Optimal local polynomial regression of noisy time varying signals

We address the problem of local-polynomial modeling of smooth time-varying signals with unknown functional form, in the presence of additive noise. The problem formulation is in the time domain and the polynomial coefficients are estimated in the pointwise minimum mean square error (PMMSE) sense. The choice of the window length for local modeling introduces a bias-variance tradeoff, which we solve optimally by using the intersection-of-confidence-intervals (ICI) technique. The combination of the local polynomial model and the ICI technique gives rise to an adaptive signal model equipped with a time-varying PMMSE-optimal window length whose performance is superior to that obtained by using a fixed window length. We also evaluate the sensitivity of the ICI technique with respect to the confidence interval width. Simulation results on electrocardiogram (ECG) signals show that at 0dB signal-to-noise ratio (SNR), one can achieve about 12dB improvement in SNR. Monte-Carlo performance analysis shows that the performance is comparable to the basic wavelet techniques. For 0 dB SNR, the adaptive window technique yields about 2-3dB higher SNR than wavelet regression techniques and for SNRs greater than 12dB, the wavelet techniques yield about 2dB higher SNR.

Online character recognition using regression techniques

This paper introduces a scheme for classification of online handwritten characters based on polynomial regression of the sampled points of the sub-strokes in a character. The segmentation is done based on the velocity profile of the written character and this requires a smoothening of the velocity profile. We propose a novel scheme for smoothening the velocity profile curve and identification of the critical points to segment the character. We also porpose another method for segmentation based on the human eye perception. We then extract two sets of features for recognition of handwritten characters. Each sub-stroke is a simple curve, a part of the character, and is represented by the distance measure of each point from the first point. This forms the first set of feature vector for each character. The second feature vector are the coeficients obtained from the B-splines fitted to the control knots obtained from the segmentation algorithm. The feature vector is fed to the SVM classifier and it indicates an efficiency of 68% using the polynomial regression technique and 74% using the spline fitting method.

Robust and High-resolution Voiced/Unvoiced Classification in Noisy Speech Using A Signal Smoothness Criterion

We propose a novel technique for robust voiced/unvoiced segment detection in noisy speech, based on local polynomial regression. The local polynomial model is well-suited for voiced segments in speech. The unvoiced segments are noise-like and do not exhibit any smooth structure. This property of smoothness is used for devising a new metric called the variance ratio metric, which, after thresholding, indicates the voiced/unvoiced boundaries with 75% accuracy for 0dB global signal-to-noise ratio (SNR). A novelty of our algorithm is that it processes the signal continuously, sample-by-sample rather than frame-by-frame. Simulation results on TIMIT speech database (downsampled to 8kHz) for various SNRs are presented to illustrate the performance of the new algorithm. Results indicate that the algorithm is robust even in high noise levels.

On the Average Case Communication Complexity for Detection in Sensor Networks

The problem of sensor-network-based distributed intrusion detection in the presence of clutter is considered. It is argued that sensing is best regarded as a local phenomenon in that only sensors in the immediate vicinity of an intruder are triggered. In such a setting, lack of knowledge of intruder location gives rise to correlated sensor readings. A signal-space viewpoint is introduced in which the noise-free sensor readings associated to intruder and clutter appear as surfaces $\mathcal{S_I}$ and $\mathcal{S_C}$ and the problem reduces to one of determining in distributed fashion, whether the current noisy sensor reading is best classified as intruder or clutter. Two approaches to distributed detection are pursued. In the first, a decision surface separating $\mathcal{S_I}$ and $\mathcal{S_C}$ is identified using Neyman-Pearson criteria. Thereafter, the individual sensor nodes interactively exchange bits to determine whether the sensor readings are on one side or the other of the decision surface. Bounds on the number of bits needed to be exchanged are derived, based on communication complexity (CC) theory. A lower bound derived for the two-party average case CC of general functions is compared against the performance of a greedy algorithm. The average case CC of the relevant greater-than (GT) function is characterized within two bits. In the second approach, each sensor node broadcasts a single bit arising from appropriate two-level quantization of its own sensor reading, keeping in mind the fusion rule to be subsequently applied at a local fusion center. The optimality of a threshold test as a quantization rule is proved under simplifying assumptions. Finally, results from a QualNet simulation of the algorithms are presented that include intruder tracking using a naive polynomial-regression algorithm.

