Statistical estimation of sequential circuit activity

Power estimation for CMOS sequential circuits is difficult because of sequential feedback loops embedded in the circuits. This paper presents a new method which applies probabilistic propagation and an iteration method to obtain the transition probability of circuit internal nodes. The time and space complexity of computation is improved by compacting the circuit before calculation. Experimental results show that our method is applicable even for large sequential circuits.

This paper describes a technique to handle temporal signal correlations during estimation of average power in sequential circuits. A key feature of the approach is that it provides an efficient and accurate way to estimate average power using a Monte Carlo based method. Results on a large number of benchmark sequential circuits confirm that the technique runs efficiently (up to two orders of magnitude better than long run simulation) and yields accurate estimation of average power (on an average within 1% of long run simulation result). Results also indicate that if temporal correlations are ignored, the estimates of average power can be off by more than 55% for some benchmark circuits.

The most complex models with the high quality of the results obtained are, as a rule, more expensive in terms of developer qualifications and computational resources. During process design, a detailed description of the object is often not required, and the accuracy of the results obtained should not be higher than the accuracy of the measuring instruments used. Thus, the optimal combination of simplicity and quality of the mathematical description of technological processes is an urgent task of mathematical modeling. To identify a cell model developed based on the theory of Markov chains, data obtained by solving discrete models of the Boltzmann equation are used. A method to identify cell models of a fluidized bed reactor has been developed using data obtained based on solving discrete models of the Boltzmann equation. The adequacy of the identified model of a fluidized bed reactor has been verified. An approach to develop computational support for a cell model based on the theory of Markov chains is presented. The analysis of the results obtained has shown an adequate description of the processes in fluidized bed reactors in terms of cell models. The models are developed based on the theory of Markov chains and identified based on the results obtained within the framework of discrete models of the Boltzmann equation. The proposed method to identify and verify cell models provides the possibility to obtain simultaneously acceptable indicators of model simplicity and the accuracy of calculation of the design and operating parameters of fluidized bed reactors.

We describe a method of polynomial simulation to calculate switching activities in a general-delay logic circuit. This method is a generalization of the exact signal probability evaluation method due to Parker and McCluskey, which has been extended to handle temporal correlation and arbitrary transport delays. The method can target both combinational and sequential circuits. Our method is parameterized by a single parameter l, which determines the speed-accuracy tradeoff. l indicates the depth in terms of logic levels over which spatial signal correlation is taken into account. This is done by only taking into account reconvergent paths whose length is at most l. The rationale is that ignoring spatial correlation for signals that reconverge after many levels of logic introduces negligible error. When l = L, where L is the total number of levels of logic in the circuit, the method will produce the exact switching activity under a zero delay model, taking into account all internal correlation. We present results that show that the error in the switching activity and power estimates is very small even for small values of l. In fact, for most of the examples, power estimates with l = 0 are within 5% of the exact. However, this error can be higher than 20% for some examples. More robust estimates are obtained with l = 2, providing a good compromise between speed and accuracy.

Risk assessment and simulation of gas pipeline leakage based on Markov chain theory

Product quality is very important because many faults have a real impact on users directly. It is significative that Markov chain theory is applied in product quality prediction. A new method of state transition probability matrix in Markov chain is used to provide fault diagnosis and quality prediction in this paper. The aim of this study is to deliver a quality prediction method for mechanical and electrical product by using the data collection and analysis techniques. Firstly, a new approach of fault diagnosis was presented by using the theory of state transition probability matrix. Then, Markov chain theory is used to build the mathematical patterns in the quality prediction with the state transition probability matrix. Finally, we illustrate the veracity rationality and science of the approved method using a numerical example of ball valves.

Application of a mathematical model — based jointly on Graph Theory and Markov chains theory — to the molecular distribution in monodimensional systems of order II (i.e. systems with functional groups belonging to two distinct co‐reactive species A and B) allows one to obtain very general matrix expressions for the molecular distribution functions of many linear copolycondensates.

