The use of traditional tools for the discovery and characterization of biological systems has resulted in a wealth of biological knowledge. Unfortunately, only a small portion of the biological world is well-understood to date, and the study of the rest remains a daunting task. This work involves using time-varying stimuli in order to more rapidly interrogate and characterize signaling pathways. The time-dependent stimulation of a signaling pathway can be used in conjunction with a model of the pathway to efficiently evaluate and test hypotheses. We are developing this technology using the yeast pheromone signal transduction pathway as a model system. The time-varying stimuli will be applied to the yeast cells via a novel microfluidic device, and the pathway output will be measured via various fluorescent reporters. The output of the pathway can then be compared to the output from a computational model of the pathway in order to test hypotheses and constrain our knowledge of the pathway. Initial work shows that a computational model can be used to identify stimuli time-courses that increase the parameter sensitivity, meaning that corresponding experiments could potentially be much more informative. / Poster presented at the 2005 ICSB meeting, held at Harvard Medical School in Boston, MA.

Every auditory event provides an information-rich signal to the brain. The signal constitutes perceptual attributes of pitch, loudness, timbre, and also, conceptual attributes like location, emotions, meaning, etc. In the present work we examine the timbre perception of time-varying signals in particular. While stationary signal timbre, by-itself is complex perceptually, the time-varying signal timbre introduces an evolving pattern, adding to its multi-dimensionality. To characterize timbre, we conduct psycho-acoustic perception tests with normal-hearing human subjects. We focus on time-varying synthetic speech signals(can be extended to music) because listeners are perceptually consistent with speech. Also, we can parametrically control the timbre and pitch glides using linear time-varying models. In order to quantify the timbre change in time-varying signals, we define the JND(Just noticeable difference) of timbre using diphthongs, synthesized using time-varying formant frequency model. The diphthong JND is defined as a two dimensional contour on the plane of percentage change of formant frequencies of terminal vowels. Thus, we simplify the perceptual probing to a lower dimensional space, i.e, 2-D even for a diphthong, which is multi-parametric. We also study the impact of pitch glide on the timbre JND of the diphthong. It is observed that timbre JND is influenced by the occurrence of pitch glide. Focusing on the magnitude of perceptual timbre change, we design a MUSHRA-like listening test using the vowel continuum in the formant-frequency space. We provide explicit anchors for reference: 0% and 100%, thus quantifying the perceptual timbre change on a 1-D scale. We also propose an objective measure of timbre change and observe that there is good correlation between the objective measure and subjective human responses of percentage timbre change. Using the above experimental methodology, we studied the influence of pitch shift on timbre perception and observed that the perceptual timbre change increases with change in pitch. We used vowels and diphthongs with 5 different types of pitch glides-(i) Constant pitch,(ii) 3-semitone linearly-up,(iii) 3 semitone linearly-down, (iv)V–like pitch glide and (v) hat-like pitch glide. The present study shows that timbre change can be measured on a 1-D scale if the perturbation is along one-dimension. We observe that for bright vowels(/a/and/i/), linearly decreasing pitch glide(dull pitch glide)causes more timbre change than linearly increasing pitch glide(bright pitch glide).For dull vowels(/u/),it is vice-versa. To summarize, in congruent pitch glides cause more perceptual timbre change than congruent pitch glides.(Congruent pitch glide implies bright pitch glide in bright vowel or dull pitch glide in dull vowel and in congruent pitch glide implies bright pitch glide in dull vowel or dull pitch glide in bright vowel.) Experiments with quadratic pitch glides show that the decay portion of pitch glide affects timbre perception more than the attack portion in short duration signals with less or no sustained part. In case of time-varying timbre, bright diphthongs show patterns similar to bright vowels. Also, for bright diphthongs(/ai/), perceived timbre change is most with decreasing pitch glide(dull pitch glide). We also observed that listeners perceive more timbre change in constant pitch than in pitch glides, congruent with the timbre or pitch glides with quadratic changes. The main conclusion of this study is that pitch and timbre do interact and in congruent pitch glides cause more timbre change than congruent pitch glides. In the case of quadratic pitch glides, listener perception of vowels is influenced by the decay than the attack in pitch glide in short duration signals. In the case of time-varying timbre also, in congruent pitch glides cause the most timbre change, followed by constant pitch glide. For congruent pitch glides and quadratic pitch glides in time-varying timbre, the listeners perceive lesser timbre change than otherwise.

