Drosophila Eye Nuclei Segmentation Based on Graph Cut and Convex Shape Prior.

The rapid advance in three-dimensional (3D) confocal imaging technologies is rapidly increasing the availability of 3D cellular images. However, the lack of robust automated methods for the extraction of cell or organelle shapes from the images is hindering researchers ability to take full advantage of the increase in experimental output. The lack of appropriate methods is particularly significant when the density of the features of interest in high, such as in the developing eye of the fruit fly. Here, we present a novel and efficient nuclei segmentation algorithm based on the combination of graph cut and convex shape prior. The main characteristic of the algorithm is that it segments nuclei foreground using a graph cut algorithm and splits overlapping or touching cell nuclei by simple convex and concavity analysis, using a convex shape assumption for nuclei contour. We evaluate the performance of our method by applying it to a library of publicly-available two-dimensional (2D) images that were hand-labeled by experts. Our algorithm yields a substantial quantitative improvement over other methods for this benchmark. For example, our method achieves a decrease of 3.2 in the Hausdorff distance and an decrease of 1.8 per slice in the merged nuclei error.

Scale invariance in the nonstationarity of human heart rate.

We introduce a segmentation algorithm to probe the temporal organization of heterogeneities in human heartbeat interval time series. We find that the lengths of segments with different local mean heart rates follow a power-law distribution and show that this scale-invariant structure is not a simple consequence of the long-range correlations present in the data. The differences in mean heart rates between consecutive segments display a common functional form, but with different parameters for healthy individuals and for heart-failure patients. These findings suggest that there is relevant physiological information hidden in the heterogeneities of the heartbeat time series.

Behavioral-independent features of complex heartbeat dynamics.

We test whether the complexity of the cardiac interbeat interval time series is simply a consequence of the wide range of scales characterizing human behavior, especially physical activity, by analyzing data taken from healthy adult subjects under three conditions with controls: (i) a "constant routine" protocol where physical activity and postural changes are kept to a minimum, (ii) sympathetic blockade, and (iii) parasympathetic blockade. We find that when fluctuations in physical activity and other behavioral modifiers are minimized, a remarkable level of complexity of heartbeat dynamics remains, while for neuroautonomic blockade the multifractal complexity decreases.

Scaling of the distribution of fluctuations of financial market indices.

We study the distribution of fluctuations of the S&P 500 index over a time scale deltat by analyzing three distinct databases. Database (i) contains approximately 1 200 000 records, sampled at 1-min intervals, for the 13-year period 1984-1996, database (ii) contains 8686 daily records for the 35-year period 1962-1996, and database (iii) contains 852 monthly records for the 71-year period 1926-1996. We compute the probability distributions of returns over a time scale deltat, where deltat varies approximately over a factor of 10(4)-from 1 min up to more than one month. We find that the distributions for deltat

Scaling of the distribution of price fluctuations of individual companies.

We present a phenomenological study of stock price fluctuations of individual companies. We systematically analyze two different databases covering securities from the three major U.S. stock markets: (a) the New York Stock Exchange, (b) the American Stock Exchange, and (c) the National Association of Securities Dealers Automated Quotation stock market. Specifically, we consider (i) the trades and quotes database, for which we analyze 40 million records for 1000 U.S. companies for the 2-yr period 1994-95; and (ii) the Center for Research and Security Prices database, for which we analyze 35 million daily records for approximately 16,000 companies in the 35-yr period 1962-96. We study the probability distribution of returns over varying time scales Delta t, where Delta t varies by a factor of approximately 10(5), from 5 min up to approximately 4 yr. For time scales from 5 min up to approximately 16 days, we find that the tails of the distributions can be well described by a power-law decay, characterized by an exponent 2.5 < proportional to < 4, well outside the stable Lévy regime 0 < alpha < 2. For time scales Delta t >> (Delta t)(x) approximately equal to 16 days, we observe results consistent with a slow convergence to Gaussian behavior. We also analyze the role of cross correlations between the returns of different companies and relate these correlations to the distribution of returns for market indices.

Scale-independent measures and pathologic cardiac dynamics.

We study several scale-independent measures of cardiac interbeat interval dynamics defined through the application of the wavelet transform. We test their performance in detecting heart disease using a database consisting of records of interbeat intervals for a group of healthy individuals and subjects with congestive heart failure. We find that scale-independent measures effectively distinguish healthy from pathologic behavior and propose a new two-variable scale-independent measure that could be clinically useful. We compare the performance of a recently proposed scale-dependent measure and find that the results depend on the database analyzed and on the analyzing wavelet.

Stochastic feedback and the regulation of biological rhythms.

We propose a general approach to the question of how biological rhythms spontaneously self-regulate, based on the concept of "stochastic feedback". We illustrate this approach by considering at a coarse-grained level the neuroautonomic regulation of the heart rate. The model generates complex dynamics and successfully acounts for key characteristics of cardiac variability, including the l/f power spectrum, the functional form and scaling of the distribution of variations, and correlations in the Fourier phases indicating nonlinear dynamics.