Sharif Digital Repository

Natural selection in structured populations is considered a crucial subject in evolutionary and population genetics. There is no explicit relationship between discrete-time stochastic models such as the Moran process and continuous-time models such as the Fisher-Kolmogorov equation. However, under specific conditions and within the limits of natural selection and weak selection, a connection can be found between these two models. To gain a better understanding of the specific relationship between these two models, we obtain partial differential equations for the spatiotemporal dynamics of natural selection by extending the birthdeath and death-birth processes of the Moran process to a... 

Due to the world's reliance on fossil fuels, the climate change situation has become more severe and has presented major challenges. One of the most promising growth avenues to address these issues in the medium to long term is widespread electrification based on renewable sources. However, this is only feasible if the energy infrastructure can support distributed and renewable energy sources without affecting the performance of the power grid. A grid is also necessary for energy systems in order to connect various technologies and guarantee proper integration of supply and demand for maximum efficiency. A novel idea called Energy Internet (EI) has been put forth to accomplish these goals,... 

This thesis abstract addresses the use of process mining techniques when event data is stored at varying levels of granularity. While most techniques assume that events have the same level of granularity, real data is often stored differently. Pre-processing techniques allow for appropriate summarization of the data, which simplifies the output while retaining important process details. The goal is to ensure an interpretable output for stakeholders and different business teams without losing critical process points. However, adding new data as a feature to the dataset can be expensive, and at times, infeasible. Therefore, existing data is the only solution. To overcome this challenge, this... 

There are a variety of notions of curvature that one could define on graphs. In this thesis, we introduce one of them which is called the ”Combinatorial Curvature”. This curvature is defined on graphs embedded on a surface, however as the name suggests,the combinatorial curvature of a vertex depends only on the combinatorial properties of the graph, and not on the geometric properties of the surface on which the graph is embedded. More precisely, the combinatorial curvature of a vertex is a function of the degree of the vertex and the faces which are incident to that vertex.In the main part of this thesis, we have tried to collect the most important results about the combinatorial curvature.... 

A set S of vertices in a graph G is a double total dominating set if every vertex of G has at least two neighbors in S. Minimum cardinality of such S is denoted by γ×2,t(G). Henning and Yeo in the article which was published in 2010 proved that ifGis a 3regular graph and is not the Heawood graph, then γ×2,t(G) ≤ 5 6n (n is the order of the graph). They also conjectured that if G is a connected graph (not the Heawood graph) and δ(G) ≥ 3, then γ×2,t(G) ≤ 5 6n. Jafari and Alipour in the article which was published in 2017 proved that for all graphs with δ(G) ≥ 4, γ×2,t(G) ≤ 4 5n. In this thesis, we give an upper bound by using Turàn theorem in the extremal graph theory for γ×2,t(G), and also... 

Environmental heterogeneity, or environmental interactions in evolutionary graphs can drastically change the population dynamics compared to the uniform environment. Such heterogeneity can be imposed in different ways. In this study we choose periodic pattern for the environmental heterogeneity with different values for amplitude and period. Imposing periodic heterogeneity on cyclic graphs, we studied the fixation probability and time. We use birth-death Moran model as the update rule. We observe that with such heterogeneity, an advantageous type in the uniform environment can turn into deleterious in the presence of heterogeneity. Also, the opposite way can happen. The results show that... 

The primary goal of this thesis is to study the chromatic number of Kneser hypergraphs that made a connection between topology and combinatorics.We mention simplicial complexes, Fan’s and Tuckers lemma’s, nerve’s lemma,and topological Tverberg theorem as some tools for investigating the chromatic number of these graphs. Many of the concepts and propositions expressed in this paper, such as those mentioned above, are topological propositions about combinatorial objects, and vice versa. Using such connections, you can use the tools of each branch in another and use their combination  

The ratio of the two first non-trivial Dirichlet eigenvalues is the subject of the Payne-Polya-Weinburger Conjecture and Inequality. The PPW Conjecture was proven by M. Ashbaugh and R. Benguria. Ashbaugh and Benguria later proved a similar result for domains on the n-sphere. On the other hand, discrete counterparts of universal inequalities from (continuous) have been studied in the graph theory setting. This thesis surveys results related to the PPW inequality on graphs  

This thesis presents a new approach to design structural output feedback controllers with stabilization and pole-placement at desired points on the S plane. It is assumed that the linear time-invariant system has no fixed mode corresponding to the specified control structure, outside the desired region of the closed-loop poles, such that the structural controller design problem is theoretically feasible. To this end, the structural output controller design problem is first transformed into a structurally equivalent problem based on the solution of a set of discrete linear programs. Then, by using the resultant structure, a new method is proposed for designing static and dynamic control loops... 

One of the crucial matters in the area of Supply Chain Management is the ability of a supply chain to act and react under different circumstances. A helpful tool to understand the supply chain is simulation modeling. With the help of simulation modeling, we can provide the opportunity for the agents in a model to perform based on the defined environment.In the current research, a complete literature review is performed on the topics of supply chain planning and various distribution models and algorithms. With the focus on the vaccine as a critical item, we propose a model to distribute vaccines based on the degree of agents, and we realize that vaccine distribution, while facing huge demand... 

