Trees and Matchings

In this article, Temperley's bijection between spanning trees of the square grid on the one hand, and perfect matchings (also known as dimer coverings) of the square grid on the other, is extended to the setting of general planar directed (and undirected) graphs, where edges carry nonnegative weights that induce a weighting on the set of spanning trees. We show that the weighted, directed spanning trees (often called arborescences) of any planar graph G can be put into a one-to-one weight-preserving correspondence with the perfect matchings of a related planar graph H. One special case of this result is a bijection between perfect matchings of the hexagonal honeycomb lattice and directed spanning trees of a triangular lattice. Another special case gives a correspondence between perfect matchings of the ``square-octagon'' lattice and directed weighted spanning trees on a directed weighted version of the cartesian lattice. In conjunction with results of Kenyon, our main theorem allows us to compute the measures of all cylinder events for random spanning trees on any (directed, weighted) planar graph. Conversely, in cases where the perfect matching model arises from a tree model, Wilson's algorithm allows us to quickly generate random samples of perfect matchings.Comment: 32 pages, 19 figures (minor revisions from version 1

Predictions of the emergence of vaccine-resistant hepatitis B in The Gambia using a mathematical model

Vaccine escape variants of hepatitis B virus (HBV) have been identified world-wide. A mathematical model of HBV transmission is used to investigate the potential pattern of emergence of such variants. Attention is focused on The Gambia as a country with high quality epidemiological data, universal infant immunization and in which escape mutants after childhood infections have been observed. We predict that a variant cannot become dominant for at least 20 years from the start of vaccination, even when using a vaccine which affords no cross protection. The dominant factor responsible for this long time scale is the low rate of infectious contacts between infected and susceptible individuals (we estimate the basic reproduction number of hepatitis B in The Gambia to be 1·7). A variant strain that achieves high prevalence will also take many years to control, and it is questionable whether emergence will be identifiable by sero-surveillance until of high prevalence. The sensitivity of the model predictions to epidemiological and demographic factors is explored

Predictions of the emergence of vaccine-resistant hepatitis B in The Gambia using a mathematical model

Vaccine escape variants of hepatitis B virus (HBV) have been identified world-wide. A mathematical model of HBV transmission is used to investigate the potential pattern of emergence of such variants. Attention is focused on The Gambia as a country with high quality epidemiological data, universal infant immunization and in which escape mutants after childhood infections have been observed. We predict that a variant cannot become dominant for at least 20 years from the start of vaccination, even when using a vaccine which affords no cross protection. The dominant factor responsible for this long time scale is the low rate of infectious contacts between infected and susceptible individuals (we estimate the basic reproduction number of hepatitis B in The Gambia to be 1·7). A variant strain that achieves high prevalence will also take many years to control, and it is questionable whether emergence will be identifiable by sero-surveillance until of high prevalence. The sensitivity of the model predictions to epidemiological and demographic factors is explored

Fattening Steers of Different Ages

Summary1. Hogs made more gain following three year old steers than when following yearling steers.2. The younger the steer the fewer the pounds of feed for a pound of gain.3. The loss, in shipping per head was greater when the cattle were fed sheaf oats enroute than when they were fed prairie hay.4. The largest gain for feed consumed was made during the first thirty days when the steers were being put on full feed.5. A longer feeding period was required to get yearling steers in a good marketable condition than was required for the two year old or the three year old steers.6. More grain was required for a pound of gain during cold than moderate weather, indicating that a large percent of the feed was required for-maintaining body heat.7. Deducting the gain made by steer No. 1; in the two year old lot of the first experiment, as it was much below the average for the two year old steers, only six pounds more gain was made by the three year olds than the two years old, and only nine pounds more was made by the two year olds than the year lings per head, showing that practically equal gains can be made with steers of different ages under the same conditions.8.When mixed with oil-meal, one-tenth by weight, the three year old steers consumed an average of forty-fivebushels, the two year olds an average of forty bushels and the yearlings an average of thirty-four bushels of corn per head during the feeding period of 127 days.9. With the three year old and the two year old lots a pound of pork was made for every five-pounds of beef produced, while with the yearling lots, one pound of pork was made for every nine pounds of beef. The production of pork being an important item in steer feeding operations and as experiments show that it is not profitable to grind corn for steers ( unless to increase the palatability)the combined gain of both cattle and hogs should be considered by the prospective feeder

Faith based institutions and youth participation in community development : issues and opportunities

