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StreamBed is a capacity planning system for stream processing. It predicts, ahead of any production deployment, the resources that a query will require to process an incoming data rate sustainably, and the appropriate configuration of these resources. StreamBed builds a capacity planning model by piloting a series of runs of the target query in a small-scale, controlled testbed. We implement StreamBed for the popular Flink DSP engine. Our evaluation with large-scale queries of the Nexmark benchmark demonstrates that StreamBed can effectively and accurately predict capacity requirements for jobs spanning more than 1,000 cores using a testbed of only 48 cores.

Many real-world processes have complex tail dependence structures that cannot be characterized using classical Gaussian processes. More flexible spatial extremes models exhibit appealing extremal dependence properties but are often exceedingly prohibitive to fit and simulate from in high dimensions. In this paper, we develop a new spatial extremes model that has flexible and non-stationary dependence properties, and we integrate it in the encoding-decoding structure of a variational autoencoder (XVAE), whose parameters are estimated via variational Bayes combined with deep learning. The XVAE can be used as a spatio-temporal emulator that characterizes the distribution of potential mechanistic model output states and produces outputs that have the same statistical properties as the inputs, especially in the tail. As an aside, our approach also provides a novel way of making fast inference with complex extreme-value processes. Through extensive simulation studies, we show that our XVAE is substantially more time-efficient than traditional Bayesian inference while also outperforming many spatial extremes models with a stationary dependence structure. To further demonstrate the computational power of the XVAE, we analyze a high-resolution satellite-derived dataset of sea surface temperature in the Red Sea, which includes 30 years of daily measurements at 16703 grid cells. We find that the extremal dependence strength is weaker in the interior of Red Sea and it has decreased slightly over time.

Auxiliary data sources have become increasingly important in epidemiological surveillance, as they are often available at a finer spatial and temporal resolution, larger coverage, and lower latency than traditional surveillance signals. We describe the problem of spatial and temporal heterogeneity in these signals derived from these data sources, where spatial and/or temporal biases are present. We present a method to use a ``guiding'' signal to correct for these biases and produce a more reliable signal that can be used for modeling and forecasting. The method assumes that the heterogeneity can be approximated by a low-rank matrix and that the temporal heterogeneity is smooth over time. We also present a hyperparameter selection algorithm to choose the parameters representing the matrix rank and degree of temporal smoothness of the corrections. In the absence of ground truth, we use maps and plots to argue that this method does indeed reduce heterogeneity. Reducing heterogeneity from auxiliary data sources greatly increases their utility in modeling and forecasting epidemics.

Langevin dynamics are widely used in sampling high-dimensional, non-Gaussian distributions whose densities are known up to a normalizing constant. In particular, there is strong interest in unadjusted Langevin algorithms (ULA), which directly discretize Langevin dynamics to estimate expectations over the target distribution. We study the use of transport maps that approximately normalize a target distribution as a way to precondition and accelerate the convergence of Langevin dynamics. We show that in continuous time, when a transport map is applied to Langevin dynamics, the result is a Riemannian manifold Langevin dynamics (RMLD) with metric defined by the transport map. We also show that applying a transport map to an irreversibly-perturbed ULA results in a geometry-informed irreversible perturbation (GiIrr) of the original dynamics. These connections suggest more systematic ways of learning metrics and perturbations, and also yield alternative discretizations of the RMLD described by the map, which we study. Under appropriate conditions, these discretized processes can be endowed with non-asymptotic bounds describing convergence to the target distribution in 2-Wasserstein distance. Illustrative numerical results complement our theoretical claims.

The growth of dendritic grains during solidification is often modelled using the Grain Envelope Model (GEM), in which the envelope of the dendrite is an interface tracked by the Phase Field Interface Capturing (PFIC) method. In the PFIC method, an phase-field equation is solved on a fixed mesh to track the position of the envelope. While being versatile and robust, PFIC introduces certain numerical artefacts. In this work, we present an alternative approach for the solution of the GEM that employs a Meshless (sharp) Interface Tracking (MIT) formulation, which uses direct, artefact-free interface tracking. In the MIT, the envelope (interface) is defined as a moving domain boundary and the interface-tracking nodes are boundary nodes for the diffusion problem solved in the domain. To increase the accuracy of the method for the diffusion-controlled moving-boundary problem, an \h-adaptive spatial discretization is used, thus, the node spacing is refined in the vicinity of the envelope. MIT combines a parametric surface reconstruction, a mesh-free discretization of the parametric surfaces and the space enclosed by them, and a high-order approximation of the partial differential operators and of the solute concentration field using radial basis functions augmented with monomials. The proposed method is demonstrated on a two-dimensional \h-adaptive solution of the diffusive growth of dendrite and evaluated by comparing the results to the PFIC approach. It is shown that MIT can reproduce the results calculated with PFIC, that it is convergent and that it can capture more details in the envelope shape than PFIC with a similar spatial discretization.

