An efficient reduction algorithm for computation of interconnect delay variability for statistical timing analysis in clock tree planning

In this paper, we propose a novel and efficient algorithm for modelling sub-65 nm clock interconnect-networks in the presence of process variation. We develop a method for delay analysis of interconnects considering the impact of Gaussian metal process variations. The resistance and capacitance of a distributed RC line are expressed as correlated Gaussian random variables which are then used to compute the standard deviation of delay Probability Distribution Function (PDF) at all nodes in the interconnect network. Main objective is to find delay PDF at a cheaper cost. Convergence of this approach is in probability distribution but not in mean of delay. We validate our approach against SPICE based Monte Carlo simulations while the current method entails significantly lower computational cost.

Understorey vegetation as an indicator of forest site potential in Southern Finland.

The relationship between site characteristics and understorey vegetation composition was analysed with quantitative methods, especially from the viewpoint of site quality estimation. Theoretical models were applied to an empirical data set collected from the upland forests of southern Finland comprising 104 sites dominated by Scots pine (Pinus sylvestris L.), and 165 sites dominated by Norway spruce (Picea abies (L.) Karsten). Site index H100 was used as an independent measure of site quality. A new model for the estimation of site quality at sites with a known understorey vegetation composition was introduced. It is based on the application of Bayes' theorem to the density function of site quality within the study area combined with the species-specific presence-absence response curves. The resulting posterior probability density function may be used for calculating an estimate for the site variable. Using this method, a jackknife estimate of site index H100 was calculated separately for pine- and spruce-dominated sites. The results indicated that the cross-validation root mean squared error (RMSEcv) of the estimates improved from 2.98 m down to 2.34 m relative to the "null" model (standard deviation of the sample distribution) in pine-dominated forests. In spruce-dominated forests RMSEcv decreased from 3.94 m down to 3.16 m. In order to assess these results, four other estimation methods based on understorey vegetation composition were applied to the same data set. The results showed that none of the methods was clearly superior to the others. In pine-dominated forests, RMSEcv varied between 2.34 and 2.47 m, and the corresponding range for spruce-dominated forests was from 3.13 to 3.57 m.

Modelling initial survival and growth of radiata pine in New Zealand.

A sensitive framework has been developed for modelling young radiata pine survival, its growth and its size class distribution, from time of planting to age 5 or 6 years. The data and analysis refer to the Central North Island region of New Zealand. The survival function is derived from a Weibull probability density function, to reflect diminishing mortality with the passage of time in young stands. An anamorphic family of trends was used, as very little between-tree competition can be expected in young stands. An exponential height function was found to fit best the lower portion of its sigmoid form. The most appropriate basal area/ha exponential function included an allometric adjustment which resulted in compatible mean height and basal area/ha models. Each of these equations successfully represented the effects of several establishment practices by making coefficients linear functions of site factors, management activities and their interactions. Height and diameter distribution modelling techniques that ensured compatibility with stand values were employed to represent the effects of management practices on crop variation. Model parameters for this research were estimated using data from site preparation experiments in the region and were tested with some independent data sets.

Narrowband random excitation of a limit cycle system

The response of the Van der Pol oscillator to stationary narrowband Gaussian excitation is considered. The central frequency of excitation is taken to be in the neighborhood of the system limit cycle frequency. The solution is obtained using a non-Gaussian closure approximation on the probability density function of the response. The validity of the solution is examined with the help of a stochastic stability analysis. Solution based on Stratonovich''s quasistatic averaging technique is also obtained. The comparison of the theoretical solutions with the digital simulations shows that the theoretical estimates are reasonably good.

Rocking response of rectangular rigid blocks under random noise base excitations

The response of a rigid rectangular block resting on a rigid foundation and acted upon simultaneously by a horizontal and a vertical random white-noise excitation is considered. In the equation of motion, the energy dissipation is modeled through a viscous damping term. Under the assumption that the body does not topple, the steady-state joint probability density function of the rotation and the rotational velocity is obtained using the Fokker-Planck equation approach. Closed form solution is obtained for a specific combination of system parameters. A more general but approximate solution to the joint probability density function based on the method of equivalent non-linearization is also presented. Further, the problem of overturning of the block is approached in the framework of the diffusion methods for first passage failure studies. The overturning of the block is deemed incipient when the response trajectories in the phase plane cross the separatrix of the conservative unforced system. Expressions for the moments of first passage time are obtained via a series solution to the governing generalized Pontriagin-Vitt equations. Numerical results illustra- tive of the theoretical solutions are presented and their validity is examined through limited amount of digital simulations.

