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Assessing the economic impacts of artificial intelligence requires integrating insights from both computer science and economics. We present the Growth and AI Transition Endogenous model (GATE), a dynamic integrated assessment model that simulates the economic effects of AI automation. GATE combines three key ingredients that have not been brought together in previous work: (1) a compute-based model of AI development, (2) an AI automation framework, and (3) a semi-endogenous growth model featuring endogenous investment and adjustment costs. The model allows users to simulate the economic effects of the transition to advanced AI across a range of potential scenarios. GATE captures the interactions between economic variables, including investment, automation, innovation, and growth, as well as AI-related inputs such as compute and algorithms. This paper explains the model's structure and functionality, emphasizing AI development for economists and economic modeling for the AI community. The model is implemented in an interactive sandbox, enabling users to explore the impact of AI under different parameter choices and policy interventions. The modeling sandbox is available at: www.epoch.ai/GATE.

Hair cells actively drive oscillations of their mechanosensitive organelles--the hair bundles that enable hearing and balance sensing in vertebrates. Why and how some hair cells expend energy by sustaining this oscillatory motion in order to fulfill their function as signal sensors and others--as amplifiers, remains unknown. We develop a stochastic thermodynamic theory to describe energy flows in a periodically-driven hair bundle. Our analysis of thermodynamic fluxes associated with hair bundles' motion and external sinusoidal stimulus reveals that these organelles operate as thermodynamic work-to-work machines under different operational modes. One operational mode transduces the signal's power into the cell, whereas another allows the external stimulus to harvest the energy supplied by the cell. These two regimes might represent thermodynamic signatures of signal sensing and amplification respectively. In addition to work transduction and energy harvesting, our model also substantiates the capability of hair-cell bundles to operate as heaters and, at the expense of external driving, as active feedback refrigerators. We quantify the performance and robustness of the work-to-work conversion by hair bundles, whose efficiency in some conditions exceeds 80 % of the applied power., Comment: 38 pages, 20 figures, 10 tables

In this paper, an automatic labelling process is presented for automotive datasets, leveraging on complementary information from LiDAR and camera. The generated labels are then used as ground truth with the corresponding 4D radar data as inputs to a proposed semantic segmentation network, to associate a class label to each spatial voxel. Promising results are shown by applying both approaches to the publicly shared RaDelft dataset, with the proposed network achieving over 65% of the LiDAR detection performance, improving 13.2% in vehicle detection probability, and reducing 0.54 m in terms of Chamfer distance, compared to variants inspired from the literature., Comment: Accepted in ICASSP 2025

A new probability distribution to study lifetime data in reliability is introduced in this paper. This one is a first approach to a non-homogeneous phase-type distribution. It is built by considering one cut-point in the non-negative semi-line of a phase-type distribution. The density function is defined and the main measures associated, such as the reliability function, hazard rate, cumulative hazard rate and the characteristic function are also worked out. This new class of distributions enables to decrease the number of parameter in the estimate when inference is considered. Besides, the likelihood distribution is built to estimate the model parameters by maximum likelihood. Several applications by considering Resistive Random Access Memories compare the adjustment when phase type distributions and one cut-point phase-type distributions are considered. The developed methodology has been computationally implemented in R-cran.

A new class of distributions based on phase-type distributions is introduced in the current paper to model lifetime data in the field of reliability analysis. This one is the natural extension of the distribution proposed by Acal et al. (2021) for more than one cut-point. Multiple interesting measures such as density function, hazard rate or moments, among others, were worked out both for the continuous and discrete case. Besides, a new EM-algorithm is provided to estimate the parameters by maximum likelihood. The results have been implemented computationally in R and simulation studies reveal that this new distribution reduces the number of parameters to be estimated in the optimization process and, in addition, it improves the fitting accuracy in comparison with the classical phase-type distributions, especially in heavy tailed distributions. An application is presented in the context of resistive memories with a new set of electron devices for non-volatile memory circuits. In particular, the voltage associated with the resistive switching processes that control the internal behaviour of resistive memories has been modelled with this new distribution to shed light on the physical mechanisms behind the operation of these memories.

