Gender Quotas on Corporate Boards: Similarities and Differences in Quota Scenarios

In this article, the use of gender quotas to strengthen gender equality on corporate boards is explored. Examining national practices in ten European countries we provide an overview, categorizing the design of various corporate board quotas (CBQs) and the contexts in which they are embedded. In particular, similarities and differences along two dimensions are investigated: the design of the CBQs in terms of their hardness and progressiveness, and the institutional context in which they are embedded. From patterns of design and context configurations, different quota scenarios are discerned. We advance the discussion of female representation and the strategies of corporate boards beyond the rather misleading dichotomy of voluntary targets versus mandatory quotas, proposing a framework for understanding various CBQ designs. Moreover, we suggest that the configuration of design and institutional context, resulting in different quota scenarios affects female representation on corporate boards

A central limit theorem via differential equations

In a paper from 1995, Wormald gave general criteria for certain parameters in a family of discrete random processes to converge to the solution of a system of differential equations. Based on this method, we show that if some further conditions are satisfied, the parameters converge to a multivariate normal distribution.Comment: Published in at http://dx.doi.org/10.1214/08-AAP557 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Piecewise deterministic optimal control problems

Piecewise deterministic control problems are problems involving stochastic disturbance of a special type. In certain situations, in an otherwise deterministic control system, it may happen that the state jumps at certain stochastic points of time. Examples are sudden oil finds, or sudden discoveries of metal deposits. Similarly, in seemingly deterministic processes, the dynamics may suddenly change character: at certain stochastic points in time, the right-hand side of the differential equation governing the system changes form, such changes being effected by jumps in a (dummy) state variable. Examples of such phenomena are sudden inventions, sudden ecological disasters, earthquakes, floods, storms, fires, the sudden capture of a criminal, that suddenly change the prospects of the firm, the society, the agriculture, the criminal... Several papers have discussed such problems, often using more or less ad hoc methods. (Sometimes it is possible to rewrite the problem so that deterministic control theory applies). A systematic method for solving such problems, based on HJB-equation (the Hamilton-Jacoby-Bellman equation) for the problem, is presented in Davis (1993). Markov Models and Optimization, and also briefly discussed below. In this paper a related method, closer to deterministic control theory, is presented first. It is easiest to apply to problems with a bound on the number of possible jumps. Thus, the main purpose of this paper is to show how some piecewise deterministic optimal control problems can be solved by techniques similar to those used in deterministic problems. The paper includes statements of several theoretical results. Proofs are given for the results involving the HJB-equation and fields of extremals, (for the HJB-equation, replicating the ones in Davis (1993))

Open mapping theorems for directionally differentiable functions

Open mapping theorems are proved for directionally differentiable Lipschitz continuous functions. It is indicated that generalizations to nonsmooth functions that are not directionally differentiable are possible. The results in the paper generalize the open mapping theorems for differentiable mappings, and are different from open mapping theorems for nonsmooth functions in the literature, when these are specialized to directionally differentiable functions

Maximum principle for stochastic control in continuous time with hard end constraints

A maximum principle is proved for certain problems of continuous time stochastic control with hard end constraints, (end constraints satis_ed a.s.) After establishing a general theorem, the results are applied to problems where the state equation (di_erential equation) changes at certain stochastic points in time, and to piecewise continuous stochastic problems (including piecewise deterministic problems)

'Men han har forskjellig farge på øynene.' Om barns møte med litteratur i skolen sett i lys av teori om mentalisering og Theory of Mind.

Utgangspunktet for artikkelen er en resepsjonsstudie av en gruppe seksåringer på barnetrinnet som leser bildeboken Bukkene Bruse på Badeland av Rørvik og Moursund (2009). I samtale om boken begynner barna å undre seg over og kommentere trollets mentale tilstander og følelser ut fra trekk ved tegningene. Hvorfor har trollet forskjellig farge på øynene? Er han sint eller kanskje redd? Hva betyr det egentlig at munnen er åpen? Er trollet glad da? Siktemålet med artikkelen er å undersøke om utsagnene til barna i studien kan forståes som forsøk på å mentalisere, å søke å forstå andre menneskers – og dermed egne – tanker og følelser. I artikkelen drøftes det om begrepet mentalisering kan bidra til å gi økt innsikt i barns litteraturlesing. Deretter drøftes det om dette perspektivet får didaktiske konsekvenser. Hvilke følger får forståelsen som ligger i begrepet mentalisering når det gjelder synet på og bruken av skjønnlitteratur i skolens morsmålsfag