The classical method of solving random walk problems involves using Markov chain theory. When the particular random walk of interest is written in matrix form using Markov chain theory, the problem must then be solved using a digital computer. To solve all but the most trivial random walk problems by hand would be extremely difficult and time consuming. Very large random walk problems may even prove difficult to solve on the smaller digital computers. This paper intends to demonstrate a method that may be used to solve large random walk problems in a quick and economical manner. This alternate method uses resistive analogues and has the added feature of extracting particular solutions without having to completely solve the problem as would be necessary using a digital computer. Many analogues of random walks may also be quickly amended to include other random walks with relative ease using this alternate method of solution. Because this method uses nothing more than a power supply, a DC voltmeter and a set of resistors, the analogue of a particular random walk problem may be left set-up without incurring any loss of time or money on a digital computer. Once the resistors are mounted in a permanent fashion, the random walk analogues may also be used as an effective demonstration of random walk probabilities in the classroom.

Brain image registration is fundamental for medical imaging to allow the matching of images from multiple modalities, temporal sequences, and people to offer spatial correlation. This is crucial for activities such as cohort studies, intervention recommendations, and treatment monitoring, where exact alignment assures consistent analysis. Notwithstanding their importance, modern brain image registration techniques have many shortcomings, including limited resistance to noise, misalignment in multi-modality images, and costly computational expenses. These limits may impede real-time clinical environment practical implementation and provide less than optimal registration accuracy. This study addresses these issues by means of an Improved Brain Image Registration Technique Using Machine Learning Algorithms (BIRT-MLA). The proposed architecture detects significant image properties by means of convolutional neural networks (CNNs), therefore enabling feature extraction. By applying a supervised learning method, it guarantees precise alignment even in noisy and demanding imaging situations by forecasting transformation parameters. Lowering the registration error by modern optimization techniques helps to save processing time and maintain remarkable accuracy even in this respect. Using CNNs, the proposed method helps to effectively classify brain images, thereby improving diagnostic support and the usefulness of registered images for downstream operations. Improving clinical judgment and simplifying processes rely on grouping registration and categorization into a logical sequence. By means of enhanced alignment precision, resistance to picture faults, and shortened computing time compared to current approaches, experimental findings expose the advantages of the suggested technology. This development may be very useful in clinical and experimental settings, thereby supporting the accuracy and efficiency of brain picture analysis.

The goal of this paper is to develop a general method to establish conditional ergodicity of infinite-dimensional Markov chains. Given a Markov chain in a product space, we aim to understand the ergodic properties of its conditional distributions given one of the components. Such questions play a fundamental role in the ergodic theory of nonlinear filters. In the setting of Harris chains, conditional ergodicity has been established under general nondegeneracy assumptions. Unfortunately, Markov chains in infinite-dimensional state spaces are rarely amenable to the classical theory of Harris chains due to the singularity of their transition probabilities, while topological and functional methods that have been developed in the ergodic theory of infinite-dimensional Markov chains are not well suited to the investigation of conditional distributions. We must therefore develop new measure-theoretic tools in the ergodic theory of Markov chains that enable the investigation of conditional ergodicity for infinite dimensional or weak-* ergodic processes. To this end, we first develop local counterparts of zero-two laws that arise in the theory of Harris chains. These results give rise to ergodic theorems for Markov chains that admit asymptotic couplings or that are locally mixing in the sense of H. F\"{o}llmer, and to a non-Markovian ergodic theorem for stationary absolutely regular sequences. We proceed to show that local ergodicity is inherited by conditioning on a nondegenerate observation process. This is used to prove stability and unique ergodicity of the nonlinear filter. Finally, we show that our abstract results can be applied to infinite-dimensional Markov processes that arise in several settings, including dissipative stochastic partial differential equations, stochastic spin systems and stochastic differential delay equations.

The quality of engineers is an important issue in industrialised countries. This quality is commonly assured by the accreditation of engineering programs and the certification, licensure, and registration of graduates. A high-quality engineering program should be concerned with the quality of education of its graduates. This paper presents an analytical method for understanding the cumulative effects of competence acquisition in courses on the quality of engineering programs, thus allowing quality enhancement from a global perspective of the program. The proposed method was developed from a model established through the theory of Markov chains, considering the cumulative effects of acquisition of competencies over the semesters on the quality of engineering graduates. In the proposed model, the quality of engineering graduates is represented by discrete levels, numbered from 1 to 5, representing the worst to the best quality, respectively. This paper does not answer the question of how to achieve the desired quality or what learning methods could be used; however, the method can predict the quality of engineering education in a program and provide information to allow the faculty an opportunity to adjust their teaching during the program. The model explains how the heterogeneity of learning affects the average quality of engineering graduates. Understanding this process is critical to proactive quality management in engineering undergraduate programs.