Distributed intrusion detection in the presence of correlated sensor readings: Signal-space and communication-complexity view-point

The problem of sensor-network-based distributed intrusion detection in the presence of clutter is considered. It is argued that sensing is best regarded as a local phenomenon in that only sensors in the immediate vicinity of an intruder are triggered. In such a setting, lack of knowledge of intruder location gives rise to correlated sensor readings. A signal-space view-point is introduced in which the noise-free sensor readings associated to intruder and clutter appear as surfaces f(s) and f(g) and the problem reduces to one of determining in distributed fashion, whether the current noisy sensor reading is best classified as intruder or clutter. Two approaches to distributed detection are pursued. In the first, a decision surface separating f(s) and f(g) is identified using Neyman-Pearson criteria. Thereafter, the individual sensor nodes interactively exchange bits to determine whether the sensor readings are on one side or the other of the decision surface. Bounds on the number of bits needed to be exchanged are derived, based on communication-complexity (CC) theory. A lower bound derived for the two-party average case CC of general functions is compared against the performance of a greedy algorithm. Extensions to the multi-party case is straightforward and is briefly discussed. The average case CC of the relevant greaterthan (CT) function is characterized within two bits. Under the second approach, each sensor node broadcasts a single bit arising from appropriate two-level quantization of its own sensor reading, keeping in mind the fusion rule to be subsequently applied at a local fusion center. The optimality of a threshold test as a quantization rule is proved under simplifying assumptions. Finally, results from a QualNet simulation of the algorithms are presented that include intruder tracking using a naive polynomial-regression algorithm. 2010 Elsevier B.V. All rights reserved.

Spectral-envelope-group-delay models for transients

Transient signals such as plosives in speech or Castanets in audio do not have a specific modulation or periodic structure in time domain. However, in the spectral domain they exhibit a prominent modulation structure, which is a direct consequence of their narrow time localization. Based on this observation, a spectral-domain AM-FM model for transients is proposed. The spectral AM-FM model is built starting from real spectral zero-crossings. The AM and FM correspond to the spectral envelope (SE) and group delay (GD), respectively. Taking into account the modulation structure and spectral continuity, a local polynomial regression technique is proposed to estimate the GD function from the real spectral zeros. The SE is estimated based on the phase function computed from the estimated GD. Since the GD estimation is parametric, the degree of smoothness can be controlled directly. Simulation results based on synthetic transient signals generated using a beta density function are presented to analyze the noise-robustness of the SEGD model. Three specific applications are considered: (1) SEGD based modeling of Castanet sounds; (2) appropriateness of the model for transient compression; and (3) determining glottal closure instants in speech using a short-time SEGD model of the linear prediction residue.

Event-triggered sampling using signal extrema for instantaneous amplitude and instantaneous frequency estimation

Event-triggered sampling (ETS) is a new approach towards efficient signal analysis. The goal of ETS need not be only signal reconstruction, but also direct estimation of desired information in the signal by skillful design of event. We show a promise of ETS approach towards better analysis of oscillatory non-stationary signals modeled by a time-varying sinusoid, when compared to existing uniform Nyquist-rate sampling based signal processing. We examine samples drawn using ETS, with events as zero-crossing (ZC), level-crossing (LC), and extrema, for additive in-band noise and jitter in detection instant. We find that extrema samples are robust, and also facilitate instantaneous amplitude (IA), and instantaneous frequency (IF) estimation in a time-varying sinusoid. The estimation is proposed solely using extrema samples, and a local polynomial regression based least-squares fitting approach. The proposed approach shows improvement, for noisy signals, over widely used analytic signal, energy separation, and ZC based approaches (which are based on uniform Nyquist-rate sampling based data-acquisition and processing). Further, extrema based ETS in general gives a sub-sampled representation (relative to Nyquistrate) of a time-varying sinusoid. For the same data-set size captured with extrema based ETS, and uniform sampling, the former gives much better IA and IF estimation. (C) 2015 Elsevier B.V. All rights reserved.

