A unification in the theory of linearization of second order nonlinear ordinary differential equations

In this letter, we introduce a new generalized linearizing transformation (GLT) for second order nonlinear ordinary differential equations (SNODEs). The well known invertible point (IPT) and non-point transformations (NPT) can be derived as sub-cases of the GLT. A wider class of nonlinear ODEs that cannot be linearized through NPT and IPT can be linearized by this GLT. We also illustrate how to construct GLTs and to identify the form of the linearizable equations and propose a procedure to derive the general solution from this GLT for the SNODEs. We demonstrate the theory with two examples which are of contemporary interest.Comment: 8 page

On the distribution of high-frequency stock market traded volume: a dynamical scenario

This manuscript reports a stochastic dynamical scenario whose associated stationary probability density function is exactly a previously proposed one to adjust high-frequency traded volume distributions. This dynamical conjecture, physically connected to superstatiscs, which is intimately related with the current nonextensive statistical mechanics framework, is based on the idea of local fluctuations in the mean traded volume associated to financial markets agents herding behaviour. The corroboration of this mesoscopic model is done by modelising NASDAQ 1 and 2 minute stock market traded volume

Retired galaxies: not to be forgotten in the quest of the star formation -- AGN connection

We propose a fresh look at the Main Galaxy Sample of the Sloan Digital Sky Survey by packing the galaxies in stellar mass and redshift bins. We show how important it is to consider the emission-line equivalent widths, in addition to the commonly used emission-line ratios, to properly identify retired galaxies (i.e. galaxies that have stopped forming stars and are ionized by their old stellar populations) and not mistake them for galaxies with low-level nuclear activity. We find that the proportion of star-forming galaxies decreases with decreasing redshift in each mass bin, while that of retired galaxies increases. Galaxies with $M_\star > 10^{11.5} M_\odot$ have formed all their stars at redshift larger than 0.4. The population of AGN hosts is never dominant for galaxy masses larger than $10^{10} M_\odot$. We warn about the effects of stacking galaxy spectra to discuss galaxy properties. We estimate the lifetimes of active galactic nuclei (AGN) relying entirely on demographic arguments --- i.e. without any assumption on the AGN radiative properties. We find upper-limit lifetimes of about 1--5 Gyr for detectable AGN in galaxies with masses between $10^{10}$--$10^{12} M_\odot$. The lifetimes of the AGN-dominated phases are a few $10^8$ yr. Finally, we compare the star-formation histories of star-forming, AGN and retired galaxies as obtained by the spectral synthesis code STARLIGHT. Once the AGN is turned on it inhibits star formation for the next $\sim$ 0.1 Gyr in galaxies with masses around $10^{10} M_\odot$, $\sim$ 1 Gyr in galaxies with masses around $10^{11} M_\odot$.Comment: accepted for MNRAS figure resolution has been degraded with respect to what will be published in MNRA

Public Health England's recovery tools: potential teaching resources?