Consider the spatial restricted three-body problem, as a model for the motion of a spacecraft relative to the Sun-Earth system. We focus on the dynamics near the equilibrium point $L_1$, located between the Sun and the Earth. We show that we can transfer the spacecraft from a quasi-periodic orbit that is nearly planar relative to the ecliptic to a quasi-periodic orbit that has large out-of-plane amplitude, at zero energy cost. (In fact, the final orbit has the maximum out-of-plane amplitude that can be obtained through the particular mechanism that we consider. Moreover, the transfer can be made through any prescribed sequence of quasi-periodic orbits in between). Our transfer mechanism is based on selecting trajectories homoclinic to a normally hyperbolic invariant manifold (NHIM) near $L_1$, and then gluing them together. We provide several explicit constructions of such transfers, and also develop an algorithm to design trajectories that achieve the \emph{shortest transfer time} for this particular mechanism. The change in the out-of-plane amplitude along a homoclic trajectory can be described via the scattering map. We develop a new tool, the `Standard Scattering Map' (SSM), which is a series representation of the exact scattering map. We use the SSM to obtain a complete description of the dynamics along homoclinic trajectories. The SSM can be used in many other situations, from Arnold diffusion problems to transport phenomena in applications., Comment: 64 pages, 23 figures, 4 tables

In this article, we study inertial algorithms for numerically solving monotone inclusions involving the sum of a maximally monotone and a cocoercive operator. In particular, we analyze the convergence of inertial and relaxed versions of the nonlinear forward-backward with momentum (NFBM). We propose an inertial version including a relaxation step, and a second version considering a double-inertial step with additional momentum. By applying NFBM to specific monotone inclusions, we derive inertial and relaxed versions of algorithms such as forward-backward, forward-half-reflect-backward (FHRB), Chambolle-Pock, Condat-V\~u, among others, thereby recovering and extending previous results from the literature for solving monotone inclusions involving maximally monotone, cocoercive, monotone and Lipschitz, and linear bounded operators. We also present numerical experiments on image restoration, comparing the proposed inertial and relaxation algorithms. In particular, we compare the inertial FHRB with its non-inertial and momentum versions. Additionally, we compare the numerical convergence for larger step-sizes versus relaxation parameters and introduce a restart strategy that incorporates larger step-sizes and inertial steps to further enhance numerical convergence., Comment: 22 pages, 5 figures, and 7 tables

Higher-dimensional sliding puzzles are constructed on the vertices of a $d$-dimensional hypercube, where $2^d-l$ vertices are distinctly coloured. Rings with the same colours are initially set randomly on the vertices of the hypercube. The goal of the puzzle is to move each of the $2^d-l$ rings to pre-defined target vertices on the cube. In this setting, the $k$-rule constraint represents a generalisation of edge collision for the movement of colours between vertices, allowing movement only when a hypercube face of dimension $k$ containing a ring is completely free of other rings. Starting from an initial configuration, what is the minimum number of moves needed to make ring colours match the vertex colours? An algorithm that provides us with such a number is called God's algorithm. When such an algorithm exists, it does not have a polynomial time complexity, at least in the case of the 15-puzzle corresponding to $k=1$ in the cubical puzzle. This paper presents a comprehensive computational study of different scenarios of the higher-dimensional puzzle. A benchmark of three computational techniques, an exact algorithm (the A* search) and two approximately optimal search techniques (an evolutionary algorithm (EA) and reinforcement learning (RL)) is presented in this work. The experiments show that all three methods can successfully solve the puzzle of dimension three for different face dimensions and across various difficulty levels. When the dimension increases, the A* search fails, and RL and EA methods can still provide a generally acceptable solution, i.e. a distribution of a number of moves with a median value of less than $30$. Overall, the EA method consistently requires less computational time, while failing in most cases to minimise the number of moves for the puzzle dimensions $d=4$ and $d=5$., Comment: 20 pages, 8 figures

The stochastic resonance phenomenon has been studied experimentally and theoretically for a state-of-art metal-oxide memristive device based on yttria-stabilized zirconium dioxide and tantalum pentoxide, which exhibits bipolar filamentary resistive switching of anionic type. The effect of white Gaussian noise superimposed on the sub-threshold sinusoidal driving signal is analyzed through the time series statistics of the resistive switching parameters, the spectral response to a periodic perturbation and the signal-to-noise ratio at the output of the nonlinear system. The stabilized resistive switching and the increased memristance response are revealed in the observed regularities at an optimal noise intensity corresponding to the stochastic resonance phenomenon and interpreted using a stochastic memristor model taking into account an external noise source added to the control voltage. The obtained results clearly show that noise and fluctuations can play a constructive role in nonlinear memristive systems far from equilibrium.

