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Purpose: We present a virtual model to optimize point of entry (POE) in lung biopsy planning systems. Our model allows to compute the quality of a biopsy sample taken from potential POE, taking into account the margin of error that arises from discrepancies between the orientation in the planning simulation and the actual orientation during the operation. Additionally, the study examines the impact of the characteristics of the lesion. Methods: The quality of the biopsy is given by a heatmap projected onto the skeleton of a patient-specific model of airways. The skeleton provides a 3D representation of airways structure, while the heatmap intensity represents the potential amount of tissue that it could be extracted from each POE. This amount of tissue is determined by the intersection of the lesion with a cone that represents the uncertainty area in the introduction of biopsy instruments. The cone, lesion, and skeleton are modelled as graphical objects that define a 3D scene of the intervention. Results: We have simulated different settings of the intervention scene from a single anatomy extracted from a CT scan and two lesions with regular and irregular shapes. The different scenarios are simulated by systematic rotation of each lesion placed at different distances from airways. Analysis of the heatmaps for the different settings show a strong impact of lesion orientation for irregular shape and the distance for both shapes. Conclusion: The proposed heatmaps help to visually assess the optimal POE and identify whether multiple optimal POEs exist in different zones of the bronchi. They also allow us to model the maximum allowable error in navigation systems and study which variables have the greatest influence on the success of the operation. Additionally, they help determine at what point this influence could potentially jeopardize the operation.

Multimode cavity optomechanics, where multiple mechanical degrees of freedom couple to optical cavity modes, provides a rich platform for exploring nonlinear dynamics and engineering complex interactions. In this work, we investigate the interplay between two mechanical modes with similar characteristics and a self-induced nonlinear modulation of intra-cavity power (self-pulsing) driven by free-carrier dispersion and thermo-optic effects in silicon. Notably, the self-pulsing dynamics adapts to the optomechanically induced perturbations from both mechanical modes, enabling simultaneous synchronous pumping and driving them into a stable state characterized by high-amplitude, self-sustained, and coherent oscillations. This result effectively overcomes the strong mode competition typically observed in modes with similar spatial distributions and frequency scales. Remarkably, this regime is achieved even when the mechanical frequencies do not satisfy a harmonic relation, leading to quasi-periodic or chaotic intra-cavity power dynamics, while the mechanical modes maintain coherent, high-amplitude oscillations. These results, supported by a numerical model that accurately predicts the dynamics of the system, open new pathways for the generation and control of multi-phonon coherent sources in chip-integrated silicon platforms.

We consider the logarithmic Schr{\"o}dinger equation in a semiclassical scaling, in the presence of a smooth, at most quadratic, external potential. For initial data under the form of a single coherent state, we identify the notion of criticality as far as the nonlinear coupling constant is concerned, in the semiclassical limit. In the critical case, we prove a general error estimate, and improve it in the case of initial Gaussian profiles. In this critical case, when the initial datum is the sum of two Gaussian coherent states with different centers in phase space, we prove a nonlinear superposition principle., Comment: 23 pages

Codd's Theorem, a fundamental result of database theory, asserts that relational algebra and relational calculus have the same expressive power on relational databases. We explore Codd's Theorem for databases over semirings and establish two different versions of this result for such databases: the first version involves the five basic operations of relational algebra, while in the second version the division operation is added to the five basic operations of relational algebra. In both versions, the difference operation of relations is given semantics using semirings with monus, while on the side of relational calculus a limited form of negation is used. The reason for considering these two different versions of Codd's theorem is that, unlike the case of ordinary relational databases, the division operation need not be expressible in terms of the five basic operations of relational algebra for databases over an arbitrary positive semiring; in fact, we show that this inexpressibility result holds even for bag databases.

We present the first characterization of the statistical relationship between a large sample of novae in M31 and their progenitor stellar populations in the form of a delay time distribution. To this end, we leverage the spatially resolved stellar age distribution of the M31 disk derived from deep HST photometry by the Panchromatic Hubble Andromeda Treasury (PHAT) survey and a large catalog of novae in M31. Our delay time distribution has two statistically significant detections: one population of nova progenitors, ages between 2 and 3.2 Gyr, with an unnormalized rate of ($3.7^{+6.8}_{-3.5} \pm 2.1) \cdot 10^{-9}$ events / $M_{\odot}$, and another of ages between 7.9 Gyr and the age of the Universe with ($4.8^{+1.0}_{-0.9} \pm 0.2) \cdot 10^{-9}$ events / $M_{\odot}$ (uncertainties are statistical and systematic, respectively). Together with the upper limits we derive at other time bins, these detections are consistent with either a constant production efficiency or a higher production efficiency of novae at earlier delay times., Comment: 14 pages, 6 figures. Submitted to The Astrophysical Journal, currently under review

