Optimal Hankel Norm Model Reduction by Truncation of Trajectories

We show how optimal Hankel-norm approximations of dynamical systems allow for a straightforward interpretation in terms of system trajectories. It is shown that for discrete time single-input systems optimal reductions are obtained by cutting 'balanced trajectories', i.e., by disconnecting the past and future in the input-output pairs relating to left- and right singular vectors of the system. A self-contained proof of optimality is given, and formulas are derived in terms of Faddeev sequences. Some parallels with the literature are briefly indicated.Optimal Hankel norm approximation;Balancing;Linear systems;l2-systems;Faddeev sequences

Wilson ratio in Yb-substituted CeCoIn5

We have investigated the effect of Yb substitution on the Pauli limited, heavy fermion superconductor, CeCoIn$_5$. Yb acts as a non-magnetic divalent substituent for Ce throughout the entire doping range, equivalent to hole doping on the rare earth site. We found that the upper critical field in (Ce,Yb)CoIn$_5$ is Pauli limited, yet the reduced (H,T) phase diagram is insensitive to disorder, as expected in the purely orbitally limited case. We use the Pauli limiting field, the superconducting condensation energy and the electronic specific heat coefficient to determine the Wilson ratio ($R_{W}$), the ratio of the specific heat coefficient to the Pauli susceptibility in CeCoIn$_5$. The method is applicable to any Pauli limited superconductor in the clean limit.Comment: 5 pages, 1 table, 4 figure

Dysflective cones: Visual function and cone reflectivity in long-term follow-up of acute bilateral foveolitis.

PURPOSE:Confocal adaptive optics scanning laser ophthalmoscope (AOSLO) images provide a sensitive measure of cone structure. However, the relationship between structural findings of diminished cone reflectivity and visual function is unclear. We used fundus-referenced testing to evaluate visual function in regions of apparent cone loss identified using confocal AOSLO images. METHODS:A patient diagnosed with acute bilateral foveolitis had spectral-domain optical coherence tomography (SD-OCT) (Spectralis HRA + OCT system [Heidelberg Engineering, Vista, CA, USA]) images indicating focal loss of the inner segment-outer segment junction band with an intact, but hyper-reflective, external limiting membrane. Five years after symptom onset, visual acuity had improved from 20/80 to 20/25, but the retinal appearance remained unchanged compared to 3 months after symptoms began. We performed structural assessments using SD-OCT, directional OCT (non-standard use of a prototype on loan from Carl Zeiss Meditec) and AOSLO (custom-built system). We also administered fundus-referenced functional tests in the region of apparent cone loss, including analysis of preferred retinal locus (PRL), AOSLO acuity, and microperimetry with tracking SLO (TSLO) (prototype system). To determine AOSLO-corrected visual acuity, the scanning laser was modulated with a tumbling E consistent with 20/30 visual acuity. Visual sensitivity was assessed in and around the lesion using TSLO microperimetry. Complete eye examination, including standard measures of best-corrected visual acuity, visual field tests, color fundus photos, and fundus auto-fluorescence were also performed. RESULTS:Despite a lack of visible cone profiles in the foveal lesion, fundus-referenced vision testing demonstrated visual function within the lesion consistent with cone function. The PRL was within the lesion of apparent cone loss at the fovea. AOSLO visual acuity tests were abnormal, but measurable: for trials in which the stimulus remained completely within the lesion, the subject got 48% correct, compared to 78% correct when the stimulus was outside the lesion. TSLO microperimetry revealed reduced, but detectible, sensitivity thresholds within the lesion. CONCLUSIONS AND IMPORTANCE:Fundus-referenced visual testing proved useful to identify functional cones despite apparent photoreceptor loss identified using AOSLO and SD-OCT. While AOSLO and SD-OCT appear to be sensitive for the detection of abnormal or absent photoreceptors, changes in photoreceptors that are identified with these imaging tools do not correlate completely with visual function in every patient. Fundus-referenced vision testing is a useful tool to indicate the presence of cones that may be amenable to recovery or response to experimental therapies despite not being visible on confocal AOSLO or SD-OCT images

Teacher learning in a Lesson Study team: a case study

Doel van deze exploratieve casestudie is om inzicht te krijgen in de rol van persoonlijke, interpersoonlijke en contextfactoren bij verschillen in opbrengsten tussen docenten in een Lesson Studyteam. Dit gebeurt aan de hand van een conceptueel model waarin de Reasoned Action Approach (RAA) van Fishbein (2008) en het padmodel voor het leren van docenten van Lewis, Perry en Hurd (2009a) zijn gecombineerd. Bij vijf wiskundedocenten die gezamenlijk gedurende een schooljaar twee Lesson Studycycli hebben doorlopen, zijn via vragenlijsten, interviews en observaties data verzameld. Alle docenten rapporteren opbrengsten, waarbij er verschillen zijn tussen docenten in concreetheid van benoemen van opbrengsten en geobserveerde doorwerking in de eigen onderwijspraktijk. Deze verschillen lijken vooral een relatie te hebben met de intentie om aan Lesson Study deel te nemen. Deze casestudie draagt bij aan een groter inzicht in opbrengsten die Lesson Study voor docenten kan hebben en de rol die genoemde factoren daarbij kunnen hebben. Voor de praktijk lijkt het van belang om bij invoering van Lesson Study expliciet rekening te houden met de intentie van docenten om eraan te gaan deelnemen