Hidden Hierarchy Research Articles

Hidden hierarchy in the rheology of dense suspensions

Hidden hierarchy in the rheology of dense suspensions

Analysis of a breast cancer mathematical model by a new method to find an optimal protocol for [formula omitted]-positive cancer

Treatment of breast cancer (positive for HER2, i.e., ERBB2) is described by a mathematical model involving non-linear ordinary differential equations with a hidden hierarchy. To reveal the hierarchy of dynamical variables of the system being considered, we applied the singular perturbed vector field (SPVF) method, where a system of equations can be decomposed to fast and slow sub-systems with explicit small parameters. This new form of the model, which is called a singular perturbed system, enables us to apply a semi-analytical method called the method of directly defining inverse mapping (MDDiM), which is based on the homotopy analysis asymptotic method. We introduced the treatment protocol in explicit form, through an analytical function that describes the exact dose and intervals between treatments in a cyclical manner. In addition, a new algorithm for the optimal dosage that causes tumour shrinkage is presented in this study. Furthermore, we took the concept of protocol optimisation a step further and derived a differential equation that represents vaccination depending on tumour size and yields an optimal protocol of different doses at every time point. We introduced the treatment protocol in explicit form, through an analytical function that describes the exact dose and intervals between treatments in a cyclical manner. In addition, a new algorithm for finding the optimal dosage that causes tumour shrinkage is presented in this study. Additionally, we took the concept of protocol optimisation a step further and derived a differential equation that represents vaccination depending on tumour size and yields an optimal protocol of different doses at every time point.

Ambiguous authority and hidden hierarchy: Collective leadership in an elite professional service firm

This study represents a detailed analysis of collective leadership in an elite professional service firm, examining the distinctive power dynamics revealed among professional peers as they attempt to act decisively in response to an acute organizational crisis. It identifies how professional peers deliberately construct and amplify ambiguity in both the composition and authority of their collective leadership group, and examines how that ambiguity can serve a functional purpose for group members. Intuitive mutual adjustment is the prevailing pattern of interaction, but this changes to a more managed form of mutual adjustment as a hidden hierarchy is revealed in response to the crisis. The study identifies the micro interactions which constitute both intuitive and managed mutual adjustment, and shows how members of a collective leadership group can maintain cohesion and act decisively, in spite of lacking the formal authority to do so. The findings challenge some foundational assumptions of collective leadership theory and extend our understanding of leadership power dynamics more generally by demonstrating how leaders can exercise considerable informal power under the cloak of ambiguity, highlighting the hidden hierarchy that can exist within a collective, and emphasizing the significance of individual ‘heroic’ leader within collective leadership.

Ambiguous Authority and Hidden Hierarchy: Collective Leadership in a Professional Service Firm

This study examines the response of a professional service firm’s (PSF's) senior leadership group to the banking crisis of 2008. It contributes to collective leadership theory, by developing a deta...

Combination of singularly perturbed vector field method and method of directly defining the inverse mapping applied to complex ODE system prostate cancer model

ABSTRACTWe propose a new method to solve a system of complex ordinary differential equations (ODEs) with hidden hierarchy. Given a complex system of the ODE, the hierarchy of the system is generally hidden. Once we reveal the hierarchy of the system, the system can be reduced into subsystems called slow and fast subsystems. This division of slow and fast subsystems reduces the analysis and hence reduces the computation time, which can be expensive. In our new method, we first apply the singularly perturbed vector field method that is the global quasi-linearization method. This method exposes the hierarchy of a given complex system. Subsequently, we apply a version of the homotopy analysis method called the method of directly defining the inverse mapping. We applied our new method to the immunotherapy of advanced prostate cancer.

On a modified version of ILDM approach: asymptotic analysis based on integral manifolds

Using the method of integral (invariant) manifolds, the intrinsic low-dimensional manifolds (ILDM) method is analysed. This is a method for identifying invariant manifolds of a system's slow dynamics and has proven to be an efficient tool in modelling of laminar and turbulent combustion. It allows treating multi-scale systems by revealing their hidden hierarchy and decomposing the system dynamics into fast and slow motions. The performed analysis shows that the original ILDM technique can be interpreted as one of the many possible realizations of the general framework, which is based on a special transformation of the original coordinates in the state space. A modification of the ILDM is proposed based on a new definition of the transformation matrix. The proposed numerical procedure is demonstrated on linear examples and highly non-linear test problems of mathematical theory of combustion and demonstrates in some cases better performance with respect to the existing one.