A mathematical programming approach to fitting general graphs

We present an algorithm for fitting general graphs to proximity data. The algorithm utilizes a mathematical programming procedure based on a penalty function approach to impose additivity constraints upon parameters. For a user-specified number of links, the algorithm seeks to provide the connected network that gives the least-squares approximation to the proximity data with the specified number of links, allowing for linear transformations of the data. The network distance is the minimum-path-length metric for connected graphs. As a limiting case, the algorithm provides a tree where each node corresponds to an object, if the number of links is set equal to the number of objects minus one. A Monte Carlo investigation indicates that the resulting networks tend to fall within one percentage point of the least-squares solution in terms of the variance accounted for, but do not always attain this global optimum. The network model is discussed in relation to ordinal network representations (Klauer 1989) and NETSCAL (Hutchinson 1989), and applied to several well-known data sets.     

Least squares algorithms for constructing constrained ultrametric and additive tree representations of symmetric proximity data

A mathematical programming algorithm is developed for fitting ultrametric or additive trees to proximity data where external constraints are imposed on the topology of the tree. The two procedures minimize a least squares loss function. The method is illustrated on both synthetic and real data. A constrained ultrametric tree analysis was performed on similarities between 32 subjects based on preferences for ten odors, while a constrained additive tree analysis was carried out on some proximity data between kinship terms. Finally, some extensions of the methodology to other tree fitting procedures are mentioned.The first author is supported as Bevoegdverklaard Navorser of the Belgian Nationaal Fonds voor Wetenschappelijk Onderzoek.     

A modified CANDECOMP method for fitting the extended INDSCAL model

A modified CANDECOMP algorithm is presented for fitting the metric version of the Extended INDSCAL model to three-way proximity data. The Extended INDSCAL model assumes, in addition to the common dimensions, a unique dimension for each object. The modified CANDECOMP algorithm fits the Extended INDSCAL model in a dimension-wise fashion and ensures that the subject weights for the common and the unique dimensions are nonnegative. A Monte Carlo study is reported to illustrate that the method is fairly insensitive to the choice of the initial parameter estimates. A second Monte Carlo study shows that the method is able to recover an underlying Extended INDSCAL structure if present in the data. Finally, the method is applied for illustrative purposes to some empirical data on pain relievers. In the final section, some other possible uses of the new method are discussed. Geert De Soete is supported as “Bevoegdverklaard Navorser” of the Belgian “Nationaal Fonds voor Wetenschappelijik Onderzoek”.     

In situ analyses of genome instability in breast cancer

Transition through telomere crisis is thought to be a crucial event in the development of most breast carcinomas. Our goal in this study was to determine where this occurs in the context of histologically defined breast cancer progression. To this end, we assessed genome instability (using fluorescence in situ hybridization) and other features associated with telomere crisis in normal ductal epithelium, usual ductal hyperplasia, ductal carcinoma in situ and invasive cancer. We modeled this process in vitro by measuring these same features in human mammary epithelial cell cultures during ZNF217-mediated transition through telomere crisis and immortalization. Taken together, the data suggest that transition through telomere crisis and immortalization in breast cancer occurs during progression from usual ductal hyperplasia to ductal carcinoma in situ.     

The decline and fate of an iron-induced subarctic phytoplankton bloom

Iron supply has a key role in stimulating phytoplankton blooms in high-nitrate low-chlorophyll oceanic waters. However, the fate of the carbon fixed by these blooms, and how efficiently it is exported into the ocean's interior, remains largely unknown. Here we report on the decline and fate of an iron-stimulated diatom bloom in the Gulf of Alaska. The bloom terminated on day 18, following the depletion of iron and then silicic acid, after which mixed-layer particulate organic carbon (POC) concentrations declined over six days. Increased particulate silica export via sinking diatoms was recorded in sediment traps at depths between 50 and 125 m from day 21, yet increased POC export was not evident until day 24. Only a small proportion of the mixed-layer POC was intercepted by the traps, with more than half of the mixed-layer POC deficit attributable to bacterial remineralization and mesozooplankton grazing. The depletion of silicic acid and the inefficient transfer of iron-increased POC below the permanent thermocline have major implications both for the biogeochemical interpretation of times of greater iron supply in the geological past, and also for proposed geo-engineering schemes to increase oceanic carbon sequestration.     

Genetics and the making of Homo sapiens

Understanding the genetic basis of the physical and behavioural traits that distinguish humans from other primates presents one of the great new challenges in biology. Of the millions of base-pair differences between humans and chimpanzees, which particular changes contributed to the evolution of human features after the separation of the Pan and Homo lineages 5-7 million years ago? How can we identify the 'smoking guns' of human genetic evolution from neutral ticks of the molecular evolutionary clock? The magnitude and rate of morphological evolution in hominids suggests that many independent and incremental developmental changes have occurred that, on the basis of recent findings in model animals, are expected to be polygenic and regulatory in nature. Comparative genomics, population genetics, gene-expression analyses and medical genetics have begun to make complementary inroads into the complex genetic architecture of human evolution.     

Genetic mechanisms and constraints governing the evolution of correlated traits in drosophilid flies

Some morphological traits differ greatly between related species, but it is not clear whether diversity evolves through changes in the same genes and whether similar, independent (that is, convergent) changes occur by the same mechanism. Pigmentation in fruitflies presents an attractive opportunity to explore these issues because pigmentation patterns are diverse, similar patterns have arisen in independent clades, and numerous genes governing their formation have been identified in Drosophila melanogaster. Here we show that both evolutionary diversification and convergence can be due to evolution at the same locus, by comparing abdominal pigmentation and trichome patterns and the expression of Bric-à-brac2 (Bab2), which regulates both traits in D. melanogaster, in 13 species representing the major clades of the subfamily Drosophilinae. Modifications of Bab2 expression are frequently correlated with diverse pigmentation and trichome patterns that evolved independently in multiple lineages. In a few species, Bab2 expression is not correlated with changes in pigmentation but is correlated with a conserved pattern of trichomes, indicating that this locus can be circumvented to evolve new patterns when a correlated trait is under different constraints.