Strong convergence rates of probabilistic integrators for ordinary differential equations

Probabilistic integration of a continuous dynamical system is a way of systematically introducing discretisation error, at scales no larger than errors introduced by standard numerical discretisation, in order to enable thorough exploration of possible responses of the system to inputs. It is thus a potentially useful approach in a number of applications such as forward uncertainty quantification, inverse problems, and data assimilation. We extend the convergence analysis of probabilistic integrators for deterministic ordinary differential equations, as proposed by Conrad et al. (Stat Comput 27(4):1065–1082, 2017. https://doi.org/10.1007/s11222-016-9671-0), to establish mean-square convergence in the uniform norm on discrete- or continuous-time solutions under relaxed regularity assumptions on the driving vector fields and their induced flows. Specifically, we show that randomised high-order integrators for globally Lipschitz flows and randomised Euler integrators for dissipative vector fields with polynomially bounded local Lipschitz constants all have the same mean-square convergence rate as their deterministic counterparts, provided that the variance of the integration noise is not of higher order than the corresponding deterministic integrator. These and similar results are proven for probabilistic integrators where the random perturbations may be state-dependent, non-Gaussian, or non-centred random variables.

     

Effects of Leadership Style,Creativity Technique and Personal Initiative on Employee Creativity

Transformational leadership is assumed to enhance employees' creativity. However, results of meta‐analytic research on the relations between transformational leadership and creativity have fallen short of expectations. The authors argue that, besides leadership style, the creativity technique that a leader employs is an important means of stimulating employees' creativity. In addition, it is assumed that leadership styles and creativity techniques may have different effects, depending on the measure of creativity output (quantitative vs qualitative). Therefore, in an experimental setting, the effects of different creativity techniques (provocation technique vs brainwriting) and leadership styles (transformational vs transactional) on both quantitative and qualitative creativity were examined. Results showed that transformational leadership and provocation technique led to higher levels of qualitative creativity than transactional leadership and brainwriting, respectively. Conversely, transactional leadership and brainwriting were more effective for quantitative creativity. The additional benefit of the provocation technique in qualitative creativity was found to be higher in the transactional leadership condition than in the transformational leadership condition. Moreover, personal initiative made a significant and independent contribution to both qualitative and quantitative creativity. Implications for practice and future research are discussed.     

Gender disparity in the C-suite: Do male and female CEOs differ in how they reached the top?

Through a comparison of the life and career trajectories of thirty male and thirty female CEOs of large organizations, this study offers insights into the genesis of gender disparity in corporate leadership positions, discusses the implications for leadership development, and puts forward a model explaining the disparity in CEO roles. We found gendered patterns in the accumulation of career relevant experiences stretching back to birth into working lives that created significant and cumulative limitations upon the ability of women to access CEO roles and the types of CEO appointments available to them. Limited access to career relevant experiences in childhood, adolescence and in organizations lead to on-going limitations in capital accumulation throughout women's careers. Implications of our findings for both theory and practice are discussed.     

Differentiated leader–member exchange,justice climate,and performance: Main and interactive effects

Leaders form different quality leader–member exchange (LMX) relationships with their subordinates. This variable treatment termed LMX differentiation can have negative effects on individuals' behavior and attitudes. In this study, we examined the cross-level main effect of justice climate on task performance and the moderating role of justice climate on the relationship between LMX differentiation and task performance. We tested these two hypotheses using a field study of 90 subordinates nested under 27 supervisors. Procedural justice climate, not distributive justice climate, was found to positively influence subordinate task performance. Further, distributive justice climate, not procedural justice climate, was found to moderate the LMX differentiation–task performance relationship; such that the relationship was positive when distributive justice climate was high and negative when distributive justice climate was low. Findings and future directions are discussed.     

A cyclical view of the relationship between corporate governance and strategic management

The vast majority of research on the relationship between corporate governance and strategic management focuses on the impact of corporate governance on strategic management. In this article we propose a cyclical model, highlighting that strategic decisions can also affect corporate governance through shaping firm ownership structure. We discuss the impacts of strategic decisions on firm ownership structure and corporate governance in the contexts of publicly traded firms, private firms, and the privatization of state-owned enterprises. We hope that our cyclical model can promote researchers to develop a more complete view about the relationships between strategic management, ownership structure, and corporate governance.     

CORRUPTION: TOP DOWN OR BOTTOM UP?

This article studies the impact of corruption on an economy with a hierarchical government. In particular, we study whether centralizing corruption within the higher level of government increases or decreases the total amount of corruption. We show that when the after-tax relative profitability of the formal sector as compared to that of the informal sector is high enough, adding a layer of government increases the total amount of corruption. By contrast, for high-enough public wages and/or an efficient monitoring technology of the bureaucratic system, centralization of corruption at the top of the government hierarchy redistributes bribe income from the lower level to the upper level. In the process, total corruption is reduced and the formal sector of the economy expands.