The basis of easy controllability in Boolean networks

Effective control of biological systems can often be achieved through the control of a surprisingly small number of distinct variables. We bring clarity to such results using the formalism of Boolean dynamical networks, analyzing the effectiveness of external control in selecting a desired final state when that state is among the original attractors of the dynamics. Analyzing 49 existing biological network models, we find strong numerical evidence that the average number of nodes that must be forced scales logarithmically with the number of original attractors. This suggests that biological networks may be typically easy to control even when the number of interacting components is large. We provide a theoretical explanation of the scaling by separating controlling nodes into three types: those that act as inputs, those that distinguish among attractors, and any remaining nodes. We further identify characteristics of dynamics that can invalidate this scaling, and speculate about how this relates more broadly to non-biological systems.

Mamdani-Type Fuzzy-Based Adaptive Nonhomogeneous Synchronization

The aim of this work is the design of an adaptive controller based on Mamdani-type fuzzy inference systems. The input control is constructed with saturation functions’ fuzzy-equivalents, which works as the adaptive scheme of the controller. This control law is designed to stabilize the error system to synchronize a pair of chaotic nonhomogeneous piecewise systems. Finally, an illustrative example as numerical evidence is developed.

Decoding cellular deformation from pseudo-simultaneously observed Rho GTPase activities

The inability to simultaneously observe all of the important Rho GTPases (Cdc42, Rac1, and RhoA) has prevented us from obtaining evidence of their coordinated regulation during cell deformation. Here, we propose Motion-Triggered Average (MTA), an algorithm that converts individually observed GTPases into pseudo-simultaneous observations. Using the time series obtained by MTA and mathematical model, we succeeded for the first time in decoding the cell edge velocity from the three GTPase activities to provide clear numerical evidence for coordinated cell edge regulation by the three GTPases. We found that the characteristics of the obtained activities were consistent with those of previous studies, and that GTPase activities and their derivatives were involved in edge regulation. Our approach provides an effective strategy for using single-molecule observations to elucidate problems hampered by the lack of simultaneous observations.

“Now or Later?” When to Deploy Qualification Screening in Open-Bid Auction for Re-Sourcing

Designing Open-bid Procurement Auction with Supplier Qualification Screenings Manufacturers often use re-sourcing initiatives to keep their suppliers’ pricing competitive; e.g., new entrant suppliers are identified and invited to compete with the incumbent supplier for supply contracts in an open-bid auction. To ensure that entrant suppliers have the capability of executing the contract, the conventional approach for many manufacturers is to conduct qualification screenings on all the entrants prior to auction bidding and only allow qualified entrant suppliers to compete in the auction. In “‘Now or Later?’ When to Deploy Qualification Screening in Open-Bid Auction for Re-Sourcing”, Zhang, Chen, and Katok explore an alternative arrangement of this process where all entrant suppliers are invited for bidding first before qualification screenings are selectively conducted afterward to determine the contract winner. This new approach helps reduce the waste of manufacturers’ screening efforts on suppliers with uncompetitive bids but in the meantime introduces incentives for less competitive supplier bidding behavior. They provide analytical and numerical evidence that this new approach could be very effective in managing manufacturers’ procurement costs.

SudoQ -- a quantum variant of the popular game

(pp781-799) doi: https://doi.org/ Abstracts: We introduce SudoQ, a quantum version of the classical game Sudoku. Allowing the entries of the grid to be (non-commutative) projections instead of integers, the solution set of SudoQ puzzles can be much larger than in the classical (commutative) setting. We introduce and analyze a randomized algorithm for computing solutions of SudoQ puzzles. Finally, we state two important conjectures relating the quantum and the classical solutions of SudoQ puzzles, corroborated by analytical and numerical evidence.

Approximate nonradial solutions for the Lane-Emden problem in the ball

In this paper we provide a numerical approximation of bifurcation branches from nodal radial solutions of the Lane Emden Dirichlet problem in the unit ball in ℝ2, as the exponent of the nonlinearity varies. We consider solutions with two or three nodal regions. In the first case our numerical results complement the analytical ones recently obtained in [11]. In the case of solutions with three nodal regions, for which no analytical results are available, our analysis gives numerical evidence of the existence of bifurcation branches. We also compute additional approximations indicating presence of an unexpected branch of solutions with six nodal regions. In all cases the numerical results allow to formulate interesting conjectures.