ENERGY AND VOLUME OF VECTOR FIELDS ON SPHERICAL DOMAINS

We present a "boundary version" for theorems about minimality of volume and energy functionals on a spherical domain of an odd-dimensional Euclidean sphere.

Solvability in the large for a class of complex vector fields on the cylinder

This work deals with global solvability of a class of complex vector fields of the form L = partial derivative/partial derivative t + (a(x, t)+ ib(x, t))partial derivative/partial derivative x, where a and b are real-valued C-infinity functions, defined on the cylinder Omega = R x S-1. Relatively compact (Sussmann) orbits are allowed. The connection with Malgrange's notion of L-convexity for supports is investigated. (C) 2011 Elsevier Masson SAS. All rights reserved.

Solvability near the characteristic set for a special class of complex vector fields

This work deals with the solvability near the characteristic set Sigma = {0} x S-1 of operators of the form L = partial derivative/partial derivative t+(x(n) a(x)+ ix(m) b(x))partial derivative/partial derivative x, b not equivalent to 0 and a(0) not equal 0, defined on Omega(epsilon) = (-epsilon, epsilon) x S-1, epsilon > 0, where a and b are real-valued smooth functions in (-epsilon, epsilon) and m >= 2n. It is shown that given f belonging to a subspace of finite codimension of C-infinity (Omega(epsilon)) there is a solution u is an element of L-infinity of the equation Lu = f in a neighborhood of Sigma; moreover, the L-infinity regularity is sharp.

Globally solvable systems of complex vector fields

We consider a class of involutive systems of n smooth vector fields on the n + 1 dimensional torus. We obtain a complete characterization for the global solvability of this class in terms of Liouville forms and of the connectedness of all sublevel and superlevel sets of the primitive of a certain 1-form in the minimal covering space.

STABLE PIECEWISE POLYNOMIAL VECTOR FIELDS

Let N = {y > 0} and S = {y < 0} be the semi-planes of R-2 having as common boundary the line D = {y = 0}. Let X and Y be polynomial vector fields defined in N and S, respectively, leading to a discontinuous piecewise polynomial vector field Z = (X, Y). This work pursues the stability and the transition analysis of solutions of Z between N and S, started by Filippov (1988) and Kozlova (1984) and reformulated by Sotomayor-Teixeira (1995) in terms of the regularization method. This method consists in analyzing a one parameter family of continuous vector fields Z(epsilon), defined by averaging X and Y. This family approaches Z when the parameter goes to zero. The results of Sotomayor-Teixeira and Sotomayor-Machado (2002) providing conditions on (X, Y) for the regularized vector fields to be structurally stable on planar compact connected regions are extended to discontinuous piecewise polynomial vector fields on R-2. Pertinent genericity results for vector fields satisfying the above stability conditions are also extended to the present case. A procedure for the study of discontinuous piecewise vector fields at infinity through a compactification is proposed here.

Measurement of buccal bone volume of dental implants by means of cone-beam computed tomography

Purpose: The aim of this study was to evaluate the accuracy of cone-beam computed tomography (CBCT) for measuring the buccal bone volume around dental implants. Materials and methods: Three to six implants were inserted into the anterior maxilla of eight skulls, depending on the availability of bone, and after this, the CBCT was performed. By means of CBCT image, measurements of the bone wall at three points of the implant were obtained, analyzed and compared with those obtained in the plaster skull casting. Results: The results showed that for the three points of the implants, no statistically significant difference in the measurements was obtained from the plaster model and CBCT images. Conclusions: CBCT can be a useful tool for assessing buccal bone volume along the implant. To cite this article:?Shiratori LN, Marotti J, Yamanouchi J, Chilvarquer I, Contin I, Tortamano-Neto P. Measurement of buccal bone volume of dental implants by means of cone-beam computed tomography.?Clin. Oral Impl. Res. 23, 2012; 797804.?doi: 10.1111/j.1600-0501.2011.02207.x

Is there a relationship between the total volume of load lifted in bench press exercise and the rating of perceived exertion?

