The law of large numbers for the free multiplicative convolution

In classical probability the law of large numbers for the multiplicative convolution follows directly from the law for the additive convolution. In free probability this is not the case. The free additive law was proved by D. Voiculescu in 1986 for probability measures with bounded support and extended to all probability measures with first moment by J. M. Lindsay and V. Pata in 1997, while the free multiplicative law was proved only recently by G. Tucci in 2010. In this paper we extend Tucci's result to measures with unbounded support while at the same time giving a more elementary proof for the case of bounded support. In contrast to the classical multiplicative convolution case, the limit measure for the free multiplicative law of large numbers is not a Dirac measure, unless the original measure is a Dirac measure. We also show that the mean value of \ln x is additive with respect to the free multiplicative convolution while the variance of \ln x is not in general additive. Furthermore we study the two parameter family (\mu_{\alpha,\beta})_{\alpha,\beta \ge 0} of measures on (0,\infty) for which the S-transform is given by S_{\mu_{\alpha,\beta}}(z) = (-z)^\beta (1+z)^{-\alpha}, 0 < z < 1.Comment: 27 pages; added references and corrected typo

Models of individual tree mortality for trembling aspen, lodgepole pine, hybrid spruce and subalpine fir in northwestern British Columbia

Density dependent mortality is an important process in forest succession. The overall predictive abilities of forest simulation models are closely related to their ability to predict mortality. Finding appropriate methods for modelling mortality have often proved to be a difficult challenge. The objective of this study was to test a method on adult trees, which was previously used for modelling density dependent mortality for saplings with good results. In the basic model mortality is predicted as a function of recent diameter growth. It was also tested if incorporating tree size into the mortality model improved it. Models were developed for four species: trembling aspen (Populus tremuloides Michx.), lodgepole pine (Pinus contorta Dougl. ex Loud. var. latifolia), hybrid spruce (a complex of white spruce (Picea glauca (Moench) Voss) and Engelmann spruce (Picea engelmanii Parry ex Engelm.)) and subalpine fir (Abies lasiocarpa (Hook.) Nutt.). The models were parameterized from field data using a maximum-likelihood method. Field data was gathered from 16 stands in the Sub-Boreal Spruce Zone in northwestern British Columbia and comprised of 337 live and 345 recently dead trees in total. The mortality models were tested by incorporating them into the individual tree, spatially explicit forest simulation model SORTIE-ND. SORTIE-ND simulations of single species even-aged stands were compared to simulations of a commonly used stand level simulation model. Furthermore, SORTIE-ND simulations of permanent sample plots in mixed species uneven-aged stands were compared to remeasurements of the plots. It was determined that incorporating tree size into the mortality models gave better fits to the field data. Tolerance to low growth decreases to a minimum at intermediate trees size for all species except for subalpine fir, where it decreases and remains low as trees growth larger. This is probably an effect of the ontogenetic characteristics of the individual species. Testing the mortality models in SORTIE-ND showed that they contribute to realistic thinning patterns in simulations of both pure even-aged stands and complex stands. However, it was evident that the performance of the mortality models is highly dependent on the underlying growth models as well as mortality models accounting for random mortality. Discrepancies in modelling results were linked to over- and underestimation of growth or inappropriate random mortality rates. Overall the tested method provides a straight forwards approach to parameterizing growth based mortality models from field data which is relatively easy to obtain.Naturlig avgång på grund av trängsel är en viktig process för den skogliga successionen. Generellt är förmågan hos modeller för skogssimulering att göra exakta prognoser nära relaterad till hur väl de hanterar självgallring. Att hitta en lämplig metod för att modellera självgallring har ofta visat sig vara en svår utmaning. Syftet med detta examensarbete var att testa en metod på vuxna träd (DBH > 5cm) som tidigare har använts för att modellera självgallring hos plantor med gott resultat. Basmodellen skattar sannolikheten för att ett enskilt träd ska dö på grund av självgallring som en funktion av de senaste årens diametertillväxt. Dessutom testades om självgallringsmodellerna potentiellt förbättrades genom att inkludera trädstorleken som oberoende variabel. Det utvecklades självgallringsmodeller för fyra olika trädslag: asp (Populus tremuloides Michx.), contortatall (Pinus contorta Dougl. ex Loud. var. latifolia), hybridgran (hybrider mellan vitgran (Picea glauca (Moench) Voss) och Engelmann-gran (Picea engelmanii Parry ex Engelm.)) och klippgran (Abies lasiocarpa (Hook.) Nutt.). Modellernas parametrar skattades med en maximum-likelihood metod från fältdata. Data insamlades i 16 bestånd i den sub-boreala gran zon i nordvästra British Columbia och består av totalt 337 levande och 345 nyligen döda träd. Självgallringsmodellerna testades i SORTIE-ND, en trädvis och avståndsberoende skogsproduktionsmodell. SORTIE-ND simuleringar av rena likåldriga bestånd jämfördes med simuleringar gjorda med en ofta använd beståndsbaserad skogsproduktionsmodell. Dessutom jämfördes SORTIE-ND simuleringar för permanenta provytor i olikåldriga blandbestånd med uppmätt utveckling på dessa provytor. Genom att inkludera individuell trädstorlek i basmodellen uppnåddes bättre anpassning till fältdata. Avgångsrisken vid låg tillväxt var minst för medelstora träd för alla trädslag förutom klippgran. För detta trädslag minskar avgångsrisken vid låg tillväxt kontinuerligt med ökad trädstorlek. Detta är en konsekvens av de enskilda trädslagens karakteristika. Självgallringsmodellerna bidrog till realistisk avgång i båda likåldriga och komplexa bestånd. Det är dock uppenbart att självgallringsmodellerna är väldigt beroende av de underliggande tillväxtmodellerna och modeller som uppskattar den stokastiska avgången i ett bestånd. Modellernas avvikelser är relaterade till över- eller underskattning av tillväxten och orealistiska nivåer på den stokastiska avgången. Den testade metoden är ett relativt enkelt sätt att härleda och estimera parametra till en tillväxtbaserad självgallringsmodell från fältdata. Dessutom är data relativt enkla att erhålla

