On the Size Effect of Additives in Amorphous Shape Memory Polymers

Small additive molecules often enhance structural relaxation in polymers. We explore this effect in a thermoplastic shape memory polymer via molecular dynamics simulations. The additive-to-monomer size ratio is shown to play a key role here. While the effect of additive-concentration on the rate of shape recovery is found to be monotonic in the investigated range, a non-monotonic dependence on the size-ratio emerges at temperatures close to the glass transition. This work thus identifies the additives’ size to be a qualitatively novel parameter for controlling the recovery process in polymer-based shape memory materials.

Changes in future precipitation mean and variability across scales

Changes in precipitation variability can have large societal consequences, whether at the short timescales of flash floods or the longer timescales of multi-year droughts. Recent studies have suggested that in future climate projections, precipitation variability rises more steeply than does its mean, leading to concerns about societal impacts. This work evaluates changes in mean precipitation over a broad range of spatial and temporal scales using a range of models from high-resolution regional simulations to millennial-scale global simulations. Results show that changes depend on the scale of aggregation and involve strong regional differences. On local scales that resolve individual rainfall events (hours and tens of kilometers), changes in precipitation distributions are complex and variances rise substantially more than means, as is required given the well-known disproportionate rise in precipitation intensity. On scales that aggregate across many events, distributional changes become simpler and variability changes smaller. At regional scale, future precipitation distributions can be largely reproduced by a simple transformation of present-day precipitation involving a multiplicative shift and a small additive term. The “extra” broadening is negatively correlated with changes in mean precipitation: in strongly “wetting” areas, distributions broaden less than expected from a simple multiplicative mean change; in “drying” areas, distributions narrow less. Precipitation variability changes are therefore of especial concern in the subtropics, which tend to dry under climate change. Outside the tropics, variability changes are similar on timescales from days to decades, i.e. show little frequency dependence. This behavior is highly robust across models, suggesting it may stem from some fundamental constraint.

Percolation Conduction of Carbon Nanocomposites

Carbon nanocomposites present a new class of nanomaterials in which conducting carbon nanoparticles are a small additive to a non-conducting matrix. A typical example of such composites is a polymer matrix doped with carbon nanotubes (CNT). Due to a high aspect ratio of CNTs, inserting rather low quantity of nanotubes (on the level of 0.01%) results in the percolation transition, which causes the enhancement in the conductivity of the material by 10–12 orders of magnitude. Another type of nanocarbon composite is a film produced as a result of reduction of graphene oxide (GO). Such a film is consisted of GO fragments whose conductivity is determined by the degree of reduction. A distinctive peculiarity of both types of nanocomposites relates to the dependence of the conductivity of those materials on the applied voltage. Such a behavior is caused by a non-ideal contact between neighboring carbon nanoparticles incorporated into the composite. The resistance of such a contact depends sharply on the electrical field strength and therefore on the distance between neighboring nanoparticles. Experiments demonstrating non-linear, non-Ohmic behavior of both above-mentioned types of carbon nanocomposites are considered in the present article. There has been a model description presented of such a behavior based on the quasi-classical approach to the problem of electron tunneling through the barrier formed by the electric field. The calculation results correspond qualitatively to the available experimental data.

Metric sub-regularity in optimal control of affine problems with free end state

The paper investigates the property of Strong Metric sub-Regularity (SMsR) of the mapping representing the first order optimality system for a Lagrange-type optimal control problem which is affine with respect to the control. The terminal time is fixed, the terminal state is free, and the control values are restricted in a convex compact set U. The SMsR property is associated with a reference solution of the optimality system and ensures that small additive perturbations in the system result in solutions which are at distance to the reference one, at most proportional to the size of the perturbations. A general sufficient condition for SMsR is obtained for appropriate space settings and then specialized in the case of a polyhedral set U and purely bang-bang reference control. Sufficient second-order optimality conditions are obtained as a by-product of the analysis. Finally, the obtained results are utilized for error analysis of the Euler discretization scheme applied to affine problems.

Considering the APOE locus in polygenic scores for Alzheimer’s disease

Polygenic scores are a strategy to aggregate the small, additive effects of single nucleotide polymorphisms across the genome. With phenotypes like Alzheimer’s disease, which have a strong and well established genomic locus (APOE), the cumulative effect of genetic variants outside of this area has not been well established in a population-representative sample. Here we examine the association between polygenic scores both with and without the APOE region at different P value thresholds. We also investigate the addition of APOE-ε4 carrier status and its effect on the polygenic score – dementia association. We found that including the APOE region through weighted variants in a polygenic score was insufficient to capture the large amount of risk attributed to this region. We recommend removing this region from polygenic score calculation and treating the APOE locus as an independent covariate.

Fractional Domination Game

Given a graph $G$, a real-valued function $f: V(G) \rightarrow [0,1]$ is a fractional dominating function if $\sum_{u \in N[v]} f(u) \ge 1$ holds for every vertex $v$ and its closed neighborhood $N[v]$ in $G$. The aim is to minimize the sum $\sum_{v \in V(G)} f(v)$. A different approach to graph domination is the domination game, introduced by Brešar et al. [SIAM J. Discrete Math. 24 (2010) 979–991]. It is played on a graph $G$ by two players, namely Dominator and Staller, who take turns choosing a vertex such that at least one previously undominated vertex becomes dominated. The game is over when all vertices are dominated. Dominator wants to finish the game as soon as possible, while Staller wants to delay the end. Assuming that both players play optimally and Dominator starts, the length of the game on $G$ is uniquely determined and is called the game domination number of $G$. We introduce and study the fractional version of the domination game, where the moves are ruled by the condition of fractional domination. Here we prove a fundamental property of this new game, namely the fractional version of the so-called Continuation Principle. Moreover, we present lower and upper bounds on the fractional game domination number of paths and cycles. These estimates are tight apart from a small additive constant. We also prove that the game domination number cannot be bounded above by any linear function of the fractional game domination number.

QTLs for Resistance to Fusarium Ear Rot in a Multiparent Advanced Generation Intercross (MAGIC) Maize Population

Alternative approaches to linkage and association mapping using inbred panels may allow further insights into loci involved in resistance to Fusarium ear rot and lead to the discovery of suitable markers for breeding programs. Here, the suitability of a maize multiparent advanced-generation intercross population for detecting quantitative trait loci (QTLs) associated with Fusarium ear rot resistance was evaluated and found to be valuable in uncovering genomic regions containing resistance-associated loci in temperate materials. In total, 13 putative minor QTLs were located over all of the chromosomes, except chromosome 5, and frequencies of favorable alleles for resistance to Fusarium ear rot were, in general, high. These findings corroborated the quantitative characteristic of resistance to Fusarium ear rot in which many loci have small additive effects. Present and previous results indicate that crucial regions such as 210 to 220 Mb in chromosome 3 and 166 to 173 Mb in chromosome 7 (B73-RefGen-v2) contain QTLs for Fusarium ear rot resistance and fumonisin content.

Additive Energy and Irregularities of Distribution

We consider strictly increasing sequences (an)n≥1 of integers and sequences of fractional parts ({anα})n≥1 where α ∈ R. We show that a small additive energy of (an)n≥1 implies that for almost all α the sequence ({anα})n≥1 has large discrepancy. We prove a general result, provide various examples, and show that the converse assertion is not necessarily true.