The strength of Ramsey Theorem for coloring relatively large sets

We characterize the computational content and the proof-theoretic strength of a Ramsey-type theorem for bi-colorings of so-called {\em exactly large} sets. An {\it exactly large} set is a set X\subset\Nat such that \card(X)=\min(X)+1. The theorem we analyze is as follows. For every infinite subset $M$ of \Nat, for every coloring $C$ of the exactly large subsets of $M$ in two colors, there exists and infinite subset $L$ of $M$ such that $C$ is constant on all exactly large subsets of $L$. This theorem is essentially due to Pudl\`ak and R\"odl and independently to Farmaki. We prove that --- over Computable Mathematics --- this theorem is equivalent to closure under the $\omega$ Turing jump (i.e., under arithmetical truth). Natural combinatorial theorems at this level of complexity are rare. Our results give a complete characterization of the theorem from the point of view of Computable Mathematics and of the Proof Theory of Arithmetic. This nicely extends the current knowledge about the strength of Ramsey Theorem. We also show that analogous results hold for a related principle based on the Regressive Ramsey Theorem. In addition we give a further characterization in terms of truth predicates over Peano Arithmetic. We conjecture that analogous results hold for larger ordinals

Enrichment of cryoconite hole anaerobes: implications for the subglacial microbiome

Glaciers have recently been recognized as ecosystems, comprised of several distinct habitats: a sunlit and oxygenated glacial surface, glacial ice and a dark, mostly anoxic glacial bed. Surface meltwaters annually flood the subglacial sediments by means of drainage channels. Glacial surfaces host aquatic microhabitats called cryoconite holes, regarded as “hot spots” of microbial abundance and activity, largely contributing to the meltwaters’ bacterial diversity. This study presents an investigation of cryoconite hole anaerobes and discusses their possible impact on subglacial microbial communities, combining 16S rRNA gene fragment amplicon sequencing and the traditional enrichment culture technique. Cryoconite hole sediment harbored bacteria belonging mainly to the Proteobacteria (21%), Bacteroidetes (16%), Actinobacteria (14%) and Planctomycetes (6%) phyla. An 8 week incubation of those sediments in Postgate C medium for sulfate reducers in air tight bottles, emulating subglacial conditions, eliminated a great majority of dominant taxa, leading to enrichment of the Firmicutes (62%), Proteobacteria (14%) and Bacteroidetes (13%), which consisted of anaerobic genera like Clostridium, Psychrosinus, Paludibacter and Acetobacterium. Enrichment of Pseudomonas spp. also occurred, suggesting it played a role as a dominant oxygen scavenger, providing a possible scenario for anaerobic niche establishment in subglacial habitats. To our knowledge this is the first paper to provide insight into the diversity of the anaerobic part of the cryoconite hole microbial community and its potential to contribute to matter turnover in anoxic, subglacial sites

Plasmids of Psychrotolerant Polaromonas spp. Isolated From Arctic and Antarctic Glaciers – Diversity and Role in Adaptation to Polar Environments

Cold-active bacteria of the genus Polaromonas (class Betaproteobacteria) are important components of glacial microbiomes. In this study, extrachromosomal replicons of 26 psychrotolerant Polaromonas strains, isolated from Arctic and Antarctic glaciers, were identified, sequenced, and characterized. The plasmidome of these strains consists of 13 replicons, ranging in size from 3,378 to 101,077 bp. In silico sequence analyses identified the conserved backbones of these plasmids, composed of genes required for plasmid replication, stable maintenance, and conjugal transfer. Host range analysis revealed that all of the identified plasmids are narrow-host-range replicons, only able to replicate in bacteria of closely related genera (Polaromonas and Variovorax) of the Comamonadaceae family. Special attention was paid to the identification of plasmid auxiliary genetic information, which may contribute to the adaptation of bacteria to environmental conditions occurring in glaciers. Detailed analysis revealed the presence of genes encoding proteins potentially involved in (i) protection against reactive oxygen species, ultraviolet radiation, and low temperatures; (ii) transport and metabolism of organic compounds; (iii) transport of metal ions; and (iv) resistance to heavy metals. Some of the plasmids also carry genes required for the molecular assembly of iron–sulfur [Fe-S] clusters. Functional analysis of the predicted heavy metal resistance determinants demonstrated that their activity varies, depending on the host strain. This study provides the first molecular insight into the mobile DNA of Polaromonas spp. inhabiting polar glaciers. It has generated valuable data on the structure and properties of a pool of plasmids and highlighted their role in the biology of psychrotolerant Polaromonas strains and their adaptation to the environmental conditions of Arctic and Antarctic glaciers

The Doping Effect of Fluorinated Aromatic Solvent on the Rate of Ruthenium Catalysed Olefin Metathesis

