EffiTest: Efficient Delay Test and Statistical Prediction for Configuring Post-silicon Tunable Buffers

At nanometer manufacturing technology nodes, process variations significantly affect circuit performance. To combat them, post- silicon clock tuning buffers can be deployed to balance timing bud- gets of critical paths for each individual chip after manufacturing. The challenge of this method is that path delays should be mea- sured for each chip to configure the tuning buffers properly. Current methods for this delay measurement rely on path-wise frequency stepping. This strategy, however, requires too much time from ex- pensive testers. In this paper, we propose an efficient delay test framework (EffiTest) to solve the post-silicon testing problem by aligning path delays using the already-existing tuning buffers in the circuit. In addition, we only test representative paths and the delays of other paths are estimated by statistical delay prediction. Exper- imental results demonstrate that the proposed method can reduce the number of frequency stepping iterations by more than 94% with only a slight yield loss.Comment: ACM/IEEE Design Automation Conference (DAC), June 201

High-Dimensional Inference with the generalized Hopfield Model: Principal Component Analysis and Corrections

We consider the problem of inferring the interactions between a set of N binary variables from the knowledge of their frequencies and pairwise correlations. The inference framework is based on the Hopfield model, a special case of the Ising model where the interaction matrix is defined through a set of patterns in the variable space, and is of rank much smaller than N. We show that Maximum Lik elihood inference is deeply related to Principal Component Analysis when the amp litude of the pattern components, xi, is negligible compared to N^1/2. Using techniques from statistical mechanics, we calculate the corrections to the patterns to the first order in xi/N^1/2. We stress that it is important to generalize the Hopfield model and include both attractive and repulsive patterns, to correctly infer networks with sparse and strong interactions. We present a simple geometrical criterion to decide how many attractive and repulsive patterns should be considered as a function of the sampling noise. We moreover discuss how many sampled configurations are required for a good inference, as a function of the system size, N and of the amplitude, xi. The inference approach is illustrated on synthetic and biological data.Comment: Physical Review E: Statistical, Nonlinear, and Soft Matter Physics (2011) to appea

Principal component analysis - an efficient tool for variable stars diagnostics

We present two diagnostic methods based on ideas of Principal Component Analysis and demonstrate their efficiency for sophisticated processing of multicolour photometric observations of variable objects.Comment: 8 pages, 4 figures. Published alread

Principal Component Analysis with Noisy and/or Missing Data

We present a method for performing Principal Component Analysis (PCA) on noisy datasets with missing values. Estimates of the measurement error are used to weight the input data such that compared to classic PCA, the resulting eigenvectors are more sensitive to the true underlying signal variations rather than being pulled by heteroskedastic measurement noise. Missing data is simply the limiting case of weight=0. The underlying algorithm is a noise weighted Expectation Maximization (EM) PCA, which has additional benefits of implementation speed and flexibility for smoothing eigenvectors to reduce the noise contribution. We present applications of this method on simulated data and QSO spectra from the Sloan Digital Sky Survey.Comment: Accepted for publication in PASP; v2 with minor updates, mostly to bibliograph

Significance analysis and statistical mechanics: an application to clustering

This paper addresses the statistical significance of structures in random data: Given a set of vectors and a measure of mutual similarity, how likely does a subset of these vectors form a cluster with enhanced similarity among its elements? The computation of this cluster p-value for randomly distributed vectors is mapped onto a well-defined problem of statistical mechanics. We solve this problem analytically, establishing a connection between the physics of quenched disorder and multiple testing statistics in clustering and related problems. In an application to gene expression data, we find a remarkable link between the statistical significance of a cluster and the functional relationships between its genes.Comment: to appear in Phys. Rev. Let

Coarse-grained dynamics of an activity bump in a neural field model

We study a stochastic nonlocal PDE, arising in the context of modelling spatially distributed neural activity, which is capable of sustaining stationary and moving spatially-localized ``activity bumps''. This system is known to undergo a pitchfork bifurcation in bump speed as a parameter (the strength of adaptation) is changed; yet increasing the noise intensity effectively slowed the motion of the bump. Here we revisit the system from the point of view of describing the high-dimensional stochastic dynamics in terms of the effective dynamics of a single scalar "coarse" variable. We show that such a reduced description in the form of an effective Langevin equation characterized by a double-well potential is quantitatively successful. The effective potential can be extracted using short, appropriately-initialized bursts of direct simulation. We demonstrate this approach in terms of (a) an experience-based "intelligent" choice of the coarse observable and (b) an observable obtained through data-mining direct simulation results, using a diffusion map approach.Comment: Corrected aknowledgement

Mesoscopic Model for Free Energy Landscape Analysis of DNA sequences

A mesoscopic model which allows us to identify and quantify the strength of binding sites in DNA sequences is proposed. The model is based on the Peyrard-Bishop-Dauxois model for the DNA chain coupled to a Brownian particle which explores the sequence interacting more importantly with open base pairs of the DNA chain. We apply the model to promoter sequences of different organisms. The free energy landscape obtained for these promoters shows a complex structure that is strongly connected to their biological behavior. The analysis method used is able to quantify free energy differences of sites within genome sequences.Comment: 7 pages, 5 figures, 1 tabl

Nonequilibrium Invariant Measure under Heat Flow

We provide an explicit representation of the nonequilibrium invariant measure for a chain of harmonic oscillators with conservative noise in the presence of stationary heat flow. By first determining the covariance matrix, we are able to express the measure as the product of Gaussian distributions aligned along some collective modes that are spatially localized with power-law tails. Numerical studies show that such a representation applies also to a purely deterministic model, the quartic Fermi-Pasta-Ulam chain

Data mining: a tool for detecting cyclical disturbances in supply networks.

Disturbances in supply chains may be either exogenous or endogenous. The ability automatically to detect, diagnose, and distinguish between the causes of disturbances is of prime importance to decision makers in order to avoid uncertainty. The spectral principal component analysis (SPCA) technique has been utilized to distinguish between real and rogue disturbances in a steel supply network. The data set used was collected from four different business units in the network and consists of 43 variables; each is described by 72 data points. The present paper will utilize the same data set to test an alternative approach to SPCA in detecting the disturbances. The new approach employs statistical data pre-processing, clustering, and classification learning techniques to analyse the supply network data. In particular, the incremental k-means clustering and the RULES-6 classification rule-learning algorithms, developed by the present authors’ team, have been applied to identify important patterns in the data set. Results show that the proposed approach has the capability automatically to detect and characterize network-wide cyclical disturbances and generate hypotheses about their root cause

Spatially Resolved Mapping of Local Polarization Dynamics in an Ergodic Phase of Ferroelectric Relaxor

Spatial variability of polarization relaxation kinetics in relaxor ferroelectric 0.9Pb(Mg1/3Nb2/3)O3-0.1PbTiO3 is studied using time-resolved Piezoresponse Force Microscopy. Local relaxation attributed to the reorientation of polar nanoregions is shown to follow stretched exponential dependence, exp(-(t/tau)^beta), with beta~~0.4, much larger than the macroscopic value determined from dielectric spectra (beta~~0.09). The spatial inhomogeneity of relaxation time distributions with the presence of 100-200 nm "fast" and "slow" regions is observed. The results are analyzed to map the Vogel-Fulcher temperatures on the nanoscale.Comment: 23 pages, 4 figures, supplementary materials attached; to be submitted to Phys. Rev. Let