Ventilation behavior during upper-body incremental exercise

Pires, FO, Hammond, J, Lima-Silva, AE, Bertuzzi, RCM, and Kiss, MAPDM. Ventilation behavior during upper-body incremental exercise. J Strength Cond Res 25(1): 225-230, 2011-This study tested the ventilation (V(E)) behavior during upper-body incremental exercise by mathematical models that calculate 1 or 2 thresholds and compared the thresholds identified by mathematical models with V-slope, ventilatory equivalent for oxygen uptake (V(E)/(V) over dotO(2)), and ventilatory equivalent for carbon dioxide uptake (V(E)/(V) over dotCO(2)). Fourteen rock climbers underwent an upper-body incremental test on a cycle ergometer with increases of approximately 20 W.min(-1) until exhaustion at a cranking frequency of approximately 90 rpm. The V(E) data were smoothed to 10-second averages for V(E) time plotting. The bisegmental and the 3-segmental linear regression models were calculated from 1 or 2 intercepts that best shared the V(E) curve in 2 or 3 linear segments. The ventilatory threshold(s) was determined mathematically by the intercept(s) obtained by bisegmental and 3-segmental models, by V-slope model, or visually by V(E)/(V) over dotO(2) and V(E)/(V) over dotCO(2). There was no difference between bisegmental (mean square error [MSE] = 35.3 +/- 32.7 l.min(-1)) and 3-segmental (MSE = 44.9 +/- 47.8 l.min(-1)) models in fitted data. There was no difference between ventilatory threshold identified by the bisegmental (28.2 +/- 6.8 ml.kg(-1).min(-1)) and second ventilatory threshold identified by the 3-segmental (30.0 +/- 5.1 ml.kg(-1).min(-1)), V(E)/(V) over dotO(2) (28.8 +/- 5.5 ml.kg(-1).min(-1)), or V-slope (28.5 +/- 5.6 ml.kg(-1).min(-1)). However, the first ventilatory threshold identified by 3-segmental (23.1 +/- 4.9 ml.kg(-1).min(-1)) or by VE/(V) over dotO(2) (24.9 +/- 4.4 ml.kg(-1).min(-1)) was different from these 4. The V(E) behavior during upper-body exercise tends to show only 1 ventilatory threshold. These findings have practical implications because this point is frequently used for aerobic training prescription in healthy subjects, athletes, and in elderly or diseased populations. The ventilatory threshold identified by V(E) curve should be used for aerobic training prescription in healthy subjects and athletes.

On the solubility of proteins as a function of pH: Mathematical development and application

Thermodynamic relations between the solubility of a protein and the solution pH are presented in this work. The hypotheses behind the development are that the protein chemical potential in liquid phase can be described by Henry`s law and that the solid-liquid equilibrium is established only between neutral molecules. The mathematical development results in an analytical expression of the solubility curve, as a function of the ionization equilibrium constants, the pH and the solubility at the isoelectric point. It is shown that the same equation can be obtained either by directly calculating the fraction of neutral protein molecules or by integrating the curve of the protein average charge. The methodology was successfully applied to the description of the solubility of porcine insulin as a function of pH at three different temperatures and of bovine beta-lactoglobulin at four different ionic strengths. (C) 2011 Elsevier B.V. All rights reserved.

Self-organized criticality and the predictability of human behavior

The behavior of normal individuals and psychiatric patients vary in a similar way following power laws. The presence of identical patterns of behavioral variation occurring in individuals with different levels of activity is suggestive of self-similarity phenomena. Based on these findings, we propose that the human behavior in social context can constitute a system exhibiting self-organized criticality (SOC). The introduction of SOC concept in psychological theories can help to approach the question of behavior predictability by taking into consideration their intrinsic stochastic character. Also, the ceteris paribus generalizations characteristic of psychological laws can be seen as a consequence of individual level description of a more complex collective phenomena. Although limited, this study suggests that, if an adequate level of description is adopted, the complexity of human behavior can be more easily approached and their individual and social components can be more realistically modeled. (C) 2009 Elsevier Ltd. All rights reserved.