Representativeness of personality and involvement preferences in a web-based survey on healthcare decision-making

Background: Obtaining a sample that is representative of the group of interest is of utmost importance in questionnaire studies. In a survey using a state authorized web-portal for citizen communication with authorities, we wanted to investigate the view of adult men on patient involvement in health care decision-making regarding Prostate-Specific Antigen test for prostatic cancer. In this paper, we report on sample characteristics and representativeness of our sample in terms of personality and baseline involvement preferences. Methods: We compared personality profiles (BFI-10) and baseline healthcare decision-making preferences (CPS) in our sample (n = 6756) to internationally available datasets. Pooled data from a) US, UK, Canada, Australia, and New Zealand (n = 1512), b) Germany, Netherlands, Switzerland, and Belgium (n = 1136), and c) Norway, Sweden, Finland, and Denmark (n = 1313) were used for BFI-10 comparisons. Regarding CPS, we compared our sample with three previous datasets relating to decision-making in cancer (n = 425, 387, and 199). Results: Although statistically significant differences particularly appeared in large dataset comparisons, sample BFI-10 and CPS profiles mostly were within the range of those previously reported. Similarity was greatest in BFI-10 comparisons with group a) where no statistically significant difference could be established in factors 'agreeableness' and 'neuroticism' (p = .095 and .578, respectively). Conclusion: Despite some variation, our sample displays personality and baseline preference profiles that are generally similar to those described in previous international studies. For example, this was the case with the BFI-10 'agreeableness' measure (incl. trust and fault-finding items), an important factor in healthcare decision-making

Injuries in male youth football: a one season prospective cohort study of 223 Danish elite players

ObjectivesThis study prospectively investigated injury prevalence, incidence, and burden in male elite under-17 football players (N = 223) during a full season.MethodsThe players weekly completed a standardized web-based injury survey (OSTRC-H2) and a physical exposure report throughout the study.ResultsAverage weekly response rate was 89.5%. Football exposure accounted for 52.4% of total physical exposure. On average (±SD), the players participated in individual football, strength, and rehabilitation practices for 1.2 ± 1.5, 3.0 ± .2.1, and 1.9 ± 3.4 h/week, respectively. In total, 742 health problems were reported. Mean weekly prevalence of health problems, injuries and illnesses were 20.1%, 16.5% and 3.8%, respectively. The injury incidence per 1,000 h of football exposure, match play and team practice were 8.28 (95% CI: 7.54–9.08), 16.77 (95% CI: 13.65–20.4), and 7.24 (95% CI: 6.5–8.04), respectively. Sudden-onset and gradual-onset injuries accounted for 36.7% and 43.4% of the total proportion of health problems. Hip/groin injuries had the highest incidence (1.58/1,000 h), whereas knee injuries had the highest burden (20.86 days lost/1,000 h). On average, the players experienced 3.33 health problems (average duration: 7.8 days). On average pr. player, 2.7 (95% CI: 2.2–3.3) wks of football exposure were lost.ConclusionSudden and gradual-onset injuries influenced player availability during the season. Health problem prevalence fluctuated markedly, and injury incidence was higher during match play than training. The players had substantial volumes of training beyond football-specific training and matches. Our findings could assist medical and sports science practitioneers in enhancing training and recovery processes to maximize player availability

