Deux points de vue sont souvent opposés dans le cadre de la modélisation des systèmes complexes.D’un côté, une modélisation microscopique cherche à reproduire précisément le comportement des nombreuses entités qui composent le système, ce qui impose des temps de calculs prohibitifs pour le passage à l’échelle de système réels. À l’inverse, l’approche phénoménologique consiste à nous concentrer sur le comportement global du système. Ces modèles macroscopiques reposent sur des lois descriptives qui autorisent des simulations plus rapides mais impliquent l’introduction de paramètres qui peuvent être difficilement identifiables dans le contexte. Pour répondre à ce problème, nous proposons de combiner les différents points de vue de modélisation et d’utiliser des simulations microscopiques pour nourrir un modèle macroscopique incomplet.L’objectif est d’obtenir une simulation descriptive rapide tout en profitant de la précision d’un modèle microscopique. Pour cela, nous proposons une architecture logicielle qui s’appuie sur la technique de la co-simulation pour généraliser la démarche de simulation redondante d’échelles de modélisation hétérogènes.Nous distinguons deux stratégies de co-simulation qui permettent de piloter un modèle macroscopique en cours de simulation. La première consiste à estimer dynamiquement, et de manière explicite, de nouvelles valeurs pour un paramètre critique donné à l’aide d’un simulateur microscopique dédié. La seconde stratégie permet de déterminer implicitement un jeu de paramètres interdépendants sur la base d’une sortie commune des différents niveaux de description simulés. Nous appliquons nos travaux au problème concret du design de structures offshore pour des conditions polaires. Nous détaillons dans un premier temps l’implémentation d’un simulateur phénoménologique d’interactions glace-structure. Dans un second temps, nous illustrons l’intérêt et l’intégration de nos stratégies de co-simulation pour, d’une part améliorer la précision des simulations des phénomènes hydrodynamiques, et d’autre part guider un modèle de plus haut niveau à des fins de prototypage rapide. / There are usually two opposite points of view for the modelling of complex systems. First, microscopical models aim at reproducing precisely the behavior of each entity of the system. In general, their great number is a major obstacle both to simulate the model in a reasonable time and to identify global behaviors. By contrast, the phenomenological approach allows the construction of efficient models from a macroscopic point of view as a superposition of phenomena. A drawback is that we often have to set empirical parameters in these descriptive models. To respond to this problem, we want to make joint use of different levels of description and to use microscopical simulations to feed incomplete macroscopical models.We would then obtain enhanced descriptive simulations with the precision of microscopical models in this way. To this end, we propose a redundant multiscale architecture which is based on the co-simulation methodology in order to generalize the redundant multiscale approach. We suggest two specific co-simulation strategies to guide a macroscopical simulation.The first one consists in dynamically and explicitly estimating critical parameters of a macroscopical model thanks to a dedicated microscopical simulator The second one allows to implicitly determine a full set of dependant parameters on the basis of an output shared by the different levels of description. Then we apply our works to the effective problem of the design offshore structures for arctic conditions. We first describe the implementation of an ice-structure simulation tool by means of a phenomenological and multi-model approach. In a second phase, we show the benefits of our co-simulation strategies to improve the precision of hydrodynamics simulations on the one hand, and on the other to pilot a more macroscopical model for the purpose of fast prototyping.