Study of the electromyographic signal dynamic behavior in Amyotrophic Lateral Sclerosis (ALS)

Amyotrophic Lateral Sclerosis (ALS) is a neurodegenerative disease characterized by motor neurons degeneration, which reduces muscular force, being very difficult to diagnose. Mathematical methods are used in order to analyze the surface electromiographic signal’s dynamic behavior (Fractal Dimension (FD) and Multiscale Entropy (MSE)), evaluate different muscle group’s synchronization (Coherence and Phase Locking Factor (PLF)) and to evaluate the signal’s complexity (Lempel-Ziv (LZ) techniques and Detrended Fluctuation Analysis (DFA)). Surface electromiographic signal acquisitions were performed in upper limb muscles, being the analysis executed for instants of contraction for ipsilateral acquisitions for patients and control groups. Results from LZ, DFA and MSE analysis present capability to distinguish between the patient group and the control group, whereas coherence, PLF and FD algorithms present results very similar for both groups. LZ, DFA and MSE algorithms appear then to be a good measure of corticospinal pathways integrity. A classification algorithm was applied to the results in combination with extracted features from the surface electromiographic signal, with an accuracy percentage higher than 70% for 118 combinations for at least one classifier. The classification results demonstrate capability to distinguish members between patients and control groups. These results can demonstrate a major importance in the disease diagnose, once surface electromyography (sEMG) may be used as an auxiliary diagnose method.

Dynamics of experimental populations of native and introduced blowflies (Diptera: Calliphoridae): mathematical modelling and the transition from asymptotic equilibrium to bounded oscillations

The equilibrium dynamics of native and introduced blowflies is modelled using a density-dependent model of population growth that takes into account important features of the life-history in these flies. A theoretical analysis indicates that the product of maximum fecundity and survival is the primary determinant of the dynamics. Cochliomyia macellaria, a blowfly native to the Americas and the introduced Chrysomya megacephala and Chrysomya putoria, differ in their dynamics in that the first species shows a damping oscillatory behavior leading to a one-point equilibrium, whereas in the last two species population numbers show a two-point limit cycle. Simulations showed that variation in fecundity has a marked effect on the dynamics and indicates the possibility of transitions from one-point equilibrium to bounded oscillations and aperiodic behavior. Variation in survival has much less influence on the dynamics.

Complementarities between mathematical and computational modeling: the case of the repeated Prisoners' Dilemma

We study the properties of the well known Replicator Dynamics when applied to a finitely repeated version of the Prisoners' Dilemma game. We characterize the behavior of such dynamics under strongly simplifying assumptions (i.e. only 3 strategies are available) and show that the basin of attraction of defection shrinks as the number of repetitions increases. After discussing the difficulties involved in trying to relax the 'strongly simplifying assumptions' above, we approach the same model by means of simulations based on genetic algorithms. The resulting simulations describe a behavior of the system very close to the one predicted by the replicator dynamics without imposing any of the assumptions of the mathematical model. Our main conclusion is that mathematical and computational models are good complements for research in social sciences. Indeed, while computational models are extremely useful to extend the scope of the analysis to complex scenarios hard to analyze mathematically, formal models can be useful to verify and to explain the outcomes of computational models.

Resurgence of HIV infection among men who have sex with men in Switzerland: mathematical modelling study.

BACKGROUND: New HIV infections in men who have sex with men (MSM) have increased in Switzerland since 2000 despite combination antiretroviral therapy (cART). The objectives of this mathematical modelling study were: to describe the dynamics of the HIV epidemic in MSM in Switzerland using national data; to explore the effects of hypothetical prevention scenarios; and to conduct a multivariate sensitivity analysis. METHODOLOGY/PRINCIPAL FINDINGS: The model describes HIV transmission, progression and the effects of cART using differential equations. The model was fitted to Swiss HIV and AIDS surveillance data and twelve unknown parameters were estimated. Predicted numbers of diagnosed HIV infections and AIDS cases fitted the observed data well. By the end of 2010, an estimated 13.5% (95% CI 12.5, 14.6%) of all HIV-infected MSM were undiagnosed and accounted for 81.8% (95% CI 81.1, 82.4%) of new HIV infections. The transmission rate was at its lowest from 1995-1999, with a nadir of 46 incident HIV infections in 1999, but increased from 2000. The estimated number of new infections continued to increase to more than 250 in 2010, although the reproduction number was still below the epidemic threshold. Prevention scenarios included temporary reductions in risk behaviour, annual test and treat, and reduction in risk behaviour to levels observed earlier in the epidemic. These led to predicted reductions in new infections from 2 to 26% by 2020. Parameters related to disease progression and relative infectiousness at different HIV stages had the greatest influence on estimates of the net transmission rate. CONCLUSIONS/SIGNIFICANCE: The model outputs suggest that the increase in HIV transmission amongst MSM in Switzerland is the result of continuing risky sexual behaviour, particularly by those unaware of their infection status. Long term reductions in the incidence of HIV infection in MSM in Switzerland will require increased and sustained uptake of effective interventions.

