Non-Decreasing Sequences

Non-decreasing sequences are a generalization of binary covering arrays, which has made research on non-decreasing sequences important in both math and computer science. A non-decreasing sequence of subsets of a finite set S of size s, {S1, S2,.... St}, length t, and strength d, is a sequence of non-empty subsets where the union of any d previous subsets in the sequence does not contain any subsequent subset. The goal of this research is to find properties of these non-decreasing sequences as the variables d, s, and t change. We also explored methods for creating a maximum length for a non-decreasing sequence given d and s. Through our research, we discovered and proved basic properties of these non-decreasing sequences. In addition to this, we can describe a method we used while trying to find the maximum length of a sequence. In the future, research can be conducted to find an exact formula that will generate a maximum length sequence given a non-decreasing sequence of strength d

Simulations of two-planet systems through all phases of stellar evolution: implications for the instability boundary and white dwarf pollution

Exoplanets have been observed at many stages of their host star's life, including the main sequence (MS), subgiant and red giant branch stages. Also, polluted white dwarfs (WDs) likely represent dynamically active systems at late times. Here, we perform 3-body simulations which include realistic post-MS stellar mass loss and span the entire lifetime of exosystems with two massive planets, from the endpoint of formation to several Gyr into the WD phase of the host star. We find that both MS and WD systems experience ejections and star-planet collisions (Lagrange instability) even if the planet-planet separation well-exceeds the analytical orbit-crossing (Hill instability) boundary. Consequently, MS-stable planets do not need to be closely-packed to experience instability during the WD phase. This instability may pollute the WD directly through collisions, or, more likely, indirectly through increased scattering of smaller bodies such as asteroids or comets. Our simulations show that this instability occurs predominately between tens of Myr to a few Gyrs of WD cooling.Comment: Accepted for publication in MNRAS; 24 pages, 19 figure

Managing the risks of being a victim of severe labour exploitation:Findings from a research project exploring the views of experts in the UK

The 2015 report published by the European Union Agency for Fundamental Rights (FRA) on the severe labour exploitation of workers in the European Union (EU) highlights the need to address the factors that increase the risk of being subjected to exploitative working conditions. This article begins by setting out the principal risks that impact upon an individual’s vulnerability to severe labour exploitation, according to the country data from the 21 EU Member States involved in this project. Then, by focusing on the empirical research conducted in the UK, the article discusses some of the measures, put forward by the UK research participants involved in the study, that could be implemented to manage the risks identified. Based upon the research participants’ recommendations, the authors will draw conclusions on how better to manage the risks of labour exploitation

Constructing a class of topological solitons in magnetohydrodynamics

We present a class of topological plasma configurations characterized by their toroidal and poloidal winding numbers, $n_t$ and $n_p$ respectively. The special case of $n_t=1$ and $n_p=1$ corresponds to the Kamchatnov-Hopf soliton, a magnetic field configuration everywhere tangent to the fibers of a Hopf fibration so that the field lines are circular, linked exactly once, and form the surfaces of nested tori. We show that for $n_t \in \mathbb{Z}^+$ and $n_p=1$ these configurations represent stable, localized solutions to the magnetohydrodynamic equations for an ideal incompressible fluid with infinite conductivity. Furthermore, we extend our stability analysis by considering a plasma with finite conductivity and estimate the soliton lifetime in such a medium as a function of the toroidal winding number.Comment: 5 pages, 3 figure

Bioinformatic Resources for Diabetic Nephropathy

The number of individuals with diabetes is increasing worldwide and a large subset of those affected will develop diabetic nephropathy. Diabetic nephropathy is the leading cause of end-stage renal disease, has serious health consequences for affected individuals, and represents a major monetary cost to healthcare providers.Technological and analytical developments have enabled large-scale, collaborative studies that are revealing risk factors associated with diabetic nephropathy. However, much of the inherited predisposition and biological mechanisms underpinning risk of this disease remain to be identified. Meta-analyses and integrated pathway studies are becoming an increasingly important part of research for diabetic nephropathy including, genetic, epigenetic, transcriptomic, proteomic research, clinical observations and the development of animal models.This report highlights current bioinformatic resources and standards of reporting to maximise interdisciplinary research for diabetic nephropathy. The identification of an -Omics profile that can lead to earlier diagnosis and / or offer improved clinical evaluation of individuals with diabetes would not only provide significant health benefits to affected individuals, but may also have major utility for the efficient use of healthcare resources

Modeling a Full Coronal Loop Observed with Hinode EIS and SDO AIA

Physical parameters measured from an observation of a coronal loop from Gupta et al. (2015) using Hinode/EIS and SDO/AIA were used as input for the hydrodynamic, impulsively heating NRLSOFM 1-d loop model. The model was run at eight different energy inputs and used the measured quantities of temperature (0.73 MK), density (10(sup 8.5)cm(sup -3) and minimum loop lifetime to evaluate the success of the model at recreating the observations. The loop was measured by us to have an unprojected length of 236 Mm and was assumed to be almost perpendicular to the solar surface (tilt of 3.5 degrees) and have a dipolar geometry. Our results show that two of our simulation runs (with input energies of 0.01 and 0.02 ergs cm(sup -3)S(sup -1) closely match the temperature/density combination exhibited by the loop observation. However, our simulated loops only remain in the temperature sensitive region of the Mg 278.4 Angstrom filter for 500 and 800 seconds respectively which is less than the 1200 seconds that the loop is observed for with EIS in order to make the temperature/density measurements over the loop's entire length. This leads us to conclude that impulsive heating of a single loop is not complex enough to explain this observation. Additional steady heating or a collection of additional strands along the line-of-sight would help to align the simulation with the observation

Probing weak force induced parity violation by high resolution mid-infrared molecular spectroscopy

To date no experiment has reached the level of sensitivity required to observe weak nuclear force induced parity violation (PV) energy differences in chiral molecules. In this paper, we present the approach, adopted at Laboratoire de Physique des Lasers (LPL), to measure frequency differences in the vibrational spectrum of enantiomers. We review different spectroscopic methods developed at LPL leading to the highest resolutions, as well as 20 years of CO2 laser stabilization work enabling such precise measurements. After a first attempt to observe PV vibrational frequency shifts using sub-Doppler saturated absorption spectroscopy in a cell, we are currently aiming at an experiment based on Doppler-free two-photon Ramsey interferometry on a supersonic beam. We report on our latest progress towards observing PV with chiral organo-metallic complexes containing a heavy rhenium atom