalámbrica de sensores para monitorizar el potencial de agua del suelo. Para el experimento en el que se cultivaba la cebada en secano, se realizaron dos prácticas de labranza (RT y MT). Los resultados mostraron que el potencial del agua del suelo aumentó de forma constante y fue consistentemente mayor en MT. Además, con independencia de todo el período de observación, RT redujo el potencial hídrico del suelo en un 43.6, 5.7 y 82.3% respectivamente en comparación con el MT a profundidades de suelo (10, 20 y 30 cm, respectivamente). También se observaron diferencias claras en los componentes del rendimiento de los cultivos y de rendimiento entre los dos sistemas de labranza, el rendimiento de grano (hasta 14%) y la producción de biomasa (hasta 8.8%) se incrementaron en RT. En el experimento donde se cultivó el maíz en regadío, se realizaron cuatro prácticas de labranza (RT, MT, ZT y CT). Los resultados revelaron que ZT y RT tenían el potencial de agua y temperatura del suelo más bajas. En comparación con el tratamiento con CT, ZT y RT disminuyó el potencial hídrico del suelo en un 72 y 23%, respectivamente, a la profundidad del suelo de 40 cm, y provocó la disminución de la temperatura del suelo en 1.1 y un 0.8 0C respectivamente, en la profundidad del suelo de 5 cm y, por otro lado, el ZT tenía la densidad aparente del suelo y resistencia a la penetración más altas, la cual retrasó el crecimiento del maíz y disminuyó el rendimiento de grano que fue del 15.4% menor que el tratamiento con CT. RT aumenta el rendimiento de grano de maíz cerca de 12.8% en comparación con la ZT. Por otra parte, no hubo diferencias significativas entre (RT, MT y CT) sobre el rendimiento del maíz. En resumen, según los resultados de estos experimentos, se puede decir que mediante el uso de la labranza de depósito, consistente en realizar depresiones después de la siembra, las superficies internas de estas depresiones se consolidan de tal manera que el agua se mantiene para filtrarse en el suelo y por lo tanto dan tiempo para aportar humedad a la zona de enraizamiento de las plantas durante un período prolongado de tiempo. La labranza del depósito podría ser utilizada como un método alternativo en regiones áridas y semiáridas dado que retiene la humedad in situ, a través de estructuras que reducen la escorrentía y por lo tanto puede resultar en la mejora de rendimiento de los cultivos. ABSTRACT Water shortage in arid and semi-arid regions stems from low rainfall and uneven distribution throughout the season, which makes rainfed agriculture a precarious enterprise. One approach to enhance and stabilize the water available for crop production in these regions is to use in-situ rainwater harvesting and conservation technologies. Adoption of in-situ soil moisture conservation systems, such as conservation tillage, is one of the strategies for upgrading agriculture management in arid and semi-arid environments. The general aim of this thesis is to develop a methodology to apply reservoir tillage to investigate the short-term effects of different tillage practices including reservoir tillage (RT), minimum tillage (MT), zero tillage (ZT), and conventional tillage (CT) on soil physical properties, as well as, soil water retention, and soil erosion control in arid and semi-arid areas. As a first approach, a review of the state of the art has been done. We found that reservoir tillage is an effective system of harvesting rainwater and conserving soil, but it has not been scientifically evaluated like other tillage systems. Experimental works covered three different conditions: laboratory experiments, field experiments in an arid region, and field experiments in a semi-arid region. To investigate and quantify water storage from RT and how it could be adapted to improve infiltration of harvested rainwater and reduce soil erosion, a laboratory-scale rainfall simulator was developed. Rainfall characteristics, including rainfall intensity, spatial uniformity and raindrop size, confirm that natural rainfall conditions are simulated with sufficient accuracy. The simulator was auto-controlled by a solenoid valve and three pressure nozzles were used to spray water corresponding to different rainfall intensities. In order to assess the RT method under different surface slopes, different soil scooping devices with identical volume were used to create depressions. The performance of the soil with these depressions was compared to a control soil surface (with no depression). Results show that RT was able to reduce soil erosion and surface runoff and significantly increase infiltration. Then, based on these results and after selecting the proper shape of depressions, a combination implement integrated reservoir tillage system (integrated RT) comprised of a single-row chisel plow, single-row spike tooth harrow, modified seeder, and spiked roller was developed and used to compared to MT and CT in an arid environment in Egypt. The field experiments were conducted to evaluate the impact of different tillage practices and their operating parameters at different tillage depths and different forward speeds on the soil physical properties, as well as on runoff, soil losses, moisture regime, water harvesting efficiency, and winter wheat productivity. Results indicated that the integrated RT drastically increased infiltration, producing a rate that was 47.51% higher than MT and 64.56% higher than CT. In addition, results showed that the lowest values of runoff and soil losses, 4.91 mm and 0.65 t ha-1 respectively, were recorded under the integrated RT, while the highest values, 11.36 mm and 1.66 t ha -1 respectively, occurred under the CT. In addition, two field experiments were carried out in semi-arid environment in Madrid with barley and maize as the main crops. For the rainfed barley experiment, two tillage practices (RT, and MT) were performed. Results showed that soil water potential increased quite steadily and were consistently greater in MT and, irrespective of the entire observation period, RT decreased soil water potential by 43.6, 5.7, and 82.3% compared to MT at soil depths (10, 20, and 30 cm, respectively). In addition, clear differences in crop yield and yield components were observed between the two tillage systems, grain yield (up to 14%) and biomass yield (up to 8.8%) were increased by RT. For the irrigated maize experiment, four tillage practices (RT, MT, ZT, and CT) were performed. Results showed that ZT and RT had the lowest soil water potential and soil temperature. Compared to CT treatment, ZT and RT decreased soil water potential by 72 and 23% respectively, at soil depth of 40 cm, and decreased soil temperature by 1.1 and 0.8 0C respectively, at soil depth of 5 cm. Also, ZT had the highest soil bulk density and penetration resistance, which delayed the maize growth and decreased the grain yield that was 15.4% lower than CT treatment. RT increased maize grain yield about 12.8% compared to ZT. On the other hand, no significant differences among (RT, MT, and CT) on maize yield were found. In summary, according to the results from these experiments using reservoir tillage to make depressions after seeding, these depression’s internal surfaces are consolidated in such a way that the water is held to percolate into the soil and thus allowing time to offer moisture to the plant rooting zone over an extended period of time. Reservoir tillage could be used as an alternative method in arid and semi-arid regions and it retains moisture in-situ, through structures that reduce runoff and thus can result in improved crop yields.

