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Context. Magnetic batteries are potential sources that may drive the generation of a seed magnetic field, even if this field is initially zero. These batteries can be the result of non-aligned thermodynamic gradients in a plasma, as well as of special and general relativistic effects. So far, magnetic batteries have only been studied in ideal magnetized fluids. Aims. We study the non-ideal fluid effects introduced by the energy flux in the vortical dynamics of a magnetized plasma in curved spacetime. We propose a novel mechanism for generating a heat flux-driven magnetic seed within a simple accretion disk model around a Schwarzschild black hole. Methods. We use the 3+1 formalism for the splitting of the space-time metric into space-like and time-like components. We study the vortical dynamics of a magnetized fluid with a heat flux in the Schwarzschild geometry in which thermodynamic and hydrodynamic quantities are only dependent on the radial coordinate. Assuming that the magnetic field is initially zero, we estimate linear time evolution of the magnetic field due to the inclusion of non-ideal fluid effects. Results. When the thermodynamic and hydrodynamic quantities vary only radially, the effect of the coupling between the heat flux, spacetime curvature and fluid velocity acts as the primary driver for an initial linearly time growing magnetic field. The plasma heat flux completely dominates the magnetic field generation at an specific distance from the black hole, where the fluid vorticity vanishes. This distance depends on the thermodynamical properties of the Keplerian plasma accretion disk. These properties control the strength of the non-ideal effects in the generation of seed magnetic fields., Comment: 6 pages, 3 Figures, accepted for publication

The Arecibo Message was a brief binary-encoded communication transmitted into space from the Arecibo Observatory on November 16, 1974, intended to demonstrate human technological prowess. In late 2018, to commemorate the 45th anniversary of this message, the Arecibo Observatory initiated the New Arecibo Message competition. Following a series of challenges, our Boriken Voyagers team was recognized as the winner of the competition in August 2020. Although the primary objective of the competition was to conceptualize rather than transmit a message, the collapse of the Arecibo Telescope in December 2020 precluded any subsequent transmission efforts. Therefore, to commemorate the 50th anniversary of the Arecibo Message, this paper presents the Last Arecibo Message, as originally developed for the Arecibo Telescope. If the original message says "we are a form of life reaching out to connect", our message says "we are ready to explore the universe together." The prospect of transmitting this or a similar message remains an open question., Comment: 12 pages, 4 figures. Additional content is available at https://phl.upr.edu/message/

Due to the difficulty of acquiring large-scale explicit user feedback, implicit feedback (e.g., clicks or other interactions) is widely applied as an alternative source of data, where user-item interactions can be modeled as a bipartite graph. Due to the noisy and biased nature of implicit real-world user-item interactions, identifying and rectifying noisy interactions are vital to enhance model performance and robustness. Previous works on purifying user-item interactions in collaborative filtering mainly focus on mining the correlation between user/item embeddings and noisy interactions, neglecting the benefit of temporal patterns in determining noisy interactions. Time information, while enhancing the model utility, also bears its natural advantage in helping to determine noisy edges, e.g., if someone usually watches horror movies at night and talk shows in the morning, a record of watching a horror movie in the morning is more likely to be noisy interaction. Armed with this observation, we introduce a simple yet effective mechanism for generating time-aware user/item embeddings and propose two strategies for denoising bipartite temporal graph in recommender systems (DeBaTeR): the first is through reweighting the adjacency matrix (DeBaTeR-A), where a reliability score is defined to reweight the edges through both soft assignment and hard assignment; the second is through reweighting the loss function (DeBaTeR-L), where weights are generated to reweight user-item samples in the losses. Extensive experiments have been conducted to demonstrate the efficacy of our methods and illustrate how time information indeed helps identifying noisy edges.

