Serious analytical inconsistencies challenge the validity of the energy balance theory.

Energy metabolism theory affirms that body weight stability is achieved as over time the average energy intake equals the average energy expenditure, a state known as energy balance. Here it is demonstrated, however, that weight stability coexists with a persistent energy imbalance. Such unexpected result emerges as a consequence of the answers to three fundamental problems: 1. Is it possible to model body weight fluctuations without the energy balance theory? And if so, what are the benefits over the energy balance strategy? 2. During energy balance, how the oxidized macronutrient distribution that underlies the average energy expenditure is related to the macronutrient distribution of the average energy intake? 3. Is energy balance possible under a low-fat diet that simultaneously satisfies the following conditions? (a) The fat fraction of the absorbed energy intake is always less than the oxidized fat fraction of the energy expenditure. (b) The carbohydrate fraction of the absorbed energy intake is always greater or equal to the oxidized carbohydrate fraction of the energy expenditure. The first of these issues is addressed with the axiomatic method while the rest are managed through analythical arguments. On the whole, this analysis identifies inconsistencies in the principle of energy balance. The axiomatic approach results also in a simple mass balance model that fits experimental data and explains body composition alterations. This model gives rise to a convincing argument that appears to elucidate the advantage of low-carbohydrate diets over isocaloric low-fat diets. It is concluded, according to the aforementioned model, that weight fluctuations are ultimately dependent on the difference between daily food mass intake and daily mass loss (e.g., excretion of macronutrient oxidation products) and not on energy imbalance. In effect, it is shown that assuming otherwise may caused unintended weight gain.

Embedded delta shocks.

In 1977 Korchinski presented a new type of shock discontinuity in conservation laws. These singular solutions were coined δ-shocks since there is a time dependent Dirac delta involved. A naive description is that such δ-shock is of the overcompressive type: a single shock wave belonging to both families, the four characteristic lines of which impinge into the shock itself. In this work, we open the fan of solutions by studying two-family waves without intermediate constant states but possessing central rarefactions or comprising δ-shocks.

Bivariate lifetime models in presence of cure fraction: a comparative study with many different copula functions.

In time-to-event studies it is common the presence of a fraction of individuals not expecting to experience the event of interest; these individuals who are immune to the event or cured for the disease during the study are known as long-term survivors. In addition, in many studies it is observed two lifetimes associated to the same individual, and in some cases there exists a dependence structure between them. In these situations, the usual existing lifetime distributions are not appropriate to model data sets with long-term survivors and dependent bivariate lifetimes. In this study, it is proposed a bivariate model based on a Weibull standard distribution with a dependence structure based on fifteen different copula functions. We assumed the Weibull distribution due to its wide use in survival data analysis and its greater flexibility and simplicity, but the presented methods can be adapted to other continuous survival distributions. Three examples, considering real data sets are introduced to illustrate the proposed methodology. A Bayesian approach is assumed to get the inferences for the parameters of the model where the posterior summaries of interest are obtained using Markov Chain Monte Carlo simulation methods and the Openbugs software. For the data analysis considering different real data sets it was assumed fifteen different copula models from which is was possible to find models with satisfactory fit for the bivariate lifetimes in presence of long-term survivors.

An alternative model to explain the vectorial capacity using as example Aedes aegypti case in dengue transmission.

Vectorial capacity (VC), as a concept that describes the potential of a vector to transmit a pathogen, has had historical problems related to lacks in dimensional significance and high error propagation from parameters that take part in the model to output. Hence, values estimated with those equations are not sufficiently reliable to consider in control strategies or vector population study. In this paper, we propose a new VC model consistent at dimensional level, i.e., the definition and the equation of VC have same and consistent units, with a parameter estimation method and mathematical structure that reduces the uncertainty in model output, using as a case of study an Aedes aegypti population of the municipality of Bello, Colombia. After a literature review, we selected one VC equation following biological, measurability and dimensional criteria, then we rendered a local and global sensitivity analysis, identifying the mortality rate of mosquitoes as a target component of the equation. Thus, we studied the Weibull and Exponential distributions as probabilistic models that represent the expectation of mosquitoes infective life, intending to include the best distribution in a selected VC structure. The proposed mortality rate estimation method includes a new parameter that represents an increase or decrease in vector mortality, as it may apply. We noticed that its estimation reduces the uncertainty associated with the expectation of mosquitoes' infective life expression, which also reduces the output range and variance in almost a half.

