Non-regularised inverse finite element analysis for 3D traction force microscopy

The tractions that cells exert on a gel substrate from the observed displacements is an increasingly attractive and valuable information in biomedical experiments. The computation of these tractions requires in general the solution of an inverse problem. Here, we resort to the discretisation with finite elements of the associated direct variational formulation, and solve the inverse analysis using a least square approach. This strategy requires the minimisation of an error functional, which is usually regularised in order to obtain a stable system of equations with a unique solution. In this paper we show that for many common threedimensional geometries, meshes and loading conditions, this regularisation is unnecessary. In these cases, the computational cost of the inverse problem becomes equivalent to a direct finite element problem. For the non-regularised functional, we deduce the necessary and sufficient conditions that the dimensions of the interpolated displacement and traction fields must preserve in order to exactly satisfy or yield a unique solution of the discrete equilibrium equations. We apply the theoretical results to some illustrative examples and to real experimental data. Due to the relevance of the results for biologists and modellers, the article concludes with some practical rules that the finite element discretisation must satisfy.Peer ReviewedPostprint (author's final draft

Sliding joints in 3D beams: conserving algorithms using the master-slave approach

This paper proposes two time-integration algorithms for motion of geometrically exact 3D beams under sliding contact conditions. The algorithms are derived using the socalled master–slave approach, in which constraint equations and the related time-integration of a system of differential and algebraic equations are eliminated by design. Specifically, we study conservation of energy and momenta when the sliding conditions on beams are imposed and discuss their algorithmic viability. Situations where the contact jumps to adjacent finite elements are analysed in detail and the results are tested on two representative numerical examples. It is concluded that an algorithmic preservation of kinematic constraint conditions is of utmost importance.Peer ReviewedPostprint (author's final draft

Intertemporal Choice of Fuzzy Soft Sets

This paper first merges two noteworthy aspects of choice. On the one hand, soft sets and fuzzy soft sets are popular models that have been largely applied to decision making problems, such as real estate valuation, medical diagnosis (glaucoma, prostate cancer, etc.), data mining, or international trade. They provide crisp or fuzzy parameterized descriptions of the universe of alternatives. On the other hand, in many decisions, costs and benefits occur at different points in time. This brings about intertemporal choices, which may involve an indefinitely large number of periods. However, the literature does not provide a model, let alone a solution, to the intertemporal problem when the alternatives are described by (fuzzy) parameterizations. In this paper, we propose a novel soft set inspired model that applies to the intertemporal framework, hence it fills an important gap in the development of fuzzy soft set theory. An algorithm allows the selection of the optimal option in intertemporal choice problems with an infinite time horizon. We illustrate its application with a numerical example involving alternative portfolios of projects that a public administration may undertake. This allows us to establish a pioneering intertemporal model of choice in the framework of extended fuzzy set theorie

Downsizing implementation and financial performance

In the present study we explore the relationship between downsizing decisions and corporate financial performance after top management has decided to downsize. Our focus is on the financial consequences arising from the amount of downsizing and the use of disengagement incentives. For this purpose, we use a sample of downsizing announcements in the Spanish press from 1995 up to 2001. Although the results show that the amount of downsizing is not significantly related to post-downsizing profitability, the evidence provided supports the finding that the use of disengagement incentives (which motivate workers to leave the organization) is negatively related to firm performance. Our analysis helps to understand the role that strategic downsizing decisions play in explaining observed variance in the performance of downsized firms. Thus, it advances scholarly organizational research by reinforcing the concept that corporate performance is not only contingent on strategies, but also influenced by the means through which these strategies are implemented

Does downsizing improve organizational performance? An analysis of Spanish manufacturing firms

The objective of this study is to examine the effect of downsizing on corporate performance, considering a sample of manufacturing firms drawn from the Spanish Survey of Business Strategies during the 1993- 2005 period. No significant differences in post-downsizing performance arise between companies which downsize and those that do not. Likewise, we find that substantial workforce reductions through collective dismissals do not either lead to improved performance levels. Downsizing, therefore, may not be a way for managers to increase performance, particularly in a context like the Spanish one, where the labour market is characterized by a high protection of employees’ rights and substantial contract termination costs