Ces travaux s'intéressent à l'estimation de la fiabilité des évacuateurs de crues vannés. Le comportement fiabilistes de ces systèmes hydrauliques dépend à la fois d'événements aléatoires discrets, mais aussi de l'évolution d'une variable déterministe continue : ce sont des systèmes dynamiques hybrides. Pour ces systèmes, l'événement redouté est réalisé lorsque le niveau de la retenue atteint un seuil de sûreté. La démarche de fiabilité dynamique proposée dans cette thèse vise à prendre en compte l’information temporelle de la modélisation à la synthèse d'indicateurs fiabilistes pour l'aide à la décision et développe deux contributions :1) L'élaboration d'une base de connaissances dédiée à la description des évacuateurs de crue en termes de fiabilité dynamique. Chaque classe de composants est décrite par un automate stochastique hybride dont les états sont les différentes phases de son fonctionnement. 2) Le suivi de la simulation de Monte Carlo et le traitement et l'analyse des "histoires" (séquence de tous les états activés et des dates d'activation) obtenues en simulation pour construire des indicateurs de fiabilité classique (probabilité d'occurrence de l'évènement redouté, identification des coupes équivalentes prépondérantes, ...). Des indicateurs de fiabilité dynamique basés sur la classification des histoires en fonction des dates de défaillance des composants concernés et sur l'estimation de l'importance dynamique sont aussi proposés / Hydraulic systems are hybrid dynamic systems whose evolution is a combination between discrete stochastic events on the one hand and continuous deterministic phenomena on the other hand. The undesired event is achieved when the dam level reaches a security threshold. In the frame of gated spillways dynamic reliability, the proposed methodology takes into account the temporal information during modeling and synthesis of reliability indicators for decision support.The first contribution of this work is the development of a knowledge base to describe a class of systems. Each component is described by a stochastic hybrid automaton whose states are the different working modes.The second contribution is Monte Carlo simulation monitoring and treatment results. A story is the sequence of all activated states and activation dates during the algorithm passage for a simulation. The analysis of results provides classical reliability indicators, such as the time evolution of the undesired event probability or the identification of predominant equivalent cuts. Our predictive approach is based on stories classification depending on components failure dates, then dynamic importance is assessed

A evolução molecular, impulsionada pela Teoria Sintética da Evolução, tornou um assunto indispensável na compreensão da evolução da vida. O crescimento genômico, etapa responsável pelo maior potencial de armazenamento de informação e estabilidade, também foi submetido à indelével ação da seleção natural. Utilizando a metodologia dos ciclos de amplificação-mutação-seleção, tal como o SELEX (systematic evolution of ligands by exponential enrichment), que mimetizam a seleção natural, e ferramentas da Teoria de Informação, foram desenvolvidos e implementados programas para simular a evolução, considerando, além de outros, um parâmetro pouco explorado na literatura: a variação do tamanho do genoma. Foram estudados dois cenários distintos; no primeiro a seleção era dependente da busca exata de uma sequência pré-determinada (o filtro). Além disso, a entropia de Shannon considerada era referente ao alinhamento da molécula toda. Avaliando configurações simples desse modelo, foi possível desenvolver uma equação analítica que descreveu bem os resultados (para tamanho de genoma constante). No segundo cenário, foram exploradas a seleção não específica de uma sequência, o número máximo de bases constante, a entropia apenas das regiões de interesse e a presença de até cinco filtros de seleção. A entropia da molécula toda se mostrou pouco significativa (primeiro cenário), diferentemente da avaliada em apenas uma região. Foi possível observar que o crescimento do genoma foi pouco acentuado, predominando as moléculas menores, mesmo com grande quantidade de filtros, o que indica que o sistema está sob \"seleção por compressão\", sendo, pois, necessário atribuir explicitamente vantagens às moléculas mais complexas para poder haver aumento no crescimento médio. / Molecular Evolution, stimulated and supported by Evolution Synthetic Theory, became essential to understand evolution of life. Genomic growth was responsible to increase the capacity of storage information and to stability of the molecule; besides, it was also submitted to natural selection. Using amplification-mutation-selection methodology, such as SELEX (systematic evolution of ligands by exponential enrichment), and tools of Information Theory, it was developed computer program to simulate macromolecule evolution taking into account, besides other, a less study parameter in specialized journal: the genome size variation. It was studied two different scenarios. In the first one, selection was dependent of a specific sequence to be searched; moreover, Shannon entropy took into account all nucleotides of all molecules and it was studied with until two sequence target. It was possible develop an analytical equation to well describe simple settings of this model. In the second scenario, in another hand, selection depends on a specific sequence, but is not required to match the whole sequence. Also, to compute Shannon entropy it was taking into account only the least Hamming distance sequence of each molecule. It was studied until five sequence target in this scenario. Entropy was not significant in first scenario as it was in the second one. Size genome evolution shows the system were under compression selection, being necessary to get other advantage to become possible an increase in genome size.