A phenomenological base semi-physical thermodynamic model for the cylinder and exhaust manifold of a natural gas 2-megawatt four-stroke internal combustion engine.

This paper presents the application of a systematic methodology to obtain a semi-physical model of phenomenological base for a 2 MW internal combustion engine to generate electric power operating with natural gas, as a function of the average thermodynamic value normally measured in industrial applications. Specifically, the application of the methodology is focused on the cylinders, exhaust manifold, and turbocharger turbine sections. The proposed model was validated with actual operating data, obtaining an error rate not exceeding 5%, which allow a thermal characterization of the Jenbacher JMS 612 GS-N based on the model. A parametric analysis is conducted; considering the volumetric efficiency, the output electric power, the effective efficiency, the exhaust gas temperature, the turbine mass flow, the specific fuel consumption under the nominal operation conditions, which is 1.16 bar in the gas pressure, 65 °C in the cooling water temperature, 35 °C in the average ambient temperature, and 1500 rpm. The results of this model can be used to evaluate the thermodynamic performance parameters of waste heat recovery systems. On the other hand, new control strategies and the implementation of state observers for the detection and diagnosis of failures can be developed based on the proposed model.

Estimation of the Solow-Cobb-Douglas economic growth model with a Kalman filter: An observability-based approach.

This work presents a novel approach for estimating the Solow-Cobb-Douglas economic growth model. In this case, an Extended Kalman Filter is used for estimating, at the same time, the time-varying parameters of the model and the system state, from subsets of partially available economic data measurements. Different from traditional econometric techniques, the proposed EKF approach is applied directly to a state-space representation of the original nonlinear model, where all the model parameters are treated as time-varying parameters. An extensive nonlinear observability analysis was carried out in order to investigate the different subsets of measurements that can be used for estimating the state of the system, and also, in order to find out theoretically necessary conditions to achieve the observability system property. Experiments with real macroeconomic data are presented in order to validate the proposed approach. While the observability analysis offer theoretically conditions for system observability, the experimental results suggest that between the subsets of available economic data, some specific economic data are more relevant than others for better estimating the model.

Oscillating delayed feedback control schemes for stabilizing equilibrium points.

Limitations of the delayed feedback control and of its extended versions have been fully treated in the literature. The oscillating delayed feedback control appears as a promising scheme to overcome this problem. Two methods based on it are dealt with in this work. It is rigorously proven that for a nonlinear scalar system, stabilization in one of its (unstable) equilibrium points is achieved if any of these methods is applied. An ad-hoc map is associated to the (continuous) controlled system and the results are derived using discrete-time system stabilization tools. Moreover, the stability parameters region is fully described and issues like control performance, rate of convergence or robustness aspects are carefully analyzed.

A new DNA-based model for finite field arithmetic.

A Galois field G F ( p n ) with p ≥ 2 a prime number and n ≥ 1 is a mathematical structure widely used in Cryptography and Error Correcting Codes Theory. In this paper, we propose a novel DNA-based model for arithmetic over G F ( p n ) . Our model has three main advantages over other previously described models. First, it has a flexible implementation in the laboratory that allows the realization arithmetic calculations in parallel for p ≥ 2 , while the tile assembly and the sticker models are limited to p = 2 . Second, the proposed model is less prone to error, because it is grounded on conventional Polymerase Chain Reaction (PCR) amplification and gel electrophoresis techniques. Hence, the problems associated to models such as tile-assembly and stickers, that arise when using more complex molecular techniques, such as hybridization and denaturation, are avoided. Third, it is simple to implement and requires 50 ng/µL per DNA double fragment used to develop the calculations, since the only feature of interest is the size of the DNA double strand fragments. The efficiency of our model has execution times of order O ( 1 ) and O ( n ) , for the addition and multiplication over G F ( p n ) , respectively. Furthermore, this paper provides one of the few experimental evidences of arithmetic calculations for molecular computing and validates the technical applicability of the proposed model to perform arithmetic operations over G F ( p n ) .

