This work proposes a unified $hp$-adaptivity framework for hybridized discontinuous Galerkin (HDG) method for a large class of partial differential equations (PDEs) of Friedrichs' type. In particular, we present unified $hp$-HDG formulations for abstract one-field and two-field structures and prove their well-posedness. In order to handle non-conforming interfaces we simply take advantage of HDG built-in mortar structures. With split-type mortars and the approximation space of trace, a numerical flux can be derived via Godunov approach and be naturally employed without any additional treatment. As a consequence, the proposed formulations are parameter-free. We perform several numerical experiments for time-independent and linear PDEs including elliptic, hyperbolic, and mixed-type to verify the proposed unified $hp$-formulations and demonstrate the effectiveness of $hp$-adaptation. Two adaptivity criteria are considered: one is based on a simple and fast error indicator, while the other is rigorous but more expensive using an adjoint-based error estimate. The numerical results show that these two approaches are comparable in terms of convergence rate even for problems with strong gradients, discontinuities, or singularities.
The adoption of decentralized, tamper-proof ledger systems is paving the way for new applications and opportunities in different contexts. While most research aims to improve their scalability, privacy, and governance issues, interoperability has received less attention. Executing transactions across various blockchains is notably instrumental in unlocking the potential of novel applications, particularly in the financial sector, where their potential would otherwise be significantly diminished. Therefore, interoperable ledgers are crucial to ensure the expansion and further adoption of such a technology in various contexts. In this paper, we present a protocol that uses a combination of trusted execution environment (TEE) and blockchains to enable interoperability over independent semi-centralized CBDC ledgers, guaranteeing the atomicity of inter-bank transfers. Our interoperability protocol uses a custom adaptation of atomic swap protocol and is executed by any pair of CBDC instances to realize a one-way transfer. It ensures features such as atomicity, verifiability, correctness, censorship resistance, and privacy while offering high scalability in terms of the number of CBDC instances. Our approach enables to possible deployment scenarios that can be combined: (1) CBDC instances represent central banks of multiple countries, and (2) CBDC instances represent the set of retail banks and a paramount central bank of a single country. We provide a detailed description of our protocol as well as an extensive analysis of its benefits, features, and security. In this WIP paper, we made a proof-of-concept implementation and made a partial evaluation, while the more extensive evaluation will be made in our future work.
During operation, aerial manipulation systems are affected by various disturbances. Among them is a gravitational torque caused by the weight of the robotic arm. Common propeller-based actuation is ineffective against such disturbances because of possible overheating and high power consumption. To overcome this issue, in this paper we propose a winchbased actuation for the crane-stationed cable-suspended aerial manipulator. Three winch-controlled suspension rigging cables produce a desired cable tension distribution to generate a wrench that reduces the effect of gravitational torque. In order to coordinate the robotic arm and the winch-based actuation, a model-based hierarchical whole-body controller is adapted. It resolves two tasks: keeping the robotic arm end-effector at the desired pose and shifting the system center of mass in the location with zero gravitational torque. The performance of the introduced actuation system as well as control strategy is validated through experimental studies.
It has been shown that Maximum Satisfiability (MaxSAT) problem instances can be effectively solved by partitioning the set of soft clauses into several disjoint sets. The partitioning methods can be based on clause weights (e.g., stratification) or based on graph representations of the formula. Afterwards, a merge procedure is applied to guarantee that an optimal solution is found. This paper proposes a new framework called UpMax that decouples the partitioning procedure from the MaxSAT solving algorithms. As a result, new partitioning procedures can be defined independently of the MaxSAT algorithm to be used. Moreover, this decoupling also allows users that build new MaxSAT formulas to propose partition schemes based on knowledge of the problem to be solved. We illustrate this approach using several problems and show that partitioning has a large impact on the performance of unsatisfiability-based MaxSAT algorithms.
We study an edge-weighted online stochastic \emph{Generalized Assignment Problem} with \emph{unknown} Poisson arrivals. In this model, we consider a bipartite graph that contains offline bins and online items, where each offline bin is associated with a $D$-dimensional capacity vector and each online item is with a $D$-dimensional demand vector. Online arrivals are sampled from a set of online item types which follow independent but not necessarily identical Poisson processes. The arrival rate for each Poisson process is unknown. Each online item will either be packed into an offline bin which will deduct the allocated bin's capacity vector and generate a reward, or be rejected. The decision should be made immediately and irrevocably upon its arrival. Our goal is to maximize the total reward of the allocation without violating the capacity constraints. We provide a sample-based multi-phase algorithm by utilizing both pre-existing offline data (named historical data) and sequentially revealed online data. We establish its performance guarantee measured by a competitive ratio. In a simplified setting where $D=1$ and all capacities and demands are equal to $1$, we prove that the ratio depends on the number of historical data size and the minimum number of arrivals for each online item type during the planning horizon, from which we analyze the effect of the historical data size and the Poisson arrival model on the algorithm's performance. We further generalize the algorithm to the general multidimensional and multi-demand setting, and present its parametric performance guarantee. The effect of the capacity's (demand's) dimension on the algorithm's performance is further analyzed based on the established parametric form. Finally, we demonstrate the effectiveness of our algorithms numerically.