Thesis (M.C.P.)--Massachusetts Institute of Technology, Dept. of Urban Studies and Planning, 2002.Includes bibliographical references (leaves 38-40).There is growing interest among schools, other public agencies, and secular non-profit organizations to involve young people in current community planning efforts. Missing from discourse, however are the roles churches and other faith-based institutions can play in involving youth. Across the nation, churches and church-affiliated community organizations provide adults opportunities to revitalize their communities. In this thesis, two types of challenges that hinder these organizations from providing similar opportunities to urban youth will be examined. One such challenge focuses on internal obstacles within faith-based organizations that dissuade new models of participation. The second challenge focuses on several relational obstacles that contribute to a disconnection between leadership of faith-based organizations and contemporary urban youth culture. In spite of these challenges, this thesis suggest that some churches and church-affiliated community organizations serving low-income communities are well positioned to include urban youth bring in their community planning efforts. This thesis will explore the merits of that claim. The goals of this thesis are (1) to identify the various institutional and relational challenges that impede collaborations between faith-based institutions and urban youth in community development; and (2) to draw the attention of youth serving- and other church-affiliated community organizations to innovative and progressive approaches for youth participation.by James W. Wilson.M.C.P

Construction and Software Design for a Microcomputer Controlled pH/Ion Titrator

The construction of an automated titration device is described. The major components include an Apple II+ Microcomputer and 8-bit parallel interface. Fisher Accumet, Model 520 Digital pH/lon Meter, Gilmont Micrometer Buret of 2.5 mL capacity, Sigma stepper motor, power supply and driver to operate the buret, and a constant temperature bath of ± 0.005 °C stability. The limitations of the system are 0.001 pH/0.1 mv for the pH/ion sensing system, and 0.125 μL per step for the buret. The system as described is designed to determine equilibrium constants for metal ion-amino acid complexes. By changing the software a variety of different pH and redox titration experiments may be performed. A computer program used to operate the stepper motor driven syringe buret and record the pH from a digital pH meter is described. The program uses both Apple BASIC and assembly language. This is a closed loop operation in which the data from the pH meter is used to control the amount of reagent delivered by the buret. The results are displayed graphically as the titration proceeds. The variance of the pH readings are calculated using an assembly language subroutine and the calculations are done with zero round-off error

Melanism as a potential thermal benefit in eastern fox squirrels (Sciurus niger)

Melanistic fox squirrels (Sciurus niger) have expanded westward and increased in frequency in the Omaha, Nebraska, and Council Bluffs, Iowa, metropolitan areas. The selective advantage of melanism is currently unknown, but thermal advantages have been hypothesized, especially in winter. No difference in metabolic response curves were measured between melanistic (black) and rufus (orange) fox squirrels. When exposed to sunny skies, both melanistic and rufus squirrels had higher surface (skin and fur) temperature as ambient temperatures increased. Melanistic squirrel surface temperatures did not differ when squirrels were exposed to sunny or cloudy skies. However, rufus individuals showed significantly lower increases in surface temperatures when under cloudy skies. During fall months, rufus individuals were about 1.5 times more active throughout the day than melanistic individuals. However, in winter, melanistic fox squirrels were approximately 30% more active in the mornings (before 13:00) compared to rufus squirrels. Pre-winter body condition was higher in melanistic (25.5 ± 1.8 g/cm) compared to rufus (20.30 ± 3.6 g/cm) fox squirrels; however, there were no significant differences between melanistic (22.8 ± 1.4 g/cm) and rufus (23.9 ± 0.8 g/cm) fox squirrel post-winter body condition. The results of this study indicate that melanistic fox squirrels may have a slight winter thermal advantage over rufus fox squirrels by maintaining higher skin temperatures

The origins of radial fracture systems and associated large lava flows on Venus

Magellan images have revealed the existence of systems of radial fractures on venus that are very similar in form to terrestrial dike swarms such as the Mackenzie swarm in Northern Canada. The association of many of the fracture systems with lava flows, calderas, and volcanic edifices further support the idea of a dike emplacement origin. A global survey of the Magellan images has allowed the location of 300 such fracture systems. Two types of fracture systems are defined. A series of models were developed to simulate the emplacement of dikes on Venus. Observations of fracture lengths and widths were then used to constrain the emplacement conditions. The model results show that the great length and relatively large width of the fractures can only be explained if the dikes that produce them were emplaced in high driving pressure (pressure buffered) conditions. Such conditions imply high rates of melt production, which is consistent with the melt being derived directly from a plume head. We have recently modeled the vertical emplacement of a dike from the top of a mantle plume and calculated the eruption rates such a dike would produce on reaching the surface. This modeling shows that eruption rates of approximately 0.1 cu km/hr can readily be generated by such a dike, consistent with the above results. However, the sensitivity of the model to dike width and therefore driving pressure means that eruption rates from dikes emplaced from the base of the crust or the head of a mantle plume could be orders of magnitude higher than this. Clearly, therefore, the model needs to be refined in order to better constrain eruption conditions. However, it is worth noting here that the initial results do show that even for moderate dike widths, eruption rates could be at least on the order of those estimated for terrestrial flood basalts