Sharif Digital Repository

Today, many real-world datasets such as social network data and web pages can be shown as graphs. Community detection and clustering of these big graphs has many applications in different fields like recommender systems in social networks and Diag- nosis of diseases in communication networks among proteins. A cluster in a graph is a sub-graph with many internal and few external edges. A new method for local cluster detection around an existing vertex is introduced in this paper. This method applies random walk algorithm for cluster detection. The time complexity of this algorithm based on the graph size is polynomial. Therefore, it can be used for clustering of big graphs. The experimental... 

In the present research, the weak level efficiency of securitise market is reviewed and examined .Therefore the “Random Walk Hypothesis” has been examined on the time series of daily efficiency index of TEHRAN SECURITISE MARKET. The main difference between this research and the previous researches which have been performed previously in Iran, is the method of Hypothesis Test. The” Variance Ratio Test” has been used as a method of Hypothesis’ Test. In the second chapter, the theoretical and experimental literatures of this research has been described in detail. In parallel with the ” Variance Ratio Test”, the impact of the Day of week and the “HETROSCEDASITY TEST” also has been... 

Communication among people over the emerging networks has been the focus of attention in different branches of science during last decades. Online Social Networks (OSNs), with more than hundreds of millions of users are powerful means for directing information within and across societies. Thus, studying various aspects of OSNs is an important issue for researchers. Due to large number of users and friendship relationships among them, gathering complete information from an OSN is not feasible. On the other hand, hiding users information and crawlers limitations are challenges for gathering complete data. A Common solution for this problem is Sampling from OSNs. Sampling from OSNs (and... 

Nowadays, the use of MEMS sensors, due to their small size, lightweight and low cost, has been welcomed in systems such as autonomous vehicles. Although the precision of MEMS gyroscopes has been extremely improved, in some aspects, such as stability of bias, they still suffer from some big error sources, like run-to run bias, which determines the sensor price but is not negligible even inexpensive sensors. In addition to the bias, there are a lot of noises in the gyroscope outputs, where ARW is one of the most important ones, which causes failure in real-signals and produces an error in the position and attitude of mobile systems. Due to the fact that run-to-run bias and ARW are stochastic... 

Miscible displacement in fluid flowing through a porous medium plays an important role in many environmental and industrial applications; for instance, miscible displacements in enhanced oil recovery processes and pollutant spreading in groundwater. A large number of numerical approaches have been developed to solve the advection-dispersion equation that describes the behavior of miscible displacement in porous media. Most of these numerical models suffer from numerical dispersion. Random walk seems to be an effective method to overcome this problem especially in heterogeneous media. Here, a random walk model was developed and used for simulating miscible displacement in heterogeneous porous... 

The fast growth of social networks and their wide range of applications have made the anal-ysis of them an interesting field of research. The growth of concern in modeling large social networksand investigation of their structural features leads studies towards community detec-tion in such networks. In recent years, a great amount of effort has been done for introducing community detection algorithms, many of which are based on optimization of a global cri-terion which needs network’s topology. However, because of big size of most of the social networks , accessing their global information tends to be impossible. Hence, local commu-nity detection algorithms have been introduced. In this... 

Schramm Loewner evolution (SLE) is a one-parameter family of random simple curves in the complex plane introduced by Schramm in 1999 which is believed to describe the scaling limit of a variety of domain interfaces at criticality. This thesis is concerned with statistical properties of watersheds dividing drainage basins. The fractal dimension of this model is 1.22 which is consistent with the known fractal dimension for several important models such as Invasion percolation and minimum spanning trees (MST). We present numerical evidences that in the scaling limit this model are SLE curves with =1.73, being the only known physical example of an
SLE with <2. This lies outside the... 

We consider a biased random walk Xn on a Galton-watson tree with leaves in the subballistic regime. We prove that there exists an explicit constant ϒ = ϒ(β) ε (0,1),such that |Xn| is of order n. If Δn be the hitting time of level n, we prove that Δn{n1{ is tight. More ever we show thatΔn{n1{ does not converge in law. We prove that along the sequences npkq Xk\ , Δn{n1{ converges to certain infinity divisible laws. Key tools for the proof are the classical Harris decomposition for Galton-Watson trees, a new variant of regeneration times and the careful analysis of triangular arrays of i.i.d. random variables  

A Markov chain on a base graph is a stochatic process that can be visualized as a particle movement such that the probability of moving from a vertex i to a vertex j is specified by the corresponding transition kernel Ka. In this thesis, based on the result of A.Daneahgar and H.Hajiabolhassa, we recall some general necessary conditions for the existence of graph homomorphism, which holds on both directed and undirected cases. A discrete-time quantum walk on a graph is the repeated application of a unitary evolution operator. In this regard, also, we explain the quantum search algorithm on the result of Grover and the algorithms that is based on the quantum walk approach of A.Ambainis,... 

Given a snapshot of a network, link preditction methods try to infer future intractions be-tween its nodes. These methods may be used in either analyzing current state of the network or predicting future links of it. Link prediction techniques have many applications among which we can mention recommendation systems. These systems are implemented for com-mercial reasons or preventing user confusion in huge amount of information available.A new perspective toward link prediction is based on supervised random walk. In such methods, a random walker starts from a node in the network and randomly traverses to one of the current node’s neighbours with a probability proportional to the chosen link’s... 

Quantum random walk is a computational model in quantum computation which is as powerful as other models like quantum circuit model. One dimensional random walks can be implemented in the laboratory by using a two-level quantum coin (e.g. the two states of a photon). For implementing higher dimensional random walks, one should simulate quantum coins with higher number of levels. This is difficult to implement experimentally. Various proposals try to bypass this problem, like the proposal of alternate walks in [C. DiFranco et al., Phys. Rev. Lett. 106, 080502(2011)]. Here we suggest an alternate solution: We use the bi-partite structure of some lattices to effectively act as a two-level... 

In this thesis, we consider the model of random interlacement on transient graghs, which was first introduced by Sznitman for the special case of Zd(d > 3) in 2010’s. in Sznitman’s case, it was shown that on Zd: for any intensity u > 0, the interlacement set is almost surely connected. The main result of this thesis says that for transient, transitive graphs, the above property holds if and only if the graph is amenable. In paticular, we show that in nonamenable transitive graphs, for small values of the intensity u the interlacement set has infinitely many infinite clusters. We also provide examples of nonamenable transitive graphs, for which the interlacement set becomes connected for... 

The PCP theorem is the result of a line of work on interactive proofs and probabilistically checkable proofs. The first theorem relating standard proofs and probabilistically checkable proofs is NEXP?PCP[poly(n),poly(n)] . Subsequently, the method used in the proof of this statement were extended to yield a proof of the PCP theorem. However, this proof is relatively long and complicated. The PCP theorem is equivalent to hardness of approximation of some optimization problems. In 2006, Irit Dinur discovered a different proof of the PCP theorem. Dinur’s proof is a rather shorter and simpler than original proof. The main purpose of this survey is to present the main concepts and tools used in... 

The diffusion process propagates information, viruses, ideas, innovations and new be-haviours over social networks. Adopting a new behaviour, which is mentioned as an in-fection, starts from a little group of people. Spreading it over more neighbors and friendscan result in an epidemic phenomenon over the network. As this infection propagates, aninformation cascade will be generated. The spread of information cascades over social net-works forms the diffusion networks. Although observing the infection time of a person ispossible, determining the source of infection is usually a difficult problem. Additionally, inmany applications we can not observe the underlying network which diffusion...