Degree of Satisfiability in Heyting Algebras

Given a finite structure $M$ and property $p$, it is a natural to study the degree of satisfiability of $p$ in $M$; i.e. to ask: what is the probability that uniformly randomly chosen elements in $M$ satisfy $p$? In group theory, a well-known result of Gustafson states that the equation $xy=yx$ has a finite satisfiability gap: its degree of satisfiability is either $1$ (in Abelian groups) or no larger than $\frac{5}{8}$. Degree of satisfiability has proven useful in the study of (finite and infinite) group-like and ring-like algebraic structures, but finite satisfiability gap questions have not been considered in lattice-like, order-theoretic settings yet. Here we investigate degree of satisfiability questions in the context of Heyting algebras and intuitionistic logic. We classify all equations in one free variable with respect to finite satisfiability gap, and determine which common principles of classical logic in multiple free variables have finite satisfiability gap. In particular we prove that, in a finite non-Boolean Heyting algebra, the probability that a randomly chosen element satisfies $x \vee \neg x = \top$ is no larger than $\frac{2}{3}$. Finally, we generalize our results to infinite Heyting algebras, and present their applications to point-set topology, black-box algebras, and the philosophy of logic.Comment: 22 pages, 2 figures. To appear in Journal of Symbolic Logic. Changes: Final version, w/ streamlined proofs and minor changes throughou

Phytoplankton-zooplankton relationships on Georges Bank

Comparisons of different oceanic regions often suggest that in the largest sense there is a direct relationship between phytoplankton and zooplankton-that is, banks and coastal areas with large concentrations of phytoplankton are likely to be rich in zooplankton, while sparser crops of both occur in deep oceanic waters. On the other hand, surveys of particular areas often show an inverse relationship, with local swarms of zooplankton occurring in phytoplankton-poor waters, alternating with dense patches of phytoplankton containing few animals...

Volume 12.Article 3. Quantitative ecology of the plankton of the western North Atlantic.

https://elischolar.library.yale.edu/bulletin_yale_bingham_oceanographic_collection/1146/thumbnail.jp

REGULATION OF COAL POLYMER DEGRADATION BY FUNGI

A variety of lignin degrading fungi mediate solubilization and subsequent biodegradation of coal macromolecules (a.k.a. coal polymer) from highly oxidized low rank coals such as leonardites. It appears that oxalate or possibly other metal chelators (i.e., certain Krebs Cycle intermediates) mediate solubilization of low rank coals while extracellular oxidases have a role in subsequent oxidation of solubilized coal macromolecule. These processes are under nutritional control. For example, in the case of P. chrysosporium, solubilization of leonardite occurred when the fungi were cultured on most but not all nutrient agars tested and subsequent biodegradation occurred only in nutrient nitrogen limited cultures. Lignin peroxidases mediate oxidation of coal macromolecule in a reaction that is dependent on the presence of veratryl alcohol and hydrogen peroxide. Kinetic evidence suggests that veratryl alcohol is oxidized to the veratryl alcohol cation radical which then mediates oxidation of the coal macromolecule. Results by others suggest that Mn peroxidases mediate formation of reactive Mn{sup 3+} complexes which also mediate oxidation of coal macromolecule. A biomimetic approach was used to study solubilization of a North Dakota leonardite. It was found that a concentration {approximately}75 mM sodium oxalate was optimal for solubilization of this low rank coal. This is important because this is well above the concentration of oxalate produced by fungi in liquid culture. Higher local concentrations probably occur in solid agar cultures and thus may account for the observation that greater solubilization occurs in agar media relative to liquid media. The characteristics of biomimetically solubilized leonardite were similar to those of biologically solubilized leonardite. Perhaps our most interesting observation was that in addition to oxalate, other common Lewis bases (phosphate/hydrogen phosphate/dihydrogen phosphate and bicarbonate/carbonate ions) are able to mediate substantial solubilization of leonardite at physiological pH values. Lastly, we present evidence that some fungi appear to possess coal solubilization ability in which the initial events of solubilization is not mediated by oxalate ion

