Mean field theory for biology inspired duplication-divergence network model

Divergence asymmetry and connected components in a general duplication-divergence graph model

This Letter introduces a generalization of known duplication-divergence models for growing random graphs. This general duplication-divergence model includes a coupled divergence asymmetry rate, which allows to obtain the structure of random growing networks by duplication divergence in a continuous range of configurations between two known limit cases: (i) complete asymmetric divergence, i.e., the divergence rates affect only the edges of either the original or the copy vertex, and (ii) symmetric divergence, i.e., the divergence rates affect with equal probability both the original and the copy vertex. Connected components emerge as the divergence asymmetry rate slightly moves from the complete asymmetric divergence case. Mean-field results of prior published models are nicely reproduced by this generalization. In special cases, the connected component size distribution C_{s} suggests a power-law scaling of the form C_{s}∼s^{-λ} for s>1, e.g., with λ≈5/3 for a divergence rate δ≈0.7.

Next-Generation Personalized Medicine: Implementation of Variability Patterns for Overcoming Drug Resistance in Chronic Diseases

Chronic diseases are a significant healthcare problem. Partial or complete non-responsiveness to chronic therapies is a significant obstacle to maintaining the long-term effect of drugs in these patients. A high degree of intra- and inter-patient variability defines pharmacodynamics, drug metabolism, and medication response. This variability is associated with partial or complete loss of drug effectiveness. Regular drug dosing schedules do not comply with physiological variability and contribute to resistance to chronic therapies. In this review, we describe a three-phase platform for overcoming drug resistance: introducing irregularity for improving drug response; establishing a deep learning, closed-loop algorithm for generating a personalized pattern of irregularity for overcoming drug resistance; and upscaling the algorithm by implementing quantified personal variability patterns along with other individualized genetic and proteomic-based ways. The closed-loop, dynamic, subject-tailored variability-based machinery can improve the efficacy of existing therapies in patients with chronic diseases.

Multiplayer Noncooperative and Cooperative Minimax H∞ Tracking Game Strategies for Linear Mean-Field Stochastic Systems With Applications to Cyber-Social Systems

The multiplayer stochastic noncooperative tracking game (NTG) with conflicting target strategy and cooperative tracking game (CTG) with a common target strategy of the mean-field stochastic jump-diffusion (MFSJD) system with external disturbance is investigated in this study. Due to the mean (collective) behavior in the system dynamic and cost function, the designs of the NTG strategy and CTG strategy for target tracking of the MFSJD system are more difficult than the conventional stochastic system. By the proposed indirect method, the NTG and CTG strategy design problems are transformed into linear matrix inequalities (LMIs)-constrained multiobjective optimization problem (MOP) and LMIs-constrained single-objective optimization problem (SOP), respectively. The LMIs-constrained MOP could be solved effectively for all Nash equilibrium solutions of NTG at the Pareto front by the proposed LMIs-constrained multiobjective evolutionary algorithm (MOEA). Two simulation examples, including the share market allocation and network security strategies in cyber-social systems, are given to illustrate the design procedure and validate the effectiveness of the proposed LMI-constrained MOEA for all Nash equilibrium solutions of NTG strategies of the MFSJD system.

Densification and structural transitions in networks that grow by node copying

We introduce a growing network model, the copying model, in which a new node attaches to a randomly selected target node and, in addition, independently to each of the neighbors of the target with copying probability p. When p<1/2, this algorithm generates sparse networks, in which the average node degree is finite. A power-law degree distribution also arises, with a nonuniversal exponent whose value is determined by a transcendental equation in p. In the sparse regime, the network is "normal," e.g., the relative fluctuations in the number of links are asymptotically negligible. For p≥1/2, the emergent networks are dense (the average degree increases with the number of nodes N), and they exhibit intriguing structural behaviors. In particular, the N dependence of the number of m cliques (complete subgraphs of m nodes) undergoes m-1 transitions from normal to progressively more anomalous behavior at an m-dependent critical values of p. Different realizations of the network, which start from the same initial state, exhibit macroscopic fluctuations in the thermodynamic limit: absence of self-averaging. When linking to second neighbors of the target node can occur, the number of links asymptotically grows as N^{2} as N→∞, so that the network is effectively complete as N→∞.