Discrete-Space Social Interaction Models: Stability and Continuous Limit

We study the equilibrium properties, including stability, of discrete-space social interaction models with a single type of agents, and their continuous limit. We show that, even though the equilibrium in discrete space can be non-unique for all finite degree of discretization, any sequence of discrete-space models' equilibria converges to the continuous-space model's unique equilibrium as the discretization of space is refined. Showing the existence of multiple equilibria resorts to the stability analysis of equilibria. A general framework for studying equilibria and their stability is presented by characterizing the discrete-space social interaction model as a potential game

Discrete-Space Agglomeration Model with Social Interactions: Multiplicity, Stability, and Continuous Limit of Equilibria

This study examines the properties of equilibrium, including the stability, of discrete-space agglomeration models with social interactions. The findings reveal that while the corresponding continuous-space model has a unique equilibrium, the equilibrium in discrete space can be non-unique for any finite degree of discretization by characterizing the discrete-space model as a potential game. Furthermore, it indicates that despite the above result, any sequence of discrete-space models' equilibria converges to the continuous-space model's unique equilibrium as the discretization of space is refined

Discrete-Space Social Interaction Models: Stability and Continuous Limit

We study the equilibrium properties, including stability, of discrete-space social interaction models with a single type of agents, and their continuous limit. We show that, even though the equilibrium in discrete space can be non-unique for all finite degree of discretization, any sequence of discrete-space models' equilibria converges to the continuous-space model's unique equilibrium as the discretization of space is refined. Showing the existence of multiple equilibria resorts to the stability analysis of equilibria. A general framework for studying equilibria and their stability is presented by characterizing the discrete-space social interaction model as a potential game

On Stable Equilibria in Discrete-Space Social Interaction Models

We investigate the differences and connections between discrete-space and continuous-space social interaction models. Although our class of continuous-space model has a unique equilibrium, we find that discretized models can have multiple equilibria for any degree of discretization, which necessitates a stability analysis of equilibria. We present a general framework for characterizations of equilibria and their stability under a broad class of evolutionary dynamics by using the properties of a potential game. Although the equilibrium population distribution in the continuous space is uniquely given by a symmetric unimodal distribution, we find that such a distribution is not always stable in a discrete space. On the other hand, we also show that any sequence of a discrete-space model's equilibria converges with the continuous-space model's unique equilibrium as the discretization is refined

On Stable Equilibria in Discrete-Space Social Interaction Models

We investigate the differences and connections between discrete-space and continuous-space social interaction models. Although our class of continuous-space model has a unique equilibrium, we find that discretized models can have multiple equilibria for any degree of discretization, which necessitates a stability analysis of equilibria. We present a general framework for characterizations of equilibria and their stability under a broad class of evolutionary dynamics by using the properties of a potential game. Although the equilibrium population distribution in the continuous space is uniquely given by a symmetric unimodal distribution, we find that such a distribution is not always stable in a discrete space. On the other hand, we also show that any sequence of a discrete-space model's equilibria converges with the continuous-space model's unique equilibrium as the discretization is refined

Discrete-Space Social Interaction Models: Stability and Continuous Limit

We study the equilibrium properties, including stability, of discrete-space social interaction models with a single type of agents, and their continuous limit. We show that, even though the equilibrium in discrete space can be non-unique for all finite degree of discretization, any sequence of discrete-space models' equilibria converges to the continuous-space model's unique equilibrium as the discretization of space is refined. Showing the existence of multiple equilibria resorts to the stability analysis of equilibria. A general framework for studying equilibria and their stability is presented by characterizing the discrete-space social interaction model as a potential game

Blockade of phonon hopping in trapped ions in the presence of multiple local phonons

Driving an ion at a motional sideband transition induces the Jaynes--Cummings (JC) interaction. This JC interaction creates an anharmonic ladder of JC eigenstates, resulting in the suppression of phonon hopping due to energy conservation. Here, we realize phonon blockade in the presence of multiple local phonons in a trapped-ion chain. Our work establishes a key technological component for quantum simulation with multiple bosonic particles, which can simulate classically intractable problems.Comment: 6 pages, 4 figure

Endothelial ROBO4 suppresses PTGS2/COX-2 expression and inflammatory diseases

Tanaka M., Shirakura K., Takayama Y., et al. Endothelial ROBO4 suppresses PTGS2/COX-2 expression and inflammatory diseases. Communications Biology 7, 599 (2024); https://doi.org/10.1038/s42003-024-06317-z .Accumulating evidence suggests that endothelial cells can be useful therapeutic targets. One of the potential targets is an endothelial cell-specific protein, Roundabout4 (ROBO4). ROBO4 has been shown to ameliorate multiple diseases in mice, including infectious diseases and sepsis. However, its mechanisms are not fully understood. In this study, using RNA-seq analysis, we found that ROBO4 downregulates prostaglandin-endoperoxide synthase 2 (PTGS2), which encodes cyclooxygenase-2. Mechanistic analysis reveals that ROBO4 interacts with IQ motif-containing GTPase-activating protein 1 (IQGAP1) and TNF receptor-associated factor 7 (TRAF7), a ubiquitin E3 ligase. In this complex, ROBO4 enhances IQGAP1 ubiquitination through TRAF7, inhibits prolonged RAC1 activation, and decreases PTGS2 expression in inflammatory endothelial cells. In addition, Robo4-deficiency in mice exacerbates PTGS2-associated inflammatory diseases, including arthritis, edema, and pain. Thus, we reveal the molecular mechanism by which ROBO4 suppresses the inflammatory response and vascular hyperpermeability, highlighting its potential as a promising therapeutic target for inflammatory diseases

Five Amino Acid Residues Responsible for the High Stability of Hydrogenobacter thermophilus Cytochrome c552

Five amino acid residues responsible for extreme stability have been identified in cytochrome c552 (HT c552) from a thermophilic bacterium, Hydrogenobacter thermophilus. The five residues, which are spatially distributed in three regions of HT c552, were replaced with the corresponding residues in the homologous but less stable cytochrome c551 (PA c551) from Pseudomonas aeruginosa. The quintuple HT c552 variant (A7F/M13V/Y34F/Y43E/I78V) showed the same stability against guanidine hydrochloride denaturation as that of PA c551, suggesting that the five residues in HT c552 necessarily and sufficiently contribute to the overall stability. In the three HT c552 variants carrying mutations in each of the three regions, the Y34F/Y43E mutations resulted in the greatest destabilization, by –13.3 kJ mol–1, followed by A7F/M13V (–3.3 kJ mol–1) and then I78V (–1.5 kJ mol–1). The order of destabilization in HT c552 was the same as that of stabilization in PA c551 with reverse mutations such as F34Y/E43Y, F7A/V13M, and V78I (13.4, 10.3, and 0.3 kJ mol–1, respectively). The results of guanidine hydrochloride denaturation were consistent with those of thermal denaturation for the same variants. The present study established a method for reciprocal mutation analysis. The effects of side-chain contacts were experimentally evaluated by swapping the residues between the two homologous proteins that differ in stability. A comparative study of the two proteins was a useful tool for assessing the amino acid contribution to the overall stability.This work was supported in part by grants from Hiroshima University, the Noda Institute for Scientific Research, and the Japanese Ministry of Education, Science and Culture (grants-in-aid for Scientific Research on Priority Areas)