Living systems are composed of discrete units, assembled through a hierarchy of structures, and active, by locally extracting energy from their environment to produce mechanical work. Hydrodynamic theories have been successfully applied to describe the large scale dynamics of active materials. Yet, the hydrodynamic limit requires a separation of scales which is not necessarily fulfilled among living systems. In this work, we propose a novel agent-based model of flexible rods exchanging active force dipoles with nematic symmetry, allowing us to explore their behavior down to the sub-agent scale. We obtain spontaneous flows and self-propulsion of $+1/2$ topological defects, hallmarks of the hydrodynamic theory of active nematics, even on scales smaller than the individual agent! Moreover, our results go beyond the hydrodynamic framework, identifying novel correlations between orientation and flows or strong asymmetries between contractile and extensile activity. Finally, we show the versatility of our agent-based model by presenting spontaneous flows in three dimensions and nematic tissue growth. Because living systems like cell tissues often exhibit several sources of activity, our framework opens the way for more integrated descriptions of living materials.

Models predict that the well-studied mass-radius relation of white dwarf stars depends on the temperature of the star, with hotter white dwarfs having larger masses at a given radius than cooler stars. In this paper, we use a catalog of 26,041 DA white dwarfs observed in Sloan Digital Sky Survey Data Releases 1-19. We measure the radial velocity, effective temperature, surface gravity, and radius for each object. By binning this catalog in radius or surface gravity, we average out the random motion component of the radial velocities for nearby white dwarfs to isolate the gravitational redshifts for these objects and use them to directly measure the mass-radius relation. For gravitational redshifts measured from binning in either radius or surface gravity, we find strong evidence for a temperature-dependent mass-radius relation, with warmer white dwarfs consistently having greater gravitational redshifts than cool objects at a fixed radius or surface gravity. For warm white dwarfs, we find that their mean radius is larger and mean surface gravity is smaller than those of cool white dwarfs at 5.2{\sigma} and 6.0{\sigma} significance, respectively. Selecting white dwarfs with similar radii or surface gravities, the significance of the difference in mean gravitational redshifts between the warm and cool samples is >6.1{\sigma} and >3.6{\sigma} for measurements binned in radius and surface gravity, respectively, in the direction predicted by theory. This is an improvement over previous implicit detections, and our technique can be expanded to precisely test the white dwarf mass-radius relation with future surveys.

We study correlations in the prepare-and-measure scenario when quantum communication is constrained by photon-number statistics. Such constraints are natural and practical control parameters for semi-device-independent certification in optical platforms. To analyse these scenarios, we show how semidefinite programming relaxations for non-commutative polynomial optimization can be used to bound the set of quantum correlations under restrictions on the photon-number distribution. The practicality of this method is demonstrated by computing optimal performance bounds on several well-known communication tasks. We then apply the method to the certification of semi-device-inpependent random number generation protocols and show how to bound the conditional Shannon entropy. We showcase this versatile tool by improving randomness extraction in established protocols based on coherent states and homodyne measurements.

We investigate how local distinguishability can restrict global properties of bi-partite states. We begin exploring how non-locality becomes limited by optimal local state discrimination and observe a non-trivial trade-off between CHSH violation and success probability of local discrimination. We extend our findings to bounding the maximally entangled sate fidelity and global observables such as the energy. Our results show that optimal local state discrimination can become a powerful tool to limit global behaviours, e.g. from entangled adversaries in quantum cryptography.

Quantum neural networks have the potential to be seamlessly integrated with quantum devices for the automatic recognition of quantum states. However, performing complex tasks requires a large number of neurons densely connected through trainable, parameterized weights - a challenging feat when using qubits. To address this, we propose leveraging bosonic modes and performing Fock basis measurements, enabling the extraction of an exponential number of features relative to the number of modes. Unlike qubits, bosons can be coupled through multiple parametric drives, with amplitudes, phases, and frequency detunings serving dual purposes: data encoding and trainable parameters. We demonstrate that these parameters, despite their differing physical dimensions, can be trained cohesively using backpropagation to solve benchmark tasks of increasing complexity. Furthermore, we show that training significantly reduces the number of measurements required for feature extraction compared to untrained quantum neural networks, such as quantum reservoir computing.