The number of type Ia supernova (SNe Ia) observations will grow significantly within the next decade, mainly thanks to the Legacy Survey of Space and Time (LSST) undertaken by the Vera Rubin Observatory in Chile. With this improvement, statistical uncertainties will decrease, and flux calibration will become the main uncertainty for the characterization of dark energy. Currently, the astronomical flux scale is anchored on the numerical models of white dwarf atmospheres from the CALSPEC catalog, and every error on the model can induce a bias over cosmological parameters inference. The StarDICE experiment proposes a new calibration reference that only relies on observations from the optical watt defined by the NIST towards the magnitude of standard stars. It is currently operating at l'Observatoire de Haute-Provence and has been collecting data since the beginning of 2023. To overcome the photometric calibration uncertainty and reach a sub-percent precision, the instrument throughput has been calibrated with a Collimated Beam Projector. It will be monitored on-site with a LED-based artificial star source calibrated with NIST photodiodes. In this proceeding, we will first illustrate how an error in the photometric calibration can impact the SNe Ia distance moduli and thus bias the measurement of cosmological parameters. Then we will present the StarDICE experiment and how we can recalibrate the CALSPEC catalog at the millimagnitude level on the NIST scale with photometric analysis.

In the asymptotic limit of a large diffusivity ratio, certain two-component reaction-diffusion (RD) systems can admit localized spike solutions on a 1-D finite domain in a far-from-equilibrium nonlinear regime. It is known that two distinct bifurcation mechanisms can occur which generate spike patterns of increased spatial complexity as the domain half-length L slowly increases; so-called spike nucleation and spike self-replication. Self-replication is found to occur via the passage beyond a saddle-node bifurcation point that can be predicted through linearization around the inner spike profile. In contrast, spike nucleation occurs through slow passage beyond the saddle-node of a nonlinear boundary-value problem defined in the outer region away from the core of a spike. Here, by treating L as a static parameter, precise conditions are established within the semi-strong interaction asymptotic regime to determine which occurs, conditions that are confirmed by numerical simulation and continuation. For the Schnakenberg and Brusselator RD models, phase diagrams in parameter space are derived that predict whether spike self-replication or spike nucleation will occur first as L is increased, or whether no such instability will occur. For the Gierer-Meinhardt model with a non-trivial activator background, spike nucleation is shown to be the only possible spike-generating mechanism. From time-dependent PDE numerical results on an exponentially slowly growing domain, it is shown that the analytical thresholds derived from the asymptotic theory accurately predict critical values of L where either spike self-replication or spike-nucleation will occur. The global bifurcation mechanism for transitions to patterns of increased spatial complexity is further elucidated by superimposing time-dependent PDE simulation results on the numerically computed solution branches of spike equilibria., Comment: 45 pages

The measurement of type Ia supernovae magnitudes provides cosmological distances, which can be used to constrain dark energy parameters. Large photometric surveys require a substantial improvement in the calibration precision of their photometry to reduce systematic uncertainties in cosmological constraints. The StarDICE experiment is designed to establish accurate broadband flux references for these surveys, aiming for sub-percent precision in magnitude measurements. This requires a precise measurement of the filter bandpasses of both the StarDICE and survey instruments with sub-nanometer accuracy. To that end, we have developed the Collimated Beam Projector (CBP), an optical device capable of calibrating the throughput of an astronomical telescope and of its filters. The CBP is built from a tunable laser source and a reversed telescope to emit a parallel monochromatic light beam that is continuously monitored in flux and wavelength. The CBP output light flux is measured using a large area photodiode, previously calibrated relative to a NIST photodiode. We derive the StarDICE telescope throughput and filter transmissions from the CBP measurements, anchoring it to the absolute calibration provided by the NIST. After analyzing the systematic uncertainties, we achieved sub-nanometer accuracy in determining filter central wavelengths, measured each filter transmission with a precision of 0.5% per 1nm bin, and detected out-of-band leakages at 0.01%. Furthermore, we have synthesized the equivalent transmission for full pupil illumination from four sample positions in the StarDICE telescope mirror, with an accuracy of approximately 0.2nm for central wavelengths and 7mmag for broadband fluxes. We demonstrated our ability to characterize a telescope throughput down to the mmag, and paved the way for future developments, such as a portable CBP version for in-situ transmission monitoring., Comment: 29 pages, 50 figures

