Nonuniform random geometric graphs with location-dependent radii

We propose a distribution-free approach to the study of random geometric graphs. The distribution of vertices follows a Poisson point process with intensity function n f(center dot), where n is an element of N, and f is a probability density function on R-d. A vertex located at x connects via directed edges to other vertices that are within a cut-off distance r(n)(x). We prove strong law results for (i) the critical cut-off function so that almost surely, the graph does not contain any node with out-degree zero for sufficiently large n and (ii) the maximum and minimum vertex degrees. We also provide a characterization of the cut-off function for which the number of nodes with out-degree zero converges in distribution to a Poisson random variable. We illustrate this result for a class of densities with compact support that have at most polynomial rates of decay to zero. Finally, we state a sufficient condition for an enhanced version of the above graph to be almost surely connected eventually.

Multidimensional data reconstruction for two color fluorescence microscopy

We propose an iterative data reconstruction technique specifically designed for multi-dimensional multi-color fluorescence imaging. Markov random field is employed (for modeling the multi-color image field) in conjunction with the classical maximum likelihood method. It is noted that, ill-posed nature of the inverse problem associated with multi-color fluorescence imaging forces iterative data reconstruction. Reconstruction of three-dimensional (3D) two-color images (obtained from nanobeads and cultured cell samples) show significant reduction in the background noise (improved signal-to-noise ratio) with an impressive overall improvement in the spatial resolution (approximate to 250 nm) of the imaging system. Proposed data reconstruction technique may find immediate application in 3D in vivo and in vitro multi-color fluorescence imaging of biological specimens. (C) 2012 American Institute of Physics. http://dx.doi.org/10.1063/1.4769058]

SPARSE SIGNAL RECONSTRUCTION BASED ON SIGNAL DEPENDENT NON-UNIFORM SAMPLES

The classical approach to A/D conversion has been uniform sampling and we get perfect reconstruction for bandlimited signals by satisfying the Nyquist Sampling Theorem. We propose a non-uniform sampling scheme based on level crossing (LC) time information. We show stable reconstruction of bandpass signals with correct scale factor and hence a unique reconstruction from only the non-uniform time information. For reconstruction from the level crossings we make use of the sparse reconstruction based optimization by constraining the bandpass signal to be sparse in its frequency content. While overdetermined system of equations is resorted to in the literature we use an undetermined approach along with sparse reconstruction formulation. We could get a reconstruction SNR > 20dB and perfect support recovery with probability close to 1, in noise-less case and with lower probability in the noisy case. Random picking of LC from different levels over the same limited signal duration and for the same length of information, is seen to be advantageous for reconstruction.

Intrinsically disordered proteins and conformational noise Implications in cancer

Intrinsically disordered proteins, IDPs, are proteins that lack a rigid 3D structure under physiological conditions, at least in vitro. Despite the lack of structure, IDPs play important roles in biological processes and transition from disorder to order upon binding to their targets. With multiple conformational states and rapid conformational dynamics, they engage in myriad and often ``promiscuous'' interactions. These stochastic interactions between IDPs and their partners, defined here as conformational noise, is an inherent characteristic of IDP interactions. The collective effect of conformational noise is an ensemble of protein network configurations, from which the most suitable can be explored in response to perturbations, conferring protein networks with remarkable flexibility and resilience. Moreover, the ubiquitous presence of IDPs as transcriptional factors and, more generally, as hubs in protein networks, is indicative of their role in propagation of transcriptional (genetic) noise. As effectors of transcriptional and conformational noise, IDPs rewire protein networks and unmask latent interactions in response to perturbations. Thus, noise-driven activation of latent pathways could underlie state-switching events such as cellular transformation in cancer. To test this hypothesis, we created a model of a protein network with the topological characteristics of a cancer protein network and tested its response to a perturbation in presence of IDP hubs and conformational noise. Because numerous IDPs are found to be epigenetic modifiers and chromatin remodelers, we hypothesize that they could further channel noise into stable, heritable genotypic changes.

Nodal length fluctuations for arithmetic random waves

Using the spectral multiplicities of the standard torus, we endow the Laplace eigenspaces with Gaussian probability measures. This induces a notion of random Gaussian Laplace eigenfunctions on the torus (''arithmetic random waves''). We study the distribution of the nodal length of random eigenfunctions for large eigenvalues, and our primary result is that the asymptotics for the variance is nonuniversal. Our result is intimately related to the arithmetic of lattice points lying on a circle with radius corresponding to the energy.

