Restricted trees: simplifying networks with bottlenecks

Suppose N is a phylogenetic network indicating a complicated relationship among individuals and taxa. Often of interest is a much simpler network, for example, a species tree T, that summarizes the most fundamental relationships. The meaning of a species tree is made more complicated by the recent discovery of the importance of hybridizations and lateral gene transfers. Hence it is desirable to describe uniform well-defined procedures that yield a tree given a network N. A useful tool toward this end is a connected surjective digraph (CSD) map f from N to N' where N' is generally a much simpler network than N. A set W of vertices in N is "restricted" if there is at most one vertex from which there is an arc into W, thus yielding a bottleneck in N. A CSD map f from N to N' is "restricted" if the inverse image of each vertex in N' is restricted in N. This paper describes a uniform procedure that, given a network N, yields a well-defined tree called the "restricted tree" of N. There is a restricted CSD map from N to the restricted tree. Many relationships in the tree can be proved to appear also in N.Comment: 17 pages, 2 figure

CSD Homomorphisms Between Phylogenetic Networks

Since Darwin, species trees have been used as a simplified description of the relationships which summarize the complicated network $N$ of reality. Recent evidence of hybridization and lateral gene transfer, however, suggest that there are situations where trees are inadequate. Consequently it is important to determine properties that characterize networks closely related to $N$ and possibly more complicated than trees but lacking the full complexity of $N$. A connected surjective digraph map (CSD) is a map $f$ from one network $N$ to another network $M$ such that every arc is either collapsed to a single vertex or is taken to an arc, such that $f$ is surjective, and such that the inverse image of a vertex is always connected. CSD maps are shown to behave well under composition. It is proved that if there is a CSD map from $N$ to $M$, then there is a way to lift an undirected version of $M$ into $N$, often with added resolution. A CSD map from $N$ to $M$ puts strong constraints on $N$. In general, it may be useful to study classes of networks such that, for any $N$, there exists a CSD map from $N$ to some standard member of that class.Comment: 19 pages, 3 figure

Comparing and simplifying distinct-cluster phylogenetic networks

Phylogenetic networks are rooted acyclic directed graphs in which the leaves are identified with members of a set X of species. The cluster of a vertex is the set of leaves that are descendants of the vertex. A network is "distinct-cluster" if distinct vertices have distinct clusters. This paper focuses on the set DC(X) of distinct-cluster networks whose leaves are identified with the members of X. For a fixed X, a metric on DC(X) is defined. There is a "cluster-preserving" simplification process by which vertices or certain arcs may be removed without changing the clusters of any remaining vertices. Many of the resulting networks may be uniquely determined without regard to the order of the simplifying operations.Comment: This is version 2. A previous version is already on ArXi

Part time employment and happiness: A cross-country analysis

The relationship between part time employment and job satisfaction is analysed for mothers in Germany, Denmark, the Netherlands, Finland, France, Spain and the UK. The impact of working part time on subjective life satisfaction and mental well-being is additionally analysed for British mothers. Cultural traditions concerning women´s role in society, and institutional differences between the countries are exploited. Results indicate that poor quality jobs can diminish any positive well-being repercussions of part time employment. The results additionally suggest that part time mothers in the UK experience higher levels of job satisfaction but not of overall life satisfaction as compared to their full time counterparts

Book Review

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/66659/2/10.1177_000992286900800608.pd

VLA, PHOENIX, and BATSE observations of an X1 flare

We present observations of an X1 flare (18 Jul. 1991) detected simultaneously with the Very Large Array (VLA), the PHOENIX Digital Radio Spectrometer and the Burst and Transient Source Experiment (BATSE) aboard the Gamma Ray Observatory (GRO). The VLA was used to produce snapshot maps of the impulsive acceleration in the higher corona several minutes before the onset of the hard x ray burst detected by BATSE. Comparisons with high spectral and temporal observations by PHOENIX reveal a variety of radio bursts at 20 cm, such as type 3 bursts, intermediate drift bursts, and quasi-periodic pulsations during different stages of the X1 flare. From the drift rates of these radio bursts we derive information on local density scale heights, the speed of radio exciters, and the local magnetic field. Radio emission at 90 cm shows a type 4 burst moving outward with a constant velocity of 240 km/s. The described X1 flare is unique in the sense that it appeared at the east limb (N06/E88), providing the most accurate information on the vertical structure of different flare tracers visible in radio wavelengths

Modeling Solar Lyman Alpha Irradiance

Solar Lyman alpha irradiance is estimated from various solar indices using linear regression analyses. Models developed with multiple linear regression analysis, including daily values and 81-day running means of solar indices, predict reasonably well both the short- and long-term variations observed in Lyman alpha. It is shown that the full disk equivalent width of the He line at 1083 nm offers the best proxy for Lyman alpha, and that the total irradiance corrected for sunspot effect also has a high correlation with Lyman alpha

Consequences of (mis)use of the Texas Assessment of Academic Skills (TAAS) for high-stakes decisions: A comment on Haney and the Texas miracle in education

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