Basins of Attraction, Commitment Sets and Phenotypes of Boolean Networks

The attractors of Boolean networks and their basins have been shown to be highly relevant for model validation and predictive modelling, e.g., in systems biology. Yet there are currently very few tools available that are able to compute and visualise not only attractors but also their basins. In the realm of asynchronous, non-deterministic modeling not only is the repertoire of software even more limited, but also the formal notions for basins of attraction are often lacking. In this setting, the difficulty both for theory and computation arises from the fact that states may be ele- ments of several distinct basins. In this paper we address this topic by partitioning the state space into sets that are committed to the same attractors. These commitment sets can easily be generalised to sets that are equivalent w.r.t. the long-term behaviours of pre-selected nodes which leads us to the notions of markers and phenotypes which we illustrate in a case study on bladder tumorigenesis. For every concept we propose equivalent CTL model checking queries and an extension of the state of the art model checking software NuSMV is made available that is capa- ble of computing the respective sets. All notions are fully integrated as three new modules in our Python package PyBoolNet, including functions for visualising the basins, commitment sets and phenotypes as quotient graphs and pie charts

Solving Gapped Hamiltonians Locally

We show that any short-range Hamiltonian with a gap between the ground and excited states can be written as a sum of local operators, such that the ground state is an approximate eigenvector of each operator separately. We then show that the ground state of any such Hamiltonian is close to a generalized matrix product state. The range of the given operators needed to obtain a good approximation to the ground state is proportional to the square of the logarithm of the system size times a characteristic "factorization length". Applications to many-body quantum simulation are discussed. We also consider density matrices of systems at non-zero temperature.Comment: 13 pages, 2 figures; minor changes to references, additional discussion of numerics; additional explanation of nonzero temperature matrix product for

Approximating attractors of Boolean networks by iterative CTL model checking

This paper introduces the notion of approximating asynchronous attractors of Boolean networks by minimal trap spaces. We define three criteria for determining the quality of an approximation: “faithfulness” which requires that the oscillating variables of all attractors in a trap space correspond to their dimensions, “univocality” which requires that there is a unique attractor in each trap space, and “completeness” which requires that there are no attractors outside of a given set of trap spaces. Each is a reachability property for which we give equivalent model checking queries. Whereas faithfulness and univocality can be decided by model checking the corresponding subnetworks, the naive query for completeness must be evaluated on the full state space. Our main result is an alternative approach which is based on the iterative refinement of an initially poor approximation. The algorithm detects so-called autonomous sets in the interaction graph, variables that contain all their regulators, and considers their intersection and extension in order to perform model checking on the smallest possible state spaces. A benchmark, in which we apply the algorithm to 18 published Boolean networks, is given. In each case, the minimal trap spaces are faithful, univocal, and complete, which suggests that they are in general good approximations for the asymptotics of Boolean networks

A review of the CEO succession literature and a future research program

Executive leadership changes are critical turning points for organizations. Over the past five decades, management scholars have generated many insights into the predictors, consequences, and contingencies of CEO succession. We first provide an overview of this research, integrating strategic management, corporate governance, strategic leadership, and organizational behavior research findings into a comprehensive framework. We find that empirical research has frequently adopted an event-based perspective on CEO succession, which is contrary to the practical evidence regarding CEO succession as a continuous process. In the second part of our paper, we develop a future research agenda for the CEO succession process. We specifically address the role of board–CEO collaborations and potential frictions during the CEO succession process. Our suggestions will help researchers gain a better understanding of boards’ governance of executive succession processes. These suggestions also have implications for directors responsible for CEO succession

Opening the black box: Unpacking board involvement in innovation

Corporate governance research suggests that boards of directors play key roles in governing company strategy. Although qualitative research has examined board-management relationships to describe board involvement in strategy, we lack detailed insights into how directors engage with organizational members for governing a complex and long-term issue such as product innovation. Our multiple-case study of four listed pharmaceutical firms reveals a sequential process of board involvement: Directors with deep expertise govern scientific innovation, followed by the full board's involvement in its strategic aspects. The nature of director involvement varies across board levels in terms of the direction (proactive or reactive), timing (regular or spontaneous), and the extent of formality of exchanges between directors and organizational members. Our study contributes to corporate governance research by introducing the concept of board behavioral diversity and by theorizing about the multilevel, structural, and temporal dimensions of board behavior and its relational characteristics