The Minigrant Model: A Strategy to Promote Local Implementation of State Cancer Plans in Appalachian Communities

East Tennessee State University (ETSU) was awarded a grant through an interagency agreement between the Centers for Disease Control and Prevention and the Appalachian Regional Commission to promote cancer control activities between state comprehensive cancer control (CCC) coalitions and local Appalachian communities. We invited representatives from CCC coalitions and Appalachian communities to a forum to develop a plan of action. The attendees recommended a minigrant model that uses a request for proposals (RFP) strategy to encourage CCC coalitions and Appalachian communities to collaboratively conduct forums and roundtables locally. They set criteria to guide the development of the RFPs and the agendas for the roundtables and forums that ensured new communication and collaboration between the CCC coalitions and the Appalachian communities. We established the roundtable agenda to focus on the presentation and discussion of state and local Appalachian community cancer risk, incidence, and death rates and introduction of state cancer plans. The forums had a more extensive agenda to present cancer data, describe state cancer plans, and describe successful cancer control programs in local Appalachian communities. This article describes the ETSU minigrant model that supports forums and roundtables and reports how this strategy improves cooperative partnerships between CCC coalitions and Appalachian communities in the local implementation of state cancer plans in Appalachia

Structured Decompositions: Structural and Algorithmic Compositionality

We introduce structured decompositions: category-theoretic generalizations of many combinatorial invariants -- including tree-width, layered tree-width, co-tree-width and graph decomposition width -- which have played a central role in the study of structural and algorithmic compositionality in both graph theory and parameterized complexity. Structured decompositions allow us to generalize combinatorial invariants to new settings (for example decompositions of matroids) in which they describe algorithmically useful structural compositionality. As an application of our theory we prove an algorithmic meta theorem for the Sub_P-composition problem which, when instantiated in the category of graphs, yields compositional algorithms for NP-hard problems such as: Maximum Bipartite Subgraph, Maximum Planar Subgraph and Longest Path

Biodegradation of Congo Red by Phanerochaete chrysosporium

The azo dye Congo Red, was degraded extensively by the wood rotting basidiomycete, Phanerochaete chrysosporium in agitated liquid cultures and in solid malt agar cultures. Upon addition of Congo Red to agitated liquid cultures, the dye was adsorbed to the mycelial pellets in both ligninolytic and non-ligninolytic cultures followed by extensive degradation only in the ligninolytic cultures. This fungus, grown from conidiospores, readily degraded up to 718 μM (500 mg/l) Congo Red in 2.0% malt agar. Decolorization of Congo Red in malt agar plates was suppressed by the addition of supplemental nutrient nitrogen indicating that the lignin degrading system of P. chrysosporium may be important in the biodegradation of this dye. This is supported by the observation that Congo Red is a substrate for purified lignin peroxidase H8. These results are of interest because it had been previously reported that Congo Red was not a substrate for lignin peroxidase nor was it extensively degraded by this fungus

Calculating Heat of Formation Values of Energetic Compounds: A Comparative Study

Heat of formation is one of several important parameters used to assess the performance of energetic compounds. We evaluated the ability of six different methods to accurately calculate gas-phase heat of formation (Δ 298,g) values for a test set of 45 nitrogencontaining energetic compounds. Density functional theory coupled with the use of isodesmic or other balanced equations yielded calculated results in which 82% (37 of 45) of the Δ 298,g values were within ±2.0 kcal/mol of the most recently recommended experimental/reference values available. This was compared to a procedure using density functional theory (DFT) coupled with an atom and group contribution method in which 51% (23 of 45) of the Δ 298,g values were within ±2.0 kcal/mol of these values. The T1 procedure and Benson’s group additivity method yielded results in which 51% (23 of 45) and 64% (23 of 36) of the Δ 298,g values, respectively, were within ±2.0 kcal/mol of these values. We also compared two relatively new semiempirical approaches (PM7 and RM1) with regard to their ability to accurately calculate Δ 298,g. Although semiempirical methods continue to improve, they were found to be less accurate than the other approaches for the test set used in this investigation