Validity of Resting Energy Expenditure Predictive Equations before and after an Energy-Restricted Diet Intervention in Obese Women

11 p.

Best Proximity Points of Generalized Semicyclic Impulsive Self-Mappings: Applications to Impulsive Differential and Difference Equations

This paper is devoted to the study of convergence properties of distances between points and the existence and uniqueness of best proximity and fixed points of the so-called semicyclic impulsive self-mappings on the union of a number of nonempty subsets in metric spaces. The convergences of distances between consecutive iterated points are studied in metric spaces, while those associated with convergence to best proximity points are set in uniformly convex Banach spaces which are simultaneously complete metric spaces. The concept of semicyclic self-mappings generalizes the well-known one of cyclic ones in the sense that the iterated sequences built through such mappings are allowed to have images located in the same subset as their pre-image. The self-mappings under study might be in the most general case impulsive in the sense that they are composite mappings consisting of two self-mappings, and one of them is eventually discontinuous. Thus, the developed formalism can be applied to the study of stability of a class of impulsive differential equations and that of their discrete counterparts. Some application examples to impulsive differential equations are also given.

Use of generalised additive models to categorise continuous variables in clinical prediction

13 P.

Advances in Nonlinear Complexity Analysis for Partial Differential Equations

1 p. -- [Editorial Material]

Prediction of Multi-Target Networks of Neuroprotective Compounds with Entropy Indices and Synthesis, Assay, and Theoretical Study of New Asymmetric 1,2-Rasagiline Carbamates

In a multi-target complex network, the links (L-ij) represent the interactions between the drug (d(i)) and the target (t(j)), characterized by different experimental measures (K-i, K-m, IC50, etc.) obtained in pharmacological assays under diverse boundary conditions (c(j)). In this work, we handle Shannon entropy measures for developing a model encompassing a multi-target network of neuroprotective/neurotoxic compounds reported in the CHEMBL database. The model predicts correctly >8300 experimental outcomes with Accuracy, Specificity, and Sensitivity above 80%-90% on training and external validation series. Indeed, the model can calculate different outcomes for >30 experimental measures in >400 different experimental protocolsin relation with >150 molecular and cellular targets on 11 different organisms (including human). Hereafter, we reported by the first time the synthesis, characterization, and experimental assays of a new series of chiral 1,2-rasagiline carbamate derivatives not reported in previous works. The experimental tests included: (1) assay in absence of neurotoxic agents; (2) in the presence of glutamate; and (3) in the presence of H2O2. Lastly, we used the new Assessing Links with Moving Averages (ALMA)-entropy model to predict possible outcomes for the new compounds in a high number of pharmacological tests not carried out experimentally.

Proposal and validation of methodologies for the categorisation of continuous variables in the development of prediction models

158 p.

Approximate Solutions by Truncated Taylor Series Expansions of Nonlinear Differential Equations and Related Shadowing Property with Applications

This paper investigates the errors of the solutions as well as the shadowing property of a class of nonlinear differential equations which possess unique solutions on a certain interval for any admissible initial condition. The class of differential equations is assumed to be approximated by well-posed truncated Taylor series expansions up to a certain order obtained about certain, in general nonperiodic, sampling points t(i) is an element of [t(0), t(J)] for i = 0, 1, . . . , J of the solution. Two examples are provided.

Bessel functions and equations of mathematical physics

The aim of this dissertation is to introduce Bessel functions to the reader, as well as studying some of their properties. Moreover, the final goal of this document is to present the most well- known applications of Bessel functions in physics.

Crank-Nicholson method for rate equations in powder random lasers

3rd International Conference on Mathematical Modeling in Physical Sciences (IC-MSQUARE 2014)