Dyschromatosis universalis hereditaria (DUH) is a rare pigmentary disorder characterized by the presence of mottled hyperpigmented and hypopigmented macules over the trunk, extremities, and face. We have presented a case series comprised of six members of a family who had numerous hyperpigmented and hypopigmented macules distributed all over the body. Histological findings were suggestive of dyschromatosis universalis hereditaria.

The goal of understanding complex biological systems and how they are perturbed to cause disease has long been a central focus of biology. The past decade has seen the creation and maturation of a number of new technologies designed to study biological pathways on a genome-wide scale. Rather than obtaining information about the function of one gene or protein at a time, such approaches can offer insight into the activity of every gene and protein in the cell all in the context of one experiment. One fundamental mode of gathering biological insight is through identifying which proteins in the cell interact physically, such as those which form protein complexes or biochemical pathways. Techniques such as yeast-two hybrid and co-immunoprecipitation followed by mass spectrometry allow the determination of a physical interaction map which details binding interactions between proteins on a large scale. Another fundamental mode of biological discovery is through assaying genetic interactions which arise when mutations in two genes produce a phenotype that is surprising in light of each mutation's individual effects. For example a synthetic lethal genetic interaction is indicated when deletions in two genes which are not essential for viability cause lethality when deleted together. Genetic interaction maps can be determined in high-throughput via SGA (Synthetic Genetic Array) technology. In Chapter 2 we derive and analyze a large physical protein interaction map centered on a set of human protein kinases and show how biological insight can be derived from such large-scale screens. In Chapter 3, we develop methods for the comparison of such physical protein interaction maps between species in order to identify proteins whose function is conserved throughout millions of years of evolution. In Chapter 4 we develop algorithms to integrate both physical and genetic interactions together for the purpose of biological pathway discovery. Moreover, our approaches create maps of genetic interactions that provide a picture of the global organization of pathways and complexes within the cell, which we apply to create a map of functional relationships among protein complexes involved in chromosomal biology. In Chapter 6, we apply this approach in two different yeast species and discover that while physical protein interactions are largely conserved across species, many genetic interactions are rewired which gives us valuable insight into pathway architecture. Finally in Chapter 7, we focus on the discovery of genetic interactions involved in the DNA damage response by assaying how different gene mutants respond to a drug which causes DNA damage and then demonstration how this elucidates pathways involved in this process

Given a probability law π on a set S and a function g: S → R, suppose one wants to estimate the mean g = ∫ g dπ. The Markov Chain Monte Carlo method consists of inventing and simulating a Markov chain with stationary distribution π. Typically one has no a priori bounds on the chain’s mixing time, so even if simulations suggest rapid mixing one cannot infer rigorous confidence intervals for. But suppose there is also a separate method which (slowly) gives samples exactly from π. Using n exact samples, one could immediately get a confidence interval of length O(n−1/2). But one can do better. Use each exact sample as the initial state of a Markov chain, and run each of these n chains for m steps. We show how to construct confidence intervals which are always valid, and which, if the (unknown) relaxation time of the chain is suffciently small relative to m=n, have length O(n-1 log n) with high probability.© 2001 Rocky Mountain Mathematics Consortium.