Training and search methods for speech recognition.

Speech recognition involves three processes: extraction of acoustic indices from the speech signal, estimation of the probability that the observed index string was caused by a hypothesized utterance segment, and determination of the recognized utterance via a search among hypothesized alternatives. This paper is not concerned with the first process. Estimation of the probability of an index string involves a model of index production by any given utterance segment (e.g., a word). Hidden Markov models (HMMs) are used for this purpose [Makhoul, J. & Schwartz, R. (1995) Proc. Natl. Acad. Sci. USA 92, 9956-9963]. Their parameters are state transition probabilities and output probability distributions associated with the transitions. The Baum algorithm that obtains the values of these parameters from speech data via their successive reestimation will be described in this paper. The recognizer wishes to find the most probable utterance that could have caused the observed acoustic index string. That probability is the product of two factors: the probability that the utterance will produce the string and the probability that the speaker will wish to produce the utterance (the language model probability). Even if the vocabulary size is moderate, it is impossible to search for the utterance exhaustively. One practical algorithm is described [Viterbi, A. J. (1967) IEEE Trans. Inf. Theory IT-13, 260-267] that, given the index string, has a high likelihood of finding the most probable utterance.

Solution of the pulse width modulation problem using orthogonal polynomials and Korteweg-de Vries equations

The mathematical underpinning of the pulse width modulation (PWM) technique lies in the attempt to represent “accurately” harmonic waveforms using only square forms of a fixed height. The accuracy can be measured using many norms, but the quality of the approximation of the analog signal (a harmonic form) by a digital one (simple pulses of a fixed high voltage level) requires the elimination of high order harmonics in the error term. The most important practical problem is in “accurate” reproduction of sine-wave using the same number of pulses as the number of high harmonics eliminated. We describe in this paper a complete solution of the PWM problem using Padé approximations, orthogonal polynomials, and solitons. The main result of the paper is the characterization of discrete pulses answering the general PWM problem in terms of the manifold of all rational solutions to Korteweg-de Vries equations.

Importance of replication in microarray gene expression studies: Statistical methods and evidence from repetitive cDNA hybridizations

We present statistical methods for analyzing replicated cDNA microarray expression data and report the results of a controlled experiment. The study was conducted to investigate inherent variability in gene expression data and the extent to which replication in an experiment produces more consistent and reliable findings. We introduce a statistical model to describe the probability that mRNA is contained in the target sample tissue, converted to probe, and ultimately detected on the slide. We also introduce a method to analyze the combined data from all replicates. Of the 288 genes considered in this controlled experiment, 32 would be expected to produce strong hybridization signals because of the known presence of repetitive sequences within them. Results based on individual replicates, however, show that there are 55, 36, and 58 highly expressed genes in replicates 1, 2, and 3, respectively. On the other hand, an analysis by using the combined data from all 3 replicates reveals that only 2 of the 288 genes are incorrectly classified as expressed. Our experiment shows that any single microarray output is subject to substantial variability. By pooling data from replicates, we can provide a more reliable analysis of gene expression data. Therefore, we conclude that designing experiments with replications will greatly reduce misclassification rates. We recommend that at least three replicates be used in designing experiments by using cDNA microarrays, particularly when gene expression data from single specimens are being analyzed.

Protonatable residues at the cytoplasmic end of transmembrane helix-2 in the signal transducer HtrI control photochemistry and function of sensory rhodopsin I.

Neutral residue replacements were made of 21 acidic and basic residues within the N-terminal half of the Halobacterium salinarium signal transducer HtrI [the halobacterial transducer for sensory rhodopsin I (SRI)] by site-specific mutagenesis. The replacements are all within the region of HtrI that we previously concluded from deletion analysis to contain sites of interaction with the phototaxis receptor SRI. Immunoblotting shows plasmid expression of the htrI-sopI operon containing the mutations produces SRI and mutant HtrI in cells at near wild-type levels. Six of the HtrI mutations perturb photochemical kinetics of SRI and one reverses the phototaxis response. Substitution with neutral amino acids of Asp-86, Glu-87, and Glu-108 accelerate, and of Arg-70, Arg-84, and Arg-99 retard, the SRI photocycle. Opposite effects on photocycle rate cancel in double mutants containing one replaced acidic and one replaced basic residue. Laser flash spectroscopy shows the kinetic perturbations are due to alteration of the rate of reprotonation of the retinylidene Schiff base. All of these mutations permit normal attractant and repellent signaling. On the other hand, the substitution of Glu-56 with the isosteric glutamine converts the normally attractant effect of orange light to a repellent signal in vivo at neutral pH (inverted signaling). Low pH corrects the inversion due to Glu-56 -> Gln and the apparent pK of the inversion is increased when arginine is substituted at position 56. The results indicate that the cytoplasmic end of transmembrane helix-2 and the initial part of the cytoplasmic domain contain interaction sites with SRI. To explain these and previous results, we propose a model in which (i) the HtrI region identified here forms part of an electrostatic bonding network that extends through the SRI protein and includes its photoactive site; (ii) alteration of this network by photoisomerization-induced Schiff base deprotonation and reprotonation shifts HtrI between attractant and repellent conformations; and (iii) HtrI mutations and extracellular pH alter the equilibrium ratios of these conformations.