Teoría de juegos aplicada al proceso de adquisición de recursos informáticos / Game theory applied to the acquisition of computing resources

En administración, se pueden presentar dos tipos de problemas de toma de decisiones: los que se solucionan en condiciones de certeza, es decir, libre de riesgo al optar por una solución, y los que dependen de la probabilidad de ocurrencia de eventos para poder tomar una decisión. En este último caso, aparecen con gran regularidad problemas de toma de decisiones en condiciones de conflicto, conocidos como teoría de juegos; como por ejemplo la adquisición de recursos informáticos, en el que la decisión de invertir en un recurso y no en otro adquiere mayor relevancia, en función de sus altos precios, y su gran demanda en cualquier rama de la sociedad. En la Facultad de Tecnología de la Universidad de Ciencias Médicas de Santiago de Cuba, se modeló el proceso de compras de estos recursos, a través de esta teoría, al no contar con opciones científicamente probadas hasta ese momento, que reportasen el mayor beneficio a la hora de adquirirlos cualquiera sea la plataforma informática. Por ello el objetivo de este trabajo es determinar desde el enfoque de la programación lineal, y específicamente la Teoría de Juegos, la estrategia óptima que bajo ciertas condiciones permitan conducir el proceso de adquisición de recursos informáticos. Como resultado se obtuvo una solución óptima, en la que se recomendaba invertir solamente en hardware para estaciones de trabajo, así como en hardware y componentes de red; lo que garantizaría la mejor forma de adaptación de los recursos invertidos, sin importar cuál sea la plataforma informática(AU)

In administration, two types of decision-making problems can be presented: those that are solved in conditions of certainty, that is, free of risk when opting for a solution, and those that depend on the probability of occurrence of events to be able to make a decision. In the last case, problems of decision-making in conditions of conflict, known as game theory, appear with great regularity; such as the purchase of computing resources, in which the decision to invest in one resource and not in another acquires greater relevance, due to its high prices and its high demand in any branch of society. In the Faculty of Technology of the University of Medical Sciences of Santiago de Cuba, the process of purchasing these resources was modeled through this theory, as it did not count with scientifically proved options until that moment, which reported the greatest benefit when purchasing them whatever the computing platform. Therefore, the objective of this work was to determine from the linear programming approach, and specifically the Games Theory, the optimal strategy that, under certain conditions, allows conducting the process of acquisition of computing resources. As a result, an optimal solution was obtained, which recommended investing only in hardware for workstations, and in hardware and network components; which would guarantee the best form of adaptation of the resources invested, no matter what the computing platform(AU)

Teoría de juegos aplicada al proceso de adquisición de recursos informáticos / Game theory applied to the acquisition of computing resources

En administración, se pueden presentar dos tipos de problemas de toma de decisiones: los que se solucionan en condiciones de certeza, es decir, libre de riesgo al optar por una solución, y los que dependen de la probabilidad de ocurrencia de eventos para poder tomar una decisión. En este último caso, aparecen con gran regularidad problemas de toma de decisiones en condiciones de conflicto, conocidos como teoría de juegos; como por ejemplo la adquisición de recursos informáticos, en el que la decisión de invertir en un recurso y no en otro adquiere mayor relevancia, en función de sus altos precios, y su gran demanda en cualquier rama de la sociedad. En la Facultad de Tecnología de la Universidad de Ciencias Médicas de Santiago de Cuba, se modeló el proceso de compras de estos recursos, a través de esta teoría, al no contar con opciones científicamente probadas hasta ese momento, que reportasen el mayor beneficio a la hora de adquirirlos cualquiera sea la plataforma informática. Por ello el objetivo de este trabajo es determinar desde el enfoque de la programación lineal, y específicamente la Teoría de Juegos, la estrategia óptima que bajo ciertas condiciones permitan conducir el proceso de adquisición de recursos informáticos. Como resultado se obtuvo una solución óptima, en la que se recomendaba invertir solamente en hardware para estaciones de trabajo, así como en hardware y componentes de red; lo que garantizaría la mejor forma de adaptación de los recursos invertidos, sin importar cuál sea la plataforma informática(AU)

