Sets Characterized by Missing Sums and Differences

A more sums than differences (MSTD) set is a finite subset S of the integers such |S+S| > |S-S|. We show that the probability that a uniform random subset of {0, 1, ..., n} is an MSTD set approaches some limit rho > 4.28 x 10^{-4}. This improves the previous result of Martin and O'Bryant that there is a lower limit of at least 2 x 10^{-7}. Monte Carlo experiments suggest that rho \approx 4.5 \x 10^{-4}. We present a deterministic algorithm that can compute rho up to arbitrary precision. We also describe the structure of a random MSTD subset S of {0, 1, ..., n}. We formalize the intuition that fringe elements are most significant, while middle elements are nearly unrestricted. For instance, the probability that any ``middle'' element is in S approaches 1/2 as n -> infinity, confirming a conjecture of Miller, Orosz, and Scheinerman. In general, our results work for any specification on the number of missing sums and the number of missing differences of S, with MSTD sets being a special case.Comment: 32 pages, 1 figure, 1 tabl

Counting MSTD Sets in Finite Abelian Groups

In an abelian group G, a more sums than differences (MSTD) set is a subset A of G such that |A+A|>|A-A|. We provide asymptotics for the number of MSTD sets in finite abelian groups, extending previous results of Nathanson. The proof contains an application of a recently resolved conjecture of Alon and Kahn on the number of independent sets in a regular graph.Comment: 17 page

Correlates of Post-traumatic Growth Following a Myocardial Infarction: A Systematic Review

Correlates of post-traumatic growth (PTG) have been examined in the area of health psychology previously, with much focus on aspects of personality, coping, and social support. This systematic review aimed to examine correlates of PTG for those who have experienced a myocardial infarction (MI). Studies which met inclusion criteria were assessed for quality and reviewed. Results showed an inconsistent strength of associations between studies and so conclusions cannot be drawn. Possible reasons for these differences are discussed and recommendations for future research are suggested

Constructing MSTD Sets Using Bidirectional Ballot Sequences

A more sums than differences (MSTD) set is a finite subset S of the integers such that |S+S| > |S-S|. We construct a new dense family of MSTD subsets of {0, 1, 2, ..., n-1}. Our construction gives Theta(2^n/n) MSTD sets, improving the previous best construction with Omega(2^n/n^4) MSTD sets by Miller, Orosz, and Scheinerman.Comment: 9 pages, 2 tables, 5 figure

Ultrasonic array imaging through reverberating layers for industrial process analysis

In this paper, ultrasonic phased arrays are investigated as an imaging tool for industrial process analysis. Noninvasive process measurement, via transmission of information through a vessel wall, typically requires a window to create an optical path between the sensor and the process. Ultrasonic array imaging provides a means to overcome this barrier as it is specifically used to image into optically opaque structures. However, the large acoustic impedance mismatch between the steel process vessel and water load results in reverberations clouding the image scene containing reflections from within the process fluid. A methodology to identify and remove this reverberation interference from the image scene is proposed using subspace analysis coupled with phase coherence imaging. A 32 element, 5 MHz finite element array model mounted to the outside of a steel vessel wall is used to demonstrate the application of this methodology to a typical industrial process environment. The final image is free of reverberation artifacts, providing a means to accurately extract quantitative information about the process from these images

Metaphylogenomic and Potential Functionality of the Limpet <i>Patella pellucida</i>’s Gastrointestinal Tract Microbiome

This study investigated the microbial diversity associated with the digestive tract of the seaweed grazing marine limpet Patella pellucida. Using a modified indirect DNA extraction protocol and performing metagenomic profiling based on specific prokaryotic marker genes, the abundance of bacterial groups was identified from the analyzed metagenome. The members of three significantly abundant phyla of Proteobacteria, Firmicutes and Bacteroidetes were characterized through the literature and their predicted functions towards the host, as well as potential applications in the industrial environment assessed

Transcriptomic analysis of the lesser spotted catshark (Scyliorhinus canicula) pancreas, liver and brain reveals molecular level conservation of vertebrate pancreas function

