Recently, Neural Ordinary Differential Equations has emerged as a powerful framework for modeling physical simulations without explicitly defining the ODEs governing the system, but instead learning them via machine learning. However, the question: "Can Bayesian learning frameworks be integrated with Neural ODE's to robustly quantify the uncertainty in the weights of a Neural ODE?" remains unanswered. In an effort to address this question, we primarily evaluate the following categories of inference methods: (a) The No-U-Turn MCMC sampler (NUTS), (b) Stochastic Gradient Hamiltonian Monte Carlo (SGHMC) and (c) Stochastic Langevin Gradient Descent (SGLD). We demonstrate the successful integration of Neural ODEs with the above Bayesian inference frameworks on classical physical systems, as well as on standard machine learning datasets like MNIST, using GPU acceleration. On the MNIST dataset, we achieve a posterior sample accuracy of 98.5% on the test ensemble of 10,000 images. Subsequently, for the first time, we demonstrate the successful integration of variational inference with normalizing flows and Neural ODEs, leading to a powerful Bayesian Neural ODE object. Finally, considering a predator-prey model and an epidemiological system, we demonstrate the probabilistic identification of model specification in partially-described dynamical systems using universal ordinary differential equations. Together, this gives a scientific machine learning tool for probabilistic estimation of epistemic uncertainties.

The precise measurement of cosmic-ray antinuclei serves as an important means for identifying the nature of dark matter and other new astrophysical phenomena, and could be used with other cosmic-ray species to understand cosmic-ray production and propagation in the Galaxy. For instance, low-energy antideuterons would provide a "smoking gun" signature of dark matter annihilation or decay, essentially free of astrophysical background. Studies in recent years have emphasized that models for cosmic-ray antideuterons must be considered together with the abundant cosmic antiprotons and any potential observation of antihelium. Therefore, a second dedicated Antideuteron Workshop was organized at UCLA in March 2019, bringing together a community of theorists and experimentalists to review the status of current observations of cosmic-ray antinuclei, the theoretical work towards understanding these signatures, and the potential of upcoming measurements to illuminate ongoing controversies. This review aims to synthesize this recent work and present implications for the upcoming decade of antinuclei observations and searches. This includes discussion of a possible dark matter signature in the AMS-02 antiproton spectrum, the most recent limits from BESS Polar-II on the cosmic antideuteron flux, and reports of candidate antihelium events by AMS-02; recent collider and cosmic-ray measurements relevant for antinuclei production models; the state of cosmic-ray transport models in light of AMS-02 and Voyager data; and the prospects for upcoming experiments, such as GAPS. This provides a roadmap for progress on cosmic antinuclei signatures of dark matter in the coming years.

Multi-objective reinforcement learning (MORL) addresses the challenge of simultaneously optimizing multiple, often conflicting, rewards, moving beyond the single-reward focus of conventional reinforcement learning (RL). This approach is essential for applications where agents must balance trade-offs between diverse goals, such as speed, energy efficiency, or stability, as a series of sequential decisions. This paper investigates the applicability and limitations of multi-objective evolutionary algorithms (MOEAs) in solving complex MORL problems. We assess whether these algorithms can effectively address the unique challenges posed by MORL and how MORL instances can serve as benchmarks to evaluate and improve MOEA performance. In particular, we propose a framework to characterize the features influencing MORL instance complexity, select representative MORL problems from the literature, and benchmark a suite of MOEAs alongside single-objective EAs using scalarized MORL formulations. Additionally, we evaluate the utility of existing multi-objective quality indicators in MORL scenarios, such as hypervolume conducting a comparison of the algorithms supported by statistical analysis. Our findings provide insights into the interplay between MORL problem characteristics and algorithmic effectiveness, highlighting opportunities for advancing both MORL research and the design of evolutionary algorithms.

Go gaming is a struggle for territory control between rival, black and white, stones on a board. We model the Go dynamics in a game by means of the Ising model whose interaction coefficients reflect essential rules and tactics employed in Go to build long-term strategies. At any step of the game, the energy functional of the model provides the control degree (strength) of a player over the board. A close fit between predictions of the model with actual games is obtained.

Monte Carlo Tree Search (MCTS) is a relatively new sampling method with multiple variants in the literature. They can be applied to a wide variety of challenging domains including board games, video games, and energy-based problems to mention a few. In this work, we explore the use of the vanilla MCTS and the MCTS with Rapid Action Value Estimation (MCTS-RAVE) in the game of Carcassonne, a stochastic game with a deceptive scoring system where limited research has been conducted. We compare the strengths of the MCTS-based methods with the Star2.5 algorithm, previously reported to yield competitive results in the game of Carcassonne when a domain-specific heuristic is used to evaluate the game states. We analyse the particularities of the strategies adopted by the algorithms when they share a common reward system. The MCTS-based methods consistently outperformed the Star2.5 algorithm given their ability to find and follow long-term strategies, with the vanilla MCTS exhibiting a more robust game-play than the MCTS-RAVE.

