Enhanced Pathological Element-Based Symbolic Nodal Analysis

A new approach to the problem of symbolic circuit analysis of large-scale circuits is presented. The methodology has been implemented in a computer program called SCAPP (symbolic circuit analysis program with partitioning). The method solves the problem by utilizing a hierarchical network approach and the sequence of expressions concept rather than a topological approach and the single expression idea which have dominated symbolic analysis in the past. The result is a linear growth in the number of terms in the symbolic solutions for the network approach versus the exponential growth exhibited by traditional methods. The analysis methodology introduces the concept of the RMNA (reduced modified nodal analysis) matrix. This allows the characterization of symbolic networks in terms of only a small subset of the network variables (external variables) rather than the complete set of variables. The analysis algorithm is most efficient when network partitioning is used. Partitioning results in a reduction in the number of terms in the symbolic solutions.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

In this paper, a new appearance-based technique called symbolic factorial discriminant analysis (symbolic FDA) is explored for face representation and recognition under varying illumination conditions. In the past few years, many appearance-based methods have been proposed to model image variations of human faces under different lighting conditions using single valued variables to represent the facial features. In the proposed symbolic factorial discriminant analysis method, we extract interval type discriminating features, which are robust to illumination changes. The minimum distance classifier with symbolic dissimilarity measure is used for classification. The proposed method has been successfully tested for face recognition using three databases, namely, Yale Face database B, CMU PIE database and Harvard database. The experimental results have demonstrated the effective performance of this method.

Symbolic circuit analysis using Mathematics A method of symbolic circuit analysis using Mathematica is reported. With the powerful symbolic manipulation capacity of Mathematica, symbolic circuit analysis is significantly simplified. The analysed circuits can be passive or active, with active devices modelled by nullors. Non-trivial circuit analysis examples are presented and the program list is given.

Analog integrated circuit designers always use closed-form design equations in design reasoning. However, most of the time, they have to derive all equations by hand. When high-order effects are of interest, manual derivation would become much harder. Although the art of symbolic circuit analysis has been making steady progress, symbolically generating closed-form equations for high-order effect is still a less well-studied subject. This paper proposes a novel symbolic computation method for generating the second-order characterization of differential cells. It is a perturbation approach that takes the advantage of structural symmetry in differential cells, and is formulated as a systematic computation procedure comprised of several intermediate steps, the computation of each step gives a compact partial expression. Examples are provided to illustrate that closed-form common-mode rejection ratio equations in pole-zero form (unknown before) for two classical operational amplifiers can be generated by applying the symbolic perturbation procedure.

A formulation approach for symbolic analysis of analog circuits modeled by nullors, is introduced. The proposed technique is based on manipulating data-structures: including only admittances, nullators and norators, instead of the nodal-admittance-matrix manipulation. By using this technique, CPU-time minimization as well as fast manipulation of complex symbolic expressions are tasks highly improved. Thus, the reduced system of equations is formulated by fill-in the reduced admittance-matrix using the nullor interconnection-properties.

We can model embedded systems as hybrid systems. Moreover, they are distributed and real-time systems. Therefore, it is important to specify and verify randomness and soft real-time properties. For the purpose of system verification, we formally define probabilistic linear hybrid automaton and its symbolic reachability analysis method. It can describe uncertainties and soft real-time characteristics. Our proposal method is the first attempt to symbolically verify probabilistic linear hybrid automata.KeywordsModel CheckLogical FormulaDiscrete TransitionHybrid AutomatonReachability AnalysisThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

New interval clustering technology for symbolic data analysis (SDA) on smart phones is shown to be beneficial for mobile computing devices for smart data analysis in this paper. A new interval clustering method that combined the rough set with interval possibilistic fuzzy C-means (IPFCM) algorithm under Euclidean distance is proposed and implemented on smart phones. Symbolic clustering algorithms (SCAs) have been widely used for pattern recognition, data mining, artificial intelligence, etc. In general, the SCA is unsupervised classification that is divided into groups according to symbolic data sets. However, the traditional interval fuzzy C-means (IFCM) clustering method still has noisy and data overlapping problems associated with these symbolic interval data. Hence, a new rough set with the interval possibilistic fuzzy C-means (RIPFCM) clustering algorithm with Euclidean distance was proposed to address the symbolic interval data (SID). That is, the proposed method can perform better than the traditional IFCM clustering algorithm for SID clustering in noisy environments and with data overlapping problems. The new RIPFCM algorithm under the Euclidean distance method was proposed to deal with SID on new applications in smart phones. Consequently, this method shows the expansion of the smart phone’s computing power and its future application in new SDA.

