A geometric approach to dense Cayley digraphs of finite Abelian groups

We give a method for constructing infinite families of dense (or eventually likely dense) Cayley digraphs of finite Abelian groups. The diameter of the digraphs is obtained by means of the related minimum distance diagrams. A dilating technique for these diagrams, which can be used for any degree of the digraph, is applied to generate the digraphs of the family. Moreover, two infinite families of digraphs with distinguished metric properties will be given using these methods. The first family contains digraphs with asymptotically large ratio between the order and the diameter as the degree increases (moreover it is the first known asymptotically dense family). The second family, for fixed degree d = 3, contains digraphs with the current best known density.Peer ReviewedPostprint (author's final draft

Abelian Cayley digraphs with asymptotically large order for any given degree

Abelian Cayley digraphs can be constructed by using a generalization to Z(n) of the concept of congruence in Z. Here we use this approach to present a family of such digraphs, which, for every fixed value of the degree, have asymptotically large number of vertices as the diameter increases. Up to now, the best known large dense results were all non-constructive.Peer ReviewedPostprint (author's final draft

How should sparse marine in situ measurements be compared to a continuous model: an example

This work demonstrates an example of the importance of an adequate method to sub-sample model results when comparing with in situ measurements. A test of model skill was performed by employing a point-to-point method to compare a multi-decadal hindcast against a sparse, unevenly distributed historic in situ dataset. The point-to-point method masked out all hindcast cells that did not have a corresponding in situ measurement in order to match each in situ measurement against its most similar cell from the model. The application of the point-to-point method showed that the model was successful at reproducing the inter-annual variability of the in situ datasets. Furthermore, this success was not immediately apparent when the measurements were aggregated to regional averages. Time series, data density and target diagrams were employed to illustrate the impact of switching from the regional average method to the point-to-point method. The comparison based on regional averages gave significantly different and sometimes contradicting results that could lead to erroneous conclusions on the model performance. Furthermore, the point-to-point technique is a more correct method to exploit sparse uneven in situ data while compensating for the variability of its sampling. We therefore recommend that researchers take into account for the limitations of the in situ datasets and process the model to resemble the data as much as possible

Monitoring of offshore geological carbon storage integrity: Implications of natural variability in the marine system and the assessment of anomaly detection criteria

The design of efficient monitoring programmes required for the assurance of offshore geological storage requires an understanding of the variability and heterogeneity of marine carbonate chemistry. In the absence of sufficient observational data and for extrapolation both spatially and seasonally, models have a significant role to play. In this study a previously evaluated hydrodynamic-biogeochemical model is used to characterise carbonate chemistry, in particular pH heterogeneity in the vicinity of the sea floor. Using three contrasting regions, the seasonal and short term variability are analysed and criteria that could be considered as indicators of anomalous carbonate chemistry identified. These criteria are then tested by imposing a number of randomised DIC perturbations on the model data, representing a comprehensive range of leakage scenarios. In conclusion optimal criteria and general rules for developing monitoring strategies are identified. Detection criteria will be site specific and vary seasonally and monitoring may be more efficient at periods of low dynamics. Analysis suggests that by using high frequency, sub-hourly monitoring anomalies as small as 0.01 of a pH unit or less may be successfully discriminated from natural variability – thereby allowing detection of small leaks or at distance from a leakage source. Conversely assurance of no leakage would be profound. Detection at deeper sites is likely to be more efficient than at shallow sites where the near bed system is closely coupled to surface processes. Although this study is based on North Sea target sites for geological storage, the model and the general conclusions are relevant to the majority of offshore storage sites lying on the continental shelf

The ellipse law: Kirchhoff meets dislocations

In this paper we consider a nonlocal energyIαwhose kernel is obtained by addingto the Coulomb potential an anisotropic term weighted by a parameterα∈R. The caseα= 0corresponds to purely logarithmic interactions, minimised by the circle law;α= 1 correspondsto the energy of interacting dislocations, minimised by the semi-circle law. We show that forα∈(0,1) the minimiser is the normalised characteristic function of the domain enclosed bytheellipseof semi-axes√1−αand√1 +α. This result is one of the very few examples wherethe minimiser of a nonlocal anisotropic energy is explicitly computed. For the proof we borrowtechniques from fluid dynamics, in particular those related to Kirchhoff’s celebrated result thatdomains enclosed by ellipses are rotating vortex patches, calledKirchhoff ellipses

Molecular gas at supernova local environments unveiled by EDGE

CO observations allow estimations of the gas content of molecular clouds, which trace the reservoir of cold gas fuelling star formation, as well as to determine extinction via H$_2$ column density, N(H$_2$). Here, we studied millimetric and optical properties at 26 supernovae (SNe) locations of different types in a sample of 23 nearby galaxies by combining molecular $^{12}$C$^{16}$O (J = 1 $\rightarrow$ 0) resolved maps from the EDGE survey and optical Integral Field Spectroscopy from the CALIFA survey. We found an even clearer separation between type II and type Ibc SNe in terms of molecular gas than what we found in the optical using H$\alpha$ emission as a proxy for current SF rate, which reinforces the fact that SNe Ibc are more associated with SF-environments. While A$_V$ at SN locations is similar for SNe II and SNe Ibc, and higher compared to SNe Ia, N(H$_2$) is significantly higher for SNe Ibc than for SNe II and SNe Ia. When compared to alternative extinction estimations directly from SN photometry and spectroscopy, we find that our SNe Ibc have also redder color excess but showed standard Na I D absorption pseudo-equivalent widths ($\sim$1 \AA). In some cases we find no extinction when estimated from the environment, but high amounts of extinction when measured from SN observations, which suggests that circumstellar material or dust sublimation may be playing a role. This work serves as a benchmark for future studies combining last generation millimeter and optical IFS instruments to reveal the local environmental properties of extragalactic SNe.Comment: MNRAS accepted, 17 pages, 8 Figures, 4 Table

Tumor dissociation of highly viable cell suspensions for single-cell omic analyses in mouse models of breast cancer.

Cell preparation with a high rate of viable cells is required to obtain reliable single-cell transcriptomic and epigenomic data. This protocol describes a technique for digestion and single-cell isolation from mouse mammary tumors to achieve ∼90% of viable cells, which can be subsequently processed in a diverse array of high-throughput single-cell "omic platforms," both in an unbiased manner or after selection of a specific cell population. For complete details on the use and execution of this protocol, please refer to Valdes-Mora et al. (2021)

On the criticality of inferred models

Advanced inference techniques allow one to reconstruct the pattern of interaction from high dimensional data sets. We focus here on the statistical properties of inferred models and argue that inference procedures are likely to yield models which are close to a phase transition. On one side, we show that the reparameterization invariant metrics in the space of probability distributions of these models (the Fisher Information) is directly related to the model's susceptibility. As a result, distinguishable models tend to accumulate close to critical points, where the susceptibility diverges in infinite systems. On the other, this region is the one where the estimate of inferred parameters is most stable. In order to illustrate these points, we discuss inference of interacting point processes with application to financial data and show that sensible choices of observation time-scales naturally yield models which are close to criticality.Comment: 6 pages, 2 figures, version to appear in JSTA