Two-Point Statistics of Statistically Self-Similar Cascades

The classical multifractal analysis is extented to higher orders in order to study the second order correlations existing between local dimensions of a class of random self-similar measures (in the sense of Arbeiter and Patzschke). Statistiques de deuxi`eme ordre sur une classe de mesures al'eatoires auto-similaires R'esum'e L'analyse multifractale classique est 'etendue aux ordres sup'erieurs afin d"etudier les corr'elations de second ordre entre les dimensions locales d'une classe de mesures al'eatoires auto-similaires (au sens de Arbeiter et Patzschke) Version fran¸caise abr'eg'ee On consid`ere une mesure ¯ (d'eterministe ou non) positive et d'efinie sur [0; 1). Soient b; n deux entiers, b 2. On consid`ere l'ensemble \Sigma n = f0; : : : ; b \Gamma 1g n et \Sigma ? = S n \Sigma n l'ensemble des mots de longueur finie. Pour tout 0 i ! b, on note oe ? i la conccat'enation du mot oe et de la lettre i (dans cet ordre). Pour n donn'e, l'intervalle [0; 1) est partitionn'e en b n..

E-assessment: past, present and future

This review of e-assessment takes a broad definition, including any use of a computer in assessment, whilst focusing on computer-marked assessment. Drivers include increased variety of assessed tasks and the provision of instantaneous feedback, as well as increased objectivity and resource saving. From the early use of multiple-choice questions and machine-readable forms, computer-marked assessment has developed to encompass sophisticated online systems, which may incorporate interoperability and be used in students’ own homes. Systems have been developed by universities, companies and as part of virtual learning environments. Some of the disadvantages of selected-response question types can be alleviated by techniques such as confidence-based marking. The use of electronic response systems (‘clickers’) in classrooms can be effective, especially when coupled with peer discussion. Student authoring of questions can also encourage dialogue around learning. More sophisticated computer-marked assessment systems have enabled mathematical questions to be broken down into steps and have provided targeted and increasing feedback. Systems that use computer algebra and provide answer matching for short-answer questions are discussed. Computer-adaptive tests use a student’s response to previous questions to alter the subsequent form of the test. More generally, e-assessment includes the use of peer-assessment and assessed e-portfolios, blogs, wikis and forums. Predictions for the future include the use of e-assessment in MOOCs (massive open online courses); the use of learning analytics; a blurring of the boundaries between teaching, assessment and learning; and the use of e-assessment to free human markers to assess what they can assess more authentically