Influence of Anisotropy on Pavement Responses Using Adaptive Sparse Polynomial Chaos Expansion

Modeling the spatial variability that exists in pavement systems can be conveniently represented by means of random fields; in this study, a probabilistic analysis that considers the spatial variability, including the anisotropic nature of the pavement layer properties, is presented. The integration of the spatially varying log-normal random fields into a linear-elastic finite difference analysis has been achieved through the expansion optimal linear estimation method. For the estimation of the critical pavement responses, metamodels based on polynomial chaos expansion (PCE) are developed to replace the computationally expensive finite-difference model. The sparse polynomial chaos expansion based on an adaptive regression-based algorithm, and enhanced by the combined use of the global sensitivity analysis (GSA) is used, with significant savings in computational effort. The effect of anisotropy in each layer on the pavement responses was studied separately, and an effort is made to identify the pavement layer wherein the introduction of anisotropic characteristics results in the most significant impact on the critical strains. It is observed that the anisotropy in the base layer has a significant but diverse effect on both critical strains. While the compressive strain tends to be considerably higher than that observed for the isotropic section, the tensile strains show a decrease in the mean value with the introduction of base-layer anisotropy. Furthermore, asphalt-layer anisotropy also tends to decrease the critical tensile strain while having little effect on the critical compressive strain. (C) 2015 American Society of Civil Engineers.

Evolutionary games with two timescales

We consider a two timescale model of learning by economic agents wherein active or 'ontogenetic' learning by individuals takes place on a fast scale and passive or 'phylogenetic' learning by society as a whole on a slow scale, each affecting the evolution of the other. The former is modelled by the Monte Carlo dynamics of physics, while the latter is modelled by the replicator dynamics of evolutionary biology. Various qualitative aspects of the dynamics are studied in some simple cases, both analytically and numerically, and its role as a useful modelling device is emphasized.

Hybrid stiff-string-polynomial basis functions for vibration analysis of high speed rotating beams

A new finite element is developed for free vibration analysis of high speed rotating beams using basis functions which use a linear combination of the solution of the governing static differential equation of a stiff-string and a cubic polynomial. These new shape functions depend on rotation speed and element position along the beam and account for the centrifugal stiffening effect. The natural frequencies predicted by the proposed element are compared with an element with stiff-string, cubic polynomial and quintic polynomial shape functions. It is found that the new element exhibits superior convergence compared to the other basis functions.

Non-linear regression model for spatial variation in precipitation chemistry for South India

Chemical composition of rainwater changes from sea to inland under the influence of several major factors - topographic location of area, its distance from sea, annual rainfall. A model is developed here to quantify the variation in precipitation chemistry under the influence of inland distance and rainfall amount. Various sites in India categorized as 'urban', 'suburban' and 'rural' have been considered for model development. pH, HCO3, NO3 and Mg do not change much from coast to inland while, SO4 and Ca change is subjected to local emissions. Cl and Na originate solely from sea salinity and are the chemistry parameters in the model. Non-linear multiple regressions performed for the various categories revealed that both rainfall amount and precipitation chemistry obeyed a power law reduction with distance from sea. Cl and Na decrease rapidly for the first 100 km distance from sea, then decrease marginally for the next 100 km, and later stabilize. Regression parameters estimated for different cases were found to be consistent (R-2 similar to 0.8). Variation in one of the parameters accounted for urbanization. Model was validated using data points from the southern peninsular region of the country. Estimates are found to be within 99.9% confidence interval. Finally, this relationship between the three parameters - rainfall amount, coastline distance, and concentration (in terms of Cl and Na) was validated with experiments conducted in a small experimental watershed in the south-west India. Chemistry estimated using the model was in good correlation with observed values with a relative error of similar to 5%. Monthly variation in the chemistry is predicted from a downscaling model and then compared with the observed data. Hence, the model developed for rain chemistry is useful in estimating the concentrations at different spatio-temporal scales and is especially applicable for south-west region of India. (C) 2008 Elsevier Ltd. All rights reserved.