Streaming services have reshaped how we discover and engage with digital entertainment. Despite these advancements, effectively understanding the wide spectrum of user search queries continues to pose a significant challenge. An accurate query understanding system that can handle a variety of entities that represent different user intents is essential for delivering an enhanced user experience. We can build such a system by training a natural language understanding (NLU) model; however, obtaining high-quality labeled training data in this specialized domain is a substantial obstacle. Manual annotation is costly and impractical for capturing users' vast vocabulary variations. To address this, we introduce a novel approach that leverages large language models (LLMs) through weak supervision to automatically annotate a vast collection of user search queries. Using prompt engineering and a diverse set of LLM personas, we generate training data that matches human annotator expectations. By incorporating domain knowledge via Chain of Thought and In-Context Learning, our approach leverages the labeled data to train low-latency models optimized for real-time inference. Extensive evaluations demonstrated that our approach outperformed the baseline with an average relative gain of 113% in recall. Furthermore, our novel prompt engineering framework yields higher quality LLM-generated data to be used for weak supervision; we observed 47.60% improvement over baseline in agreement rate between LLM predictions and human annotations with respect to F1 score, weighted according to the distribution of occurrences of the search queries. Our persona selection routing mechanism further adds an additional 3.67% increase in weighted F1 score on top of our novel prompt engineering framework., Comment: 6 pages, 5 figures

General conditions are established under which reaction-cross-diffusion systems can undergo spatiotemporal pattern-forming instabilities. Recent work has focused on designing systems theoretically and experimentally to exhibit patterns with specific features, but the case of non-diagonal diffusion matrices has yet to be analysed. Here, a framework is presented for the design of general $n$-component reaction-cross-diffusion systems that exhibit Turing and wave instabilities of a given wavelength. For a fixed set of reaction kinetics, it is shown how to choose diffusion matrices that produce each instability; conversely, for a given diffusion tensor, how to choose linearised kinetics. The theory is applied to several examples including a hyperbolic reaction-diffusion system, two different 3-component models, and a spatio-temporal version of the Ross-Macdonald model for the spread of malaria., Comment: 49 pages, 14 figures

Weakly nonlinear amplitude equations are derived for the onset of spatially extended patterns on a general class of $n$-component bulk-surface reaction-diffusion systems in a ball, under the assumption of linear kinetics in the bulk. Linear analysis shows conditions under which various pattern modes can become unstable to either generalised pitchfork or transcritical bifurcations depending on the parity of the spatial wavenumber. Weakly nonlinear analysis is used to derive general expressions for the multi-component amplitude equations of different patterned states. These reduced-order systems are found to agree with prior normal forms for pattern formation bifurcations with $O(3)$ symmetry and provide information on the stability of bifurcating patterns of different symmetry types. The analysis is complemented with numerical results using a dedicated finite-element method. The theory is illustrated in two examples; a bulk-surface version of the Brusselator, and a four-component cell-polarity model.

This document replicates the main results from Santos Silva and Tenreyro (2006 in R. The original results were obtained in TSP back in 2006. The idea here is to be explicit regarding the conceptual approach to regression in R. For most of the replication I used base R without external libraries except when it was absolutely necessary. The findings are consistent with the original article and reveal that the replication effort is minimal, without the need to contact the authors for clarifications or incur into data transformations or filtering not mentioned in the article., Comment: 9 pages, 0 figures, 1 table

This article compares `cpp11armadillo` and `cpp11eigen`, new R packages that integrate the powerful Armadillo and Eigen C++ libraries for linear algebra into the R programming environment. This article provides a detailed comparison between Armadillo and Eigen speed and syntax. The goal of these packages is to simplify a part of the process of solving bottlenecks by using C++ within R, these offer additional ease of integration for users who require high-performance linear algebra operations in their R workflows. This document aims to discuss the tradeoff between computational efficiency and accessibility., Comment: 21 pages, 0 figures, 13 tables

tabulapdf is an R package that utilizes the Tabula Java library to import tables from PDF files directly into R. This tool can reduce time and effort in data extraction processes in fields like investigative journalism. It allows for automatic and manual table extraction, the latter facilitated through a Shiny interface, enabling manual areas selection with a computer mouse for data retrieval., Comment: 10 pages, 1 figure

