The increasing use of mathematical techniques in scientific research leads to the interdisciplinarity of applied mathematics. This viewpoint is validated quantitatively here by statistical and network analysis on the corpus PNAS 1999–2013. A network describing the interdisciplinary relationships between disciplines in a panoramic view is built based on the corpus. Specific network indicators show the hub role of applied mathematics in interdisciplinary research. The statistical analysis on the corpus content finds that algorithms, a primary topic of applied mathematics, positively correlates, increasingly co-occurs, and has an equilibrium relationship in the long-run with certain typical research paradigms and methodologies. The finding can be understood as an intrinsic cause of the interdisciplinarity of applied mathematics.

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Quantitative Analysis of the Interdisciplinarity of Applied Mathematics.

Pekka Neittaanmaki, Sergey Repin and Tero Tuovinen (Eds.). Mathematical Modeling and Optimization of Complex Structures; Series: Computational Methods in Applied Sciences.
 Springer International Publishing AG, Switzerland; 2016. E-book, XXI, 328 pages, ISBN: 9783319235646, Hard-cover ISBN: 9783319235639, Library of Congress Control Number: 2015947948, DOI 10.1007/978-3-319-23564-6
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Mathematical modeling and optimization of complex structures: a review

Under mild Markov assumptions, sufficient conditions for strict minimax optimality of sequential tests for multiple hypotheses under distributional uncertainty are derived. First, the design of optimal sequential tests for simple hypotheses is revisited and it is shown that the partial derivatives of the corresponding cost function are closely related to the performance metrics of the underlying sequential test. Second, an implicit characterization of the least favorable distributions for a given testing policy is stated. By combining the results on optimal sequential tests and least favorable distributions, sufficient conditions for a sequential test to be minimax optimal under general distributional uncertainties are obtained. The cost function of the minimax optimal test is further identified as a generalized $f$-dissimilarity and the least favorable distributions as those that are most similar with respect to this dissimilarity. Numerical examples for minimax optimal sequential tests under different uncertainties illustrate the theoretical results.

Minimax Optimal Sequential Hypothesis Tests for Markov Processes

Cutaneous leishmaniasis is one of the infectious diseases that affects public health and represents a real threat especially in developing countries The disease is transmitted by the bite of certain species of sandflies and occurs predominantly in warm, humid and tropical climate Finding the source of cutaneous leishmaniasis and identifying factors that promote its spread could help to a good prediction of the epidemic in time The aim of this study is the construction of a statistical model that reproduces the number of affected cases using climate factors influencing the presence of sandflies Given the extensive development of the Generalized Linear Models and their performance in modeling count data as well as their adaptation to the problem of overdispersed data, we present the utility and the basic foundations of Poisson and quasi-Poisson regression models Thereafter, we build a forecasting model that could predict the number of monthly cases of the cutaneous leishmaniasis from climatic factors during the period 2008-2011 in the province of Msila which is one of the Algerian provinces heavily affected by the epidemic in question In our case the temperature and trend factor were retained in the model Poisson regression gave a good result after eliminating the effect of overdispersion

http://www.issr-journals.org/links/papers.php?journal=ijias&application=pdf&article=IJIAS-14-292-06

Cutaneous Leishmaniasis Modeling: the case of Msila Province in Algeria

The Applied Mathematics, Modelling, and Computational Science (AMMCS) conference aims to promote interdisciplinary research and collaboration. The contributions in this volume cover the latest research in mathematical and computational sciences, modeling, and simulation as well as their applications in natural and social sciences, engineering and technology, industry, and finance. The 2013 conference, the second in a series of AMMCS meetings, was held August 2630 and organized in cooperation with AIMS and SIAM, with support from the Fields Institute in Toronto, and Wilfrid Laurier University. There were many young scientists at AMMCS-2013, both as presenters and as organizers. This proceedings contains refereed papers contributed by the participants of the AMMCS-2013 after the conference.This volume is suitable for researchers and graduate students, mathematicians and engineers, industrialists, and anyone who would like to delve into the interdisciplinary research of applied and computational mathematics and its areas of applications.

Hasan Shodiev

Papers

Interdisciplinary Topics in Applied Mathematics, Modeling and Computational Science