Bayesian operational modal analysis of closely spaced modes for monitoring wind turbines

In this study, the applicability of Bayesian operational modal analysis (BAYOMA) to an operating onshore concrete-steel hybrid wind turbine tower is investigated. The results of the identification then provide reliable parameters for the structural health monitoring (SHM) of the tower. In the context of wind turbines, typical assumptions of linear time-invariant OMA methods are violated, so the validity of the identification uncertainties of BAYOMA is not necessarily given. In addition, closely spaced modes occur, for which the mode shape in particular is subject to high uncertainty. It can be stated, that the main part of the mode shape uncertainty corresponds to the alignment of these in the mode subspace. Due of these challenges, mode shapes are generally not taken into account when monitoring wind turbine towers. In order to include the mode shape in SHM scheme, the second-order modal assurance criterion (S2MAC) is applied in this study. This metric is able to eliminate the alignment uncertainty by comparing the mode shape with a mode subspace. Besides mode shapes, the reliability of natural frequencies and damping can also be better quantified by knowing the identification uncertainty. This finally enables a well-founded selection of suitable monitoring parameters for the future application of SHM for wind turbines. Preprint submitted to Engineering Structures

Identification Uncertainties of Bending Modes of an Onshore Wind Turbine for Vibration-Based Monitoring

This study considers the identification uncertainties of closely spaced bending modes of an operating onshore concrete-steel hybrid wind turbine tower. The knowledge gained contributes to making mode shapes applicable to wind turbine tower monitoring rather than just mode tracking. One reason is that closely spaced modes make it difficult to determine reliable mode shapes for them. For example, the well-known covariance-driven stochastic subspace identification (SSI-COV) yields complex mode shapes with multiple mean phases in the complex plane, which does not allow error-free transformation to the real space. In contrast, the Bayesian Operational Modal Analysis (BAYOMA) allows the determination of real mode shapes. The application of BAYOMA presents a further challenge when quantifying the associated uncertainties, as the typical assumption of a linear, time-invariant system is violated. Therefore, validity is not self-evident and a comprehensive investigation and comparison of results is required. It has already been shown in a previous study that the significant part of the uncertainty in the mode shapes corresponds to their orientation in the mode subspace (MSS). Despite all the challenges mentioned, there is still a great need to develop reliable monitoring parameters (MPs) for Structural Health Monitoring (SHM). This study contributes to this by analysing metrics for comparing mode shapes. In addition to the well-known Modal Assurance Criteria (MAC), the Second-Order MAC (S2MAC) is also used to eliminate the alignment uncertainty by comparing the mode shape with a MSS. In addition, the mode shape identification uncertainties of BAYOMA are also considered. Including uncertainties is also essential for the typically used natural frequencies and damping ratios, which can be more appropriately used if the identification uncertainty is known

Translational potential of metabolomics on animal models of inflammatory bowel disease:a systematic critical review

In the development of inflammatory bowel disease (IBD), the gut microbiota has been established as a key factor. Recently, metabolomics has become important for understanding the functional relevance of gut microbial changes in disease. Animal models for IBD enable the study of factors involved in disease development. However, results from animal studies may not represent the human situation. The aim of this study was to investigate whether results from metabolomics studies on animal models for IBD were similar to those from studies on IBD patients. Medline and Embase were searched for relevant studies up to May 2017. The Covidence systematic review software was used for study screening, and quality assessment was conducted for all included studies. Data showed a convergence of ~17% for metabolites differentiated between IBD and controls in human and animal studies with amino acids being the most differentiated metabolite subclass. The acute dextran sodium sulfate model appeared as a good model for analysis of systemic metabolites in IBD, but analytical platform, age, and biological sample type did not show clear correlations with any significant metabolites. In conclusion, this systematic review highlights the variation in metabolomics results, and emphasizes the importance of expanding the applied detection methods to ensure greater coverage and convergence between the various different patient phenotypes and animal models of inflammatory bowel disease