We characterize the critical parameter of oriented percolation on $\mathbb{Z}^2$ through the value of a zero-sum game. Specifically, we define a zero-sum game on a percolation configuration of $\mathbb{Z}^2$, where two players move a token along the non-oriented edges of $\mathbb{Z}^2$, collecting a cost of 1 for each edge that is open, and 0 otherwise. The total cost is given by the limit superior of the average cost. We demonstrate that the value of this game is deterministic and equals 1 if and only if the percolation parameter exceeds $p_c$, the critical exponent of oriented percolation. Additionally, we establish that the value of the game is continuous at $p_c$. Finally, we show that for $p$ close to 0, the value of the game is equal to 0.

This article introduces 'cpp11armadillo', a new R package that integrates the powerful Armadillo C++ library for linear algebra into the R programming environment. Targeted primarily at social scientists and other non-programmers, this article explains the computational benefits of moving code to C++ in terms of speed and syntax. We provide a comprehensive overview of Armadillo's capabilities, highlighting its user-friendly syntax akin to MATLAB and its efficiency for computationally intensive tasks. The 'cpp11armadillo' package simplifies a part of the process of using C++ within R by offering additional ease of integration for those who require high-performance linear algebra operations in their R workflows. This work aims to bridge the gap between computational efficiency and accessibility, making advanced linear algebra operations more approachable for R users without extensive programming backgrounds., Comment: 23 pages, 0 figures

The kendallknight package introduces an efficient implementation of Kendall's correlation coefficient computation, significantly improving the processing time for large datasets without sacrificing accuracy. The kendallknight package, following Knight (1966) and posterior literature, reduces the computational complexity resulting in drastic reductions in computation time, transforming operations that would take minutes or hours into milliseconds or minutes, while maintaining precision and correctly handling edge cases and errors. The package is particularly advantageous in econometric and statistical contexts where rapid and accurate calculation of Kendall's correlation coefficient is desirable. Benchmarks demonstrate substantial performance gains over the base R implementation, especially for large datasets., Comment: 9 pages with references, 2 tables, 2 figures

This work is a thorough and detailed study on the geometry of the unit sphere of certain Banach spaces of homogeneous polynomials in ${\mathbb{R}}^2$. Specifically, we provide a complete description of the unit spheres, identify the extreme points of the unit balls, derive explicit formulas for the corresponding polynomial norms, and describe the techniques required to tackle these questions. To enhance the comprehensiveness of this work, we complement the results and their proofs with suitable diagrams and figures. The new results presented here settle some open questions posed in the past. For the sake of completeness of this work, we briefly discuss previous known results and provide directions of research and applications of our results., Comment: 46 pages, 18 figures

The out-of-equilibrium heterogeneous microstructure typical of AlSi10Mg processed by Laser Powder Bed Fusion (LPBF) is often modified by further heat treatment to improve its ductility. According to literature, extensive experimental investigations are generally required in order to optimize these heat treatments. In the present work, a phase-field approach is developed based on an extended Kim-Kim-Suzuki (KKS) model to guide and accelerate the post-treatment optimization. Combined with CALculation of PHAse Diagrams (CALPHAD) data, this extended KKS model predicts microstructural changes under anisothermal conditions. To ensure a more physical approach, it takes into account the enhanced diffusion by quenched-in excess vacancies as well as the elastic energy due to matrix/precipitate lattice mismatch. As the developed model includes the computation of the evolution of the thermo-physical properties, its results are validated through comparison with experimental DSC curves measured during the non-isothermal loading of as-built LPBF AlSi10Mg. The computed microstructure evolution reproduces the microstructural observation and successfully explains the peaks in the DSC heat flow curve. It thus elucidates the detailed microstructural evolution inside the eutectic silicon phase by considering the growth and coalescence of silicon precipitates and the matrix desaturation.