Le changement climatique continue d'affecter la dynamique des paysages forestiers à grande échelle. Cependant, il demeure incertain comment ces changements affecteront les forêts futures et en particulier les épidémies des insectes ravageurs forestiers. Le changement climatique affecte l’émergence des insectes, en perturbant notamment la synchronisation phénologique entre les insectes herbivores et leurs arbres hôtes. De telles perturbations peuvent avoir des conséquences importantes sur le moment de l’émergence, l'étendue et la gravité de l'épidémie. Cette étude vise à comprendre comment le changement climatique pourrait affecter la synchronie phénologique entre la tordeuse des bourgeons de l'épinette (Choristoneura fumiferana), un défoliateur indigène, et ses espèces hôtes (Abies balsamea et Picea mariana) et comment cela pourrait affecter l'étendue des épidémies de la tordeuse des bourgeons de l'épinette dans la région de la Côte-Nord au Québec, Canada. Nous avons exploré les effets de deux facteurs expérimentaux sur l'étendue des épidémies à l'aide d'un modèle de simulation stochastique spatialement explicite à base d’agents (MBA): (1) la température quotidienne représentée selon deux niveaux d'augmentation (+2°C et +4°C) relative à une base de référence 2016 et (2) la variation de la phénologie des arbres hôtes correspondant aux différents niveaux d'incertitude (SD) concernant le moment du débourrement des bourgeons. Nous avons évalué comment ces facteurs ont affecté la variation de l'étendue des épidémies de la tordeuse des bourgeons de l'épinette et la complexité spatiale du patch épidémique sur un horizon de simulation de 20 ans. Nos résultats de simulation indiquent que la synchronisation phénologique arbres hôtes-insectes est fortement affectée par les changements de température, mais de manière non linéaire. Une augmentation de 2°C a permis de réduire l'étendue de l'épidémie en raison de la faible survie des larves, tandis qu'une augmentation de 4°C a entraîné une survie plus élevée des insectes et des épidémies plus importantes. Notre modèle peut aider à prévoir la dynamique future des forêts et faciliter l'élaboration de meilleures stratégies de gestion pour réduire l'effet des épidémies sur les paysages forestiers. / Climate change continues to affect forest landscape dynamics at a global scale. However, it remains uncertain how these changes will affect future forests and in particular outbreaks of forest insect pests. Climate change can affect outbreaking insects by disrupting phenological synchrony between herbivorous insects and their host trees. Such disruptions can have important consequences for outbreak timing, extent, and severity. This study aims to understand how climate change could affect the phenological synchrony between the spruce budworm (Choristoneura fumiferana), a native outbreaking defoliator, and its host trees (Abies balsamea and Picea mariana), and how this might affect the extent of spruce budworm outbreaks in the Côte-Nord region in Quebec, Canada. We explored the effects of two experimental factors on outbreak extent using a spatially explicit stochastic agent-based simulation model (ABM): (1) daily temperature represented as two levels of increase (+2°C and +4 °C) relative to a 2016 baseline, and (2) variation in host phenology represented as four different levels of uncertainty (SD) around the timing of budburst. We assessed how these factors affected variation in spruce budworm outbreak extent and outbreak patch spatial complexity over a 20-year simulation horizon. Our simulation results indicate that host trees-insect phenological synchrony is strongly affected by temperature changes, but in a non-linear way. An increase of 2°C was found to reduce outbreak extent due to poor larval survival, while an increase of 4°C resulted in higher insect survival and larger outbreaks. Our model can help to forecast future forest dynamics and facilitate the development of better management strategies to reduce the effect of outbreaks on forest landscapes.

This qualitative two-case study draws from the intersection of three theoretical perspectives: sociocultural theory, transactional theory, and complex systems theory. Guided by two research questions, this qualitative study explored the conditions two seventh grade English language arts teachers set for teaching expository writing and their implications. Deductive coding based on seven a priori patterns of powerful writing instruction (empathy, inquiry, dialogue, authenticity, apprenticeship, re-visioning, and deep content learning) revealed six conditions for teaching expository writing. Inductive pattern analysis of these conditions revealed three emergent themes: reinforcing structures, mediating transactions, and balancing tensions. These findings suggest that teaching expository writing is a complex system filled with dialectical relationships. As interdependent pairs, these relationships encompass the entire system of expository writing instruction, including the structural and transactional aspects of teaching and learning to write. The overlapping conditions and themes demonstrate that expository writing appears ambiguous at times; however, routine, yet responsive instruction, framed by apprenticeship and a balance of reading and writing activities designed to inspire self-discovery are fundamental to the process of teaching expository writing. The final chapter includes instructional implications and a discussion about the significance of setting conditions for generative literacy learning. Recommendations for future research include writing research based on complexity theory, connections between expository writing and empathy, and critical thinking relative to critical action.

