Microbial differences between dental plaque and historic dental calculus are related to oral biofilm maturation stage

Dental calculus, calcified oral plaque biofilm, contains microbial and host biomolecules that can be used to study historic microbiome communities and host responses. Dental calculus does not typically accumulate as much today as historically, and clinical oral microbiome research studies focus primarily on living dental plaque biofilm. However, plaque and calculus reflect different conditions of the oral biofilm, and the differences in microbial characteristics between the sample types have not yet been systematically explored. Here, we compare the microbial profiles of modern dental plaque, modern dental calculus, and historic dental calculus to establish expected differences between these substrates.- Background - Results -- Authentication of a preserved oral biofilm in calculus samples -- Dental calculus and plaque biofilm communities are distinct -- Health-associated communities of dental plaque and calculus are distinct -- Signatures of health and of disease are shared in modern and historic calculus samples -- Microbial community differences between health and disease in calculus are poorly resolved -- Absence of caries-specific microbial profiles in dental calculus -- Microbial co-exclusion patterns in plaque and calculus reflect biofilm maturity -- Microbial complexes in plaque and calculus -- Functional prediction in calculus is poorly predictive of health status -- Proteomic profiles of historic healthy site calculus -- Correlations between taxonomic, proteomic, and metabolomic profiles - Discussion - Conclusions - Materials and methods --Historic and modern calculus sample collection DNA extraction -- DNA library construction and high-throughput sequencing -- DNA sequence processing -- Genetic assessment of historic calculus sample preservation -- Genetic microbial taxonomic profiling -- Principal component analysis -- Assessment of differentially abundant taxa -- Sparse partial least squares-discriminant analysis -- Assessment of microbial co-exclusion patterns -- Gene functional categorization with SEED -- Proteomics -- Metabolomics -- Regularized canonical correlation analysi

Trees from Functions as Processes

Levy-Longo Trees and Bohm Trees are the best known tree structures on the {\lambda}-calculus. We give general conditions under which an encoding of the {\lambda}-calculus into the {\pi}-calculus is sound and complete with respect to such trees. We apply these conditions to various encodings of the call-by-name {\lambda}-calculus, showing how the two kinds of tree can be obtained by varying the behavioural equivalence adopted in the {\pi}-calculus and/or the encoding

A Fully Abstract Symbolic Semantics for Psi-Calculi

We present a symbolic transition system and bisimulation equivalence for psi-calculi, and show that it is fully abstract with respect to bisimulation congruence in the non-symbolic semantics. A psi-calculus is an extension of the pi-calculus with nominal data types for data structures and for logical assertions representing facts about data. These can be transmitted between processes and their names can be statically scoped using the standard pi-calculus mechanism to allow for scope migrations. Psi-calculi can be more general than other proposed extensions of the pi-calculus such as the applied pi-calculus, the spi-calculus, the fusion calculus, or the concurrent constraint pi-calculus. Symbolic semantics are necessary for an efficient implementation of the calculus in automated tools exploring state spaces, and the full abstraction property means the semantics of a process does not change from the original

If Archimedes would have known functions

These are notes and slides from a Pecha-Kucha talk given on March 6, 2013. The presentation tinkered with the question whether calculus on graphs could have emerged by the time of Archimedes, if the concept of a function would have been available 2300 years ago. The text first attempts to boil down discrete single and multivariable calculus to one page each, then presents the slides with additional remarks and finally includes 40 "calculus problems" in a discrete or so-called 'quantum calculus' setting. We also added some sample Mathematica code, gave a short overview over the emergence of the function concept in calculus and included comments on the development of calculus textbooks over time.Comment: 31 pages, 36 figure

The Computational Complexity of Propositional Cirquent Calculus

Introduced in 2006 by Japaridze, cirquent calculus is a refinement of sequent calculus. The advent of cirquent calculus arose from the need for a deductive system with a more explicit ability to reason about resources. Unlike the more traditional proof-theoretic approaches that manipulate tree-like objects (formulas, sequents, etc.), cirquent calculus is based on circuit-style structures called cirquents, in which different "peer" (sibling, cousin, etc.) substructures may share components. It is this resource sharing mechanism to which cirquent calculus owes its novelty (and its virtues). From its inception, cirquent calculus has been paired with an abstract resource semantics. This semantics allows for reasoning about the interaction between a resource provider and a resource user, where resources are understood in the their most general and intuitive sense. Interpreting resources in a more restricted computational sense has made cirquent calculus instrumental in axiomatizing various fundamental fragments of Computability Logic, a formal theory of (interactive) computability. The so-called "classical" rules of cirquent calculus, in the absence of the particularly troublesome contraction rule, produce a sound and complete system CL5 for Computability Logic. In this paper, we investigate the computational complexity of CL5, showing it is $\Sigma_2^p$-complete. We also show that CL5 without the duplication rule has polynomial size proofs and is NP-complete