A general framework for accurate statistical timing analysis considering correlations

The impact of parameter variations on timing due to process variations has become significant in recent years. In this paper, we present a statistical timing analysis (STA) framework with quadratic gate delay models that also captures spatial correlations. Our technique does not make any assumption about the distribution of the parameter variations, gate delays, and arrival times. We propose a Taylor-series expansion-based quadratic representation of gate delays and arrival times which are able to effectively capture the nonlinear dependencies that arise due to increasing parameter variations. In order to reduce the computational complexity introduced due to quadratic modeling during STA, we also propose an efficient linear modeling driven quadratic STA scheme. We ran two sets of experiments assuming the global parameters to have uniform and Gaussian distributions, respectively. On an average, the quadratic STA scheme had 20.5times speedup in runtime as compared to Monte Carlo simulations with an rms error of 0.00135 units between the two timing cummulative density functions (CDFs). The linear modeling driven quadratic STA scheme had 51.5times speedup in runtime as compared to Monte Carlo simulations with an rms error of 0.0015 units between the two CDFs. Our proposed technique is generic and can be applied to arbitrary variations in the underlying parameters under any spatial correlation model

Statistical Static Timing Analysis has received wide attention recently and emerged as a viable technique for manufacturability analysis. To be useful, however, it is important that the error introduced in SSTA be significantly smaller than the manufacturing variations being modeled. Achieving such accuracy requires careful attention to the delay models and to the algorithms applied. In this paper, we propose a new sparse-matrix based framework for accurate path-based SSTA, motivated by the observation that the number of timing paths in practice is sub-quadratic based on a study of industrial circuits and the ISCAS89 benchmarks. Our sparse-matrix based formulation has the following advantages: (a) It places no restrictions on process parameter distributions; (b) It embeds accurate polynomial-based delay model which takes into account slope propagation naturally; (c) It takes advantage of the matrix sparsity and high performance linear algebra for efficient implementation. Our experimental results are very promising.

In conventional delay testing, the test clock is a single pre-defined parameter that is often set to be the same as the system clock. This paper discusses the potential of enhancing test efficiency by using multiple clock frequencies. The intuition behind our work is that for a given set of AC delay patterns, a carefully-selected, tighter clock would result in higher effectiveness to screen out the potential defective chips. Then, by using a smarter test clock scheme and combining with a second set of AC delay patterns, the overall quality of AC delay test can be enhanced while the cost of including the second pattern set can be minimized. We demonstrate these concepts through analysis and experiments using a statistical timing analysis framework with defect-injected simulation.

In this paper, we propose a new methodology for diagnosis of delay defects in the deep sub micron domain. The key difference between our diagnosis framework and other traditional diagnosis methods lies in our assumptions of the statistical circuit timing and the statistical delay defect size. Due to the statistical nature of the problem, achieving 100% diagnosis resolution cannot be guaranteed. To enhance diagnosis resolution, we propose a 3-phase diagnosis methodology. In the first phase, our goal is to quickly identify a set of candidate suspect faults that are most likely to cause the failing behavior based on logic constraints. In the second phase, we obtain a much smaller suspect fault set by applying a novel diagnosis algorithm that can effectively utilize the statistical timing information based upon a single defect assumption. In the third phase, our goal is to apply additional fine-tuned patterns to successfully narrow down to more exact suspect defect locations. Using a statistical timing analysis framework, we demonstrate the effectiveness of the proposed methodology for delay defect diagnosis, and discuss experimental results based on benchmark circuits.

The main objective of this paper is to present first and second-order sensitivity analysis of vibro-acoustic systems in the statistical energy analysis (SEA) frame work. Equations for computing these sensitivities for a general SEA model are obtained from two different approaches: (1) direct method and (2) adjoint method. The above equations are applied to a simple model of three plates, joined in the form of a ‘Z’, to minimize the total energy of one of the plates. It has been verified that these approaches lead to the same results and the difference between them is only with respect to the computational efficiency. The design sensitivity results calculated from the proposed analytical methods are compared with those obtained from the finite difference method, which show good agreement. The results of this paper can be useful to optimization of vibro-acoustic systems at the drawing board stage in the SEA framework.

