Calculation of the Stability Index in Parameter-Dependent Calculus of Variations Problems: Buckling of a Twisted Elastic Strut

We consider the problem of minimizing the energy of an inextensible elastic strut with length 1 subject to an imposed twist angle and force. In a standard calculus of variations approach, one first locates equilibria by solving the Euler--Lagrange ODE with boundary conditions at arclength values 0 and 1. Then one classifies each equilibrium by counting conjugate points, with local minima corresponding to equilibria with no conjugate points. These conjugate points are arclength values $\sigma \le 1$ at which a second ODE (the Jacobi equation) has a solution vanishing at $0$ and $\sigma$. Finding conjugate points normally involves the numerical solution of a set of initial value problems for the Jacobi equation. For problems involving a parameter $\lambda$, such as the force or twist angle in the elastic strut, this computation must be repeated for every value of $\lambda$ of interest. Here we present an alternative approach that takes advantage of the presence of a parameter $\lambda$. Rather than search for conjugate points $\sigma \le 1$ at a fixed value of $\lambda$, we search for a set of special parameter values $\lambda_m$ (with corresponding Jacobi solution \bfzeta^m) for which $\sigma=1$ is a conjugate point. We show that, under appropriate assumptions, the index of an equilibrium at any $\lambda$ equals the number of these \bfzeta^m for which \langle \bfzeta^m, \Op \bfzeta^m \rangle < 0, where \Op is the Jacobi differential operator at $\lambda$. This computation is particularly simple when $\lambda$ appears linearly in \Op. We apply this approach to the elastic strut, in which the force appears linearly in \Op, and, as a result, we locate the conjugate points for any twisted unbuckled rod configuration without resorting to numerical solution of differential equations. In addition, we numerically compute two-dimensional sheets of buckled equilibria (as the two parameters of force and twist are varied) via a coordinated family of one-dimensional parameter continuation computations. Conjugate points for these buckled equilibria are determined by numerical solution of the Jacobi ODE

Expressions 1985

PRODUCTION STAFFLOUISE AUSTINDANA Z. BEHRENDSENAMBER HEWITTTOSHIA SOUTHRANDY STANDLEYSHELLY WILSONhttps://openspace.dmacc.edu/expressions/1006/thumbnail.jp

Identification of emulsifier potato peptides by bioinformatics: application to omega-3 delivery emulsions and release from potato industry side streams

We are grateful for the financial support from Innovation Fund Denmark (Grant nr: 7045-00021B, PROVIDE project). We also acknowledge K.M.C. amba (Brande, Denmark) and A.K.V. amba (Langholt, Denmark) for providing the potato samples used in this study.In this work, we developed a novel approach combining bioinformatics, testing of functionality and bottom-up proteomics to obtain peptide emulsifiers from potato side-streams. This is a significant advancement in the process to obtain emulsifier peptides and it is applicable to any type of protein. Our results indicated that structure at the interface is the major determining factor of the emulsifying activity of peptide emulsifiers. Fish oil-in-water emulsions with high physical stability were stabilized with peptides to be predicted to have facial amphiphilicity: (i) peptides with predominantly α-helix conformation at the interface and having 18–29 amino acids, and (ii) peptides with predominantly β-strand conformation at the interface and having 13–15 amino acids. In addition, high physically stable emulsions were obtained with peptides that were predicted to have axial hydrophobic/hydrophilic regions. Peptides containing the sequence FCLKVGV showed high in vitro antioxidant activity and led to emulsions with high oxidative stability. Peptide-level proteomics data and sequence analysis revealed the feasibility to obtain the potent emulsifier peptides found in this study (e.g. γ-1) by trypsin-based hydrolysis of different side streams in the potato industry.Innovation Fund Denmark 7045-00021

3 years of liraglutide versus placebo for type 2 diabetes risk reduction and weight management in individuals with prediabetes: a randomised, double-blind trial