Wi-Fi facilitates the Internet connectivity of billions of devices worldwide, making it an indispensable technology for modern life. Wi-Fi networks are becoming significantly denser, making energy consumption and its effects on operational costs and environmental sustainability crucial considerations. Wi-Fi has already introduced several mechanisms to enhance the energy efficiency of non-Access Point (non-AP) stations (STAs). However, the reduction of energy consumption of APs has never been a priority. Always-on APs operating at their highest capabilities consume significant power, which affects the energy costs of the infrastructure owner, aggravates the environmental impact, and decreases the lifetime of battery-powered APs. IEEE 802.11bn, which will be the basis of Wi-Fi 8, makes a big leap forward by introducing the AP Power Save (PS) framework. In this article, we describe and analyze the main proposals discussed in the IEEE 802.11bn Task Group (TGbn), such as Scheduled Power Save, (Semi-)Dynamic Power Save, and Cross Link Power Save. We also consider other proposals that are being discussed in TGbn, namely the integration of Wake-up Radios (WuR) and STA offloading. We then showcase the potential benefits of AP PS using a public dataset collected from 470 real APs deployed in a university campus. Our numerical analysis reveals that AP power consumption could be decreased on average by at least 28%. Finally, we outline the open challenges that need to be addressed to optimally integrate AP PS in Wi-Fi and ensure its compatibility with legacy devices.

Many studies have predicted SocioEconomic Position (SEP) for aggregated spatial units such as villages using satellite data, but SEP prediction at the household level and other sources of imagery have not been yet explored. We assembled a dataset of 975 households in a semi-rural district in southern Mozambique, consisting of self-reported asset, expenditure, and income SEP data, as well as multimodal imagery including satellite images and a ground-based photograph survey of 11 household elements. We fine-tuned a convolutional neural network to extract feature vectors from the images, which we then used in regression analyzes to model household SEP using different sets of image types. The best prediction performance was found when modeling asset-based SEP using random forest models with all image types, while the performance for expenditure- and income-based SEP was lower. Using SHAP, we observed clear differences between the images with the largest positive and negative effects, as well as identified the most relevant household elements in the predictions. Finally, we fitted an additional reduced model using only the identified relevant household elements, which had an only slightly lower performance compared to models using all images. Our results show how ground-based household photographs allow to zoom in from an area-level to an individual household prediction while minimizing the data collection effort by using explainable machine learning. The developed workflow can be potentially integrated into routine household surveys, where the collected household imagery could be used for other purposes, such as refined asset characterization and environmental exposure assessment.

This study aims to explore the impact of expansion strategies and specific attributes of hotel establishments on the performance of international hotel chains, focusing on four key performance indicators: RevPAR, efficiency, occupancy, and asset turnover. Data were collected from 255 hotels across various international hotel chains, providing a comprehensive assessment of how different expansion strategies and hotel attributes influence performance. The research employs compositional data analysis (CoDA) to address the methodological limitations of traditional financial ratios in statistical analysis. The findings indicate that ownership-based expansion strategies result in higher operational performance, as measured by revenue per available room, but yield lower economic performance due to the high capital investment required. Non-ownership strategies, such as management contracts and franchising, show superior economic efficiency, offering more flexibility and reduced financial risk. This study contributes to the hospitality management literature by applying CoDA, a novel methodological approach in this field, to examine the performance of different hotel expansion strategies with a sound and more appropriate method. The insights provided can guide hotel managers and investors in making informed decisions to optimize both operational and economic performance., Comment: 21 pages

Homotopical localizations with respect to (possibly proper) classes of maps are known to exist assuming the validity of a large-cardinal axiom from set theory called Vop\v{e}nka's principle. In this article, we prove that each of the following statements is equivalent to an axiom of lower consistency strength than Vop\v{e}nka's principle, known as weak Vop\v{e}nka's principle: (a) Localization with respect to any class of maps exists in the homotopy category of simplicial sets; (b) Localization with respect to any class of maps exists in the homotopy category of spectra; (c) Localization with respect to any class of morphisms exists in any presentable $\infty$-category; (d) Every full subcategory closed under products and fibres in a triangulated category with locally presentable models is reflective. Our results are established using Wilson's 2020 solution to a long-standing open problem concerning the relative consistency of weak Vop\v{e}nka's principle within the large-cardinal hierarchy., Comment: 30 pages