Aim. The purpose of the study was to investigate the relationship between the total volume of load lifted (TVLL) and the rating of perceived exertion (RPE) measures during different resistance training (RT) schemes using the bench press exercise. Methods. The present study was divided into two experiments. In the first experiment, 18 healthy men performed three different RT schemes: a strength oriented scheme (SS), a muscular endurance oriented scheme (ES) and a hypertrophy oriented scheme (HS). TVLL was calculated for each scheme. Mean-RPE and session-RPE were assessed. In the second experiment, 23 men performed two resistance exercise bouts at different intensities (50 %-1RM and 75%-1RM) with matched TVLL. Mean-RPE and session-RPE were also assessed. Results. SS and HS showed higher TVLL and greater RPE scores as compared to ES (P<0.05). No significant difference was observed between SS and HS. It was verified significant positive correlations between TVLL and session-RPE (SS r=0.63, HS r=0.64, ES r=0.56; P<0.05), and between mean-RPE and TVLL (SS r=0.55, HS r=0.52, ES r=0.47; P<0.05) for all schemes. No differences were observed for mean-RPE, session-RPE and TVLL between the 50%-1RM and 75%1RM. Significant positive relationships between TVLL and session-RPE (50 %-1RM r=0.61, 75 %-1RM r=0.66; p<0.05) and between TVLL and mean-RPE (50 %-1RM r=0.51, 75%1RM r=0.49; P<0.05) were observed. Conclusion. The results of this study have shown that the TVLL in RT influences RPE measures. These findings corroborates the existence of a relationship between total work performed (external training load) and perception of effort (internal training load).

Identifying regulational alterations in gene regulatory networks by state space representation of vector autoregressive models and variational annealing

Background: In the analysis of effects by cell treatment such as drug dosing, identifying changes on gene network structures between normal and treated cells is a key task. A possible way for identifying the changes is to compare structures of networks estimated from data on normal and treated cells separately. However, this approach usually fails to estimate accurate gene networks due to the limited length of time series data and measurement noise. Thus, approaches that identify changes on regulations by using time series data on both conditions in an efficient manner are demanded. Methods: We propose a new statistical approach that is based on the state space representation of the vector autoregressive model and estimates gene networks on two different conditions in order to identify changes on regulations between the conditions. In the mathematical model of our approach, hidden binary variables are newly introduced to indicate the presence of regulations on each condition. The use of the hidden binary variables enables an efficient data usage; data on both conditions are used for commonly existing regulations, while for condition specific regulations corresponding data are only applied. Also, the similarity of networks on two conditions is automatically considered from the design of the potential function for the hidden binary variables. For the estimation of the hidden binary variables, we derive a new variational annealing method that searches the configuration of the binary variables maximizing the marginal likelihood. Results: For the performance evaluation, we use time series data from two topologically similar synthetic networks, and confirm that our proposed approach estimates commonly existing regulations as well as changes on regulations with higher coverage and precision than other existing approaches in almost all the experimental settings. For a real data application, our proposed approach is applied to time series data from normal Human lung cells and Human lung cells treated by stimulating EGF-receptors and dosing an anticancer drug termed Gefitinib. In the treated lung cells, a cancer cell condition is simulated by the stimulation of EGF-receptors, but the effect would be counteracted due to the selective inhibition of EGF-receptors by Gefitinib. However, gene expression profiles are actually different between the conditions, and the genes related to the identified changes are considered as possible off-targets of Gefitinib. Conclusions: From the synthetically generated time series data, our proposed approach can identify changes on regulations more accurately than existing methods. By applying the proposed approach to the time series data on normal and treated Human lung cells, candidates of off-target genes of Gefitinib are found. According to the published clinical information, one of the genes can be related to a factor of interstitial pneumonia, which is known as a side effect of Gefitinib.

