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Sets of periods of continuous

Some integrable systems

We represent the protein structure of scTIM with a graph-theoretic model. We construct a hierarchical graph with three layers - a top level, a midlevel and a bottom level. The top level graph is a representation of the protein in which its vertices each represent a substructure of the protein. In turn, each substructure of the protein is represented by a graph whose vertices are amino acids. Finally, each amino acid is represented as a graph where the vertices are atoms. We use this representation to model the effects of a mutation on the protein. Methods: There are 19 vertices (substructures) in the top level graph and thus there are 19 distinct graphs at the midlevel. The vertices of each of the 19 graphs at the midlevel represent amino acids. Each amino acid is represented by a graph where the vertices are atoms in the residue structure. All edges are determined by proximity in the protein's 3D structure. The vertices in the bottom level are labelled by the corresponding molecular mass of the atom that it represents. We use graph-theoretic measures that incorporate vertex weights to assign graph based attributes to the amino acid graphs. The attributes of the corresponding amino acids are used as vertex weights for the substructure graphs at the midlevel. Graph-theoretic measures based on vertex weighted graphs are subsequently calculated for each of the midlevel graphs. Finally, the vertices of the top level graph are weighted with attributes of the corresponding substructure graph in the midlevel. Results: We can visualize which mutations are more influential than others by using properties such as vertex size to correspond with an increase or decrease in a graph-theoretic measure. Global graph-theoretic measures such as the number of triangles or the number of spanning trees can change as the result. Hence this method provides a way to visualize these global changes resulting from a small, seemingly inconsequential local change. Conclusions: This modelling method provides a novel approach to the visualization of protein structures and the consequences of amino acid deletions, insertions or substitutions and provides a new way to gain insight on the consequences of diseases caused by genetic mutations.

Ambient mass spectrometry is an analytical approach that enables ionization of molecules under open-air conditions with no sample preparation and very fast sampling times. Rapid evaporative ionization mass spectrometry (REIMS) is a relatively new type of ambient mass spectrometry that has demonstrated applications in both human health and food science. Here, we present an evaluation of REIMS as a tool to generate molecular scale information as an objective measure for the assessment of beef quality attributes. Eight different machine learning algorithms were compared to generate predictive models using REIMS data to classify beef quality attributes based on the United States Department of Agriculture (USDA) quality grade, production background, breed type and muscle tenderness. The results revealed that the optimal machine learning algorithm, as assessed by predictive accuracy, was different depending on the classification problem, suggesting that a “one size fits all” approach to developing predictive models from REIMS data is not appropriate. The highest performing models for each classification achieved prediction accuracies between 81.5–99%, indicating the potential of the approach to complement current methods for classifying quality attributes in beef.

Background: Determining the secondary structure of RNA from the primary structure is a challenging computational problem. A number of algorithms have been developed to predict the secondary structure from the primary structure. It is agreed that there is still room for improvement in each of these approaches. In this work we build a predictive model for secondary RNA structure using a graph-theoretic tree representation of secondary RNA structure. We model the bonding of two RNA secondary structures to form a larger secondary structure with a graph operation we call merge. We consider all combinatorial possibilities using all possible tree inputs, both those that are RNA-like in structure and those that are not. The resulting data from each tree merge operation is represented by a vector. We use these vectors as input values for a neural network and train the network to recognize a tree as RNA-like or not, based on the merge data vector. The network estimates the probability of a tree being RNA-like.Results: The network correctly assigned a high probability of RNA-likeness to trees previously identified as RNA-like and a low probability of RNA-likeness to those classified as not RNA-like. We then used the neural network to predict the RNA-likeness of the unclassified trees.Conclusions: There are a number of secondary RNA structure prediction algorithms available online. These programs are based on finding the secondary structure with the lowest total free energy. In this work, we create a predictive tool for secondary RNA structures using graph-theoretic values as input for a neural network. The use of a graph operation to theoretically describe the bonding of secondary RNA is novel and is an entirely different approach to the prediction of secondary RNA structures. Our method correctly predicted trees to be RNA-like or not RNA-like for all known cases. In addition, our results convey a measure of likelihood that a tree is RNA-like or not RNA-like. Given that the majority of secondary RNA folding algorithms return more than one possible outcome, our method provides a means of determining the best or most likely structures among all of the possible outcomes.

A mathematical model is developed for the reliability of a system made up of m unreliable nodes arranged in a ring. The model can be used to calculate the reliability of single-ring networks where the network recovery mechanism depends on bypassing failed stations, but link signal power margins are inadequate to overcome losses due to more than n bypass switches in series. Computational complexity is O(n2m + nm2/2) in time, and O(m2/2) in memory requirements.

One of Leo Moser's geometry problems is referred to as the Worm Problem [10]: "What is the (convex) region of smallest area which will accommodate (or cover) every planar arc of length 1?" For example, it is easy to show that the circular disk with diameter 1 will cover every planar arc of length 1. The area of the disk is approximately 0.78539. Here we show that a solution to the Worm Problem of Moser is a region with area less than 0.27524.

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We evaluated the effectiveness of two types of tandem-set fyke nets (round and D-shaped) for sampling fish in five lakes and compared fyke-net catches with contemporaneous gill-net catches. Fyke nets captured more benthic and cover-oriented species than gill nets, whereas gill nets captured more pelagic species. Seasonal variation in species composition and catch per unit effort (CPUE) was observed with fyke nets as well as gill nets. When sampling with fyke nets was limited to one season, large sample sizes were needed to detect changes in CPUE. Efficiency, ease of use, and low mortality of captured fish make tandem-set fyke nets a viable alternative to gill nets for assessing changes in community structure of benthic fishes in individual lakes. However, the large sampling effort required to detect changes in CPUE (unless target species are very abundant) limits the utility of fyke nets for monitoring the relative abundance of benthic species over time.