We investigate the product structure of hereditary graph classes admitting strongly sublinear separators. We characterise such classes as subgraphs of the strong product of a star and a complete graph of strongly sublinear size. In a more precise result, we show that if any hereditary graph class $\mathcal{G}$ admits $O(n^{1-\epsilon})$ separators, then for any fixed $\delta\in(0,\epsilon)$ every $n$-vertex graph in $\mathcal{G}$ is a subgraph of the strong product of a graph $H$ with bounded tree-depth and a complete graph of size $O(n^{1-\epsilon+\delta})$. This result holds with $\delta=0$ if we allow $H$ to have tree-depth $O(\log\log n)$. Moreover, using extensions of classical isoperimetric inequalties for grids graphs, we show the dependence on $\delta$ in our results and the above $\text{td}(H)\in O(\log\log n)$ bound are both best possible. We prove that $n$-vertex graphs of bounded treewidth are subgraphs of the product of a graph with tree-depth $t$ and a complete graph of size $O(n^{1/t})$, which is best possible. Finally, we investigate the conjecture that for any hereditary graph class $\mathcal{G}$ that admits $O(n^{1-\epsilon})$ separators, every $n$-vertex graph in $\mathcal{G}$ is a subgraph of the strong product of a graph $H$ with bounded tree-width and a complete graph of size $O(n^{1-\epsilon})$. We prove this for various classes $\mathcal{G}$ of interest.

Current deep neural networks (DNNs) for autonomous driving computer vision are typically trained on specific datasets that only involve a single type of data and urban scenes. Consequently, these models struggle to handle new objects, noise, nighttime conditions, and diverse scenarios, which is essential for safety-critical applications. Despite ongoing efforts to enhance the resilience of computer vision DNNs, progress has been sluggish, partly due to the absence of benchmarks featuring multiple modalities. We introduce a novel and versatile dataset named InfraParis that supports multiple tasks across three modalities: RGB, depth, and infrared. We assess various state-of-the-art baseline techniques, encompassing models for the tasks of semantic segmentation, object detection, and depth estimation.

We show how quantum-inspired 2d tensor networks can be used to efficiently and accurately simulate the largest quantum processors from IBM, namely Eagle (127 qubits), Osprey (433 qubits) and Condor (1121 qubits). We simulate the dynamics of a complex quantum many-body system -- specifically, the kicked Ising experiment considered recently by IBM in Nature 618, p. 500-505 (2023) -- using graph-based Projected Entangled Pair States (gPEPS), which was proposed by some of us in PRB 99, 195105 (2019). Our results show that simple tensor updates are already sufficient to achieve very large unprecedented accuracy with remarkably low computational resources for this model. Apart from simulating the original experiment for 127 qubits, we also extend our results to 433 and 1121 qubits, thus setting a benchmark for the newest IBM quantum machines. We also report accurate simulations for infinitely-many qubits. Our results show that gPEPS are a natural tool to efficiently simulate quantum computers with an underlying lattice-based qubit connectivity, such as all quantum processors based on superconducting qubits.

While significant advancements in artificial intelligence (AI) have catalyzed progress across various domains, its full potential in understanding visual perception remains underexplored. We propose an artificial neural network dubbed VISION, an acronym for "Visual Interface System for Imaging Output of Neural activity," to mimic the human brain and show how it can foster neuroscientific inquiries. Using visual and contextual inputs, this multimodal model predicts the brain's functional magnetic resonance imaging (fMRI) scan response to natural images. VISION successfully predicts human hemodynamic responses as fMRI voxel values to visual inputs with an accuracy exceeding state-of-the-art performance by 45%. We further probe the trained networks to reveal representational biases in different visual areas, generate experimentally testable hypotheses, and formulate an interpretable metric to associate these hypotheses with cortical functions. With both a model and evaluation metric, the cost and time burdens associated with designing and implementing functional analysis on the visual cortex could be reduced. Our work suggests that the evolution of computational models may shed light on our fundamental understanding of the visual cortex and provide a viable approach toward reliable brain-machine interfaces.

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.