We address two major conceptual developments introduced by Aharonov and collaborators through a \textit{quantum phase space} approach: the concept of \textit{modular variables} devised to explain the phenomena of quantum dynamical non-locality and the \textit{two-state formalism} for Quantum Mechanics which is a retrocausal time-symmetric interpretation of quantum physics which led to the discovery of \textit{weak values.} We propose that a quantum phase space structure underlies these profound physical insights in a unifying manner. For this, we briefly review the Weyl-Wigner and the coherent state formalisms as well as the inherent symplectic structures of quantum projective spaces in order to gain a deeper understanding of the weak value concept. We also review Schwinger's finite quantum kinematics so that we may apply this discrete formalism to understand Aharonov's modular variable concept in a different manner that has been proposed before in the literature. We discuss why we believe that this\ is indeed the correct kinematic framework for the modular variable concept and how this may shine some light on the physical distinction between quantum dynamical non-locality and the kinematic non-locality, generally associated with entangled quantum systems.

We study an expanding two-fluid model of non-relativistic dark matter and radiation which are allowed to interact during a certain time span and to establish an approximate thermal equilibrium. Such interaction which generates an effective bulk viscous pressure at background level is expected to be relevant for times around the transition from radiation to matter dominance. We quantify the magnitude of this pressure for dark matter particles masses within the range $1 {\rm eV} \lesssim m_{\chi} \lesssim 10 {\rm eV}$ around the matter-radiation equality epoch (i.e., redshift $z_{\rm eq}\sim 3400$) and demonstrate that the existence of a transient bulk viscosity has consequences which may be relevant for addressing current tensions of the standard cosmological model: i) the additional (negative) pressure contribution modifies the expansion rate around $z_{\rm eq}$, yielding a larger $H_0$ value and ii) large-scale structure formation is impacted by suppressing the amplitude of matter overdensity growth via a new viscous friction-term contribution to the Mészáros effect. As a result, both the $H_0$ and the $S_8$ tensions of the current standard cosmological model are significantly alleviated.

Deep Metric Learning (DML) aims to learn embedding functions that map semantically similar inputs to proximate points in a metric space while separating dissimilar ones. Existing methods, such as pairwise losses, are hindered by complex sampling requirements and slow convergence. In contrast, proxy-based losses, despite their improved scalability, often fail to optimize global distribution properties. The Decidability-based Loss (D-Loss) addresses this by targeting the decidability index (d') to enhance distribution separability, but its reliance on large mini-batches imposes significant computational constraints. We introduce Proxy-Decidability Loss (PD-Loss), a novel objective that integrates learnable proxies with the statistical framework of d' to optimize embedding spaces efficiently. By estimating genuine and impostor distributions through proxies, PD-Loss combines the computational efficiency of proxy-based methods with the principled separability of D-Loss, offering a scalable approach to distribution-aware DML. Experiments across various tasks, including fine-grained classification and face verification, demonstrate that PD-Loss achieves performance comparable to that of state-of-the-art methods while introducing a new perspective on embedding optimization, with potential for broader applications.

In statistical physics, phase transitions are arguably among the most extensively studied phenomena. In the computational approach to this field, the development of algorithms capable of estimating entropy across the entire energy spectrum in a single execution has highlighted the efficacy of microcanonical inflection point analysis, while Fisher's zeros technique has re-emerged as a powerful methodology for investigating these phenomena. This paper presents an alternative protocol for analyzing phase transitions using a parameterization of entropy function in the microcanonical ensemble. We also provide a clear demonstration of the relation of the linear pattern of the Fisher's zeros on the complex inverse temperature map (a circle in the complex $x=e^{-\beta \varepsilon}$ map) with the order of the transition, showing that the latent heat is inversely related to the distance between the zeros. We study various model systems, including the Lennard-Jones cluster, the Ising, the XY, and the Zeeman models. By examining the behavior of thermodynamic quantities such as entropy and its derivatives in the microcanonical ensemble, we identify key features, such as loops and discontinuities in parametric curves, which signal phase transitions' presence and nature. This approach can facilitate the classification of phase transitions across various physical systems.

We investigate the critical properties of kinetic continuous opinion dynamics using deep learning techniques. The system consists of $N$ continuous spin variables in the interval $[-1,1]$. Dense neural networks are trained on spin configuration data generated via kinetic Monte Carlo simulations, accurately identifying the critical point on both square and triangular lattices. Classical unsupervised learning with principal component analysis reproduces the magnetization and allows estimation of critical exponents. Additionally, variational autoencoders are implemented to study the phase transition through the loss function, which behaves as an order parameter. A correlation function between real and reconstructed data is defined and found to be universal at the critical point.

