The views expressed in this report are those of the authors and do not reflect the official policy or position of the Department of Defense or U.S. Government. ; This report contains project summaries of the research projects in the Department of Applied Mathematics. A list ofrecent publications is also included, which consists of conference presentations and publications, books, contributions to books, published journal papers, and technical reports. Thesis abstracts of students advised by faculty in the Department are also included.
In this paper we model the role of a government of a large population as a mean field optimal control problem. Such control problems are constrained by a PDE of continuity-type, governing the dynamics of the probability distribution of the agent population. We show the existence of mean field optimal controls both in the stochastic and deterministic setting. We derive rigorously the first order optimality conditions useful for numerical computation of mean field optimal controls. We introduce a novel approximating hierarchy of sub-optimal controls based on a Boltzmann approach, whose computation requires a very moderate numerical complexity with respect to the one of the optimal control. We provide numerical experiments for models in opinion formation comparing the behavior of the control hierarchy. ; ERC advanced Grant 668998 (OCLOC) ; (VLID)2523620
It is important to monitor and assess the physiological strain of individuals working in hot environments to avoid heat illness and performance degradation. The body core temperature (Tc) is a reliable indicator of thermal work strain. However, measuring Tc is invasive and often inconvenient and impractical for real-time monitoring of workers in high heat strain environments. Seeking a better solution, the main aim of the present study was to investigate the Kalman filter method to enable the estimation of heat strain from non-invasive measurements (heart rate (HR) and chest skin temperature (ST)) obtained 'online' via wearable body sensors. In particular, we developed two Kalman filter models. First, an extended Kalman filter (EFK) was implemented in a cubic state space modelling framework (HR versus Tc) with a stage-wise, autoregressive exogenous model (incorporating HR and ST) as the time update model. Under the second model, the online Kalman filter (OFK) approach builds up the time update equation depending only on the initial value of Tc and the latest value of the exogenous variables. Both models were trained and validated using data from laboratory- and outfield-based heat strain profiling studies in which subjects performed a high intensity military foot march. While both the EKF and OKF models provided satisfactory estimates of Tc, the results showed an overall superior performance of the OKF model (overall root mean square error, RMSE = 0.31°C) compared to the EKF model (RMSE = 0.45°C).
The Government of Montenegro nationalized 2030 Agenda on Sustainable Development by adopting the National Strategy for Sustainable Development (NSSD) in 2016, together with a corresponding Action Plan for its implementation. The NSSD is umbrella, horizontal and long-term development strategy of Montenegro that relates not only to environment and economics, but also to human resources, valuable social capital that should ensure prosperous development, recommendations for establishing the framework of financing and governance for sustainable development. The NSSD represents strategic framework for the transposition of the UN sustainable development goals (SDGs) and its indicators into national context. The NSSD Action plan, divided into 6 thematic areas with 30 strategic goals of sustainable development of Montenegro and their 102 measures and 601 sub-measures, represents very complex mechanism for monitoring and reporting about achieving the UN sustainable development goals (SDGs) in Montenegro. Hence, measuring progress in the NSSD implementation is the focus of this research. Effective measuring of the progress in the NSSD implementation could be achieved under the following preconditions: developed coordination mechanism for reporting, methodology of designing indicators, IT support for data collection and reporting, and strengthening of inter-linkages between the EU agenda and UN 2030 Agenda.
The study aims to develop a mathematical model that can explain the effect of national defense on economic growth from various works of literature and developments. The overall impact of military spending on growth can be analyzed by dividing the economy into sectors. We wish to demonstrate the formation of a general mathematical model. The model building is based on the neoclassical production function approach developed by Feder and Deninson. The source of Deninson's growth model uses a supply-side description of changes in aggregate output. It describes aggregate growth in terms of changes in capital and labor. The resulting aggregate growth equation shows the combination of externality and productivity effects.