This paper describes a new approach for dynamic code analysis. It combines dynamic symbolic execution and static code analysis with fuzzing to increase efficiency of each component. During fuzzing we recover indirect function calls and pass that information to the static analysis engine. This improves static path detection in the control flow graph of a program. Detected paths are used in dynamic symbolic execution to construct inputs which will cover new paths during execution. These inputs are used by the fuzzing tool to improve test-case generation and increase code coverage. The proposed approach can be used for classic fuzzing when the main goal is achieving high code coverage. As well it can be used for targeted analysis of paths and code fragments in the program. In this case the fuzzing tool accepts a set of programs addresses with potential defects and passes them to the static analysis engine. The engine constructs all paths connecting program entry point to the given addresses. Finally, dynamic symbolic execution is used to construct the set of inputs, which will cover these paths. Experimental results have shown that the proposed method can effectively detect different program defects.

SummaryKnowing the Network Function (NF) pertaining to a certain input–output couple individuated inside a linear electrical network (LEN) is crucial, as it provides a synthetic and effective description of the input–output relationship and allows one to derive several key features of the subject system as well as to devise proper strategies to modify them.From a mathematical point of view, an NF may be expressed as the product of a real number, called the gain constant (GC), by a real rational function of the complex variables, whose numerator and denominator are called the zero polynomial (ZP) and the characteristic polynomial (CP), respectively, and may be obtained by calculating the determinants of proper matrices. However, when a design‐oriented symbolic hand analysis is needed, calculating the said polynomials in this manner may turn out to be tediously cumbersome; and above all, such a route may fail to illuminate the way that their coefficients depend on the circuit elements. The same may be said of numerical computer methods, which are suited to providing a global description of the NF in the frequency domain rather than analytical expressions of its coefficients. In this paper, a method is proposed that permits one to obtain the ZP without calculating any determinants. With respect to other methods that achieve the same goal, the present one does not require prior calculation of the CP or a nullator‐norator pair (NNP) to be compulsorily inserted in the subject circuit. Instead, it is based on applying the Andreani‐Mattisson extension (AME) of the Cochrun–Grabel algorithm (CGA) for the calculation of the CP to a circuit obtained from the assigned one by inserting in the latter a proper dependent source. The nature of such new circuit allows the worker to employ the classical tools of LEN theory so as to make the analysis as simple as possible and often performable by straightforward inspection, without the need for possibly involved equilibrium equations. Moreover, it is shown how the same technique can be applied to a properly modified version of the original network in order to calculate the CP as well. In this case (not compulsorily but if judged convenient for simplifying the calculations), a NNP may be employed in conjunction with the dependent source. The proposed method once again allows one to exploit the classic tools of LEN theory so as to considerably, if not drastically, simplify the analysis associated with the direct application of the AME to the original network. Finally, the calculation of the GC (that completes the knowledge of the whole NF under study) as well as circuit degeneracy are discussed and practical examples of application of the proposed techniques are given. Copyright © 2013 John Wiley &amp; Sons, Ltd.

This paper presents a new approach to symbolic network analysis. The procedure is entirely topology oriented because it operates with a netlist description of the analyzed circuit. The obtained network function has nested form. The method introduces a graph representation of the factorization process, that is constructed directly from a given circuit description. Therefore, it is named Topology Decision Diagram (TDD). This graph serves as a skeleton for network function generation. TDD construction starts from the original circuit and spreads to simplified subcircuits. Every subsequent subcircuit is obtained by replacing a circuit branch with an open or a short. The proposed procedure generates the network function in reverse order. It starts from a single circuit parameter placed as a leaf of TDD. Thereafter, the circuit function grows instantiating the other circuit parameter one by one in a sequential order. The proposed method was developed for analogue CMOS circuits and, consequently, recognizes R, L, C and gm as circuit components.

