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Актуальность темы магистерской диссертации заключается в ее тесной связи с глобальной пандемией нового коронавируса, при этом особое внимание уделяется распространению эпидемии и борьбе с ней. Целью исследования является предоставление научной и научно обоснованной поддержки путем разработки моделей и симуляций политики профилактики эпидемий в сообществе. Основная цель диссертационной работы – оценить факторы, влияющие на эффективность стратегий профилактики и контроля, а также раскрыть ключевые факторы и механизмы передачи эпидемии. Посредством симуляционных экспериментов, анализа и сравнения результатов создается исчерпывающая информация, которая поможет лицам, принимающим решения, формулировать и осуществлять более эффективную политику профилактики эпидемий на уровне сообщества. Целью данного исследования является изучение влияния мобильности населения и планировки жилого массива на передачу заболеваний и эффективность стратегий профилактики эпидемий. Предметом исследования является разработка системы моделирования и симуляции политики предотвращения эпидемий на уровне сообщества с использованием модели SIR и сети «малого мира» в жилом сообществе с численностью населения 500 человек. Научная новизна данного исследования заключается в сочетании классической модели SIR с сетевой моделью маленького мира, а также в использовании агентной модели и программного обеспечения NetLogo для моделирования. Этот инновационный подход учитывает взаимодействие и связи между людьми в сообществе, позволяя более точно моделировать распространение болезней и оценивать эффекты различных стратегий профилактики эпидемий. Практическая значимость исследования заключается в обеспечении научной основы и руководства для лиц, принимающих решения. Путем проведения симуляционных экспериментов и анализа результатов исследование оптимизирует разработку и реализацию политики профилактики эпидемий на уровне сообщества, эффективно контролируя распространение заболеваний, защищая здоровье населения и решая проблемы, связанные с инфекционными заболеваниями. / The relevance of the master's thesis topic lies in its close connection to the global novel coronavirus pandemic, specifically focusing on the spread and control of the epidemic. The research aims to provide scientific and evidence-based support by developing community epidemic prevention policy models and simulations. The main goal of the thesis is to evaluate the factors influencing the effectiveness of prevention and control strategies and uncover the key factors and mechanisms of epidemic transmission. Through simulation experiments, analysis, and comparison of results, comprehensive information is generated to assist decision makers in formulating and implementing more effective community epidemic prevention policies. The objective of this study is to examine the influence of population mobility and the layout of a residential community on disease transmission and the effectiveness of epidemic prevention strategies. The subject of research focuses on developing a modeling and simulation framework for community epidemic prevention policies using the SIR model and small-world network in a residential community with a population size of 500 individuals. The scientific novelty of this study lies in the combination of the classic SIR model with the small-world network model, along with the introduction of the agent model and NetLogo software for simulation. This innovative approach considers the interactions and connections between individuals in a community, enabling a more accurate modeling of disease spread and evaluation of the effects of different epidemic prevention policies. The practical significance of the research lies in its provision of scientific basis and guidance to decision makers. By conducting simulation experiments and analyzing the results, the study optimizes the formulation and implementation of community epidemic prevention policies, effectively controlling the spread of diseases, protecting public health, and addressing the challenges posed by infectious diseases.

