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In this paper we study the problem of maximizing the distance to a given point over an intersection of balls. It was already known that this problem can be solved in polynomial time and space if the given point is not in the convex hull of the balls centers. The cases where the given point is in the convex hull of the balls centers include all NP-complete problems as we show. Some novel results are given in this area. A novel projection algorithm is developed then applied in the context of the Subset Sum Problem (SSP). Under the assumption that the SSP has at most one solution, we provide a quasi-polynomial algorithm, which decreases the radius of an initial ball containing the solution to the SSP. We perform some numerical tests which show the effectiveness of the proposed algorithm.

In uniform-price markets, suppliers compete to supply a resource to consumers, resulting in a single market price determined by their competition. For sufficient flexibility, producers and consumers prefer to commit to a function as their strategies, indicating their preferred quantity at any given market price. Producers and consumers may wish to act as both, i.e., prosumers. In this paper, we examine the behavior of profit-maximizing prosumers in a uniform-price market for resource allocation with the objective of maximizing the social welfare. We propose a scalar-parameterized function bidding mechanism for the prosumers, in which we establish the existence and uniqueness of Nash equilibrium. Furthermore, we provide an efficient way to compute the Nash equilibrium through the computation of the market allocation at the Nash equilibrium. Finally, we present a case study to illustrate the welfare loss under different variations of market parameters, such as the market's supply capacity and inelastic demand.

Machine learning models have become increasingly popular for predicting the results of soccer matches, however, the lack of publicly-available benchmark datasets has made model evaluation challenging. The 2023 Soccer Prediction Challenge required the prediction of match results first in terms of the exact goals scored by each team, and second, in terms of the probabilities for a win, draw, and loss. The original training set of matches and features, which was provided for the competition, was augmented with additional matches that were played between 4 April and 13 April 2023, representing the period after which the training set ended, but prior to the first matches that were to be predicted (upon which the performance was evaluated). A CatBoost model was employed using pi-ratings as the features, which were initially identified as the optimal choice for calculating the win/draw/loss probabilities. Notably, deep learning models have frequently been disregarded in this particular task. Therefore, in this study, we aimed to assess the performance of a deep learning model and determine the optimal feature set for a gradient-boosted tree model. The model was trained using the most recent five years of data, and three training and validation sets were used in a hyperparameter grid search. The results from the validation sets show that our model had strong performance and stability compared to previously published models from the 2017 Soccer Prediction Challenge for win/draw/loss prediction.

When giving directions to a lost-looking tourist, would you first reference the street-names, cardinal directions, landmarks, or simply tell them to walk five hundred metres in one direction then turn left? Depending on the circumstances, one could reasonably make use of any of these direction giving styles. However, research on direction giving with a robot does not often look at how these different direction styles impact perceptions of the robots intelligence, nor does it take into account how users prior dispositions may impact ratings. In this work, we look at generating natural language for two navigation styles using a created system for a Furhat robot, before measuring perceived intelligence and animacy alongside users prior dispositions to robots in a small preliminary study (N=7). Our results confirm findings by previous work that prior negative attitudes towards robots correlates negatively with propensity to trust robots, and also suggests avenues for future research. For example, more data is needed to explore the link between perceived intelligence and direction style. We end by discussing our plan to run a larger scale experiment, and how to improve our existing study design.

In ski jumping, low repetition rates of jumps limit the effectiveness of training. Thus, increasing learning rate within every single jump is key to success. A critical element of athlete training is motor learning, which has been shown to be accelerated by feedback methods. In particular, a fine-grained control of the center of gravity in the in-run is essential. This is because the actual takeoff occurs within a blink of an eye ($\sim$300ms), thus any unbalanced body posture during the in-run will affect flight. This paper presents a smart, compact, and energy-efficient wireless sensor system for real-time performance analysis and biofeedback during ski jumping. The system operates by gauging foot pressures at three distinct points on the insoles of the ski boot at 100Hz. Foot pressure data can either be directly sent to coaches to improve their feedback, or fed into a ML model to give athletes instantaneous in-action feedback using a vibration motor in the ski boot. In the biofeedback scenario, foot pressures act as input variables for an optimized XGBoost model. We achieve a high predictive accuracy of 92.7% for center of mass predictions (dorsal shift, neutral stand, ventral shift). Subsequently, we parallelized and fine-tuned our XGBoost model for a RISC-V based low power parallel processor (GAP9), based on the PULP architecture. We demonstrate real-time detection and feedback (0.0109ms/inference) using our on-chip deployment. The proposed smart system is unobtrusive with a slim form factor (13mm baseboard, 3.2mm antenna) and a lightweight build (26g). Power consumption analysis reveals that the system's energy-efficient design enables sustained operation over multiple days (up to 300 hours) without requiring recharge.

