Encyclopedia of Applied and Computational Mathematics

doi:10.1007/978-3-540-70529-1

Cited by 20 publications

(3 citation statements)

References 13 publications

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“…of the types of drugs that the user wants to focus on, the size of this set can be further modified. For example, in [14], the authors use the set of U.S. Food and Drug Administration (FDA) approved drugs, which selects a set of 1500 direct drug-target proteins out of a total of approx 20 000 proteins 7 (excluding post-translational modification and other variants of these, such as phosphorilation, acetilation, etc.). This set can be enlarged…”

Section: Proofmentioning

confidence: 99%

“…Then, we will (approximately) compute the generic rank Srank OC p (A, B S , C T ), and we will compare it with the maximal choice Srank OC p (A, B S , C T ). The generic rank of a matrix cannot be computed in polynomial time [7]. However, it is known from early works on structural network controllability [21,29] that Fixed Parameter Algorithms and Hardness of Approximation Results for the Structural Target Controllability Problem 127 for any LTIS (A, B, C T ), the set…”

Section: An Algebraic Approach For Solving the Driver Restricted Stru...mentioning

confidence: 99%

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Fixed Parameter Algorithms and Hardness of Approximation Results for the Structural Target Controllability Problem

Czeizler¹,

Popa²,

Popescu³

2022

SACS

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Recent research has revealed new and unexpected applications of network control science within biomedicine, pharmacology, and medical therapeutics. These new insights and new applications generated in turn a rediscovery of some old, unresolved algorithmic problems. One of these problems is the Structural Target Control optimization problem, known in previous literature also as Structural Output Controllability problem, which is defined as follows. Given a directed network and a target subset of nodes, the task is to select a small (or the smallest) set of nodes from which the target can be independently controlled, i.e., there exists a set of paths from the selected set of nodes (called driver nodes) to the target nodes such that no two paths intersect at the same distance from their targets. Recently, Structural Target Control optimization problem has been shown to be NP-hard, and several heuristic algorithms were introduced and analyzed, both on randomly generated networks, and on biomedical ones. In this paper, we show that the Structural Target Controllability problem is fixed parameter tractable when parameterized by the number of target nodes. We also prove that the problem is hard to approximate at a factor better than O(log n). Taking into consideration the real case formulations of this problem we identify two more parameters which are naturally constrained by smaller bounds: the maximal length of a controlling path and the size of the set of nodes from which the control can start. With these new parameters we provide an approximation algorithm which is of exponential complexity in the size of the set of nodes from which the control can start and polynomial in all the other parameters.

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Section: Proofmentioning

confidence: 99%

Section: An Algebraic Approach For Solving the Driver Restricted Stru...mentioning

confidence: 99%

Fixed Parameter Algorithms and Hardness of Approximation Results for the Structural Target Controllability Problem

Czeizler¹,

Popa²,

Popescu³

2022

SACS

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“…by lack of nutrient or physical stresses. Similar oscillators are known to produce circadian rhythms in plants [41,42] and there are also analogues in abiotic chemical systems in vitro, such as the well-known BZ reaction [43]. Such chemical oscillators require a minimum of two components, each influencing the production of the other, although in vivo there are many more than this.…”

Section: Introductionmentioning

confidence: 95%

The role of the cell cycle in collective cell dynamics

Li,

Schnyder,

Turner

et al. 2020

Preprint

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Cells coexist together in colonies or as tissues. Their behaviour is controlled by an interplay between intercellular forces and biochemical regulation. We develop a simple model of the cell cycle, the fundamental regulatory network controlling growth and division, and couple this to the physical forces arising within the cell collective. We analyse this model using both particle-based computer simulations and a continuum theory. We focus on 2D colonies confined in a channel. These develop moving growth fronts of dividing cells with quiescent cells in the interior. The profile and speed of these fronts are non-trivially related to the substrate friction and the cell cycle parameters, providing a possible approach to measure such parameters in experiments.

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