Cramer-Rao-Type Bounds for Sparse Bayesian Learning

In this paper, we derive Hybrid, Bayesian and Marginalized Cramer-Rao lower bounds (HCRB, BCRB and MCRB) for the single and multiple measurement vector Sparse Bayesian Learning (SBL) problem of estimating compressible vectors and their prior distribution parameters. We assume the unknown vector to be drawn from a compressible Student-prior distribution. We derive CRBs that encompass the deterministic or random nature of the unknown parameters of the prior distribution and the regression noise variance. We extend the MCRB to the case where the compressible vector is distributed according to a general compressible prior distribution, of which the generalized Pareto distribution is a special case. We use the derived bounds to uncover the relationship between the compressibility and Mean Square Error (MSE) in the estimates. Further, we illustrate the tightness and utility of the bounds through simulations, by comparing them with the MSE performance of two popular SBL-based estimators. We find that the MCRB is generally the tightest among the bounds derived and that the MSE performance of the Expectation-Maximization (EM) algorithm coincides with the MCRB for the compressible vector. We also illustrate the dependence of the MSE performance of SBL based estimators on the compressibility of the vector for several values of the number of observations and at different signal powers.

A low-noise low-power noise-adaptive neural amplifier in 0.13um CMOS technology

Chronic recording of neural signals is indispensable in designing efficient brain machine interfaces and in elucidating human neurophysiology. The advent of multichannel microelectrode arrays has driven the need for electronics to record neural signals from many neurons. The dynamic range of the system is limited by background system noise which varies over time. We propose a neural amplifier in UMC 130 nm, 2P8M CMOS technology. It can be biased adaptively from 200 nA to 2 uA, modulating input referred noise from 9.92 uV to 3.9 uV. We also describe a low noise design technique which minimizes the noise contribution of the load circuitry. The amplifier can pass signal from 5 Hz to 7 kHz while rejecting input DC offsets at electrode-electrolyte interface. The bandwidth of the amplifier can be tuned by the pseudo-resistor for selectively recording low field potentials (LFP) or extra cellular action potentials (EAP). The amplifier achieves a mid-band voltage gain of 37 dB and minimizes the attenuation of the signal from neuron to the gate of the input transistor. It is used in fully differential configuration to reject noise of bias circuitry and to achieve high PSRR.

Parabolized stability equation models for predicting large-scale mixing noise of turbulent round jets

Parabolized stability equation (PSE) models are being deve loped to predict the evolu-tion of low-frequency, large-scale wavepacket structures and their radiated sound in high-speed turbulent round jets. Linear PSE wavepacket models were previously shown to be in reasonably good agreement with the amplitude envelope and phase measured using a microphone array placed just outside the jet shear layer. 1,2 Here we show they also in very good agreement with hot-wire measurements at the jet center line in the potential core,for a different set of experiments. 3 When used as a model source for acoustic analogy, the predicted far field noise radiation is in reasonably good agreement with microphone measurements for aft angles where contributions from large -scale structures dominate the acoustic field. Nonlinear PSE is then employed in order to determine the relative impor-tance of the mode interactions on the wavepackets. A series of nonlinear computations with randomized initial conditions are use in order to obtain bounds for the evolution of the modes in the natural turbulent jet flow. It was found that n onlinearity has a very limited impact on the evolution of the wavepackets for St≥0. 3. Finally, the nonlinear mechanism for the generation of a low-frequency mode as the difference-frequency mode 4,5 of two forced frequencies is investigated in the scope of the high Reynolds number jets considered in this paper.

Random forest algorithm with derived geographical layers for improved classification of remote sensing data

Effective conservation and management of natural resources requires up-to-date information of the land cover (LC) types and their dynamics. The LC dynamics are being captured using multi-resolution remote sensing (RS) data with appropriate classification strategies. RS data with important environmental layers (either remotely acquired or derived from ground measurements) would however be more effective in addressing LC dynamics and associated changes. These ancillary layers provide additional information for delineating LC classes' decision boundaries compared to the conventional classification techniques. This communication ascertains the possibility of improved classification accuracy of RS data with ancillary and derived geographical layers such as vegetation index, temperature, digital elevation model (DEM), aspect, slope and texture. This has been implemented in three terrains of varying topography. The study would help in the selection of appropriate ancillary data depending on the terrain for better classified information.

Variance-Reduced Particle Filters for Structural System Identification Problems

A few variance reduction schemes are proposed within the broad framework of a particle filter as applied to the problem of structural system identification. Whereas the first scheme uses a directional descent step, possibly of the Newton or quasi-Newton type, within the prediction stage of the filter, the second relies on replacing the more conventional Monte Carlo simulation involving pseudorandom sequence with one using quasi-random sequences along with a Brownian bridge discretization while representing the process noise terms. As evidenced through the derivations and subsequent numerical work on the identification of a shear frame, the combined effect of the proposed approaches in yielding variance-reduced estimates of the model parameters appears to be quite noticeable. DOI: 10.1061/(ASCE)EM.1943-7889.0000480. (C) 2013 American Society of Civil Engineers.