Clustering clients into groups that exhibit relatively homogeneous data distributions represents one of the major means of improving the performance of federated learning (FL) in non-independent and identically distributed (non-IID) data settings. Yet, the applicability of current state-of-the-art approaches remains limited as these approaches cluster clients based on information, such as the evolution of local model parameters, that is only obtainable through actual on-client training. On the other hand, there is a need to make FL models available to clients who are not able to perform the training themselves, as they do not have the processing capabilities required for training, or simply want to use the model without participating in the training. Furthermore, the existing alternative approaches that avert the training still require that individual clients have a sufficient amount of labeled data upon which the clustering is based, essentially assuming that each client is a data annotator. In this paper, we present REPA, an approach to client clustering in non-IID FL settings that requires neither training nor labeled data collection. REPA uses a novel supervised autoencoder-based method to create embeddings that profile a client's underlying data-generating processes without exposing the data to the server and without requiring local training. Our experimental analysis over three different datasets demonstrates that REPA delivers state-of-the-art model performance while expanding the applicability of cluster-based FL to previously uncovered use cases.

In this paper, we investigate how the initial models and the final models for the polynomial functors can be uniformly specified in matching logic.

Denoisers play a central role in many applications, from noise suppression in low-grade imaging sensors, to empowering score-based generative models. The latter category of methods makes use of Tweedie's formula, which links the posterior mean in Gaussian denoising (i.e., the minimum MSE denoiser) with the score of the data distribution. Here, we derive a fundamental relation between the higher-order central moments of the posterior distribution, and the higher-order derivatives of the posterior mean. We harness this result for uncertainty quantification of pre-trained denoisers. Particularly, we show how to efficiently compute the principal components of the posterior distribution for any desired region of an image, as well as to approximate the full marginal distribution along those (or any other) one-dimensional directions. Our method is fast and memory efficient, as it does not explicitly compute or store the high-order moment tensors and it requires no training or fine tuning of the denoiser. Code and examples are available on the project's webpage in //hilamanor.github.io/GaussianDenoisingPosterior/

Recommender systems often struggle to strike a balance between matching users' tastes and providing unexpected recommendations. When recommendations are too narrow and fail to cover the full range of users' preferences, the system is perceived as useless. Conversely, when the system suggests too many items that users don't like, it is considered impersonal or ineffective. To better understand user sentiment about the breadth of recommendations given by a movie recommender, we conducted interviews and surveys and found out that many users considered narrow recommendations to be useful, while a smaller number explicitly wanted greater breadth. Additionally, we designed and ran an online field experiment with a larger user group, evaluating two new interfaces designed to provide users with greater access to broader recommendations. We looked at user preferences and behavior for two groups of users: those with higher initial movie diversity and those with lower diversity. Among our findings, we discovered that different level of exploration control and users' subjective preferences on interfaces are more predictive of their satisfaction with the recommender.

The goal of text ranking is to generate an ordered list of texts retrieved from a corpus in response to a query. Although the most common formulation of text ranking is search, instances of the task can also be found in many natural language processing applications. This survey provides an overview of text ranking with neural network architectures known as transformers, of which BERT is the best-known example. The combination of transformers and self-supervised pretraining has, without exaggeration, revolutionized the fields of natural language processing (NLP), information retrieval (IR), and beyond. In this survey, we provide a synthesis of existing work as a single point of entry for practitioners who wish to gain a better understanding of how to apply transformers to text ranking problems and researchers who wish to pursue work in this area. We cover a wide range of modern techniques, grouped into two high-level categories: transformer models that perform reranking in multi-stage ranking architectures and learned dense representations that attempt to perform ranking directly. There are two themes that pervade our survey: techniques for handling long documents, beyond the typical sentence-by-sentence processing approaches used in NLP, and techniques for addressing the tradeoff between effectiveness (result quality) and efficiency (query latency). Although transformer architectures and pretraining techniques are recent innovations, many aspects of how they are applied to text ranking are relatively well understood and represent mature techniques. However, there remain many open research questions, and thus in addition to laying out the foundations of pretrained transformers for text ranking, this survey also attempts to prognosticate where the field is heading.