We present and discuss seven different open problems in applied combinatorics. The application areas relevant to this compilation include quantum computing, algorithmic differentiation, topological data analysis, iterative methods, hypergraph cut algorithms, and power systems.

AI documentation is a rapidly-growing channel for coordinating the design of AI technologies with policies for transparency and accessibility. Calls to standardize and enact documentation of algorithmic harms and impacts are now commonplace. However, documentation standards for AI remain inchoate, and fail to match the capabilities and social effects of increasingly impactful architectures such as Large Language Models (LLMs). In this paper, we show the limits of present documentation protocols, and argue for dynamic documentation as a new paradigm for understanding and evaluating AI systems. We first review canonical approaches to system documentation outside the context of AI, focusing on the complex history of Environmental Impact Statements (EISs). We next compare critical elements of the EIS framework to present challenges with algorithmic documentation, which have inherited the limitations of EISs without incorporating their strengths. These challenges are specifically illustrated through the growing popularity of Model Cards and two case studies of algorithmic impact assessment in China and Canada. Finally, we evaluate more recent proposals, including Reward Reports, as potential components of fully dynamic AI documentation protocols.

We present a novel pipeline for learning the conditional distribution of a building roof mesh given pixels from an aerial image, under the assumption that roof geometry follows a set of regular patterns. Unlike alternative methods that require multiple images of the same object, our approach enables estimating 3D roof meshes using only a single image for predictions. The approach employs the PolyGen, a deep generative transformer architecture for 3D meshes. We apply this model in a new domain and investigate the sensitivity of the image resolution. We propose a novel metric to evaluate the performance of the inferred meshes, and our results show that the model is robust even at lower resolutions, while qualitatively producing realistic representations for out-of-distribution samples.

Aerial scene classification, which aims to semantically label remote sensing images in a set of predefined classes (e.g., agricultural, beach, and harbor), is a very challenging task in remote sensing due to high intra-class variability and the different scales and orientations of the objects present in the dataset images. In remote sensing area, the use of CNN architectures as an alternative solution is also a reality for scene classification tasks. Generally, these CNNs are used to perform the traditional image classification task. However, another less used way to classify remote sensing image might be the one that uses deep metric learning (DML) approaches. In this sense, this work proposes to employ six DML approaches for aerial scene classification tasks, analysing their behave with four different pre-trained CNNs as well as combining them through the use of evolutionary computation algorithm (UMDA). In performed experiments, it is possible to observe than DML approaches can achieve the best classification results when compared to traditional pre-trained CNNs for three well-known remote sensing aerial scene datasets. In addition, the UMDA algorithm proved to be a promising strategy to combine DML approaches when there is diversity among them, managing to improve at least 5.6% of accuracy in the classification results using almost 50\% of the available classifiers for the construction of the final ensemble of classifiers.

While power systems research relies on the availability of real-world network datasets, data owners (e.g., system operators) are hesitant to share data due to security and privacy risks. To control these risks, we develop privacy-preserving algorithms for the synthetic generation of optimization and machine learning datasets. Taking a real-world dataset as input, the algorithms output its noisy, synthetic version, which preserves the accuracy of the real data on a specific downstream model or even a large population of those. We control the privacy loss using Laplace and Exponential mechanisms of differential privacy and preserve data accuracy using a post-processing convex optimization. We apply the algorithms to generate synthetic network parameters and wind power data.

In complex large-scale systems such as climate, important effects are caused by a combination of confounding processes that are not fully observable. The identification of sources from observations of system state is vital for attribution and prediction, which inform critical policy decisions. The difficulty of these types of inverse problems lies in the inability to isolate sources and the cost of simulating computational models. Surrogate models may enable the many-query algorithms required for source identification, but data challenges arise from high dimensionality of the state and source, limited ensembles of costly model simulations to train a surrogate model, and few and potentially noisy state observations for inversion due to measurement limitations. The influence of auxiliary processes adds an additional layer of uncertainty that further confounds source identification. We introduce a framework based on (1) calibrating deep neural network surrogates to the flow maps provided by an ensemble of simulations obtained by varying sources, and (2) using these surrogates in a Bayesian framework to identify sources from observations via optimization. Focusing on an atmospheric dispersion exemplar, we find that the expressive and computationally efficient nature of the deep neural network operator surrogates in appropriately reduced dimension allows for source identification with uncertainty quantification using limited data. Introducing a variable wind field as an auxiliary process, we find that a Bayesian approximation error approach is essential for reliable source inversion when uncertainty due to wind stresses the algorithm.

