Mixed-state localization operators: Cohen's class and trace class operators

We study mixed-state localization operators from the perspective of Werner's operator convolutions which allows us to extend known results from the rank-one case to trace class operators. The idea of localizing a signal to a domain in phase space is approached from various directions such as bounds on the spreading function, probability densities associated to mixed-state localization operators, positive operator valued measures, positive correspondence rules and variants of Tauberian theorems for operator translates. Our results include a rigorous treatment of multiwindow-STFT filters and a characterization of mixed-state localization operators as positive correspondence rules. Furthermore, we provide a description of the Cohen class in terms of Werner's convolution of operators and deduce consequences on positive Cohen class distributions, an uncertainty principle, uniqueness and phase retrieval for general elements of Cohen's class.Comment: We call generalized localization operators now mixed-state localization operators. In addition to a change of title and other parts involving generalized localization operators. We did a major revision of the manuscript incorporating suggestions by reviewer

On accumulated Cohen's class distributions and mixed-state localization operators

Recently we introduced mixed-state localization operators associated to a density operator and a (compact) domain in phase space. We continue the investigations of their eigenvalues and eigenvectors. Our main focus is the definition of a time-frequency distribution which is based on the Cohen class distribution associated to the density operator and the eigenvectors of the mixed-state localization operator. This time-frequency distribution is called the accumulated Cohen class distribution. If the trace class operator is a rank-one operator, then the mixed-state localization operators and the accumulated Cohen class distribution reduce to Daubechies' localization operators and the accumulated spectrogram. We extend all the results about the accumulated spectrogram to the accumulated Cohen class distribution. The techniques used in the case of spectrograms cannot be adapted to other distributions in Cohen's class since they rely on the reproducing kernel property of the short-time Fourier transform. Our approach is based on quantum harmonic analysis on phase space which also provides the tools and notions to introduce the analogues of the accumulated spectrogram for mixed-state localization operators; the accumulated Cohen's class distributions

Quantum harmonic analysis on lattices and Gabor multipliers

We develop a theory of quantum harmonic analysis on lattices in $\mathbb{R}^{2d}$. Convolutions of a sequence with an operator and of two operators are defined over a lattice, and using corresponding Fourier transforms of sequences and operators we develop a version of harmonic analysis for these objects. We prove analogues of results from classical harmonic analysis and the quantum harmonic analysis of Werner, including Tauberian theorems and a Wiener division lemma. Gabor multipliers from time-frequency analysis are described as convolutions in this setting. The quantum harmonic analysis is thus a conceptual framework for the study of Gabor multipliers, and several of the results include results on Gabor multipliers as special cases.Comment: 36 pages. Second version: Minor changes, some added references. Accepted for publication in Journal of Fourier Analysis and Application

Fysisk aktiv læring som undervisningsmetode i vidaregåande skule.