Antimicrobial resistance is a threat to public health with millions of deaths linked to drug resistant infections every year. To mitigate resistance, common strategies that are used are combination therapies and therapy switching. However, the stochastic nature of pathogenic mutation makes the optimization of these strategies challenging. Here, we propose a two-scale stochastic model that considers the effective evolution of therapies in a multidimensional efficacy space, where each dimension represents the efficacy of a specific drug in the therapy. The diffusion of therapies within this space is subject to stochastic resets, representing therapy switches. The boundaries of the space, inferred from coarser pathogen-host dynamics, can be either reflecting or absorbing. Reflecting boundaries impede full recovery of the host, while absorbing boundaries represent the development of antimicrobial resistance, leading to therapy failure. We derive analytical expressions for the average absorption times, accounting for both continuous and discrete genomic changes using the frameworks of Langevin and Master equations, respectively. These expressions allow us to evaluate the relevance of times between drug-switches and the number of simultaneous drugs in relation to typical timescales for drug resistance development. We also explore realistic scenarios where therapy constraints are imposed to the number of administered therapies and/or their costs, finding non-trivial optimal drug-switching protocols that maximize the time before antimicrobial resistance develops while reducing therapy costs.

Cerebral aneurysms and arteriovenous malformations are life-threatening hemodynamic pathologies of the brain. While surgical intervention is often essential to prevent fatal outcomes, it carries significant risks both during the procedure and in the postoperative period, making the management of these conditions highly challenging. Parameters of cerebral blood flow, routinely monitored during medical interventions or with modern noninvasive high-resolution imaging methods, could potentially be utilized in machine learning-assisted protocols for risk assessment and therapeutic prognosis. To this end, we developed a linear oscillatory model of blood velocity and pressure for clinical data acquired from neurosurgical operations. Using the method of Sparse Identification of Nonlinear Dynamics (SINDy), the parameters of our model can be reconstructed online within milliseconds from a short time series of the hemodynamic variables. The identified parameter values enable automated classification of the blood-flow pathologies by means of logistic regression, achieving an accuracy of 73 \%}. Our results demonstrate the potential of this model for both diagnostic and prognostic applications, providing a robust and interpretable framework for assessing cerebral blood vessel conditions., Comment: 15 pages, 6 main figures, 5 supplementary figures, 2 supplementary tables

Variability in memristive devices based on h-BN dielectrics is studied in depth. Different numerical techniques to extract the reset voltage are described and the corresponding cycle-to-cycle variability is characterized by means of the coefficient of variance. The charge-flux domain was employed to develop one of the extraction techniques, the calculation of the integrals of current and voltage to obtain the charge and flux allows to minimize the effects of electric noise and the inherent stochasticity of resistive switching on the measurement data. A model to reproduce charge versus flux curves has been successfully employed. The device variability is also described by means of the time series analysis to assess the memory effect along a resistive switching series. Finally, we analyzed I-V curves under ramped voltage stress utilizing a simulator based on circuit breakers, the formation and rupture of the percolation paths that constitute the conductive nanofilaments is studied to describe the set and reset processes behind the resistive switching operation.

Resistive memories are outstanding electron devices that have displayed a large potential in a plethora of applications such as nonvolatile data storage, neuromorphic computing, hardware cryptography, etc. Their fabrication control and performance have been notably improved in the last few years to cope with the requirements of massive industrial production. However, the most important hurdle to progress in their development is the so-called cycle-to-cycle variability, which is inherently rooted in the resistive switching mechanism behind the operational principle of these devices. In order to achieve the whole picture, variability must be assessed from different viewpoints going from the experimental characterization to the adequation of modeling and simulation techniques. Herein, special emphasis is put on the modeling part because the accurate representation of the phenomenon is critical for circuit designers. In this respect, a number of approaches are used to the date: stochastic, behavioral, mesoscopic..., each of them covering particular aspects of the electron and ion transport mechanisms occurring within the switching material. These subjects are dealt with in this review, with the aim of presenting the most recent advancements in the treatment of variability in resistive memories.

This paper is motivated by modeling the cycle-to-cycle variability associated with the resistive switching operation behind memristors. As the data are by nature curves, functional principal component analysis is a suitable candidate to explain the main modes of variability. Taking into account this data-driven motivation, in this paper we propose two new forecasting approaches based on studying the sequential cross-dependence between and within a multivariate functional time series in terms of vector autoregressive modeling of the most explicative functional principal component scores. The main difference between the two methods lies in whether a univariate or multivariate PCA is performed so that we have a different set of principal component scores for each functional time series or the same one for all of them. Finally, the sample performance of the proposed methodologies is illustrated by an application on a bivariate functional time series of reset-set curves.