Bibliography: p. 221-233. ; This thesis is concerned with the problem of how to effectively address the complex issue of poverty in the context of limited resources. Poverty is a multi-dimensional problem that affects different communities in different ways. In order to use the available resources in such a way as to most effectively tackle poverty, a means of measuring and benchmarking outcomes as well as evaluating choices of intervention is required. However, smart methods of allocating scarce resources are not in themselves sufficient, if they are not regarded as legitimate by the participants of the process. The imperative of legitimacy demands that we both address the issue of quantitative rigour in resource allocation methods and that we look beyond and explore too the mechanics of effective participatory methods. The approach of developmental local government adopted by the new South African government post apartheid, places this complex problem in the sphere of local government. The primary tool available to local administrators for addressing poverty, amongst other issues, is that of integrated development planning. This process draws together the stakeholders who fall broadly into three groups of participants, namely the communities that live in the municipality, the municipal officials and the elected politicians, and allocates them the task of identifying and prioritising community and municipal issues, and developing appropriate plans to address them. This package of plans or projects is compiled into a municipal budget that targets priority issues for the area, in an integrated and coherent manner. This thesis proposes a new method for tackling this specific group decision making problem, namely Participative Multi-Criteria Decision Analysis. This method was developed in an action research setting in the municipality of Stellenbosch, South Africa, and applied to their 2001/2002 integrated development planning process. The method is grounded in the principles of participative action research in which the participation of all interested and affected patties is valued, and in which there is a commitment to work for change to the fundamental fabric of knowledge and power, leading to a greater empowerment of ordinary people. This participative framework strengthens the legitimacy of the approach by promoting a stronger sense of ownership of process and products by all participants. Within this participative framework, tools of multi-criteria decision analysis are used to support the decision making process by quantifying difficult decisions that need to be addressed. It is the synthesis of these two approaches (action research and multi-criteria decision analysis) that provides both legitimacy and rigour for this method within a highly contested and complex public decision making arena. In the spirit of action research, the method is developed by drawing on theory about developmental local government and poverty, as well as multi-criteria decision analysis. In the process of the research, over forty community workshops were held throughout the Stellenbosch municipal area. Community representatives identified and prioritised the issues of their areas; and in conjunction with municipal officials, developed and evaluated projects in response to these issues. These evaluations assisted the local council to compile the final budget for 2001/2002 in Stellenbosch. In this process, the communities (divided into nine development areas) also developed community development measurement scales which formed the basis for the project evaluations and an ongoing basis for monitoring progress in these communities. It unfolded during the course of this research that a fundamental component of this proposed participative public decision making approach is the role of a central co-ordinating person, not connected to or answerable to any of the constituent groups, who can manage the process of participation, promote an awareness of effective and informative data; ensure the appropriate use of quantification tools and maintain a focus on sustainable poverty alleviation. The method developed in this thesis was successfully applied to the process of identifying, prioritising and making choices about community issues in Stellenbosch, under conditions of significant polarisation of the constituent decision making groups, conclude that this method can be used to implement key aspects of integrated development planning as it addresses the issues of legitimacy and rigour in participative public decision making.
The dissertation studies the influence of military mass mobilization on the top income shares in the society, and therefore on inequality levels, in the United States and Europe over the last one hundred years. More precisely, one of the main results in this work shows that when the individual external fighting effort in a conflict with another country is high, thus during military mass mobilization, then the internal fighting efforts for appropriation or rent seeking between rich and the rest of the society decrease, and in turn the inequality levels inside the society are lower. On the contrary, during periods of professional army, thus when the individual external fighting effort is low, then inside the society the internal fighting efforts for appropriation or rent seeking between rich and the rest of the society increase, and in turn the inequality levels increase. These implications are shown using models of inequality and conflict that are based on contest success functions. The dissertation also includes statistical evidence in support of the main hypothesis of this work. Several statistical tests are presented that show that periods of conscription are correlated with low levels of the top 1 and top 10 percent income shares using data over the last one hundred years. The dissertation ends with an analysis of the cases considered from North America and Western Europe. A comparative analysis and difference in difference method is employed to distinguish between different periods and systems.
PUBLISHED ; Motivated by the notorious di culties in determining the rst quantum corrections to the spectrum of short strings in AdS 5 S 5 from rst principles, we study closed bosonic strings in this background employing a static gauge. In this gauge the world-sheet Hamiltonian density is constant along the extension of the string and directly proportional to the square of the spacetime energy. We quantize this sys- tem in a minisuperspace approach, in which we consider only a single AdS 5 string mode excitation next to an arbitrary particle like zero-mode contribution in the full AdS 5 S 5 background. We determine the quantum spectrum using this method to the next-to-next-to-leading order in the large 't Hooft coupling expansion. We ar- gue for an ordering prescription which should arise from supersymmetrization and indeed recover the integrability based predictions for the spectrum of the lightest excitation, dual to the Konishi eld scaling dimensions. The higher excitations fail to agree, but this is shown to be a consequence of the string mode truncation employed. Despite this simple setup, our system reveals intriguing features, such as a close connection to particles in AdS 6 , classical integrability and preservation of the isometries of AdS 5 S 5 at the quantum level ; We thank Harald Dorn, Chrysostomos Kalousios, Thomas Klose, Joe Minahan, Jonas Pollok and Tristan McLoughlin for useful discussions. G.J. thanks the Humboldt University Berlin and the Max-Planck Institute for Gravitational Physics (Albert-Einstein-Institute) in Potsdam for warm hospitality. M.H. thanks Nordita in Stockholm for kind hospitality. The research leading to these results has received funding from the Volkswagen-Foundation, the International Max Planck Research School for Geometric Analysis, Gravitation and String Theory, and the People Programme (Marie Curie Actions) of the European Union's Seventh Framework Programme FP7/2007-2013/ under REA Grant Agreement No 317089. S.F. is supported by a DFG grant in the framework of the SFB 647 Raum - Zeit - Materie. Analytische und Geometrische Strukturen and by the Science Foundation Ireland under Grant 09/RFP/PHY2142.
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S/N 003-003-02373-6. ; "Issued October 1981." ; "National Engineering Laboratory, National Bureau of Standards. ; Includes bibliographical references. ; Mode of access: Internet.
