The Significance of the CC-Numerical Range and the Local CC-Numerical Range in Quantum Control and Quantum Information

This paper shows how C-numerical-range related new strucures may arise from practical problems in quantum control--and vice versa, how an understanding of these structures helps to tackle hot topics in quantum information. We start out with an overview on the role of C-numerical ranges in current research problems in quantum theory: the quantum mechanical task of maximising the projection of a point on the unitary orbit of an initial state onto a target state C relates to the C-numerical radius of A via maximising the trace function |\tr \{C^\dagger UAU^\dagger\}|. In quantum control of n qubits one may be interested (i) in having U\in SU(2^n) for the entire dynamics, or (ii) in restricting the dynamics to {\em local} operations on each qubit, i.e. to the n-fold tensor product SU(2)\otimes SU(2)\otimes >...\otimes SU(2). Interestingly, the latter then leads to a novel entity, the {\em local} C-numerical range W_{\rm loc}(C,A), whose intricate geometry is neither star-shaped nor simply connected in contrast to the conventional C-numerical range. This is shown in the accompanying paper (math-ph/0702005). We present novel applications of the C-numerical range in quantum control assisted by gradient flows on the local unitary group: (1) they serve as powerful tools for deciding whether a quantum interaction can be inverted in time (in a sense generalising Hahn's famous spin echo); (2) they allow for optimising witnesses of quantum entanglement. We conclude by relating the relative C-numerical range to problems of constrained quantum optimisation, for which we also give Lagrange-type gradient flow algorithms.Comment: update relating to math-ph/070200

Sibling relationships and family functioning in siblings of early adolescents, adolescents and young adults with autism spectrum disorder

The purpose of the study was to investigate how family functioning (defined as the ability that family members hold to manage stressful events, and intimate and social relationships), the degree to which family members feel happy and fulfilled with each other (called family satisfaction), and the demographical characteristics of siblings (age and gender) impacted on sibling relationships. The Circumplex Model of Marital and Family Systems and Behavioral Systems constituted the theoretical frameworks that guided our study. Eighty-six typically developing adolescents and young adults having a sister or a brother with autism spectrum disorder were enrolled. Results indicated that the youngest age group (early adolescents) reported to engage more frequently in negative behaviors with their siblings with ASD than the two older age groups (middle adolescents and young adults). No significant differences were found among the three age groups regarding behaviors derived from attachment, caregiving and affiliative systems. Family satisfaction and age significantly predicted behaviors during sibling interactions. Suggestions on prevention and intervention programs were discussed in order to prevent parentification among typically developing siblings and decrease episodes of quarrels and overt conflicts between brothers and sisters with and without AS

Treating attention-deficit/hyperactivity disorder beyond symptom control alone in children and adolescents: a review of the potential benefits of long-acting stimulants

Attention-deficit/hyperactivity disorder (ADHD), one of the most common neuropsychiatric conditions of childhood, often has a chronic course and persists into adulthood in many individuals. ADHD may have a clinically important impact on health-related quality of life in children, a significant impact on parents’ emotional health and interfere with family activities/cohesion. To date, the main targets of ADHD treatment have focused on reducing the severity of symptoms during the school day and improving academic performance. However, the treatment of ADHD should reach beyond symptom control to address the issues of social competencies and improvement of health-related quality of life from the perspectives of individuals with ADHD and their families, to support them in reaching their full developmental potential. Methylphenidate (MPH) is recognised as the first-line choice of pharmacotherapy for ADHD in children and adolescents. This paper focuses on the importance and benefits to child development of ADHD symptom control beyond the school day only, i.e. extending into late afternoon and evening and uses the example of an extended-release MPH formulation (OROS® MPH) to demonstrate the potential benefits of active full day coverage (12 h) with a single daily dose. Concerns of long-term stimulant treatment are also discussed