Data expansion with Huffman codes

The following topics were dealt with: Shannon theory; universal lossless source coding; CDMA; turbo codes; broadband networks and protocols; signal processing and coding; coded modulation; information theory and applications; universal lossy source coding; algebraic geometry codes; modelling analysis and stability in networks; trellis structures and trellis decoding; channel capacity; recording channels; fading channels; convolutional codes; neural networks and learning; estimation; Gaussian channels; rate distortion theory; constrained channels; 2D channel coding; nonparametric estimation and classification; data compression; synchronisation and interference in communication systems; cyclic codes; signal detection; group codes; multiuser systems; entropy and noiseless source coding; dispersive channels and equalisation; block codes; cryptography; image processing; quantisation; random processes; wavelets; sequences for synchronisation; iterative decoding; optical communications

The Braids on your Blanket

In this expositional essay, we introduce some elements of the study of groups by analysing the braid pattern on a knitted blanket. We determine that the blanket features pure braids with a minimal number of crossings. Moreover, we determine polynomial invariants associated to the links obtained by closing the braid patterns of the blanket.Comment: Expositional article for a general readership. 32 pages, several figure

Modeling the dynamics of bivalent histone modifications

Epigenetic modifications to histones may promote either activation or repression of the transcription of nearby genes. Recent experimental studies show that the promoters of many lineage-control genes in stem cells have "bivalent domains" in which the nucleosomes contain both active (H3K4me3) and repressive (H3K27me3) marks. It is generally agreed that bivalent domains play an important role in stem cell differentiation, but the underlying mechanisms remain unclear. Here we formulate a mathematical model to investigate the dynamic properties of histone modification patterns. We then illustrate that our modeling framework can be used to capture key features of experimentally observed combinatorial chromatin states.Comment: 23 pages, 10 figure

Mathematical Model for finding Locations and Sizes of Company Warehouses

A large Canadian company with headquarters in the Greater Toronto area handles approximately 20,000 products provided by about 150 vendors supplying over 200 branches. To minimize transportation and storage costs, this company is planning to open a second warehouse. Decisions like this are often made with the aid of the solution to an mathematical optimization problem. This project will determine the size and location of its next warehouse. In this project, we will formulate and solve this large optimization problem taking into account fixed land and building costs, variable operation costs, and transportation costs. We will suggest the new location and determine which branches will be supplied by the new and existing warehouses. Preliminary research for the model has determined necessary and sufficient variable constraints which will yield an accurate solution

Retinoids Regulate a Developmental Checkpoint for Tissue Regeneration in Drosophila

SummaryDamage to Drosophila imaginal discs elicits a robust regenerative response from the surviving tissue [1–4]. However, as in other organisms, developmental progression and differentiation can restrict the regenerative capacity of Drosophila tissues. Experiments in Drosophila and other holometabolous insects have demonstrated that either damage to imaginal tissues [5, 6] or transplantation of a damaged imaginal disc [7, 8] delays the onset of metamorphosis. Therefore, in Drosophila there appears to be a mechanism that senses tissue damage and extends the larval phase to coordinate tissue regeneration with the overall developmental program of the organism. However, how such a pathway functions remains unknown. Here we demonstrate that a developmental checkpoint extends larval growth after imaginal disc damage by inhibiting the transcription of the gene encoding PTTH, a neuropeptide that promotes the release of the steroid hormone ecdysone. Using a genetic screen, we identify a previously unsuspected role for retinoid biosynthesis in regulating PTTH expression and delaying development in response to tissue damage. Retinoid signaling plays an important but poorly defined role in several vertebrate regeneration models [9–11]. Our findings demonstrate that retinoid biosynthesis in Drosophila is important for the maintenance of a condition that is permissive for regenerative growth

The effects of electronic cigarettes and vaping products on arterial stiffness

BACKGROUND: Electronic cigarettes (e-cigarettes) are nicotine delivery systems that generate an aerosol that can be inhaled and come in a variety of attractive designs and e- liquid flavorings. E-cigarettes are the second most commonly used tobacco product in the United States and are predominantly used by youth and young adults. The cardiovascular health risk of combustible cigarette use is well-established, but whether e-cigarettes increase the risk of cardiovascular events is less clear. Evaluating the short-term vascular effects of e-cigarette use is an approach to gain insight into the cardiovascular health impact. Limited studies have shown that acute e-cigarette use in combustible cigarette users was associated with increased central hemodynamic values and arterial stiffness. Few studies have assessed the effects of chronic e-cigarette use on arterial stiffness, particularly in young adults. OBJECTIVE: To assess the effects of e-cigarette use on central hemodynamics and arterial stiffness in regular e-cigarette users in comparison to combustible cigarette users and non-users. METHODS: Combustible cigarette users, e-cigarette users, and non-users without known cardiovascular disease (CVD) or CVD risk factors between the ages of 18 and 45 were enrolled in the ongoing Cardiovascular Injury due to Tobacco Products 2.0 (CITU 2.0) study at the Boston University School of Medicine and the University of Louisville School of Medicine starting from 2019. Non-invasive arterial tonometry, using the SphygmoCor system, was performed to measure peripheral artery waveforms to obtain central hemodynamic values and arterial stiffness parameters: augmentation index (AIx), carotid-radial (CR) and carotid-femoral pulse wave velocities (CFPWV). RESULTS: We had available arterial stiffness measures in 209 study participants (mean age 26±7, 48% female) across 3 tobacco product use groups: combustible cigarette users (N=51), e-cigarette users (N=97), and non-users (N=61). Amongst the e-cigarette users, 41 were dual users (use of both e-cigarettes and combustible cigarettes), 25 were exclusive e-cigarette users who were former combustible cigarette users, and 31 were exclusive e-cigarette users who were never combustible cigarette users. The majority (87%) of e-cigarette users used a pod-based product with fruit and mint/wintergreen or menthol as the most popular e-liquid flavors. In unadjusted analyses, central systolic blood pressure, AIx, CRPWV, and CFPWV differed across the three tobacco product use categories. In multivariable regression models adjusting for age, sex, race and study site, e-cigarette users and combustible cigarette users had higher central systolic blood pressure (β=3.9±2.0, p=0.048 and β=4.8±2.4, p=0.04, respectively) whereas combustible cigarette smokers also had higher central AIx, and CRPWV compared to non-users (β=6.9±3.3, p=0.04 and β=0.97±0.31, p=0.002, respectively). In unadjusted analyses across the five groups, we found similar patterns of differences in vascular measures. In multivariable regression models comparing to combustible cigarette users, dual product users had similar measures of vascular function whereas exclusive e-cigarette users who were former smokers had lower CRPWV (β=-0.95±0.36, p=0.009), and exclusive e- cigarette users who were never combustible cigarette users had lower AIx (β=-9.0±4.2, 0.04). CONCLUSIONS: Our findings suggest that in young adults, combustible cigarette use is associated with measures of arterial stiffness. Dual e-cigarette use was largely similar to combustible cigarette use whereas exclusive e-cigarette use had a lesser degree of vascular stiffening. Further studies are needed to evaluate the long-term impact of e- cigarette use on cardiovascular health

Frozen in time: a new method using cryo-scanning electron microscopy to visualize root-fungal interactions

• A new method of sample preparation for cryo-scanning electron microscopy was used to visualize internal infection of wheat (Triticum aestivum) roots by the pathogenic fungus Rhizoctonia solani AG-8. The new method retained fungal hyphae and root cell