An Exact Solution of BPS Domain Wall Junction

An exact solution of domain wall junction is obtained in a four-dimensional N=1 supersymmetric U(1) X U(1)' gauge theory with three pairs of chiral superfields which is motivated by the N=2 SU(2) gauge theory with one flavor perturbed by an adjoint scalar mass. The solution allows us to evaluate various quantities including a new central charge Y_k associated with the junction besides Z_k which appears already in domain walls. We find that the new central charge Y_k gives a negative contribution to the mass of the domain wall junction whereas the central charge Z_k gives a dominant positive contribution. One has to be cautious to identify the central charge Y_k alone as the mass of the junction.Comment: LaTeX file, 13 page, 1 ps figur

Structure and mechanisms of the DsbB–DsbA disulfide bond generation machine

AbstractAll organisms possess specific cellular machinery that introduces disulfide bonds into proteins newly synthesized and transported out of the cytosol. In E. coli, the membrane-integrated DsbB protein cooperates with ubiquinone to generate a disulfide bond, which is transferred to DsbA, a periplasmic dithiol oxido-reductase that serves as the direct disulfide bond donor to proteins folding oxidatively in this compartment. Despite the extensive accumulation of knowledge on this oxidation system, molecular details of the DsbB reaction mechanisms had been controversial due partly to the lack of structural information until our recent determination of the crystal structure of a DsbA–DsbB–ubiquinone complex. In this review we discuss the structural and chemical nature of reaction intermediates in the DsbB catalysis and the illuminated molecular mechanisms that account for the de novo formation of a disulfide bond and its donation to DsbA. It is suggested that DsbB gains the ability to oxidize its specific substrate, DsbA, having very high redox potential, by undergoing a DsbA-induced rearrangement of cysteine residues. One of the DsbB cysteines that are now reduced then interacts with ubiquinone to form a charge transfer complex, leading to the regeneration of a disulfide at the DsbB active site, and the cycle can begin anew

Entropic Model Predictive Optimal Transport for Underactuated Linear Systems

This letter investigates dynamical optimal transport of underactuated linear systems over an infinite time horizon. In our previous work, we proposed to integrate model predictive control and the celebrated Sinkhorn algorithm to perform efficient dynamical transport of agents. However, the proposed method requires the invertibility of input matrices, which severely limits its applicability. To resolve this issue, we extend the method to (possibly underactuated) controllable linear systems. In addition, we ensure the convergence properties of the method for general controllable linear systems. The effectiveness of the proposed method is demonstrated by a numerical example.Comment: Published in IEEE Control Systems Letter

Maximum Entropy Density Control of Discrete-Time Linear Systems with Quadratic Cost

This paper addresses the problem of steering the distribution of the state of a discrete-time linear system to a given target distribution while minimizing an entropy-regularized cost functional. This problem is called a maximum entropy (MaxEnt) density control problem. Specifically, the running cost is given by quadratic forms of the state and the control input, and the initial and final distributions are Gaussian. We first reveal that our problem boils down to solving two Riccati difference equations coupled through their boundary values. Based on them, we give the closed-form expression of the unique optimal policy. Next, we show that the optimal policy for the density control of the time-reversed system can be obtained simultaneously with the forward-time optimal policy. Finally, by considering the limit where the entropy regularization vanishes, we derive the optimal policy for the unregularized density control problem.Comment: 16 page

Multiscale Meteorological Systems Resulted in Meteorological Tsunamis

Meteorological tsunami is a kind of the ocean long wave with the tsunami frequency band from several minutes to 2 h driven by atmospheric forcing at the sea interface. The multiplying of resonance and amplification effects enhanced the wave higher than 1 m with the destructive damage. The direct forcing of meteorological tsunami is the meso-β-scale disturbance, such as mesoscale convection system or internal gravity wave in the troposphere. The events on the destructive meteorological tsunamis were reported mainly on the mid-latitude regions such as Europe and US East Coast. Whatever the kind of the disturbance was, the intrusion of the dry air played important roles in unstable structure of the middle troposphere to travel the disturbance with a long disturbance. The backward trajectory of the air particle on the tsunami-enhancing region showed that the lifting of anomalous warm moist air mass from the lower latitude was significant to form the atmospheric structure over the targeted seas. Such characteristics in the large-scale atmosphere provide the possibility of the mid-term prediction on meteorological tsunamis, linking with the state-of-art observation technologies in satellite remote sensing, radar observation, in situ measurement network and so on

Entropic model predictive optimal transport over dynamical systems

We consider the optimal control problem of steering an agent population to a desired distribution over an infinite horizon. This is an optimal transport problem over dynamical systems, which is challenging due to its high computational cost. In this paper, by using entropy regularization, we propose Sinkhorn MPC, which is a dynamical transport algorithm integrating model predictive control (MPC) and the so-called Sinkhorn algorithm. The notable feature of the proposed method is that it achieves cost-effective transport in real time by performing control and transport planning simultaneously, which is illustrated in numerical examples. Moreover, under some assumption on iterations of the Sinkhorn algorithm integrated in MPC, we reveal the global convergence property for Sinkhorn MPC thanks to the entropy regularization. Furthermore, focusing on a quadratic control cost, without the aforementioned assumption we show the ultimate boundedness and the local asymptotic stability for Sinkhorn MPC