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In this thesis, inspired by foundational discussions about the concepts of energy and entropy in the gravitational theory, we study the definitions of these concepts and the roles they play in that theory. The definitions considered in this thesis are derived from canonical formalism. To this end, first of all, the variational principle and the canonical structure in the gravitational theory, especially in situations where the spacetime is bounded, is carefully studied and the boundary and corner actions as well as the canonical structure on the boundaries in three cases of non-null, null and general boundaries are derived. Based on this study, two canonical approaches, namely the... 

Let M be a connected, compact, Riemannian manifold. Geodesic flow is a flow on the unit tangent bundle of M . This flow can be studied in dynamics prespective. for example entropy or complexity of the geodesic flow. in this thesis we will follow methods of entropy estimation or computing for geodesic flow. we will follow the method of anthony manning and Ricardo Mañe for proving such result. Maning present two results linking the topological entropy of the geodesic flow on M. we expalin how he find exponential growth rate volume of balls in universal cover as a lower bound for topologycal entropy. another theorem , Mañe represent the equlity between exponential growth rate of avrage of... 

Today Software Defined Networks are being considered as a new approach in the IT industry. In the architecture of this type of network, the control plane is separated from the data plane and this control layer is collected centrally in a unit called the controller that manages packet routing in the network. Switches and other components in the data layer are only responsible for transmitting packets in the network. Software Defined Networks are now widely used by leading companies. One of the most basic security requirements in any network architecture is the issue of full network accessibility for users. Denial of service attacks are known to pose a serious threat to network accessibility.... 

Experiments conducted in recent two decades indicated critical behavior in neural activity at different scales. Theoretically occurrences of these critical and power-law behavior can significantly facilitate brain activities correspondent to computation and memory tasks, but attaining the critical point essentially demands externally fine-tuning which has not been established yet. This fine-tuning often lies with placing system at transition point. Recent studies of group showed that a transition from synchronous to asynchronous phase could be achievable by a change in external parameters. At the very transition point, neuronal avalanches statistically demonstrate a power-law behavior which... 

Due to time symmetry in the fundamental laws of physics, time has no preferred direction at the microscopic level. However, in our daily lives, we encounter phenomena and processes that never occur in nature inversely. Therefore, it is quite obvious that at the macroscopic level we are facing some kind of asymmetry in time. This means that the flow of time is always in one direction (from the past to the future), which is referred to as the arrow of time. The thermodynamic arrow of time is one of the most important arrows and can be the origin of some other arrows of time. In this thesis, an attempt is made to analyze the origin of the thermodynamic arrow as much as possible and explain the... 

In this thesis, the aim is to provide lower or upper bounds for the entropy of the geodesic flow on Riemannian manifolds. There are well-known results in this area derived from the works of mathematicians such as Sarnak, Osserman, Mane, and others. Our focus is primarily on geometric bounds that are expressed in terms of Riemannian curvature. We will attempt to examine these results in detail and consider some of their applications  

Chaos in dynamical systems refers to the presence of extreme sensitivity to initial conditions in the system’s behavior, which renders the long-term prediction of the sys- tem’s behavior either impossible or highly challenging. This chaotic behavior is also present in deterministic systems. The observation of this concept, besides philosophical changes it has brought about, has been scrutinized in various domains and has provided an explanation for many observed physical, chemical, and biological phenomena. This phenomenon has been studied in diverse sectors such as fluid dynamics, neuronal dy- namics, and chemical reactions. In this research, we intend to analyze chaotic dynamical systems... 

In recent years, a series of deep connections have been found between the ideas that used to be in the Algebraic Theory of Quantum Fields and the important problems of High Energy and Fundamental Physics. In the 1960s and later, some people who were mostly closer to mathematicians were trying to formulate the basics and principles of Quantum Field Theory in mathematically precise way. Many and various efforts have been made in this direction. One of these important efforts has been the Algebraic Theory of Quantum Fields. The main motivation in the Algebraic Theory of Quantum Fields is to focus on the operators and observables of the theory and study the algebraic structure between them instead... 

Medical images contain human body pictures and are widely used for diag-nosis and surgical purposes. Compression is needed for medical images for some applications such as profiling a patient's data or transmission systems. Due to the importance of the information of medical images, lossless or visually lossless compression is preferred. Lossless compression mainly consists of transformation and encoding steps. On the other hand, hardware implementation of lossless compression algorithm accelerates real time tasks such as online diagnosis and telemedicine. Lossless JPEG, JPEG-LS and lossless version of JPEG2000 are few well known methods for lossless compression. In this thesis, we introduce... 

One of the important issues in the fundamental physics is the arrow of time. According to the fundamental theories, motion is symmetry with respect to the passage of time while on a macroscopic level time has direction. In the macroscopic models the arrow of time is provided by the Second Law of Thermodynamics.The thermodynamic arrow is often linked to the cosmological arrow of time, because it is ultimately about the boundary conditions of the early universe.Recently people have tried to suppose this challenge as a fundamental issue and use this as fundamental assumption in their theories.A number of models have attempted to solve the problem based on the concept of information.... 

