RESUMO
The search for symmetry, as an unusual yet profoundly appealing phenomenon, and the origin of regular, repeating configuration patterns have long been a central focus of complexity science and physics. To better grasp and understand symmetry of configurations in decentralized toroidal architectures, we employ group-theoretic methods, which allow us to identify and enumerate these inputs, and argue about irreversible system behaviors with undesired effects on many computational problems. The concept of so-called "configuration shift-symmetry" is applied to two-dimensional cellular automata as an ideal model of computation. Regardless of the transition function, the results show the universal insolvability of crucial distributed tasks, such as leader election, pattern recognition, hashing, and encryption. By using compact enumeration formulas and bounding the number of shift-symmetric configurations for a given lattice size, we efficiently calculate the probability of a configuration being shift-symmetric for a uniform or density-uniform distribution. Further, we devise an algorithm detecting the presence of shift-symmetry in a configuration. Given the resource constraints, the enumeration and probability formulas can directly help to lower the minimal expected error and provide recommendations for system's size and initialization. Besides cellular automata, the shift-symmetry analysis can be used to study the nonlinear behavior in various synchronous rule-based systems that include inference engines, Boolean networks, neural networks, and systolic arrays.
RESUMO
T follicular helper (Tfh) cells are a highly plastic subset of CD4+ T cells specialized in providing B cell help and promoting inflammatory and effector responses during infectious and immune-mediate diseases. Helicobacter pylori is the dominant member of the gastric microbiota and exerts both beneficial and harmful effects on the host. Chronic inflammation in the context of H. pylori has been linked to an upregulation in T helper (Th)1 and Th17 CD4+ T cell phenotypes, controlled in part by the cytokine, interleukin-21. This study investigates the differentiation and regulation of Tfh cells, major producers of IL-21, in the immune response to H. pylori challenge. To better understand the conditions influencing the promotion and inhibition of a chronically elevated Tfh population, we used top-down and bottom-up approaches to develop computational models of Tfh and T follicular regulatory (Tfr) cell differentiation. Stability analysis was used to characterize the presence of two bi-stable steady states in the calibrated Tfh/Tfr models. Stochastic simulation was used to illustrate the ability of the parameter set to dictate two distinct behavioral patterns. Furthermore, sensitivity analysis helped identify the importance of various parameters on the establishment of Tfh and Tfr cell populations. The core network model was expanded into a more comprehensive and predictive model by including cytokine production and signaling pathways. From the expanded network, the interaction between TGFB-Induced Factor Homeobox 1 (Tgif1) and the retinoid X receptor (RXR) was displayed to exert control over the determination of the Tfh response. Model simulations predict that Tgif1 and RXR respectively induce and curtail Tfh responses. This computational hypothesis was validated experimentally by assaying Tgif1, RXR and Tfh in stomachs of mice infected with H. pylori.