Quasisymmetric Schur functions

We introduce a new basis for quasisymmetric functions, which arise from a specialization of nonsymmetric Macdonald polynomials to standard bases, also known as Demazure atoms. Our new basis is called the basis of quasisymmetric Schur functions, since the basis elements refine Schur functions in a natural way. We derive expansions for quasisymmetric Schur functions in terms of monomial and fundamental quasisymmetric functions, which give rise to quasisymmetric refinements of Kostka numbers and standard (reverse) tableaux. From here we derive a Pieri rule for quasisymmetric Schur functions that naturally refines the Pieri rule for Schur functions. After surveying combinatorial formulas for Macdonald polynomials, including an expansion of Macdonald polynomials into fundamental quasisymmetric functions, we show how some of our results can be extended to include the $t$ parameter from Hall-Littlewood theory.Comment: 30 pages; references added; new subsections on transition matrices, how to include the $t$ parameter from Hall-Littlewood theory and further avenues; new survey of combinatorial formulas for Macdonald polynomials, including an expansion of Macdonald polynomials into fundamental quasisymmetric function

Criteria voor goed rechtswetenschappelijk onderzoek. De omgekeerde route

FdR – Publicaties niet-programma gebonde

How is precision regulated in maintaining trunk posture?

Precision of limb control is associated with increased joint stiffness caused by antagonistic co-activation. The aim of this study was to examine whether this strategy also applies to precision of trunk postural control. To this end, thirteen subjects performed static postural tasks, aiming at a target object with a cursor that responded to 2D trunk angles. By manipulating target dimensions, different levels of precision were imposed in the frontal and sagittal planes. Trunk angle and electromyography (EMG) of abdominal and back muscles were recorded. Repeated measures ANOVAs revealed significant effects of target dimensions on kinematic variability in both movement planes. Specifically, standard deviation (SD) of trunk angle decreased significantly when target size in the same direction decreased, regardless of the precision demands in the other direction. Thus, precision control of trunk posture was directionally specific. However, no consistent effect of precision demands was found on trunk muscle activity, when averaged over time series. Therefore, it was concluded that stiffness regulation by antagonistic co-activation was not used to meet increased precision demands in trunk postural control. Instead, results from additional analyses suggest that precision of trunk angle was controlled in a feedback mode

Comparing lumbo-pelvic kinematics in people with and without back pain: A systematic review and meta-analysis

Background: Clinicians commonly examine posture and movement in people with the belief that correcting dysfunctional movement may reduce pain. If dysfunctional movement is to be accurately identified, clinicians should know what constitutes normal movement and how this differs in people with low back pain (LBP). This systematic review examined studies that compared biomechanical aspects of lumbo-pelvic movement in people with and without LBP. Methods. MEDLINE, Cochrane Central, EMBASE, AMI, CINAHL, Scopus, AMED, ISI Web of Science were searched from inception until January 2014 for relevant studies. Studies had to compare adults with and without LBP using skin surface measurement techniques to measure lumbo-pelvic posture or movement. Two reviewers independently applied inclusion and exclusion criteria, and identified and extracted data. Standardised mean differences and 95% confidence intervals were estimated for group differences between people with and without LBP, and where possible, meta-analyses were performed. Within-group variability in all measurements was also compared. Results: The search identified 43 eligible studies. Compared to people without LBP, on average, people with LBP display: (i) no difference in lordosis angle (8 studies), (ii) reduced lumbar ROM (19 studies), (iii) no difference in lumbar relative to hip contribution to end-range flexion (4 studies), (iv) no difference in standing pelvic tilt angle (3 studies), (v) slower movement (8 studies), and (vi) reduced proprioception (17 studies). Movement variability appeared greater for people with LBP for flexion, lateral flexion and rotation ROM, and movement speed, but not for other movement characteristics. Considerable heterogeneity exists between studies, including a lack of detail or standardization between studies on the criteria used to define participants as people with LBP (cases) or without LBP (controls). Conclusions: On average, people with LBP have reduced lumbar ROM and proprioception, and move more slowly compared to people without LBP. Whether these deficits exist prior to LBP onset is unknown

Casuïstiek en scherpe normen in het materiële strafrecht

In het artikel wordt betoogd dat casuïstische rechtspraak een geëigende manier kan zijn om evenwicht te bereiken tussen het belang van rechtszekerheid en het belang van geïndividualiseerde (bewijs)motiveringen. De met enige regelmaat geuite onvrede over het gebrek aan scherpe(re) regels in de jurisprudentie van de Hoge Raad is daarom voor een belangrijk deel misplaatst. Van de Hoge Raad moet niet zozeer worden verwacht dat hij invulling geeft aan zijn rechtsvormende taak door nieuwe, scherpe regels op te stellen. Het gaat er vooral om dat hij zoveel mogelijk duidelijkheid verschaft over de (ir)relevantie van de specifieke omstandigheden die feitenrechters aandragen ter onderbouwing van hun oordelen

Skew quasisymmetric Schur functions and noncommutative Schur functions

AbstractRecently a new basis for the Hopf algebra of quasisymmetric functions QSym, called quasisymmetric Schur functions, has been introduced by Haglund, Luoto, Mason, van Willigenburg. In this paper we extend the definition of quasisymmetric Schur functions to introduce skew quasisymmetric Schur functions. These functions include both classical skew Schur functions and quasisymmetric Schur functions as examples, and give rise to a new poset LC that is analogous to Young's lattice. We also introduce a new basis for the Hopf algebra of noncommutative symmetric functions NSym. This basis of NSym is dual to the basis of quasisymmetric Schur functions and its elements are the pre-image of the Schur functions under the forgetful map χ:NSym→Sym. We prove that the multiplicative structure constants of the noncommutative Schur functions, equivalently the coefficients of the skew quasisymmetric Schur functions when expanded in the quasisymmetric Schur basis, are nonnegative integers, satisfying a Littlewood–Richardson rule analogue that reduces to the classical Littlewood–Richardson rule under χ.As an application we show that the morphism of algebras from the algebra of Poirier–Reutenauer to Sym factors through NSym. We also extend the definition of Schur functions in noncommuting variables of Rosas–Sagan in the algebra NCSym to define quasisymmetric Schur functions in the algebra NCQSym. We prove these latter functions refine the former and their properties, and project onto quasisymmetric Schur functions under the forgetful map. Lastly, we show that by suitably labeling LC, skew quasisymmetric Schur functions arise in the theory of Pieri operators on posets