Comment penser la relation entre les cultures scientifiques contemporaines et l’usage grandissant de l’ordinateur dans la production des savoirs ? Cette thèse se propose de donner une réponse à telle question à partir de l’analyse historique et sociologique d’un domaine scientifique fondé par le Santa Fe Institute (SFI) dans les années 1980 aux États-Unis : les « sciences des systèmes complexes » (SSC). Rendues célèbres par des publications grand-public, les SSC se répandent au cours des années 1990 et 2000 en Europe et dans d’autres pays du monde. Ce travail propose une histoire de la fondation de ce domaine en se concentrant sur le SFI et sur le Réseau National des Systèmes Complexes français. Avec un regard sociologique ancré dans les Science & Technology Studies et dans le courant pragmatiste, elle pose ensuite des questions sur le statut socio-épistémique de ce domaine, sur les modalités de l’administration de la preuve dans des savoirs fondés sur la simulation numérique et enfin sur les engagements épistémiques tenus par les spécialistes des systèmes complexes. Le matériau empirique – composé d’environ 200 entretiens, plusieurs milliers de pages d’archives et quelques visites de laboratoire – nous amène non seulement à mieux connaître ce champ de recherche – dont le langage est très répandu aujourd’hui, mais peu étudié par les historiens et les sociologues ; il nous porte aussi à questionner trois opinions courantes dans la littérature humaniste à propos des sciences numériques. À savoir : 1) l’ordinateur produit des connaissances de plus en plus interdisciplinaires, 2) il donne vie à des savoirs de type nouveau qui nécessitent une toute autre épistémologie pour être pensés et 3) il fait inévitablement advenir des visions du monde néolibérales. Or, cette thèse déconstruit ces trois formes de déterminisme technologique concernant les effets de l’ordinateur sur les pratiques scientifiques, en montrant d’abord que, dans les sciences computationnelles, les rapports interdisciplinaires ne se font pas sans effort ni pacifiquement ou sur pied d’égalité ; ensuite que les chercheurs et les chercheuses des SSC mobilisent des formes d’administration de la preuve déjà mises au point dans d’autres disciplines ; et enfin que les engagements épistémiques des scientifiques peuvent prendre une forme proche de la vision (néo)libérale, mais aussi des formes qui s’en éloignent ou qui s’y opposent. / How to think the relationship between contemporary scientific cultures and the rising usage of computer in the production of knowledge ? This thesis offers to give an answer to such a question, by analyzing historically and sociologically a scientific domain founded by the Santa Fe Institute (SFI) in the 1980s in the United States : the « complex systems sciences » (CSS). Become well-known thanks to popular books and articles, CSS have spread in Europe and in other countries of the world in the course of the 1990s and the 2000s. This work proposes a history of the foundation of this domain, by focussing on the SFI and on the French Complex Systems National Network. With a sociological take rooted into Science & Technology Studies and into pragmatism, it then asks some questions about the socio-epistemic status of such a domain, about the modalities of production of evidence as they are employed in the context of digital simulation and, finally, about the epistemic engagements hold by complexity specialists. Empirical material – composed by circa 200 interviews, several thousands archival pages and a small number of laboratory visits – allows us not only to improve knowledge about this field – whose language is very common today, but little studied by historians and sociologists ; it also brings us to question three current opinions in the human and social sciences literature regarding digital sciences. That is : 1) that the computer produces more and more interdisciplinary knowledge, 2) that it gives birth to a new type of knowledge which needs an entirely new epistemology to be well understood and 3) that it inevitably brings about neoliberal visions of the world. Now, this thesis deconstructs these three forms of technological determinism concerning the effects of computer on scientific practices, by showing firstly that, in digital sciences, the interdisciplinary collaborations are not made without any effort and in a symetrical and pacific way ; secondly, that CSS’ researchers mobilize a kind of evidence production techniques which are well known in other disciplines ; and, thirdly, that scientists’ epistemic engagements can take (neo)liberal forms, but also other forms that depart from neoliberalism or that stand against it.

