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Abstract We prove the convergence of a Wasserstein gradient flow of a free energy in inhomogeneous media. Both the energy and media can depend on the spatial variable in a fast oscillatory manner. In particular, we show that the gradient-flow structure is preserved in the limit, which is expressed in terms of an effective energy and Wasserstein metric. The gradient flow and its limiting behavior are analysed through an energy dissipation inequality. The result is consistent with asymptotic analysis in the realm of homogenisation. However, we note that the effective metric is in general different from that obtained from the Gromov–Hausdorff convergence of metric spaces. We apply our framework to a linear Fokker–Planck equation, but we believe the approach is robust enough to be applicable in a broader context. 

Locomotion on dynamic rigid surface (i.e., rigid surface accelerating in an inertial frame) presents complex challenges for controller design, which are essential to address for deploying humanoid robots in dynamic real-world environments such as moving trains, ships, and airplanes. This paper introduces a real-time, provably stabilizing control approach for humanoid walking on periodically swaying rigid surface. The first key contribution is an analytical extension of the classical angular momentum-based linear inverted pendulum model from static to swaying grounds whose motion period may be different than the robot’s gait period. This extension results in a time-varying, nonhomogeneous robot model, which is fundamentally different from the existing pendulum models. We synthesize a discrete footstep control law for the model and derive a new set of sufficient stability conditions that verify the controller’s stabilizing effect. Finally, experiments conducted on a Digit humanoid robot, both in simulations and on hardware, demonstrate the framework’s effectiveness in addressing bipedal locomotion on swaying ground, even under uncertain surface motions and unknown external pushes. 

Tâtonnement is a simple, intuitive market process where prices are iteratively adjusted based on the difference between demand and supply. Many variants under different market assumptions have been studied and shown to converge to a market equilibrium, in some cases at a fast rate. However, the classical case of linear Fisher markets have long eluded the analyses, and it remains unclear whether tâtonnement converges in this case. We show that, for a sufficiently small stepsize, the prices given by the tâtonnement process are guaranteed to converge to equilibrium prices, up to a small approximation radius that depends on the stepsize. To achieve this, we consider the dual Eisenberg-Gale convex program in the price space, view tâtonnement as subgradient descent on this convex program, and utilize novel last-iterate convergence results for subgradient descent under error bound conditions. In doing so, we show that the convex program satisfies a particular error bound condition, the quadratic growth condition, and that the price sequence generated by tâtonnement is bounded above and away from zero. We also show that a similar convergence result holds for tâtonnement in quasi-linear Fisher markets. Numerical experiments are conducted to demonstrate that the theoretical linear convergence aligns with empirical observations. 

The microservices architecture simplifies application development by breaking monolithic applications into manageable microservices. However, this distributed microservice “service mesh” leads to new challenges due to the more complex application topology. Particularly, each service component scales up and down independently creating load imbalance problems on shared backend services accessed by multiple components. Traditional load balancing algorithms do not port over well to a distributed microservice architecture where load balancers are deployed client-side. In this article, we propose a self-managing load balancing system, BLOC, which provides consistent response times to users without using a centralized metadata store or explicit messaging between nodes. BLOC uses overload control approaches to provide feedback to the load balancers. We show that this performs significantly better in solving the incast problem in microservice architectures. A critical component of BLOC is the dynamic capacity estimation algorithm. We show that a well-tuned capacity estimate can outperform even join-the-shortest-queue, a nearly optimal algorithm, while a reasonable dynamic estimate still outperforms Least Connection, a distributed implementation of join-the-shortest-queue. Evaluating this framework, we found that BLOC improves the response time distribution range, between the 10th and 90th percentiles, by 2 –4 times and the tail, 99th percentile, latency by 2 times. 

Abstract Accurate control of a humanoid robot's global position (i.e., its three-dimensional (3D) position in the world) is critical to the reliable execution of high-risk tasks such as avoiding collision with pedestrians in a crowded environment. This paper introduces a time-based nonlinear control approach that achieves accurate global-position tracking (GPT) for multi-domain bipedal walking. Deriving a tracking controller for bipedal robots is challenging due to the highly complex robot dynamics that are time-varying and hybrid, especially for multi-domain walking that involves multiple phases/domains of full actuation, over actuation, and underactuation. To tackle this challenge, we introduce a continuous-phase GPT control law for multi-domain walking, which provably ensures the exponential convergence of the entire error state within the full and over actuation domains and that of the directly regulated error state within the underactuation domain. We then construct sufficient multiple-Lyapunov stability conditions for the hybrid multi-domain tracking error system under the proposed GPT control law. We illustrate the proposed controller design through both three-domain walking with all motors activated and two-domain gait with inactive ankle motors. Simulations of a ROBOTIS OP3 bipedal humanoid robot demonstrate the satisfactory accuracy and convergence rate of the proposed control approach under two different cases of multi-domain walking as well as various walking speed and desired paths. 

Abstract Catalytic enantioconvergent nucleophilic substitution reactions of alkyl halides are highly valuable transformations, but they are notoriously difficult to implement. Specifically, nucleophilic fluorination is a renowned challenge, especially when inexpensive alkali metal fluorides are used as fluorinating reagents due to their low solubility, high hygroscopicity and Brønsted basicity. Here we report a solution by developing the concept of synergistic hydrogen bonding phase-transfer catalysis. Key to our strategy is the combination of a chiralbis-urea hydrogen bond donor (HBD) and an onium salt—two phase-transfer catalysts essential for the solubilization of potassium fluoride—as a well-characterized ternary HBD–onium fluoride complex. Mechanistic investigations indicate that this chiral ternary complex is capable of enantiodiscrimination of racemic benzylic bromides and α-bromoketones, and upon fluoride delivery affords fluorinated products in high yields and enantioselectivities. This work provides a foundation for enantioconvergent fluorination chemistry enabled through the combination of a HBD catalyst with a co-catalyst specifically curated to meet the requirement of the electrophile.