MAPPING, ORGANIC MATTER MASS AND WATER VOLUME OF A PEATLAND IN SERRA DO ESPINHACO MERIDIONAL

Peatlands form in areas where net primary of organic matter production exceeds losses due to the decomposition, leaching or disturbance. Due to their chemical and physical characteristics, bogs can influence water dynamics because they can store large volumes of water in the rainy season and gradually release this water during the other months of the year. In Diamantina, Minas Gerais, Brazil, a peatland in the environmental protection area of Pau-de-Fruta ensures the water supply of 40,000 inhabitants. The hypothesis of this study is that the peat bogs in Pau-de-Fruta act as an environment for carbon storage and a regulator of water flow in the Corrego das Pedras basin. The objective of this study was to estimate the water volume and organic matter mass in this peatland and to study the influence of this environment on the water flow in the Corrego das Pedras basin. The peatland was mapped using 57 transects, at intervals of 100 m. Along all transects, the depth of the peat bog, the Universal Transverse Mercator (UTM) coordinates and altitude were recorded every 20 m and used to calculate the area and volume of the peatland. The water volume was estimated, using a method developed in this study, and the mass of organic matter based on samples from 106 profiles. The peatland covered 81.7 hectares (ha), and stored 497,767 m(3) of water, representing 83.7 % of the total volume of the peat bog. The total amount of organic matter (OM) was 45,148 t, corresponding to 552 t ha(-1) of OM. The peat bog occupies 11.9 % of the area covered by the Corrego das Pedras basin and stores 77.6 % of the annual water surplus, thus controlling the water flow in the basin and consequently regulating the water course.

Effect of external fields in Axelrod's model of social dynamics

The study of the effects of spatially uniform fields on the steady-state properties of Axelrod's model has yielded plenty of counterintuitive results. Here, we reexamine the impact of this type of field for a selection of parameters such that the field-free steady state of the model is heterogeneous or multicultural. Analyses of both one- and two-dimensional versions of Axelrod's model indicate that the steady state remains heterogeneous regardless of the value of the field strength. Turning on the field leads to a discontinuous decrease on the number of cultural domains, which we argue is due to the instability of zero-field heterogeneous absorbing configurations. We find, however, that spatially nonuniform fields that implement a consensus rule among the neighborhood of the agents enforce homogenization. Although the overall effects of the fields are essentially the same irrespective of the dimensionality of the model, we argue that the dimensionality has a significant impact on the stability of the field-free homogeneous steady state.

Small volume of hypertonic saline as the initial fluid replacement in experimental hypodynamic sepsis

Abstract Introduction We conducted the present study to examine the effects of hypertonic saline solution (7.5%) on cardiovascular function and splanchnic perfusion in experimental sepsis. Methods Anesthetized and mechanically ventilated mongrel dogs received an intravenous infusion of live Escherichia coli over 30 minutes. After 30 minutes, they were randomized to receive lactated Ringer's solution 32 ml/kg (LR; n = 7) over 30 minutes or 7.5% hypertonic saline solution 4 ml/kg (HS; n = 8) over 5 minutes. They were observed without additional interventions for 120 minutes. Cardiac output (CO), mean arterial pressure (MAP), portal and renal blood flow (PBF and RBF, respectively), gastric partial pressure of CO2 (pCO2; gas tonometry), blood gases and lactate levels were assessed. Results E. coli infusion promoted significant reductions in CO, MAP, PBF and RBF (approximately 45%, 12%, 45% and 25%, respectively) accompanied by an increase in lactate levels and systemic and mesenteric oxygen extraction (sO2ER and mO2ER). Widening of venous-arterial (approximately 15 mmHg), portal-arterial (approximately 18 mmHg) and gastric mucosal-arterial (approximately 55 mmHg) pCO2 gradients were also observed. LR and HS infusion transiently improved systemic and regional blood flow. However, HS infusion was associated with a significant and sustained reduction of systemic (18 ± 2.6 versus 38 ± 5.9%) and mesenteric oxygen extraction (18.5 ± 1.9 versus 36.5 ± 5.4%), without worsening other perfusional markers. Conclusion A large volume of LR or a small volume of HS promoted similar transient hemodynamic benefits in this sepsis model. However, a single bolus of HS did promote sustained reduction of systemic and mesenteric oxygen extraction, suggesting that hypertonic saline solution could be used as a salutary intervention during fluid resuscitation in septic patients.