It is well known that Cauchy problem for Laplace equations is an ill-posed problem in Hadamard's sense. Small deviations in Cauchy data may lead to large errors in the solutions. It is observed that if a bound is imposed on the solution, there exists a conditional stability estimate. This gives a reasonable way to construct stable algorithms. However, it is impossible to have good results at all points in the domain. Although numerical methods for Cauchy problems for Laplace equations have been widely studied for quite a long time, there are still some unclear points, for example, how to evaluate the numerical solutions, which means whether we can approximate the Cauchy data well and keep the bound of the solution, and at which points the numerical results are reliable? In this paper, we will prove the conditional stability estimate which is quantitatively related to harmonic measures. The harmonic measure can be used as an indicate function to pointwisely evaluate the numerical result, which further enables us to find a reliable subdomain where the local convergence rate is higher than a certain order.
In the past decade, we have witnessed the rise of deep learning to dominate the field of artificial intelligence. Advances in artificial neural networks alongside corresponding advances in hardware accelerators with large memory capacity, together with the availability of large datasets enabled researchers and practitioners alike to train and deploy sophisticated neural network models that achieve state-of-the-art performance on tasks across several fields spanning computer vision, natural language processing, and reinforcement learning. However, as these neural networks become bigger, more complex, and more widely used, fundamental problems with current deep learning models become more apparent. State-of-the-art deep learning models are known to suffer from issues that range from poor robustness, inability to adapt to novel task settings, to requiring rigid and inflexible configuration assumptions. Ideas from collective intelligence, in particular concepts from complex systems such as self-organization, emergent behavior, swarm optimization, and cellular systems tend to produce solutions that are robust, adaptable, and have less rigid assumptions about the environment configuration. It is therefore natural to see these ideas incorporated into newer deep learning methods. In this review, we will provide a historical context of neural network research's involvement with complex systems, and highlight several active areas in modern deep learning research that incorporate the principles of collective intelligence to advance its current capabilities. To facilitate a bi-directional flow of ideas, we also discuss work that utilize modern deep learning models to help advance complex systems research. We hope this review can serve as a bridge between complex systems and deep learning communities to facilitate the cross pollination of ideas and foster new collaborations across disciplines.
Recommender systems have been widely applied in different real-life scenarios to help us find useful information. Recently, Reinforcement Learning (RL) based recommender systems have become an emerging research topic. It often surpasses traditional recommendation models even most deep learning-based methods, owing to its interactive nature and autonomous learning ability. Nevertheless, there are various challenges of RL when applying in recommender systems. Toward this end, we firstly provide a thorough overview, comparisons, and summarization of RL approaches for five typical recommendation scenarios, following three main categories of RL: value-function, policy search, and Actor-Critic. Then, we systematically analyze the challenges and relevant solutions on the basis of existing literature. Finally, under discussion for open issues of RL and its limitations of recommendation, we highlight some potential research directions in this field.
Multi-agent influence diagrams (MAIDs) are a popular form of graphical model that, for certain classes of games, have been shown to offer key complexity and explainability advantages over traditional extensive form game (EFG) representations. In this paper, we extend previous work on MAIDs by introducing the concept of a MAID subgame, as well as subgame perfect and trembling hand perfect equilibrium refinements. We then prove several equivalence results between MAIDs and EFGs. Finally, we describe an open source implementation for reasoning about MAIDs and computing their equilibria.
Meta-reinforcement learning algorithms can enable robots to acquire new skills much more quickly, by leveraging prior experience to learn how to learn. However, much of the current research on meta-reinforcement learning focuses on task distributions that are very narrow. For example, a commonly used meta-reinforcement learning benchmark uses different running velocities for a simulated robot as different tasks. When policies are meta-trained on such narrow task distributions, they cannot possibly generalize to more quickly acquire entirely new tasks. Therefore, if the aim of these methods is to enable faster acquisition of entirely new behaviors, we must evaluate them on task distributions that are sufficiently broad to enable generalization to new behaviors. In this paper, we propose an open-source simulated benchmark for meta-reinforcement learning and multi-task learning consisting of 50 distinct robotic manipulation tasks. Our aim is to make it possible to develop algorithms that generalize to accelerate the acquisition of entirely new, held-out tasks. We evaluate 6 state-of-the-art meta-reinforcement learning and multi-task learning algorithms on these tasks. Surprisingly, while each task and its variations (e.g., with different object positions) can be learned with reasonable success, these algorithms struggle to learn with multiple tasks at the same time, even with as few as ten distinct training tasks. Our analysis and open-source environments pave the way for future research in multi-task learning and meta-learning that can enable meaningful generalization, thereby unlocking the full potential of these methods.
Recommender System (RS) is a hot area where artificial intelligence (AI) techniques can be effectively applied to improve performance. Since the well-known Netflix Challenge, collaborative filtering (CF) has become the most popular and effective recommendation method. Despite their success in CF, various AI techniques still have to face the data sparsity and cold start problems. Previous works tried to solve these two problems by utilizing auxiliary information, such as social connections among users and meta-data of items. However, they process different types of information separately, leading to information loss. In this work, we propose to utilize Heterogeneous Information Network (HIN), which is a natural and general representation of different types of data, to enhance CF-based recommending methods. HIN-based recommender systems face two problems: how to represent high-level semantics for recommendation and how to fuse the heterogeneous information to recommend. To address these problems, we propose to applying meta-graph to HIN-based RS and solve the information fusion problem with a "matrix factorization (MF) + factorization machine (FM)" framework. For the "MF" part, we obtain user-item similarity matrices from each meta-graph and adopt low-rank matrix approximation to get latent features for both users and items. For the "FM" part, we propose to apply FM with Group lasso (FMG) on the obtained features to simultaneously predict missing ratings and select useful meta-graphs. Experimental results on two large real-world datasets, i.e., Amazon and Yelp, show that our proposed approach is better than that of the state-of-the-art FM and other HIN-based recommending methods.