Model-Based Deconvolution of Cell Cycle Time-Series Data Reveals Gene Expression Details at High Resolution

In both prokaryotic and eukaryotic cells, gene expression is regulated across the cell cycle to ensure “just-in-time” assembly of select cellular structures and molecular machines. However, present in all time-series gene expression measurements is variability that arises from both systematic error in the cell synchrony process and variance in the timing of cell division at the level of the single cell. Thus, gene or protein expression data collected from a population of synchronized cells is an inaccurate measure of what occurs in the average single-cell across a cell cycle. Here, we present a general computational method to extract “single-cell”-like information from population-level time-series expression data. This method removes the effects of 1) variance in growth rate and 2) variance in the physiological and developmental state of the cell. Moreover, this method represents an advance in the deconvolution of molecular expression data in its flexibility, minimal assumptions, and the use of a cross-validation analysis to determine the appropriate level of regularization. Applying our deconvolution algorithm to cell cycle gene expression data from the dimorphic bacterium Caulobacter crescentus, we recovered critical features of cell cycle regulation in essential genes, including ctrA and ftsZ, that were obscured in population-based measurements. In doing so, we highlight the problem with using population data alone to decipher cellular regulatory mechanisms and demonstrate how our deconvolution algorithm can be applied to produce a more realistic picture of temporal regulation in a cell

Transform Domain Motion Estimation

This Paper Introduces an Algorithm for Estimating the Displacement of Moving Objects in a Television Scene from Spatial Transform Coefficients of Successive Frames. the Algorithm Works Recursively in Such a Way that the Displacement Estimates Are Updated from Coefficient to Coefficient. a Promising Application of This Algorithm is in Motion‐compensated Interframe Hybrid Transform‐dpcm Image Coding. We Give a Statistical Analysis of the Transform Domain Displacement Estimation Algorithm and Prove its Convergence under Certain Realistic Conditions. an Analytical Derivation is Presented that Gives Sufficient Conditions for the Rate of Convergence of the Algorithm to Be Independent of the Transform Type. This Result is Supported by a Number of Simulation Examples using Hadamard, Haar, and Slant Transforms. We Also Describe an Extension of the Algorithm that Adaptively Updates Displacement Estimation According to the Local Features of the Moving Objects. Simulation Results Demonstrate that the Adaptive Displacement Estimation Algorithm Has Good Convergence Properties in Estimating Displacement Even for Very Noisy Images. © 1979 the Bell System Technical Journa

STRENGTH DISTRIBUTION OF CARBORUNDUM POLYCRYSTALLINE SIC FIBERS AS DERIVED FROM THE SINGLE-FIBER-COMPOSITE TEST

The single-fibre-composite (s.f.c) test, in which a fibre is embedded in an epoxy matrix and the composite tested in tension, was employed to obtain the statistical strength distribution of Carborundum SiC ceramic fibres over the range of gauge lengths from 0.5 to 20 mm. The raw s.f.c. test data was organized into three independent forms: the number of fibre breaks versus applied stress; the fibre fragment length distribution at the end of the test; and the fibre strength versus fragment length during testing. The data was interpreted using two different models of the fibre/epoxy-matrix interface, and it was found that a constant shear stress model could not self- consistently fit a II of the s.f.c. data, whereas an elastic interface model provided good fits to all of the data. The applicability of the elastic interface model was supported by the absence of interfacial debonding and the rough fibre/matrix interface, which promoted mechanical interlocking. The s.f.c. test derived strength of sigma(0) = 1500 MPa at a gauge length of 20 mm, with a Weibull modulus of m = 9, agreed fairly well with independent tension test results obtained on 254 mm length samples. Obtaining self-consistent fits to all of the manifestations of the s.f.c. data requires careful testing and analysis, but the present work demonstrates that the s.f.c. test can be a powerful tool for the accurate and independent assessment of fibre strengths at small gauge lengths