Semidefinite complementarity reformulation for robust Nash equilibrium problems with Euclidean uncertainty sets

Consider the N-person non-cooperative game in which each player’s cost function and the opponents’ strategies are uncertain. For such an incomplete information game, the new solution concept called a robust Nash equilibrium has attracted much attention over the past several years. The robust Nash equilibrium results from each player’s decision-making based on the robust optimization policy. In this paper, we focus on the robust Nash equilibrium problem in which each player’s cost function is quadratic, and the uncertainty sets for the opponents’ strategies and the cost matrices are represented by means of Euclidean and Frobenius norms, respectively. Then, we show that the robust Nash equilibrium problem can be reformulated as a semidefinite complementarity problem (SDCP), by utilizing the semidefinite programming (SDP) reformulation technique in robust optimization. We also give some numerical example to illustrate the behavior of robust Nash equilibria.     

Therapeutic targets in the ASK1-dependent stress signaling pathways

Apoptosis signal-regulating kinase 1 (ASK1) is a member of the mitogen-activated protein kinase kinase kinase (MAP3K) family that activates downstream MAP kinases (MAPKs), c-Jun N-terminal kinases (JNKs) and p38 MAPKs, in response to various stresses, such as reactive oxygen species (ROS), endoplasmic reticulum (ER) stress, lipopolysaccharide, and calcium overload. Activation of the JNK and p38 pathways induces stress responses such as cell death, differentiation, and the production of inflammatory cytokines. A series of studies using ASK1-deficient mice have indicated that ASK1 plays important roles in many stress-related diseases, including cardiovascular and neurodegenerative diseases, suggesting that small compounds that inhibit ASK1 activity could possibly be used for the amelioration of the development and/or progression of these diseases. In this review, we provide an overview of the pathophysiological roles of ASK1-dependent signaling pathways and discuss the mechanistic basis for how these could serve as potential therapeutic targets.     

Momentum transfer in nonequilibrium steady states

When a Brownian object interacts with noninteracting gas particles under nonequilibrium conditions, energy dissipation associated with Brownian motion causes an additional force on the object as a "momentum transfer deficit." This principle is demonstrated first by a new nonequilibrium steady state model and then applied to several known models such as an adiabatic piston for which a simple explanation has been lacking.     

Lewis-Pairing-Induced Electrochemiluminescence Enhancement from Electron Donor-Acceptor Diads Decorated with Tris(pentafluorophenyl)borane as an Electrochemical Protector

This study reports an effective peripheral decoration of organic donor-acceptor diads with B(C₆F₅)₃ for stabilizing electrogenerated radical ions. By employing a common p-type organic semiconductor benzothienobenzothiophene (BTBT) as the donor, tetracoordinate boron complexes showed improved solution electrochemiluminescence (ECL) intensity, reaching a 156-fold increase compared to that of the parent diad. The unprecedented Lewis-pairing-induced ECL enhancement is attributed to the multiple roles of B(C₆F₅)₃: 1) redistributing frontier orbitals, 2) facilitating electrochemical excitation, and 3) restricting molecular motions. Furthermore, B(C₆F₅)₃ converted the molecular arrangement of BTBT from conventional 2D herringbones into 1D π-stacks. This robust, highly ordered columnar nanostructure allowed red-shifting of the crystalline film ECL with electrochemical doping through the electronic coupling pathways of BTBT. Our approach will facilitate the development of elaborate metal-free ECL systems.     

Impedance Effect on Ion Transport in a Temperature‐Sensitive Gel Membrane

The impedance effect on the ion transport of lithium chloride through temperature‐ and pH‐sensitive gel membranes was investigated. Both conductance and loss tangent show a relatively high value at temperatures near the lower critical solution temperature (14°C), followed by an abrupt drop with a further rise in temperature. The Figure shows an example of changes in absolute complex conductance (Y ), real conductance (G ), and imaginary conductance (B) for a poly(acryloyl‐L ‐proline methyl ester) gel membrane.