This study discusses the behavior analysis model of the Susceptible-Infected-Recovered (SIR) epidemic of the spread of measles based on age structure. The total population is grouped into four age groups, the first age group (0-4 years), the second age group (5-9 years), the third age group (10-14 years), and the fourth age group (> 15 years). The steps in analyzing the behavior of the model can be done by determining the equilibrium point, basic reproduction number, and stability analysis at the equilibrium point. In the measles distribution model with four age groups, where each age group has no interaction with other age groups, sixteen equilibrium points are obtained, which are a combination of the disease-free equilibrium and endemic equilibrium points separately. The stability properties of each equilibrium point can be determined by the value of the basic reproduction number (R_0) which is the product of the basic reproduction number of each age group. The measles disease-free equilibrium point will be locally asymptotically stable when R_01. This research contributes to providing information to both the government and the public
The specific connectivity of a neuronal network is reflected in the dynamics of the signals recorded on its nodes. The analysis of how the activity in one node predicts the behaviour of another gives the directionality in their relationship. However, each node is composed of many different elements which define the properties of the links. For instance, excitatory and inhibitory neuronal subtypes determine the functionality of the connection. Classic indexes such as the Granger causality (GC) quantifies these interactions, but they do not infer into the mechanism behind them. Here, we introduce an extension of the well-known GC that analyses the correlation associated to the specific influence that a transmitter node has over the receiver. This way, the G-causal link has a positive or negative effect if the predicted activity follows directly or inversely, respectively, the dynamics of the sender. The method is validated in a neuronal population model, testing the paradigm that excitatory and inhibitory neurons have a differential effect in the connectivity. Our approach correctly infers the positive or negative coupling produced by different types of neurons. Our results suggest that the proposed approach provides additional information on the characterization of G-causal connections, which is potentially relevant when it comes to understanding interactions in the brain circuits. ; This work was supported by the Spanish Ministry of Economy and Competitiveness (Project Nos. TEC2016–80063-C3-3-R, TEC2016-80063-C3-2-R, and BFU2015-64380-C2-1-R), the European Union through the Horizon 2020 programme (Grant Agreement No. 668863, SyBil-AA), the Spanish State Research Agency (SEV- 2013-0317), the Brazilian Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (Grant Nos. 88881.120309/2016-01 and 88881.068077/2014-01), the Brazilian Conselho Nacional de Desenvolvimento Cientìfico e Tecnològico (Grant No. 432429/2016-6) and the US National Science Foundation (grant NSF IIS-1515022). V.J.L. was supported by a predoctoral fellowship La Caixa-Severo Ochoa from Obra Social La Caixa. SC and CM acknowledge the Spanish State Research Agency, through the Severo Ochoa and María de Maeztu Program for Centers and Units of Excellence in R&D (SEV-2017-0723 and MDM-2017-0711, respectively).
Population composition in a country by sex and age-structure often illustrated through the Population Pyramid. In this study, an age-structure model will be constructed to predict the population pyramid shape in the coming year. It is assumed that changes in population are affected by natality and mortality number in each age group, ignoring migration rates. The proposed age structure model formulated as a first-order partial differential equation with the non-negative initial condition. The boundary condition is given by the number of births which is proportional to the number of women at childbearing age. Then, this age structure model implemented utilizing United Nations Data to predict population pyramids of Indonesia, Brazil, Japan, the USA, and Russia. The population pyramid prediction of the five countries shows different characteristics, according to whether it is a developing or developed country. The results of this study indicate that the age structure model can be used to predict the composition of the population in a country in the next few years. Indonesia is predicted to be the highest populated country in 2066, compared to the other four countries. This result can be used as a reference for the government to plan policies and strategies according to age groups to control population explosion in the future.
The distribution of mutational fitness effects (DMFE) is crucial to the evolutionary fate of quasispecies. In this article we analyze the effect of the DMFE on the dynamics of a large quasispecies by means of a phenotypic version of the classic Eigen's model that incorporates beneficial, neutral, deleterious, and lethal mutations. By parameterizing the model with available experimental data on the DMFE of Vesicular stomatitis virus (VSV) and Tobacco etch virus (TEV), we found that increasing mutation does not totally push the entire viral quasispecies towards deleterious or lethal regions of the phenotypic sequence space. The probability of finding regions in the parameter space of the general model that results in a quasispecies only composed by lethal phenotypes is extremely small at equilibrium and in transient times. The implications of our findings can be extended to other scenarios, such as lethal mutagenesis or genomically unstable cancer, where increased mutagenesis has been suggested as a potential therapy. ; This work was partially funded by the Botín Foundation (JS, RVS), by the Spanish Secretaria de Estado de Investigación, Desarrollo e Innovación grants MTM2010-16425 (CS, RM) and BFU2012-30805 (SFE), by grant 2009-SGR-67 from the Catalan government (CS, RM), by grant NSF PHY05-51164 (JS, SFE), and by the Santa Fe Institute (RVS, SFE).
