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We present an immersed boundary method to simulate the creeping motion of a rigid particle in a fluid described by the Stokes equations discretized thanks to a finite element strategy on unfitted meshes, called Phi-FEM, that uses the description of the solid with a level-set function. One of the advantages of our method is the use of standard finite element spaces and classical integration tools, while maintaining the optimal convergence (theoretically in the H1 norm for the velocity and L2 for pressure; numerically also in the L2 norm for the velocity).

The finite-state model checking of software is still limited by the notorious state-explosion problem. The dependence-based program slicing is effective to reduce the verification time and is orthogonal to other reduction techniques of model checking. However, within slicing concurrent programs for model checking, the conversions between multiple irreplaceable models and the calculation of dependencies for some variables irrelevant to the verified property produce redundant calculating costs. Thus, we propose a Program Dependence Net (PDNet) as a unified model combining the control-flow structure with dependencies to avoid the model conversions. For reduction, we propose a PDNet slicing to capture the relevant variables' dependencies on demand. The calculating costs could be significantly compressed by our unified model and on-demand slicing based on PDNet. Then, we implemented a concurrent program model checking tool based on PDNet and its slice. Finally, we validated the advantages of our methods.

In the sequential decision making setting, an agent aims to achieve systematic generalization over a large, possibly infinite, set of environments. Such environments are modeled as discrete Markov decision processes with both states and actions represented through a feature vector. The underlying structure of the environments allows the transition dynamics to be factored into two components: one that is environment-specific and another that is shared. Consider a set of environments that share the laws of motion as an example. In this setting, the agent can take a finite amount of reward-free interactions from a subset of these environments. The agent then must be able to approximately solve any planning task defined over any environment in the original set, relying on the above interactions only. Can we design a provably efficient algorithm that achieves this ambitious goal of systematic generalization? In this paper, we give a partially positive answer to this question. First, we provide a tractable formulation of systematic generalization by employing a causal viewpoint. Then, under specific structural assumptions, we provide a simple learning algorithm that guarantees any desired planning error up to an unavoidable sub-optimality term, while showcasing a polynomial sample complexity.

This paper introduces a new parameterization of deep neural networks (both fully-connected and convolutional) with guaranteed Lipschitz bounds, i.e. limited sensitivity to perturbations. The Lipschitz guarantees are equivalent to the tightest-known bounds based on certification via a semidefinite program (SDP), which does not scale to large models. In contrast to the SDP approach, we provide a ``direct'' parameterization, i.e. a smooth mapping from $\mathbb R^N$ onto the set of weights of Lipschitz-bounded networks. This enables training via standard gradient methods, without any computationally intensive projections or barrier terms. The new parameterization can equivalently be thought of as either a new layer type (the \textit{sandwich layer}), or a novel parameterization of standard feedforward networks with parameter sharing between neighbouring layers. We illustrate the method with some applications in image classification (MNIST and CIFAR-10).

This paper presents Odyssey, a novel distributed data-series processing framework that efficiently addresses the critical challenges of exhibiting good speedup and ensuring high scalability in data series processing by taking advantage of the full computational capacity of modern clusters comprised of multi-core servers. Odyssey addresses a number of challenges in designing efficient and highly scalable distributed data series index, including efficient scheduling, and load-balancing without paying the prohibitive cost of moving data around. It also supports a flexible partial replication scheme, which enables Odyssey to navigate through a fundamental trade-off between data scalability and good performance during query answering. Through a wide range of configurations and using several real and synthetic datasets, our experimental analysis demonstrates that Odyssey achieves its challenging goals.

Hyperdimensional computing (HDC) uses binary vectors of high dimensions to perform classification. Due to its simplicity and massive parallelism, HDC can be highly energy-efficient and well-suited for resource-constrained platforms. However, in trading off orthogonality with efficiency, hypervectors may use tens of thousands of dimensions. In this paper, we will examine the necessity for such high dimensions. In particular, we give a detailed theoretical analysis of the relationship among dimensions of hypervectors, accuracy, and orthogonality. The main conclusion of this study is that a much lower dimension, typically less than 100, can also achieve similar or even higher detecting accuracy compared with other state-of-the-art HDC models. Based on this insight, we propose a suite of novel techniques to build HDC models that use binary hypervectors of dimensions that are orders of magnitude smaller than those found in the state-of-the-art HDC models, yet yield equivalent or even improved accuracy and efficiency. For image classification, we achieved an HDC accuracy of 96.88\% with a dimension of only 32 on the MNIST dataset. We further explore our methods on more complex datasets like CIFAR-10 and show the limits of HDC computing.