Variable-Temperature EPR and Transport Studies on Poly(4,4'-methylenedianiline): Evidence for Bipolarons

The correlation between magnetic and transport properties is examined by studying poly(4,4'-methylenedianiline)(PMDA) salts and their bases using EPR and conductivity measurements. Five different PMDA salts (doped polymers)were prepared by chemical polymerization of 4,4'-methylenedianiline using different protonic acids. The PMDA bases were obtained by dedoping the salts using ammonium hydroxide. Ambient temperature electrical conductivity measurements show evidence for the doped PMDA system to be highly disordered. The EPR spectra of the samples were recorded in the range 20-200 "C, and the results were analyzed on the basis of the polaron-bipolaron model, which is typical of nondegenerate systems. Both PMDA salts and their bases consist of self-trapped, highly mobile polarons or radical cations. EPR studies on PMDA salts show evidence for the presence of thermally activated and temperature independent (or Pauli type) paramagnetism while the bases show thermally activated, Pauli and Curie-Weiss types of paramagnetism. The paramagnetism arises due to polarons.It is proposed that charge transport takes place through both polarons and bipolarons.

Realizing the 'hindered charge ordered phase' in nanoscale charge ordered manganites: magnetization, magneto-transport and EPR investigations

We report three prominent observations made on the nanoscale charge ordered ( CO) manganites RE(1-x)AE(x)MnO(3) (RE = Nd, Pr; AE = Ca; x = 0.5) probed by temperature dependent magnetization and magneto-transport, coupled with electron magnetic/paramagnetic resonance spectroscopy (EMR/EPR). First, evidence is presented to show that the predominant ground state magnetic phase in nanoscale CO manganites is ferromagnetic and it coexists with a residual anti-ferromagnetic phase. Secondly, the shallow minimum in the temperature dependence of the EPR linewidth shows the presence of a charge ordered phase in nanoscale manganites which was shown to be absent from the DC static magnetization and transport measurements. Thirdly, the EPR linewidth, reflective of spin dynamics, increases significantly with a decrease of particle size in CO manganites. We discuss the interesting observations made on various samples of different particle sizes and give possible explanations. We have shown that EMR spectroscopy is a highly useful technique to probe the 'hindered charge ordered phase' in nanoscale CO manganites, which is not possible by static DC magnetization and transport measurements.

A fuzzy multistage evolutionary (FUME) clustering technique

n this paper, a multistage evolutionary scheme is proposed for clustering in a large data base, like speech data. This is achieved by clustering a small subset of the entire sample set in each stage and treating the cluster centroids so obtained as samples, together with another subset of samples not considered previously, as input data to the next stage. This is continued till the whole sample set is exhausted. The clustering is accomplished by constructing a fuzzy similarity matrix and using the fuzzy techniques proposed here. The technique is illustrated by an efficient scheme for voiced-unvoiced-silence classification of speech.

EPR observation of phase transitions in calcium cadmium acetate hexahydrate: Using Mn2+ and Cu2+ ions as probe

Results of temperature dependence of EPR spectra of Mn2+ and Cu2+ ions doped calcium cadmium acetate hexahydrate (CaCd(CH3COO)4•6H2O) have been reported. The investigation has been carried out in the temperature range between room temperature ( 300 K) and liquid nitrogen temperature. A I-order phase transition at 146 ± 0.5 K has been confirmed. In addition a new II-order phase transition at 128 ± 1 K has been detected for the first time. There is evidence of large amplitude hindered rotations of CH3 groups which become frozen at 128 K. The incorporation of Cu2+ and Mn2+ probes at Ca2+ and Cd2+ sites respectively provide evidence that the phase transitions are caused by the molecular rearrangements of the common coordinating acetate groups between Ca2+ and Cd2+ sites. In contradiction to the previous reports of a change of symmetry from tetragonal to orthorhombic below 140 K, the symmetry of the host is concluded to remain tetragonal in all the three observed phases between room temperature and liquid nitrogen temperature.