This dissertation is devoted to study of complex systems in human physiology particularly heartbeats and brain dynamics. We have studied the dynamics of heartbeats that has been a subject of investigation of two independent groups. The first group emphasized the multifractal nature of the heartbeat dynamics of healthy subjects, whereas the second group had established a close connection between healthy subjects and the occurrence of crucial events. We have analyzed the same set of data and established that in fact the heartbeats are characterized by the occurrence of crucial and Poisson events. An increase in the percentage of crucial events makes the multifractal spectrum broader, thereby bridging the results of the former group with the results of the latter group. The crucial events are characterized by a power index that signals the occurrence of 1/f noise for complex systems in the best physiological condition. These results led us to focus our analysis on the statistical properties of crucial events. We have adopted the same statistical analysis to study the statistical properties of the heartbeat dynamics of subjects practicing meditation. The heartbeats of people doing meditation are known to produce coherent fluctuations. In addition to this effect, we made the surprising discovery that meditation makes the heartbeat depart from the ideal condition of 1/f noise. We also discussed how to combine the wave-like nature of the dynamics of the brain with the existence of crucial events that are responsible for the 1/f noise. We showed that the anomalous scaling generated by the crucial events could be established by means of a direct analysis of raw data. The efficiency of the direct analysis procedure is made possible by the fact that periodicity and crucial events is the product of a spontaneous process of self-organization. We argue that the results of this study can be used to shed light into the nature of this process of self-organization.

Many IT-systems are when created not designed to be flexible and dynamic resulting in old and complex systems hard to maintain. Systems usually build their functionality and capability on the data contained in their databases. The database underlines such system, and when data do not correspond between different and synchronizing systems, it is a troublesome debugging process. This is because systems are complex and the software architecture is not always easy to understand. Due to increasing complexity in systems over time, making systems harder to debug and understand, there is a need for a system that decreases debugging costs. Furthermore, result in better transaction costs. This study proposes a system based on blockchain technology to accomplish this.   An ERP system based on blockchain with encrypted transactions was constructed to determine if the proposed system can contribute in better transaction costs. A case study at multiple IT-companies and comparison to an existing ERP system module validated the system. A successful simulation showed that multiple parts could read and append data to an immutable storage system for one truth of data. By all counts, and with proven results, the constructed blockchain solution based on encrypted transactions for an ERP system can reduce debugging costs.   It is also shown that a centralized database structure where external and internal systems can get one truth of data, decreases transaction costs. However, it is the decision makers in companies that need to be convinced for the constructed system to be implemented. A problem is also when modifications to the object type, then historical transactions cannot be changed in an immutable storage solution. Blockchain is still a new technology, and the knowledge of the technology and the evolution of the system determines if the proposed software architecture will result in better transaction costs.

La presente investigación abordó, inicialmente, la teoría de la complejidad como base de entendimiento de los sistemas adaptativos complejos y la aplicación de algunas variantes de esta teoría, como la teoría fractal en el campo de la gestión estratégica en las organizaciones. Para lograr un mejor entendimiento de estos enfoques se dividió el estudio en dos etapas. La primera explicó el desarrollo y evolución de las teorías del caos y la complejidad en la administración y la segunda presentó el paradigma de la dinamicidad y la aplicación del enfoque fractal en el ámbito de la gestión empresarial, así como su estudio. El desarrollo constante de la ciencia y la tecnología aplicada a la gestión y los cambios de paradigmas presentados a lo largo de su evolución, desde la Revolución Industrial a la era del conocimiento, han llevado a la aplicación de diversas teorías científicas cuya aplicación inicial distaba de centrarse en la gestión empresarial y que, sin embargo, ha contribuido a un mejor entendimiento de esta. Tal es el caso de la teoría de la fractalidad y su origen en las ciencias abstractas producto del paso de la geometría clásica a la geometría fractal. En el caso de este estudio, se mostró el aporte de la teoría de la complejidad para facilitar la comprensión de los fenómenos organizacionales, traduciéndose su aplicación al desarrollo de figuras como la “fábrica fractal- organización fractal”, como soporte de los debates de la ciencia y la tecnología de la administración o su utilización como base para el diseño y construcción de los sistemas, subsistemas, modelos, métodos y procedimientos. También se mostró la evolución de los principales aportes teóricos respecto a la teoría de la complejidad, sus bases, definiciones, principios y aplicaciones y, por último, el comportamiento como sistemas complejos expuestos en las organizaciones. / This research initially presents the theory of complexity as a basis of understanding of complex adaptive systems, and the application of some variants of this theory such as fractal theory, in the field of strategic management in organizations. To achieve a better understanding of