Some Examples of Rigid Representations

*Research partially supported by INTAS grant 97-1644.

Geometric Stable Laws Through Series Representations

Let (Xi ) be a sequence of i.i.d. random variables, and let N be a geometric random variable independent of (Xi ). Geometric stable distributions are weak limits of (normalized) geometric compounds, SN = X1 + · · · + XN , when the mean of N converges to infinity. By an appropriate representation of the individual summands in SN we obtain series representation of the limiting geometric stable distribution. In addition, we study the asymptotic behavior of the partial sum process SN (t) = ⅀( i=1 ... [N t] ) Xi , and derive series representations of the limiting geometric stable process and the corresponding stochastic integral. We also obtain strong invariance principles for stable and geometric stable laws.

Representations and Positive Definite Functions on Hypergroups

Some relationships between representations of a hypergroup X, its algebras, and positive definite functions on X are studied. Also, various types of convergence of positive definite functions on X are discussed.

From icon to naturalised icon:a linguistic analysis of media representations of the BP Deepwater Horizon crisis

This research explores how news media reports construct representations of a business crisis through language. In an innovative approach to dealing with the vast pool of potentially relevant texts, media texts concerning the BP Deepwater Horizon oil spill are gathered from three different time points: immediately after the explosion in 2010, one year later in 2011 and again in 2012. The three sets of 'BP texts' are investigated using discourse analysis and semi-quantitative methods within a semiotic framework that gives an account of language at the semiotic levels of sign, code, mythical meaning and ideology. The research finds in the texts three discourses of representation concerning the crisis that show a movement from the ostensibly representational to the symbolic and conventional: a discourse of 'objective factuality', a discourse of 'positioning' and a discourse of 'redeployment'. This progression can be shown to have useful parallels with Peirce's sign classes of Icon, Index and Symbol, with their implied movement from a clear motivation by the Object (in this case the disaster events), to an arbitrary, socially-agreed connection. However, the naturalisation of signs, whereby ideologies are encoded in ways of speaking and writing that present them as 'taken for granted' is at its most complete when it is least discernible. The findings suggest that media coverage is likely to move on from symbolic representation to a new kind of iconicity, through a fourth discourse of 'naturalisation'. Here the representation turns back towards ostensible factuality or iconicity, to become the 'naturalised icon'. This work adds to the study of media representation a heuristic for understanding how the meaning-making of a news story progresses. It offers a detailed account of what the stages of this progression 'look like' linguistically, and suggests scope for future research into both language characteristics of phases and different news-reported phenomena.

On Representations of Algebraic Polynomials by Superpositions of Plane Waves

* The author was supported by NSF Grant No. DMS 9706883.

Linear Classifiers Based on Binary Distributed Representations

Binary distributed representations of vector data (numerical, textual, visual) are investigated in classification tasks. A comparative analysis of results for various methods and tasks using artificial and real-world data is given.

Bridging the Gap Between Human Language and Computer-Oriented Representations

Information can be expressed in many ways according to the different capacities of humans to perceive it. Current systems deals with multimedia, multiformat and multiplatform systems but another « multi » is still pending to guarantee global access to information, that is, multilinguality. Different languages imply different replications of the systems according to the language in question. No solutions appear to represent the bridge between the human representation (natural language) and a system-oriented representation. The United Nations University defined in 1997 a language to be the support of effective multilinguism in Internet. In this paper, we describe this language and its possible applications beyond multilingual services as the possible future standard for different language independent applications.

Adherence to treatment in children and adolescents with cystic fibrosis:a cross-sectional, multi-method study investigating the influence of beliefs about treatment and parental depressive symptoms

Background: Adherence to treatment is often reported to be low in children with cystic fibrosis. Adherence in cystic fibrosis is an important research area and more research is needed to better understand family barriers to adherence in order for clinicians to provide appropriate intervention. The aim of this study was to evaluate adherence to enzyme supplements, vitamins and chest physiotherapy in children with cystic fibrosis and to determine if any modifiable risk factors are associated with adherence. Methods: A sample of 100 children (≤18 years) with cystic fibrosis (44 male; median [range] 10.1 [0.2-18.6] years) and their parents were recruited to the study from the Northern Ireland Paediatric Cystic Fibrosis Centre. Adherence to enzyme supplements, vitamins and chest physiotherapy was assessed using a multi-method approach including; Medication Adherence Report Scale, pharmacy prescription refill data and general practitioner prescription issue data. Beliefs about treatments were assessed using refined versions of the Beliefs about Medicines Questionnaire-specific. Parental depressive symptoms were assessed using the Center for Epidemiologic Studies Depression Scale. Results: Using the multi-method approach 72% of children were classified as low-adherers to enzyme supplements, 59% low-adherers to vitamins and 49% low-adherers to chest physiotherapy. Variations in adherence were observed between measurement methods, treatments and respondents. Parental necessity beliefs and child age were significant independent predictors of child adherence to enzyme supplements and chest physiotherapy, but parental depressive symptoms were not found to be predictive of adherence. Conclusions: Child age and parental beliefs about treatments should be taken into account by clinicians when addressing adherence at routine clinic appointments. Low adherence is more likely to occur in older children, whereas, better adherence to cystic fibrosis therapies is more likely in children whose parents strongly believe the treatments are necessary. The necessity of treatments should be reinforced regularly to both parents and children.