BACKGROUND: Understanding the evolution of the vertebrate pancreas is key to understanding its functions. The chondrichthyes (cartilaginous fish such as sharks and rays) have often been suggested to possess the most ancient example of a distinct pancreas with both hormonal (endocrine) and digestive (exocrine) roles. The lack of genetic, genomic and transcriptomic data for cartilaginous fish has hindered a more thorough understanding of the molecular-level functions of the chondrichthyan pancreas, particularly with respect to their “unusual” energy metabolism (where ketone bodies and amino acids are the main oxidative fuel source) and their paradoxical ability to both maintain stable blood glucose levels and tolerate extensive periods of hypoglycemia. In order to shed light on some of these processes, we carried out the first large-scale comparative transcriptomic survey of multiple cartilaginous fish tissues: the pancreas, brain and liver of the lesser spotted catshark, Scyliorhinus canicula. RESULTS: We generated a mutli-tissue assembly comprising 86,006 contigs, of which 44,794 were assigned to a particular tissue or combination of tissues based on mapping of sequencing reads. We have characterised transcripts encoding genes involved in insulin regulation, glucose sensing, transcriptional regulation, signaling and digestion, as well as many peptide hormone precursors and their receptors for the first time. Comparisons to mammalian pancreas transcriptomes reveals that mechanisms of glucose sensing and insulin regulation used to establish and maintain a stable internal environment are conserved across jawed vertebrates and likely pre-date the vertebrate radiation. Conservation of pancreatic hormones and genes encoding digestive proteins support the single, early evolution of a distinct pancreatic gland with endocrine and exocrine functions in jawed vertebrates. In addition, we demonstrate that chondrichthyes lack pancreatic polypeptide (PP) and that reports of PP in the literature are likely due cross-reaction with PYY and/or NPY in the pancreas. A three hormone islet organ is therefore the ancestral jawed vertebrate condition, later elaborated upon only in the tetrapod lineage. CONCLUSIONS: The cartilaginous fish are a great untapped resource for the reconstruction of patterns and processes of vertebrate evolution and new approaches such as those described in this paper will greatly facilitate their incorporation into the rank of “model organism”. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/1471-2164-15-1074) contains supplementary material, which is available to authorized users

Determination of Bubble Size Distribution using Ultrasound Array Imaging

In this article, ultrasonic phased arrays are deployed as an imaging tool for industrial process analysis. Such arrays are typically used for sonar, medical diagnosis, and nondestructive testing; however, they have not yet been applied to industrial process analysis. The precise positioning of array elements and high frequencies possible with this technology mean that highly focused images can be generated, which cannot currently be achieved using ultrasound tomography. This article aims to highlight the potential of this technology for the measurement of bubble size distribution (BSD) and to demonstrate its application to both intrusive and noninvasive process measurements. Ultrasound images of bubble reflectors are generated using the total focusing method deployed using a 32-element, 5-MHz linear phased array, and an image processing algorithm for BSD determination is presented and evaluated under stationary and dynamic acquisition conditions. It is found that the sizing accuracy is within 10% for stationary reflectors larger than 4λ in diameter and that the algorithm is stable across the expected spatial variation of reflectors. The phased array is coupled to a six-axis robotic arm to scan a solid sample containing bubble reflectors at velocities up to 500 mms-1. The sizing accuracy is within 45% for bubbles larger than 4λ in diameter and at velocities up to 300 mms-1. However, above this velocity, the algorithm breaks down for reflectors smaller than 9λ in diameter. The ultrasound system is applied to a stream of air bubbles rising through water, which is verified via photographic analysis. Images were generated both intrusive and noninvasive, via a 10-mm Perspex barrier, to the process stream. The high bubble density in the process stream introduced scattering, limiting the measurement repeatability and the sample size in the measured distribution. Notwithstanding, this result demonstrates the potential of this technology to size bubbles for intrusive and noninvasive process analyses

Enhanced phased array imaging through reverberating interfaces

A key challenge to achieve non-invasive industrial process analysis is the transmission of information through the vessel wall. Typical non-invasive technologies, such as Raman spectroscopy, require an optically transparent 'window' into the process to acquire the process data. In this work, ultrasonic phased arrays were used to image a dynamic process through planar steel vessel walls into a fluid load. Due to the acoustic impedance mismatch at the steel-fluid interface, only a small fraction of the excitation energy comes back to the receiver in the form of useful echoes from the process. Also, the ultrasonic energy that is not transmitted across the steel-fluid interface reverberates within the vessel wall, masking signals that are reflected from within the process. Here, the ultrasonic array was deployed using Full Matrix Capture (FMC) followed by the Total Focusing Method (TFM) that focusses the ultrasonic beam at every pixel in the image. However, the TFM algorithm is not spatial resolved, leading to multiples of the reverberations interfering throughout the desired image region. To extract the signals corresponding to the process fluid, a method has been developed called the Reverberation Pattern Gain Correction Method (RP-GCM). Firstly, the algorithm uses ray-tracing to predict the path length of reverberations from the steel-fluid interface. The signals in the FMC data set corresponding to those reverberations are then windowed and a gain filter applied, prior to application of the regular TFM process. The RP-GCM has been applied to a simulated FMC data set, developed in PZFlex (OnScale, USA). Initial results demonstrate the effectiveness of this method in separating the vessel reverberations from the ultrasonic echoes of interest relating to the process