these approaches, the study has been divided into two stages: 1) Development and evolution of chaos and complexity in administration; 2) The Paradigm of dynamicity and application of the fractal approach in the field of business management and its study. The constant development of science and technology applied to the management and paradigm shifts presented throughout its evolution from the industrial revolution to the age of knowledge has led to the application of various scientific theories whose initial application was far from focusing on business management and which, however, has contributed to a better understanding of it. This is the case of the theory of fractality whose origin in abstract sciences resulting from the transition from classical geometry to fractal geometry. The contribution of the theory of complexity to facilitate the understanding of organizational phenomena will be shown; translating its application in the development of figures such as the “fractal factory- fractal organization” to support the debates of the science and technology of administration or its use as support for the design and construction of systems, subsystems, models, methods and procedures. It shows the evolution of the main theoretical contributions regarding the theory complexity, its bases or definitions, principles and applications and, finally, behavior as complex systems exposed in organizations. / Trabajo de Suficiencia Profesional

Abstract in English / Mathematical modeling of the spread of infectious diseases in a population has always been recognized as a powerful tool that can help decision-makers understand how a disease evolves over time. With the evolution of science and humanity, it has become evident that Mathematical models are too simplistic and have some limitations in modeling environmental phenomena, such as the spread of epidemics in a population, when they are applied without combining them with other sciences. In understanding the dynamics of epidemics in a population, the weakness of these models is their difficulty in grasping the complexity inherent in the spread of diseases in real life because, life is supported by human interactions and behaviors that are understood through networks of social and spatial interactions. Modeling the spread of epidemics which takes this reality into account requires the implementation of new tools to refine the results already obtained by mathematical models. The aim of this thesis is to explore and attempt to extend new developments in mathematical modeling of the spread of infectious diseases by proposing new tools based on mathematical models from differential equations and agent-based models from intelligent agents derived from artificial intelligence. To achieve this objective, the study starts from a comparative study of two ways of modeling and simulation of the spread of infectious diseases in the population, namely mathematical modeling and agent-based modeling with a concrete case study of the spread of tuberculosis based on data from the Democratic Republic of the Congo (DRC). Then comes a coupling study of these two approaches in a single model and its implementation in a multi-scale environment. The results show that the coupled model is more realistic compared to mathematical models generally implemented in the literature. Four case studies are presented in this thesis. Mathematical modeling based on differential equations is used in the first and second cases. The third case is based on intelligent agents model while the last one is based on the coupling of mathematical models and agent-based models. Application of implemented models to the spread of tuberculosis reveals that detection of people with latent tuberculosis and their treatment are among the actions to be taken into account in addition to those currently carried out by the Congolese health system. The models assert that the current TB situation in DRC remains endemic and that the necessary measures need to be taken to reduce the burden of TB, especially to control it, through the tuberculosis elimination strategy and its elimination in the future in accordance with the Sustainable Development Goals. Our hybrid model benefiting from the advantages of EBM and ABM confirms that taking the individual into account as a fully-fledged entity and managing their behavior gives the microscopic aspect of the model set up and brings it closer as much as possible to reality. Mathematical management of the spread of the disease in cities gives a macroscopic aspect to the model. Numerical simulations of this last model on a multi-scale virtual environment affirm that the mobility of individuals from city to city has a significant impact on the spread of tuberculosis in the population. Controlling the rate of population mobility from one city to another is one of the most important measures for large-scale disease control. This model therefore draws its richness from this dynamic at two different scales (two time scales modeling approaches: at the microscopic/individual level (ABM) and macroscopic/city level (ODE)), which gives the emergence of the model at the global level. As a result, it seems that the coupling of mathematical models to agent-based models should be applied when the dynamics of the complex system under consideration is at different scales. Based on our research results, it seems that the choice of an approach must depend on how the modeler would like to achieve the expected results. Mathematical models remain essential due to their analytical and synthetic aspect, but their coupling with intelligent agent-based models makes it possible to refine known results and thus reflect the reality of real life, because the resulting model integrate interactions of individuals and their heterogeneous behaviors that are necessary for understanding the spread of infectious diseases in the population that only mathematical models based on differential equations can not capture. / Mathematical Sciences / Ph D. (Applied Mathematics)