Context. The transition from left-hand to right-hand polarized Alfv\'en waves depends on the wavenumber, the ratio of kinetic to magnetic pressure $\beta$, temperature anisotropy, and ion composition of the plasma. Along with the temperature anisotropy, the electron-to-proton temperature ratio $T_e/T_p$ is of great relevance for the characterization of the thermal properties of a plasma. This ratio varies significantly between different space plasma environments. Thus, studying how variations on this ratio affect the polarisation properties of electromagnetic waves becomes highly relevant for our understanding of the dynamics of space plasmas. Aim. We present an extensive study on the effect of the thermal properties of electrons on the behaviour and characteristics of Alfv\'enic waves in fully kinetic linear theory, as well as on the transition from electromagnetic ion-cyclotron (EMIC) to kinetic Alfv\'en waves (KAW). Method. We solve the fully kinetic dispersion relation for oblique electromagnetic waves of the Alfv\'en branch in a homogenous Maxwellian electron-proton plasma. We quantify the effect of the thermal properties of electrons by varying the electron-to-proton temperature ratio for different configurations of the propagation angle, $\beta_p=8\pi nkT_p/B^2$, and wavenumber. Results. We show that the temperature ratio $T_e/T_p$ has strong and non-trivial effects on the polarisation of the Alfv\'enic modes, especially at kinetic scales and $\beta_e+\beta_p>0.5$. We conclude that electron inertia plays an important role in the kinetic scale physics of the KAW in the warm plasma regime, and thus cannot be excluded in hybrid models for computer simulations., Comment: 13 pages, 7 figures

This study presents a mathematical model that describes the relationship between the Puma concolor and its prey using delay differential equations, a Holling type III functional response, logistic growth for the prey, and a Ricker-type function to model intraspecific competition of the pumas. For positive equilibrium, conditions guaranteeing absolute stability are established, based on the delay value and model parameters. The analysis demonstrates the existence of a unique maximal solution for the proposed model, which remains non-negative for nonnegative initial conditions and is well-defined for all $t$ greater than zero. Furthermore, numerical simulations with different parameter values were performed to investigate the effects of systematically removing a percentage of predators or prey. Numerical simulations attempt to exemplify and put into practice the theorems proved in this article., Comment: 26 pages, 11 figures

The initial-boundary value problem in a bounded domain with moving boundaries and nonhomogeneous boundary conditions for a higher order nonlinear Schr\"odinger (HNLS) equation is considered. Existence and uniqueness of global weak solutions are proved as well as the stability of the solution. Additionally, a conservative numerical method of finite differences is introduced that also verifies stability properties with respect to the $L^2$-norm, and along with proving its convergence, some interesting numerical examples are shown that illustrate the behavior of the solution.

We revisit a subexponential bound for the $abc$ conjecture due to the first author, and we establish a variation of it using linear forms in logarithms. As an application, we prove an unconditional subexponential bound towards the $4$-terms $abc$ conjecture under a suitable hypothesis on the size of the variables.

This paper is devoted to the solution and stability of a one-dimensional model depicting Rao--Nakra sandwich beams, incorporating damping terms characterized by fractional derivative types within the domain, specifically a generalized Caputo derivative with exponential weight. To address existence, uniqueness, stability, and numerical results, fractional derivatives are substituted by diffusion equations relative to a new independent variable, $\xi$, resulting in an augmented model with a dissipative semigroup operator. Polynomial decay of energy is achieved, with a decay rate depending on the fractional derivative parameters. Both the polynomial decay and its dependency on the parameters of the generalized Caputo derivative are numerically validated. To this end, an energy-conserving finite difference numerical scheme is employed., Comment: 23 pages, 14 figures

This paper explores the potential of large language models (LLMs) to make the Aeronautical Regulations of Colombia (RAC) more accessible. Given the complexity and extensive technicality of the RAC, this study introduces a novel approach to simplifying these regulations for broader understanding. By developing the first-ever RAC database, which contains 24,478 expertly labeled question-and-answer pairs, and fine-tuning LLMs specifically for RAC applications, the paper outlines the methodology for dataset assembly, expert-led annotation, and model training. Utilizing the Gemma1.1 2b model along with advanced techniques like Unsloth for efficient VRAM usage and flash attention mechanisms, the research aims to expedite training processes. This initiative establishes a foundation to enhance the comprehensibility and accessibility of RAC, potentially benefiting novices and reducing dependence on expert consultations for navigating the aviation industry's regulatory landscape. You can visit the dataset (https://huggingface.co/somosnlp/gemma-1.1-2b-it_ColombiaRAC_FullyCurated_format_chatML_V1) and the model (https://huggingface.co/datasets/somosnlp/ColombiaRAC_FullyCurated) here.

