Squigonometry

Trigonometry is the study of circular functions - functions defined on the unit circle where distances are measured with respect to the Euclidean norm. In our research, we develop a parallel theory of trigonometric and inverse trigonometric functions for the p-norm. This is called squigonometry because the resulting functions are defined on a squircle. This approach leads to new transcendental periods, formulas, and identities. It also extends to exponential, hyperbolic, and logarithmic functions in the p-norm.https://ir.library.illinoisstate.edu/urs2021mat/1001/thumbnail.jp

A cellular automaton model of crystalline cellulose hydrolysis by cellulases

<p>Abstract</p> <p>Background</p> <p>Cellulose from plant biomass is an abundant, renewable material which could be a major feedstock for low emissions transport fuels such as cellulosic ethanol. Cellulase enzymes that break down cellulose into fermentable sugars are composed of different types - cellobiohydrolases I and II, endoglucanase and β-glucosidase - with separate functions. They form a complex interacting network between themselves, soluble hydrolysis product molecules, solution and solid phase substrates and inhibitors. There have been many models proposed for enzymatic saccharification however none have yet employed a cellular automaton approach, which allows important phenomena, such as enzyme crowding on the surface of solid substrates, denaturation and substrate inhibition, to be considered in the model.</p> <p>Results</p> <p>The Cellulase 4D model was developed <it>de novo </it>taking into account the size and composition of the substrate and surface-acting enzymes were ascribed behaviors based on their movements, catalytic activities and rates, affinity for, and potential for crowding of, the cellulose surface, substrates and inhibitors, and denaturation rates. A basic case modeled on literature-derived parameters obtained from <it>Trichoderma reesei </it>cellulases resulted in cellulose hydrolysis curves that closely matched curves obtained from published experimental data. Scenarios were tested in the model, which included variation of enzyme loadings, adsorption strengths of surface acting enzymes and reaction periods, and the effect on saccharide production over time was assessed. The model simulations indicated an optimal enzyme loading of between 0.5 and 2 of the base case concentrations where a balance was obtained between enzyme crowding on the cellulose crystal, and that the affinities of enzymes for the cellulose surface had a large effect on cellulose hydrolysis. In addition, improvements to the cellobiohydrolase I activity period substantially improved overall glucose production.</p> <p>Conclusions</p> <p>Cellulase 4D simulates the enzymatic hydrolysis of cellulose to glucose by surface and solution phase-acting enzymes and accounts for complex phenomena that have previously not been included in cellulose hydrolysis models. The model is intended as a tool for industry, researchers and educators alike to explore options for enzyme engineering and process development and to test hypotheses regarding cellulase mechanisms.</p

The Effects of Management and Vegetation on Soil Carbon Stocks in Temperate Australian Grazing Systems

The natural spatial variability in soil organic carbon (SOC) found under perennial pasture systems can make it difficult to determine differences between contrasting agricultural management practices. Pasture composition in large, extensively grazed paddocks can give an indication of pasture growth, utilisation and fertility that influence SOC and are a result of management over the longer-term. This paper examines SOC stocks on the central and southern tablelands of NSW, Australia (average rainfall from 615 to 915 mm and average annual temperature from 10.6 to 15.6°C) at three scales (regional, between similar sites and within site) to determine the influence of management, pasture composition, herbage mass and root mass. After allowing for variability due to climate, landscape and soil properties there were no differences in management comparisons, e.g. high v low fertiliser input, introduced v native pastures and rotational grazing v set stocking. The total herbage mass measured at the time of sampling had a significant relationship with SOC between and within sites and the presence of some species was associated with lower SOC. Root mass measured at an intensively monitored site showed a significant relationship with SOC. These results reflect the complexity of grazing/pasture systems, with natural variability explaining most of the variability in SOC stock; and pasture productivity leading to higher root production explaining differences in SOC levels rather than grazing management

Topical Nutrients Promote Engraftment and Inhibit Wound Contraction of Cultured Skin Substitutes in Athymic Mice

