Sharif Digital Repository

A diverse range of natural and artificial self-propelled particles are known and are used nowadays. Among them, active Brownian particles (ABPs) and run-and-tumble particles (RTPs) are two important classes. We numerically study non-interacting ABPs and RTPs strongly confined to different maze geometries in two dimensions. We demonstrate that by means of geometrical confinement alone, ABPs are separable from RTPs. By investigating Matryoshka-like mazes with nested shells, we show that a circular maze has the best filtration efficiency. Results on the mean first-passage time reveal that ABPs escape faster from the center of the maze, while RTPs reach the center from the rim more easily.... 

We introduce a 'high probability' framework for repeated games with incomplete information. In our non-equilibrium setting, players aim to guarantee a certain payoff with high probability, rather than in expected value. We provide a high probability counterpart of the classical result of Mertens and Zamir for the zero-sum repeated games. Any payoff that can be guaranteed with high probability can be guaranteed in expectation, but the reverse is not true. Hence, unlike the average payoff case where the payoff guaranteed by each player is the negative of the payoff by the other player, the two guaranteed payoffs would differ in the high probability framework. One motivation for this framework... 

In this paper, we address aircraft conflict detection on a mid-term horizon. We adopt a probabilistic approach and provide a simple method to estimate the probability of two aircraft getting closer than some minimum predefined distance, based on a commonly adopted Gaussian model of the deviation from their planned trajectories. A key feature of our method is that the probability estimate is accompanied by a deterministic accuracy certificate. This is achieved by adopting a geometric approach to conflict probability estimation and jointly computing a lower and an upper bound on the conflict probability. These bounds can be inspected and refined if the resulting accuracy of the probability... 

QBism is one of the main candidates for an epistemic interpretation of quantum mechanics. According to QBism, the quantum state or the wavefunction represents the subjective degrees of belief of the agent assigning the state. But, although the quantum state is not part of the furniture of the world, quantum mechanics grasps the real via the Born rule which is a consistency condition for the probability assignments of the agent. In this paper, we evaluate the plausibility of recent criticism of QBism. We focus on the consequences of the subjective character of the quantum state, the issue of realism and the problem of the evolution of the quantum state in QBism. In particular, drawing upon... 

Assuming the completeness of quantum mechanics, Mohrhoff has recently presented a new interpretation in which the probabilistic description of quantum mechanics is introduced on the basis of counterfactual statements. The macroscopic positions are assumed to be intrinsic, self-indicating and real, while the properties of the microscopic world are contingent and extrinsic, depending on what happens in the macro-world. Mohrhoff's interpretation emphasizes the objective fuzziness of all quantum phenomena, assigning objective probabilities to the possible outcomes of unperformed measurements. He extends this non-valuedness and fuzziness to the concepts of space and time and introduces a new... 

The random PRF method has been suggested for the design of LPD (low probability of detection) radar signals. The LPD improvement in using this kind of signal is discussed quantitatively. First, a detection theoretic approach is used to find the optimum detectors of the unauthorised receiver (ESM receiver) and their performance for both constant PRF and random PRF signals. Then, the effect of the random PRF method on the authorised receiver (radar receiver) is investigated. Based on these analyses and definition of a proper measure, the constant PRF signals are compared with random PRF signals from the LPD point of view. By finding a simple formula for the improvement caused by the random PRF... 

This book focuses on a central question in the field of complex systems: Given a fluctuating (in time or space), uni- or multi-variant sequentially measured set of experimental data (even noisy data), how should one analyse non-parametrically the data, assess underlying trends, uncover characteristics of the fluctuations (including diffusion and jump contributions), and construct a stochastic evolution equation?
Here, the term "non-parametrically" exemplifies that all the functions and parameters of the constructed stochastic evolution equation can be determined directly from the measured data.
The book provides an overview of methods that have been developed for the analysis of... 

The ongoing COVOD-19(SARS-CoV-2) outbreak has had a devastating impact on the economy, education and businesses. In this paper, the behavior of an epidemic is simulated on different contact networks. Herein, it is assumed that the infection may be transmitted at each contact from an infected person to a susceptible individual with a given probability. The probability of transmitting the disease may change due to the individuals' social behavior or interventions prescribed by the authorities. We utilized simulation on the contact networks to demonstrate how seesaw scenarios of lockdown can curb infection and level the pandemic without maximum pressure on the poor societies. Soft scenarios... 

The ongoing COVOD-19(SARS-CoV-2) outbreak has had a devastating impact on the economy, education and businesses. In this paper, the behavior of an epidemic is simulated on different contact networks. Herein, it is assumed that the infection may be transmitted at each contact from an infected person to a susceptible individual with a given probability. The probability of transmitting the disease may change due to the individuals' social behavior or interventions prescribed by the authorities. We utilized simulation on the contact networks to demonstrate how seesaw scenarios of lockdown can curb infection and level the pandemic without maximum pressure on the poor societies. Soft scenarios... 

