Dynamic rain model for linear stochastic environments

To develop modem agriculture, a vision of an integral management is required, where the complexity of interactions between climatic, biological, economical, social and political factors involved in the food production must systematically be analyzed in a context of regional conditions. At the same time, it is necessary to develop the ability to forecast both the climatic variations and their possible impact on society. The minimization of this impact on agriculture through consistent practices adequate to local climates, is not only commendable, but basically necessary, besides, the usefulness of these studies in acquiring a better knowledge of those areas with an inversion risk for agricultural and cattle rising development is high. In this paper a statistical model is used to accomplish the objectives above mentioned. The rainfall variability in several areas of the Tlaxcala State (Mexico) is analyzed with due regard to both inter- and intra-annual relations, considering that the cumulative rainfall, in the former case, follows a logistic curve and in the latter it follows a linear, first order, stochastic process.

Entropy-Based Behavioural Efficiency of the Financial Market

The most known and used abstract model of the financial market is based on the concept of the informational efficiency (EMH) of that market. The paper proposes an alternative which could be named the behavioural efficiency of the financial market, which is based on the behavioural entropy instead of the informational entropy. More specifically, the paper supports the idea that, in the financial market, the only measure (if any) of the entropy is the available behaviours indicated by the implicit information. Therefore, the behavioural entropy is linked to the concept of behavioural efficiency. The paper argues that, in fact, in the financial markets, there is not a (real) informational efficiency, but there exists a behavioural efficiency instead. The proposal is based both on a new typology of information in the financial market (which provides the concept of implicit information—that is, that information ”translated” by the economic agents from observing the actual behaviours) and on a non-linear (more exactly, a logistic) curve linking the behavioural entropy to the behavioural efficiency of the financial markets. Finally, the paper proposes a synergic overcoming of both EMH and AMH based on the new concept of behavioural entropy in the financial market.

Simulations reveal that different responses to cell crowding determine the expansion of p53 and Notch mutant clones in squamous epithelia

During ageing, normal epithelial tissues progressively accumulate clones carrying mutations that increase mutant cell fitness above that of wild-type cells. Such mutants spread widely through the tissues, yet despite this cellular homeostasis and functional integrity of the epithelia are maintained. Two of the genes most commonly mutated in human skin and oesophagus are p53 and Notch1 , both of which are also recurrently mutated in cancers of these tissues. From observations taken in human and mouse epithelia, we find that clones carrying p53 and Notch pathway mutations have different clone dynamics which can be explained by their different responses to local cell crowding. p53 mutant clone growth in mouse epidermis approximates a logistic curve, but feedbacks responding to local crowding are required to maintain tissue homeostasis. We go on to show that the observed ability of Notch pathway mutant cells to displace the wild-type population in the mouse oesophageal epithelium reflects a local density feedback that affects both mutant and wild-type cells equally. We then show how these distinct feedbacks are consistent with the distribution of mutations observed in human datasets and are suggestive of a putative mechanism to constrain these cancer-associated mutants.

Fitting the Portuguese population from 1850 to 2010 to a logistic growth model

This work explores how the Portuguese population fits a logistic growth model. The present study is divided into two main sections. The first one consists on the qualitative and quantitative study of the logistic equation. Qualitatively, I will look at various aspects of the differential equation, such as the equilibria and their stability and possible inflections of solutions. Quantitatively, I will use the separation of variables to find explicit solutions. Given the lack of accuracy in the linear fitting to the proportional growth rate against the population, in second chapter, I attempted a polynomial trendline fitting to the growth rate against the population. This led the focus to creating an adapted form of the logistic curve that fits the Portuguese population from 1850 to 2010. With a certain degree of accuracy, the adapted form of the logistic growth model fits the Portuguese population in the period mentioned.

Management of High-Risk Atherosclerotic Patients by Statins May Be Supported by Logistic Model of Intima-Media Thickening

While the use of statins in treating patients with atherosclerosis is an undisputed success, the questions regarding an optimal starting time for treatment and its strength remain open. We proposed in our earlier paper published in Int. J. Mol. Sci. (2019, 20) that the growth of intima-media thickness of the carotid artery follows an S-shape (i.e., logistic) curve. In our subsequent paper in PLoS ONE (2020, 15), we incorporated this feature into a logistic control-theoretic model of atherosclerosis progression and showed that some combinations of patient age and intima-media thickness are better suited than others to start treatment. In this study, we perform a new and comprehensive calibration of our logistic model using a recent clinical database. This allows us to propose a procedure for inferring an optimal age to start statin treatment for a particular group of patients. We argue that a decrease in the slope of the IMT logistic growth curve, induced by statin treatment, is most efficient where the curve is at its steepest, whereby the efficiency means lowering the future IMT levels. Using the procedure on an aggregate group of severely sick men, 38 years of age is observed to correlate with the steepest point of the logistic curve, and, thus, it is the preferred time to start statin treatment. We believe that detecting the logistic curve’s steepest fragment and commencing statin administration on that fragment are courses of action that agree with clinician intuition and may support decision-making processes.

Binomial GLMs

GLMs with a binomial distribution are designed for the analysis of binomial counts (how many times something occurred relative to the total number of possible times it could have occurred). A logistic link function constrains predictions to be above zero and below the maximum using the S-shaped logistic curve. Overdispersion can be diagnosed and dealt with using a quasi-maximum likelihood extension to GLM analysis.

Construction of appropriate model for Enrolment Projection of India

There are different models used for enrolment projection in the education system. Of them ARIMA, double exponential, logistic curve method, reconstructive cohort, and regression model, method are commonly used. Every model has its suitability under certain conditions and with prior assumptions. In India, no attempt was made to estimate enrolment except in 1996. The logistic curve method was adopted to estimate enrolment between 1996 – 2001. In the present situation, an attempt has been made to estimate school enrolment for the next years. The present paper discusses fitting the best model for estimating enrolment for the next few years.

A new formulation of compartmental epidemic modelling for arbitrary distributions of incubation and removal times

The paradigm for compartment models in epidemiology assumes exponentially distributed incubation and removal times, which is not realistic in actual populations. Commonly used variations with multiple exponentially distributed variables are more flexible, yet do not allow for arbitrary distributions. We present a new formulation, focussing on the SEIR concept that allows to include general distributions of incubation and removal times. We compare the solution to two types of agent-based model simulations, a spatially homogeneous one where infection occurs by proximity, and a model on a scale-free network with varying clustering properties, where the infection between any two agents occurs via their link if it exists. We find good agreement in both cases. Furthermore a family of asymptotic solutions of the equations is found in terms of a logistic curve, which after a non-universal time shift, fits extremely well all the microdynamical simulations. The formulation allows for a simple numerical approach; software in Julia and Python is provided.