The phase of the channel state information (CSI) is underutilized as a source of information in wireless sensing due to its sensitivity to synchronization errors of the signal reception. A linear transformation of the phase is commonly applied to correct linear offsets and, in a few cases, some filtering in time or frequency is carried out to smooth the data. This paper presents a novel processing method of the CSI phase to improve the accuracy of human activity recognition (HAR) in indoor environments. This new method, coined Time Smoothing and Frequency Rebuild (TSFR), consists of performing a CSI phase sanitization method to remove phase impairments based on a linear regression transformation method, then a time domain filtering stage with a Savitzy-Golay (SG) filter for denoising purposes and, finally, the phase is rebuilt, eliminating distortions in frequency caused by SG filtering. The TSFR method has been tested on five datasets obtained from experimental measurements, using three different deep learning algorithms, and compared against five other types of CSI phase processing. The results show an accuracy improvement using TSFR in all the cases. Concretely, accuracy performance higher than 90\% in most of the studied scenarios has been achieved with the proposed solution. In few-shot learning strategies, TSFR outperforms the state-of-the-art performance from 35% to 85%.

In this paper we formulate the problem of packing unequal rectangles/squares into a fixed size circular container as a mixed-integer nonlinear program. Here we pack rectangles so as to maximise some objective (e.g. maximise the number of rectangles packed or maximise the total area of the rectangles packed). We show how we can eliminate a nonlinear maximisation term that arises in one of the constraints in our formulation. We indicate the amendments that can be made to the formulation for the special case where we are maximising the number of squares packed. A formulation space search heuristic is presented and computational results given for publicly available test problems involving up to 30 rectangles/squares. Our heuristic deals with the case where the rectangles are of fixed orientation (so cannot be rotated) and with the case where the rectangles can be rotated through ninety degrees.

A nonlinear frequency response based adaptive vibration controller is proposed for a class of nonlinear mechanical systems. In order to obtain the nonlinear Frequency Response Function (FRF), the convergence properties of the system are studied by using the convergence (contraction) theory. If the system under consideration is: 1) convergent, it directly enables to derive a nonlinear FRF for a band of excitation inputs, 2) non-convergent, first a controller is used to obtain the convergence and then the corresponding FRF for a band of excitation inputs is derived. Now the gains of the proposed adaptive controller are tuned such that a desired closed-loop frequency response, in the presence of excitation inputs is achieved. Finally, a building structure with nonlinear cubic stiffness and a satellite system are considered to illustrate the theoretical results.

Compilation of the six contributions to the ICRC conference 2021 by the CORSIKA 8 Collaboration. The status of the project is illustrated. In particular, the secondary hadron as well as the electromagnetic cascades are being validated individually, and current results are reviewed. A novel framework for radio emission simulations is presented, which is designed given the modular nature of CORSIKA 8 to support, both, the CoREAS as well as the ZHS formalism. At the same time, first Cherenkov emission calculations are shown which are based on CORSIKA 8 coupled with a GPU Cherenkov emission code. Finally, a new powerful feature of CORSIKA 8 is illustrated, where the entire genealogy of air shower particles can be studied in all details.

We examine the tuning of cooperative behavior in repeated multi-agent games using an analytically tractable, continuous-time, nonlinear model of opinion dynamics. Each modeled agent updates its real-valued opinion about each available strategy in response to payoffs and other agent opinions, as observed over a network. We show how the model provides a principled and systematic means to investigate behavior of agents that select strategies using rationality and reciprocity, key features of human decision-making in social dilemmas. For two-strategy games, we use bifurcation analysis to prove conditions for the bistability of two equilibria and conditions for the first (second) equilibrium to reflect all agents favoring the first (second) strategy. We prove how model parameters, e.g., level of attention to opinions of others (reciprocity), network structure, and payoffs, influence dynamics and, notably, the size of the region of attraction to each stable equilibrium. We provide insights by examining the tuning of the bistability of mutual cooperation and mutual defection and their regions of attraction for the repeated prisoner's dilemma and the repeated multi-agent public goods game. Our results generalize to games with more strategies, heterogeneity, and additional feedback dynamics, such as those designed to elicit cooperation.

