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We give a classification of minimal algebras generated in degree 1, defined over any field k of characteristic different from 2, up to dimension 6. This recovers the classification of nilpotent Lie algebras over k up to dimension 6. In the case of a field k of characteristic zero, we obtain the classification of nilmanifolds of dimension less than or equal to 6, up to k-homotopy type. Finally, we determine which rational homotopy types of such nilmanifolds carry a symplectic structure., MICINN, Depto. de Álgebra, Geometría y Topología, Fac. de Ciencias Matemáticas, TRUE, pub

We study the formality of the mapping torus of an orientation-preserving diffeomorphism of a manifold. In particular, we give conditions under which a mapping torus has a non-zero Massey product. As an application we prove that there are non-formal compact co-symplectic manifolds of dimension m and with first Betti number b if and only if m = 3 and b >= 2, or m >= 5 and b >= 1. Explicit examples for each one of these cases are given., MICINN (Spain), UPV/EHU, Depto. de Álgebra, Geometría y Topología, Fac. de Ciencias Matemáticas, TRUE, pub

Understanding the complex dynamics of tumor growth to develop more efficient therapeutic strategies is one of the most challenging problems in biomedicine. Three-dimensional (3D) tumor spheroids, reflecting avascular microregions within a tumor, are an advanced in vitro model system to assess the curative effect of combinatorial radio(chemo)therapy. Tumor spheroids exhibit particular crucial pathophysiological characteristics such as a radial oxygen gradient that critically affect the sensitivity of the malignant cell population to treatment. However, spheroid experiments remain laborious, and determining long-term radio(chemo)therapy outcomes is challenging. Mathematical models of spheroid dynamics have the potential to enhance the informative value of experimental data, and can support study design; however, they typically face one of two limitations: while non-spatial models are computationally cheap, they lack the spatial resolution to predict oxygen-dependent radioresponse, whereas models that describe spatial cell dynamics are computationally expensive and often heavily parameterized, impeding the required calibration to experimental data. Here, we present an effectively one-dimensional mathematical model based on the cell dynamics within and across radial spheres which fully incorporates the 3D dynamics of tumor spheroids by exploiting their approximate rotational symmetry. We demonstrate that this radial-shell (RS) model reproduces experimental spheroid growth curves of several cell lines with and without radiotherapy, showing equal or better performance than published models such as 3D agent-based models. Notably, the RS model is sufficiently efficient to enable multi-parametric optimization within previously reported and/or physiologically reasonable ranges based on experimental data. Analysis of the model reveals that the characteristic change of dynamics observed in experiments at small spheroid volume originates from the spatial scale of cell interactions.

The dissolution of polymer-coated, controlled-release urea fertilisers by means of a simple, Fickian diffusion-based model is described. This is in contrast to prior contributions that invoke non-Fickian mechanisms or take a more quantitative view. Within a quasi-static approximation, simple expressions for the granule radius and release profile as a function of time are obtained in terms of experimentally accessible parameters. Predictions compare well with available experimental data, although the full model is required to capture the gradual saturation of released urea in the late stages of the process. If scaled appropriately, a wide range of experimental data for different coatings turn out to collapse onto what for all intents and purposes can be called a universal curve. This suggests that extensive experimental testing can be avoided if the properties of the coating are known beforehand.

In this work we derive the Bekenstein-Hawking entropy formula, S=A4l2p, from the following minimal assumptions: (i) there is a minimum area, Amin, proportional to l2p; (ii) the event horizon area, A, is tessellated by N=A/Amin distinguishable units; and (iii) the internal structure of these units is that of an infinite tower of internal levels. Although our results are model independent, this internal structure can be realized as the excitations of more fundamental entities such as, for instance, strings or loop quantum gravity spin networks. Even more, once the microstates of the black hole are taken to be singlets formed within the infinite tower of states describing the whole event horizon, the correction term −32logA emerges from our model. Finally, some comments regarding the applicability of the present model to extremal black holes, as well as possible relationships with spectral geometry and other approaches are pointed out. Our results are independent of the dimension of the black hole and whether it is rotating or not.