Les grands incendies de forêts sont responsables de la quasi-totalité de la surface brulée et contribuent, par les émissions de particules et de gaz à effet de serre qu’ils génèrent, au réchauffement climatique. Des observations satellitaires ont mis en évidence un comportement fractal que l’on attribue aux hétérogénéités locales (topographie, végétation, conditions météorologiques) rencontrées par ces feux lors de leur propagation. Le présent travail a été consacré au développement et à la validation d’un modèle hybride de propagation d’incendie, capable de reproduire ce comportement. Ce modèle est une extension du modèle original de réseau de « petit monde » où les phénomènes qui se produisent à l’échelle macroscopique, comme le rayonnement du front de flammes et l’inflammation pilotée de la strate végétale sont traités de façon déterministe. Pour décrire le rayonnement, nous avons utilisé un modèle de flamme solide couplé à une méthode de Monte Carlo. La validation a porté sur des configurations simples, mais aussi plus complexes, comme le rayonnement d’un front hétérogène de flammes ou celui d’une flamme d’éthanol. Un modèle d’inflammation a ensuite été élaboré et appliqué à des litières d’aiguilles de pin. Les paramètres du modèle ont été optimisés par un algorithme génétique, conduisant au meilleur accord avec les résultats expérimentaux, en termes de temps d‘inflammation et de perte de masses. Il a été montré que l’oxydation du résidu charbonneux joue un rôle prépondérant sur l’inflammation à bas flux. Le modèle de propagation de petit monde a été validé sur un brûlage dirigé et sur un feu historique, montrant un bon accord en termes de surface brûlée, de vitesse de propagation, de contours de feu, et de propriétés fractales. On a montré qu’il pouvait être utilisé pour le dimensionnement d’ouvrages de défense, comme les coupures de combustible, ou pour expliquer le comportement atypique du feu dans certaines situations (talweg, ruptures de pente, etc.). Son application a également permis d’optimiser le nombre et l’emplacement d’un réseau de capteurs déployés dans la végétation dans le but de localiser précisément et détecter précocement le départ d’un feu. / Most of the area burned by forest fires is attributable to the few fires that escape initial attack to become large. As a consequence large-scale fires produce a large amount of green-house gases and particles which contribute to the global warming. Heterogeneous conditions of weather, fuel, and topography are generally encountered during the propagation of large fires. This shapes irregular contours and fractal post-fire patterns, as revealed by satellite maps. Among existing wildfire spread models, stochastic models seem to be good candidates for studying the erratic behavior of large fires, due to the above-mentioned heterogeneous conditions. The model we developed is a variant of the so-called small-world network model. Flame radiation and fuel piloted ignition are taken into account in a deterministic way at the macroscopic scale. The radiative interaction domain of a burning cell is determined from Monte Carlo simulation using the solid flame model. Some cases are studied, ranging from relatively simple to more complex geometries like an irregular flame fronts or an ethanol pool fire. Then, a numerical model is developed to investigate the piloted ignition of litters composed of maritime pine needles. A genetic algorithm is used to locate a set of model parameters that provide optimal agreement between the model predictions and the experimental data in terms of ignition time and mass loss. The model results had shown the importance of char surface oxidation for heat fluxes close to the critical flux for ignition. Finally, the small-world network model was used to simulate fire patterns in heterogeneous landscapes. Model validation was achieved to an acceptable degree in terms of contours, burned area and fractal properties, through comparison of results with data from a small controlled bushfire experiment and a historical Mediterranean fire. Therefore, it has been proven to be a powerful tool in the sizing of fortifications as fuel break areas at the wildland urban interface or in the understanding of atypical behavior in particular configurations (talweg, slope breaking, etc.). It has also been used for the optimization of an in-situ sensor network whose purpose is to detect precociously and to locate precisely small fires, preventing them from spreading and burning out of control. Our objective was to determine the minimum number and placement of sensors deployed in the forest.