In this communication, we report on the results of the second phase of the Exoplanet Imaging Data Challenge started in 2019. This second phase focuses on the characterization of point sources (exoplanet signals) within multispectral high-contrast images from ground-based telescopes. We collected eight data sets from two high-contrast integral field spectrographs (namely Gemini-S/GPI and VLT/SPHERE-IFS) that we calibrated homogeneously, and in which we injected a handful of synthetic planetary signals (ground truth) to be characterized by the data challenge participants. The tasks of the participants consist of (1) extracting the precise astrometry of each injected planetary signals, and (2) extracting the precise spectro-photometry of each injected planetary signal. Additionally, the participants may provide the 1-sigma uncertainties on their estimation for further analyses. When available, the participants can also provide the posterior distribution used to estimate the position/spectrum and uncertainties. The data are permanently available on a Zenodo repository and the participants can submit their results through the EvalAI platform. The EvalAI submission platform opened on April 2022 and closed on the 31st of May 2024. In total, we received 4 valid submissions for the astrometry estimation and 4 valid submissions for the spectrophotometry (each submission, corresponding to one pipeline, has been submitted by a unique participant). In this communication, we present an analysis and interpretation of the results., Comment: Submitted to SPIE Astronomical Telescopes + Instrumentation 2024, Adaptive Optics Systems IX, Paper 13097-40

We show that bipartite bound entangled states make possible violations of correlation inequalities in the prepare-and-measure scenario. These inequalities are satisfied by all classical models as well as by all quantum models that do not feature entanglement. In contrast to the known Bell inequality violations from bound entangled states, we find that the violations in the prepare-and-measure scenario are sizeable and significantly noise-tolerant. Furthermore, we evidence that significantly stronger quantum correlations are made possible by considering bound entanglement with a larger dimension.

In this paper, we consider a Stochastic Delay Differential Equation with constant delay $r>0$ and, under the same conditions on the coefficients needed to ensure the smoothness of the density plus an ellipticity condition on the diffusion term, we prove that the density function of the solution is strictly positive in its support. In order to prove it, we give a Gaussian-type lower bound for the density of the solution combining the Nourdin and Viens' density bounding method together with Kohatsu-Higa's method., Comment: 23 pages

Panel data arise when time series measurements are collected from multiple, dynamically independent but structurally related systems. In such cases, each system's time series can be modeled as a partially observed Markov process (POMP), and the ensemble of these models is called a PanelPOMP. If the time series are relatively short, statistical inference for each time series must draw information from across the entire panel. Every time series has a name, called its unit label, which may correspond to an object on which that time series was collected. Differences between units may be of direct inferential interest or may be a nuisance for studying the commonalities. The R package panelPomp supports analysis of panel data via a general class of PanelPOMP models. This includes a suite of tools for manipulation of models and data that take advantage of the panel structure. The panelPomp package currently emphasizes recent advances enabling likelihood-based inference via simulation-based algorithms. However, the general framework provided by panelPomp supports development of additional, new inference methodology for panel data.

We discover a novel class of dissipative light bullets whose spatial profiles may be drastically reshaped along the bulk, edges and corners of the Su-Schrieffer-Heeger lattice owing to the dissipative and topological nature of the system. These light bullets appear due to resonances with different modes in lattice spectrum and may have very rich shapes that can be adiabatically controlled by varying the frequency of the external laser source. We report on robust stationary bullets and breathers which are understood from the corresponding bifurcation analysis. Our results provide a new route to realisation of reconfigurable and robust 3D light forms in topologically nontrivial systems., Comment: 7 pages, 4 figures, comments welcome

We introduce semidefinite programming hierarchies for benchmarking relevant entanglement properties in the high-dimensional steering scenario. Firstly, we provide a general method for detecting the entanglement dimensionality through certification of the Schmidt number. Its key feature is that the computational cost is independent of the Schmidt number under consideration. Secondly, we provide a method to estimate the fidelity of the source with any maximally entangled state. Using only basic computational means, we demonstrate the usefulness of these methods, which can be directly used to analyse experiments on high-dimensional systems.

The rising interest in leveraging higher-order interactions present in complex systems has led to a surge in more expressive models exploiting high-order structures in the data, especially in topological deep learning (TDL), which designs neural networks on high-order domains such as simplicial complexes. However, progress in this field is hindered by the scarcity of datasets for benchmarking these architectures. To address this gap, we introduce MANTRA, the first large-scale, diverse, and intrinsically high order dataset for benchmarking high-order models, comprising over 43,000 and 249,000 triangulations of surfaces and three-dimensional manifolds, respectively. With MANTRA, we assess several graph- and simplicial complex-based models on three topological classification tasks. We demonstrate that while simplicial complex-based neural networks generally outperform their graph-based counterparts in capturing simple topological invariants, they also struggle, suggesting a rethink of TDL. Thus, MANTRA serves as a benchmark for assessing and advancing topological methods, leading the way for more effective high-order models., Comment: 26 pages, 2 figures, 22 tables