The integrated minimal model allows assessment of clinical diagnosis indices, for example, insulin sensitivity (SI ) and glucose effectiveness (SG ), from data of the insulin-modified intravenous glucose tolerance test (IVGTT), which is laborious with an intense sampling schedule, up to 32 samples. The aim of this study was to propose a more informative, although less laborious, IVGTT design to be used for model-based assessment of SI and SG . The IVGTT design was optimized simultaneously for all design variables: glucose and insulin infusion doses, time of glucose dose and start of insulin infusion, insulin infusion duration, sampling times, and number of samples. Design efficiency was used to compare among different designs. The simultaneously optimized designs showed a profound higher efficiency than both standard rich (32 samples) and sparse (10 samples) designs. The optimized designs, after removing replicate sample times, were 1.9 and 7.1 times more efficient than the standard rich and sparse designs, respectively. After including practical aspects of the designs, for example, sufficient duration between samples and avoidance of prolonged hypoglycemia, we propose 2 practical designs with fewer sampling times and lower input of glucose and insulin than standard designs, constrained to prevent hypoglycemia. The optimized practical rich design is equally efficient in assessing SI and SG as the rich standard design, but with half the number of the samples, while the optimized practical sparse design has 1 less sample and requires 4.6 times fewer individuals for equal certainty when assessing SI and SG than the sparse standard design.

The integrated minimal model allows assessment of clinical diagnosis indices, for example, insulin sensitivity (SI ) and glucose effectiveness (SG ), from data of the insulin-modified intravenous glucose tolerance test (IVGTT), which is laborious with an intense sampling schedule, up to 32 samples. The aim of this study was to propose a more informative, although less laborious, IVGTT design to be used for model-based assessment of SI and SG . The IVGTT design was optimized simultaneously for all design variables: glucose and insulin infusion doses, time of glucose dose and start of insulin infusion, insulin infusion duration, sampling times, and number of samples. Design efficiency was used to compare among different designs. The simultaneously optimized designs showed a profound higher efficiency than both standard rich (32 samples) and sparse (10 samples) designs. The optimized designs, after removing replicate sample times, were 1.9 and 7.1 times more efficient than the standard rich and sparse designs, respectively. After including practical aspects of the designs, for example, sufficient duration between samples and avoidance of prolonged hypoglycemia, we propose 2 practical designs with fewer sampling times and lower input of glucose and insulin than standard designs, constrained to prevent hypoglycemia. The optimized practical rich design is equally efficient in assessing SI and SG as the rich standard design, but with half the number of the samples, while the optimized practical sparse design has 1 less sample and requires 4.6 times fewer individuals for equal certainty when assessing SI and SG than the sparse standard design.

The integrated minimal model allows assessment of clinical diagnosis indices, for example, insulin sensitivity (SI ) and glucose effectiveness (SG ), from data of the insulin-modified intravenous glucose tolerance test (IVGTT), which is laborious with an intense sampling schedule, up to 32 samples. The aim of this study was to propose a more informative, although less laborious, IVGTT design to be used for model-based assessment of SI and SG . The IVGTT design was optimized simultaneously for all design variables: glucose and insulin infusion doses, time of glucose dose and start of insulin infusion, insulin infusion duration, sampling times, and number of samples. Design efficiency was used to compare among different designs. The simultaneously optimized designs showed a profound higher efficiency than both standard rich (32 samples) and sparse (10 samples) designs. The optimized designs, after removing replicate sample times, were 1.9 and 7.1 times more efficient than the standard rich and sparse designs, respectively. After including practical aspects of the designs, for example, sufficient duration between samples and avoidance of prolonged hypoglycemia, we propose 2 practical designs with fewer sampling times and lower input of glucose and insulin than standard designs, constrained to prevent hypoglycemia. The optimized practical rich design is equally efficient in assessing SI and SG as the rich standard design, but with half the number of the samples, while the optimized practical sparse design has 1 less sample and requires 4.6 times fewer individuals for equal certainty when assessing SI and SG than the sparse standard design.