Prompt engineering is crucial for unlocking the potential of Large Language Models (LLMs). Still, since manual prompt design is often complex, non-intuitive, and time-consuming, automatic prompt optimization has emerged as a research area. However, a significant challenge in prompt optimization is managing the inherent trade-off between task performance, such as accuracy, and context size. Most existing automated methods focus on a single objective, typically performance, thereby failing to explore the critical spectrum of efficiency and effectiveness. This paper introduces the MOPrompt, a novel Multi-objective Evolutionary Optimization (EMO) framework designed to optimize prompts for both accuracy and context size (measured in tokens) simultaneously. Our framework maps the Pareto front of prompt solutions, presenting practitioners with a set of trade-offs between context size and performance, a crucial tool for deploying Large Language Models (LLMs) in real-world applications. We evaluate MOPrompt on a sentiment analysis task in Portuguese, using Gemma-2B and Sabiazinho-3 as evaluation models. Our findings show that MOPrompt substantially outperforms the baseline framework. For the Sabiazinho model, MOPrompt identifies a prompt that achieves the same peak accuracy (0.97) as the best baseline solution, but with a 31% reduction in token length.

The structure of astrophysical objects is usually modeled under the assumption of hydrostatic equilibrium. However, actual configurations may deviate from perfect spherical or isotropic properties. Consequently, cosmic objects are expected to exhibit some degree of anisotropy. This consideration also extends to hypothetical dark structures, such as dark stars and dark matter halos. Although the nature of dark matter remains unknown, axion-like particles (ALPs) are strong candidates, suggesting that dark matter halos may have originated from bosonic configurations undergoing gravitational collapse, sustained by boson-boson interactions in the condensate state. This system is described by the Gross-Pitaevskii-Poisson equation. Furthermore, within the framework of the Bohm-de Broglie approach, quantum effects,encapsulated in the so-called quantum potential, may play a significant role in equilibrium astrophysical configurations. In this study, we examine a class of static anisotropic boson stars which are non-minimally coupled to gravity. By including all these factors, we derive a generalized Lane-Emden-like equation and conduct a detailed analysis of the maximum degree of anisotropy that such systems can sustain, thereby identifying physically viable equilibrium configurations. Apart from focusing on the impact of anisotropic contributions, we find that for the so-called Quantum Polytropes (when the quantum potential is the main responsible for the equilibrium condition), the anisotropic factor and the gravitational field have opposite roles compared to the classical case. This leads to a new class of hydrostatic equilibrium objects.

This work originates from part of a final year undergraduate research project on the Eisenhart lift for Hamiltonian systems. The Eisenhart lift is a procedure to describe trajectories of a classical natural Hamiltonian system as geodesics in an enlarged space. We point out that it can be easily obtained from basic principles of Hamiltonian dynamics, and as such it represents a useful didactical way to introduce graduate students to several modern concepts of geometry applied to physics: curved spaces, both Riemannian and Lorentzian, conformal transformations, geometrisation of interactions and extra dimensions, geometrisation of dynamical symmetries. For all these concepts the Eisenhart lift can be used as a theoretical tool that provides easily achievable examples, with the added benefit of also being a topic of current research with several applications, among which the study of dynamical systems and non-relativistic holography.

Automated Feature Engineering (AutoFE) has become an important task for any machine learning project, as it can help improve model performance and gain more information for statistical analysis. However, most current approaches for AutoFE rely on manual feature creation or use methods that can generate a large number of features, which can be computationally intensive and lead to overfitting. To address these challenges, we propose a novel convolutional method called FeatGeNN that extracts and creates new features using correlation as a pooling function. Unlike traditional pooling functions like max-pooling, correlation-based pooling considers the linear relationship between the features in the data matrix, making it more suitable for tabular data. We evaluate our method on various benchmark datasets and demonstrate that FeatGeNN outperforms existing AutoFE approaches regarding model performance. Our results suggest that correlation-based pooling can be a promising alternative to max-pooling for AutoFE in tabular data applications.