Can outreach inspire and lead to research and vice versa? In this work, we introduce our approach to the gamification of research in mathematics and computer science through three illustrative examples. We discuss our primary motivations and provide insights into what makes our proposed gamification effective for three research topics in discrete and computational geometry and topology: (1) DominatriX, an art gallery problem involving polyominoes with rooks and queens; (2) Cubical Sliding Puzzles, an exploration of the discrete configuration spaces of sliding puzzles on the $d$-cube with topological obstructions; and (3) The Fence Challenge, a participatory isoperimetric problem based on polyforms. Additionally, we report on the collaborative development of the game Le Carr\'e du Diable, inspired by The Fence Challenge and created during the workshop Let's talk about outreach!, held in October 2022 in Les Diablerets, Switzerland. All of our outreach encounters and creations are designed and curated with an inclusive culture and a strong commitment to welcoming the most diverse audience possible., Comment: 16 pages, 11 figures

Maser emission of SiO, H$_2$O and, OH is widespread in Asymptotic Giant Branch (AGB) stars with oxygen(O)-rich envelopes. This emission quickly disappear during the post-AGB phase and is extremely rare in planetary nebulae (PN). So far, only eight PNe have been confirmed to show OH and/or H$_2$O maser emission, and none has ever been found to show SiO maser emission. We intend to obtain the first detection of a SiO maser from a PNe. Such a detection would provide us with a useful tool to probe mass-loss in PNe at a scales of a few AU from the central star, much shorter than the scales traced by H$_2$ or OH masers. We compiled two different samples. The first one comprises all known PNe with confirmed OH and/or H$_2$O maser emission, as well as two candidate PNe showing OH masers. For the second sample we compiled single-dish SiO maser detections in the literature, and compared them with catalogs of PNe and radio continuum emission (which could trace photoionized gas in a PNe). We identified five targets (either PN or radio continuum sources) within the beam of the single-dish SiO maser observations. We then carried out interferometric observations of both samples with the Australia Telescope Compact Array, to confirm the spatial association between continuum and SiO maser emission. We found no SiO maser emission associated with any confirmed or candidate PN. In all targets, except IRAS 17390$-$3014, there is no spatial coincidence between SiO masers and radio continuum emission. While in IRAS 17390$-$3014 we cannot completely rule out a possible association, it is unlikely that the radio continuum emission arises from a planetary nebula. The absence of SiO maser emission in PNe showing OH or H$_2$O masers is of special interest, since thermal SiO emission has been reported in at least one of these targets, indicating that SiO molecules can be present in gas phase., Comment: 15 pages, 7 figures, 4 tables. Accepted for publication in A&A

We introduce a single-qubit quantum measurement engine fuelled by backaction energy input. To reduce energetic costs associated with information processing, the measurement outcomes are only used with a prescribed laziness probability in the feedback step. As a result, we show that the work extracted over consecutive cycles is a second-order Markov process, analogous to a run-and-tumble process with transient anomalous diffusion. We derive exact analytical expressions for the work finite-time moments and first-passage-time statistics. Furthermore, we find the optimal laziness probability maximizing the mean power extracted per cycle., Comment: Supplementary Material included

IRAS 22568+6141 has been classified as a low-ionisation planetary nebula (PN) and presents non-thermal radio continuum emission, which could be a signature of nascent PNe. We present intermediate-resolution long-slit spectra obtained in 2021 and 2023, high-resolution long-slit spectra taken in 2023, and a light curve at the $r$-filter between 1953 and 2019, that reveal changes in IRAS 22568+6141 with timescales of decades and a few years. The object underwent an energetic event around 1990 that suddenly increased its brightness which has been fading since then. A comparison with a published spectrum from 1988 shows an increase of the H$\beta$ flux in 2021 by factor of $\simeq$6 and the [O III] emission lines that were absent in 1988. Between 2021 and 2023 the H$\beta$ flux decreased by a factor of $\simeq$1.7, and the [O III] emission lines almost vanished. These results and the variability observed in other emission lines indicate that IRAS 22568+6141 is recombining and cooling down between 2021 and 2023, and probably since 2005, as suggested by archival radio continuum and mid-IR observations. The intermediate- and high-resolution spectra show that the excitation of the emission lines is dominated by shocks in 2021 and 2023, and, probably, also in 1988, which may be related to the non-thermal radio continuum emission from the object. Although the variability might be due to changes in the physical conditions in the shocks or in a nova-like eruption, it accommodates better to that expected from a late thermal pulse, which is further suggested by a comparison with other similar objects. New observations and monitoring in the coming years are crucial to corroborate the origin of the variability., Comment: 11 pages, 8 figures, 6 tables. Accepted for publication in A&A