Routine treatment of burns with cultured skin substitutes (CSS) has been limited by poor engraftment and by scarring. Hypothetically, topical application of essential nutrients and/or growth factors may support epithelial survival temporarily during graft vascularization, CSS, composed of human epidermal keratinocytes and dermal fibroblasts attached to collagen-glycosaminoglycan substrates, were incubated for 19 d in media optimized for keratinocytes. CSS, human xenografts, murine autografts, or no grafts were applied orthotopically to full-thickness skin wounds (2 × 2 cm) in athymic mice. Wounds were irrigated for 14 d with 1 ml/d modified cell culture medium or with saline containing epidermal growth factor, or were treated with dry dressings. After 6 weeks, treated sites were scored for percentage original wound area (mean ± SEM) and percentage HLA- ABC-positive healed wounds [(number positive/n) × 100], and tested for significance (analysis of variance, p < 0.0001; Tukey test, p < 0.05). The data showed that CSS irrigated with nutrient medium were not statistically different in wound area (67.8 ± 5.1%) from murine autografts (63.3 ± 2.9%) but were statistically larger than human xenograft, no graft, or CSS treated with saline irrigation or dry dressings. HLA- ABC expression was 100% in CSS with nutrient irrigation, 86% in CSS with saline irrigation, 83% In CSS without irrigation, and 75% in xenografts with nutrient irrigation. These findings suggest that availability of essential nutrients supports keratinocyte viability during graft vascularization of CSS

Progressive skeletal benefits of physical activity when young as assessed at the midshaft humerus in male baseball players

Physical activity benefits the skeleton, but there is contrasting evidence regarding whether benefits differ at different stages of growth. The current study demonstrates that physical activity should be encouraged at the earliest age possible and be continued into early adulthood to gain most skeletal benefits. INTRODUCTION: The current study explored physical activity-induced bone adaptation at different stages of somatic maturity by comparing side-to-side differences in midshaft humerus properties between male throwing athletes and controls. Throwers present an internally controlled model, while inclusion of control subjects removes normal arm dominance influences. METHODS: Throwing athletes (n = 90) and controls (n = 51) were categorized into maturity groups (pre, peri, post-early, post-mid, and post-late) based on estimated years from peak height velocity (10 years). Side-to-side percent differences in midshaft humerus cortical volumetric bone mineral density (Ct.vBMD) and bone mineral content (Ct.BMC); total (Tt.Ar), medullary (Me.Ar), and cortical (Ct.Ar) areas; average cortical thickness (Ct.Th); and polar Strength Strain Index (SSIP) were assessed. RESULTS: Significant interactions between physical activity and maturity on side-to-side differences in Ct.BMC, Tt.Ar, Ct.Ar, Me.Ar, Ct.Th, and SSIP resulted from the following: (1) greater throwing-to-nonthrowing arm differences than dominant-to-nondominant arm differences in controls (all p < 0.05) and (2) throwing-to-nonthrowing arm differences in throwers being progressively greater across maturity groups (all p < 0.05). Regional analyses revealed greatest adaptation in medial and lateral sectors, particularly in the three post-maturity groups. Years throwing predicted 59% of the variance of the variance in throwing-to-nonthrowing arm difference in SSIP (p < 0.001). CONCLUSION: These data suggest that physical activity has skeletal benefits beginning prior to and continuing beyond somatic maturation and that a longer duration of exposure to physical activity has cumulative skeletal benefits. Thus, physical activity should be encouraged at the earliest age possible and be continued into early adulthood to optimize skeletal benefits

Antiinflammatory effects of dexamethasone are partly dependent on induction of dual specificity phosphatase 1

Glucocorticoids (GCs), which are used in the treatment of immune-mediated inflammatory diseases, inhibit the expression of many inflammatory mediators. They can also induce the expression of dual specificity phosphatase 1 (DUSP1; otherwise known as mitogen-activated protein kinase [MAPK] phosphatase 1), which dephosphorylates and inactivates MAPKs. We investigated the role of DUSP1 in the antiinflammatory action of the GC dexamethasone (Dex). Dex-mediated inhibition of c-Jun N-terminal kinase and p38 MAPK was abrogated in DUSP1−/− mouse macrophages. Dex-mediated suppression of several proinflammatory genes (including tumor necrosis factor, cyclooxygenase 2, and interleukin 1α and 1β) was impaired in DUSP1−/− mouse macrophages, whereas other proinflammatory genes were inhibited by Dex in a DUSP1-independent manner. In vivo antiinflammatory effects of Dex on zymosan-induced inflammation were impaired in DUSP1−/− mice. Therefore, the expression of DUSP1 is required for the inhibition of proinflammatory signaling pathways by Dex in mouse macrophages. Furthermore, DUSP1 contributes to the antiinflammatory effects of Dex in vitro and in vivo