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#### The spherical ensemble and uniform distribution of points on the sphere

, Article Electronic Journal of Probability ; Volume 20 , 2015 , 23, 27 pp ; 10836489 (ISSN) ; Zamani, M ; Sharif University of Technology
University of Washington
2015

Abstract

The spherical ensemble is a well-studied determinantal process with a fixed number of points on $2. The points of this process correspond to the generalized eigenvalues of two appropriately chosen random matrices, mapped to the surface of the sphere by stereographic projection. This model can be considered as a spherical analogue for other random matrix models on the unit circle and complex plane such as the circular unitary ensemble or the Ginibre ensemble, and is one of the most natural constructions of a (statistically) rotation invariant point process with repelling property on the sphere. In this paper we study the spherical ensemble and its local repelling property by investigating the...

#### Determinantal Processes

, M.Sc. Thesis Sharif University of Technology ; Alishahi, Kasra (Supervisor)
Abstract

Determinantal processes are a special family of stochastic processes that arise in physics (fermions), random matrices (eigenvalues), and in combinatorics (random spanning trees and non-intersecting paths). These processes have repelling property (points close to each other are chosen with low probability). Because of this repelling property, determinantal processes are approporiat for modeling some physical quantities (e.g. the position of electrons). Their probabilistic structure is described by operators on complex vector spaces and their eigenvalues. Determinantal processes have interesting properties, e.g. number of points in a region is a sum of independent Bernoulli random variables....

#### Continuous-time user modeling in presence of badges: a probabilistic approach

, Article ACM Transactions on Knowledge Discovery from Data ; Volume 12, Issue 3 , 2018 ; 15564681 (ISSN) ; Hosseini, A ; Tavakoli, E ; Rabiee, H. R ; Sharif University of Technology
Association for Computing Machinery
2018

Abstract

User modeling plays an important role in delivering customized web services to the users and improving their engagement. However, most user models in the literature do not explicitly consider the temporal behavior of users. More recently, continuous-time user modeling has gained considerable attention and many user behavior models have been proposed based on temporal point processes. However, typical point process-based models often considered the impact of peer influence and content on the user participation and neglected other factors. Gamification elements are among those factors that are neglected, while they have a strong impact on user participation in online services. In this article,...

#### Rigidity and Tolerance for Perturbed Lattic

, M.Sc. Thesis Sharif University of Technology ; Haji Mirsadeghi, Mir Omid (Supervisor)
Abstract

A perturbed lattice is a point process π={x+Y_x ∶x ∈Z^d} where the lattice points in Z^d are perturbed by i.i.d . random variables {Y_x }_(x∈Z^d ). A random point process π is said to be rigid if π∩B_1 (0) , the number of points in a ball , can be exactly determined given π∩B_1^c (0) , the points outside the ball . The process π is called deletion tolerant if removing one point of π yields a process with distribution indistinguishable from that of π . Suppose that Y_x~N_d (0,σ^2 I) are Gaussian vectors with d independent components of variance σ^2 . Holroyd and Soo showed that in dimensions d = 1 , 2 the resulting Gaussian perturbed lattice π is rigid and deletion...

#### Point-map-probabilities of a point process and Mecke's invariant measure equation

, Article Annals of Probability ; Volume 45, Issue 3 , 2017 , Pages 1723-1751 ; 00911798 (ISSN) ; Haji Mirsadeghi, M. O ; Sharif University of Technology
Institute of Mathematical Statistics
2017

Abstract

A compatible point-shift F maps, in a translation invariant way, each point of a stationary point process Φ to some point of Φ. It is fully determined by its associated point-map, f, which gives the image of the origin by F. It was proved by J. Mecke that if F is bijective, then the Palm probability of Φ is left invariant by the translation of -f . The initial question motivating this paper is the following generalization of this invariance result: in the nonbijective case, what probability measures on the set of counting measures are left invariant by the translation of -f ? The point-map-probabilities of Φ are defined from the action of the semigroup of point-map translations on the space...

#### Point-shift foliation of a point process

, Article Electronic Journal of Probability ; Volume 23 , 2018 ; 10836489 (ISSN) ; Haji Mirsadeghi, M. O ; Sharif University of Technology
University of Washington
2018

Abstract

A point-shift F maps each point of a point process Φ to some point of Φ. For all translation invariant point-shifts F, the F-foliation of Φ is a partition of the support of Φ which is the discrete analogue of the stable manifold of F on Φ. It is first shown that foliations lead to a classification of the behavior of point-shifts on point processes. Both qualitative and quantitative properties of foliations are then established. It is shown that for all point-shifts F, there exists a point-shift F⊥, the orbits of which are the F-foils of Φ, and which is measure-preserving. The foils are not always stationary point processes. Nevertheless, they admit relative intensities with respect to one...

