Chirality in a quaternionic representation of the genetic code

A quaternionic representation of the genetic code, previously reported by the authors, is updated in order to incorporate chirality of nucleotide bases and amino acids. The original representation assigns to each nucleotide base a prime integer quaternion of norm 7 and involves a function that associates with each codon, represented by three of these quaternions, another integer quaternion (amino acid type quaternion) in such a way that the essentials of the standard genetic code (particulaty its degeneration) are preserved. To show the advantages of such a quaternionic representation we have, in turn, associated with each amino acid of a given protein, besides of the type quaternion, another real one according to its order along the protein (order quaternion) and have designed an algorithm to go from the primary to the tertiary structure of the protein by using type and order quaternions. In this context, we incorporate chirality in our representation by observing that the set of eight integer quaternions of norm 7 can be partitioned into a pair of subsets of cardinality four each with their elements mutually conjugates and by putting they in correspondence one to one with the two sets of enantiomers (D and L) of the four nucleotide bases adenine, cytosine, guanine and uracil, respectively. Thus, guided by two diagrams proposed for the codes evolution, we define functions that in each case assign a L- (D-) amino acid type integer quaternion to the triplets of D- (L-) bases. The assignation is such that for a given D-amino acid, the associated integer quaternion is the conjugate of that one corresponding to the enantiomer L. The chiral type quaternions obtained for the amino acids are used, together with a common set of order quaternions, to describe the folding of the two classes, L and D, of homochiral proteins.Comment: 17 pages, 9 figures. arXiv admin note: substantial text overlap with arXiv:1505.0465

Quaternionic representation of the genetic code

A heuristic diagram of the evolution of the standard genetic code is presented. It incorporates, in a way that resembles the energy levels of an atom, the physical notion of broken symmetry and it is consistent with original ideas by Crick on the origin and evolution of the code as well as with the chronological order of appearence of the amino acids along the evolution as inferred from work that mixtures known experimental results with theoretical speculations. Suggested by the diagram we propose a Hamilton quaternions based mathematical representation of the code as it stands now-a-days. The central object in the description is a codon function that assigns to each amino acid an integer quaternion in such a way that the observed code degeneration is preserved. We emphasize the advantages of a quaternionic representation of amino acids taking as an example the folding of proteins. With this aim we propose an algorithm to go from the quaternions sequence to the protein three dimensional structure which can be compared with the corresponding experimental one stored at the Protein Data Bank. In our criterion the mathematical representation of the genetic code in terms of quaternions merits to be taken into account because it describes not only most of the known properties of the genetic code but also opens new perspectives that are mainly derived from the close relationship between quaternions and rotations.Comment: 19 pages, 11 figure

Exact predictions from Edwards ensemble vs. realistic simulations of tapped narrow two-dimensional granular columns

We simulate via a Discrete Element Method the tapping of a narrow column of disk under gravity. For frictionless disks, this system has a simple analytic expression for the density of states in the Edwards volume ensemble. We compare the predictions of the ensemble at constant compactivity against the results for the steady states obtained in the simulations. We show that the steady states cannot be properly described since the microstates sampled are not in correspondence with the predicted distributions, suggesting that the postulates of flat measure and ergodicity are, either or both, invalid for this simple realization of a static granular system. However, we show that certain qualitative features of the volume fluctuations difficult to predict from simple arguments are captured by the theory.Comment: 11 pages, 6 figure

Econometric Modeling and Analysis of Residential Water Demand Based on Unbalanced Panel Data

This paper develops an econometric methodology devised to analyze a sample of time unbalanced panel data on residential water consumption in the French island La Reunion with the purpose to bring out the main determinants of household water consumption and estimate the importance of water consumption by uses. For this purpose, we specify a daily panel econometric model and derive, by performing a time aggregation, a general linear regression model accounting for water consumption data recorded on periods of any calendar date and time length. To esti-mate efficiently the parameters of this model we develop a feasible two step generalized least square method. Using the principle of best linear unbiased prediction, we finally develop an approach allowing to consistently break down the volume of water consumption recorded on household water bills by uses, namely by enforcing this estimated decomposition to add up to the observed total. The application of this methodology to a sample of 437 unbalanced panel observations shows the scope of this approach for the empirical analysis of actual data.econometric modeling; water consumption; panel data

Intruder in a two-dimensional granular system: statics and dynamics of force networks in an experimental system experiencing stick-slip dynamics

In quasi-two-dimensional experiments with photoelastic particles confined to an annular region, an intruder constrained to move in a circular path halfway between the annular walls experiences stick-slip dynamics. We discuss the response of the granular medium to the driven intruder, focusing on the evolution of the force network during sticking periods. Because the available experimental data does not include precise information about individual contact forces, we use an approach developed in our previous work (Basak et al, J. Eng. Mechanics (2021)) based on networks constructed from measurements of the integrated strain magnitude on each particle. These networks are analyzed using topological measures based on persistence diagrams, revealing that force networks evolve smoothly but in a nontrivial manner throughout each sticking period, even though the intruder and granular particles are stationary. Characteristic features of persistence diagrams show identifiable changes as a slip is approaching, indicating the existence of slip precursors. Key features of the dynamics are similar for granular materials composed of disks or pentagons, but some details are consistently different. In particular, we find significantly larger fluctuations of the measures computed based on persistence diagrams, and therefore of the underlying networks, for systems of pentagonal particles

Effect of packing fraction on the jamming of granular flow through small apertures

We investigate the flow and jamming through small apertures of a column of granular disks via a pseudo-dynamic model. We focus on the effect that the preparation of the granular assembly has on the size of the avalanches obtained. Ensembles of packings with different mean packing fractions are created by tapping the system at different intensities. Surprisingly, packing fraction is not a good indicator of the ability of the deposit to jam a given orifice. Different mean avalanche sizes are obtained for deposits with the same mean packing fraction that were prepared with very different tap intensities. It has been speculated that the number and size of arches in the bulk of the granular column should be correlated with the ability of the system to jam a small opening. We show that this correlation, if exists, is rather poor. A comparison between bulk arches and jamming arches (i.e., arches that block the opening) reveals that the aperture imposes a lower cut-off on the horizontal span of the arches which is greater than the actual size of the opening. This is related to the fact that blocking arches have to have the appropriate orientation to fit the gap between two piles of grains resting at each side of the aperture.Comment: 13 pages, 9 figure

An after-school football session transiently improves cognitive function in children

The aim of the present study was to evaluate the effect of a real-world after-school football session on subsequent cognitive function in primary school children. Following ethical approval, 100 children (aged 8–9 year) from the same after-school football club were randomly assigned to either an intervention (60 min football activity) or control (continued to rest) group. Cognitive function (selective visual attention, short term memory and long-term memory) was assessed prior to, immediately following and 45 min following the football session (and at the respective timepoints in the control group). Data were analysed via two-way (group * time) mixed methods ANOVA. The pattern of change in all domains of cognition over time, was different between the football and control groups (group * time, all p < 0.001). Specifically, performance on all cognitive tasks was greater immediately following the football session in the intervention group compared to the control group (selective visual attention, p = 0.003; short-term memory, p = 0.004; long-term memory, p < 0.001). However, there was no difference between the group 45 min following the football session (p = 0.132–0.393). These findings suggest that an after-school football session enhances cognition immediately post-activity in primary school children