About the maximal rank of 3-tensors over the real and the complex number field

High dimensional array data, tensor data, is becoming important in recent days. Then maximal rank of tensors is important in theory and applications. In this paper we consider the maximal rank of 3 tensors. It can be attacked from various viewpoints, however, we trace the method of Atkinson-Stephens(1979) and Atkinson-Lloyd(1980). They treated the problem in the complex field, and we will present various bounds over the real field by proving several lemmas and propositions, which is real counterparts of their results.Comment: 13 pages, no figure v2: correction and improvemen

Some light-traffic and heavy-traffic results for the GI/G/n/0 queue using the GM Heuristic

Проаналізовано ймовірность втрати вимоги в багатоканальній системі обслуговування з відмовами GI/G/n/0 як у випадку малого навантаження, так і великого. Аналіз оснований на евристиці GM , для якої випадок помірного навантаження детально вивчено раніше. Знайдено достатні умови для асимптотичної точності евристики GM у випадку малого навантаження. Ця евристика має вказану властивість також у випадку великого навантаження, якщо число каналів n прямує до нескінченності.In this paper we carry out both light-traffic and heavy-traffic analyses for the calculation of steady-state loss probabilities in the general multi-server queueing loss system, the GI /G/n/0 queue. The analysis makes use of a heuristic approach called the GM Heuristic, for which a detailed analysis in normal traffic has previously been published. Sufficient conditions are given for the GM Heuristic to be asymptotically exact in light traffic. The heuristic is also shown to be asymptotically exact in heavy-traffic when the number of servers n tends to infinity. These results are illustrated numerically using two-phase Coxian distributions for both the inter-arrival time and service time

Regularization-independent study of renormalized non-perturbative quenched QED

A recently proposed regularization-independent method is used for the first time to solve the renormalized fermion Schwinger-Dyson equation numerically in quenched QED$_4$. The Curtis-Pennington vertex is used to illustrate the technique and to facilitate comparison with previous calculations which used the alternative regularization schemes of modified ultraviolet cut-off and dimensional regularization. Our new results are in excellent numerical agreement with these, and so we can now conclude with confidence that there is no residual regularization dependence in these results. Moreover, from a computational point of view the regularization independent method has enormous advantages, since all integrals are absolutely convergent by construction, and so do not mix small and arbitrarily large momentum scales. We analytically predict power law behaviour in the asymptotic region, which is confirmed numerically with high precision. The successful demonstration of this efficient new technique opens the way for studies of unquenched QED to be undertaken in the near future.Comment: 20 pages,5 figure

Developing and validating a school-based screening tool of Fundamental Movement Skills (FUNMOVES) using Rasch analysis

Background A large proportion of children are not able to perform age-appropriate fundamental movement skills (FMS). Thus, it is important to assess FMS so that children needing additional support can be identified in a timely fashion. There is great potential for universal screening of FMS in schools, but research has established that current assessment tools are not fit for purpose. Objective To develop and validate the psychometric properties of a FMS assessment tool designed specifically to meet the demands of universal screening in schools. Methods A working group consisting of academics from developmental psychology, public health and behavioural epidemiology developed an assessment tool (FUNMOVES) based on theory and prior evidence. Over three studies, 814 children aged 4 to 11 years were assessed in school using FUNMOVES. Rasch analysis was used to evaluate structural validity and modifications were then made to FUNMOVES activities after each study based on Rasch results and implementation fidelity. Results The initial Rasch analysis found numerous psychometric problems including multidimensionality, disordered thresholds, local dependency, and misfitting items. Study 2 showed a unidimensional measure, with acceptable internal consistency and no local dependency, but that did not fit the Rasch model. Performance on a jumping task was misfitting, and there were issues with disordered thresholds (for jumping, hopping and balance tasks). Study 3 revealed a unidimensional assessment tool with good fit to the Rasch model, and no further issues, once jumping and hopping scoring were modified.Implications The finalised version of FUNMOVES (after three iterations) meets standards for accurate measurement, is free and able to assess a whole class in under an hour using resources available in schools. Thus FUNMOVES has the potential to allow schools to efficiently screen FMS to ensure that targeted support can be provided and disability barriers removed.</p

Developing and implementing a school-led motor intervention for children with handwriting difficulties

We describe the development of an evidence-based motor intervention and an implementation pilot study in ten primary schools, involving 515 children (4–11 years). ‘Helping Handwriting SHINE’ (HHS) is a novel, school-led, group-based handwriting intervention. Teaching staff delivered HHS and provided feedback through a questionnaire, reporting that: (i) the children found the tasks enjoyable; (ii) the background and booklet instructions were easy to understand, (iii) there was a need for more comprehensive staff training. The teaching staff made recommendations about session duration, group size, resource availability, and age differentiation of tasks. These suggestions are applicable to the development of any school-based group-led motor intervention, and we used this feedback to refine the HHS intervention. This study shows that implementing school-led motor interventions at scale is possible. Moreover, the work provides insights into the factors to consider when developing school-based motor interventions prior to conducting randomized controlled trials (RCT). The process outlined in this manuscript has led to an RCT to test the effectiveness of HHS within primary schools.</p