The integrated minimal model allows assessment of clinical diagnosis indices, for example, insulin sensitivity (SI ) and glucose effectiveness (SG ), from data of the insulin-modified intravenous glucose tolerance test (IVGTT), which is laborious with an intense sampling schedule, up to 32 samples. The aim of this study was to propose a more informative, although less laborious, IVGTT design to be used for model-based assessment of SI and SG . The IVGTT design was optimized simultaneously for all design variables: glucose and insulin infusion doses, time of glucose dose and start of insulin infusion, insulin infusion duration, sampling times, and number of samples. Design efficiency was used to compare among different designs. The simultaneously optimized designs showed a profound higher efficiency than both standard rich (32 samples) and sparse (10 samples) designs. The optimized designs, after removing replicate sample times, were 1.9 and 7.1 times more efficient than the standard rich and sparse designs, respectively. After including practical aspects of the designs, for example, sufficient duration between samples and avoidance of prolonged hypoglycemia, we propose 2 practical designs with fewer sampling times and lower input of glucose and insulin than standard designs, constrained to prevent hypoglycemia. The optimized practical rich design is equally efficient in assessing SI and SG as the rich standard design, but with half the number of the samples, while the optimized practical sparse design has 1 less sample and requires 4.6 times fewer individuals for equal certainty when assessing SI and SG than the sparse standard design.

The integrated minimal model allows assessment of clinical diagnosis indices, for example, insulin sensitivity (SI ) and glucose effectiveness (SG ), from data of the insulin-modified intravenous glucose tolerance test (IVGTT), which is laborious with an intense sampling schedule, up to 32 samples. The aim of this study was to propose a more informative, although less laborious, IVGTT design to be used for model-based assessment of SI and SG . The IVGTT design was optimized simultaneously for all design variables: glucose and insulin infusion doses, time of glucose dose and start of insulin infusion, insulin infusion duration, sampling times, and number of samples. Design efficiency was used to compare among different designs. The simultaneously optimized designs showed a profound higher efficiency than both standard rich (32 samples) and sparse (10 samples) designs. The optimized designs, after removing replicate sample times, were 1.9 and 7.1 times more efficient than the standard rich and sparse designs, respectively. After including practical aspects of the designs, for example, sufficient duration between samples and avoidance of prolonged hypoglycemia, we propose 2 practical designs with fewer sampling times and lower input of glucose and insulin than standard designs, constrained to prevent hypoglycemia. The optimized practical rich design is equally efficient in assessing SI and SG as the rich standard design, but with half the number of the samples, while the optimized practical sparse design has 1 less sample and requires 4.6 times fewer individuals for equal certainty when assessing SI and SG than the sparse standard design.

Over the past two decades, multi-component dryland vegetation models have been successful in qualitatively reproducing the spatial vegetation patterns widely observed in nature. In the two-component (water, vegetation) Klausmeier model, water flow from bare to vegetated areas drives pattern formation. The more elaborate Rietkerk and Gilad three-component models make a distinction between soil and surface water. In this article the three models are approximated from within a unifying framework, with a focus on processes that drive pattern formation, in order to promote the understanding of similarities and differences between these models. Reduction from a model with a separate soil and surface water component, to a model with a single water component, preserves Turing instability in all but one of the cases studied.

Biofilms offer an excellent example of ecological interaction among bacteria. Temporal and spatial oscillations in biofilms are an emerging topic. In this paper, we describe the metabolic oscillations in Bacillus subtilis biofilms by applying the smallest theoretical chemical reaction system showing Hopf bifurcation proposed by Wilhelm and Heinrich in 1995. The system involves three differential equations and a single bilinear term. We specifically select parameters that are suitable for the biological scenario of biofilm oscillations. We perform computer simulations and a detailed analysis of the system including bifurcation analysis and quasi-steady-state approximation. We also discuss the feedback structure of the system and the correspondence of the simulations to biological observations. Our theoretical work suggests potential scenarios about the oscillatory behaviour of biofilms and also serves as an application of a previously described chemical oscillator to a biological system.

The intrinsic anomalous Hall conductance σxyint of a minimal model of the twodimensional disordered Chern insulator is investigated in the framework of Kubo quantum theory of linear response. The electron momentum relaxation is assumed to be due to electron scattering by Gaussian white-noise potential. The explicit expressions for the density of states and σxyint are obtained in the self-consistent Born approximation. The numerical analysis of these expressions at the different values of parameters of the considered model shows that calculated σxyint takes a quantized value e 2/4π when the Fermi level lies within the energy gap. This gap is narrowed as disorder increases that leads to decreasing of the Hall plateau width. © Published under licence by IOP Publishing Ltd.