For time-varying signals such as speech and audio, short-time analysis becomes necessary to compute specific signal attributes and to keep track of their evolution. The standard technique is the short-time Fourier transform (STFT), using which one decomposes a signal in terms of windowed Fourier bases. An advancement over STFT is the wavelet analysis in which a function is represented in terms of shifted and dilated versions of a localized function called the wavelet. A specific modeling approach particularly in the context of speech is based on short-time linear prediction or short-time Wiener filtering of noisy speech. In most nonstationary signal processing formalisms, the key idea is to analyze the properties of the signal locally, either by first truncating the signal and then performing a basis expansion (as in the case of STFT), or by choosing compactly-supported basis functions (as in the case of wavelets). We retain the same motivation as these approaches, but use polynomials to model the signal on a short-time basis (“short-time polynomial representation”). To emphasize the local nature of the modeling aspect, we refer to it as “local polynomial modeling (LPM).” We pursue two main threads of research in this thesis: (i) Short-time approaches for speech enhancement; and (ii) LPM for enhancing smooth signals, with applications to ECG, noisy nonuniformly-sampled signals, and voiced/unvoiced segmentation in noisy speech. Improved iterative Wiener filtering for speech enhancement A constrained iterative Wiener filter solution for speech enhancement was proposed by Hansen and Clements. Sreenivas and Kirnapure improved the performance of the technique by imposing codebook-based constraints in the process of parameter estimation. The key advantage is that the optimal parameter search space is confined to the codebook. The Nonstationary signal enhancement solutions assume stationary noise. However, in practical applications, noise is not stationary and hence updating the noise statistics becomes necessary. We present a new approach to perform reliable noise estimation based on spectral subtraction. We first estimate the signal spectrum and perform signal subtraction to estimate the noise power spectral density. We further smooth the estimated noise spectrum to ensure reliability. The key contributions are: (i) Adaptation of the technique for non-stationary noises; (ii) A new initialization procedure for faster convergence and higher accuracy; (iii) Experimental determination of the optimal LP-parameter space; and (iv) Objective criteria and speech recognition tests for performance comparison. Optimal local polynomial modeling and applications We next address the problem of fitting a piecewise-polynomial model to a smooth signal corrupted by additive noise. Since the signal is smooth, it can be represented using low-order polynomial functions provided that they are locally adapted to the signal. We choose the mean-square error as the criterion of optimality. Since the model is local, it preserves the temporal structure of the signal and can also handle nonstationary noise. We show that there is a trade-off between the adaptability of the model to local signal variations and robustness to noise (bias-variance trade-off), which we solve using a stochastic optimization technique known as the intersection of confidence intervals (ICI) technique. The key trade-off parameter is the duration of the window over which the optimum LPM is computed. Within the LPM framework, we address three problems: (i) Signal reconstruction from noisy uniform samples; (ii) Signal reconstruction from noisy nonuniform samples; and (iii) Classification of speech signals into voiced and unvoiced segments. The generic signal model is x(tn)=s(tn)+d(tn),0 ≤ n ≤ N - 1. In problems (i) and (iii) above, tn=nT(uniform sampling); in (ii) the samples are taken at nonuniform instants. The signal s(t)is assumed to be smooth; i.e., it should admit a local polynomial representation. The problem in (i) and (ii) is to estimate s(t)from x(tn); i.e., we are interested in optimal signal reconstruction on a continuous domain starting from uniform or nonuniform samples. We show that, in both cases, the bias and variance take the general form: The mean square error (MSE) is given by where L is the length of the window over which the polynomial fitting is performed, f is a function of s(t), which typically comprises the higher-order derivatives of s(t), the order itself dependent on the order of the polynomial, and g is a function of the noise variance. It is clear that the bias and variance have complementary characteristics with respect to L. Directly optimizing for the MSE would give a value of L, which involves the functions f and g. The function g may be estimated, but f is not known since s(t)is unknown. Hence, it is not practical to compute the minimum MSE (MMSE) solution. Therefore, we obtain an approximate result by solving the bias-variance trade-off in a probabilistic sense using the ICI technique. We also propose a new approach to optimally select the ICI technique parameters, based on a new cost function that is the sum of the probability of false alarm and the area covered over the confidence interval. In addition, we address issues related to optimal model-order selection, search space for window lengths, accuracy of noise estimation, etc. The next issue addressed is that of voiced/unvoiced segmentation of speech signal. Speech segments show different spectral and temporal characteristics based on whether the segment is voiced or unvoiced. Most speech processing techniques process the two segments differently. The challenge lies in making detection techniques offer robust performance in the presence of noise. We propose a new technique for voiced/unvoiced clas-sification by taking into account the fact that voiced segments have a certain degree of regularity, and that the unvoiced segments do not possess any smoothness. In order to capture the regularity in voiced regions, we employ the LPM. The key idea is that regions where the LPM is inaccurate are more likely to be unvoiced than voiced. Within this frame-work, we formulate a hypothesis testing problem based on the accuracy of the LPM fit and devise a test statistic for performing V/UV classification. Since the technique is based on LPM, it is capable of adapting to nonstationary noises. We present Monte Carlo results to demonstrate the accuracy of the proposed technique.