On the uniform approximation of Cauchy continuous functions

In the context of real-valued functions defined on metric spaces, it is known that the locally Lipschitz functions are uniformly dense in the continuous functions and that the Lipschitz in the small functions - the locally Lipschitz functions where both the local Lipschitz constant and the size of the neighborhood can be chosen independent of the point - are uniformly dense in the uniformly continuous functions. Between these two basic classes of continuous functions lies the class of Cauchy continuous functions, i.e., the functions that map Cauchy sequences in the domain to Cauchy sequences in the target space. Here, we exhibit an intermediate class of Cauchy continuous locally Lipschitz functions that is uniformly dense in the real-valued Cauchy continuous functions. In fact, our result is valid when our target space is an arbitrary Banach space.

Carbon assimilation, herbage accumulation, nutritive value, and grazing efficiency of Mulato II brachiariagrass under continuous stocking

Grazed pastures are the backbone of the Brazilian livestock industry and grasses of the genus Brachiaria (syn. Urochloa) are some of most used tropical forages in the country. Although the dependence on the forage resource is high, grazing management is often empirical and based on broad and non-specific guidelines. Mulato II brachiariagrass (Convert HD 364, Dow AgroSciences, São Paulo, Brazil) (B. brizantha × B. ruziziensis × B. decumbens), a new Brachiaria hybrid, was released as an option for a broad range of environmental conditions. There is no scientific information on specific management practices for Mulato II under continuous stocking in Brazil. The objectives of this research were to describe and explain variations in carbon assimilation, herbage accumulation (HA), plant-part accumulation, nutritive value, and grazing efficiency (GE) of Mulato II brachiariagrass as affected by canopy height and growth rate, the latter imposed by N fertilization rate, under continuous stocking. An experiment was carried out in Piracicaba, SP, Brazil, during two summer grazing seasons. The experimental design was a randomized complete block, with a 3 x 2 factorial arrangement, corresponding to three steady-state canopy heights (10, 25 and 40 cm) maintained by mimicked continuous stocking and two growth rates (imposed as 50 and 250 kg N ha-1 yr-1), with three replications. There were no height × N rate interactions for most of the responses studied. The HA of Mulato II increased linearly (8640 to 13400 kg DM ha-1 yr-1), the in vitro digestible organic matter (IVDOM) decreased linearly (652 to 586 g kg-1), and the GE decreased (65 to 44%) as canopy height increased. Thus, although GE and IVDOM were greatest at 10 cm height, HA was 36% less for the 10- than for the 40-cm height. The leaf carbon assimilation was greater for the shortest canopy (10 cm), but canopy assimilation was less than in taller canopies, likely a result of less leaf area index (LAI). The reductions in HA, plant-part accumulation, and LAI, were not associated with other signs of stand deterioration. Leaf was the main plant-part accumulated, at a rate that increased from 70 to 100 kg DM ha-1 d-1 as canopy height increased from 10 to 40 cm. Mulato II was less productive (7940 vs. 13380 kg ha-1 yr-1) and had lesser IVDOM (581 vs. 652 g kg-1) at the lower N rate. The increase in N rate affected plant growth, increasing carbon assimilation, LAI, rates of plant-part accumulation (leaf, stem, and dead), and HA. The results indicate that the increase in the rate of dead material accumulation due to more N applied is a result of overall increase in the accumulation rates of all plant-parts. Taller canopies (25 or 40 cm) are advantageous for herbage accumulation of Mulato II, but nutritive value and GE was greater for 25 cm, suggesting that maintaining ∼25-cm canopy height is optimal for continuously stocked Mulato II.