We prove the existence of minimal models à la Sullivan for operads with non trivial arity zero. So up-to-homotopy algebras with strict units are just operad algebras over these minimal models. As an application we give another proof of the formality of the unitary n -little disks operad over the rationals., Preprint

Under gradual change of a driver, complex systems may switch between contrasting stable states. For many ecosystems it is unknown how rapidly such a critical transition unfolds. Here we explore the rate of change during the degradation of a semiarid ecosystem with a model coupling the vegetation and geomorphological system. Two stable states-vegetated and bare-are identified, and it is shown that the change between these states is a critical transition. Surprisingly, the critical transition between the vegetated and bare state can unfold either rapidly over a few years or gradually over decennia up to millennia, depending on parameter values. An important condition for the phenomenon is the linkage between slow and fast ecosystems components. Our results show that, next to climate change and disturbance rates, the geological and geomorphological setting of a semiarid ecosystem is crucial in predicting its fate.

[EN] Type 1 diabetes mellitus is a chronic disease characterized by the increase of glucose in the blood due to a defect in the action or in the production of insulin. For completely autonomous glycemic regulation, a model would be required which permits the future evolution of blood glucose to be estimated. One of the main problems in identifying models is the high variability of glucose profiles both from one patient to another, and in the same patient under not very different conditions. In this paper, we propose a method using an evolutionary algorithm to define the values of the parameters of a minimal model based on standard clinical therapy for a several-day horizon. The algorithm is able to show the trend of blood glucose in a 5-day profile by adjusting the glucose model.

[EN] Type 1 diabetes mellitus is a chronic disease characterized by the increase of glucose in the blood due to a defect in the action or in the production of insulin. For completely autonomous glycemic regulation, a model would be required which permits the future evolution of blood glucose to be estimated. One of the main problems in identifying models is the high variability of glucose profiles both from one patient to another, and in the same patient under not very different conditions. In this paper, we propose a method using an evolutionary algorithm to define the values of the parameters of a minimal model based on standard clinical therapy for a several-day horizon. The algorithm is able to show the trend of blood glucose in a 5-day profile by adjusting the glucose model.

Debido a la importancia que actualmente tiene la diabetes como enfermedad que se perfila ser una pandemia a nivel mundial, se hace necesario estudiar y comprender, desde diferentes disciplinas, los procesos que se involucran para una mejor identificación y tratamiento de la misma. El presente artículo describe el modelamiento matemático de los niveles de glucosa e insulina presentes en el cuerpo basado en el trabajo de Ackerman realizando una modificación del sistema de ecuaciones diferenciales acopladas (SEDA) en el modelo mínimo incluyendo un aumento gradual exógeno para considerar variaciones exógenas de tales niveles. A partir de la curva experimental se consideraron diferentes casos, de manera que cada familia de curvas correspondiente se analizó en función de la cantidad de glucosa e insulina, respectivamente. La solución aproximada del SEDA se obtuvo usando el método de Runge Kutta de cuarto orden y se comparó con resultados experimentales reportados. Se encontró que pequeños aumentos en la cantidad de Glucosa produce un incremento en la Insulina debido a que el cuerpo aumenta su producción para regularla a niveles normales., Due to the importance that diabetes is nowadays, a disease that is worldwide nominated as a pandemic, it is necessary to study and understand from different disciplines the processes that are involved in a better identification and treatment of it. Thus the mathematical modeling of the glucose and insulin levels present in the body was done making a modification of the minimal model, to consider exogenous variations of the glucose and insulin levels. For that, the study was based on the work done by Ackerman and the minimal model, and the system of differential equations connected (SDEC) was modified in order to include a gradual exogenous increase of the glucose and insulin amount. The approximate solution of the SDEC was obtained using the Runge Kutta method of fourth order and it was compared with the reported experimental results, finding a good behavior. Based on the experimental curve, different cases were modeled where the insulin and glucose amount varies, and for each case, the group of corresponding curves was analyzed according to the insulin and glucose amount respectively. It was found that small increases of the glucose amount causes an increase of the insulin production and this is because the body increases the insulin production to regulate it to the normal levels.