A study concerning the effect of using a fluorinated aromatic solvent as the medium for olefin metathesis reactions catalysed by ruthenium complexes bearing N-heterocyclic carbene ligands is presented. The use of fluorinated aromatic hydrocarbons (FAH) as solvents for olefin metathesis reactions catalysed by standard commercially available ruthenium pre-catalysts allows substantially higher yields of the desired products to be obtained,especially in the case of demanding polyfunctional molecules, including natural and biologically active compounds. Interactions between the FAH and the second-generation ruthenium catalysts, which apparently improve the efficiency of the olefin metathesis transformation, have been studied by X-ray structure analysis and computations, as well as by carrying out a number of metathesis experiments. The optimisation of reaction conditions by using an FAH can be regarded as a complementary approach for the design of new improved ruthenium catalysts. Fluorinated aromatic solvents are an attractive alternative medium for promoting challenging olefin metathesis reactions

Eta Epsilon Chapter Spring Initiation, 2016

Report on the spring 2016, initiation for the Eta Epsilon chapter of Sigma Gamma Epsilon at Southern Utah University

Bounded Arithmetic in Free Logic

One of the central open questions in bounded arithmetic is whether Buss' hierarchy of theories of bounded arithmetic collapses or not. In this paper, we reformulate Buss' theories using free logic and conjecture that such theories are easier to handle. To show this, we first prove that Buss' theories prove consistencies of induction-free fragments of our theories whose formulae have bounded complexity. Next, we prove that although our theories are based on an apparently weaker logic, we can interpret theories in Buss' hierarchy by our theories using a simple translation. Finally, we investigate finitistic G\"odel sentences in our systems in the hope of proving that a theory in a lower level of Buss' hierarchy cannot prove consistency of induction-free fragments of our theories whose formulae have higher complexity

Microbial community changes along the Ecology Glacier ablation zone (King George Island, Antarctica)

In recent years glacial surfaces have received much attention as microbial habitats of diverse photoautotrophic and heterotrophic cells. Supraglacial ecosystems are annually covered and uncovered by snow. The aim of this study was to investigate the microbial community response to changing environmental conditions in a transect following the receding snow line on the surface of Ecology Glacier (King George Island, Antarctica). Parameters of surface ice and cryoconite holes included chemical composition of ice and sediment, Bacteria diversity by denaturating gradient gel electrophoresis (DGGE), microbial functional diversity (Biolog Ecoplates), and microbial counts (epifluorescence microscopy, colony forming units - CFU). Data demonstrated profound differences between surface ice and cryoconite holes. Changing environmental factors along the transect influenced composition and abundance of the microbiocenosis in both habitat types. Several parameters correlated positively with distance from the glacier edge, including the cell morphotype Shannon Index, chlorophyll a, nitrogen and seston concentrations. Suspended solids content positively correlated with microbial 2 abundance and diversity. Nitrogen and phosphorus were limiting factors of microbial growth as amounts of organic nitrogen and phosphorus positively correlated with the cell numbers, fission rates and photoautotroph contribution. Our findings indicate that microbial community shows a response in terms of abundance and diversity to exposure of the glacial surface as snow-cover melts. To our knowledge this is the first study to recognize a microbial development pattern on a glacier surface in connection with the receding snow line. This may help better understand variability within supraglacial habitats, correct sampling procedures and inform biocenotic development models

Evidence of adaptation, niche separation and microevolution within the genus Polaromonas on Arctic and Antarctic glacial surfaces

Polaromonas is one of the most abundant genera found on glacier surfaces, yet it’s ecology remains poorly described. Investigations made to date point towards a uniform distribution of Polaromonas phylotypes across the globe. We compared 43 Polaromonas isolates obtained from surfaces of Arctic and Antarctic glaciers to address this issue. 16S rRNA gene sequences, intergenic transcribed spacers (ITS) and metabolic fingerprinting showed great differences between hemispheres but also between neighboring glaciers. Phylogenetic distance between Arctic and Antarctic isolates indicated separate species. The Arctic group clustered similarly, when constructing dendrograms based on 16S rRNA gene and ITS sequences, as well as metabolic traits. The Antarctic strains, although almost identical considering 16S rRNA genes, diverged into 2 groups based on the ITS sequences and metabolic traits, suggesting recent niche separation. Certain phenotypic traits pointed towardscell adaptation to specific conditions on a particular glacier, like varying pH levels. Collected data suggest, that seeding of glacial surfaces with Polaromonas cells transported by various means, is of greater efficiency on local than global scales. Selection mechanisms present of glacial surfaces reduce the deposited Polaromonas diversity, causing subsequent adaptation to prevailing environmental conditions. Furthermore, interactions with other supraglacial microbiota, like algae cells may drive postselectional niche separation and microevolution within the Polaromonas genus