Existence of optimal nonanticipating controls in piecewise deterministic control problems

Optimal nonanticipating controls are shown to exist in nonautonomous piecewise deterministic control problems with hard terminal restrictions. The assumptions needed are completely analogous to those needed to obtain optimal controls in deterministic control problems. The proof is based on well-known results on existence of deterministic optimal controls

Pareto improvements of Nash equilibria in differential games

This paper yields sufficient conditions for Pareto inoptimality of controls forming Nash equilibria in differential games. In Appendix a result on existence of open loop Nash equilibria is added

Measurements of carotid intima media thickness in non-invasive high-frequency ultrasound images: the effect of dynamic range setting

Background Carotid intima media thickness (CIMT) measured with ultrasound (US) is widely used as biomarker for arteriosclerosis and as surrogate endpoint in interventional studies to assess efficacy of drug therapies. Strict US protocols are necessary to ensure reproducibility. The range of US signal intensities used for image formation, the dynamic range (DR), is rarely reported in studies and little is known about its effect on CIMT measurements in humans. The purpose of this study was to quantify the impact of DR on measurements of CIMT. Methods US was used to examine 313 carotid arteries in participants from two different clinical studies. For each artery, images with DR of 40, 55, 70 and 85 dB were captured from the same frozen US frame. Mean CIMT (CIMTmean), maximum CIMT (CIMTmax) and standard deviation of CIMT (CIMTsd) were obtained for all images. CIMT for different DRs were compared using student t-test. Results CIMTmean for 40, 55, 70 and 85 dB were 0.529, 0.564, 0.590 and 0.605 mm respectively. For CIMTmax the corresponding values were 0.626, 0.667, 0.698, and 0.716 mm. CIMTmean and CIMTmax increased significantly for increasing DR steps (p < 0.01). The relative change in CIMTmean and CIMTmax were largest between 40 and 55 dB (6.7% and 7.0%) and smallest between 70 and 85 dB (2.6% and 2.7%) indicating a declining dependency for increasing DR. Conclusions DR significantly changes CIMT measurements and the changes are most prominent for lower DRs. The effect of changing DR is larger in human arteries than in phantoms. Reporting the DR will therefore increase the validity of CIMT data

Quantitative analysis of diffusion-weighted magnetic resonance imaging in malignant breast lesions using different b value combinations

OBJECTIVES: To explore how apparent diffusion coefficients (ADCs) in malignant breast lesions are affected by selection of b values in the monoexponential model and to compare ADCs with diffusion coefficients (Ds) obtained from the biexponential model. METHODS: Twenty-four women (mean age 51.3 years) with locally advanced breast cancer were included in this study. Pre-treatment diffusion-weighted magnetic resonance imaging was performed using a 1.5-T system with b values of 0, 50, 100, 250 and 800 s/mm(2). Thirteen different b value combinations were used to derive individual monoexponential ADC maps. All b values were used in the biexponential model. RESULTS: Median ADC (including all b values) and D were 1.04 × 10(-3) mm(2)/s (range 0.82–1.61 × 10(-3) mm(2)/s) and 0.84 × 10(-3) mm(2)/s (range 0.17–1.56 × 10(-3) mm(2)/s), respectively. There was a strong positive correlation between ADCs and Ds. For clinically relevant b value combinations, maximum deviation between ADCs including and excluding low b values (<100 s/mm(2)) was 11.8 %. CONCLUSION: Selection of b values strongly affects ADCs of malignant breast lesions. However, by excluding low b values, ADCs approach biexponential Ds, demonstrating that microperfusion influences the diffusion signal. Thus, care should be taken when ADC calculation includes low b values. KEY POINTS: • Diffusion-weighted sequences are increasingly used in breast magnetic resonance imaging • Diffusion-weighting (b) values strongly influence apparent diffusion coefficients of malignant lesions • Exclusion of low b values reduces the apparent diffusion coefficient • Flow-insensitive monoexponential apparent diffusion coefficients approach biexponential diffusion coefficient