In the near future, the Jefferson Lab $b_1$ experiment will provide the second measurement of tensor polarized asymmetries in inclusive DIS on the deuteron. In this asymmetry, 4 independent tensor polarized structure functions contribute. This necessitates systematic approximations in the extraction of the leading twist structure function $b_1$ from a single tensor asymmetry measurement. Contamination from higher twist structure functions and kinematic effects is discussed here. Using a deuteron convolution model, we quantify the systematic errors from these approximations for two different choices for the target polarization direction (momentum transfer, electron beam direction). For Jefferson Lab 12 GeV kinematics, the systematic error turns out to be comparable between the two polarization options, while at higher $Q^2$ values the momentum transfer direction is preferred., Comment: 11 pages, 11 figures, submitted as part of the EPJA Topical Collection on Tensor Spin Observables

In this article, we study the ccs-Daugavet, ccs-$\Delta$, super-Daugavet, super-$\Delta$, Daugavet, $\Delta$, and $\nabla$ points in the unit balls of vector-valued function spaces $C_0(L, X)$, $A(K, X)$, $L_\infty(\mu, X)$, and $L_1(\mu, X)$. To partially or fully characterize these diametral points, we first provide improvements of several stability results under $\oplus_\infty$ and $\oplus_1$-sums shown in the literature. For complex Banach spaces, $\nabla$ points are identical to Daugavet points, and so the study of $\nabla$ points only makes sense when a Banach space is real. Consequently, we obtain that the seven notions of diametral points are equivalent for $L_\infty(\mu)$ and uniform algebra when $K$ is infinite., Comment: 30 pages, 1 figure

The teaching innovation project SpaceRaceEdu: development of an educational multiplayer video game for self-study and self-assessment has been carried out under the INNOVA call of the Autonomous University of Madrid during the 2022-2023 academic year. In this project, a functional prototype of SpaceRaceEdu has been developed: a multiplayer video game with a social and educational nature, which can be used both by teachers as a training and evaluation activity and by students as a tool for study and evaluation. In SpaceRaceEdu, several student teams try to launch a rocket before everyone else. To meet this objective, they must gather a series of resources by going through a scenario and answering questions of different types. The teachers can introduce these questions according to the contents of their subject. The videogame balances competition and cooperation to promote participation and learning. Competition occurs between teams who strive to answer all their questions correctly before their rivals. In contrast, cooperation occurs between students on the same team who can organize and support each other to be more effective., Comment: 8 pages, in Spanish language, 3 figures

We propose a theoretical model for a colloidal heat engine driven by a feedback protocol that is able to fully convert the net heat absorbed by the hot bath into extracted work. The feedback protocol, inspired by gambling strategies, executes a sudden quench at zero work cost when the particle position satisfies a specific first-passage condition. As a result, the engine enhances both power and efficiency with respect to a standard Carnot cycle, surpassing Carnot's efficiency at maximum power. Using first-passage and martingale theory, we derive analytical expressions for the power and efficiency far beyond the quasistatic limit and provide scaling arguments for their dependency with the cycle duration. Numerical simulations are in perfect agreement with our theoretical findings, and illustrate the impact of the data acquisition rate on the engine's performance., Comment: 20 pages (including supplemental material), 8 figures (including supplemental figures)

Computational modeling is an integral part of catalysis research. With it, new methodologies are being developed and implemented to improve the accuracy of simulations while reducing the computational cost. In particular, specific machine-learning techniques have been applied to build interatomic potential from ab initio results. Here, We report an energy-free machine-learning calculator that combines three individually trained neural networks to predict the energy and atomic forces of particulate matter. Three structures were investigated: a monometallic nanoparticle, a bimetallic nanoalloy, and a supported metal crystallites. Atomic energies were predicted via a graph neural network, leading to a mean absolute error (MAE) within 0.004 eV from Density Functional Theory (DFT) calculations. The task of predicting atomic forces was split over two feedforward networks, one predicting the force's norm and another its direction. The force prediction resulted in a MAE within 0.080 eV/A against DFT results. The interpretability of the graph neural network predictions was demonstrated by underlying the physics of the monometallic particle in the form of cohesion energy.

