Sharif Digital Repository

We examine quantum normal typicality and ergodicity properties for quantum systems whose dynamics are generated by Hamiltonians which have residual degeneracy in their spectrum and resonance in their energy gaps. Such systems can be considered atypical in the sense that degeneracy, which is usually a sign of symmetry, is naturally broken in typical systems due to stochastic perturbations. In particular, we prove a version of von Neumann's quantum ergodic theorem, where a modified condition needs to hold in order to have normal typicality and ergodicity. As a result, we show that degeneracy of spectrum does not considerably modify the condition of the theorem, whereas the existence of... 

We investigate the stochasticity in temperature fluctuations in the cosmic microwave background (CMB) radiation data from the Wilkinson Microwave Anisotropy Probe. We show that the angular fluctuation of the temperature is a Markov process with a Markov angular scale, ΘMarkov = 1.01 -0.07+0.09. We characterize the complexity of the CMB fluctuations by means of a Fokker-Planck or Langevin equation and measure the associated Kramers-Moyal coefficients for the fluctuating temperature field T (n̂)and its increment, ∇ T = T(n̂2). Through this method we show that temperature fluctuations in the CMB have fat tails compared to a Gaussian distribution. © 2006 IOP Publishing Ltd and SISSA  

We use multifractal detrended fluctuation analysis (MF-DFA), to study sunspot number fluctuations. The result of the MF-DFA shows that there are three crossover timescales in the fluctuation function. We discuss how the existence of the crossover timescales is related to a sinusoidal trend. Using Fourier detrended fluctuation analysis, the sinusoidal trend is eliminated. The Hurst exponent of the time series without the sinusoidal trend is 0.12 ± 0.01. Also we find that these fluctuations have multifractal nature. Comparing the MF-DFA results for the remaining data set to those for shuffled and surrogate series, we conclude that its multifractal nature is almost entirely due to long range... 

In economic design of profiles, parameters of a profile are determined such that the total implementation cost is minimized. These parameters consist of the number of set points, n, the interval between two successive sampling, h, and the parameters of a control chart used for monitoring. In this paper, the Lorenzen-Vance cost function is extended to model the costs associated with implementing profiles. The in-control and the out-of-control average run lengths, ARL0 and ARL1, respectively, are used as two statistical measures to evaluate the statistical performances of the proposed model. A genetic algorithm (GA) is developed for solving both the economic and the economic-statistical... 

We insert some asymmetries into the continuous Abelian sandpile models, such as directedness and ellipticity. We analyze probability distribution of different heights and also find the corresponding field theories. Also we find the fields associated with some height variables. © 2008 IOP Publishing Ltd  

The Abelian sandpile model (ASM) is a paradigm of self-organized criticality (SOC) which is related to c ≤ -2 conformal field theory. The conformal fields corresponding to some height clusters have been suggested before. Here we derive the first corrections to such fields, in a field theoretical approach, when the lattice parameter is non-vanishing, and consider them in the presence of a boundary. © 2007 IOP Publishing Ltd  

Autocorrelation receiver (AcR) is usually used as the general receiver for transmitted reference (TR) communication systems on a quite intuitive basis. In this paper, we apply the principle of statistical invariance to obtain the optimum TR receiver on a decision-theoretic basis, and it is shown that the autocorrelation receiver is optimal only in a special case. Performance of the optimum receiver and the suboptimum AcR for some important modulation schemes is also evaluated. The results imply that allocating a part of the transmitted energy and bandwidth to reference pulses would not help improve the performance of the system and the optimal performance might be achieved via much simpler... 

In the framework of the Tsallis statistical mechanics, we study the change of the population of states when the parameter q is varied, for some model systems; the results show that the difference between predictions of the Boltzmann-Gibbs and Tsallis statistics can be much smaller than the precision of any existing experiment. Also, the relation between privilege of rare and frequent events and the value of q is restudied. It is shown that positive q privilege frequent and negative q privilege rare events. Finally, the convergence criteria of the partition function of some simple model systems, in the framework of Tsallis statistical mechanics, is studied. Based on this study, we conjecture... 

In this paper, two methods to solve multi-response statistical problems are presented. In these methods, desirability function, genetic algorithm and simulation methodology are applied. The desirability function is responsible for modeling the multi-response statistical problem, the genetic algorithm tries to optimize the model and, finally, the simulation approach generates the required input data from a simulated system. The methods differ from each other in controlling the randomness of the problem. In the first method, replications control this randomness, while, in the second method, the randomness is controlled by a statistical test. Furthermore, these methods are compared by designed... 