股票市場對投資者而言是以極大化自有資產為目的，因此如何辨別不同景氣區間對股市的影響為投資者感興趣的議題。傳統上，使用統計資料來幫助我們比較不同景氣區間之差異，然而股票市場之複雜、非線性及不可預測性也經常成為各統計資料失準的關鍵，因此，本篇論文以複雜網路作為分析股票市場之模型，並將各個股票表示成節點、股價變化之關聯性作為連結下，建立出複雜網路，藉此探討股市中的景氣差異。 　　在本研究中，先利用國發會制定的景氣對策信號，來幫助我們選取四段景氣區間，接著將台積電作為網路核心建構個股的相關網路。並以最小生成樹(Minimum Spanning Tree) 將複雜的股票網路簡單化。同時我們計算出各股相關網路之全域網路參數(Global Network Parameters)及區域網路參數(Regional Network Parameters)，以利我們討論兩段景氣好區間與兩段景氣差區間之差異。最後，我們將股市相關網路以分層樹(Hierarchical Tree)來表示，以了解網路分群的結果。 　　結果顯示，我們建構的個股相關網路符合小世界網路特性，在全域網路參數中，景氣好相關網路之常規化平均特徵路徑(Normalization Average Characteristic Path Length)及景氣差相關網路中之平均群聚係數(Average Clustering Coefficient)、平均特徵路徑(Average Characteristic Path Length)、常規化平均特徵路徑(Normalization Average Characteristic Path Length)有顯著差異。 在區域網路參數中，在景氣好相關網路中，被選為網路樞紐並有顯著差異之個股有台達化、宜進與華通，景氣差相關網路則有瑞利、日月光、矽品及萬企。在景氣好相關網路比較時，台積電的連結度與點效率皆具有顯著差異。

擴散權重影像與神經纖維追蹤可以用來探討腦區域之間的連結性，目前透過網路分析方式已經證實腦網路是有小世界的特性，最近也有研究不同受試者或者是病人之間的網路連結量測集中程度，但是擴散權重影像所運算出來的網路參數中間要經過很多步驟，這些中間步驟可能會影響到網路參數。所以有必要對於量測網路參數的受試者間變異性和重複量測重現性進行研究。本研究的目標是利用機率式神經纖維追蹤術量測大腦網路參數的重現性，探討三個會影響計算網路參數的重現性的變因，分別是，路徑定義方式、有無損耗正規化、受試者群體的網路連結篩選機制。變異係數定義（Coefficient of Variance, CV）為標準差除以平均值，分別計算二次量測之間的變異係數（CVwithin），以及受試者之間的變異係數（CVbetween），另外也計算組內相關係數（Intraclass correlation coefficient, ICC）。 掃描30受試者（15男，15女，年齡20~26）。每人掃描二次，並利用機率式神經纖維追蹤術計算網路連結，網路節點則是使用AAL標準模板定義的節點。若使用Wij = 1 – Pij定義長度，三項網路參數（區域效率、全域效率及損耗）重現性皆可接受（CVwithin<1.08%, CVwithin ≤ 10% and ICC > 0.7）。如果使用Wij=1/Pij定義長度，其損耗的CVwithin相較於Wij = 1 – Pij的大。如果長度的全距大，區域效率會不尋常地增加。如果二次掃描分別實施連結篩選，全域效率的CVwithin會較大。 本研究探討不同的網路建構方式將會影響測試內重現度，不同的研究團隊，縱使是採用相同的受試者群體和相同的儀器，所發表出來的網路參數可能會因為纖維追蹤術造成的誤差而不一致，因此實驗必須謹慎的分析資料以及闡述結果。 / Diffusion tensor imaging (DTI) with associate tractography can be used to access the connectivity of cortical regions in brain. Network analysis applied to connectivity matrix has demonstrated that brain has small world property. Recent studies also use network analysis to study the variation of concentricity among different group of subjects and patients. However the estimation of network metrics from DTI takes sophisticated processing steps. These intermediate steps may influence the estimation of network metric. It is therefore needed to investigate the potential variation of estimated network metrics using reproducibility test. The goal is to study the reproducibility of network properties derived from diffusion connectivity matrix constructed using probabilistic tractography. The effects of three factors on the reproducibility of network metrics estimation were studied. They are definition of path lengths of network matrix, path with and without cost normalization, the application of threshold to subjects groups. Coefficient of Variation (CV) defined as standard deviation divided by mean is used to test the intra-session (CVwithin) and inter subject (CVbetween) variability. Intra-class correlation coefficient (ICC) was also calculated. Images were acquired from 30 healthy participants (15 male, 15 female, aged 20-26 years). Each subject was scanned twice, denoted as N1 and N2. Probabilistic tractography was performed to mapping of cortico-cortical anatomical connections between regions defined from an anatomical atlas. All three of the tested network metrics (local efficiency, global efficiency and cost) were identified as acceptable (CVwithin < 1.08%, CVwithin ≤ 10% and ICC > 0.7) using path length defined as Wij = 1 – Pij. When the path length is defined as Wij = 1/Pij, cost showed higher CVwithin compared to Wij = 1 – Pij. It is unusual that local efficiency increase when the range of path length of edges is large. Global efficiency showed higher CVwithin as threshold is applied to N1 and N2 separately compared to both scans together. The present study revealed that different ways to construct cortical network had an effect on intra-session reproducibility. Our study also showed that despite evaluation of identical subjects using the same MRI system, variation of network metrics may be found by different research groups due to the potential errors from tractography. Replication of the experiment need to be carefully analyzed and interpreted.