#### Irregularities of Some Random Point Processes

, M.Sc. Thesis Sharif University of Technology ; Alishahi, Kasra (Supervisor)
Abstract

The spherical ensemble is a well-studied determinantal process with a fixed number of points on the sphere. The points of this process correspond to the generalized eigenvalues of two appropriately chosen random matrices, mapped to the surface of the sphere by stereographic projection. This model can be considered as a spherical analogue for other random matrix models on the unit circle and complex plane such as the circular unitary ensemble or the Ginibre ensemble, and is one of the most natural constructions of a (statistically) rotation invariant point process with repelling property on the sphere. In this dissertation we study the spherical ensemble and its local repelling property by...

#### Optimal paths on the space-time SINR random graph

, Article Advances in Applied Probability ; Volume 43, Issue 1 , 2011 , Pages 131-150 ; 00018678 (ISSN) ; Blaszczyszyn, B ; Haji Mirsadeghi, M. O ; Sharif University of Technology
Abstract

We analyze a class of signal-to-interference-and-noise-ratio (SINR) random graphs. These random graphs arise in the modeling packet transmissions in wireless networks. Tn contrast to previous studies on STNR graphs, we consider both a space and a time dimension. The spatial aspect originates from the random locations of the network nodes in the Euclidean plane. The time aspect stems from the random transmission policy followed by each network node and from the time variations of the wireless channel characteristics. The combination of these random space and time aspects leads to fluctuations of the SINR experienced by the wireless channels, which in turn determine the progression of packets...

#### On the performance of amplifier-aware dense networks: Finite block-length analysis

, Article International Conference on Computing, Networking and Communications, 15 February 2016 through 18 February 2016 ; 2016 ; 9781467385794 (ISBN) ; Fang, C ; Svensson, T ; Nasiri Kenari, M ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc

Abstract

In this paper, we investigate the performance of dense Poisson-point-process-based cellular networks using finite length codewords. Taking the properties of the power amplifiers (PAs) into account, we derive the outage probability, the per-user throughput and the area spectral efficiency in different conditions. Our analysis is based on some recent results on the achievable rates of finite-length codes and we investigate the effect of the codeword length/PAs properties on the system performance. Our numerical and analytical results indicate that the inefficiency of the PAs affects the performance of dense networks substantially. Also, for a given number of information nats per codeword,...

#### Hybrid approach to analyze the impact of vehicular traffic on performance of 802.11p protocol for safety communications in vehicular ad hoc networks: a quantitative analysis

, Article Wireless Personal Communications ; Volume 97, Issue 3 , 2017 , Pages 4493-4528 ; 09296212 (ISSN) ; Afshin Hemmatyar, A. M ; Sharif University of Technology
Abstract

The rapid developments in wireless communications have introduced the vehicular ad hoc networks as an efficient tool to improve the safety of traffic through Dedicated Short Range Communications systems on highways. This paper addresses the broadcast mode of the 802.11p protocol and it quantitatively analyzes the impact of the highway vehicular traffic on its performance in terms of the packet delivery ratio and the packet transmission delay. To this aim, we propose to consider the number of the contending vehicles as a traffic-dependent stochastic counting process, which can be computed by analyzing the inter-vehicle spacing distribution in different traffic conditions. Based on the...

#### Delay-sensitive area spectral efficiency: a performance metric for delay-constrained green networks

, Article IEEE Transactions on Communications ; Volume 65, Issue 6 , 2017 , Pages 2467-2480 ; 00906778 (ISSN) ; Fang, C ; Svensson, T ; Nasiri Kenari, M ; Zorzi, M ; Sharif University of Technology
Abstract

This paper introduces a new metric, referred to as delay-sensitive area spectral efficiency (DASE), to analyze the performance of delay-constrained wireless networks. We study DASE in different point-to-point, spectrum sharing, interference, and Poisson-point process-based dense network configurations and with different levels of channel state information (CSI) at the transmitters. Also, we determine the optimal rates/powers optimizing DASE. Finally, we use some recent results on finite block-length codes to analyze the effect of the codewords length on the network DASE. As demonstrated, DASE is a useful metric for analyzing delay-sensitive green networks. Moreover, adaptive power allocation...

#### RedQueen: an online algorithm for smart broadcasting in social networks

, Article WSDM 2017 - Proceedings of the 10th ACM International Conference on Web Search and Data Mining, 2 February 2017 ; 2017 , Pages 51-60 ; 9781450346757 (ISBN) ; Upadhyay, U ; Rabiee, H. R ; Gomez Rodriguez, M ; Sharif University of Technology
Association for Computing Machinery, Inc
2017

Abstract

Users in social networks whose posts stay at the top of their followers' feeds the longest time are more likely to be noticed. Can we design an online algorithm to help them decide when to post to stay at the top? In this paper, we address this question as a novel optimal control problem for jump stochastic differential equations. For a wide variety of feed dynamics, we show that the optimal broadcasting intensity for any user is surprisingly simple - it is given by the position of her most recent post on each of her follower's feeds. As a consequence, we are able to develop a simple and highly efficient online algorithm, RedQueen, to sample the optimal times for the user to post....

