We show that there is a fast algorithm that embeds hierarchical structures in three-dimensional Minkowski spacetime. The correlation of data ends up purely encoded in the causal structure. Our model relies solely on oriented token pairs -- local hierarchical signals -- with no access to global symbolic structure. We apply our method to the corpus of \textit{WordNet}. We provide a perfect embedding of the mammal sub-tree including ambiguities (more than one hierarchy per node) in such a way that the hierarchical structures get completely codified in the geometry and exactly reproduce the ground-truth. We extend this to a perfect embedding of the maximal unambiguous subset of the \textit{WordNet} with 82{,}115 noun tokens and a single hierarchy per token. We introduce a novel retrieval mechanism in which causality, not distance, governs hierarchical access. Our results seem to indicate that all discrete data has a perfect geometrical representation that is three-dimensional. The resulting embeddings are nearly conformally invariant, indicating deep connections with general relativity and field theory. These results suggest that concepts, categories, and their interrelations, namely hierarchical meaning itself, is geometric.

Foundational models have emerged as a powerful paradigm in deep learning field, leveraging their capacity to learn robust representations from large-scale datasets and effectively to diverse downstream applications such as classification. In this paper, we present Astromer 2 a foundational model specifically designed for extracting light curve embeddings. We introduce Astromer 2 as an enhanced iteration of our self-supervised model for light curve analysis. This paper highlights the advantages of its pre-trained embeddings, compares its performance with that of its predecessor, Astromer 1, and provides a detailed empirical analysis of its capabilities, offering deeper insights into the model's representations. Astromer 2 is pretrained on 1.5 million single-band light curves from the MACHO survey using a self-supervised learning task that predicts randomly masked observations within sequences. Fine-tuning on a smaller labeled dataset allows us to assess its performance in classification tasks. The quality of the embeddings is measured by the F1 score of an MLP classifier trained on Astromer-generated embeddings. Our results demonstrate that Astromer 2 significantly outperforms Astromer 1 across all evaluated scenarios, including limited datasets of 20, 100, and 500 samples per class. The use of weighted per-sample embeddings, which integrate intermediate representations from Astromer's attention blocks, is particularly impactful. Notably, Astromer 2 achieves a 15% improvement in F1 score on the ATLAS dataset compared to prior models, showcasing robust generalization to new datasets. This enhanced performance, especially with minimal labeled data, underscores the potential of Astromer 2 for more efficient and scalable light curve analysis.

Mining machinery operating in variable environments faces high wear and unpredictable stress, challenging Predictive Maintenance (PdM). This paper introduces the Edge Sensor Network for Predictive Maintenance (ESN-PdM), a hierarchical inference framework across edge devices, gateways, and cloud services for real-time condition monitoring. The system dynamically adjusts inference locations--on-device, on-gateway, or on-cloud--based on trade-offs among accuracy, latency, and battery life, leveraging Tiny Machine Learning (TinyML) techniques for model optimization on resource-constrained devices. Performance evaluations showed that on-sensor and on-gateway inference modes achieved over 90\% classification accuracy, while cloud-based inference reached 99\%. On-sensor inference reduced power consumption by approximately 44\%, enabling up to 104 hours of operation. Latency was lowest for on-device inference (3.33 ms), increasing when offloading to the gateway (146.67 ms) or cloud (641.71 ms). The ESN-PdM framework provides a scalable, adaptive solution for reliable anomaly detection and PdM, crucial for maintaining machinery uptime in remote environments. By balancing accuracy, latency, and energy consumption, this approach advances PdM frameworks for industrial applications.

Random utility maximisation (RUM) models are one of the cornerstones of discrete choice modelling. However, specifying the utility function of RUM models is not straightforward and has a considerable impact on the resulting interpretable outcomes and welfare measures. In this paper, we propose a new discrete choice model based on artificial neural networks (ANNs) named "Alternative-Specific and Shared weights Neural Network (ASS-NN)", which provides a further balance between flexible utility approximation from the data and consistency with two assumptions: RUM theory and fungibility of money (i.e., "one euro is one euro"). Therefore, the ASS-NN can derive economically-consistent outcomes, such as marginal utilities or willingness to pay, without explicitly specifying the utility functional form. Using a Monte Carlo experiment and empirical data from the Swissmetro dataset, we show that ASS-NN outperforms (in terms of goodness of fit) conventional multinomial logit (MNL) models under different utility specifications. Furthermore, we show how the ASS-NN is used to derive marginal utilities and willingness to pay measures.

An important number of these alerts analysis of multiple massive datasets in real time, are bogus artifacts created by the image reduction pipelines, prompting the development of multi-stream machine hence, the importance of creating real/bogus classification learning models. In this work, we study algorithms which have proven to be extremely useful for Domain Adaptation (DA) for real/bogus classification detecting real astrophysical phenomena. During the last of astronomical alerts using four different decade, most of these algorithms have been based on Convolutional datasets: HiTS, DES, ATLAS, and ZTF. We Neural Networks (Cabrera-Vives et al., 2016; 2017; study the domain shift between these datasets, Reyes et al., 2018; Duev et al., 2019; Turpin et al., 2020; Yin and improve a naive deep learning classification et al., 2021; Rabeendran & Denneau, 2021) which need a model by using a fine tuning approach and significant amount of data to be trained.