The file attached to this record is the author's final peer reviewed version.Training to combat chemical and radiation accidents, incidents or attacks is critical for health professionals due to recent events involving these hazards or their use as unconventional weapons, such as the use of the nerve agent novichok in Salisbury, UK. Health professionals need to have appropriate knowledge and skills to effectively respond to future events involving any of these substances, which requires a rapid and coordinated response from different professionals to protect the environment and minimise the number of people exposed and reduce morbidity and mortality. However, despite chemical and radiation incidents becoming increasingly prevalent, literature reviews have shown that there is a lack of teaching of appropriate competences to face future crises in Europe, particularly amongst clinicians and other health professionals that would be part of the initial response. Thus, De Montfort University (DMU, UK) in collaboration with different academics from the University of Alcalá (Spain) and researchers from Public Health England (PHE) with comprehensive experience in environmental decontamination and restoration, have created a short training course for providing undergraduate/postgraduate students with basic skills to respond to chemical incidents, basic skills that are based on the major competences recently identified by the European Commission [1]. This novel training has been tested with students from different backgrounds in various European universities, recording high degrees of acquisition of the various basic competences that we developed to initially respond to chemical events [2]. To develop the practical part of this chemical training, we have incorporated the novel guidance and methodology developed by PHE to successfully tailor a protection and recovery response to any incident involving chemical substances, which is available in the “UK Recovery Handbook for Chemical Incidents” [3] and its web-based tools: “Chemical Recovery Navigation Tool” (CRNT, [4]) and “Chemical Recovery Record Form” (CRRF, [5]). These innovative resources aid the user to select effective protection, decontamination and restoration techniques or strategies from a pool of up-to-date options applicable to different environments according to the physicochemical properties of the chemical(s) involved and the area affected. The CRNT is accompanied by the CRRF, which facilitates collection and analysis of the necessary data to inform decisions, and an e-learning resource named “Chemical Recovery: Background” (CRB, [6]), which could facilitate the learning of environmental decontamination and restoration. We are currently developing a short training course to cover minor radiation incidents; this radiation training will follow the same methods used to develop the chemical training, but with the specific PHE recovery tools to tackle such events, specifically the “UK Recovery Handbooks for Radiation Incidents” [7] and its associated web-based tools “Radiation Recovery Navigation Tool” (Rad RNT, [8]), one for each environment: food production systems, inhabited areas and drinking water supplies. This communication will explore the use of the PHE’s Recovery Navigation Tools as potential resources to facilitate the acquisition of basic knowledge to tailor protection and recovery interventions for minor chemical and radiation incidents to protect the public

Is global ocean sprawl a cause of jellyfish blooms?

Jellyfish (Cnidaria, Scyphozoa) blooms appear to be increasing in both intensity and frequency in many coastal areas worldwide, due to multiple hypothesized anthropogenic stressors. Here, we propose that the proliferation of artificial structures – associated with (1) the exponential growth in shipping, aquaculture, and other coastal industries, and (2) coastal protection (collectively, “ocean sprawl”) – provides habitat for jellyfish polyps and may be an important driver of the global increase in jellyfish blooms. However, the habitat of the benthic polyps that commonly result in coastal jellyfish blooms has remained elusive, limiting our understanding of the drivers of these blooms. Support for the hypothesized role of ocean sprawl in promoting jellyfish blooms is provided by observations and experimental evidence demonstrating that jellyfish larvae settle in large numbers on artificial structures in coastal waters and develop into dense concentrations of jellyfish-producing polyps

A probabilistic approach to emission-line galaxy classification

We invoke a Gaussian mixture model (GMM) to jointly analyse two traditional emission-line classification schemes of galaxy ionization sources: the Baldwin-Phillips-Terlevich (BPT) and $\rm W_{H\alpha}$ vs. [NII]/H$\alpha$ (WHAN) diagrams, using spectroscopic data from the Sloan Digital Sky Survey Data Release 7 and SEAGal/STARLIGHT datasets. We apply a GMM to empirically define classes of galaxies in a three-dimensional space spanned by the $\log$ [OIII]/H$\beta$, $\log$ [NII]/H$\alpha$, and $\log$ EW(H${\alpha}$), optical parameters. The best-fit GMM based on several statistical criteria suggests a solution around four Gaussian components (GCs), which are capable to explain up to 97 per cent of the data variance. Using elements of information theory, we compare each GC to their respective astronomical counterpart. GC1 and GC4 are associated with star-forming galaxies, suggesting the need to define a new starburst subgroup. GC2 is associated with BPT's Active Galaxy Nuclei (AGN) class and WHAN's weak AGN class. GC3 is associated with BPT's composite class and WHAN's strong AGN class. Conversely, there is no statistical evidence -- based on four GCs -- for the existence of a Seyfert/LINER dichotomy in our sample. Notwithstanding, the inclusion of an additional GC5 unravels it. The GC5 appears associated to the LINER and Passive galaxies on the BPT and WHAN diagrams respectively. Subtleties aside, we demonstrate the potential of our methodology to recover/unravel different objects inside the wilderness of astronomical datasets, without lacking the ability to convey physically interpretable results. The probabilistic classifications from the GMM analysis are publicly available within the COINtoolbox (https://cointoolbox.github.io/GMM\_Catalogue/).Comment: Accepted for publication in MNRA