Objective: A major challenge in designing closed-loop brain-computer interfaces is finding optimal stimulation patterns as a function of ongoing neural activity for different subjects and objectives. Approach: To achieve goal-directed closed-loop neurostimulation, we propose "neural co-processors" which use artificial neural networks and deep learning to learn optimal closed-loop stimulation policies, shaping neural activity and bridging injured neural circuits for targeted repair and rehabilitation. The co-processor adapts the stimulation policy as the biological circuit itself adapts to the stimulation, achieving a form of brain-device co-adaptation. Here we use simulations to lay the groundwork for future in vivo tests of neural co-processors. We leverage a cortical model of grasping, to which we applied various forms of simulated lesions, allowing us to develop the critical learning algorithms and study adaptations to non-stationarity. Main results: Our simulations show the ability of a neural co-processor to learn a stimulation policy using a supervised learning approach, and to adapt that policy as the underlying brain and sensors change. Our co-processor successfully co-adapted with the simulated brain to accomplish the reach-and-grasp task after a variety of lesions were applied, achieving recovery towards healthy function. Significance: Our results provide the first proof-of-concept demonstration of a co-processor for adaptive activity-dependent closed-loop neurostimulation, optimizing for a rehabilitation goal. While a gap remains between simulations and applications, our results provide insights on how co-processors may be developed for learning complex adaptive stimulation policies for a variety of neural rehabilitation and neuroprosthetic applications.

Overcoming the time scale limitations of atomistics can be achieved by switching from the state-space representation of Molecular Dynamics (MD) to a statistical-mechanics-based representation in phase space, where approximations such as maximum-entropy or Gaussian phase packets (GPP) evolve the atomistic ensemble in a time-coarsened fashion. In practice, this requires the computation of expensive high-dimensional integrals over all of phase space of an atomistic ensemble. This, in turn, is commonly accomplished efficiently by low-order numerical quadrature. We show that numerical quadrature in this context, unfortunately, comes with a set of inherent problems, which corrupt the accuracy of simulations -- especially when dealing with crystal lattices with imperfections. As a remedy, we demonstrate that Graph Neural Networks, trained on Monte-Carlo data, can serve as a replacement for commonly used numerical quadrature rules, overcoming their deficiencies and significantly improving the accuracy. This is showcased by three benchmarks: the thermal expansion of copper, the martensitic phase transition of iron, and the energy of grain boundaries. We illustrate the benefits of the proposed technique over classically used third- and fifth-order Gaussian quadrature, we highlight the impact on time-coarsened atomistic predictions, and we discuss the computational efficiency. The latter is of general importance when performing frequent evaluation of phase space or other high-dimensional integrals, which is why the proposed framework promises applications beyond the scope of atomistics.

Discover these top 20 future-proof careers for a child in the age of AI – as our world becomes more (and more!) reliant on technology. Plus, learn 20 tips for ethically raising an AI-ready child to ensure they develop the skills and values they need to succeed in an AI-driven world. As a parent to a 12-year-old boy, I often find myself wondering what he will be doing in his career – considering today's ever-evolving technological world. Of course the future is impossible to predict! But one thing is certain – AI and technology will continue to play an increasingly important role in all aspects of life – whether we like it or not.

Solar panels have become a popular source of renewable energy in a variety of industries, from agriculture and transportation to construction and hospitality. By harnessing the power of the sun, we can generate electricity without harming the environment. However, there are challenges associated with using solar panels, and one of the biggest is the accumulation of dust on their surfaces. This can significantly reduce their efficiency and limit their usefulness for energy production and other applications. To address this issue, automation can play a key role in ensuring regular and timely maintenance of solar panels. By automating the cleaning process, we can increase productivity and efficiency, while also reducing the environmental impact of energy generation. Overall, the potential benefits of solar panels are vast and varied, and with the help of automation, we can overcome the challenges associated with their use and continue to drive progress in this exciting and rapidly-evolving field.