$\rm{Ge}_{1-x-y}Si_{x}Sn_{y}$ alloys were grown on Ge buffer layers at ultra-low temperature using reactions of $\rm SnH_{4}$ and $\rm GeH_{3}Cl$ for the first time. The latter is a newly introduced CVD source designed for epitaxial development of group IV semiconductors under low thermal budgets and CMOS compatible conditions. The $\rm{Ge}_{1-x-y}Si_{x}Sn_{y}$ films were produced between 160-200oC with 3-5% Si and ~ 5-11 % Sn, which traverses the indirect to direct gap transition in Ge-Sn materials. The films were fully strained to Ge and exhibited defect-free microstructures, flat surfaces, homogeneous compositions, uniform thicknesses and sharp interfaces as required for device manufacturing. A comparative study was then conducted to investigate the applicability of $\rm GeH_{3}Cl$ for the synthesis of $\rm Ge_{1-y}Sn_{y}$ binaries under similar experimental conditions. The$\rm Ge_{1-y}Sn_{y}$ films were grown fully strained to Ge, but with reduced Sn compositions ranging from ~ 2 - 7 % and lower thicknesses relative to $\rm{Ge}_{1-x-y}Si_{x}Sn_{y}$. This prompted efforts to further investigate the growth behavior of $\rm Ge_{1-y}Sn_{y}$ using the $\rm GeH_{3}Cl$ method, bypassing the Ge buffer to produce samples directly on Si, with the aim of exploring how to manage interface strain. In this case the $\rm Ge_{1-y}Sn_{y}$ on Si films exhibited compositions and thicknesses comparable to $\rm Ge_{1-y}Sn_{y}$-on-Ge films; however, their strain states were mostly relaxed, presumably due to the large misfit between $\rm Ge_{1-y}Sn_{y}$ and Si. Efforts to increase the concentration and thickness of these samples resulted in non-homogeneous multi-phase materials containing large amounts of interstitial Sn impurities., Comment: 16 pages, 9 figures

Atomic broadcast is a reliable communication abstraction ensuring that all processes deliver the same set of messages in a common global order. It is a fundamental building block for implementing fault-tolerant services using either active (aka state-machine) or passive (aka primary-backup) replication. We consider the problem of implementing reconfigurable atomic broadcast, which further allows users to dynamically alter the set of participating processes, e.g., in response to failures or changes in the load. We give a complete safety and liveness specification of this communication abstraction and propose a new protocol implementing it, called Vertical Atomic Broadcast, which uses an auxiliary service to facilitate reconfiguration. In contrast to prior proposals, our protocol significantly reduces system downtime when reconfiguring from a functional configuration by allowing it to continue processing messages while agreement on the next configuration is in progress. Furthermore, we show that this advantage can be maintained even when our protocol is modified to support a stronger variant of atomic broadcast required for passive replication., Comment: Extended version of a paper in DISC'24: International Symposium on Distributed Computing

The weighted kappa coefficient of a binary diagnostic test is a measure of the beyond-chance agreement between the diagnostic test and the gold standard, and depends on the sensitivity and specificity of the diagnostic test, on the disease prevalence and on the relative importance between the false positives and the false negatives. This article studies the comparison of the weighted kappa coefficients of two binary diagnostic tests subject to a paired design through confidence intervals. Three asymptotic confidence intervals are studied for the difference between the parameters and five other intervals for the ratio. Simulation experiments were carried out to study the coverage probabilities and the average lengths of the intervals, giving some general rules for application. A method is also proposed to calculate the sample size necessary to compare the two weighted kappa coefficients through a confidence interval. A program in R has been written to solve the problem studied and it is available as supplementary material. The results were applied to a real example of the diagnosis of malaria., Comment: 43 pages, 10 tables

Positive and negative likelihood ratios are parameters which are used to assess and compare the effectiveness of binary diagnostic tests. Both parameters only depend on the sensitivity and specificity of the diagnostic test and are equivalent to a relative risk. This article studies the comparison of the likelihood ratios of two binary diagnostic tests subject to a paired design through confidence intervals. Six approximate confidence intervals are presented for the ratio of the likelihood ratios, and simulation experiments are carried out to study the coverage probabilities and the average lengths of the intervals considered, and some general rules of application are proposed. A method is also proposed to determine the sample size necessary to estimate the ratio between the likelihood ratios with a determined precision. The results were applied to the diagnosis of coronary artery disease., Comment: 35 pages, 7 tables