One of the central considerations in the theory of Markov chains is their convergence to an equilibrium. Coefficients of ergodicity provide an efficient method for such an analysis. Besides giving sufficient and sometimes necessary conditions for convergence, they additionally measure its rate. In this paper we explore coefficients of ergodicity for the case of imprecise Markov chains. The latter provide a convenient way of modelling dynamical systems where parameters are not determined precisely. In such cases a tool for measuring the rate of convergence is even more important than in the case of precisely determined Markov chains, since most of the existing methods of estimating the limit distributions are iterative. We define a new coefficient of ergodicity that provides necessary and sufficient conditions for convergence of the most commonly used class of imprecise Markov chains. This so-called weak coefficient of ergodicity is defined through an endowment of the structure of a metric space to the class of imprecise probabilities. Therefore we first make a detailed analysis of the metric properties of imprecise probabilities.

We propose an inter-disciplinary approach to particle swarm optimization (PSO) by establishing a molecular dynamics (MD) formulation of the algorithm, leading to a physical theory for the swarm environment. The physical theory provides new insights on the operational mechanism of the PSO method. In particular, a thermodynamic analysis, which is based on the MD formulation, is introduced to provide deeper understanding of the convergence behavior of the basic classical PSO algorithm. The thermodynamic theory is used to propose a new acceleration technique for the PSO. This technique is applied to the problem of synthesis of linear array antennas and very good improvement in the convergence performance is observed. A macroscopic study of the PSO is conducted by formulating a diffusion model for the swarm environment. The Einstein’s diffusion equation is solved for the corresponding probability density function (pdf) of the particles trajectory. The diffusion model for the classical PSO is used, in conjunction with Schrodinger’s equation for the quantum PSO, to propose a generalized version of the PSO algorithm based on the theory of Markov chains. This unifies the two versions of the PSO, classical and quantum, by eliminating the velocity and introducing position-only update equations based on the probability law of the method.

Research on query cost estimation for local database systems in a multidatabase system (MDBS) has attracted many researchers in the database area recently. Obtaining good query cost estimates is crucial for performing effective global query optimization in an MDBS. However, most techniques suggested so far, including database calibrating and query sampling, consider only a static multidatabase environment. Recently, we proposed a qualitative approach to developing cost models for a dynamic multidatabase environment. It has been shown that this approach is promising in estimating the cost of a query run in any given contention state for a dynamic environment. However, a large (cost) query in practice may experience multiple contention states during its execution, which cannot be directly handled by the qualitative approach. In this paper, we propose two new techniques, i.e., fractional analysis and probabilistic approach, to solve the problem. The fractional analysis technique, which is suitable for a system environment that changes contention states gradually and smoothly, estimates a query cost by analyzing its fractions. The probabilistic approach, which is suitable for a system environment that changes contention states rapidly and randomly, estimates a query cost based on the theory of Markov chains. Cost estimation formulas for both techniques are derived, and their properties are studied. Our experimental results demonstrate that the suggested techniques are quite promising in estimating costs for large queries in a dynamic multidatabase environment.

A major challenge of the heterogeneous wireless networks is how to jointly utilize the resources of different radio access technologies (RATs) in an efficient manner while simultaneously achieving the desired multi-service quality of service (QoS) and minimizing the service cost. To meet the challenge, this paper proposes an adaptive common radio resource management (CRRM) scheme in the context of wireless wide area network (WWAN) and wireless local area network (WLAN). The key parameters of the scheme are service type, user mobility and location information, load information, and service cost. The effectiveness of the proposed CRRM scheme is assessed analytically using the theory of Markov chains. Numerical results show that the proposed scheme minimizes the rate of unnecessary vertical handoffs (VHO), thereby providing stable communication without degrading call blocking performance and increasing service cost.