In administration, two types of decision-making problems can be presented: those that are solved in conditions of certainty, that is, free of risk when opting for a solution, and those that depend on the probability of occurrence of events to be able to make a decision. In the last case, problems of decision-making in conditions of conflict, known as game theory, appear with great regularity; such as the purchase of computing resources, in which the decision to invest in one resource and not in another acquires greater relevance, due to its high prices and its high demand in any branch of society. In the Faculty of Technology of the University of Medical Sciences of Santiago de Cuba, the process of purchasing these resources was modeled through this theory, as it did not count with scientifically proved options until that moment, which reported the greatest benefit when purchasing them whatever the computing platform. Therefore, the objective of this work was to determine from the linear programming approach, and specifically the Games Theory, the optimal strategy that, under certain conditions, allows conducting the process of acquisition of computing resources. As a result, an optimal solution was obtained, which recommended investing only in hardware for workstations, and in hardware and network components; which would guarantee the best form of adaptation of the resources invested, no matter what the computing platform(AU)

Cadenas de markov aplicadas al análisis de la ejecución de proyectos de investigación / Markov chains applied to the analyzis of the progress of research projets

La administración moderna requiere el apoyo de herramientas de diferentes ramas de la ciencia que ayuden al proceso de toma de decisiones, como por ejemplo la Matemática Aplicada. En este contexto aparecen variables aleatorias que con el transcurso del tiempo cambian, y que pueden ser representadas a través de modelos cuantitativos. Cuando en estos modelos el estado presente de dichas variables resume toda la información anterior para describir cómo se comportarán en el futuro, se dice que se está en presencia de una cadena de Markov; una herramienta eficiente para el análisis de procesos de esta naturaleza, como por ejemplo la ejecución de proyectos de investigación, el cual reviste gran importancia en la gestión de ciencia e innovación tecnológica; área de resultados clave en cualquier universidad. En la Facultad de Tecnología de la Universidad de Ciencias Médicas de Santiago de Cuba, el análisis de la ejecución de los proyectos de investigación se consideró como una cadena de Markov, definiendo los diferentes estados por los que puede estar un proyecto, y las probabilidades de que este se encuentre en un estado determinado a partir del estado en que se encontraba. Así se determinaron elementos que permiten apoyar la toma de decisiones a corto y a largo plazo, a partir de datos históricos durante el trienio 2013 - 2015, relacionados con la cantidad promedio de inspecciones a los mismos, probabilidades de un proyecto cerrar, etc.; permitiendo pronosticar en términos de probabilidades el estado de este subsistema en el futuro(AU)

Modern management tools require support from different branches of science to help the decision-making process, such as Applied Mathematics. In this context, random variables with change over time, and that can be represented by quantitative models appear. When these models in the present state of these variables summarizes all the previous information to describe how they will behave in the future, it is said that we are in the presence of a Markov chain; an efficient tool for the analysis of processes of this nature, such as the execution of research projects, which is of great importance in the management of science and technological innovation; key result area at any university. In the Faculty of Technology, University of Medical Sciences of Santiago de Cuba, the analysis of the implementation of research projects was considered as a Markov chain, defining the different states through which can be a project and the odds of this is in a certain state from the state it was. And support elements that enable decision-making in the short and long term, from historical data in the period 2013 - 2015 were determined, related to the average number of inspections to a project, the probability of a project likely to close, etc.; allowing to predict in terms of probabilities the status of this subsystem in the future(AU)

Thermodynamic restrictions on linear reversible and irreversible thermo-electro-magneto-mechanical processes.

A unified thermodynamic framework for the characterization of functional materials is developed. This framework encompasses linear reversible and irreversible processes with thermal, electrical, magnetic, and/or mechanical effects coupled. The comprehensive framework combines the principles of classical equilibrium and non-equilibrium thermodynamics with electrodynamics of continua in the infinitesimal strain regime. In the first part of this paper, linear Thermo-Electro-Magneto-Mechanical (TEMM) quasistatic processes are characterized. Thermodynamic stability conditions are further imposed on the linear constitutive model and restrictions on the corresponding material constants are derived. The framework is then extended to irreversible transport phenomena including thermoelectric, thermomagnetic and the state-of-the-art spintronic and spin caloritronic effects. Using Onsager's reciprocity relationships and the dissipation inequality, restrictions on the kinetic coefficients corresponding to charge, heat and spin transport processes are derived. All the constitutive models are accompanied by multiphysics interaction diagrams that highlight the various processes that can be characterized using this framework.