Predictive values are measures of the clinical accuracy of a binary diagnostic test, and depend on the sensitivity and the specificity of the test and on the disease prevalence among the population being studied. This article studies hypothesis tests to simultaneously compare the predictive values of two binary diagnostic tests in the presence of missing data. The hypothesis tests were solved applying two computational methods: the EM and SEM algorithms and multiple imputation. Simulation experiments were carried out to study the sizes and the power of the hypothesis tests, giving some general rules of application. Two R programmes were written to apply each method, and they are available as supplementary material for the manuscript. The results were applied to the diagnosis of Alzheimer's disease., Comment: 47 pages, 7 tables

Dynamics in glassy systems near the phase transition is characterized by particle jumps. Approaches to describe these dynamics are based on models in which the time and length scales defining the jumps are parameters to be determined. We instead propose a model-independent method to detect these jumps. Our method uses the theory of the inspection paradox to analyze particle trajectories and reveals the time and length scales defining a jump without free parameters. Given its simplicity and generality, our method can be applied to resolve hopping motion in a broad class of systems, including experimental ones., Comment: 7 pages, 7 figures

We consider the dynamics of a population spatially structured in colonies that are vulnerable to catastrophic events occurring at random times, which randomly reduce their population size and compel survivors to disperse to neighboring areas. The dispersion behavior of survivors is critically significant for the survival of the entire species. In this paper, we consider an uniform dispersion scheme, where all possible survivor groupings are equally probable. The aim of the survivors is to establish new colonies, with individuals who settle in empty sites potentially initiating a new colony by themselves. However, all other individuals succumb to the catastrophe. We consider the number of dispersal options for surviving individuals in the aftermath of a catastrophe to be a fixed value $d$ within the neighborhood. In this context, we conceptualize the evolution of population dynamics occurring over a homogeneous tree. We investigate the conditions necessary for these populations to survive, presenting pertinent bounds for survival probability, the number of colonized vertices, the extent of dispersion within the population, and the mean time to extinction for the entire population., Comment: 22 pages

The 30 MacMahon colored cubes have each face painted with one of six colors and every color appears on at least one face. One puzzle involving these cubes is to create a $2\times2\times2$ model with eight distinct MacMahon cubes to recreate a larger version with the external coloring of a specified target cube, also a MacMahon cube, and touching interior faces are the same color. J.H. Conway is credited with arranging the cubes in a $6\times6$ tableau that gives a solution to this puzzle. In fact, the particular set of eight cubes that solves this puzzle can be arranged in exactly \textit{two} distinct ways to solve the puzzle. We study a less restrictive puzzle without requiring interior face matching. We describe solutions to the $2\times2\times2$ puzzle and the number of distinct solutions attainable for a collection of eight cubes. Additionally, given a collection of eight MacMahon cubes, we study the number of target cubes that can be built in a $2\times2\times2$ model. We calculate the distribution of the number of cubes that can be built over all collections of eight cubes (the maximum number is five) and provide a complete characterization of the collections that can build five distinct cubes. Furthermore, we identify nine new sets of twelve cubes, called Minimum Universal sets, from which all 30 cubes can be built., Comment: 22 pages, 12 figures, 3 Tables

The COVID-19 pandemic created a historic, global disruption in the labor market. In the short term, the labor force participation rate dropped precipitously as workers were laid off or furloughed, especially in sectors that were most affected by social distancing protocols, such as hospitality, travel and leisure, and retail (Lund et al., 2021). While the labor market has rebounded since 2020, the pandemic has reshaped the future of work for America. Meanwhile, community and technical colleges around the country are responding to low levels of student enrollment after the pandemic (Barrington, 2022). These institutions are often tasked with filling the skills gap in their local economies through career and technical education (CTE) programs. Furthermore, community and technical colleges are increasingly being held accountable, through state and federal policy, for ensuring that the programs and credentials that they offer are relevant to the skills demanded by the labor market. This brief describes findings from a statewide survey in Florida that sheds light on how community and technical colleges are examining student and economic data, creating processes for program review and market alignment, engaging industries and businesses, and supporting student success in CTE after the pandemic. [An additional publisher of this brief is University of Tennessee, Knoxville, Education Research & Opportunity Center.]