Purpose: Osteoarthritis (OA) is a common degenerative disease involving a variety of structural changes in the affected joint. In addition to narrowing of the articular space, recent studies involving statistical shape analysis methods have suggested that specific bone shapes might be associated with the disease. We aim to investigate the feasibility of using the recently introduced framework of functional shapes (Fshape) to extract morphological features of OA that combine shape variability of articular surfaces of the tibia (or femur) together with the changes of the joint space. Approach: Our study uses a dataset of three-dimensional cone-beam CT volumes of 17 knees without OA and 17 knees with OA. Each knee is then represented as an object (Fshape) consisting of a triangulated tibial (or femoral) articular surface and a map of joint space widths (JSWs) measured at the points of this surface (joint space map, JSM). We introduce a generative atlas model to estimate a template (mean) Fshape of the sample population together with template-centered variables that model the transformations from the template to each subject. This approach has two potential advantages compared with other statistical shape modeling methods that have been investigated in knee OA: (i)Fshapes simultaneously consider the variability in bone shape and JSW, and (ii)Fshape atlas estimation is based on a diffeomorphic transformation model of surfaces that does not require a priori landmark correspondences between the subjects. The estimated atlas-to-subject Fshape transformations were used as input to principal component analysis dimensionality reduction combined with a linear support vector machine (SVM) classifier to identify the morphological features of OA. Results: Using tibial articular surface as the shape component of the Fshape, we found leave-one-out cross validation scores of for the classification based on the bone surface transformations alone, for the classification based on the residual JSM, and for the classification using both Fshape components. Similar results were obtained using femoral articular surfaces. The discriminant directions identified in the statistical analysis were associated with medial narrowing of the joint space, steeper intercondylar eminence, and relative deepening of the medial tibial plateau. Conclusions: The proposed approach provides an integrated framework for combined statistical analysis of shape and JSPs. It can successfully extract features correlated to OA that appear consistent with previous studies in the field. Although future large-scale study is necessary to confirm the significance of these findings, our results suggest that the functional shape methodology is a promising new tool for morphological analysis of OA and orthopedics data in general.

ROOT — A C++ framework for petabyte data storage, statistical analysis and visualization

Convolutional Neural Networks (CNNs) are widely used in computer vision, natural language processing, and so on, which generally require low power and high efficiency in real applications. Thus, energy efficiency has become a critical indicator of CNN accelerators. Considering that asynchronous circuits have the advantages of low power consumption, high speed, and no clock distribution problems, we design and implement an energy-efficient asynchronous CNN accelerator with a 65 nm Complementary Metal Oxide Semiconductor (CMOS) process. Given the absence of a commercial design tool flow for asynchronous circuits, we develop a novel design flow to implement Click-based asynchronous bundled data circuits efficiently to mask layout with conventional Electronic Design Automation (EDA) tools. We also introduce an adaptive delay matching method and perform accurate static timing analysis for the circuits to ensure correct timing. The accelerator for handwriting recognition network (LeNet-5 model) is implemented. Silicon test results show that the asynchronous accelerator has 30% less power in computing array than the synchronous one and that the energy efficiency of the asynchronous accelerator achieves 1.538 TOPS/W, which is 12% higher than that of the synchronous chip.

A low-power Si bipolar standard cell LSI design methodology for gigabit/second signal processing is described. To obtain high-speed operation, it features a pair of differential clock channels inside cells, differential clock distribution with the placement of differential wires of equal length and load, a performance-driven layout, and a highly accurate static timing analysis. A computer-aided-design-based optimization technology for power dissipation makes cell currents minimum while maintaining the circuit speed. A 5.6-K gate synchronous digital hierarchy signal-processing LSI operating at 1.6 Gbit/s with only 3.9 W power consumption demonstrates the effectiveness of this design method.

We propose a novel hierarchical clustering for distribution valued dissimilarities. Analysis of large and complex data has attracted significant interest. Symbolic Data Analysis (SDA) was proposed by Diday in 1980’s, which provides a new framework for statistical analysis. In SDA, we analyze an object with internal variation, including an interval, a histogram and a distribution, called a symbolic object. In the study, we focus on a cluster analysis for distribution valued dissimilarities, one of the symbolic objects. A hierarchical clustering has two steps in general: find out step and update step. In the find out step, we find the nearest pair of clusters. We extend it for distribution valued dissimilarities, introducing a measure on their order relations. In the update step, dissimilarities between clusters are redefined by mixture of distributions with a mixing ratio. We show an actual example of the proposed method and a simulation study.

The ordered probit model serves as an appropriate framework for statistical analysis whenever survey responses are ordinal as distinct from numerical. In this article we provide motivation for using the model, outline the underlying theory, illustrate the use of the model with a practical example on physiotherapists' beliefs regarding pain, and explain how the model's results should be interpreted. This article should be of interest to researchers in any field who require a rapid introduction to the method.