On a Ratio of Functions of Exponential Random Variables and Some Applications

Consider L independent and identically distributed exponential random variables (r.vs) X-1, X-2 ,..., X-L and positive scalars b(1), b(2) ,..., b(L). In this letter, we present the probability density function (pdf), cumulative distribution function and the Laplace transform of the pdf of the composite r.v Z = (Sigma(L)(j=1) X-j)(2) / (Sigma(L)(j=1) b(j)X(j)). We show that the r.v Z appears in various communication systems such as i) maximal ratio combining of signals received over multiple channels with mismatched noise variances, ii)M-ary phase-shift keying with spatial diversity and imperfect channel estimation, and iii) coded multi-carrier code-division multiple access reception affected by an unknown narrow-band interference, and the statistics of the r.v Z derived here enable us to carry out the performance analysis of such systems in closed-form.

Conditional linearization in nonlinear random vibration

In this paper, an improved probabilistic linearization approach is developed to study the response of nonlinear single degree of freedom (SDOF) systems under narrow-band inputs. An integral equation for the probability density function (PDF) of the envelope is derived. This equation is solved using an iterative scheme. The technique is applied to study the hardening type Duffing's oscillator under narrow-band excitation. The results compare favorably with those obtained using numerical simulation. In particular, the bimodal nature of the PDF for the response envelope for certain parameter ranges is brought out.

Stochastic dynamics modeling of the protein sequence length distribution in genomes: implications for microbial evolution

In this paper, we report an analysis of the protein sequence length distribution for 13 bacteria, four archaea and one eukaryote whose genomes have been completely sequenced, The frequency distribution of protein sequence length for all the 18 organisms are remarkably similar, independent of genome size and can be described in terms of a lognormal probability distribution function. A simple stochastic model based on multiplicative processes has been proposed to explain the sequence length distribution. The stochastic model supports the random-origin hypothesis of protein sequences in genomes. Distributions of large proteins deviate from the overall lognormal behavior. Their cumulative distribution follows a power-law analogous to Pareto's law used to describe the income distribution of the wealthy. The protein sequence length distribution in genomes of organisms has important implications for microbial evolution and applications. (C) 1999 Elsevier Science B.V. All rights reserved.

A Complete Characterization of an Optimal Timer Based Selection Scheme

Timer-based mechanisms are often used in several wireless systems to help a given (sink) node select the best helper node among many available nodes. Specifically, a node transmits a packet when its timer expires, and the timer value is a function of its local suitability metric. In practice, the best node gets selected successfully only if no other node's timer expires within a `vulnerability' window after its timer expiry. In this paper, we provide a complete closed-form characterization of the optimal metric-to-timer mapping that maximizes the probability of success for any probability distribution function of the metric. The optimal scheme is scalable, distributed, and much better than the popular inverse metric timer mapping. We also develop an asymptotic characterization of the optimal scheme that is elegant and insightful, and accurate even for a small number of nodes.

Particle dynamics in a turbulent particle–gas suspension at high Stokes number. Part 1. Velocity and acceleration distributions

The effect of fluid velocity fluctuations on the dynamics of the particles in a turbulent gas–solid suspension is analysed in the low-Reynolds-number and high Stokes number limits, where the particle relaxation time is long compared with the correlation time for the fluid velocity fluctuations, and the drag force on the particles due to the fluid can be expressed by the modified Stokes law. The direct numerical simulation procedure is used for solving the Navier–Stokes equations for the fluid, the particles are modelled as hard spheres which undergo elastic collisions and a one-way coupling algorithm is used where the force exerted by the fluid on the particles is incorporated, but not the reverse force exerted by the particles on the fluid. The particle mean and root-mean-square (RMS) fluctuating velocities, as well as the probability distribution function for the particle velocity fluctuations and the distribution of acceleration of the particles in the central region of the Couette (where the velocity profile is linear and the RMS velocities are nearly constant), are examined. It is found that the distribution of particle velocities is very different from a Gaussian, especially in the spanwise and wall-normal directions. However, the distribution of the acceleration fluctuation on the particles is found to be close to a Gaussian, though the distribution is highly anisotropic and there is a correlation between the fluctuations in the flow and gradient directions. The non-Gaussian nature of the particle velocity fluctuations is found to be due to inter-particle collisions induced by the large particle velocity fluctuations in the flow direction. It is also found that the acceleration distribution on the particles is in very good agreement with the distribution that is calculated from the velocity fluctuations in the fluid, using the Stokes drag law, indicating that there is very little correlation between the fluid velocity fluctuations and the particle velocity fluctuations in the presence of one-way coupling. All of these results indicate that the effect of the turbulent fluid velocity fluctuations can be accurately represented by an anisotropic Gaussian white noise.