Low-cost reduced graphene oxide sponges functionalized with manganese oxide were used as electrodes for the disinfection of Escherichia coli in water. Manganese oxide was doped with amino groups MnxOyNH2 to strengthen the bond with the graphene coating and improve the electrochemical stability of the sponge. The Mn II and Mn III incorporated into the graphene coating favored the formation of oxygen vacancies and enhanced the electric and catalytic properties of the anode. Electrooxidation of real tap water at 29 A m2 resulted in 2.2 log removal of E. coli. After storing the treated samples for 18 h at 25 and 37 {\deg}C, the removal of E. coli increased to 3.3 and 4.6 log, respectively, demonstrating the irreparable damage to the bacterial cells via low-voltage electroporation, and the key role of storage temperature in their further inactivation. The energy consumption of the system treating real low conductivity tap water was 1.2-1.6 kWh m-3. Finally, experiments with intermittent current suggest the contribution of the pseudo-capacitance of the graphene sponge to electrochemical disinfection during the OFF periods. This study demonstrates the feasibility of manganese oxide-functionalized graphene sponges for the chlorine-free disinfection of water., Comment: 33 pages, 7 figures, 1 table, and supplementary material with 14 figures and 7 tables

Deep generative models that learn from the distribution of natural protein sequences and structures may enable the design of new proteins with valuable functions. While the majority of today's models focus on generating either sequences or structures, emerging co-generation methods promise more accurate and controllable protein design, ideally achieved by modeling both modalities simultaneously. Here we review recent advances in deep generative models for protein design, with a particular focus on sequence-structure co-generation methods. We describe the key methodological and evaluation principles underlying these methods, highlight recent advances from the literature, and discuss opportunities for continued development of sequence-structure co-generation approaches.

Current and upcoming imaging galaxy surveys are pushing galaxy samples to higher and higher redshifts. This push will be more pronounced for lens galaxies, for which we only need to measure galaxy positions, not shapes. As a result, we will increasingly often have lens galaxy samples at redshifts higher than those of source galaxies, changing the traditional configuration of galaxy-galaxy lensing (GGL). In this paper, we explore this situation, where lens galaxies are behind source galaxies, which we call inverse galaxy-galaxy lensing (IGGL). We take projected lens and source sample specifications from the Vera Rubin Observatory LSST Dark Energy Science Collaboration (DESC) to compare astrophysical and cosmological constraints between traditional GGL and IGGL. We find IGGL to behave in a different way than GGL, being especially sensitive to lensing magnification, intrinsic alignments (IA) and cosmology, but largely independent of galaxy bias (as opposed to traditional GGL). In this way, we find IGGL can provide independent and robust cosmological constraints without combination with galaxy clustering, and can also probe IA at high redshift and baryonic effects at small scales without being entwined with the effects of non-linear galaxy bias. When combined with cosmic shear, we find IGGL to improve $S_8$ constraints by 25\% compared to cosmic shear alone, while also providing tighter and more robust constraints on IA and baryons., Comment: 17 pages plus references, 14 figures. To be submitted to PRD. Comments welcomed

This paper presents an algebraic study of a family of logics related to Abelian logic ($Ab$), the logic of Abelian lattice-ordeded groups. $Ab$ is treated as the basic, weakest logic, and its expansions are referred to as superabelian logics. To account for the language differences in Lukasiewicz logics, we introduced the expansion of $Ab$ with an additional constant and call it pointed Abelian logic ($pAb$), with semantics based on pointed Abelian $l$-groups. We take the first steps in the study of infinitary extensions of $Ab$, give a completeness theorem for $pAb$, and obtain axiomatizations of Lukasiewicz unbound logics relative to $pAb$. The paper concludes with an exploration of other significant extensions of $pAb$ and their algebraic characterizations.

Stochastic optimal control (SOC) aims to direct the behavior of noisy systems and has widespread applications in science, engineering, and artificial intelligence. In particular, reward fine-tuning of diffusion and flow matching models and sampling from unnormalized methods can be recast as SOC problems. A recent work has introduced Adjoint Matching (Domingo-Enrich et al., 2024), a loss function for SOC problems that vastly outperforms existing loss functions in the reward fine-tuning setup. The goal of this work is to clarify the connections between all the existing (and some new) SOC loss functions. Namely, we show that SOC loss functions can be grouped into classes that share the same gradient in expectation, which means that their optimization landscape is the same; they only differ in their gradient variance. We perform simple SOC experiments to understand the strengths and weaknesses of different loss functions.