Debido a la importancia que actualmente tiene la diabetes como enfermedad que se perfila ser una pandemia a nivel mundial, se hace necesario estudiar y comprender, desde diferentes disciplinas, los procesos que se involucran para una mejor identificación y tratamiento de la misma. El presente artículo describe el modelamiento matemático de los niveles de glucosa e insulina presentes en el cuerpo basado en el trabajo de Ackerman realizando una modificación del sistema de ecuaciones diferenciales acopladas (SEDA) en el modelo mínimo incluyendo un aumento gradual exógeno para considerar variaciones exógenas de tales niveles. A partir de la curva experimental se consideraron diferentes casos, de manera que cada familia de curvas correspondiente se analizó en función de la cantidad de glucosa e insulina, respectivamente. La solución aproximada del SEDA se obtuvo usando el método de Runge Kutta de cuarto orden y se comparó con resultados experimentales reportados. Se encontró que pequeños aumentos en la cantidad de Glucosa produce un incremento en la Insulina debido a que el cuerpo aumenta su producción para regularla a niveles normales., Due to the importance that diabetes is nowadays, a disease that is worldwide nominated as a pandemic, it is necessary to study and understand from different disciplines the processes that are involved in a better identification and treatment of it. Thus the mathematical modeling of the glucose and insulin levels present in the body was done making a modification of the minimal model, to consider exogenous variations of the glucose and insulin levels. For that, the study was based on the work done by Ackerman and the minimal model, and the system of differential equations connected (SDEC) was modified in order to include a gradual exogenous increase of the glucose and insulin amount. The approximate solution of the SDEC was obtained using the Runge Kutta method of fourth order and it was compared with the reported experimental results, finding a good behavior. Based on the experimental curve, different cases were modeled where the insulin and glucose amount varies, and for each case, the group of corresponding curves was analyzed according to the insulin and glucose amount respectively. It was found that small increases of the glucose amount causes an increase of the insulin production and this is because the body increases the insulin production to regulate it to the normal levels.

In this paper a new mathematical model of the glucose-insulin system is presented. The proposed model represents Type 1 Diabetes Mellitus patients and seeks to give a suitable model of the malfunction of the pancreas. Based on the classic minimal model, this new approach takes into account the description of the glucose dynamic in the subcutaneous layer and a meal disturbance term, together with an additional term that represents the insulin injections, which make this proposal a more realistic approach. Virtual data from UVA/Padova T1DMS software are used for rst evaluations of the effectiveness of the proposed model.

In this paper a new mathematical model of the glucose-insulin system is presented. The proposed model represents Type 1 Diabetes Mellitus patients and seeks to give a suitable model of the malfunction of the pancreas. Based on the classic minimal model, this new approach takes into account the description of the glucose dynamic in the subcutaneous layer and a meal disturbance term, together with an additional term that represents the insulin injections, which make this proposal a more realistic approach. Virtual data from UVA/Padova T1DMS software are used for rst evaluations of the effectiveness of the proposed model.

Deleanu, Frei and Hilton have developed the notion of generalized Adams completion in a categorical context; they have also suggested the dual notion, namely, Adams cocompletion of anobject in a category. The concept of rational homotopy theory was first characterized by Quillen. In fact in rational homotopy theory Sullivan introduced the concept of minimal model. In this note under a reasonable assumption, the minimal model of a 1-connected differential graded algebra can be expressed as the Adams cocompletion of the differential graded algebra with respect to a chosen set in the category of 1-connected differential graded algebras (in short d.g.a.’s) over the field of rationales and d.g.a.-homomorphisms

Deleanu, Frei and Hilton have developed the notion of generalized Adams completion in a categorical context; they have also suggested the dual notion, namely, Adams cocompletion of anobject in a category. The concept of rational homotopy theory was first characterized by Quillen. In fact in rational homotopy theory Sullivan introduced the concept of minimal model. In this note under a reasonable assumption, the minimal model of a 1-connected differential graded algebra can be expressed as the Adams cocompletion of the differential graded algebra with respect to a chosen set in the category of 1-connected differential graded algebras (in short d.g.a.’s) over the field of rationales and d.g.a.-homomorphisms

