Fractional Euler-Lagrange differential equations via Caputo derivatives

We review some recent results of the fractional variational calculus. Necessary optimality conditions of Euler-Lagrange type for functionals with a Lagrangian containing left and right Caputo derivatives are given. Several problems are considered: with fixed or free boundary conditions, and in presence of integral constraints that also depend on Caputo derivatives.Comment: This is a preprint of a paper whose final and definite form will appear as Chapter 9 of the book Fractional Dynamics and Control, D. Baleanu et al. (eds.), Springer New York, 2012, DOI:10.1007/978-1-4614-0457-6_9, in pres

Direct and Inverse Variational Problems on Time Scales: A Survey

We deal with direct and inverse problems of the calculus of variations on arbitrary time scales. Firstly, using the Euler-Lagrange equation and the strengthened Legendre condition, we give a general form for a variational functional to attain a local minimum at a given point of the vector space. Furthermore, we provide a necessary condition for a dynamic integro-differential equation to be an Euler-Lagrange equation (Helmholtz's problem of the calculus of variations on time scales). New and interesting results for the discrete and quantum settings are obtained as particular cases. Finally, we consider very general problems of the calculus of variations given by the composition of a certain scalar function with delta and nabla integrals of a vector valued field.Comment: This is a preprint of a paper whose final and definite form will be published in the Springer Volume 'Modeling, Dynamics, Optimization and Bioeconomics II', Edited by A. A. Pinto and D. Zilberman (Eds.), Springer Proceedings in Mathematics & Statistics. Submitted 03/Sept/2014; Accepted, after a revision, 19/Jan/201

Improving on legacy conferences by moving online

Scientific conferences and meetings have an important role in research, but they also suffer from a number of disadvantages: in particular, they can have a massive carbon footprint, they are time-consuming, and the high costs involved in attending can exclude many potential participants. The COVID-19 pandemic has led to the cancellation of many conferences, forcing the scientific community to explore online alternatives. Here, we report on our experiences of organizing an online neuroscience conference, neuromatch, that attracted some 3000 participants and featured two days of talks, debates, panel discussions, and one-on-one meetings facilitated by a matching algorithm. By offering most of the benefits of traditional conferences, several clear advantages, and with fewer of the downsides, we feel that online conferences have the potential to replace many legacy conferences

Physicochemical Characterization of Polymer-Stabilized Coacervate Protocells

The bottom-up construction of cell mimics has produced a range of membrane-bound protocells that have been endowed with functionality and biochemical processes reminiscent of living systems. The contents of these compartments, however, experience semidilute conditions, whereas macromolecules in the cytosol exist in protein-rich, crowded environments that affect their physicochemical properties, such as diffusion and catalytic activity. Recently, complex coacervates have emerged as attractive protocellular models because their condensed interiors would be expected to mimic this crowding better. Here we explore some relevant physicochemical properties of a recently developed polymer-stabilized coacervate system, such as the diffusion of macromolecules in the condensed coacervate phase, relative to in dilute solutions, the buffering capacity of the core, the molecular organization of the polymer membrane, the permeability characteristics of this membrane towards a wide range of compounds, and the behavior of a simple enzymatic reaction. In addition, either the coacervate charge or the cargo charge is engineered to allow the selective loading of protein cargo into the coacervate protocells. Our in-depth characterization has revealed that these polymer-stabilized coacervate protocells have many desirable properties, thus making them attractive candidates for the investigation of biochemical processes in stable, controlled, tunable, and increasingly cell-like environments

Effects of a single administration of prostaglandin F2alpha, or a combination of prostaglandin F2alpha and prostaglandin E2, or placebo on fertility variables in dairy cows 3–5 weeks post partum, a randomized, double-blind clinical trial

