Alpine glacial loss is resulting in the rapid change and even emergence of downstream lakes; however, little is known about the processes regulating development in these new ecosystems. The unique properties of glacial meltwater impose physical and chemical constraints on lake ecosystem processes, but the degree to which these constraints interact or relax as glaciers recede is not well understood. The nature of these constraints have direct consequences for the fundamental ecological characteristics of the ecosystem. For example, glacial inputs rich in sediment may reduce light thereby limiting primary production, whereas glacial inputs rich nutrients may promote primary production. As these inputs fade, the response of lake biota determine the corresponding changes in biogeochemical cycling. Understanding the relative importance of glacial inputs to the metabolism of emerging aquatic ecosystems may help preserve them and build a framework to predict their trajectory of ecosystem development and future ecological state. In addition, aquatic systems will likely shift from net autotrophic carbon sinks to net heterotrophic carbon sources as glaciers disappear and vegetation colonizes alpine catchments.

The welfare of rural households depends upon income from agricultural production. The adoption of new agricultural practices can improve farmer welfare by increasing yield and/or lowering production costs. But farmers do not always adopt beneficial new practices. Barriers include uncertainty about effectiveness, high up-front costs, or lack of information about the new practices. I will examine whether the use of social media for information influences pasture management practices among cattle farmers in Rondônia, Brazil. Rondônia is on the edge of the Amazon region. The state is heavily deforested for use as farmland. Farms in this state predominantly raise cattle for dairy and beef production, relying heavily on pastures for feed. Traditional pasture management in Rondônia entails extensive grazing that degrades the soil over time. Farmers address degraded pasture through periodic, costly, input-intensive interventions to restore pasture health, or deforestation for new land. Sustainable practices exist which reduce degradation and household production costs. Existing literature on adoption of agricultural practices widely explores the influence of risk, credit access, and access to information from agricultural extension or neighbors. Farmers tend to trust information from other farmers most, as they have the kind of practical experience that farmers care about. The use of social media connects farmers to a greater variety of other farmers than before. Such a connection provides more access to information and at a much lower cost than typical avenues like agricultural extension.

Social media use increases the potential to learn about and adopt new agricultural practices, but few researchers have investigated to what extent it causes farmers to actually change their agricultural decisions. If any correlation exists, it may suffer from selection bias. Farmers who tend to adopt all kinds of new technologies or who prefer novelty may be more likely to use both social media and new pasture practices. I will estimate the effect of information from social media on the adoption of pasture management practices using regression with covariates, propensity score matching, and an endogenous switching regression. Results will be compared across each estimation method, as well as between farmers who use traditional and sustainable management practices. Increased adoption of pasture practices would provide evidence in favor of using social media to spread information about other agricultural practices and in other countries. Data comes from the Connections between Water and Rural Production project, which surveyed farm households in Rondônia on a variety of agricultural topics. This dataset contains 1385 households who responded to questions on pasture management and social media use.

If you are on a budget, how may you go about finding the best drink and entrée combination at a restaurant? You may simple choose the least expensive items, but a water and side salad is not a great dinner. Instead, you may want to judge the ten least expensive drink and entrée combinations to pick your favorite. If you create a list of drink prices and a list of entrée prices, then all possible combinations of a drink and an entrée would be the Cartesian product of the two lists. Then, you would want to choose from the ten least expensive meals produced by the Cartesian product.

Finding the smallest k values from the Cartesian product X+Y, where X and Y are lists of values X = {x1, x2,...}, Y = {y1, y2,...}, is a well-studied fundamental problem of computer science. There have been several methods which solve this problem with a runtime proportional to n + k, where n is the length of the lists. This is the best runtime possible since all input and output values much be touched at least once. The generalization of the problem, where the Cartesian product is on many lists X1+X2+···+ Xm, has never seen a fast algorithm. We present an algorithm for the generalization which is faster than m•n + k•m. This is remarkable because to load m lists, each with n values, has runtime m•n and looking up k values in m lists has runtime k•m.

In computer science, there are many different structures used to store data. In order to get a fast runtime, we use a new data structure called a "layer-ordered heap" which gives information about the ordering of the values in a list while still not completely sorting the data. It may seem intuitive to use sorting since we want to find the smallest values; however, sorting a list of k values has a runtime of at least k•log(k). In the runtime of our method, we want the term which grows with k to be faster than k•log(k) so we can not use sorting. Keeping the data organized in such a way that it has some ordering to it but is not completely sorted is the key to our algorithm.

One important application of our algorithm is to calculate the most abundant isotopes of a molecule. The isotopes of an element (e.g. oxygen) are all the ways in which an element may have a different number of neutrons. For example, carbon dioxide CO2 is made up of one carbon and two oxygens. Carbon has two isotopes which appear in nature, 12C and 13C, while oxygen has three, 16O, 17O, and 18O. This means that carbon and oxygen may naturally form six different combinations of isotopes, which is the Cartesian product of three lists: {12C, 13C}, {16O, 17O, 18O}, and {16O, 17O, 18O}. Six possible isotopes may seem trivial, but for very large molecules there may be millions of possible isotopes, being able to efficiently compute only the top k is very helpful.