The production of toxins by some species of phytoplankton is known to have several economic, ecological, and human health impacts. However, the role of toxins on the spatial distribution of phytoplankton is not well understood. In the present study, the spatial dynamics of a nutrient-phytoplankton system with toxic effect on phytoplankton is investigated. We analyze the linear stability of the system and obtain the condition for Turing instability. In the presence of toxic effect, we find that the distribution of nutrient and phytoplankton becomes inhomogeneous in space and results in different patterns, like stripes, spots, and the mixture of them depending on the toxicity level. We also observe that the distribution of nutrient and phytoplankton shows spatiotemporal oscillation for certain toxicity level. (C) 2015 Elsevier Inc. All rights reserved.

Mathematical modeling of the glucose–insulin feedback system is necessary to the understanding of the homeostatic control, to analyze experimental data, to identify and quantify relevant biophysical parameters, to design clinical trials and to evaluate diabetes prevention or disease modification therapies. Much work has been made over the last 30 years, and the time now seems ripe to provide a comprehensive review. The one here proposed is focused on the most important clinical/experimental tests performed to understand the mechanism of glucose homeostasis. The review proceeds from models of pancreatic insulin production, with a coarser/finer level of detail ranging over cellular and subcellular scales, to short-term organ/tissue models accounting for the intra-venous and the oral glucose tolerance tests as well as for the euglycemic hyperinsulinemic clamp, to total-body, long-term diabetes models aiming to represent disease progression in terms of b-cell population dynamics over a long period of years

The minimal two-dimensional model of bursting neuronal dynamics is used to study the influence of time-delay on the properties of synchronization of bursting neurons. Generic properties of bursting and dependence of the stability of synchronization on the time-lag and the strength of coupling are described, and compared with the two common types of synaptical coupling, i.e., time-delayed chemical and electrical synapses.

Circadian rhythms, which occur spontaneously with a period of about 24 h in a variety of organisms, allow their adaptation to the periodic variations of the environment. These rhythms are generated by a genetic regulatory network involving a negative feedback loop on transcription. Mathematical models based on the negative autoregulation of gene expression by the protein product of a clock gene account for the occurrence of self-sustained circadian oscillations. These models differ by their degree of complexity and, hence, by the number of variables considered. Some of these models can be considered as minimal because they contain a reduced number of biochemical processes and variables capable of producing sustained oscillations. In three of these minimal models, the period of the oscillations significantly changes with the rate of degradation of the clock protein. However, depending on the model considered, the period increases, decreases or passes through a maximum as a function of the protein degradation rate. We clarify the bases for these markedly different results by bringing to light the roles of (i) protein phosphorylation, which is required for protein degradation, and (ii) the velocity and degree of saturation of mRNA and protein degradation. Changes in the parameter values of the more complex of the minimal models can produce the period profiles observed in the other two models. The analysis allows us to reconcile the contradictory predictions for the dependence of the period on the clock protein degradation rate in three minimal models used to describe circadian rhythms., Comparative Study, Journal Article, Research Support, Non-U.S. Gov't, info:eu-repo/semantics/published

Circadian rhythms, which occur spontaneously with a period of about 24 h in a variety of organisms, allow their adaptation to the periodic variations of the environment. These rhythms are generated by a genetic regulatory network involving a negative feedback loop on transcription. Mathematical models based on the negative autoregulation of gene expression by the protein product of a clock gene account for the occurrence of self-sustained circadian oscillations. These models differ by their degree of complexity and, hence, by the number of variables considered. Some of these models can be considered as minimal because they contain a reduced number of biochemical processes and variables capable of producing sustained oscillations. In three of these minimal models, the period of the oscillations significantly changes with the rate of degradation of the clock protein. However, depending on the model considered, the period increases, decreases or passes through a maximum as a function of the protein degradation rate. We clarify the bases for these markedly different results by bringing to light the roles of (i) protein phosphorylation, which is required for protein degradation, and (ii) the velocity and degree of saturation of mRNA and protein degradation. Changes in the parameter values of the more complex of the minimal models can produce the period profiles observed in the other two models. The analysis allows us to reconcile the contradictory predictions for the dependence of the period on the clock protein degradation rate in three minimal models used to describe circadian rhythms., Comparative Study, Journal Article, Research Support, Non-U.S. Gov't, info:eu-repo/semantics/published