Plume structure in high-Rayleigh-number convection

Near-wall structures in turbulent natural convection at Rayleigh numbers of $10^{10}$ to $10^{11}$ at A Schmidt number of 602 are visualized by a new method of driving the convection across a fine membrane using concentration differences of sodium chloride. The visualizations show the near-wall flow to consist of sheet plumes. A wide variety of large-scale flow cells, scaling with the cross-section dimension, are observed. Multiple large-scale flow cells are seen at aspect ratio (AR)= 0.65, while only a single circulation cell is detected at AR= 0.435. The cells (or the mean wind) are driven by plumes coming together to form columns of rising lighter fluid. The wind in turn aligns the sheet plumes along the direction of shear. the mean wind direction is seen to change with time. The near-wall dynamics show plumes initiated at points, which elongate to form sheets and then merge. Increase in rayleigh number results in a larger number of closely and regularly spaced plumes. The plume spacings show a common log–normal probability distribution function, independent of the rayleigh number and the aspect ratio. We propose that the near-wall structure is made of laminar natural-convection boundary layers, which become unstable to give rise to sheet plumes, and show that the predictions of a model constructed on this hypothesis match the experiments. Based on these findings, we conclude that in the presence of a mean wind, the local near-wall boundary layers associated with each sheet plume in high-rayleigh-number turbulent natural convection are likely to be laminar mixed convection type.

Universality and scaling behavior of injected power in elastic turbulence in wormlike micellar gel

We study the statistical properties of spatially averaged global injected power fluctuations for Taylor-Couette flow of a wormlike micellar gel formed by surfactant cetyltrimethylammonium tosylate. At sufficiently high Weissenberg numbers the shear rate, and hence the injected power p(t), at a constant applied stress shows large irregular fluctuations in time. The nature of the probability distribution function (PDF) of p(t) and the power-law decay of its power spectrum are very similar to that observed in recent studies of elastic turbulence for polymer solutions. Remarkably, these non-Gaussian PDFs can be well described by a universal, large deviation functional form given by the generalized Gumbel distribution observed in the context of spatially averaged global measures in diverse classes of highly correlated systems. We show by in situ rheology and polarized light scattering experiments that in the elastic turbulent regime the flow is spatially smooth but random in time, in agreement with a recent hypothesis for elastic turbulence.

GMM basedbayesian approach to speech enhancement in signal/transform domain

Considering a general linear model of signal degradation, by modeling the probability density function (PDF) of the clean signal using a Gaussian mixture model (GMM) and additive noise by a Gaussian PDF, we derive the minimum mean square error (MMSE) estimator.The derived MMSE estimator is non-linear and the linear MMSE estimator is shown to be a special case. For speech signal corrupted by independent additive noise, by modeling the joint PDF of time-domain speech samples of a speech frame using a GMM, we propose a speech enhancement method based on the derived MMSE estimator. We also show that the same estimator can be used for transform-domain speech enhancement.

Spectral Efficiency of Channel-Aware Schedulers in Non-identical Composite Links with Interference

Accurate system planning and performance evaluation requires knowledge of the joint impact of scheduling, interference, and fading. However, current analyses either require costly numerical simulations or make simplifying assumptions that limit the applicability of the results. In this paper, we derive analytical expressions for the spectral efficiency of cellular systems that use either the channel-unaware but fair round robin scheduler or the greedy, channel-aware but unfair maximum signal to interference ratio scheduler. As is the case in real deployments, non-identical co-channel interference at each user, both Rayleigh fading and lognormal shadowing, and limited modulation constellation sizes are accounted for in the analysis. We show that using a simple moment generating function-based lognormal approximation technique and an accurate Gaussian-Q function approximation leads to results that match simulations well. These results are more accurate than erstwhile results that instead used the moment-matching Fenton-Wilkinson approximation method and bounds on the Q function. The spectral efficiency of cellular systems is strongly influenced by the channel scheduler and the small constellation size that is typically used in third generation cellular systems.

Multi-agent Search using Voronoi partitions

This paper addresses the problem of multiagent search in an unknown environment. The agents are autonomous in nature and are equipped with necessary sensors to carry out the search operation. The uncertainty, or lack of information about the search area is known a priori as a probability density function. The agents are deployed in an optimal way so as to maximize the one step uncertainty reduction. The agents continue to deploy themselves and reduce uncertainty till the uncertainty density is reduced over the search space below a minimum acceptable level. It has been shown, using LaSalle’s invariance principle, that a distributed control law which moves each of the agents towards the centroid of its Voronoi partition, modified by the sensor range leads to single step optimal deployment. This principle is now used to devise search trajectories for the agents. The simulations were carried out in 2D space with saturation on speeds of the agents. The results show that the control strategy per step indeed moves the agents to the respective centroid and the algorithm reduces the uncertainty distribution to the required level within a few steps.