Calmness modulus of linear semi-infinite programs

Our main goal is to compute or estimate the calmness modulus of the argmin mapping of linear semi-infinite optimization problems under canonical perturbations, i.e., perturbations of the objective function together with continuous perturbations of the right-hand side of the constraint system (with respect to an index ranging in a compact Hausdorff space). Specifically, we provide a lower bound on the calmness modulus for semi-infinite programs with unique optimal solution which turns out to be the exact modulus when the problem is finitely constrained. The relationship between the calmness of the argmin mapping and the same property for the (sub)level set mapping (with respect to the objective function), for semi-infinite programs and without requiring the uniqueness of the nominal solution, is explored, too, providing an upper bound on the calmness modulus of the argmin mapping. When confined to finitely constrained problems, we also provide a computable upper bound as it only relies on the nominal data and parameters, not involving elements in a neighborhood. Illustrative examples are provided.

Generalized Variational Inequalities for Upper Hemicontinuous and Demi Operators with Applications to Fixed Point Theorems in Hilbert Spaces

∗ The final version of this paper was sent to the editor when the author was supported by an ARC Small Grant of Dr. E. Tarafdar.

Strontium isotopes and sedimentology of a marine Triassic succession (upper Ladinian) of the westernmost Tethys, Spain

Chemical Stratigraphy, or the study of the variation of chemical elements within sedimentary sequences, has gradually become an experienced tool in the research and correlation of global geologic events. In this paper 87Sr/ 86Sr ratios of the Triassic marine carbonates (Muschelkalk facies) of southeast Iberian Ranges, Iberian Peninsula, are presented and the representative Sr-isotopic curve constructed for the upper Ladinian interval. The studied stratigraphic succession is 102 meters thick, continuous, and well preserved. Previous paleontological data from macro and micro, ammonites, bivalves, foraminifera, conodonts and palynological assemblages, suggest a Fassanian-Longobardian age (Late Ladinian). Although diagenetic minerals are present in small amounts, the elemental data content of bulk carbonate samples, especially Sr contents, show a major variation that probably reflects palaeoenvironmental changes. The 87Sr/86Sr ratios curve shows a rise from 0.707649 near the base of the section to 0.707741 and then declines rapidly to 0.707624, with a final values rise up to 0.70787 in the upper part. The data up to meter 80 in the studied succession is broadly concurrent with 87Sr/86Sr ratios of sequences of similar age and complements these data. Moreover, the sequence stratigraphic framework and its key surfaces, which are difficult to be recognised just based in the facies analysis, are characterised by combining variations of the Ca, Mg, Mn, Sr and CaCO3 contents

Big bang bifurcations in von Bertalanffy’s dynamics with strong and weak Allee effects

The main purpose of this work was to study population dynamic discrete models in which the growth of the population is described by generalized von Bertalanffy's functions, with an adjustment or correction factor of polynomial type. The consideration of this correction factor is made with the aim to introduce the Allee effect. To the class of generalized von Bertalanffy's functions is identified and characterized subclasses of strong and weak Allee's functions and functions with no Allee effect. This classification is founded on the concepts of strong and weak Allee's effects to population growth rates associated. A complete description of the dynamic behavior is given, where we provide necessary conditions for the occurrence of unconditional and essential extinction types. The bifurcation structures of the parameter plane are analyzed regarding the evolution of the Allee limit with the aim to understand how the transition from strong Allee effect to no Allee effect, passing through the weak Allee effect, is realized. To generalized von Bertalanffy's functions with strong and weak Allee effects is identified an Allee's effect region, to which is associated the concepts of chaotic semistability curve and Allee's bifurcation point. We verified that under some sufficient conditions, generalized von Bertalanffy's functions have a particular bifurcation structure: the big bang bifurcations of the so-called box-within-a-box type. To this family of maps, the Allee bifurcation points and the big bang bifurcation points are characterized by the symmetric of Allee's limit and by a null intrinsic growth rate. The present paper is also a significant contribution in the framework of the big bang bifurcation analysis for continuous 1D maps and unveil their relationship with the explosion birth and the extinction phenomena.