Humans possess innate collaborative capacities. However, effective teamwork often remains challenging. This study delves into the feasibility of collaboration within teams of rational, self-interested agents who engage in teamwork without the obligation to contribute. Drawing from psychological and game theoretical frameworks, we formalise teamwork as a one-shot aggregative game, integrating insights from Steiner's theory of group productivity. We characterise this novel game's Nash equilibria and propose a multiagent multi-armed bandit system that learns to converge to approximations of such equilibria. Our research contributes value to the areas of game theory and multiagent systems, paving the way for a better understanding of voluntary collaborative dynamics. We examine how team heterogeneity, task typology, and assessment difficulty influence agents' strategies and resulting teamwork outcomes. Finally, we empirically study the behaviour of work teams under incentive systems that defy analytical treatment. Our agents demonstrate human-like behaviour patterns, corroborating findings from social psychology research.

Given two ideals $I$ and $J$ of the ring $\mathcal O_n$ of analytic function germs $f:(\mathbb C^n,0)\to \mathbb C$, we show a sharp lower bound for the log canonical threshold of $IJ$ in terms of the sequences of mixed {\L}ojasiewicz exponents of them. In particular, in the case where $J$ is the maximal ideal, the corresponding equality holds if and only if the integral closure of $I$ equals some power of the maximal ideal.

For a prime $p$, fusion systems over discrete $p$-toral groups are categories that model and generalize the $p$-local structure of Lie groups and certain other infinite groups in the same way that fusion systems over finite $p$-groups model and generalize the $p$-local structure of finite groups. In the finite case, it is natural to say that a fusion system $\mathcal{F}$ is realizable if it is isomorphic to the fusion system of a finite group, but it is less clear what realizability should mean in the discrete $p$-toral case. In this paper, we look at some of the different types of realizability for fusion systems over discrete $p$-toral groups, including realizability by linear torsion groups and sequential realizability, of which the latter is the most general. After showing that fusion systems of compact Lie groups are always realized by linear torsion groups (hence sequentially realizable), we give some new tools for showing that certain fusion systems are not sequentially realizable, and illustrate it with two large families of examples.

Dynamical generative models that produce samples through an iterative process, such as Flow Matching and denoising diffusion models, have seen widespread use, but there have not been many theoretically-sound methods for improving these models with reward fine-tuning. In this work, we cast reward fine-tuning as stochastic optimal control (SOC). Critically, we prove that a very specific memoryless noise schedule must be enforced during fine-tuning, in order to account for the dependency between the noise variable and the generated samples. We also propose a new algorithm named Adjoint Matching which outperforms existing SOC algorithms, by casting SOC problems as a regression problem. We find that our approach significantly improves over existing methods for reward fine-tuning, achieving better consistency, realism, and generalization to unseen human preference reward models, while retaining sample diversity.

We carry out a survey on curves defined over finite fields that are Diophantine stable; that is, with the property that the set of points of the curve is not altered under a proper field extension. First, we derive some general results of such curves and then we analyze several families of curves that happen to be Diophantine stable.

Image color consistency is the key problem in digital imaging consistency when creating datasets. Here, we propose an improved 3D Thin-Plate Splines (TPS3D) color correction method to be used, in conjunction with color charts (i.e. Macbeth ColorChecker) or other machine-readable patterns, to achieve image consistency by post-processing. Also, we benchmark our method against its former implementation and the alternative methods reported to date with an augmented dataset based on the Gehler's ColorChecker dataset. Benchmark includes how corrected images resemble the ground-truth images and how fast these implementations are. Results demonstrate that the TPS3D is the best candidate to achieve image consistency. Furthermore, our Smooth-TPS3D method shows equivalent results compared to the original method and reduced the 11-15% of ill-conditioned scenarios which the previous method failed to less than 1%. Moreover, we demonstrate that the Smooth-TPS method is 20% faster than the original method. Finally, we discuss how different methods offer different compromises between quality, correction accuracy and computational load.

Within the context of creating new Socially Assistive Robots, emotion recognition has become a key development factor, as it allows the robot to adapt to the user's emotional state in the wild. In this work, we focused on the analysis of two voice recording Spanish datasets: ELRA-S0329 and EmoMatchSpanishDB. Specifically, we centered our work in the paralanguage, e.~g. the vocal characteristics that go along with the message and clarifies the meaning. We proposed the use of the DeepSpectrum method, which consists of extracting a visual representation of the audio tracks and feeding them to a pretrained CNN model. For the classification task, DeepSpectrum is often paired with a Support Vector Classifier --DS-SVC--, or a Fully-Connected deep-learning classifier --DS-FC--. We compared the results of the DS-SVC and DS-FC architectures with the state-of-the-art (SOTA) for ELRA-S0329 and EmoMatchSpanishDB. Moreover, we proposed our own classifier based upon Attention Mechanisms, namely DS-AM. We trained all models against both datasets, and we found that our DS-AM model outperforms the SOTA models for the datasets and the SOTA DeepSpectrum architectures. Finally, we trained our DS-AM model in one dataset and tested it in the other, to simulate real-world conditions on how biased is the model to the dataset.

