A Generic Framework for Engineering Graph Canonization Algorithms

The state-of-the-art tools for practical graph canonization are all based on the individualization-refinement paradigm, and their difference is primarily in the choice of heuristics they include and in the actual tool implementation. It is thus not possible to make a direct comparison of how individual algorithmic ideas affect the performance on different graph classes. We present an algorithmic software framework that facilitates implementation of heuristics as independent extensions to a common core algorithm. It therefore becomes easy to perform a detailed comparison of the performance and behaviour of different algorithmic ideas. Implementations are provided of a range of algorithms for tree traversal, target cell selection, and node invariant, including choices from the literature and new variations. The framework readily supports extraction and visualization of detailed data from separate algorithm executions for subsequent analysis and development of new heuristics. Using collections of different graph classes we investigate the effect of varying the selections of heuristics, often revealing exactly which individual algorithmic choice is responsible for particularly good or bad performance. On several benchmark collections, including a newly proposed class of difficult instances, we additionally find that our implementation performs better than the current state-of-the-art tools

Cellular structures using Uq\textbf{U}_q-tilting modules

We use the theory of $\textbf{U}_q$-tilting modules to construct cellular bases for centralizer algebras. Our methods are quite general and work for any quantum group $\textbf{U}_q$ attached to a Cartan matrix and include the non-semisimple cases for $q$ being a root of unity and ground fields of positive characteristic. Our approach also generalizes to certain categories containing infinite-dimensional modules. As applications, we give a new semisimplicty criterion for centralizer algebras, and recover the cellularity of several known algebras (with partially new cellular bases) which all fit into our general setup.Comment: 31 pages, lots of figures, substantially rewritten (following the suggestions of some referees), changed numbering, comments welcom

Narasin as a Manure Additive to Reduce Methane Production from Swine Manure

Animal production systems are an important source of anthropogenic methane emissions. Production of methane results from microbial activity by anaerobic bacteria populations within the stored manure that breaks down organic material and converts it to biogas. Swine manures obtained from three deep pit storages in Central Iowa were dosed with Narasin, an ionophore, to evaluate its inhibitory effects on methane and biogas production. Four Narasin dosing rates were evaluated, these included 0 (Control), 7.5, 15, and 30 mg Narasin/kg of manure. Overall, the results indicated that Narasin had an inhibitory effect on methane and biogas production, with greater inhibition being seen at higher dosing rates. The inhibitory effect weakened with time such that after 120 days of incubation there was no statistical difference in cumulative methane production between samples dosed with Narasin and the control. Two additional treatments, based on the addition of an easily available carbohydrate, sugar, were also evaluated. Sugar (10 g per kg of manure) was added to manure both with (15 mg Narasin/kg) and without (0 mg Narasin/kg manure) Narasin amendment. The addition of sugar was performed to evaluate the impact an easily available substrate had on the inhibitory effects of Narasin. The results suggested that methane production was initially increased by the addition of sugar, but that the increased methane production lasted for less than 6 days, at which point cumulative methane production was similar to the control. When treated with both Narasin and sugar the inhibitory effect did not impact the gas production during the sugar digestion phase, but did result in reduced methane and biogas production thereafter. Overall the results indicated that Narasin can be an effective pit additive but further study is needed to recommend dosing frequency and to evaluate how the continuous addition of manure impacts Narasin effectiveness. Thus, this paper will describe a scaled up lab experiment that will be used to evaluate the effect of dosing frequency of Narasin to determine how producers could most effectively use it at the farm scale

Manure Management Concerns Caused By Recent Wet Weather

The wet spring has raised many concerns about manure management for Iowa crop and livestock farmers. The following is a quick list of issues and possible responses to the issues. Farmers are encouraged to contact their local ISU Extension and Outreach ag engineer, field agronomist or livestock specialist, or the local DNR field office for additional information and assistance

Chemical Transformation Motifs - Modelling Pathways as Integer Hyperflows

We present an elaborate framework for formally modelling pathways in chemical reaction networks on a mechanistic level. Networks are modelled mathematically as directed multi-hypergraphs, with vertices corresponding to molecules and hyperedges to reactions. Pathways are modelled as integer hyperflows and we expand the network model by detailed routing constraints. In contrast to the more traditional approaches like Flux Balance Analysis or Elementary Mode analysis we insist on integer-valued flows. While this choice makes it necessary to solve possibly hard integer linear programs, it has the advantage that more detailed mechanistic questions can be formulated. It is thus possible to query networks for general transformation motifs, and to automatically enumerate optimal and near-optimal pathways. Similarities and differences between our work and traditional approaches in metabolic network analysis are discussed in detail. To demonstrate the applicability of the mathematical framework to real-life problems we first explore the design space of possible non-oxidative glycolysis pathways and show that recent manually designed pathways can be further optimised. We then use a model of sugar chemistry to investigate pathways in the autocatalytic formose process. A graph transformation-based approach is used to automatically generate the reaction networks of interest