We prove that if $G$ is a totally bounded abelian group \st\ its dual group $\widehat{G}_p$ equipped with the finite-open topology is a Baire group, then every compact subset of $G$ must be finite. This solves an open question by Chasco, Dom\'inguez and Tkachenko. {Among other consequences, we obtain an example of a group that is $g$-dense in its completion but is not $g$-barrelled. This solves a question proposed by Au${\beta}$enhofer and Dikranjan.}

In this paper we study the qualitative features induces by corrections to GR coming from String Theory, on the shadows of rotating black holes. We deal with the slowly rotating black hole solutions up to order $\mathcal{O}(a^3)$, to first order in $\alpha'$, including also the dilaton. We provide a detailed characterization of the geometry, as well as the innermost stable circular orbit (ISCO) and photon ring, and then we proceed to obtain the black hole images within the relativistic thin-disk model. We characterize the images by computing the diameter, displacement and asymmetry. A comparison with the Kerr case, indicates that all these quantities grow due to the $\alpha'$ correction, and that the departure from GR for different observable is enhanced depending on the angle of view, namely for the diameter the maximum departure is obtained when the system is face-on, while for the displacement and asymmetry the departure from GR is maximized for edge-on point of view., Comment: 14 pages, 8 figures. V2: small changes, references added, accepted in PRD

We generalize the definition of topological entropy given by Adler, Konheim, and McAndrew (AKM) for piecewise continuous self-maps defined on a compact interval (pc-maps). For this notion of entropy, we prove that the properties of the AKM-entropy in the compact-continuous setting get naturally extended, including that it can be estimated using Bowen's formula disregarding the metric used to compute it. Additionally, for piecewise strictly monotonic pc-maps, we prove that the Misiurewicz-Szlenk formula based on the asymptotic behavior of the number of monotony pieces for iterations of the map coincides with our notion of topological entropy. In this way, we unify the notions of entropy commonly used for piecewise continuous interval maps, proving that they all coincide when the space is compact., Comment: 25 pages

In this work, a new relationship is established between the solutions of higher fractional differential equations and a Wright-type transformation. Solutions could be interpreted as expected values of functions in a random time process. As applications, we solve the fractional beam equation, fractional electric circuits with special functions as external sources, and derive dAlemberts formula for the fractional wave equation. Due to this relationship, we present two methods for simulating solutions of fractional differential equations. The two approaches use the interpretation of the Caputo derivative of a function as a Wright-type transformation of the higher derivative of the function. In the first approach, we use the Runge-Kutta method of hybrid orders 4 and 5 to solve ordinary differential equations combined with the Monte Carlo integration to conduct the Wrighttype transformation. The second method uses a feedforward neural network to simulate the fractional differential equation.

HD 21997 is host to a prototypical "hybrid" debris disk characterized by debris disk-like dust properties and a CO gas mass comparable to a protoplanetary disk. We use Transiting Exoplanet Survey Satellite time series photometry to demonstrate that HD 21997 is a high-frequency delta Scuti pulsator. If the mode identification can be unambiguously determined in future works, an asteroseismic age of HD 21997 may become feasible., Comment: 3 pages, 1 figure, submitted to RNAAS

We study non-invertible topological symmetry operators in massive quantum field theories in (1+1) dimensions. In phases where this symmetry is spontaneously broken we show that the particle spectrum often has degeneracies dictated by the non-invertible symmetry and we deduce a procedure to determine the allowed multiplets. These degeneracies are robust predictions and do not require integrability or other special features of renormalization group flows. We exhibit these conclusions in examples where the spectrum is known, recovering soliton and particle degeneracies. For instance, the Tricritical Ising model deformed by the subleading Z2 odd operator flows to a gapped phase with two degenerate vacua. This flow enjoys a Fibonacci fusion category symmetry which implies a threefold degeneracy of its particle states, relating the mass of solitons interpolating between vacua and particles supported in a single vacuum., Comment: 43 pages, 2 figures, 1 table, v2: added references, minor typos corrected