The R package panelPomp supports analysis of panel data via a general class of partially observed Markov process models (PanelPOMP). This package tutorial describes how the mathematical concept of a PanelPOMP is represented in the software and demonstrates typical use-cases of panelPomp. Monte Carlo methods used for POMP models require adaptation for PanelPOMP models due to the higher dimensionality of panel data. The package takes advantage of recent advances for PanelPOMP, including an iterated filtering algorithm, Monte Carlo adjusted profile methodology and block optimization methodology to assist with the large parameter spaces that can arise with panel models. In addition, tools for manipulation of models and data are provided that take advantage of the panel structure.

We consider the nonlinear Schr{\"o}dinger equation with a potential, also known as Gross-Pitaevskii equation. By introducing a suitable spectral localization, we prove low regularity error estimates for the time discretization corresponding to an adapted Lie-Trotter splitting scheme. The proof is based on tools from spectral theory and pseudodifferential calculus in order to obtain various estimates on the spectral localization, including discrete Strichartz estimates which support the nonlinear analysis., Comment: An inconsistency in the assumption on the nonlinearity in Th. 1.6 was fixed

Long-range frequency hopping spread spectrum (LR-FHSS) is a pivotal advancement in the LoRaWAN protocol that is designed to enhance the network's capacity and robustness, particularly in densely populated environments. Although energy consumption is paramount in LoRaWAN-based end devices, {this is the first study} in the literature, to our knowledge, that models the impact of this novel mechanism on energy consumption. In this article, we provide a comprehensive energy consumption analytical model of LR-FHSS, focusing on three critical metrics: average current consumption, battery lifetime, and energy efficiency of data transmission. The model is based on measurements performed on real hardware in a fully operational LR-FHSS network. While in our evaluation, LR-FHSS can show worse consumption figures than LoRa, we find that with optimal configuration, the battery lifetime of LR-FHSS end devices can reach 2.5 years for a 50 min notification period. For the most energy-efficient payload size, this lifespan can be extended to a theoretical maximum of up to 16 years with a one-day notification interval using a cell-coin battery.

Carbon abundances in first-ascent giant stars are usually lower than those of their main-sequence counterparts. At moderate metallicities, stellar evolution of single stars cannot account for the existence of red-giant branch stars with enhanced carbon abundances. The phenomenon is usually interpreted as resulting from past mass transfer from an evolved binary companion now in the white dwarf evolutionary stage. Aims: We aim to confirm the links between [C/O] enhancement, s-process element enhancement and binary fraction using large-scale catalogues of stellar abundances and probable binary stars. Methods: We use a large data set from the 17 data release of the SDSS-IV/APOGEE~2 survey to identify carbon-enhanced stars in the Galactic disk. We identify a continuum of carbon enrichment throughout three different sub-populations of disk stars and explore links between the degree of carbon enrichment and binary frequency, metallicity and chemical compositions. Results: We verify a clear correlation between binary frequency and enhancement in the abundances of both carbon and cerium, lending support to the scenario whereby carbon-enhanced stars are the result of mass transfer by an evolved binary companion. In addition, we identify clustering in the carbon abundances of high-$\alpha$ disk stars, suggesting that those on the high metallicity end are likely younger, in agreement with theoretical predictions for the presence of a starburst population following the gas-rich merger of the Gaia-Enceladus/Sausage system., Comment: 20 pages

We unveil a new scenario for the formation of dissipative localised structures in nonlinear systems. Commonly, the formation of such structures arises from the connection of a homogeneous steady state with either another homogeneous solution or a pattern. Both scenarios, typically found in cavities with normal and anomalous dispersion, respectively, exhibit unique fingerprints and particular features that characterise their behaviour. However, we show that the introduction of a periodic non-Hermitian modulation in Kerr cavities hybridises the two established soliton formation mechanisms, embodying the particular fingerprints of both. In the resulting novel scenario, the stationary states acquire a dual behaviour, playing the role that was unambiguously attributed to either homogeneous states or patterns. These fundamental findings have profound practical implications for frequency comb generation, introducing unprecedented reversible mechanisms for real-time manipulation., Comment: 6 pages, 4 figures, to appear in Physical Review Letters. Comments welcomed