Background: Liraglutide 3·0 mg was shown to reduce bodyweight and improve glucose metabolism after the 56-week period of this trial, one of four trials in the SCALE programme. In the 3-year assessment of the SCALE Obesity and Prediabetes trial we aimed to evaluate the proportion of individuals with prediabetes who were diagnosed with type 2 diabetes. Methods: In this randomised, double-blind, placebo-controlled trial, adults with prediabetes and a body-mass index of at least 30 kg/m2, or at least 27 kg/m2 with comorbidities, were randomised 2:1, using a telephone or web-based system, to once-daily subcutaneous liraglutide 3·0 mg or matched placebo, as an adjunct to a reduced-calorie diet and increased physical activity. Time to diabetes onset by 160 weeks was the primary outcome, evaluated in all randomised treated individuals with at least one post-baseline assessment. The trial was conducted at 191 clinical research sites in 27 countries and is registered with ClinicalTrials.gov, number NCT01272219. Findings: The study ran between June 1, 2011, and March 2, 2015. We randomly assigned 2254 patients to receive liraglutide (n=1505) or placebo (n=749). 1128 (50%) participants completed the study up to week 160, after withdrawal of 714 (47%) participants in the liraglutide group and 412 (55%) participants in the placebo group. By week 160, 26 (2%) of 1472 individuals in the liraglutide group versus 46 (6%) of 738 in the placebo group were diagnosed with diabetes while on treatment. The mean time from randomisation to diagnosis was 99 (SD 47) weeks for the 26 individuals in the liraglutide group versus 87 (47) weeks for the 46 individuals in the placebo group. Taking the different diagnosis frequencies between the treatment groups into account, the time to onset of diabetes over 160 weeks among all randomised individuals was 2·7 times longer with liraglutide than with placebo (95% CI 1·9 to 3·9, p&lt;0·0001), corresponding with a hazard ratio of 0·21 (95% CI 0·13–0·34). Liraglutide induced greater weight loss than placebo at week 160 (–6·1 [SD 7·3] vs −1·9% [6·3]; estimated treatment difference −4·3%, 95% CI −4·9 to −3·7, p&lt;0·0001). Serious adverse events were reported by 227 (15%) of 1501 randomised treated individuals in the liraglutide group versus 96 (13%) of 747 individuals in the placebo group. Interpretation: In this trial, we provide results for 3 years of treatment, with the limitation that withdrawn individuals were not followed up after discontinuation. Liraglutide 3·0 mg might provide health benefits in terms of reduced risk of diabetes in individuals with obesity and prediabetes. Funding: Novo Nordisk, Denmark

Finishing the euchromatic sequence of the human genome

The sequence of the human genome encodes the genetic instructions for human physiology, as well as rich information about human evolution. In 2001, the International Human Genome Sequencing Consortium reported a draft sequence of the euchromatic portion of the human genome. Since then, the international collaboration has worked to convert this draft into a genome sequence with high accuracy and nearly complete coverage. Here, we report the result of this finishing process. The current genome sequence (Build 35) contains 2.85 billion nucleotides interrupted by only 341 gaps. It covers ∼99% of the euchromatic genome and is accurate to an error rate of ∼1 event per 100,000 bases. Many of the remaining euchromatic gaps are associated with segmental duplications and will require focused work with new methods. The near-complete sequence, the first for a vertebrate, greatly improves the precision of biological analyses of the human genome including studies of gene number, birth and death. Notably, the human enome seems to encode only 20,000-25,000 protein-coding genes. The genome sequence reported here should serve as a firm foundation for biomedical research in the decades ahead

31st Annual Meeting and Associated Programs of the Society for Immunotherapy of Cancer (SITC 2016) : part two

Background The immunological escape of tumors represents one of the main ob- stacles to the treatment of malignancies. The blockade of PD-1 or CTLA-4 receptors represented a milestone in the history of immunotherapy. However, immune checkpoint inhibitors seem to be effective in specific cohorts of patients. It has been proposed that their efficacy relies on the presence of an immunological response. Thus, we hypothesized that disruption of the PD-L1/PD-1 axis would synergize with our oncolytic vaccine platform PeptiCRAd. Methods We used murine B16OVA in vivo tumor models and flow cytometry analysis to investigate the immunological background. Results First, we found that high-burden B16OVA tumors were refractory to combination immunotherapy. However, with a more aggressive schedule, tumors with a lower burden were more susceptible to the combination of PeptiCRAd and PD-L1 blockade. The therapy signifi- cantly increased the median survival of mice (Fig. 7). Interestingly, the reduced growth of contralaterally injected B16F10 cells sug- gested the presence of a long lasting immunological memory also against non-targeted antigens. Concerning the functional state of tumor infiltrating lymphocytes (TILs), we found that all the immune therapies would enhance the percentage of activated (PD-1pos TIM- 3neg) T lymphocytes and reduce the amount of exhausted (PD-1pos TIM-3pos) cells compared to placebo. As expected, we found that PeptiCRAd monotherapy could increase the number of antigen spe- cific CD8+ T cells compared to other treatments. However, only the combination with PD-L1 blockade could significantly increase the ra- tio between activated and exhausted pentamer positive cells (p= 0.0058), suggesting that by disrupting the PD-1/PD-L1 axis we could decrease the amount of dysfunctional antigen specific T cells. We ob- served that the anatomical location deeply influenced the state of CD4+ and CD8+ T lymphocytes. In fact, TIM-3 expression was in- creased by 2 fold on TILs compared to splenic and lymphoid T cells. In the CD8+ compartment, the expression of PD-1 on the surface seemed to be restricted to the tumor micro-environment, while CD4 + T cells had a high expression of PD-1 also in lymphoid organs. Interestingly, we found that the levels of PD-1 were significantly higher on CD8+ T cells than on CD4+ T cells into the tumor micro- environment (p < 0.0001). Conclusions In conclusion, we demonstrated that the efficacy of immune check- point inhibitors might be strongly enhanced by their combination with cancer vaccines. PeptiCRAd was able to increase the number of antigen-specific T cells and PD-L1 blockade prevented their exhaus- tion, resulting in long-lasting immunological memory and increased median survival

Monitoring and managing recreational use in backcountry landscapes using computer-based simulation modeling

Section: Workshop: Travel simulation modeling for recreation plannin