Free inertial processes driven by Gaussian noise: Probability distributions, anomalous diffusion and fractal behavior

We study the motion of an unbound particle under the influence of a random force modeled as Gaussian colored noise with an arbitrary correlation function. We derive exact equations for the joint and marginal probability density functions and find the associated solutions. We analyze in detail anomalous diffusion behaviors along with the fractal structure of the trajectories of the particle and explore possible connections between dynamical exponents of the variance and the fractal dimension of the trajectories.

Exact long-time behavior of a network of oscillators under random fields

We present an exact solution for the order parameters that characterize the stationary behavior of a population of Kuramotos phase oscillators under random external fields [Y. Kuramoto, in International Symposium on Mathematical Problems in Theoretical Physics, Lecture Notes in Physics, Vol. 39 (Springer, Berlin, 1975), p. 420]. From these results it is possible to generate the phase diagram of models with an arbitrary distribution of random frequencies and random fields.

Modeling dynamic behavior in tilting pad gas journal bearings

Thisresearch deals with the dynamic modeling of gas lubricated tilting pad journal bearings provided with spring supported pads, including experimental verification of the computation. On the basis of a mathematical model of a film bearing, a computer program has been developed, which can be used for the simulation of a special type of tilting pad gas journal bearing supported by a rotary spring under different loading conditions time dependently (transient running conditions due to geometry variations in time externally imposed). On the basis of literature, different transformations have been used in the model to achieve simpler calculation. The numerical simulation is used to solve a non-stationary case of a gasfilm. The simulation results were compared with literature results in a stationary case (steady running conditions) and they were found to be equal. In addition to this, comparisons were made with a number of stationary and non-stationary bearing tests, which were performed at Lappeenranta University of Technology using bearings designed with the simulation program. A study was also made using numerical simulation and literature to establish the influence of the different bearing parameters on the stability of the bearing. Comparison work was done with literature on tilting pad gas bearings. This bearing type is rarely used. One literature reference has studied the same bearing type as that used in LUT. A new design of tilting pad gas bearing is introduced. It is based on a stainless steel body and electron beam welding of the bearing parts. It has good operation characteristics and is easier to tune and faster to manufacture than traditional constructions. It is also suitable for large serial production.

Selective catalytic reduction of nitrogen oxides with ammonia in forced unsteady state reactors - Case based reasoning and mathematical model simulation reasoning