Bakgrunn: Fysisk aktivitet har vist å vera viktig for kognitive funksjonar. I overgangen mellom barn og ungdom fell aktivitetsnivået drastisk, og ein gjennomsnittleg 15 åring sit/ligg mellom 17-19 timar i døgnet (Helsedirektoratet, 2019). Ein meir aktiv skulekvardagen kan derfor potensielt bidra til å auke kognitive funksjonar, og med det læringsutbytte blant norske ungdommar. Fysisk aktiv læring er ein læringsmetode som kombinerer fysisk aktivitet og teoretiske skulefag (Watson et al. 2017). Hensikt med denne studien er å finne ut korleis elevar i vidaregåande skule opplever at fysisk aktiv læring påverkar deira læringsutbytte. Metode: Deltakarane i studien består av 15 elevar i vidaregåande skule. Desse elevane deltok i to ulike økter med fysisk aktiv læring som undervisningsmetode. I etterkant av begge øktene gav kvar elev ei individuell tilbakemelding på si oppleving av økta, ved å svare på eit digitalt spørjeskjema. Etter siste økt deltok seks av desse elevane i fokusgruppeintervju. Dette for å grundigare utdjupe korleis fysisk aktiv læring hadde påverking deira opplevde læringsutbytte. Data frå både spørjeskjema og fokusgruppeintervju vart analysert ved hjelp av tematisert analyse. Funn vart kategorisert, og data frå både spørjeskjema og fokusgruppeintervju vart samordna. Resultat: Funn gjort i studien viser at elevar i vidaregåande skule opplever at bruk av fysisk aktiv læring har ei positiv innverking på deira læringsutbytte. Elevane viser til ei oppleving av auka motivasjon, konsentrasjon, variasjon, gode meistringsopplevingar og betre læringsmiljø i klassen når fysisk aktiv læring vert nytta som undervisningsmetode. Konklusjon: Bruk av fysisk aktiv læring i vidaregåande skule, kan vera eit nyttig tiltak for å auke elevane sitt opplevde læringsutbytte.Background: Physical activity has been shown to be important for cognitive functions. An average 15-year-old sits/lies between 17-19 hours a day (Directorate of Health, 2019). A more active schoolday can therefore potentially contribute in increasing cognitive functions, and with that influence the learning outcome among Norwegian students. Physically active learning is a learning method that combines physical activity and theoretical knowlegde (Watson et al. 2017). The purpose of this study is to find how students in high school experience how physical active learning affects their learning outcomes. Method: The participants in the study consist of 15 students in high school. These students participated in two different sessions with physically active learning as a teaching method. After both sessions each student gave individual feedback on their experience of the session, by answering a digital questionnaire. After the last session, six of the students took part in a focus group interview. This in order to elaborate more thoroughly how physically active learning had an impact on their perceived learning outcome. Data from both the questionnaire and focus group interview were analyzed using thematization analysis. Findings were categorized, and data from both questionnaires and focus group interviews were coordinated. Result: Findings made in the study show that students in high school experience that the use of physical active learning has a positive impact on their learning outcome. The students refer to an experience of increased motivation, concentration, variety, self-efficacy and a better learning environment, when physically active learning is used as a teaching method. Conclusion: Use of physically active learning in hich school can be a useful teaching method to increase the students perceived learning outcomes

Time-Frequency Analysis and Coorbit Spaces of Operators

We introduce an operator valued Short-Time Fourier Transform for certain classes of operators with operator windows, and show that the transform acts in an analogous way to the Short-Time Fourier Transform for functions, in particular giving rise to a family of vector-valued reproducing kernel Banach spaces, the so called coorbit spaces, as spaces of operators. As a result of this structure the operators generating equivalent norms on the function modulation spaces are fully classified. We show that these operator spaces have the same atomic decomposition properties as the function spaces, and use this to give a characterisation of the spaces using localisation operators

Cohort profile: the Norwegian Registry of Persons Assessed for Cognitive Symptoms (NorCog) - a national research and quality registry with a biomaterial collection

Purpose: The Norwegian Registry of Persons Assessed for Cognitive Symptoms (NorCog) was established to harmonise and improve the quality of diagnostic practice across clinics assessing persons with cognitive symptoms in Norwegian specialist healthcare units and to establish a large research cohort with extensive clinical data. Participants: The registry recruits patients who are referred for assessment of cognitive symptoms and suspected dementia at outpatient clinics in Norwegian specialist healthcare units. In total, 18 120 patients have been included in NorCog during the period of 2009–2021. The average age at inclusion was 73.7 years. About half of the patients (46%) were diagnosed with dementia at the baseline assessment, 35% with mild cognitive impairment and 13% with no or subjective cognitive impairment; 7% received other specified diagnoses such as mood disorders. Findings to date: All patients have a detailed baseline characterisation involving lifestyle and demographic variables; activities of daily living; caregiver situation; medical history; medication; psychiatric, physical and neurological examinations; neurocognitive testing; blood laboratory work-up; and structural or functional brain imaging. Diagnoses are set according to standardised diagnostic criteria. The research biobank stores DNA and blood samples from 4000 patients as well as cerebrospinal fluid from 800 patients. Data from NorCog have been used in a wide range of research projects evaluating and validating dementia-related assessment tools, and identifying patient characteristics, symptoms, functioning and needs, as well as caregiver burden and requirement of available resources. Future plans: The finish date of NorCog was originally in 2029. In 2021, the registry’s legal basis was reformalised and NorCog got approval to collect and keep data for as long as is necessary to achieve the purpose of the registry. In 2022, the registry underwent major changes. Paper-based data collection was replaced with digital registration, and the number of variables collected was reduced. Future plans involve expanding the registry to include patients from primary care centres.publishedVersio