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This paper describes two new methods to solve the following estimation problem. Given n1 noisy measurements (yi1, i = 1,..., n1) of the response of a system to a known input [A1(t) where t indicates time], and n2 noisy measurements (yi2, i = 1,..., n2) of the response of a system to an unknown input [A2(t)], obtain an estimate of A2(t) and K(t) (the unit impulse response function of the system) under the model: [formula: see text] where Eij are independent identically distributed random variables. Both methods use spline functions to represent the unknown functions, and they automatically select the spline functions representing the unknown input and unit impulse response functions. The first method estimates separately the unit impulse response function and the input, recasting the problem in terms of inequality-constrained linear regression. The second method jointly estimates the unit impulse response function and the input function, recasting the problem in terms of inequality-constrained nonlinear regression. Simulated and real data analysis are reported.
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The potential evoked by a 'train' of N equally spaced auditory clicks, with an inter-click period shorter than the duration of the response to an isolated click, is said to be a steady-state response (SSR). Extracting the individual responses evoked by the clicks of the train during steady state can be key to understanding of the neurophysiological mechanisms underlying SSR generation. In the literature, this task has been dealt with only under the (unwarranted) assumption that the response of the system does not vary during the presentation of the clicks, i.e. no neurophysiological adaptation is present. In this work, a new, non-parametric algorithm is proposed that, relaxing the time-invariance hypothesis, allows the extraction from the SSR of the N waveforms individually evoked by the N clicks of the train. The performance of the approach is evaluated on simulated SSRs and on real data recorded from the temporal cortex of awake rats. Results show that the method is able to detect and assess possible adaptation of the neurophysiological system in the generation of SSRs.
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We analyze in detail the estimation problem associated with the following problem. Given n noisy measurements (yi, i = 1, ..., n) of the response of a system to an input (A(t) where t indicates time), obtain an estimate of A(t) given a known K(t) (the unit impulse response function of the system) under the model: yi = integral of 0(ti) A(s)K(ti - s)ds + epsilon i where epsilon 1, ... ,epsilon n are independent identically distributed random variables with mean zero and common finite variance. In the solution to the problem, the unknown function is represented by a spline function, and the problem is recast in terms of (inequality constrained) linear regression. The main issues addressed are: (a) the comparison of different nonparametric regression methods in this context, and (b) how to do model selection, i.e., given a (finite) set of candidate spline functions, select the (possibly unique) best one using some (statistically based) selection criteria. Different spline candidate sets, and different asymptotic and resampling-based statistical selection criteria are compared by means of simulations. Due to the particular nature of the estimation problem, modifications to the criteria are suggested. Applications to simulated and real pharmacokinetics data are reported.
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The Maximum Entropy approach is applied to restore and sharpen scanning tunneling microscopy (STM) images with atomic resolution. Based on the STM theory of Tersoff and Hamann the process of data acquisition can be approximated by the convolution of a localised atomic density of states (i.e. narrow spots in the reconstruction) of the sample and a Gaussian resolution function which limits the resolution. In STM practice a good and robust estimation of the atomic core positions is necessary for different reasons, such as to be able to calculate the characteristics of the atomic lattice or to study non-periodicities.
A method was developed for dynamic spectrophotometric measurements in vivo in the presence of non-specific spectral changes due to external disturbances. This method was used to measure changes in mitochondrial respiratory pigment redox states in photoreceptor cells of live, white-eyed mutants of the blowfly Calliphora vicina. The changes were brought about by exchanging the atmosphere around an immobilised animal from air to N2 and back again by a rapid gas exchange system. During an experiment reflectance spectra were measured by a linear CCD array spectrophotometer. This method involves the pre-processing steps of difference spectra calculation and digital filtering in one and two dimensions. These were followed by time-domain principal component analysis (PCA). PCA yielded seven significant time domain principal component vectors and seven corresponding spectral score vectors. In addition, through PCA we also obtained a time course of changes common to all wavelengths-the residual vector, corresponding to non-specific spectral changes due to preparation movement or mitochondrial swelling. In the final step the redox state time courses were obtained by fitting linear combinations of respiratory pigment difference spectra to each of the seven score vectors. The resulting matrix of factors was then multiplied by the matrix of seven principal component vectors to yield the time courses of respiratory pigment redox states. The method can be used, with minor modifications, in many cases of time-resolved optical measurements of multiple overlapping spectral components, especially in situations where non-specific external influences cannot be disregarded.
We describe in detail a custom-built two-photon microscope based on a modified confocal scanhead (Olympus Fluoview) and mode-locked Ti:sapphire laser (Coherent Mira 900). This system has internal detectors as well as external whole-field detection and an electrooptical modulator for blanking the beam on flyback and effecting fast changes in excitation intensity. This microscope can be used in deep, scattering samples for quantitative measurements with a wide range of fluorophores (GFP, fura, calcium green, calcium orange, fluo-3, DiI, DiO, fluorescein, rhodamine), for fluorescent photobleaching recovery and for uncaging. Images obtained with this system can be deconvolved with the Estimation Maximization algorithm using the program XCOSM (freeware available at: http://www.ibc.wustl.edu/bcl/ xcosm/).
Transcranial magnetic stimulation (TMS) is a noninvasive method for local stimulation of cerebral cortex using a small coil's pulsed magnetic field. TMS response maps consist of measured responses to stimulations at points on a scalp-referenced grid and are used to study the topography of the brain's inhibitory and excitatory response. Because the magnetic field distributions of stimulation coils are 1-2 centimeters wide and 2-3 centimeters long, and the induced electric fields are even broader, the resolution of TMS maps is limited and the actual region of cortical stimulation is poorly defined. To better characterize the activation pattern, a practical mathematical procedure was developed for deconvolving a spherical model approximation of the coil's induced electric field distribution (here measured in a phantom) from the TMS response maps. This procedure offers an integrated, internally consistent method for processing TMS response maps to estimate the spatial distribution of motor cortex activations and inhibitions.
Evolution of the triplet code is reconstructed on the basis of consensus temporal order of appearance of amino acids. Several important predictions are confirmed by computational sequence analyses. The earliest amino acids, alanine and glycine, have been encoded by GCC and GGC codons, as today. They were succeeded, respectively, by A- and G-series of amino acids, encoded by pyrimidine-central and purine-central codons. The length of the earliest proteins is estimated to be 6-7 residues. The earliest mRNAs were short G+C-rich molecules. These short sequences could have formed hairpins. This is confirmed by analysis of modern prokaryotic mRNA sequences. Predominant size of detected ancient hairpins also corresponds to 6-7 amino acids, as above. Vestiges of last common ancestor can be found in extant proteins in form of entirely conserved short sequences of size six to nine residues present in all or almost all sequenced prokaryotic proteomes (omnipresent motifs). The functions of the topmost conserved octamers are not involved in the basic elementary syntheses. This suggests an initial abiotic supply of amino acids, bases and sugars.
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