The application of forced unsteady-state reactors in case of selective catalytic reduction of nitrogen oxides (NOx) with ammonia (NH3) is sustained by the fact that favorable temperature and composition distributions which cannot be achieved in any steady-state regime can be obtained by means of unsteady-state operations. In a normal way of operation the low exothermicity of the selective catalytic reduction (SCR) reaction (usually carried out in the range of 280-350°C) is not enough to maintain by itself the chemical reaction. A normal mode of operation usually requires supply of supplementary heat increasing in this way the overall process operation cost. Through forced unsteady-state operation, the main advantage that can be obtained when exothermic reactions take place is the possibility of trapping, beside the ammonia, the moving heat wave inside the catalytic bed. The unsteady state-operation enables the exploitation of the thermal storage capacity of the catalyticbed. The catalytic bed acts as a regenerative heat exchanger allowing auto-thermal behaviour when the adiabatic temperature rise is low. Finding the optimum reactor configuration, employing the most suitable operation model and identifying the reactor behavior are highly important steps in order to configure a proper device for industrial applications. The Reverse Flow Reactor (RFR) - a forced unsteady state reactor - corresponds to the above mentioned characteristics and may be employed as an efficient device for the treatment of dilute pollutant mixtures. As a main disadvantage, beside its advantages, the RFR presents the 'wash out' phenomena. This phenomenon represents emissions of unconverted reactants at every switch of the flow direction. As a consequence our attention was focused on finding an alternative reactor configuration for RFR which is not affected by the incontrollable emissions of unconverted reactants. In this respect the Reactor Network (RN) was investigated. Its configuration consists of several reactors connected in a closed sequence, simulating a moving bed by changing the reactants feeding position. In the RN the flow direction is maintained in the same way ensuring uniformcatalyst exploitation and in the same time the 'wash out' phenomena is annulated. The simulated moving bed (SMB) can operate in transient mode giving practically constant exit concentration and high conversion levels. The main advantage of the reactor network operation is emphasizedby the possibility to obtain auto-thermal behavior with nearly uniformcatalyst utilization. However, the reactor network presents only a small range of switching times which allow to reach and to maintain an ignited state. Even so a proper study of the complex behavior of the RN may give the necessary information to overcome all the difficulties that can appear in the RN operation. The unsteady-state reactors complexity arises from the fact that these reactor types are characterized by short contact times and complex interaction between heat and mass transportphenomena. Such complex interactions can give rise to a remarkable complex dynamic behavior characterized by a set of spatial-temporal patterns, chaotic changes in concentration and traveling waves of heat or chemical reactivity. The main efforts of the current research studies concern the improvement of contact modalities between reactants, the possibility of thermal wave storage inside the reactor and the improvement of the kinetic activity of the catalyst used. Paying attention to the above mentioned aspects is important when higher activity even at low feeding temperatures and low emissions of unconverted reactants are the main operation concerns. Also, the prediction of the reactor pseudo or steady-state performance (regarding the conversion, selectivity and thermal behavior) and the dynamicreactor response during exploitation are important aspects in finding the optimal control strategy for the forced unsteady state catalytic tubular reactors. The design of an adapted reactor requires knowledge about the influence of its operating conditions on the overall process performance and a precise evaluation of the operating parameters rage for which a sustained dynamic behavior is obtained. An apriori estimation of the system parameters result in diminution of the computational efforts. Usually the convergence of unsteady state reactor systems requires integration over hundreds of cycles depending on the initial guess of the parameter values. The investigation of various operation models and thermal transfer strategies give reliable means to obtain recuperative and regenerative devices which are capable to maintain an auto-thermal behavior in case of low exothermic reactions. In the present research work a gradual analysis of the SCR of NOx with ammonia process in forced unsteady-state reactors was realized. The investigation covers the presentationof the general problematic related to the effect of noxious emissions in the environment, the analysis of the suitable catalysts types for the process, the mathematical analysis approach for modeling and finding the system solutions and the experimental investigation of the device found to be more suitable for the present process. In order to gain information about the forced unsteady state reactor design, operation, important system parameters and their values, mathematical description, mathematicalmethod for solving systems of partial differential equations and other specific aspects, in a fast and easy way, and a case based reasoning (CBR) approach has been used. This approach, using the experience of past similarproblems and their adapted solutions, may provide a method for gaining informations and solutions for new problems related to the forced unsteady state reactors technology. As a consequence a CBR system was implemented and a corresponding tool was developed. Further on, grooving up the hypothesis of isothermal operation, the investigation by means of numerical simulation of the feasibility of the SCR of NOx with ammonia in the RFRand in the RN with variable feeding position was realized. The hypothesis of non-isothermal operation was taken into account because in our opinion ifa commercial catalyst is considered, is not possible to modify the chemical activity and its adsorptive capacity to improve the operation butis possible to change the operation regime. In order to identify the most suitable device for the unsteady state reduction of NOx with ammonia, considering the perspective of recuperative and regenerative devices, a comparative analysis of the above mentioned two devices performance was realized. The assumption of isothermal conditions in the beginningof the forced unsteadystate investigation allowed the simplification of the analysis enabling to focus on the impact of the conditions and mode of operation on the dynamic features caused by the trapping of one reactant in the reactor, without considering the impact of thermal effect on overall reactor performance. The non-isothermal system approach has been investigated in order to point out the important influence of the thermal effect on overall reactor performance, studying the possibility of RFR and RN utilization as recuperative and regenerative devices and the possibility of achieving a sustained auto-thermal behavior in case of lowexothermic reaction of SCR of NOx with ammonia and low temperature gasfeeding. Beside the influence of the thermal effect, the influence of the principal operating parameters, as switching time, inlet flow rate and initial catalyst temperature have been stressed. This analysis is important not only because it allows a comparison between the two devices and optimisation of the operation, but also the switching time is the main operating parameter. An appropriate choice of this parameter enables the fulfilment of the process constraints. The level of the conversions achieved, the more uniform temperature profiles, the uniformity ofcatalyst exploitation and the much simpler mode of operation imposed the RN as a much more suitable device for SCR of NOx with ammonia, in usual operation and also in the perspective of control strategy implementation. Theoretical simplified models have also been proposed in order to describe the forced unsteady state reactors performance and to estimate their internal temperature and concentration profiles. The general idea was to extend the study of catalytic reactor dynamics taking into account the perspectives that haven't been analyzed yet. The experimental investigation ofRN revealed a good agreement between the data obtained by model simulation and the ones obtained experimentally.

