Sharif Digital Repository

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... 

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,... 

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... 

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... 

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... 

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,... 

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... 

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... 

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.... 

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,... 

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...