In this work we propose a batch Bayesian optimization method for combinatorial problems on permutations, which is well suited for expensive-to-evaluate objectives. We first introduce LAW, an efficient batch acquisition method based on determinantal point processes using the acquisition weighted kernel. Relying on multiple parallel evaluations, LAW enables accelerated search on combinatorial spaces. We then apply the framework to permutation problems, which have so far received little attention in the Bayesian Optimization literature, despite their practical importance. We call this method LAW2ORDER. On the theoretical front, we prove that LAW2ORDER has vanishing simple regret by showing that the batch cumulative regret is sublinear. Empirically, we assess the method on several standard combinatorial problems involving permutations such as quadratic assignment, flowshop scheduling and the traveling salesman, as well as on a structure learning task.

Convergence (virtual) bidding is an important part of two-settlement electric power markets as it can effectively reduce discrepancies between the day-ahead and real-time markets. Consequently, there is extensive research into the bidding strategies of virtual participants aiming to obtain optimal bids to submit to the day-ahead market. In this paper, we introduce a price-based general stochastic optimization framework to obtain optimal convergence bid curves. Within this framework, we develop a computationally tractable linear programming-based optimization model, which produces bid prices and volumes simultaneously. We also show that different approximations and simplifications in the general model lead naturally to state-of-the-art convergence bidding approaches, such as self-scheduling and opportunistic approaches. Our general framework also provides a straightforward way to compare the performance of these models, which is demonstrated by numerical experiments on the California (CAISO) market.

Understanding causality helps to structure interventions to achieve specific goals and enables predictions under interventions. With the growing importance of learning causal relationships, causal discovery tasks have transitioned from using traditional methods to infer potential causal structures from observational data to the field of pattern recognition involved in deep learning. The rapid accumulation of massive data promotes the emergence of causal search methods with brilliant scalability. Existing summaries of causal discovery methods mainly focus on traditional methods based on constraints, scores and FCMs, there is a lack of perfect sorting and elaboration for deep learning-based methods, also lacking some considers and exploration of causal discovery methods from the perspective of variable paradigms. Therefore, we divide the possible causal discovery tasks into three types according to the variable paradigm and give the definitions of the three tasks respectively, define and instantiate the relevant datasets for each task and the final causal model constructed at the same time, then reviews the main existing causal discovery methods for different tasks. Finally, we propose some roadmaps from different perspectives for the current research gaps in the field of causal discovery and point out future research directions.

In large-scale systems there are fundamental challenges when centralised techniques are used for task allocation. The number of interactions is limited by resource constraints such as on computation, storage, and network communication. We can increase scalability by implementing the system as a distributed task-allocation system, sharing tasks across many agents. However, this also increases the resource cost of communications and synchronisation, and is difficult to scale. In this paper we present four algorithms to solve these problems. The combination of these algorithms enable each agent to improve their task allocation strategy through reinforcement learning, while changing how much they explore the system in response to how optimal they believe their current strategy is, given their past experience. We focus on distributed agent systems where the agents' behaviours are constrained by resource usage limits, limiting agents to local rather than system-wide knowledge. We evaluate these algorithms in a simulated environment where agents are given a task composed of multiple subtasks that must be allocated to other agents with differing capabilities, to then carry out those tasks. We also simulate real-life system effects such as networking instability. Our solution is shown to solve the task allocation problem to 6.7% of the theoretical optimal within the system configurations considered. It provides 5x better performance recovery over no-knowledge retention approaches when system connectivity is impacted, and is tested against systems up to 100 agents with less than a 9% impact on the algorithms' performance.