Sharif Digital Repository

In this paper, we propose CodedSketch, as a distributed straggler-resistant scheme to compute an approximation of the multiplication of two massive matrices. The objective is to reduce the recovery threshold, defined as the total number of worker nodes that the master node needs to wait for to be able to recover the final result. To exploit the fact that only an approximated result is required, in reducing the recovery threshold, some sorts of pre-compression are required. However, compression inherently involves some randomness that would lose the structure of the matrices. On the other hand, considering the structure of the matrices is crucial to reduce the recovery threshold. In... 

In this paper, we propose CodedSketch, as a distributed straggler-resistant scheme to compute an approximation of the multiplication of two massive matrices. The objective is to reduce the recovery threshold, defined as the total number of worker nodes that the master node needs to wait for to be able to recover the final result. To exploit the fact that only an approximated result is required, in reducing the recovery threshold, some sorts of pre-compression are required. However, compression inherently involves some randomness that would lose the structure of the matrices. On the other hand, considering the structure of the matrices is crucial to reduce the recovery threshold. In... 

One of the major challenges in using distributed learning to train complicated models with large data sets is to deal with stragglers effect. As a solution, coded computation has been recently proposed to efficiently add redundancy to the computation tasks. In this technique, coding is used across data sets, and computation is done over coded data, such that the results of an arbitrary subset of worker nodes with a certain size are enough to recover the final results. The major drawbacks with those approaches are (1) they are limited to polynomial functions, (2) the number of servers that we need to wait for grows with the degree of the model, (3) they are not numerically stable for... 

To study efficiency of the genetic algorithms (GAs) in optimization of aerodynamic shapes, shape of an airfoil is optimized by a genetic algorithm to obtain maximum lift to drag ratio and maximum lift. The flow field is assumed to be two dimensional, viscous, and transonic and is analyzed numerically. The camber line and thickness distribution of the airfoil are modeled by a fourth order polynomial. The airfoil chord length is assumed constant. Also, proper boundary conditions are applied. A finite volume method using the first order Roe's flux approximation and time marching (explicit) method is used for flow analysis. The simple genetic algorithm (SGA) is used for optimization. This... 

In an acceptance-sampling plan, where items of an incoming batch of products are inspected one by one, if the number of conforming items between successive non conforming items falls below a lower control threshold, the batch is rejected. If it falls above an upper control threshold, the batch is accepted, and if it lies within the thresholds then the process of inspecting the items continues. The purpose of this article is to develop an optimization model to determine the optimum values of the thresholds such that constraints on the probability of Type I and Type II errors are satisfied. This article starts by developing a Markovian model to derive the expected total cost of the inspection... 

If at least one out of two serial machines that produce a specific product in manufacturing environments malfunctions, there will be non conforming items produced. Determining the optimal time of the machines' maintenance is the one of major concerns. While a convenient common practice for this kind of problem is to fit a single probability distribution to the combined defect data, it does not adequately capture the fact that there are two different underlying causes of failures. A better approach is to view the defects as arising from a mixture population: one due to the first machine failures and the other due to the second one. In this article, a mixture model along with both Bayesian... 

A new approach is developed in this paper to detect general mean shifts of multivariate quality control systems and to determine the quality characteristic(s) responsible for the shift. This approach takes advantage of both a decomposition method and an EWMA-based control statistics that are employed for multivariate normal distributions. In order to evaluate the performance of the proposed methodology, simulation studies are provided to estimate the in- and out-of-control average run lengths under different mean and variance shift scenarios. Simulation experiments are also given to compare the performances of the proposed procedure with the ones of the well-known MEWMA and MCUSUM methods.... 

In this paper, a heuristic threshold policy is developed to detect and classify the states of a multivariate quality control system. In this approach, a probability measure called belief is first assigned to the quality characteristics and then the posterior belief of out-of-control characteristics is updated by taking new observations and using a Bayesian rule. If the posterior belief is more than a decision threshold, called minimum acceptable belief determined using a heuristic threshold policy, then the corresponding quality characteristic is classified out-of-control. Besides using a different approach, the main difference between the current research and previous works is that the... 

In this research, an iterative approach is employed to analyze and classify the states of uni-variate quality control systems. To do this, a measure (called the belief that process is in-control) is first defined and then an equation is developed to update the belief recursively by taking new observations on the quality characteristic under consideration. Finally, the upper and the lower control limits on the belief are derived such that when the updated belief falls outside the control limits an out-of-control alarm is received. In order to understand the proposed methodology and to evaluate its performance, some numerical examples are provided by means of simulation. In these examples, the... 