With the increasing volume of astronomical data generated by modern survey telescopes, automated pipelines and machine learning techniques have become crucial for analyzing and extracting knowledge from these datasets. Anomaly detection, i.e. the task of identifying irregular or unexpected patterns in the data, is a complex challenge in astronomy. In this paper, we propose Multi-Class Deep Support Vector Data Description (MCDSVDD), an extension of the state-of-the-art anomaly detection algorithm One-Class Deep SVDD, specifically designed to handle different inlier categories with distinct data distributions. MCDSVDD uses a neural network to map the data into hyperspheres, where each hypersphere represents a specific inlier category. The distance of each sample from the centers of these hyperspheres determines the anomaly score. We evaluate the effectiveness of MCDSVDD by comparing its performance with several anomaly detection algorithms on a large dataset of astronomical light-curves obtained from the Zwicky Transient Facility. Our results demonstrate the efficacy of MCDSVDD in detecting anomalous sources while leveraging the presence of different inlier categories. The code and the data needed to reproduce our results are publicly available at https://github.com/mperezcarrasco/AnomalyALeRCE.

Multi-agent pathfinding (MAPF) is an NP-hard problem. As such, dense maps may be very hard to solve optimally. In such scenarios, compilation-based approaches, via Boolean satisfiability (SAT) and answer set programming (ASP), have been shown to outperform heuristic-search-based approaches, such as conflict-based search (CBS). In this paper, we propose a new Boolean encoding for MAPF, and show how to implement it in ASP and MaxSAT. A feature that distinguishes our encoding from existing ones is that swap and follow conflicts are encoded using binary clauses, which can be exploited by current conflict-driven clause learning (CDCL) solvers. In addition, the number of clauses used to encode swap and follow conflicts do not depend on the number of agents, allowing us to scale better. For MaxSAT, we study different ways in which we may combine the MSU3 and LSU algorithms for maximum performance. In our experimental evaluation, we used square grids, ranging from 20 x 20 to 50 x 50 cells, and warehouse maps, with a varying number of agents and obstacles. We compared against representative solvers of the state-of-the-art, including the search-based algorithm CBS, the ASP-based solver ASP-MAPF, and the branch-and-cut-and-price hybrid solver, BCP. We observe that the ASP implementation of our encoding, ASP-MAPF2 outperforms other solvers in most of our experiments. The MaxSAT implementation of our encoding, MtMS shows best performance in relatively small warehouse maps when the number of agents is large, which are the instances with closer resemblance to hard puzzle-like problems.

Technology evolution is no longer keeping pace with the growth of data. We are facing problems storing and processing the huge amounts of data produced every day. People rely on data-intensive applications and new paradigms (for example, edge computing) to try to keep computation closer to where data is produced and needed. Thus, the need to store and query data in devices where capacity is surpassed by data volume is routine today, ranging from astronomy data to be processed by supercomputers, to personal data to be processed by wearable sensors. The scale is different, yet the underlying problem is the same.

Time-Bounded A* is a real-time, single-agent, deterministic search algorithm that expands states of a graph in the same order as A* does, but that unlike A* interleaves search and action execution. Known to outperform state-of-the-art real-time search algorithms based on Korf's Learning Real-Time A* (LRTA*) in some benchmarks, it has not been studied in detail and is sometimes not considered as a ``true'' real-time search algorithm since it fails in non-reversible problems even it the goal is still reachable from the current state. In this paper we propose and study Time-Bounded Best-First Search (TB(BFS)) a straightforward generalization of the time-bounded approach to any best-first search algorithm. Furthermore, we propose Restarting Time-Bounded Weighted A* (TB_R(WA*)), an algorithm that deals more adequately with non-reversible search graphs, eliminating ``backtracking moves'' and incorporating search restarts and heuristic learning. In non-reversible problems we prove that TB(BFS) terminates and we deduce cost bounds for the solutions returned by Time-Bounded Weighted A* (TB(WA*)), an instance of TB(BFS). Furthermore, we prove TB_R(WA*), under reasonable conditions, terminates. We evaluate TB(WA) in both grid pathfinding and the 15-puzzle. In addition, we evaluate TB_R(WA*) on the racetrack problem. We compare our algorithms to LSS-LRTWA*, a variant of LRTA* that can exploit lookahead search and a weighted heuristic. A general observation is that the performance of both TB(WA*) and TB_R(WA*) improves as the weight parameter is increased. In addition, our time-bounded algorithms almost always outperform LSS-LRTWA* by a significant margin.

Many applications, ranging from video games to dynamic robotics, require solving single-agent, deterministic search problems in partially known environments under very tight time constraints. Real-Time Heuristic Search (RTHS) algorithms are specifically designed for those applications. As a subroutine, most of them invoke a standard, but bounded, search algorithm that searches for the goal. In this paper we present FRIT, a simple approach for single-agent deterministic search problems under tight constraints and partially known environments that unlike traditional RTHS does not search for the goal but rather searches for a path that connects the current state with a so-called ideal tree T . When the agent observes that an arc in the tree cannot be traversed in the actual environment, it removes such an arc from T and then carries out a reconnection search whose objective is to find a path between the current state and any node in T . The reconnection search is done using an algorithm that is passed as a parameter to FRIT. If such a parameter is an RTHS algorithm, then the resulting algorithm can be an RTHS algorithm. We show, in addition, that FRIT may be fed with a (bounded) complete blind-search algorithm. We evaluate our approach over grid pathfinding benchmarks including game maps and mazes. Our results show that FRIT, used with RTAA*, a standard RTHS algorithm, outperforms RTAA* significantly; by one order of magnitude under tight time constraints. In addition, FRIT(daRTAA*) substantially outperforms daRTAA*, a state-of-the-art RTHS algorithm, usually obtaining solutions 50% cheaper on average when performing the same search effort. Finally, FRIT(BFS), i.e., FRIT using breadth-first-search, obtains best-quality solutions when time is limited compared to Adaptive A* and Repeated A*. Finally we show that Bug2, a pathfinding-specific navigation algorithm, outperforms FRIT(BFS) when planning time is extremely limited, but when given more time, the situation reverses.