This chapter summarizes the analysis and design of analog integrated circuits (ICs) using the nullor concept and pathological elements. First, the usefulness of the nullor concept and pathological elements is highlighted through modeling the behavior of several active devices, which are used to perform symbolic nodal analysis of analog integrated circuits. Second, the nullator and norator elements are used to develop a binary genetic encoding (BGE) technique for the systematic design of active devices. For instance, we show the computational synthesis of current mirrors (CMs), and we discuss the synthesis of four unity-gain cells, which are combined for the design of mixed-mode amplifiers, such as: current conveyors and current-feedback operational amplifiers. Finally, those active devices are biased and sized (optimized) by applying evolutionary algorithms. Several applications of the active devices, e.g. to implement filters and oscillators, are described herein, while novel applications are provided in the following chapters.

Lcapy is an open-source Python package for solving linear circuits symbolically. It uses a superposition of DC analysis, AC (phasor) analysis, transient (Laplace) analysis, and noise analysis. Expressions are evaluated using the computer algebra system SymPy. Lcapy can model circuits comprised of combinations of one-port and two-port networks or circuits specified using a netlist with a Spice-like notation. Lcapy can present the system of equations produced from nodal analysis, modified nodal analysis, loop analysis, and state-space analysis. Expressions can be formatted into many representations, parameterized, and transformed to other domains. Dimensional analysis is performed to reduce user errors and to present results with units. Both continuous and discrete signals are supported. Lcapy produces high-quality output. Textbook quality schematics in a number of different formats can be generated from netlists and customized for different conventions. Expressions can be formatted into LaTeX format for inclusion into a document or numerically evaluated and plotted. An overview of the features and capabilities of Lcapy is presented, along with implementation details and performance considerations.

In this paper, we propose a direction-of-arrival (DOA) estimation method, which uses deep neural network (DNN) with regression to learn the mapping from the array covariance matrix to the DOAs of multiple source signals. Simulation results demonstrate that the proposed method is efficient in both training and testing stages over the existing DNN based classification method. In particular, the training time and the testing time spent by the proposed method are about 9 times and 2 times less than those by the DNN based classification methods, respectively. Furthermore, it performs significantly better than the classical multiple signal classification method (MUSIC) in terms of efficiency. On the other hand, the root mean square error (RMSE) of DOA estimates by the proposed method is much higher than that by the MUSIC method and approaches to the CRB in harsh conditions such as low SNRs and/or closely spaced source signals.

Symbolic circuit analysis suffers as the symbolic terms increases by many folds with the increase in the size of the circuit. Hence simplification techniques are used for the analysis of the circuits which are larger in size. In this work, multi‐objective evolutionary optimisation algorithms for obtaining simplified symbolic expressions of analog amplifier circuits are presented which are not only very efficient in terms of speed and the amount of circuit reduction but also solve the accuracy problems. Initially, all MOSFETs are replaced with their nullor equivalent model. Then, the formulation of accurate fully‐symbolic noise expressions is carried out by the application of symbolic nodal analysis. The derived exact symbolic expressions are then simplified using an evolutionary approach. This method has been successfully coded in MATLAB. The numerical results obtained before and after simplification are compared with SPICE simulation to demonstrate the efficiency of the proposed methodology.

A new approach to data processing and uncertainty modeling based on the use of computational probabilistic analysis is considered. The basis of computational probabilistic analysis is numerical operations on probability density functions represented by piecewise polynomial functions. The problems of predicting the time series of distributions and estimating the probability densities of solutions of boundary value problems and systems of nonlinear equations with random coefficients are considered. Interval analysis, functional data analysis, symbolic data analysis and Monte Carlo method are currently used to study such data. A comparison of these approaches is given. Numerical examples show the effectiveness of the proposed approaches.