Alternate furrow irrigation of four fresh-market tomato cultivars under semi-arid condition of Ethiopia – Part I: Effect on fruit yield and quality

Scarcity of freshwater due to recurrent drought threatens the sustainable crop production in semi-arid regions of Ethiopia. Deficit irrigation is thought to be one of the promising strategies to increase water use efficiency (WUE) under scarce water resources. A study was carried out to investigate the effect of alternate furrow irrigation (AFI), deficit irrigation (DI) and full irrigation (FI) on marketable fruit yield, WUE and physio-chemical quality of four fresh-market tomato cultivars (Fetan, Chali, Cochoro and ARP Tomato d2) in 2013 and 2014. The results showed that marketable yield, numbers of fruits per plant and fruit size were not significantly affected by AFI and DI irrigations. WUE under AFI and DI increased by 36.7% and 26.1%, respectively with close to 30% irrigation water savings achieved. A different response of cultivars to irrigation treatments was found for marketable yield, number of fruits and fruit size, WUE, total soluble solids (TSS) of the fruit juice, titratable acids (TA) and skin thickness. Cochoro and Fetan performed well under both deficit irrigation treatments exhibited by bigger fruit size which led to higher WUE. ARP Tomato d2 showed good yields under well-watered conditions. Chali had consistently lower marketable fruit yield and WUE. TSS and TA tended to increase under deficit irrigation; however, the overall variations were more explained by irrigation treatments than by cultivars. It was shown that AFI is a suitable deficit irrigation practice to increase fresh yield, WUE and quality of tomato in areas with low water availability. However, AFI requires suitable cultivars in order to exploit its water saving potential.

Reduced Insulin Clearance And Lower Insulin-degrading Enzyme Expression In The Liver Might Contribute To The Thrifty Phenotype Of Protein-restricted Mice.

Nutrient restriction during the early stages of life usually leads to alterations in glucose homeostasis, mainly insulin secretion and sensitivity, increasing the risk of metabolic disorders in adulthood. Despite growing evidence regarding the importance of insulin clearance during glucose homeostasis in health and disease, no information exists about this process in malnourished animals. Thus, in the present study, we aimed to determine the effect of a nutrient-restricted diet on insulin clearance using a model in which 30-d-old C57BL/6 mice were exposed to a protein-restricted diet for 14 weeks. After this period, we evaluated many metabolic variables and extracted pancreatic islet, liver, gastrocnemius muscle (GCK) and white adipose tissue samples from the control (normal-protein diet) and restricted (low-protein diet, LP) mice. Insulin concentrations were determined using RIA and protein expression and phosphorylation by Western blot analysis. The LP mice exhibited lower body weight, glycaemia, and insulinaemia, increased glucose tolerance and altered insulin dynamics after the glucose challenge. The improved glucose tolerance could partially be explained by an increase in insulin sensitivity through the phosphorylation of the insulin receptor/protein kinase B and AMP-activated protein kinase/acetyl-CoA carboxylase in the liver, whereas the changes in insulin dynamics could be attributed to reduced insulin secretion coupled with reduced insulin clearance and lower insulin-degrading enzyme (IDE) expression in the liver and GCK. In summary, protein-restricted mice not only produce and secrete less insulin, but also remove and degrade less insulin. This phenomenon has the double benefit of sparing insulin while prolonging and potentiating its effects, probably due to the lower expression of IDE in the liver, possibly with long-term consequences.

The relationship between birth weight and insulin resistance in childhood

Chronic diseases that are typical of adulthood may originate in intra-uterine life through inadequate fetal development. The present epidemiological cohort study of 506 healthy children aged 5\20138 years evaluated the relationship between birth weight and insulin resistance in an age group that has been assessed in few similar studies. Insulin concentration was determined by chemiluminescence and insulin resistance by the homeostasis model assessment (HOMA). Blood glucose, total cholesterol and fractions (LDL cholesterol and HDL cholesterol) and TAG concentrations were determined by automated enzymatic methods. Linear regression analysis investigated the relationship between birth weight (assessed as a continuous variable and in three categories: small for gestational age, SGA; adequate for gestational age and large for gestational age) and the HOMA index, using backward stepwise selection and biological models to explain the causal pathway of the relationship. There were negativeassociations between birth weight (P < 0·001), SGA (P = 0·027) and the HOMA index, and a positive association between waist circumference (P < 0·001) and the HOMA index. Considering the significant associations between birth weight and waist circumference (P < 0·001) and waist circumference and insulin resistance (P < 0·001), we can probably suspect that lower birth weight is a common cause of higher waist circumference and insulin resistance. In summary, the results of the present study showed increased insulin resistance in apparently healthy, young children, who had lower weight at birth and higher measurements of waist circumference. There is a need to develop public health policies that adopt preventive measures to promote adequate maternal-fetal and child development and enable early diagnosis of metabolic abnormalities