In some quality control applications, processes consist of multiple components, stations or stages to finish the final products or the services. Some quality characteristics in each stage of these processes (called multistage processes) can be represented by a relationship between a response and one or more explanatory variables which is named as profile. In this paper, a general model is proposed for monitoring multivariate profiles in multistage processes. To this aim, the multivariate form of the U transformation approach is first used to remove the effect of the cascade property between the stages. Then, three control schemes are employed to monitor the parameters of multivariate simple... 

The multivariate exponentially weighted moving average, MEWMA, control chart is an effective statistical tool for detecting small shifts in process mean vectors. On the one hand, the economic design process of a MEWMA control chart involves determining the main parameters of the chart, namely, the sample size n, the sampling interval h, the smoothing constant r, and the control limit L such that a quality cost function is minimized. On the other hand, the statistically constrained economic design of MEWMA chart is to determine the chart parameters such that a cost function is minimized while the statistical performance of the chart is maintained at a desire level. In this paper, the... 

Pore network modeling uses a network of pores connected by throats to model the void space of a porous medium and tries to predict its various characteristics during multiphase flow of various fluids. In most cases, a non-realistic regular lattice of pores is used to model the characteristics of a porous medium. Although some methodologies for extracting geologically realistic irregular networks from pore space images have been presented, these methods require some experimental data which are either unavailable or costly to obtain. 3-dimensional image or 2-dimensional SEM images are among these types of data. In this paper a new irregular lattice algorithm for the construction of these... 

We present an image steganographic technique to preserve the first-order and the second-order statistics of the host image. Experimental results show that the proposed method can preserve the image quality and also resists typical statistical analysis based attacks. The new steganography method solves the distortion problem with the HKC algorithm and hence thwarts the Kuo attack. The method is based on the idea of histogram shift, in which two empty bins are produced in the image histogram that are then filled up using their neighboring bins through the embedding process. © 2009 IEEE  

In some quality control applications, processes consist of multiple components, stations or stages to finish the final products or the services. Some quality characteristics in each stage of these processes (called multistage processes) can be represented by a relationship between a response and one or more explanatory variables which is named as profile. In this paper, a general model is proposed for monitoring multivariate profiles in multistage processes. To this aim, the multivariate form of the U transformation approach is first used to remove the effect of the cascade property between the stages. Then, three control schemes are employed to monitor the parameters of multivariate simple... 

A Bernoulli Mixture Model (BMM) is a finite mixture of random binary vectors with independent dimensions. The problem of clustering BMM data arises in a variety of real-world applications, ranging from population genetics to activity analysis in social networks. In this paper, we analyze the clusterability of BMMs from a theoretical perspective, when the number of clusters is unknown. In particular, we stipulate a set of conditions on the sample complexity and dimension of the model in order to guarantee the Probably Approximately Correct (PAC)-clusterability of a dataset. To the best of our knowledge, these findings are the first non-asymptotic bounds on the sample complexity of learning or... 

In this paper, we study a particular deformation of the Jackiw-Teitelboim gravity recently considered by Maxfield, Turiaci, and independently by Witten. We will compute the partition function of this model as well as its higher order correlators to all orders in genus expansion in the low temperature limit for small perturbations. In this limit, the results match with those obtained from the Airy limit of a Hermitian random matrix ensemble. Using this result, we will also study the free energy of the model. One observes that although the annealed free energy has pathological behaviors, under certain assumptions, the quenched free energy evaluated by replica trick exhibits the desired... 

It is proved that the out-of-phase autocorrelation of a well-known class of multiplexed sequences for cryptographic and spread spectrum applications is necessarily high for relatively small values of the phase shifts. Related design criteria for the multiplexer generator including the use of full positive difference sets are proposed. By generalizing the classical occupancy problem, higher order statistical weaknesses of multiplexed sequences are also established. © 2002 Elsevier Science (USA)  

In this paper, we present a deep insight into the behavior of optical code-division multiple-access (OCDMA) systems based on an incoherent, intensity encoding/decoding technique using a well-known class of codes, namely, optical orthogonal codes (OOCs). As opposed to parts I and II of this paper, where OOCs with cross-correlation lambda=1 were considered, we consider generalized OOCs with 1leslambdalesw, where w is the weight of the corresponding codes. To enhance the performance of such systems, we propose the use of an optical and logic gate receiver, which, in an ideal case, e.g., in the absence of any noise source, except the optical multiple-access interference, is optimum. Using some...