Some advances in mathematical models for preference relations

Preference relations, and their modeling, have played a crucial role in both social sciences and applied mathematics. A special category of preference relations is represented by cardinal preference relations, which are nothing other than relations which can also take into account the degree of relation. Preference relations play a pivotal role in most of multi criteria decision making methods and in the operational research. This thesis aims at showing some recent advances in their methodology. Actually, there are a number of open issues in this field and the contributions presented in this thesis can be grouped accordingly. The first issue regards the estimation of a weight vector given a preference relation. A new and efficient algorithm for estimating the priority vector of a reciprocal relation, i.e. a special type of preference relation, is going to be presented. The same section contains the proof that twenty methods already proposed in literature lead to unsatisfactory results as they employ a conflicting constraint in their optimization model. The second area of interest concerns consistency evaluation and it is possibly the kernel of the thesis. This thesis contains the proofs that some indices are equivalent and that therefore, some seemingly different formulae, end up leading to the very same result. Moreover, some numerical simulations are presented. The section ends with some consideration of a new method for fairly evaluating consistency. The third matter regards incomplete relations and how to estimate missing comparisons. This section reports a numerical study of the methods already proposed in literature and analyzes their behavior in different situations. The fourth, and last, topic, proposes a way to deal with group decision making by means of connecting preference relations with social network analysis.

Mathematical models to describe the volumetric shrinkage rate of red beans during drying

The present study aimed to determine the volumetric shrinkage rate of bean (Phaseolus vulgaris L.) seeds during air-drying under different conditions of air, temperature and relative humidity, and to adjust several mathematical models to the empiric values observed, and select the one that best represents the phenomenon. Six mathematical models were adjusted to the experimental values to represent the phenomenon. It was determined the degree of adjustment of each model from the value of the coefficient of determination, the behavior of the distribution of the residuals, and the magnitude of the average relative and estimated errors. The rate of volumetric shrinkage that occurred in bean seeds during drying is between 25 and 37%. It basically depends on the final moisture content, regardless of the air conditions during drying. The Modified Bala & Woods' model best represented the process.

Forecasting financial weather - can we foresee market sentiment? Spectrum of stock price behavior - NYSE case study

The desire to create a statistical or mathematical model, which would allow predicting the future changes in stock prices, was born many years ago. Economists and mathematicians are trying to solve this task by applying statistical analysis and physical laws, but there are still no satisfactory results. The main reason for this is that a stock exchange is a non-stationary, unstable and complex system, which is influenced by many factors. In this thesis the New York Stock Exchange was considered as the system to be explored. A topological analysis, basic statistical tools and singular value decomposition were conducted for understanding the behavior of the market. Two methods for normalization of initial daily closure prices by Dow Jones and S&P500 were introduced and applied for further analysis. As a result, some unexpected features were identified, such as a shape of distribution of correlation matrix, a bulk of which is shifted to the right hand side with respect to zero. Also non-ergodicity of NYSE was confirmed graphically. It was shown, that singular vectors differ from each other by a constant factor. There are for certain results no clear conclusions from this work, but it creates a good basis for the further analysis of market topology.