Teaching our children when to eat:how parental feeding practices inform the development of emotional eating-a longitudinal experimental design

Background: Emotional eating in children has been related to the consumption of energy-dense foods and obesity, but the development of emotional eating in young children is poorly understood. Objectives: We evaluated whether emotional eating can be induced in 5-7-y-old children in the laboratory and assessed whether parental use of overly controlling feeding practices at 3-5 y of age predicts a greater subsequent tendency for children to eat under conditions of mild stress at ages 5-7 y. Design: Forty-one parent-child dyads were recruited to participate in this longitudinal study, which involved parents and children being observed consuming a standard lunch, completing questionnaire measures of parental feeding practices, participating in a research procedure to induce child emotion (or a control procedure), and observing children's consumption of snack foods. Results: Children at ages 5-7 y who were exposed to a mild emotional stressor consumed significantly more calories from snack foods in the absence of hunger than did children in a control group. Parents who reported the use of more food as a reward and restriction of food for health reasons with their children at ages 3-5 y were more likely to have children who ate more under conditions of negative emotion at ages 5-7 y. Conclusions: Parents who overly control children's food intake may unintentionally teach children to rely on palatable foods to cope with negative emotions. Additional research is needed to evaluate the implications of these findings for children's food intake and weight outside of the laboratory setting. This trial was registered at clinicaltrials.gov as NCT01122290.

Integral Representations of Generalized Mathieu Series Via Mittag-Leffler Type Functions

Mathematics Subject Classification: 33C05, 33C10, 33C20, 33C60, 33E12, 33E20, 40A30

Representations of Inverse Functions by the Integral Transform with the Sign Kernel

Mathematics Subject Classification: Primary 30C40

Integral Representations of the Logarithmic Derivative of the Selberg Zeta Function

AMS Subj. Classification: MSC2010: 11F72, 11M36, 58J37

One's own country and familiar places in the mind's eye:different topological representations for navigational and non-navigational contents

Visual mental imagery is a process that draws on different cognitive abilities and is affected by the contents of mental images. Several studies have demonstrated that different brain areas subtend the mental imagery of navigational and non-navigational contents. Here, we set out to determine whether there are distinct representations for navigational and geographical images. Specifically, we used a Spatial Compatibility Task (SCT) to assess the mental representation of a familiar navigational space (the campus), a familiar geographical space (the map of Italy) and familiar objects (the clock). Twenty-one participants judged whether the vertical or the horizontal arrangement of items was correct. We found that distinct representational strategies were preferred to solve different categories on the SCT, namely, the horizontal perspective for the campus and the vertical perspective for the clock and the map of Italy. Furthermore, we found significant effects due to individual differences in the vividness of mental images and in preferences for verbal versus visual strategies, which selectively affect the contents of mental images. Our results suggest that imagining a familiar navigational space is somewhat different from imagining a familiar geographical space. © 2014 Elsevier Ireland Ltd.

Parental confidence in managing food allergy:development of the Food Allergy Self-Efficacy Scale for parents (FASE-P)

Background: Food allergy is often a life-long condition that requires constant vigilance in order to prevent accidental exposure and avoid potentially life-threatening symptoms. Parents’ confidence in managing their child’s food allergy may relate to the poor quality of life anxiety and worry reported by parents of food allergic children. Objective: The aim of the current study was to develop and validate the first scale to measure parental confidence (self-efficacy) in managing food allergy in their child. Methods: The Food Allergy Self-Efficacy Scale for Parents (FASE-P) was developed through interviews with 53 parents, consultation of the literature and experts in the area. The FASE-P was then completed by 434 parents of food allergic children from a general population sample in addition to the General Self-Efficacy Scale (GSES), the Food Allergy Quality of Life Parental Burden Scale (FAQL-PB), the General Health Questionnaire (GHQ12) and the Food Allergy Impact Measure (FAIM). A total of 250 parents completed the re-test of the FASE-P. Results: Factor and reliability analysis resulted in a 21 item scale with 5 sub-scales. The overall scale and sub-scales has good to excellent internal consistency (α’s of 0.63-0.89) and the scale is stable over time. There were low to moderate significant correlations with the GSES, FAIM and GHQ12 and strong correlations with the FAQL-PB, with better parental confidence relating to better general self-efficacy, better quality of life and better mental health in the parent. Poorer self-efficacy was related to egg and milk allergy; self-efficacy was not related to severity of allergy. Conclusions and clinical relevance: The FASE-P is a reliable and valid scale for use with parents from a general population. Its application within clinical settings could aid provision of advice and improve targeted interventions by identifying areas where parents have less confidence in managing their child’s food allergy.

How different are the visual representations used for object recognition in middle childhood and adulthood?

Recent experimental studies have shown that development towards adult performance levels in configural processing in object recognition is delayed through middle childhood. Whilst partchanges to animal and artefact stimuli are processed with similar to adult levels of accuracy from 7 years of age, relative size changes to stimuli result in a significant decrease in relative performance for participants aged between 7 and 10. Two sets of computational experiments were run using the JIM3 artificial neural network with adult and 'immature' versions to simulate these results. One set progressively decreased the number of neurons involved in the representation of view-independent metric relations within multi-geon objects. A second set of computational experiments involved decreasing the number of neurons that represent view-dependent (nonrelational) object attributes in JIM3's Surface Map. The simulation results which show the best qualitative match to empirical data occurred when artificial neurons representing metric-precision relations were entirely eliminated. These results therefore provide further evidence for the late development of relational processing in object recognition and suggest that children in middle childhood may recognise objects without forming structural description representations.