In this research, we employ Bayesian inference and stochastic dynamic programming approaches to select the binomial population with the largest probability of success from n independent Bernoulli populations based upon the sample information. To do this, we first define a probability measure called belief for the event of selecting the best population. Second, we explain the way to model the selection problem using Bayesian inference. Third, we clarify the model by which we improve the beliefs and prove that it converges to select the best population. In this iterative approach, we update the beliefs by taking new observations on the populations under study. This is performed using Bayesian... 

One of the most important properties of the maximally flat (MF) FIR fractional delay (FD) filter is its equivalence with the Lagrange interpolator for uniformly sampled signals. In this article, to provide the required background for the reader, we first propose a straightforward algebraic proof for this equivalence. This proof is given by simply demonstrating that the system of linear equations governing the maximally flatness property of this filter is the same as the one from which the coefficients of the Lagrange interpolator are computed. We then present the main contribution of the paper, which is a frequency domain proof for the same equivalence. In contrast with its classic... 

Compartment noise has gained significant importance to meet customer expectation. One of the dominant sources of noise from whole engine as a system is the one which is induced from fresh air intake. Geometrical features in air induction systems (AIS) airflow path are often responsible for unusual noise due to the complex air flow structure and its interaction with the internal acoustic field. To reduce air intake noise basically resonator and expansion chamber are used on automotive vehicles. Resonators are widely used for noise reduction of air induction systems. Although, airflow bench tests are faster to evaluate various alternate design geometries, understanding the mechanism of such... 

Although the fractional delay filtering literature is full of design methods and implementation techniques for fractional sample interpolators, a fundamental need for the proposition of low-order efficient designs still strongly exists. Proposed is such a system for half-sample interpolation. In contrast to the typical systems studied in the literature for fractional delay filtering, the system proposed continuously adapts its interpolation kernel to the statistical variations of the input signal, and this is in fact the reason for it being needless of having a high order. Satisfactory performance of the proposed structure has been demonstrated via simulation  

The maximally flat (MF) fractional-delay (FD) allpass filter, also known as Thiran's allpass filter, is one of the most popular IIR FD systems which is typically deployed in its causal forms. It is shown that if this causality constraint is removed, MFFD allpass filters with considerably wider bandwidths can be obtained. In many applications this extra bandwidth is worth having a non-causal system  

The maximally flat (MF) fractional delay (FD) filter which is in fact a Lagrange interpolator for uniformly sampled signals, has previously been shown to be equal to the scaled binomially windowed shifted version of the sinc function; the ideal interpolation kernel for band-limited signals. In this paper, another proof for this equivalence is presented. Unlike its counterparts available in the literature, the proof given here is neither strictly algebraic, nor deploys the explicit coefficient formulas of the MFFD filter. It follows a frequency domain approach based on the definition of this filter instead, and aims to provide more insight into the corresponding equivalence. © 2009 Elsevier... 

The maximally flat (MF) fractional delay (FD) filter which is in fact a Lagrange interpolator for uniformly sampled signals, has previously been shown to be equal to the scaled binomially windowed shifted version of the sinc function; the ideal interpolation kernel for band-limited signals. In this paper, another proof for this equivalence is presented. Unlike its counterparts available in the literature, the proof given here is neither strictly algebraic, nor deploys the explicit coefficient formulas of the MFFD filter. It follows a frequency domain approach based on the definition of this filter instead, and aims to provide more insight into the corresponding equivalence. © 2009 Elsevier... 

The Taylor series-based representation of the maximally flat (MF) FIR fractional delay (FD) filter is manipulated to obtain a FD filter with a wider band-width. The band-width of the proposed filter can approach π / 2 rads / s, which is 1.5 times that of the prototype one. The design has closed-form coefficient formulas as well as a modular implementation. These two properties make it a practically favourable one. © 2008 Elsevier B.V. All rights reserved  

A fast and simple procedure for designing relatively wide band fractional delay (FD) all-pass filters is proposed and filters designed based on it are compared to those designed using Thiran’s method, which is one of the simplest, fastest and widely used approaches in designing FD all-pass filters. It is shown that filters designed using the introduced method have wider fractional group delay (fgpd) bandwidths compared to those obtained via Thiran’s technique, as well as some other desired properties. The designed filters are also demonstrated to be stable for several pairs of filter orders and fgpd values. r2007 Elsevier B.V. All rights reserved  

A fast and simple procedure for designing relatively wide band fractional delay (FD) all-pass filters is proposed and filters designed based on it are compared to those designed using Thiran's method, which is one of the simplest, fastest and widely used approaches in designing FD all-pass filters. It is shown that filters designed using the introduced method have wider fractional group delay (fgpd) bandwidths compared to those obtained via Thiran's technique, as well as some other desired properties. The designed filters are also demonstrated to be stable for several pairs of filter orders and fgpd values. © 2007 Elsevier B.V. All rights reserved