Non-western contexts: the invisible half

Like many other disciplines within the broad area of social sciences (e.g., anthropology, gender studies, psychology, sociology, etc.), consumer research is also highly navigated by scholars from Western countries. This, however, does not mean, by any means, that consumer research is devoted to studying Western contexts only. As evident from the ever-increasing number of regional conferences (e.g., Asia-Pacific and Latin American conferences of the Association for Consumer Research) and non-Western students' enrolment in doctoral programs at Western universities, there are many more researchers (from non-Western countries) who are entering the field and enriching it by their colourful contributions. Yet, given the low number of publications on consumer research in non-Western contexts, it seems that our current knowledge in these societies has a long way to go to flourish. More specifically, and in the domain of consumption culture research, this gap is even further widened by the fact that the culture of consumption in such contexts is largely interpreted with reference to the 'grand narratives' of Western scholars (e.g., Foucault, Mafessoli, Bourdieu, Deleuze, Baudrillard, Nietzsche, Durkheim, Derrida, etc.). Therefore, from an ontological perspective, it seems that our existing knowledge about non-Western societies lies heavily on the 'theoretical structures' that are 'constructed' by Western philosophy as a set of ideas, beliefs, and practices (Said, 1978). As Belk (1995) reminds us, consumption culture always existed in all human societies. What makes contemporary societies different from that of our predecessors' is not the fact that consumption culture did not exist in those societies, but that consumption culture has become a prevailing feature in modern society (Slater, 1997; Lury, 1996; Fırat and Venkatesh, 1995; McCracken, 1988). Therefore, the nature and dynamics of consumption culture in each society should be studied not only against the sociocultural, historical, and economic background of a given context (Western or non-Western) but also with reference to the philosophical and epistemological viewpoints that analyse and interpret cultural practices of that society from within that culture. Addressing such issues, this paper discusses some of the key reasons for lack of theory development in the field from non-western contexts. The paper invites scholars in non-Western contexts to introduce the less articulated, and sometime hidden, body of knowledge from their own contexts into the field of marketing in general and consumer research in particular

Bringing closure: towards achieving a better understanding of Israel

We wholeheartedly endorse Richard Horton’s timely Comment, in which he addresses the global rise of anti-Semitism particularly evident in Europe and the USA. Horton stresses the need to educate medical students and health-care professionals of the evil and disastrous consequences of ignoring the historical reality of the Holocaust. It will remind the world, 75 years on, that the call Never Again remains highly relevant

Color Transparency versus Quantum Coherence in Electroproduction of Vector Mesons off Nuclei

So far no theoretical tool for the comprehensive description of exclusive electroproduction of vector mesons off nuclei at medium energies has been developed. We suggest a light-cone QCD formalism which is valid at any energy and incorporates formation effects (color transparency), the coherence length and the gluon shadowing. At medium energies color transparency (CT) and the onset of coherence length (CL) effects are not easily separated. Indeed, although nuclear transparency measured by the HERMES experiment rises with Q^2, it agrees with predictions of the vector dominance model (VDM) without any CT effects. Our new results and observations are: (i) the good agreement with the VDM found earlier is accidental and related to the specific correlation between Q^2 and CL for HERMES kinematics; (ii) CT effects are much larger than have been estimated earlier within the two channel approximation. They are even stronger at low than at high energies and can be easily identified by HERMES or at JLab; (iii) gluon shadowing which is important at high energies is calculated and included; (iv) our parameter-free calculations explain well available data for variation of nuclear transparency with virtuality and energy of the photon; (v) predictions for electroproduction of \rho and \phi are provided for future measurements at HERMES and JLab.Comment: Latex 57 pages and 17 figure

Stellar structure and compact objects before 1940: Towards relativistic astrophysics

Since the mid-1920s, different strands of research used stars as "physics laboratories" for investigating the nature of matter under extreme densities and pressures, impossible to realize on Earth. To trace this process this paper is following the evolution of the concept of a dense core in stars, which was important both for an understanding of stellar evolution and as a testing ground for the fast-evolving field of nuclear physics. In spite of the divide between physicists and astrophysicists, some key actors working in the cross-fertilized soil of overlapping but different scientific cultures formulated models and tentative theories that gradually evolved into more realistic and structured astrophysical objects. These investigations culminated in the first contact with general relativity in 1939, when J. Robert Oppenheimer and his students George Volkoff and Hartland Snyder systematically applied the theory to the dense core of a collapsing neutron star. This pioneering application of Einstein's theory to an astrophysical compact object can be regarded as a milestone in the path eventually leading to the emergence of relativistic astrophysics in the early 1960s.Comment: 83 pages, 4 figures, submitted to the European Physical Journal

Microsimulation as a tool for evaluating redistribution policies

During the last twenty years, microsimulation models have been increasingly applied in qualitative and quantitative analysis of public policies. This paper provides a discussion on microsimulation techniques and their theoretical background as a tool for the analysis of public policies with particular attention to redistribution and social policies. Basic principles in using microsimulation models and interpreting their results are analyzed, with particular emphasis on tax incidence, redistribution and poverty analysis. Social welfare analysis permitted by microsimulation techniques is also discussed. Finally, the paper points to limits of present approaches and directions for future research.Au cours des vingt dernières années, l'utilisation des modèles de microsimulation des politiques de redistribution n'a cessé de croître. Cet article offre un rapide survol de ces modèles, l'accent étant mis sur les développements récents dans ce domaine de l'économie appliquée et sur quelques directions de recherche future