BACKGROUND: Delayed uterine involution has negative effects on the fertility of cows; use of prostaglandin F2alpha alone as a single treatment has not been shown to consistently improve fertility. Combined administration of PGF2alpha and PGE2 increased uterine pressure in healthy cows. We hypothesized, that the combination of both prostaglandins would accelerate uterine involution and have, therefore, a positive effect on fertility variables. In commercial dairy farming, the benefit of a single post partum combined prostaglandin treatment should be demonstrated. METHODS: 383 cows from commercial dairy farms were included in this study. Uterine size and secretion were evaluated at treatment 21–35 days post partum and 14 days later. Cows were randomly allocated to one of three treatment groups: PGF2alpha and PGE2, PGF2alpha or placebo. For every animal participating in the study, the following reproduction variables were recorded: Interval from calving to first insemination, days open, number of artificial inseminations (AI) to conception; subsequent treatment of uterus, subsequent treatment of ovaries. Plasma progesterone level at time of treatment was used as a covariable. For continuous measurements, analysis of variance was performed. Fisher's exact test for categorical non-ordered data and exact Kruskal-Wallis test for ordered data were used; pairwise group comparisons with Bonferroni adjustment of significance level were performed. RESULTS: There was no significant difference among treatment groups in uterine size. Furthermore, there was no significant difference among treatments concerning days open, number of AI, and subsequent treatment of uterus and ovaries. Days from calving to first insemination tended to be shorter for cows with low progesterone level given PGF2alpha and PGE2 in combination than for the placebo-group (P = 0.024). CONCLUSION: The results of this study indicate that the administration of PGF2alpha or a combination of PGF2alpha and PGE2 21 to 35 days post partum had no beneficial effect upon measured fertility variables. The exception was a tendency for a shorter interval from calving to first insemination after administration of the combination of PGF2alpha and PGE2, as compared to the placebo group. Further research should be done in herds with reduced fertility and/or an increased incidence of postpartum vaginal discharge

Comparison of Muscle Transcriptome between Pigs with Divergent Meat Quality Phenotypes Identifies Genes Related to Muscle Metabolism and Structure

Background: Meat quality depends on physiological processes taking place in muscle tissue, which could involve a large pattern of genes associated with both muscle structural and metabolic features. Understanding the biological phenomena underlying muscle phenotype at slaughter is necessary to uncover meat quality development. Therefore, a muscle transcriptome analysis was undertaken to compare gene expression profiles between two highly contrasted pig breeds, Large White (LW) and Basque (B), reared in two different housing systems themselves influencing meat quality. LW is the most predominant breed used in pig industry, which exhibits standard meat quality attributes. B is an indigenous breed with low lean meat and high fat contents, high meat quality characteristics, and is genetically distant from other European pig breeds. Methodology/Principal Findings: Transcriptome analysis undertaken using a custom 15 K microarray, highlighted 1233 genes differentially expressed between breeds (multiple-test adjusted P-value,0.05), out of which 635 were highly expressed in the B and 598 highly expressed in the LW pigs. No difference in gene expression was found between housing systems. Besides, expression level of 12 differentially expressed genes quantified by real-time RT-PCR validated microarray data. Functional annotation clustering emphasized four main clusters associated to transcriptome breed differences: metabolic processes, skeletal muscle structure and organization, extracellular matrix, lysosome, and proteolysis, thereb

Loss of coral reef growth capacity to track future increases in sea level

Water-depths above coral reefs is predicted to increase due to global sea-level rise (SLR). As ecological degradation inhibits the vertical accretion of coral reefs, it is likely that coastal wave exposure will increase but there currently exists a lack of data in projections concerning local rates of reef growth and local SLR. In this study we have aggregated ecological data of more than 200 tropical western Atlantic and Indian Ocean reefs and calculated their vertical growth which we have then compared with recent and projected rates of SLR across different Representative Concentration Pathway (RCP) scenarios. While many reefs currently show vertical growth that would be sufficient to keep-up with recent historic SLR, future projections under scenario RCP4.5 reveal that without substantial ecological recovery many reefs will not have the capacity to track SLR. Under RCP8.5, we predict that mean water depth will increase by over half a metre by 2100 across the majority of reefs. We found that coral cover strongly predicted whether a reef could track SLR, but that the majority of reefs had coral cover significantly lower than that required to prevent reef submergence. To limit reef submergence, and thus the impacts of waves and storms on adjacent coasts, climate mitigation and local impacts that reduce coral cover (e.g., local pollution and physical damage through development land reclamation) will be necessary

An optimal control approach to Herglotz variational problems

We address the generalized variational problem of Herglotz from an optimal control point of view. Using the theory of optimal control, we derive a generalized Euler-Lagrange equation, a transversality condition, a DuBois-Reymond necessary optimality condition and Noether’s theorem for Herglotz’s fundamental problem, valid for piece- wise smooth functions