A magma is called equidecomposable when the operation is injective, or, in other words, if $x+y=x'+y'$ implies that $x=x'$ and $y=y'$. A magma is free iff it is equidecomposable and graded, hence the notion of equidecomposability is very related to the notion of freeness although it is not sufficient. We study main properties of such magmas. In particular, an alternative characterization of freeness, which uses a weaker condition, is proved. We show how equidecomposable magmas can be split into two disjoint submagmas, one of which is free. Certain tranformations on finite presentations permit to obtain a reduced form which allows us identify all the finite presented equidecomposable magmas up to isomorphisms., Comment: 26 pages

We survey free magmas and we explore the structure of their submagmas. By equipping the cyclic free magma with a second distributive operation we obtain a ringoid-like structure with some primitive arithmetical properties. A submagma is $k$-maximal when there are only $k-1$ submagmas between it and the free magma itself. These two tools, arithmetic and maximality, allow us to study the lattice of the submagmas of a free magma., Comment: 26 pages, 4 figures

The simplest way to generate a lattice of convex sets is to consider an initial set of points and draw segments, triangles, and any convex hull from it, then intersect them to obtain new points, and so forth. The result is an infinite lattice for most sets, while only a few initial sets of points perform a finite lattice. By giving an adequate notion of the configuration of points, we identify which sets in the plane define a finite convex hull lattice: four regular families and one sporadic configuration. We explore configurations in the space and higher dimensions., Comment: 19 pages, 6 figures. Under revision ar Journal od discrete & computational geometry

A subset $X$ of a groupoid is said to be deficient if $|X \cdot X|\leq |X|$. It is well-known that the probability that a random groupoid has a deficient $t$-element set with $t\geq 3$ is zero. However, as conjectured in [4], we show that the probability is not zero in the case of sets of two elements and calculate the exact value. We explore some generalisations on deficient sets and their likelihoods., Comment: 11 pages, 1 figure. Under review at Algebra Universalis

We study the relation between the multigraded Castelnuovo-Mumford regularity of a multihomogeneous ideal $I$ and the multidegrees of a Gr\"obner basis of $I$ with respect to the degree reverse lexicographical monomial order in generic coordinates. For the single graded case, forty years ago, Bayer and Stillman unravelled all aspects of this relation, which in turn the use to complexity estimates for the computation with Gr\"obner bases. We build on their work to introduce a bounding region of the multidegrees of minimal generators of multigraded Gr\"obner bases for $I$. We also use this region to certify the presence of some minimal generators close to its boundary. Finally, we show that, up to a certain shift, this region is related to the multigraded Castelnuovo-Mumford regularity of $I$.

We present our contribution to the 7th ABAW challenge at ECCV 2024, by utilizing a Dual-Direction Attention Mixed Feature Network (DDAMFN) for multitask facial expression recognition, we achieve results far beyond the proposed baseline for the Multi-Task ABAW challenge. Our proposal uses the well-known DDAMFN architecture as base to effectively predict valence-arousal, emotion recognition, and facial action units. We demonstrate the architecture ability to handle these tasks simultaneously, providing insights into its architecture and the rationale behind its design. Additionally, we compare our results for a multitask solution with independent single-task performance., Comment: 11 pages

Binding affinity optimization is crucial in early-stage drug discovery. While numerous machine learning methods exist for predicting ligand potency, their comparative efficacy remains unclear. This study evaluates the performance of classical tree-based models and advanced neural networks in protein-ligand binding affinity prediction. Our comprehensive benchmarking encompasses 2D models utilizing ligand-only RDKit embeddings and Large Language Model (LLM) ligand representations, as well as 3D neural networks incorporating bound protein-ligand conformations. We assess these models across multiple standard datasets, examining various predictive scenarios including classification, ranking, regression, and active learning. Results indicate that simpler models can surpass more complex ones in specific tasks, while 3D models leveraging structural information become increasingly competitive with larger training datasets containing compounds with labelled affinity data against multiple targets. Pre-trained 3D models, by incorporating protein pocket environments, demonstrate significant advantages in data-scarce scenarios for specific binding pockets. Additionally, LLM pretraining on 2D ligand data enhances complex model performance, providing versatile embeddings that outperform traditional RDKit features in computational efficiency. Finally, we show that combining 2D and 3D model strengths improves active learning outcomes beyond current state-of-the-art approaches. These findings offer valuable insights for optimizing machine learning strategies in drug discovery pipelines., Comment: 20 pages, 14 figures, 1 table