Government of Spain

In this paper we provide a positive version of Miljutin's theorem. Namely, we show that for any uncountable compact metric spaces K and L there exists a positive isomorphism T:C(K)⟶ C(L). Moreover, the inverse of T is a regular operator, and T may be chosen so that T_r·T^-1_r≤ 9+6√(3). The method also gives positive versions of classical nonmetrizable results for Miljutin and Dugundji compacta. In particular, if G and H are infinite compact groups of the same weight, then C(G) and C(H) are positively and regularly isomorphic with the same uniform quantitative estimate.

This document presents the development of two mathematical models for an industrial lithium battery. For this purpose, a 48 V, 3500 Wh Li-FePO4 battery from the Pylontech brand was used. This battery operates within a photovoltaic system with energy storage installed at the laboratory of the "Centro de Energias Renovables y Uso Racional de la Energia de la Universidad Nacional de Ingenieria" (Center for Renewable Energy and Rational Use of Energy of the National University of Engineering), located in Lima, Peru. The mathematical models include the dynamic and thermal models of the lithium battery. The electrical behavior observed in the battery is not solely attributed to the battery as an electrochemical element but is also influenced by the power system that connects it to the photovoltaic system, the control system and the internal instrumentation. The developed models are validated using experimental data from the electrical response of the battery when the photovoltaic system operates under a specific photovoltaic production and consumption profile. Additionally, it is observed that noise in the current signal increases as its value decreases. Therefore, to achieve results with acceptable precision, two algorithms were implemented for smoothing the current signal, which serves as an input variable for the developed models. A total of 96% of the calculated NRMSE values fall below 5%, encompassing comparisons between measured and simulated voltage, current, and power of the battery under the various operating conditions evaluated, which provides clear evidence of the strong performance of the proposed models.

In the fast paced world, digital payment systems have generated such massive retail transaction volumes that real-time anomaly detection pipelines must detect fraud while protecting consumers and minimizing operational losses. The effectiveness of anomaly detection systems which use statistical thresholds and batch-based machine learning decreases when operating under high-speed data streams and complex behavioral contexts. The paper introduces a Streaming Analytics LLM framework which includes three new modules: the Prismatic Alert Module (PAM) generates contextualized streaming embeddings through large language models (LLM) for alerting anomalous events, the Agile Response Module (ARM) uses reinforcement learning to detect high-risk transaction streams and the Trajectory Fusion Module (TFM) applies biologically inspired methods to combine multiple features from transaction streams. It involves domain-specific performance metrics that include Detection Lead Time (DLT), Streaming Throughput Stability (STS), Alert Relevance Index (ARI), and Fusion Coherence Score (FCS). The indicated pipeline demonstrates superior performance in detecting anomalies through experimental testing on large retail data collections because it reduces lead time by 4.7 times and improves alert relevance by 3.2 times and decreases false financial burden by 2.9 times when compared to LSTM, Transformer and Spectral FNO architectures.

Cosmic rays below a few hundred GeV and solar energetic particles are key to understanding how the Sun is interacting with its own solar system, as they respond to the magnetic field that fills the entire heliosphere, not only during quiet times, but also during episodes of solar activity, as they change the propagation conditions of cosmic rays and solar energetic particles through the heliosphere. Direct observations of these two types of energetic particles can be made in space using detectors aboard spacecraft such as the Energetic Particle Detector Aboard Solar Orbiter and/or the AMS aboard the International Space Station, for example, and indirect observations using ground-based detectors such as neutron monitors and muon telescopes that measure secondary particles produced through the interaction between cosmic rays and solar energetic particles with atmospheric nuclei. An ideal ground-based detector to investigate the solar-terrestrial relationship should provide the flux of energetic particles, their energy, their identity and their spatial distribution. Neutron monitors and muon telescopes are the usual instruments for this purpose. Neutron monitors can give the neutron count rate although they may have some response to protons and muons. Although direct measurement of the energy/rigidity of energetic particles is not possible, the combination of several neutron monitor stations at different geomagnetic latitudes can provide a spectrum for these particles and the level of directional isotropy on Earth. A rough estimate of this energy can also be provided by a single neutron monitor if it can detect multiplicities by recording the time between successive neutron detections or by capturing pulse heights. Muon telescopes provide count rates of charged particles, mainly muons, entering the detector; their configuration usually allows estimation of incoming particle directions, and a better estimate can be achieved if several geographically well separated muon telescopes are used. However, due to the energy threshold for muon production, these detectors are less sensitive to solar energetic particles than neutron monitors. In recent years, our group has developed and deployed a type of detector that can provide both neutron and muon count rates, information about the cosmic and solar particle spectra, and the arrival directions of muons in the detector volume. This is a combination of a neutron monitor and a muon telescope that share the same structure. Currently, one of them is operating at the Spanish Antarctic Base Juan Carlos I and a second one is operating at the Izaña Atmospheric Observatory, on the slope of Mount Teide, on the island of Tenerife. We present our ground-based detectors, including our first neutron monitor, CaLMa, and our minineutron monitor, miniCaLMa, a multipurpose neutron monitor, as well as our latest results on solar events and the response of neutron monitors as a function of altitude.