We present an elementary proof establishing the equality of the right and left-sided $\sqrt{\kappa}$-quantum lengths for an SLE$_\kappa$ curve, where $\kappa\in (0,4]$. We achieve this by demonstrating that the$\sqrt{\kappa}$-quantum length is equal to the $(\sqrt{\kappa}/2)$-Gaussian multiplicative chaos with reference measure given by half the conformal Minkowski content of the curve, multiplied by $2/(4-\kappa)$ for $\kappa\in (0,4)$ and by $1$ for $\kappa=4$. Our proof relies on a novel "one-sided" approximation of the conformal Minkowski content, which is compatible with the conformal change of coordinates formula.

In this note we show that there exist a $2^\mathfrak{c}$-generated free algebra $\mathcal{S} \subset \mathbb{R}^\mathbb{R}$ of Riemann integrable functions and a free algebra $\mathcal{C} \subset \mathbb{R}^{[0,1]}$ of continuous functions, having $\mathfrak{c}$-generators, such that $r \circ c$ is not Riemann integrable for any $r \in \mathcal{S}$ and $c \in \mathcal{C}$. This result is the best possible one in terms of lineability within these families of functions and, at the same time, an improvement of a precious result (\cite[Theorem 2.7]{A}). In order to achieve our results we shall employ set theoretical tools such as the Fichtenholz-Kantorovich-Hausdorff theorem, Cantor-Smith-Volterra--type sets, and classical real analysis techniques.

Reconstructing an object from photos and placing it virtually in a new environment goes beyond the standard novel view synthesis task as the appearance of the object has to not only adapt to the novel viewpoint but also to the new lighting conditions and yet evaluations of inverse rendering methods rely on novel view synthesis data or simplistic synthetic datasets for quantitative analysis. This work presents a real-world dataset for measuring the reconstruction and rendering of objects for relighting. To this end, we capture the environment lighting and ground truth images of the same objects in multiple environments allowing to reconstruct the objects from images taken in one environment and quantify the quality of the rendered views for the unseen lighting environments. Further, we introduce a simple baseline composed of off-the-shelf methods and test several state-of-the-art methods on the relighting task and show that novel view synthesis is not a reliable proxy to measure performance. Code and dataset are available at https://github.com/isl-org/objects-with-lighting ., Comment: Accepted at 3DV 2024, Oral presentation. For the project page see https://github.com/isl-org/objects-with-lighting

This paper proposes two realistic and biologically viable methods for Wolbachia-based biocontrol of Aedes aegypti mosquitoes, assuming imperfect maternal transmission of the Wolbachia bacterium, incomplete cytoplasmic incompatibility, and direct loss of Wolbachia infection caused by thermal stress. Both methods are based on optimization approaches and allow for the stable persistence of Wolbachia-infected mosquitoes in the wild Ae. aegypti populations in a minimum time and using the smallest quantity of Wolbachia-carrying insects to release. The first method stems from the continuous-time optimal release strategy, which is further transformed into a sequence of suboptimal impulses mimicking instantaneous releases of Wolbachia-carrying insects. The second method constitutes a novel alternative to all existing techniques aimed at the design of release strategies. It is developed using metaheuristics ($\epsilon$-constraint method combined with the genetic algorithm) and directly produces a discrete sequence of decisions, where each element represents the quantity of Wolbachia-carrying mosquitoes to be released instantaneously and only once per a specified time unit. It turns out that a direct discrete-time optimization (second method) renders better quantifiable results compared to transforming a continuous-time optimal release function into a sequence of suboptimal impulses (first method). As an illustration, we provide examples of daily, weekly, and fortnightly release strategies designed by both methods for two Wolbachia strains, wMel and wMelPop., Comment: 28 pages, 9 figures