We establish the existence of a positive fully nontrivial solution $(u,v)$ to the weakly coupled elliptic system% \left\{ \begin{tabular} [c]{l}% $-\Delta u=\mu_{1}|u|^{{2}^{\ast}-2}u+\lambda\alpha|u|^{\alpha-2}|v|^{\beta }u,$\\ $-\Delta v=\mu_{2}|v|^{{2}^{\ast}-2}v+\lambda\beta|u|^{\alpha}|v|^{\beta{-2}% }v,$\\ $u,v\in D^{1,2}(\mathbb{R}^{N}),$% \end{tabular} \ \right. where $N\geq4,$ $2^{\ast}:=\frac{2N}{N-2}$ is the critical Sobolev exponent, $\alpha,\beta\in(1,2],$ $\alpha+\beta=2^{\ast},$ \mu_{1},\mu_{2}>0, and \lambda<0. We show that these solutions exhibit phase separation as $\lambda\rightarrow-\infty,$ and we give a precise description of their limit domains. If $\mu_{1}=\mu_{2}$ and $\alpha=\beta$, we prove that the system has infinitely many fully nontrivial solutions, which are not conformally equivalent.

How do galaxy properties (such as stellar mass, luminosity, star formation rate, and morphology) and their evolution depend on the mass of their host dark matter halo? Using the Galaxy and Mass Assembly (GAMA) group catalogue, we address this question by exploring the dependence on host halo mass of the luminosity function (LF) and stellar mass function (SMF) for grouped galaxies subdivided by colour, morphology and central/satellite. We find that spheroidal galaxies in particular dominate the bright and massive ends of the LF and SMF, respectively. More massive haloes host more massive and more luminous central galaxies. The satellite LF and SMF respectively show a systematic brightening of characteristic magnitude, and increase in characteristic mass, with increasing halo mass. In contrast to some previous results, the faint-end and low-mass slopes show little systematic dependence on halo mass. Semi-analytic models and simulations show similar or enhanced dependence of central mass and luminosity on halo mass. Faint and low-mass simulated satellite galaxies are remarkably independent of halo mass, but the most massive satellites are more common in more massive groups. In the first investigation of low-redshift LF and SMF evolution in group environments, we find that the red/blue ratio of galaxies in groups has increased since redshift $z \approx 0.3$ relative to the field population. This observation strongly suggests that quenching of star formation in galaxies as they are accreted into galaxy groups is a significant and ongoing process.

We report the results of 24 years of photometric and spectroscopic monitoring of CI Cam since its outburst in 1998. In the early years of our research, we identified a system component responsible for the emission of the He II 4686 line, which moves in an elliptical orbit with a period of 19.407 days and an eccentricity from 0.44 to 0.49. Variations in optical brightness with the same period were observed, with an average amplitude of 0.04 magnitudes. The total amplitude of the He II radial velocity variations was approximately 380 kilometers per second. The equivalent width of the line varied on timescales of tens of minutes as well as with the orbital period, reaching maximum values when the companion passed the descending node of the orbit. The intensity of the He II 4686 emission has gradually increased over time. Our photometric monitoring revealed pulsations of the main B component of the CI Cam system. Between 2005 and 2009, the B star exhibited multiperiodic pulsations, however, since 2012, it pulsated in a single mode. We interpret the pulsations from 2005 to 2009 as a resonance of radial modes, with the residual stable mode being the first overtone. The pulsations are coherent over several months, with average amplitudes from 0.02 to 0.04 magnitudes in the V band. The pulsation data constrain the spectral type of the primary component of B0 to B2 III, the distance to the system from 2.5 to 4.5 kpc. The classification of the main component of CI Cam as a supergiant is ruled out due to the observed pulsation periods. CI Cam is likely in the stage after the first mass exchange and may belong to the FS CMa-type objects.

Dissipative systems play a very important role in several physical models, most notably in Celestial Mechanics, where the dissipation drives the motion of natural and artificial satellites, leading them to migration of orbits, resonant states, etc. Hence the need to develop theories that ensure the existence of structures such as invariant tori or periodic orbits and device efficient computational methods. In this work we concentrate on the existence of invariant tori for the specific case of dissipative systems known as "conformally symplectic" systems, which have the property that they transform the symplectic form into a multiple of itself. To give explicit examples of conformally symplectic systems, we will present two different models: a discrete system, the standard map, and a continuous system, the spin-orbit problem. In both cases we will consider the conservative and dissipative versions, that will help to highlight the differences between the symplectic and conformally symplectic dynamics. For such dissipative systems we will present a KAM theorem in an a-posteriori format. The method of proof is based on extending geometric identities originally developed in [39] for the symplectic case. Besides leading to streamlined proofs of KAM theorem, this method provides a very efficient algorithm which has been implemented. Coupling an efficient numerical algorithm with an a-posteriori theorem, we have a very efficient way to provide rigorous estimates close to optimal. Indeed, the method gives a criterion (the Sobolev blow up criterion) that allows to compute numerically the breakdown. We will review this method as well as an extension of J. Greene's method and present the results in the conservative and dissipative standard maps. Computing close to the breakdown, allows to discover new mathematical phenomena such as the "bundle collapse mechanism".

