Sharif Digital Repository

In this thesis, following a short introduction to investment problem, this problem is investigated with both probabilistic and universal approach. Using the concept of the set of reference algorithms, we present a mathematical definition for universality. We then give examples of universal algorithms for investment and prove their universality. These algorithms are:
Universal Portfolios without Side Information, Universal Portfolios with Side Information, Universal Portfolios with Semi-Constant Rebalanced Portfolio, Universal Portfolios with Switching.
We then present a new algorithm called “Universal Portfolio with Multiple Side Information Sources”. This algorithm is applied in... 

Taking into account the fast and ever-increasing pace of data growth, clustering algorithms emerge as the key tools for data analysis in new researches. Clustering remain as a method for decomposing data into clusters, in such a way that similar data coalesce in the same group. Different algorithms conduct clustering according to a series of initial hypotheses, without being informed about the clusters’ form and aims. Hence, in case with no conformity between initial hypothesis and the clustering aim, one cannot expect adequate response from the clustering algorithm. Exploitation of side information in clustering can play an impactful role in introduction of real models into clustering... 

In  this  dissertation,  we  investigate  the  frequency  hopped  spread  spectrum  systems  which are extensively used in many communication systems. We derive the capacity region  of  Synchronous  Frequency  Hopped  Multiple  Access  (FHMA)  channels  (for  any  kind of noisy or nonselective fading environment) by using the side information which exists in the multi‐user detection. We assume that random hopping patterns are used by all the transmitters, and the common receiver knows the hopping patterns. We also compute  the  capacities  of  FHMA  with  and  without  power  control  for  AWGN  and  noiseless MFSK (in particular BFSK) modulated systems and compare the ... 

Clustering is one of the important problems in machine learning, data mining, and pattern recognition fields. When the considered feature space for data representation is not suitable for discrimination of data groups, the data clustering problem may be a difficult problem that cannot be solved properly. In the other words, when the Euclidean distance cannot describe the dissimilarity of data pairs appropriately, the common clustering algorithms may not be helpful and the clusters show arbitrary shapes and spread in such spaces. Although since the late 1990’s several algorithms have been proposed for finding clusters of arbitrary structures, these algorithms cannot yield desirable... 

Wireless Sensor Networks (WSNs) attracted lots of researchers in recent years, these sensors are small and have limited computational resources and are not expensive in comparision with conventional sensors. These sensors can sense, measure, gathering information from environment and send them to user, they are typically characterized by limited communication capabilities due to tight energy and bandwidth constraints. As a result, WSNs have inspired a resurgence in research on decentralized algorithms, structure of these networks are variable and dynamic, sensors may deleted from the network or added to the network, so using models which don’t require precies specifications of environment is... 

In this thesis, the problem of secret key agreement in the channel model with side information is studiedx. In order to investigate the problem, we consider three models according to the different ways of side information availability which are the state-dependent broadcast channel; the state-dependent broadcast channel in presence of public channel and the state-dependent wiretap channel with degraded versions of the channel state information.For the problem of secret key agreement in broadcast channels, two models, the state-dependent wiretap channel and state-dependent three receivers broadcast channel, are considered. We obtain inner and outer bounds of the secret key capacity region for... 

In this dissertation we discuss various results presented in the literature on single user channels with causal or noncausal side information and multiuser channels with side information such as multiple access channel and broadcast channel. The Series Relay Networks (SRN) with delays, with and without channel state information (CSI) are investigated from an information theoretic point of view. For SRN with unlimited look ahead where the relays can use the whole received block to encode, upper and lower bounds on the capacity are derived which are tight for the degraded case. For SRN without-delay where the relays have access to the present received symbols in addition to the past symbols,... 

Due to the remarkable growth in using communication networks such as ad-hoc, wireless and sensor networks, studying the building blocks of these networks (e.g., relay channel and interference channel) from information theoretic viewpoint and investigating cooperative strategies have recently received considerable attention. Also, owing to wide range of applications, state-dependent channels have been widely studied. In this dissertation, at first, we consider a state-dependent relay channel (SD-RC). For the cases wherein channel states are available causally or non-causally at different nodes, we propose new achievable rates for this channel using compress-and-forward strategy. Also we...