Noise tolerance under risk minimization

In this paper, we explore noise-tolerant learning of classifiers. We formulate the problem as follows. We assume that there is an unobservable training set that is noise free. The actual training set given to the learning algorithm is obtained from this ideal data set by corrupting the class label of each example. The probability that the class label of an example is corrupted is a function of the feature vector of the example. This would account for most kinds of noisy data one encounters in practice. We say that a learning method is noise tolerant if the classifiers learnt with noise-free data and with noisy data, both have the same classification accuracy on the noise-free data. In this paper, we analyze the noise-tolerance properties of risk minimization (under different loss functions). We show that risk minimization under 0-1 loss function has impressive noise-tolerance properties and that under squared error loss is tolerant only to uniform noise; risk minimization under other loss functions is not noise tolerant. We conclude this paper with some discussion on the implications of these theoretical results.

Suppression Of Barkhausen Noise Due To Exchange Biasing In Fe-FeMn Bilalayers

Exchange biased Fe(FM)-FeMn(AFM) bilayers were grown by pulsed laser ablation in UHV and probed by SQUID magnetometer and planar Hall effect measurements. A suppression of barkhausen avalanches was observed during the switching of the bilayer when compared to that of pure Fe, which is indicative of a change in the reversal mechanism.

Application of the random eigenvalue problem in forced response analysis of a linear stochastic structure

The random eigenvalue problem arises in frequency and mode shape determination for a linear system with uncertainties in structural properties. Among several methods of characterizing this random eigenvalue problem, one computationally fast method that gives good accuracy is a weak formulation using polynomial chaos expansion (PCE). In this method, the eigenvalues and eigenvectors are expanded in PCE, and the residual is minimized by a Galerkin projection. The goals of the current work are (i) to implement this PCE-characterized random eigenvalue problem in the dynamic response calculation under random loading and (ii) to explore the computational advantages and challenges. In the proposed method, the response quantities are also expressed in PCE followed by a Galerkin projection. A numerical comparison with a perturbation method and the Monte Carlo simulation shows that when the loading has a random amplitude but deterministic frequency content, the proposed method gives more accurate results than a first-order perturbation method and a comparable accuracy as the Monte Carlo simulation in a lower computational time. However, as the frequency content of the loading becomes random, or for general random process loadings, the method loses its accuracy and computational efficiency. Issues in implementation, limitations, and further challenges are also addressed.

A Novel Monte-Carlo-Sampling-Based Receiver for Large-Scale Uplink Multiuser MIMO Systems

In this paper, we propose low-complexity algorithms based on Monte Carlo sampling for signal detection and channel estimation on the uplink in large-scale multiuser multiple-input-multiple-output (MIMO) systems with tens to hundreds of antennas at the base station (BS) and a similar number of uplink users. A BS receiver that employs a novel mixed sampling technique (which makes a probabilistic choice between Gibbs sampling and random uniform sampling in each coordinate update) for detection and a Gibbs-sampling-based method for channel estimation is proposed. The algorithm proposed for detection alleviates the stalling problem encountered at high signal-to-noise ratios (SNRs) in conventional Gibbs-sampling-based detection and achieves near-optimal performance in large systems with M-ary quadrature amplitude modulation (M-QAM). A novel ingredient in the detection algorithm that is responsible for achieving near-optimal performance at low complexity is the joint use of a mixed Gibbs sampling (MGS) strategy coupled with a multiple restart (MR) strategy with an efficient restart criterion. Near-optimal detection performance is demonstrated for a large number of BS antennas and users (e. g., 64 and 128 BS antennas and users). The proposed Gibbs-sampling-based channel estimation algorithm refines an initial estimate of the channel obtained during the pilot phase through iterations with the proposed MGS-based detection during the data phase. In time-division duplex systems where channel reciprocity holds, these channel estimates can be used for multiuser MIMO precoding on the downlink. The proposed receiver is shown to achieve good performance and scale well for large dimensions.

Wide Voltage Input Receiver with Hysteresis Characteristic to Reduce Input Signal Noise Effect

In this paper, an input receiver with a hysteresis characteristic that can work at voltage levels between 0.9 V and 5 V is proposed. The input receiver can be used as a wide voltage range Schmitt trigger also. At the same time, reliable circuit operation is ensured. According to the research findings, this is the first time a wide voltage range Schmitt trigger is being reported. The proposed circuit is compared with previously reported input receivers, and it is shown that the circuit has better noise immunity. The proposed input receiver ends the need for a separate Schmitt trigger and input buffer. The frequency of operation is also higher than that of the previously reported receiver. The circuit is simulated using HSPICE at 035-mu m standard thin oxide technology. Monte Carlo analysis is conducted at different process conditions, showing that the proposed circuit works well for different process conditions at different voltage levels of operation. A noise impulse of (V-CC/2) magnitude is added to the input voltage to show that the receiver receives the correct logic level even in the presence of noise. Here, V-CC is the fixed voltage supply of 3.3 V.