Mapping, organic matter mass and water volume of a peatland in Serra do Espinhaço Meridional

Peatlands form in areas where net primary of organic matter production exceeds losses due to the decomposition, leaching or disturbance. Due to their chemical and physical characteristics, bogs can influence water dynamics because they can store large volumes of water in the rainy season and gradually release this water during the other months of the year. In Diamantina, Minas Gerais, Brazil, a peatland in the environmental protection area of Pau-de-Fruta ensures the water supply of 40,000 inhabitants. The hypothesis of this study is that the peat bogs in Pau-de-Fruta act as an environment for carbon storage and a regulator of water flow in the Córrego das Pedras basin. The objective of this study was to estimate the water volume and organic matter mass in this peatland and to study the influence of this environment on the water flow in the Córrego das Pedras basin. The peatland was mapped using 57 transects, at intervals of 100 m. Along all transects, the depth of the peat bog, the Universal Transverse Mercator (UTM) coordinates and altitude were recorded every 20 m and used to calculate the area and volume of the peatland. The water volume was estimated, using a method developed in this study, and the mass of organic matter based on samples from 106 profiles. The peatland covered 81.7 hectares (ha), and stored 497,767 m³ of water, representing 83.7 % of the total volume of the peat bog. The total amount of organic matter (OM) was 45,148 t, corresponding to 552 t ha-1 of OM. The peat bog occupies 11.9 % of the area covered by the Córrego das Pedras basin and stores 77.6 % of the annual water surplus, thus controlling the water flow in the basin and consequently regulating the water course.

A comparative analysis of the relative efficacy of vector-control strategies against dengue fever

Dengue is considered one of the most important vector-borne infection, affecting almost half of the world population with 50 to 100 million cases every year. In this paper, we present one of the simplest models that can encapsulate all the important variables related to vector control of dengue fever. The model considers the human population, the adult mosquito population and the population of immature stages, which includes eggs, larvae and pupae. The model also considers the vertical transmission of dengue in the mosquitoes and the seasonal variation in the mosquito population. From this basic model describing the dynamics of dengue infection, we deduce thresholds for avoiding the introduction of the disease and for the elimination of the disease. In particular, we deduce a Basic Reproduction Number for dengue that includes parameters related to the immature stages of the mosquito. By neglecting seasonal variation, we calculate the equilibrium values of the model’s variables. We also present a sensitivity analysis of the impact of four vector-control strategies on the Basic Reproduction Number, on the Force of Infection and on the human prevalence of dengue. Each of the strategies was studied separately from the others. The analysis presented allows us to conclude that of the available vector control strategies, adulticide application is the most effective, followed by the reduction of the exposure to mosquito bites, locating and destroying breeding places and, finally, larvicides. Current vector-control methods are concentrated on mechanical destruction of mosquitoes’ breeding places. Our results suggest that reducing the contact between vector and hosts (biting rates) is as efficient as the logistically difficult but very efficient adult mosquito’s control.

Flow Visualization with Quantified Spatial and Temporal Errors Using Edge Maps

Robust analysis of vector fields has been established as an important tool for deriving insights from the complex systems these fields model. Traditional analysis and visualization techniques rely primarily on computing streamlines through numerical integration. The inherent numerical errors of such approaches are usually ignored, leading to inconsistencies that cause unreliable visualizations and can ultimately prevent in-depth analysis. We propose a new representation for vector fields on surfaces that replaces numerical integration through triangles with maps from the triangle boundaries to themselves. This representation, called edge maps, permits a concise description of flow behaviors and is equivalent to computing all possible streamlines at a user defined error threshold. Independent of this error streamlines computed using edge maps are guaranteed to be consistent up to floating point precision, enabling the stable extraction of features such as the topological skeleton. Furthermore, our representation explicitly stores spatial and temporal errors which we use to produce more informative visualizations. This work describes the construction of edge maps, the error quantification, and a refinement procedure to adhere to a user defined error bound. Finally, we introduce new visualizations using the additional information provided by edge maps to indicate the uncertainty involved in computing streamlines and topological structures.

The sigma-isotypic decomposition and the sigma-index of reversible-equivariant systems

This work is concerned with dynamical systems in presence of symmetries and reversing symmetries. We describe a construction process of subspaces that are invariant by linear Gamma-reversible-equivariant mappings, where Gamma is the compact Lie group of all the symmetries and reversing symmetries of such systems. These subspaces are the sigma-isotypic components, first introduced by Lamb and Roberts in (1999) [10] and that correspond to the isotypic components for purely equivariant systems. In addition, by representation theory methods derived from the topological structure of the group Gamma, two algebraic formulae are established for the computation of the sigma-index of a closed subgroup of Gamma. The results obtained here are to be applied to general reversible-equivariant systems, but are of particular interest for the more subtle of the two possible cases, namely the non-self-dual case. Some examples are presented. (C) 2011 Elsevier BM. All rights reserved.