In this thesis, the notion of nowhere-zero flow on graphs in defined with values is an Abelian group. It is shown that the existence of nowhere-zero flow with values in H depends on only the cardinal of H. Also the existence of nowhere-zero flowwith values on Zk is equivalent to the existence of the nowhere-zero flow with values in the set 1,2,...,k-1 on group Z.It is a easily seen that the nowhere zero flow on the graph with bridge doesn’t exist. Also has been proved any graph with no bridge has nowhere-zero 6 flow.Concidentally, the existence of nowhere-zero 5 flow for graphs with no bridge isstill an open problem.In 3-flow case, recently it is shown that any 8-edge connected graph has... 

In this thesis, a new method is proposed to find the class of stabilizing control structures for interconnected systems from a graphtheoretic
perspective. The objective is to classify all possible control structures (static or dynamic), capable of stabilizing the closedloop system. The method can be formulated by using the characteristics of fixed modes of the system for arbitrary control structures.To this end, first, a method is proposed based on solving a set of discrete linear programming to determine whether a system is stabilizable via a decentralized controller. Subsequently, by solving a set of discrete linear feasibility problems, all possible stabilizing controller structures... 

A city is a complex system which consists of many interactive sub-systems. It is affected by diverse factors including governmental land policies, population growth, market behavior and transportation infrastructure. Traffic congestion is one of the most critical challenges of transport infrastructure which became everyday occurrence in the last decades. The traffic planners and traffic engineers have faced real obstacles due to the growth of motorization and the resulted external consequences. Furthermore the capacity of the traffic networks saturates during rush hours. Generally, network transport performance can be improved in two ways, optimizing network structure (Hard Strategy) or... 

The problem of quadrotors formation flying via optimal approach is investigated using the idea of cooperative and multi-level control. In this respect, a low level optimal control formulation of quadrotors is formulated for stability and tracking where the required tracking commands are generated via the high level controller over a simpler translational dynamics of quads. The idea of multi-level controllers enables one to develop formation keeping controls for complex dynamics systems, where varying agents in terms of dynamics and platform could be utilized. Due to inherent difficulties in implementing acceleration commands emanated out of the high level controller, an inverse dynamic... 

According to the importance of obstacle and collision avoidance for multiple Autonomous underwater vehicle (AUV) that are synchronized for starting the path following, in this study the coordination path following controller for a group of underactuated underwater vehicle with considering of obstacle and collision avoidance presented. The proposed control method is based on graph theory and back stepping with modeling of obstacle using limit cycle. At first, for controller design the back stepping method for path following of one AUV is used. Then the designed controller using of principles of graph theory, has been extended for multiple AUV and as the result multiple AUV is synchronized and... 

Supply networks are often faced with disruptions that hampered the flow of goods, and have brought irreparable consequences. In this thesis, we evaluate the robustness of three echelon scale free supply chain networks consist of manufacturers, distributers and retailers from the perspective of complex network topologies and investigate the effect of assortativity and disassortativity level on the robustness of scale free supply networks. For this purpose, we use the degree preserving rewiring approach in order to increase and decrease assortativity and disassortativity of scale free networks. Then we use metrics in order to investigate the robustness and flexibility of supply networks and... 

Controlling dynamical systems is an important area of research, having many applications in related practical fields. One class of dynamical systems which have obtained ever-growing importance in recent years are networked dynamical systems, in which dynamic behavior is observed on nodes interacting in a networked setting. This is mainly due to the rise of complex networks, e.g. social networks, as an important and powerful method of capturing dynamic behavior that exists in different systems. One important aspect of such systems is that in many scenarios, actors that participate in them are selfish and act rationally based on their own self interest. Therefore guiding such systems to... 

This work describes a new approach to the so called “Engineering Requirements Process” based on abilities to develop a meaningful task. We first describe how a meaningful is created from scratch and then we explain how requirements could be added to a level where the predefined task is no-longer doable. The process is then applied to design of an aircraft wing to show how requirements could be avoided during a design process. The method is expected to be applicable to all aircraft sub-systems and parts. The process is particularly useful where all design requirements are not available at once, rather they increase as time goes on and new stakeholders become apparent. In this work, we have... 

In the current situation, kidney transplantation is the most appropriate and least costly treatment for patients with end-stage renal disease (ESRD). Related or altruistic living donors, as well as deceased donors, are considered as a supply source for donated kidneys. Researches have shown deceased donor kidney may not work as well as a living donor kidney because the deceased donor kidney is outside the donor's body for a longer time. If the donor has an incompatibility with the patient (in terms of the blood group, HLA, etc.), a kidney exchange between the pairs can be used to resolve the issue and make the transplantation possible. Pairs with blood group compatibility have also... 

Facility layout is one of the most important problems in industrial engineering and Operation Research. Facility layout problem is concerned with the determination of the most effective arrangement and configuration of physical facilities. The most successful heuristic approaches are based on graph theoretic concepts. solving facility layout problem by graph theory consists of two stages. In the first stage a planar graph which specifies desired adjacencies is obtained and in the second stage a Block layout is achieved from the planar graph which satisfies adjacency and area requirements. In this Research, a branch and bound algorithm will be suggested for WMPG Problem. The algorithm can...