We investigate the Markov property of rough surfaces. Using stochastic analysis, we characterize the complexity of the surface roughness by means of a Fokker-Planck or Langevin equation. The obtained Langevin equation enables us to regenerate surfaces with similar statistical properties compared with the observed morphology by atomic force microscopy. © 2003 The American Physical Society  

Reliability analysis of combinational logic circuits using error probabilities methods, such as PTM, has been widely developed and used in literature. However, using these methods for reliability analysis of sequential logic circuits will lead to inaccurate results, because of existence of loops in their architecture. In this paper a new method is proposed based on converting the sequential circuit to a secondary combinational circuit and applying an iterative reliability analysis to the resulting configuration. Experimental results demonstrate good accuracy levels for this method  

We introduce a 'high-probability' framework for repeated games with incomplete information. In our non-equilibrium setting, players aim to guarantee a certain payoff with high probability, rather than in expected value. We provide a high-probability counterpart of the classical result of Mertens and Zamir for the zero-sum repeated games. Any payoff that can be guaranteed with high probability can be guaranteed in expectation, but the reverse is not true. Hence, unlike the average payoff case where the payoff guaranteed by each player is the negative of the payoff by the other player, the two guaranteed payoffs would differ in the high-probability framework. One motivation for this framework... 

We derive bounds on the expected capacity and outage capacity of a three-node relay network for UWB communications. We also provide a simple tight approximation for the derived upper bound on the capacity and then using this bound we obtain the outage probability of the network. Numerical results show that a significant improvement in the system capacity and outage probability is obtained by adding a relay node. Moreover, our theoretical results reveal that the diversity gain of a relay channel substantially increases by using UWB links instead of NB links. We also derive these bounds when we have a constraint on the total transmitted power of the source and the relay nodes. © 2009 IEEE  

In this paper, we prove the existence of capacity achieving linear codes with random binary sparse generating matrices over the Binary Symmetric Channel (BSC). The results on the existence of capacity achieving linear codes in the literature are limited to the random binary codes with equal probability generating matrix elements and sparse parity-check matrices. Moreover, the codes with sparse generating matrices reported in the literature are not proved to be capacity achieving for channels other than Binary Erasure Channel. As opposed to the existing results in the literature, which are based on optimal maximum a posteriori decoders, the proposed approach is based on a different decoder... 

A master equation for the Kardar-Parisi-Zhang (KPZ) equation in 2+1 dimensions is developed. In the fully nonlinear regime we determine the finite time scale of the singularity formation in terms of the characteristics of forcing. The exact probability density function of the one point height field is obtained correspondingly  

The turbulent limit of three dimensional Burger equation was studied. An adjusting parameter emerged through the calculations, based on mean field analysis, that was the scaling exponent of conditional density-density correlations. Two kinds of solutions were also shown for velocity-increment probability density function (PDF)  

In this article, a new method for solving multidimensional population balance (PB) equations for agglomeration is presented. First, discretized 2-dimensional PB (DPB) is derived and by applying probability approach, this method is extended to n-dimensional PB. The discretization of size intervals is in the form of v(j) = 2j-i v(i) and the volume based PB is used. Because of conservative nature of volume, all internal coordinates are converted to some independent volumes. A simple and clear procedure for solving multidimensional PB is proposed using probability concept. In addition, various types of birth and death mechanisms involved in PB are analyzed separately. Moreover, results of... 

The effect of strong femto-second laser pulses on the dissociation probability of methane has been investigated analytically in various arrangements. The ellipticity dependence of the dissociation probability at intensities from 1014 W cm-2 to 1016 W cm-2 for Ti:Sapphire laser is presented. A reliable calculation of the dissociation probability based on 3D time-dependent Schrodinger equation with an improved model of time-dependent density-functional theory is presented. These calculations are carried out for three different cases of elliptically polarized laser pulse, optimum convolution of dual short pulses, and two-color mixed nonresonant laser pulses. It is found that the rescattering... 

This paper considers a cooperative space-frequency (SF) coded OFDM system and evaluates its performance over quasi-static frequency selective Rayleigh fading channels. An expression for exact outage error probability is derived and its tight closed form lower bound is presented. The tightness of the lower bound is demonstrated through the Monte Carlo simulations. The asymptotic analysis indicates that the proposed protocol achieves full spatial and frequency diversities available in the cooperative communication system. The theoretical analysis of the proposed space-frequency coded cooperation protocol is further confirmed by computer simulations. © 2007 IEEE  

We consider chaperone-assisted translocation of biopolymers with two distinct monomers or bases A and B, with the size of the chaperones being λα, where α is a monomer's size. The probability that A and B are neighbors in the biopolymer is PAB. A master equation is used, together with the detailed-balanced condition, in order to derive analytical results for the statistics of the first-passage times of the biopolymer as a function of PAB, λ, and the biopolymer's configuration. Monte Carlo simulations have also been carried out in order to compute the same quantities for biopolymers with 100-900 monomers and several λ. The results indicate nontrivial dependence of the variance of the...