We employ deep learning techniques to investigate the critical properties of the continuous phase transition in the majority vote model. In addition to deep learning, principal component analysis is utilized to analyze the transition. For supervised learning, dense neural networks are trained on spin configuration data generated via the kinetic Monte Carlo method. Using independently simulated configuration data, the neural network accurately identifies the critical point on both square and triangular lattices. Classical unsupervised learning with principal component analysis reproduces the magnetization and enables estimation of critical exponents, typically obtained via Monte Carlo importance sampling. Furthermore, deep unsupervised learning is performed using variational autoencoders, which reconstruct input spin configurations and generate artificial outputs. The autoencoders detect the phase transition through the loss function, quantifying the preservation of essential data features. We define a correlation function between the real and reconstructed data, and find that this correlation function is universal at the critical point. Variational autoencoders also serve as generative models, producing artificial spin configurations.

Community detection in complex networks is fundamental across social, biological, and technological domains. While traditional single-objective methods like Louvain and Leiden are computationally efficient, they suffer from resolution bias and structural degeneracy. Multi-objective evolutionary algorithms (MOEAs) address these limitations by simultaneously optimizing conflicting structural criteria, however, their high computational costs have historically limited their application to small networks. We present HP-MOCD, a High-Performance Evolutionary Multiobjective Community Detection Algorithm built on Non-dominated Sorting Genetic Algorithm II (NSGA-II), which overcomes these barriers through topology-aware genetic operators, full parallelization, and bit-level optimizations, achieving theoretical O(GN_p|V|) complexity. We conduct experiments on both synthetic and real-world networks. Results demonstrate strong scalability, with HP-MOCD processing networks of over 1,000,000 nodes while maintaining high quality across varying noise levels. It outperforms other MOEAs by more than 531 times in runtime on synthetic datasets, achieving runtimes as low as 57 seconds for graphs with 40,000 nodes on moderately powered hardware. Across 14 real-world networks, HP-MOCD was the only MOEA capable of processing the six largest datasets within a reasonable time, with results competitive with single-objective approaches. Unlike single-solution methods, HP-MOCD produces a Pareto Front, enabling individual-specific trade-offs and providing decision-makers with a spectrum of high-quality community structures. It introduces the first open-source Python MOEA library compatible with networkx and igraph for large-scale community detection.

Estimating the nutritional content of food from images is a critical task with significant implications for health and dietary monitoring. This is challenging, especially when relying solely on 2D images, due to the variability in food presentation, lighting, and the inherent difficulty in inferring volume and mass without depth information. Furthermore, reproducibility in this domain is hampered by the reliance of state-of-the-art methods on proprietary datasets for large-scale pre-training. In this paper, we investigate the impact of large-scale pre-training datasets on the performance of deep learning models for nutritional estimation using only 2D images. We fine-tune and evaluate Vision Transformer (ViT) models pre-trained on two large public datasets, ImageNet and COYO, comparing their performance against baseline CNN models (InceptionV2 and ResNet-50) and a state-of-the-art method pre-trained on the proprietary JFT-300M dataset. We conduct extensive experiments on the Nutrition5k dataset, a large-scale collection of real-world food plates with high-precision nutritional annotations. Our evaluation using Mean Absolute Error (MAE) and Mean Absolute Percentage Error (MAE%) reveals that models pre-trained on JFT-300M significantly outperform those pre-trained on public datasets. Unexpectedly, the model pre-trained on the massive COYO dataset performs worse than the model pre-trained on ImageNet for this specific regression task, refuting our initial hypothesis. Our analysis provides quantitative evidence highlighting the critical role of pre-training dataset characteristics, including scale, domain relevance, and curation quality, for effective transfer learning in 2D nutritional estimation.

This work considers the general task of estimating the sum of a bounded function over the edges of a graph, given neighborhood query access and where access to the entire network is prohibitively expensive. To estimate this sum, prior work proposes Markov chain Monte Carlo (MCMC) methods that use random walks started at some seed vertex and whose equilibrium distribution is the uniform distribution over all edges, eliminating the need to iterate over all edges. Unfortunately, these existing estimators are not scalable to massive real-world graphs. In this paper, we introduce Ripple, an MCMC-based estimator that achieves unprecedented scalability by stratifying the Markov chain state space into ordered strata with a new technique that we denote {\em sequential stratified regenerations}. We show that the Ripple estimator is consistent, highly parallelizable, and scales well. We empirically evaluate our method by applying Ripple to the task of estimating connected, induced subgraph counts given some input graph. Therein, we demonstrate that Ripple is accurate and can estimate counts of up to $12$-node subgraphs, which is a task at a scale that has been considered unreachable, not only by prior MCMC-based methods but also by other sampling approaches. For instance, in this target application, we present results in which the Markov chain state space is as large as $10^{43}$, for which Ripple computes estimates in less than $4$ hours, on average.