We introduce the construction of polarized intensity cubes $P$(RA, Dec, $\Phi$) and their visualization as movies, as a powerful technique for interpreting Faraday structure. $P$ is constructed from maps of peak polarized intensity P(RA, Dec) with their corresponding Faraday depth maps $\Phi$(RA, Dec). We illustrate the extensive scientific potential of such visualizations with a variety of science use cases from ASKAP and MeerKAT, presenting models that are consistent with the data but not necessarily unique. We demonstrate how one can, in principle, distinguish between cube structures which originate from unrelated foreground screens from those due to magnetized plasmas local to the emitting source. Other science use cases illustrate how variations in the local $n_e$ $B$, and line-of-sight distance to the synchrotron emitting regions can be distinguished using Faraday rotation. We show, for the first time, how the line-of-sight orientation of AGN jets can be determined. We also examine the case of M87 to show how internal jet magnetic field configurations can be identified, and extend earlier results. We recommend using this technique to re-evaluate all previous analyses of polarized sources that are well-resolved both spatially and in Faraday depth. Recognizing the subjective nature of interpretations at this early stage, we also highlight the need and utility for further scientific and technical developments.

Atmospheric convection is an essential aspect of atmospheric movement, and it is a source of errors in Climate Models. Being able to generate approximate limit formulas and compare the estimations they produce, could give a way to reduce them. In this article, it is shown that it is enough to assume that the velocity's $L^2$-norm is bounded, has locally integrable, $L^1_{loc}$, weak partial derivatives up to order two, and a negligible variation of its first velocity's coordinate in direction parallel to the surface, to obtain a Reynolds' limit formula for a Dorodnitzyn's compressible gaseous Boundary Layer in atmospheric conditions.

Prosecutors are essential in combating organized crime, making key decisions about prosecution, target selection, and structuring imputation strategies. Despite their importance, the configuration of these strategies remains empirically underexplored. This study analyzes cases investigated by the International Commission Against Impunity in Guatemala (CICIG) using a multilevel network approach to examine legal interventions targeting criminal networks. The research employs a multilevel Exponential Random Graph Model (ERGM), integrating three networks: the criminal network of actors involved in illegal activities, the legal framework network represents offenses, and the prosecution network connects actors to offenses. This approach identifies structural patterns in prosecutorial strategies for individual actors and co-offenders. Findings show a strong tendency for triangular configurations, where two co-offenders are linked to a shared offense. Additionally, individuals are more likely to be involved in diverse offenses, spanning corruption-related and non-corruption-related activities, than in similar types of offenses. This highlights a strategic focus on addressing varied criminal behaviors within interconnected networks. Notably, by capturing the interplay between legal framework, criminal network, and prosecution strategy, the findings of this study emphasize the value of multilevel network analysis for enhancing the effectiveness of legal interventions, underscore the critical role of prosecutors in dismantling complex criminal networks, and offers a novel framework for improving prosecution strategies in combating organized crime.

In recent years, the analysis of economic crime and corruption in procurement has benefited from integrative studies that acknowledge the interconnected nature of the procurement ecosystem. Following this line of research, we present a networks approach for the analysis of shell-companies operations in procurement that makes use of contracting and ownership data under one framework to gain knowledge about the organized crime behavior that emerges in this setting. In this approach, ownership and management data are used to identify connected components in shell-company networks that, together with the contracting data, allows to develop an alternative representation of the traditional buyer-supplier network: the module-component bipartite network, where the modules are groups of buyers and the connected components are groups of suppliers. This is applied to two documented cases of procurement corruption in Mexico characterized by the involvement of large groups of shell-companies in the misappropriation of millions of dollars across many sectors. We quantify the economic impact of single versus connected shell-companies operations. In addition, we incorporate metrics for the diversity of operations and favoritism levels. This paper builds into the quantitative organized crime in the private sector studies and contributes by proposing a networks approach for preventing fraud and understanding the need for legal reforms.