Generalised risk-sensitive control with full and partial state observation

This paper generalises the risk-sensitive cost functional by introducing noise dependent penalties on the state and control variables. The optimal control problems for the full and partial state observation are considered. Using a change of probability measure approach, explicit closed-form solutions are found in both cases. This has resulted in a new risk-sensitive regulator and filter, which are generalisations of the well-known classical results

Crystal structure and chemistry of barium-graphite intercalation compounds

Graphite can accommodate various chemical species between graphene layers to form graphite intercalation compounds (GIC) [1]. Alkali metals can easily lead to bulk stage-1 intercalation compounds by vapor transport but for more electronegative elements, such as alkaline-earth metals or lanthanides, only a superficial intercalation is obtained and other synthesis methods have to be envisaged. Molten alloys, formed between an alkali metal and the targeted metal, have demonstrated their efficiency to prepare bulk and homogeneous GIC from these latter elements, for example the superconducting CaC6 phase [2], but some elements remain difficult to intercalate by this method. More recently, our team developed a method based on the work of Hagiwara et al., consisting in using a LiCl-KCl eutectic molten medium [3], which for example allowed to prepare for the first time a bulk SrC6 compound [4]. This work is focused on the intercalation of barium into graphite from the LiCl-KCl molten salts method. A bulk stage-1 BaC6 compound has been prepared and X-ray diffraction measurements confirmed its crystal structure [5]. Moreover, by varying the experimental conditions, two completely novel phases, denoted α and β, have been isolated. From ion beam analyses, Li0,2K0,6Ba0,35C6 and Li0,2K0,75Ba0,6C6 chemical formulae have been determined for α and β phases, respectively, showing that lithium and potassium are intercalated together with barium. X- ray diffraction led to the determination of the stacking sequence of each compound, and their planar unit cells. Lastly, a reaction mechanism is proposed, which explains the formation of the different phases observed in this study

Discrete integrable systems, positivity, and continued fraction rearrangements

In this review article, we present a unified approach to solving discrete, integrable, possibly non-commutative, dynamical systems, including the $Q$- and $T$-systems based on $A_r$. The initial data of the systems are seen as cluster variables in a suitable cluster algebra, and may evolve by local mutations. We show that the solutions are always expressed as Laurent polynomials of the initial data with non-negative integer coefficients. This is done by reformulating the mutations of initial data as local rearrangements of continued fractions generating some particular solutions, that preserve manifest positivity. We also show how these techniques apply as well to non-commutative settings.Comment: 24 pages, 2 figure

Exploring the effect of ADHD traits on the moment‐to‐moment interplay between provocation and aggression: Evidence from dynamic structural equation modeling

The relation between attention deficit hyperactivity disorder (ADHD) symptoms and aggression is well documented; however, the processes that account for higher levels of aggression associated with ADHD in the course of daily life are little understood. The current study used ecological momentary assessment to explore how ADHD traits relate to individual differences in perceiving provocation from others and the resultant aggressive behaviors; and the strengths of the links between provocation and aggression in the flow of daily life. A dynamic structural equation model was fit using data from a subpopulation of young adults involved in the longitudinal z‐proso study (n = 259, median‐age 20). Data on provocation and aggression was collected at four quasi‐random time periods per day over a 14‐day period. Individuals with higher ADHD trait levels reported higher instances of provocation and aggression, with ADHD traits significantly moderating aggression inertia such that those with higher levels of ADHD traits showed greater persistence of aggressive behavior over time. However, ADHD trait levels did not significantly moderate any of the observed cross‐lagged effects. Our findings suggest that individuals with higher levels of ADHD traits are at greater risk of exposure to interpersonal interactions involving interpersonal provocation, show higher levels of aggressive behavior in daily life, and find it more difficult to reduce their aggression once triggered. These findings support the importance of targeting factors such as social skills and emotion regulation that may underpin the increased difficulties in interpersonal interactions often experienced by individuals with high levels of ADHD symptoms

Examining maternal cardiometabolic markers in pregnancy on child emotional and behaviour trajectories:Using growth curve models on a cohort study

Background Poor maternal cardiometabolic health in pregnancy is associated with negative effects on child health outcomes, but there is limited literature on child and adolescent socio-emotional outcomes. The study aims to investigate associations between maternal cardiometabolic markers during pregnancy with child and adolescence socio-emotional trajectories. Methods Growth curve models were run to examine how maternal cardiometabolic markers in pregnancy affected child socio-emotional trajectories from age 4 to 16. Models were adjusted for all pregnancy trimesters, maternal, child, and socioeconomic covariates. This study used the Avon Longitudinal Study of Parents and Children (United Kingdom) cohort. Participants consisted of mother-child pairs (n=15,133). Maternal predictors of fasting glucose, triglycerides, high-density lipoprotein cholesterol (HDL), low-density lipoprotein cholesterol (LDL), and body mass index (BMI) were taken from each pregnancy trimester (T1, T2, T3). Child outcomes included emotional problems, conduct problems, and hyperactivity problems from the Strengths and Difficulties Questionnaire (SDQ). Results Fully adjusted models showed significant associations between elevated T1 fasting glucose and increased conduct problems, higher T1 BMI and increased hyperactivity problems, lowered T1 HDL and decreased hyperactivity problems, and elevated T2 triglycerides and increased hyperactivity problems. Conclusions Maternal cardiometabolic risk is associated with conduct and hyperactivity outcomes from age 4 to 16. This study suggests that maternal markers of fasting glucose, LDL, HDL, and triglycerides during pregnancy could be added as supplements for clinical measures of risk when predicting child and adolescence’s socio-emotional trajectories.peerReviewe

Q-systems, Heaps, Paths and Cluster Positivity

We consider the cluster algebra associated to the $Q$-system for $A_r$ as a tool for relating $Q$-system solutions to all possible sets of initial data. We show that the conserved quantities of the $Q$-system are partition functions for hard particles on particular target graphs with weights, which are determined by the choice of initial data. This allows us to interpret the simplest solutions of the Q-system as generating functions for Viennot's heaps on these target graphs, and equivalently as generating functions of weighted paths on suitable dual target graphs. The generating functions take the form of finite continued fractions. In this setting, the cluster mutations correspond to local rearrangements of the fractions which leave their final value unchanged. Finally, the general solutions of the $Q$-system are interpreted as partition functions for strongly non-intersecting families of lattice paths on target lattices. This expresses all cluster variables as manifestly positive Laurent polynomials of any initial data, thus proving the cluster positivity conjecture for the $A_r$ $Q$-system. We also give an alternative formulation in terms of domino tilings of deformed Aztec diamonds with defects.Comment: 106 pages, 38 figure

The solution of the quantum A1A_1 T-system for arbitrary boundary

We solve the quantum version of the $A_1$ $T$-system by use of quantum networks. The system is interpreted as a particular set of mutations of a suitable (infinite-rank) quantum cluster algebra, and Laurent positivity follows from our solution. As an application we re-derive the corresponding quantum network solution to the quantum $A_1$ $Q$-system and generalize it to the fully non-commutative case. We give the relation between the quantum $T$-system and the quantum lattice Liouville equation, which is the quantized $Y$-system.Comment: 24 pages, 18 figure