In the framework of the probabilistic method in combinatorics, we revisit the entropy compression method clarifying the setting in which it can be applied and providing a theorem yielding a general constructive criterion. We finally elucidate, through topical examples, the effectiveness of the entropy-compression criterion in comparison with the Lovasz Local Lemma criterion and, in particular, with the improved criterion based on cluster expansion.

Student dropout is a significant challenge in educational systems worldwide, leading to substantial social and economic costs. Predicting students at risk of dropout allows for timely interventions. While traditional Machine Learning (ML) models operating on tabular data have shown promise, Graph Neural Networks (GNNs) offer a potential advantage by capturing complex relationships inherent in student data if structured as graphs. This paper investigates whether transforming tabular student data into graph structures, primarily using clustering techniques, enhances dropout prediction accuracy. We compare the performance of GNNs (a custom Graph Convolutional Network (GCN) and GraphSAGE) on these generated graphs against established tabular models (Random Forest (RF), XGBoost, and TabNet) using a real-world student dataset. Our experiments explore various graph construction strategies based on different clustering algorithms (K-Means, HDBSCAN) and dimensionality reduction techniques (Principal Component Analysis (PCA), Uniform Manifold Approximation and Projection (UMAP)). Our findings demonstrate that a specific GNN configuration, GraphSAGE on a graph derived from PCA-KMeans clustering, achieved superior performance, notably improving the macro F1-score by approximately 7 percentage points and accuracy by nearly 2 percentage points over the strongest tabular baseline (XGBoost). However, other GNN configurations and graph construction methods did not consistently surpass tabular models, emphasizing the critical role of the graph generation strategy and GNN architecture selection. This highlights both the potential of GNNs and the challenges in optimally transforming tabular data for graph-based learning in this domain.

We revisit an old tree graph formula, namely the Brydges-Federbush tree identity, and use it to get new bounds for the convergence radius of the Mayer series for gases of continuous particles interacting via non absolutely summable pair potentials with an attractive tail including Lennard-Jones type pair potentials.

Automatic License Plate Recognition (ALPR) has been the focus of many researches in the past years. In general, ALPR is divided into the following problems: detection of on-track vehicles, license plates detection, segmention of license plate characters and optical character recognition (OCR). Even though commercial solutions are available for controlled acquisition conditions, e.g., the entrance of a parking lot, ALPR is still an open problem when dealing with data acquired from uncontrolled environments, such as roads and highways when relying only on imaging sensors. Due to the multiple orientations and scales of the license plates captured by the camera, a very challenging task of the ALPR is the License Plate Character Segmentation (LPCS) step, which effectiveness is required to be (near) optimal to achieve a high recognition rate by the OCR. To tackle the LPCS problem, this work proposes a novel benchmark composed of a dataset designed to focus specifically on the character segmentation step of the ALPR within an evaluation protocol. Furthermore, we propose the Jaccard-Centroid coefficient, a new evaluation measure more suitable than the Jaccard coefficient regarding the location of the bounding box within the ground-truth annotation. The dataset is composed of 2,000 Brazilian license plates consisting of 14,000 alphanumeric symbols and their corresponding bounding box annotations. We also present a new straightforward approach to perform LPCS efficiently. Finally, we provide an experimental evaluation for the dataset based on four LPCS approaches and demonstrate the importance of character segmentation for achieving an accurate OCR.

The Thief Orienteering Problem (ThOP) is a multi-component problem that combines features of two classic combinatorial optimization problems: Orienteering Problem and Knapsack Problem. The ThOP is challenging due to the given time constraint and the interaction between its components. We propose an Ant Colony Optimization algorithm together with a new packing heuristic to deal individually and interactively with problem components. Our approach outperforms existing work on more than 90% of the benchmarking instances, with an average improvement of over 300%.

Kepler's rescaling becomes, when "Eisenhart-Duval lifted" to $5$-dimensional "Bargmann" gravitational wave spacetime, an ordinary spacetime symmetry for motion along null geodesics, which are the lifts of Keplerian trajectories. The lifted rescaling generates a well-behaved conserved Noether charge upstairs, which takes an unconventional form when expressed in conventional terms. This conserved quantity seems to have escaped attention so far. Applications include the Virial Theorem and also Kepler's Third Law. The lifted Kepler rescaling is a Chrono-Projective transformation. The results extend to celestial mechanics and Newtonian Cosmology.

This is a short pedagogical introduction to the subject of Killing-Stackel and Killing-Yano tensors and their role in the integrability of various types of equations that are of physical interest in curved spacetime, the main application being higher dimensional rotating black holes with cosmological constant.