BackgroundOne of the most common goals of hierarchical clustering is finding those branches of a tree that form quantifiably distinct data subtypes. Achieving this goal in a statistically meaningful way requires (a) a measure of distinctness of a branch and (b) a test to determine the significance of the observed measure, applicable to all branches and across multiple scales of dissimilarity.ResultsWe formulate a method termed Tree Branches Evaluated Statistically for Tightness (TBEST) for identifying significantly distinct tree branches in hierarchical clusters. For each branch of the tree a measure of distinctness, or tightness, is defined as a rational function of heights, both of the branch and of its parent. A statistical procedure is then developed to determine the significance of the observed values of tightness. We test TBEST as a tool for tree-based data partitioning by applying it to five benchmark datasets, one of them synthetic and the other four each from a different area of biology. For each dataset there is a well-defined partition of the data into classes. In all test cases TBEST performs on par with or better than the existing techniques.ConclusionsBased on our benchmark analysis, TBEST is a tool of choice for detection of significantly distinct branches in hierarchical trees grown from biological data. An R language implementation of the method is available from the Comprehensive R Archive Network: http://www.cran.r-project.org/web/packages/TBEST/index.html.Electronic supplementary materialThe online version of this article (doi:10.1186/1471-2164-15-1000) contains supplementary material, which is available to authorized users.

The unprecedented amount of user generated content from emerging social media platforms like Facebook and Twitter make them invaluable sources of information for research. Twitter in particular has about 500 million registered accounts globally who are generating approximately 340 million messages daily containing personal updates, general life observations, opinions, moods, etc. Twitter's vast amount of data, which is generally available, offers an ideal source for mining entities' behaviors. This thesis explores two research streams involving mining Twitter data. In the first work, we seek to understand the Twitter-based stakeholder communication strategies of firms. We analyze tweets posted by firms to build a system that can automatically predict target stakeholder groups of a given tweet. We also examine and incorporate firm characteristics into the system for performance improvement. The result will potentially provide valuable business intelligence to market analysts who would like to discover social media strategies and behaviors of firms. In the second work, we investigate how readers from different parts of the world react to news headlines through their Twitter messages. We design a framework for data collection, statistical analysis, sentiment analysis, and language model comparison to understand the interests and reactions of Twitter users towards news headlines. The results from this work can possibly help news organizations have better understanding of their audience for better services. Though the two research directions may seem distinct, there are points of connection. In both cases, we are interested in the impact of companies (firms and news organizations). Moreover the methods used are similar. Our results illustrate that just by gathering Twitter data stream and developing a framework to examine them, we are able to discover many interesting insights about news readers and firms.

Fisheries biology encompasses a tremendous diversity of research questions, methods, and models. Many sub-fields use observational or experimental data to make inference about biological characteristics that are not directly observed (called “latent states”), such as heritability of phenotypic traits, habitat suitability, and population densities to name a few. Latent states will generally cause model residuals to be correlated, violating the assumption of statistical independence made in many statistical modelling approaches. In this exposition, we argue that mixed-effect modelling (i) is an important and generic solution to non-independence caused by latent states; (ii) provides a unifying framework for disparate statistical methods such as time-series, spatial, and individual-based models; and (iii) is increasingly practical to implement and customize for problem-specific models. We proceed by summarizing the distinctions between fixed and random effects, reviewing a generic approach for parameter estimation, and distinguishing general categories of non-linear mixed-effect models. We then provide four worked examples, including state-space, spatial, individual-level variability, and quantitative genetics applications (with working code for each), while providing comparison with conventional fixed-effect implementations. We conclude by summarizing directions for future research in this important framework for modelling and statistical analysis in fisheries biology.

The integration of renewable energy reduces electrical power system inertia, increasing vulnerability to disturbances. Conventional transient stability analysis suffers from event selectivity limitations. Hence, predetermined “worst case” scenarios overlook the risk associated with critical vulnerability patterns. This paper demonstrates that high-throughput simulation can systematically explore the entire contingency pattern to identify essential clusters of vulnerability. The automated framework reduces simulation time by 85 % while enabling statistical analysis across different inertia levels (<tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$2 ~\mathrm{s}, 8 ~\mathrm{s}$</tex>, 16s) and disturbance magnitudes (<tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$250-1000 \text{MW}$</tex>) using the IEEJ EAST 10-machine system. The RoCoF and Nadir results reveal distinct spatial vulnerability clustering, with buses 18, 19, 20, 36, 37, and 47 consistently exhibiting the highest impacts regardless of operating conditions. These topology-dependent vulnerability patterns require comprehensive rather than selective analysis for practical power system security assessment.