Generalized nonlinear timing/phase macromodeling: Theory, numerical methods and applications

Abstract—We extend the concept of timing/phase macromodels, pre-viously established rigorously only for oscillators, to apply to gen-eral systems, both non-oscillatory and oscillatory. We do so by first establishing a solid foundation for the timing/phase response of any nonlinear dynamical system, then deriving a timing/phase macromodel via nonlinear perturbation analysis. The macromodel that emerges is a scalar, nonlinear time-varying equation that accurately characterizes the system’s phase/timing responses. We establish strong links of this technique with projection frameworks for model order reduction. We then present numerical methods to compute the phase model. The computation involves a full Floquet decomposition – we discuss numerical issues that arise if direct computation of the monodromy matrix is used for Floquet analysis, and propose an alternative method that are numerically superior. The new method has elegant connections to the Jacobian matrix in harmonic balance method (readily available in most RF simulators). We validate the technique on several highly nonlinear systems, in-cluding an inverter chain and a firing neuron. We demonstrate that the new scalar nonlinear phase model captures phase responses under various types of input perturbations, achieving accuracies consider-ably superior to those of reduced models obtained using LTI/LPTV MOR methods. Thus, we establish a powerful new way to extract timing models of combinatorial/sequential systems and memory (e.g., SRAMs/DRAMs), synchronization systems based on oscillator enslaving (e.g., PLLs, injection-locked oscillators, CDR systems, neural processing, energy grids), signal-processing blocks (e.g., ADCs/DACs, FIR/IIR filters), etc.. I

An efficient, fully nonlinear, variability-aware non-monte-carlo yield estimation procedure with applications to SRAM cells and ring oscillators

Abstract — Failures and yield problems due to parameter vari-ations have become a significant issue for sub-90-nm technologies. As a result, CAD algorithms and tools that provide designers the ability to estimate the effects of variability quickly and accurately are being urgently sought. The need for such tools is particularly acute for static RAM (SRAM) cells and integrated oscillators, for such circuits require expensive and high-accuracy simulation during design. We present a novel technique for fast computation of parametric yield. The technique is based on efficient, adaptive geometric calculation of probabilistic hypervolumes subtended by the boundary separating pass/fail regions in parameter space. A key feature of the method is that it is far more efficient than Monte-Carlo, while at the same time achieving better accuracy in typical applications. The method works equally well with parameters specified as corners, or with full statistical distributions; importantly, it scales well when many parameters are varied. We apply the method to an SRAM cell and a ring oscillator and provide extensive comparisons against full Monte-Carlo, demonstrating speedups of 100-1000×. I

Lattice model constructions for gapless domain walls between topological phases

Domain walls between different topological phases are one of the most interesting phenomena that reveal the non-trivial bulk properties of topological phases. Very recently, gapped domain walls between different topological phases have been intensively studied. In this paper, we systematically construct a large class of lattice models for gapless domain walls between twisted and untwisted gauge theories with arbitrary finite group $G$. As simple examples, we numerically study several finite groups(including both Abelian and non-Abelian finite group such as $S_3$) in $2$D using the state-of-the-art loop optimization of tensor network renormalization algorithm. We also propose a physical mechanism for understanding the gapless nature of these particular domain wall models. Finally, by taking advantage of the classification and construction of twisted gauge theories using group cohomology theory, we generalize such constructions into arbitrary dimensions, which might provide us a systematical way to understand gapless domain walls and topological quantum phase transitions.Comment: Non-Abelian examples adde

Enforced symmetry breaking by invertible topological order

It is well known that two-dimensional fermionic systems with a nonzero Chern number must break the time reversal symmetry, manifested by the appearance of chiral edge modes on an open boundary. Such an incompatibility between topology and symmetry can occur more generally. We will refer to this phenomenon as enforced symmetry breaking by topological orders. In this work, we systematically study enforced breaking of a general finite group $G_f$ by a class of topological orders, namely 0D, 1D and 2D fermionic invertible topological orders. Mathematically, the symmetry group $G_f$ is a central extension of a bosonic group $G$ by the fermion parity group $Z_2^f$, characterized by a 2-cocycle $\lambda$ $\in H^2(G,Z_2)$. With some minor assumptions and for given $G$ and $\lambda$, we are able to obtain a series of criteria on the existence or non-existence of enforced symmetry breaking by the fermionic invertible topological orders. Using these criteria, we discover many examples that are not known previously. For 2D systems, we define the physical quantities to describe symmetry-enriched invertible topological orders and derive some obstruction functions using both fermionic and bosonic languages. In the latter case which is done via gauging the fermion parity, we find that some obstruction functions are consequences of conditional anomalies of the bosonic symmetry-enriched topological states, with the conditions inherited from the original fermionic system. We also study enforced breaking of the continuous group $SU_f(N)$ by 2D invertible topological orders through a different argument.Comment: 29 pages, 4 figures, 6 tables, comment and suggestion are welcom

Enlarged Training Dataset by Pairwise GANs for Molecular-Based Brain Tumor Classification

This paper addresses issues of brain tumor subtype classification using Magnetic Resonance Images (MRIs) from different scanner modalities like T1 weighted, T1 weighted with contrast-enhanced, T2 weighted and FLAIR images. Currently most available glioma datasets are relatively moderate in size,and often accompanied with incomplete MRIs in different modalities. To tackle the commonly encountered problems of insufficiently large brain tumor datasets and incomplete modality of image for deep learning, we propose to add augmented brain MR images to enlarge the training dataset by employing a pairwise Generative Adversarial Network (GAN) model. The pairwise GAN is able to generate synthetic MRIs across different modalities. To achieve the patient-level diagnostic result, we propose a post-processing strategy to combine the slice-level glioma subtype classification results by majority voting. A two-stage course-to-fine training strategy is proposed to learn the glioma feature using GAN-augmented MRIs followed by real MRIs. To evaluate the effectiveness of the proposed scheme, experiments have been conducted on a brain tumor dataset for classifying glioma molecular subtypes: isocitrate dehydrogenase 1 (IDH1) mutation and IDH1 wild-type. Our results on the dataset have shown good performance (with test accuracy 88.82%). Comparisons with several state-of-the-art methods are also included

Deep semi-supervised learning for brain tumor classification

Background: This paper addresses issues of brain tumor, glioma, classification from four modalities of Magnetic Resonance Image (MRI) scans (i.e., T1 weighted MRI, T1 weighted MRI with contrast-enhanced, T2 weighted MRI and FLAIR). Currently, many available glioma datasets often contain some unlabeled brain scans, and many datasets are moderate in size. Methods: We propose to exploit deep semi-supervised learning to make full use of the unlabeled data. Deep CNN features were incorporated into a new graph-based semi-supervised learning framework for learning the labels of the unlabeled data, where a new 3D-2D consistent constraint is added to make consistent classifications for the 2D slices from the same 3D brain scan. A deep-learning classifier is then trained to classify different glioma types using both labeled and unlabeled data with estimated labels. To alleviate the overfitting caused by moderate-size datasets, synthetic MRIs generated by Generative Adversarial Networks (GANs) are added in the training of CNNs. Results: The proposed scheme has been tested on two glioma datasets, TCGA dataset for IDH-mutation prediction (molecular-based glioma subtype classification) and MICCAI dataset for glioma grading. Our results have shown good performance (with test accuracies 86.53% on TCGA dataset and 90.70% on MICCAI dataset). Conclusions: The proposed scheme is effective for glioma IDH-mutation prediction and glioma grading, and its performance is comparable to the state-of-the-art