#### Steering social activity: a stochastic optimal control point of view

, Article Journal of Machine Learning Research ; Volume 18 , 2018 , Pages 1-35 ; 15324435 (ISSN) ; De, A ; Upadhyay, U ; Rabiee, H.R ; Gomez Rodriguez, M ; Sharif University of Technology
Microtome Publishing
2018

Abstract

User engagement in online social networking depends critically on the level of social activity in the corresponding platform-the number of online actions, such as posts, shares or replies, taken by their users. Can we design data-driven algorithms to increase social activity? At a user level, such algorithms may increase activity by helping users decide when to take an action to be more likely to be noticed by their peers. At a network level, they may increase activity by incentivizing a few influential users to take more actions, which in turn will trigger additional actions by other users. In this paper, we model social activity using the framework of marked temporal point processes,...

#### Routing on Stochastic Geometric Graphs

, Ph.D. Dissertation Sharif University of Technology ; Daneshgar, Amir (Supervisor) ; Baccelli, François (Supervisor)#### Improving The Performance of Recommendation Systems by Exploiting Relationships and Temporal Behavior of Users in Social Networks

, M.Sc. Thesis Sharif University of Technology ; Rabiee, Hamid Reza (Supervisor)
Abstract

Online social services and stores has become more popular in recent years . With the growing number of products and services available in these online stores and websites , recommendation systems play an important role in predicting which products and services are good for each user so that they can buy the product they need or use the online services they want without wasting their time to find the right ones . We propose a method called Temporal Socio-Content Poisson Factorization (TSCPF) which aims to recommend the most probable document to be read by each user at any given time . We model users’ behaviors and interests by using temporal point processes to capture temporal dynamics of...

#### Analysis and Modeling of User Behavior over Social Media

, Ph.D. Dissertation Sharif University of Technology ; Rabiee, Hamid Reza (Supervisor)
Abstract

Nowadays many of us spend a big part of our daily times on social media.One of the most important research problems in social media analysis is how to engage users. The trace of user activity over these websites is a valuable resource for user understanding and engagement, but this data is very huge and unstructured. An approach to deal with this problem is user behavior modeling. In this process, first a behavioral model is considered for users, then using the activity data and the behavioral model, some parameters are learned. Finally, using the learned parameters, a user profile is constructed for each user. This profile can be used for user engagement and many other applications....

#### Performance Analysis of Flooding-based Broadcasting in Wireless Networks

, Ph.D. Dissertation Sharif University of Technology ; Hossein Khalaj, Babak (Supervisor)
Abstract

Broadcasting in wireless ad hoc networks serves many important tasks such as data dissemination and route establishment in which one node sends its data to all other network nodes. The most popular form of broadcasting adopted by many ad-hoc protocols is flooding. In flooding, each node receiving a packet from a neighboring node rebroadcasts it exactly once. Wide adoption of flooding for broadcasting traffic is mainly due to its simplicity. The importance of performance analysis of flooding lies on its aforementioned popularity. The parameters of interest in analysis of flooding are network coverage, energy consumption and broadcast throughput while network coverage is the average percentage...

#### Modeling and Analysis of Information Diffusion over Social Networks using Point Processes

, M.Sc. Thesis Sharif University of Technology ; Rabiee, Hamid Reza (Supervisor)
Abstract

Social networks play an important role in the spread of information, news and users’decisions. An important type of these networks are location-based networks where users can post the time and location of their checks in diﬀerent places. Check-ins of a user may incentivize her friends to visit the same location in the near future.This phenomena is called diﬀusion process. Previous works often assume that the generation of an event just increases the probability of subsequent events in a near future. Even though the assumption is quite valid in the social networks like Twitter,it is not the sufcient assumption in spatio-temporal social networks where the users’physical limitations and...

#### Event History Analysis in Complex Networks

, Ph.D. Dissertation Sharif University of Technology ; Rabiee, Hamid Reza (Supervisor)
Abstract

Event history analysis is a classic problem in stochastic process, that recently attracts the researchers' attention in complex networks. The goal is to model the time of events, like check in a restaurant check-in or post a message, given their history, and then control them. In this thesis we try to improve both aspects of the problem. In event modeling, we focus on two challenging cases. The first case removes the independence assumption in diffusion of cascades in social networks, and investigate the correlated cascades. We use a multidimensional Hawkes process with soft-max mark function, to model the competitive and cooperative cascades. We infer parameters of the problem using...

#### Performance analysis of the clustered caching wireless networks considering stochastic geometry approach

, Article 2016 8th International Symposium on Telecommunications, IST 2016, 27 September 2016 through 29 September 2016 ; 2017 , Pages 320-324 ; 9781509034345 (ISBN) ; Zeinalpour Yazdi, Z ; Hossein Khalaj, B ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
2017

Abstract

Recently, caching of the popularity video files in the caches near to the users has been proposed as a promising way to reduce data traffic. These caches can be considered as the nodes which their transmission ranges are limited but have significant storage capacity and are known as the helper nodes. To evaluate the performance and efficiency of the caches, a suitable model for their distributions should be taken into account. Stochastic geometry is a useful tool for modeling these nodes. In this paper, the helper nodes and users are distributed according to the Poisson point process distribution. However, to manage the interferences and their access to a distributed cache, the helper nodes...