The fluorometric procedure of determining coproporphyrin has been adapted to determine coproporphyrin on random urine specimens. This adaptation depends on determining both coproporphyrin and creatinine. A mathematical relationship is established for the amount of coproporphyrin excreted when 1200 mg. of creatinine is excreted. An important advantage of the random procedure is the elimination o...

This article treats the problem of learning a dictionary providing sparse representations for a given signal class, via l1 minimisation. The problem is to identify a dictionary Φ from a set of training samples Y knowing that Y = ΦX for some coefficient matrix X. Using a characterisation of coefficient matrices X that allow to recover any basis as a local minimum of an l1 minimisation problem, i...

We study the probability that a sample of independent, identically distributed random variables with a geometric distribution is gap-free, that is, that the sizes of the variables in the sample form an interval. We indicate that this problem is closely related to the asymptotic probability that a random composition of an integer n is likewise gap-free.

This paper examines the detection of parameterized shapes in multidimensional noisy grayscale images. A novel shape detection algorithm utilizing random sample theory is presented. Although the method can be generalized, line detection is detailed. Each line in the image corresponds to a point in the line parameter space. The method creates hypothesis lines by randomly selecting parameter space...

Statisticians routinely plot ordered observations against expected values to validate a model using a random sample. In fact, it is possible to construct a probability plot for a random sample from any continuous distribution function, and this is accommodated by the probability integral transform which facilitates a uniform probability plot of the ordered transformed observations against their...

Eigenvectors and eigenvalues of discrete graph Laplacians are often used for manifold learning and nonlinear dimensionality reduction. It was previously proved by Belkin and Niyogi [3] that the eigenvectors and eigenvalues of the graph Laplacian converge to the eigenfunctions and eigenvalues of the Laplace-Beltrami operator of the manifold in the limit of infinitely many data points sampled ind...

Motivated by applications in enumerative combinatorics and the analysis of algorithms we investigate the number of gaps and the length of the longest gap in a discrete random sample from a general distribution. We obtain necessary and sufficient conditions on the underlying distribution for the gaps to vanish asymptotically (with probability 1, or in probability), and we study the limiting dist...

We propose an accelerated CTMC simulation method that is exact in the sense that it produces all of the transitions involved. We call our method Path Sampling Simulation as it samples from the distribution of trajectories and the distribution of time given some particular trajectory. Sampling from the trajectory space rather than the transition space means that we need to generate fewer random ...

Random sampling is a well-known technique for approximate processing of large datasets. We introduce a set of algorithms for incremental maintenance of large random samples on secondary storage. We show that the sample maintenance cost can be reduced by refreshing the sample in a deferred manner. We introduce a novel type of log file which follows the intuition that only a “sample” of the opera...