Insulin sensitivity decreases during pregnancy, presumably an adaptation ensuring sufficient glucose supply to feto-placental tissues. Feeds high in non-structural carbohydrates are also linked to diminished insulin sensitivity in horses. Because the equine fetus is highly glucose reliant, maternal glucose and insulin dynamics during pregnancy may have implications for optimal fetal development in horses. Mismanagement of maternal nutrition during gestation could predispose the offspring to metabolic disorders (e.g. insulin resistance) later in life. In horses, insulin resistance is associated with increased risk for development of laminitis. These studies measured insulin sensitivity and glucose dynamics in pregnant and non-pregnant mares fed high sugar and starch (SS) or high fat and fiber (FF) feeds, as well as neonatal foals born from pregnant mares fed SS and FF feed. Insulin modified frequently sampled intravenous glucose tolerance tests (FSIGT) were applied to pregnant Thoroughbred mares (n = 22) at 28 ± 3 wks (Period 1) and 47 wks (Period 2) gestation, as well as non-pregnant mares (n=10) measured simultaneously. Following the first FSIGT mares were fed SS or FF feed for the remainder of the study. After 11 wks adaptation to feeding, a subset of mares were evaluated with hourly blood samples for 24 h to assess glycemic and insulinemic response to three times daily feeding while on pasture. Neonatal foal FSIGTs (n=20) were conducted at 5 ± 1 d of age. The minimal model of glucose and insulin dynamics was used to determine insulin sensitivity (SI), glucose effectiveness (Sg), acute insulin response to glucose (AIRg) and disposition index (DI). Pregnant mares during Period 1 exhibited lowered SI, Sg and elevated AIRg relative to non-pregnant mares. Pregnant mares demonstrated greater glycemic and insulinemic responses to feeding of both SS and FF meals than non-pregnant mares consuming the same feeds. Also, SS feed elicited greater glycemic and insulinemic area

Glucose is a fundamental energy source, the utilization and regulation of which impacts exercise performance and health. These studies have used modeling techniques to evaluate glucose kinetics and dynamics in equids and developed tests to evaluate the status of glucose metabolism. In Part I, 12 exercise-trained Arabians underwent insulin-modified FSIGT (with minimal model analysis) and single-injection glucose tracer (with compartmental analysis) studies at rest and during exercise to evaluate the effects of exercise on glucose kinetics and dynamics. These geldings were maintained on pasture, but adapted for 4 months to twice-daily feeding of feeds rich in sugar and starch (SS, n=6: NSC 45%, Fat 3%, NDF 24%) or fat and fiber (FF, n=6:NSC 13%, Fat 11%, NDF 45% ). Exercise increased insulin sensitivity (P = 0.070) and glucose transport (P < 0.038). Although variables were not different between FF and SS horses at rest, during exercise SS horses tended to have lower (P = 0.085) insulin sensitivity and increased (P = 0.043) glucose utilization compared to FF horses. In Part II, satisfactory proxies for minimal model parameters were developed to facilitate the evaluation of insulin sensitivity in larger populations. These proxies were applied to a population of 163 ponies and used to characterize metabolic differences between ponies predisposed to pasture laminitis (PL) from ponies not predisposed (NL). A subset of 14 ponies (7 PL, 7 NL) also underwent the FSIGT for minimal model analysis. Ponies predisposed to laminitis were found to have lower insulin sensitivity (P < 0.007) and higher insulin secretory response (P < 0.045) by both the minimal model and proxies, and higher (P < 0.001) circulating triglycerides and body condition score. Cut-point analysis for these variables was used to define a pre-laminitic metabolic syndrome with total predictive power of 78% to identifity ponies at risk for developing pasture laminitis. Increased insulin resistance and prevalence o

