Construction of Self-Dual Integral Normal Bases in Abelian Extensions of Finite and Local Fields

Let $F/E$ be a finite Galois extension of fields with abelian Galois group $\Gamma$. A self-dual normal basis for $F/E$ is a normal basis with the additional property that $Tr_{F/E}(g(x),h(x))=\delta_{g,h}$ for $g,h\in\Gamma$. Bayer-Fluckiger and Lenstra have shown that when $char(E)\neq 2$, then $F$ admits a self-dual normal basis if and only if $[F:E]$ is odd. If $F/E$ is an extension of finite fields and $char(E)=2$, then $F$ admits a self-dual normal basis if and only if the exponent of $\Gamma$ is not divisible by $4$. In this paper we construct self-dual normal basis generators for finite extensions of finite fields whenever they exist. Now let $K$ be a finite extension of \Q_p, let $L/K$ be a finite abelian Galois extension of odd degree and let \bo_L be the valuation ring of $L$. We define $A_{L/K}$ to be the unique fractional \bo_L-ideal with square equal to the inverse different of $L/K$. It is known that a self-dual integral normal basis exists for $A_{L/K}$ if and only if $L/K$ is weakly ramified. Assuming $p\neq 2$, we construct such bases whenever they exist

Context-sensitive affect sensing and metaphor identification in virtual drama

Affect interpretation from story/dialogue context and metaphorical expressions is challenging but essential for the development of emotion inspired intelligent user interfaces. In order to achieve this research goal, we previously developed an AI actor with the integration of an affect detection component on detecting 25 emotions from literal text-based improvisational input. In this paper, we report updated development on metaphorical affect interpretation especially for sensory & cooking metaphors. Contextual affect detection with the integration of emotion modeling is also explored. Evaluation results for the new developments are provided. Our work benefits systems with intention to employ emotions embedded in the scenarios/characters and open-ended input for visual representation without detracting users from learning situations

An intervention that increases parental sensitivity in families referred to Child Protective Services also changes toddlers’ parasympathetic regulation

Experiencing maltreatment in early childhood predicts poor parasympathetic regulation, characterized by low baseline parasympathetic activity and strong withdrawal of parasympathetic influence in response to tasks. The Promoting First Relationships® (PFR) program improves parental sensitivity toward young children in families identified as maltreating. Using a subsample from a randomized control trial, we examined whether parental participation in PFR had lasting effects on toddlers' parasympathetic regulation, as measured by respiratory sinus arrhythmia (RSA), relative to a resource and referral control condition. In addition, we examined whether parental sensitive and responsive behavior mediated or moderated associations between parent treatment group and children's RSA. More than 6 months after completing treatment, 29 families in the PFR condition and 30 families in the control condition were visited at home, and toddlers' RSA was assessed at baseline and during five moderately challenging tasks. Groups did not differ in baseline RSA, but differed in RSA reactivity to the tasks. Across tasks, toddlers of parents in the control condition manifested significantly larger RSA decreases than toddlers of parents in the PFR condition. Parental behavior showed divergent associations with RSA change for toddlers of parents in the PFR versus control condition, with PFR treatment predicting RSA change ranging from small decreases to increases in toddlers of parents who showed the most sensitive, responsive behavior in the 6 months following treatment. This preliminary study showed that the same intervention that improved parenting also improved toddlers' parasympathetic regulation in response to everyday activities, warranting further experimental investigation