The p53 transcription factor is a key mediator in cellular responses to various stress signals including DNA repair, cell cycle arrest, and apoptosis. In this work, we employ landscape and flux theory to investigate underlying mechanisms of p53-regulated cell fate decisions. Based on a p53 regulatory network, we quantified the potential landscape and probabilistic flux for the p53 system. The landscape topography unifies and quantifies three cell fate states, including the limit cycle oscillations (representing cell cycle arrest), high p53 state (characterizing apoptosis), and low p53 state (characterizing the normal proliferative state). Landscape and flux results provide a quantitative explanation for the biphasic dynamics of the p53 system. In the oscillatory phase (first phase), the landscape attracts the system into the ring valley and flux drives the system cyclically moving, leading to cell cycle arrest. In the fate decision-making phase (second phase), the ring valley shape of the landscape provides an efficient way for cells to return to the normal proliferative state once DNA damage is repaired. If the damage is unrepairable with larger flux, the system may cross the barrier between two states and switch to the apoptotic state with a high p53 level. By landscape-flux decomposition, we revealed a trade-off between stability (guaranteed by landscape) and function (driven by flux) in cellular systems. Cells need to keep a balance between appropriate speed to repair DNA damage and appropriate stability to survive. This is further supported by flux landscape analysis showing that flux may provide the dynamical origin of phase transition in a non-equilibrium system by changing landscape topography.
In this paper, we propose two communication-efficient decentralized optimization algorithms over a general directed multi-agent network. The first algorithm, termed Compressed Push-Pull (CPP), combines the gradient tracking Push-Pull method with communication compression. We show that CPP is applicable to a general class of unbiased compression operators and achieves linear convergence rate for strongly convex and smooth objective functions. The second algorithm is a broadcast-like version of CPP (B-CPP), and it also achieves linear convergence rate under the same conditions on the objective functions. B-CPP can be applied in an asynchronous broadcast setting and further reduce communication costs compared to CPP. Numerical experiments complement the theoretical analysis and confirm the effectiveness of the proposed methods.
In this work, we consider the decentralized optimization problem in which a network of n agents, each possessing a smooth and convex objective function, wish to collaboratively minimize the average of all the objective functions through peer-to-peer communication in a directed graph. To solve the problem, we propose two accelerated Push-DIGing methods termed APD and APD-SC for minimizing non-strongly convex objective functions and strongly convex ones, respectively. We show that APD and APD-SC respectively converge at the rates O 1 k 2 and O 1 − C µ L k up to constant factors depending only on the mixing matrix. To the best of our knowledge, APD and APD-SC are the first decentralized methods to achieve provable acceleration over unbalanced directed graphs. Numerical experiments demonstrate the effectiveness of both methods.
In this paper, we focus on solving the decentralized optimization problem of minimizing the sum of n objective functions over a multi-agent network. The agents are embedded in an undirected graph where they can only send/receive information directly to/from their immediate neighbors. Assuming smooth and strongly convex objective functions, we propose an Optimal Gradient Tracking (OGT) method that achieves the optimal gradient computation complexity O √ κ log 1 ǫ and the optimal communication complexity O
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