Diets rich in hydrolyzable carbohydrates induce a hyperglycemic/insulinemic response and may increase the incidence of metabolic disorders associated with some types of laminitis, exertional rhabdomyolysis and osteochondrosis in horses. This study applied the minimal model of glucose and insulin dynamics to determine the effect of diet on metabolites and hormones that regulate glucose metabolism in young horses. Twelve Thoroughbred foals were raised on pasture and supplemented twice daily with a feed high in either sugar and starch (SS) or fat and fiber (FF). As weanlings (age 199 ± 19 d, weight 274 ± 18 kg), the subjects underwent a modified frequent sampling intravenous glucose tolerance test during which they remained in stalls and had access to grass hay and water ad libitum. Samples were colleted at -60, -45, 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 16, 19, 22, 23, 24, 25, 27, 30, 35, 40, 50, 60 , 70 , 80, 90, 100, 120, 150, 180, 210, 240, 270, 300, 330 and 360 min with a glucose bolus of 300 mg/kg BW at 0 min and an insulin bolus of 1.5 mU/kg BW at 20 min. Plasma was analyzed for glucose, insulin, growth hormone (GH) and insulin-like growth factor-I (IGF-I) concentrations. Insulin sensitivity, glucose effectiveness, acute insulin response to glucose and disposition index were derived using Minmod Millennium and WinSAAM software. Diet groups were compared using the non-parametric Kruskal-Wallis test or the sign test. Time interactions were compared using a mixed model with repeated effects. Rank-ordered linear regression was used for correlations. Basal glucose did not differ between groups (P = 0.75). There was nearly a trend towards higher basal (P = 0.11), and median insulin was higher in the sugar and starch foals at all 36 sample points (P = 0.030). The basal glucose:basal insulin ratio for the sugar and starch supplemented foals was lower than for fat and fiber foals (P = 0.025). Insulin sensitivity (SI) was lower in foals fed sugar and starch than foals fed

Diets rich in hydrolyzable carbohydrates induce a hyperglycemic/insulinemic response and may increase the incidence of metabolic disorders associated with some types of laminitis, exertional rhabdomyolysis and osteochondrosis in horses. This study applied the minimal model of glucose and insulin dynamics to determine the effect of diet on metabolites and hormones that regulate glucose metabolism in young horses. Twelve Thoroughbred foals were raised on pasture and supplemented twice daily with a feed high in either sugar and starch (SS) or fat and fiber (FF). As weanlings (age 199 ± 19 d, weight 274 ± 18 kg), the subjects underwent a modified frequent sampling intravenous glucose tolerance test during which they remained in stalls and had access to grass hay and water ad libitum. Samples were colleted at -60, -45, 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 16, 19, 22, 23, 24, 25, 27, 30, 35, 40, 50, 60 , 70 , 80, 90, 100, 120, 150, 180, 210, 240, 270, 300, 330 and 360 min with a glucose bolus of 300 mg/kg BW at 0 min and an insulin bolus of 1.5 mU/kg BW at 20 min. Plasma was analyzed for glucose, insulin, growth hormone (GH) and insulin-like growth factor-I (IGF-I) concentrations. Insulin sensitivity, glucose effectiveness, acute insulin response to glucose and disposition index were derived using Minmod Millennium and WinSAAM software. Diet groups were compared using the non-parametric Kruskal-Wallis test or the sign test. Time interactions were compared using a mixed model with repeated effects. Rank-ordered linear regression was used for correlations. Basal glucose did not differ between groups (P = 0.75). There was nearly a trend towards higher basal (P = 0.11), and median insulin was higher in the sugar and starch foals at all 36 sample points (P = 0.030). The basal glucose:basal insulin ratio for the sugar and starch supplemented foals was lower than for fat and fiber foals (P = 0.025). Insulin sensitivity (SI) was lower in foals fed sugar and starch than foals fed f

Sullivan approach to Rational homotopy theory of connected nilpotent simplicial sets of finite ℚ-rank is extended to connected locally nilpotent simplicial sets of arbitrary ℚ-rank. Rational proper homotopy type and rational proper homotopy type at infinity of connected, one-ended, proper nilpotent and nilpotent at infinity, locally finite simplicial sets are also defined. In particular, the notion of minimal algebras and minimal models in these setting are introduced in such a way that the indecomposable elements for such a minimal model are identified in each case, with the dual, as ℚ-vector space, of the corresponding version of the homotopy groups of the given simplicial set. © 2010 Topology Proceedings.