Reducing interconnection costs on chip and power consumption are important issues in designing processors. In a processor, a significant amount of total chip power is consumed in the interconnection. The goal of this research is to find a way to reduce power consumption in the interconnection. In this project we propose a new data sending method in which an LZW-like compression algorithm is exploited to compress data before sending it over the interconnection. Then, the codes of the compressed data are sent through the interconnection in order to reduce the number of dynamic cycles. The simulation results show that using this method can reduce 52% of dynamic power consumption  

One of the important questions in mathematics is generalized. In case of metric spaces, one of the questions is: Can we extend notions of Riemannian geometry to arbitrary metric spaces smoothly? Ricci curvature is one of the most important concepts in differential geometry. Ricci curvature is defined for the Riemannian manifold and has many applications in mathematics and physics like Einstein’s equation in relativity theory. There is a good notion for a metric space having “sectional curvature bounded below by K” or “sectional curvature bounded above by K”, due to Alexandrov. Can we define the concept of Ricci curvature in metric space? A motivation for this question comes from Gromov’s... 

Undoubtedly, the concept of information has an outstanding role in our description of physical systems and biological processes. In the framework of pragmatic approach, information is a useful notion through which any physical event gets its significance. In this approach, information can be understood and recognized while it is capable of producing new information. Thus, the meaning of information depends on our recognition and understanding as conscious beings. Accordingly, the following question may arise: where is the role of conscious being in the emergence of physical properties in Nature? To answer this fundamental question, we first investigate how information enters the physics, in... 

In recent years, the Cognitive Radio Network has received significant attentions due to its high potential for better employment of the spectrum. One of the most important parts of this technology is the spectrum sensing that requires being fast and accurate. The conventional algorithms proposed so far encounter some fundamental challenges at low SNR regimes and in wideband sensing. On the other hand, the compressed sensing algorithms, which take advantages of the sparsity of the signal of interest and utilize measurements instead of the samples, can reduce the sampling rate and thus decrease the complexity associated with the wideband sensing. In this thesis, by exploiting the... 

The synchronization phenomena are abundant is science, nature, engineering, and social life. Systems as diverse as clocks, singing crickets, cardiac pacemakers, firing neurons, and applauding audiences exhibit a tendency to operate in synchrony. These phenomena are universal and can be understood within a common framework based on modern nonlinear dynamics. First chapter of this thesis describes the basic ideas of the synchronization in an intuitive way. The main physical concepts are presented with experimental examples.
One of the main effects of synchronization is the ability to infer the directionality of coupling for two time series. Uncovering the directionality of coupling is a... 

Security Protocols are a set of protocols for the exchange of messages that both side of communication use in order to create the secure communication channel. Usually in such a case, both sides agree on one encrypted key. The purpose of these protocols is to obtain some features such as Authentication, Secrecy, Integrity, Non Repudiation, privacy and freshness. Freshness is one of the most important and vital features in communication protocols which is gained with Challenge and Response, timestamp and sequence number methods. Can interpret freshness as new and up-to-date. From the perspective of a participating agent in execute of protocol, a phrase take into account as fresh when it... 

Distributed Denial of Service attacks are threats that target availability of network resources. One feature of this type of attacks is high volume of traffic or service request from huge number of illegitimate attackers that organize botnets together, which cause performance decrease of network. Nowadays, distinguishing huge number of legitimate users during Flash Crowd is one of the most challenging issues for network security experts. Most of proposed methods so far, did not have enough performance or were only applicable in short term, due to increasing attackers’ knowledge in mimicking legitimate users behavior. Methods based on extracting statistic features usually, have better... 

In quantum mechanics, every system is described by a state function. The state function determines the probability of different outcomes of a certain measurement which is performed on the physical system. The connection between uncertainties about different measurements is presented by inequalities best known as Heisenberg’s uncertainty inequality. In face, the uncertainty relations state that there exist incompatible measurements, to which the outcomes of measurements cannot be predicted simultaneously. Although the uncertainty relations can be inferred from mathematical formalism of quantum mechanics, there is a profound relationship with other aspects of physics. Here we investigate the... 

A web-based system is designed and implemented at cira.civil.sharif.edu as a risk communication tool to incentivize the society to take seismic risk mitigation measures. Risk denotes the expected monetary and social losses herein. The objective of this system is to raise the awareness of two groups of audience, i.e., the general public and policymakers,about the significant seismic risk in Iran. To address the general public, the system employs the notion of risk perception to put the results of sophisticated earthquake engineering risk analyses into perspective. The system also treats the epistemic uncertainty in the user input due to general public’s lack of technical knowledge through the... 

In this dissertation we study the derivation of the second law of thermodynamics from an underlying physics. After discussing different methods for this derivation, we conclude that the only way to fulfill this, is to use a probabilistic mechanics which has probability as an inherent concept in itself, not as a supplementary one like statistical mechanics. This mechanics in contrary to the Newtonian mechanics, should be indeterministic