Sentiment analysis serves as a pivotal component in Natural Language Processing (NLP). Advancements in multilingual pre-trained models such as XLM-R and mT5 have contributed to the increasing interest in cross-lingual sentiment analysis. The recent emergence in Large Language Models (LLM) has significantly advanced general NLP tasks, however, the capability of such LLMs in cross-lingual sentiment analysis has not been fully studied. This work undertakes an empirical analysis to compare the cross-lingual transfer capability of public Small Multilingual Language Models (SMLM) like XLM-R, against English-centric LLMs such as Llama-3, in the context of sentiment analysis across English, Spanish, French and Chinese. Our findings reveal that among public models, SMLMs exhibit superior zero-shot cross-lingual performance relative to LLMs. However, in few-shot cross-lingual settings, public LLMs demonstrate an enhanced adaptive potential. In addition, we observe that proprietary GPT-3.5 and GPT-4 lead in zero-shot cross-lingual capability, but are outpaced by public models in few-shot scenarios., Comment: Accepted to WASSA workshop at ACL2024

The detection of multiple extended targets in complex environments using high-resolution automotive radar is considered. A data-driven approach is proposed where unlabeled synchronized lidar data is used as ground truth to train a neural network with only radar data as input. To this end, the novel, large-scale, real-life, and multi-sensor RaDelft dataset has been recorded using a demonstrator vehicle in different locations in the city of Delft. The dataset, as well as the documentation and example code, is publicly available for those researchers in the field of automotive radar or machine perception. The proposed data-driven detector is able to generate lidar-like point clouds using only radar data from a high-resolution system, which preserves the shape and size of extended targets. The results are compared against conventional CFAR detectors as well as variations of the method to emulate the available approaches in the literature, using the probability of detection, the probability of false alarm, and the Chamfer distance as performance metrics. Moreover, an ablation study was carried out to assess the impact of Doppler and temporal information on detection performance. The proposed method outperforms the different baselines in terms of Chamfer distance, achieving a reduction of 75% against conventional CFAR detectors and 10% against the modified state-of-the-art deep learning-based approaches., Comment: Published at IEEE Transaction in Radar Systems

We study the set $\operatorname{MA}(X,Y)$ of operators between Banach spaces $X$ and $Y$ that attain their minimum norm, and the set $\operatorname{QMA}(X,Y)$ of operators that quasi attain their minimum norm. We characterize the Radon-Nikodym property in terms of operators that attain their minimum norm and obtain some related results about the density of the sets $\operatorname{MA}(X,Y)$ and $\operatorname{QMA}(X,Y)$. We show that every infinite-dimensional Banach space $X$ has an isomorphic space $Y$ such that not every operator from $X$ to $Y$ quasi attains its minimum norm. We introduce and study Bishop-Phelps-Bollob\'as type properties for the minimum norm, including the ones already considered in the literature, and we exhibit a wide variety of results and examples, as well as exploring the relations between them., Comment: 22 pages including references. 1 figure

We consider two simple stochastic models for a pathogen population in the presence of an immune response, where we assume that the immune system must first get rid of the pathogen type with the lowest fitness in each ancestral lineage of pathogen types present in the host. In the first model, the pathogens reproduce independently at rate $\lambda$ without spatial restrictions. The second model is similar but evolves on a graph. In this case, each pathogen occupies a site and can only place offspring on adjacent empty sites. In both models, when a new pathogen is born, it has the same type as its parent with probability $1-r$. Conversely, with probability $r$, a beneficial mutation occurs, generating a new pathogen type with a higher fitness than its parent's type. We assume that the immune system develops an effective immune response, independently at rate 1, for each pathogen type without ancestral types that are still alive, which simultaneously kills all pathogens of that type. Our main results are a complete characterization of the survival-extinction phase diagram of the first model, and sufficient conditions for survival and extinction of the second model on $\mathbb{Z}^d.$ A comparison with similar models introduced by Schinazi and Schweinsberg (2008), where mutations are not necessarily beneficial and the immune response for each pathogen type occurs independently at rate 1, reveals that the first and second models exhibit more complex and comparable behaviors, respectively., Comment: 25 pages, 3 figures

We solve two main questions on linear structures of (non-)norm-attaining Lipschitz functions. First, we show that for every infinite metric space $M$, the set consisting of Lipschitz functions on $M$ which do not strongly attain their norm and the zero contains an isometric copy of $\ell_\infty$, and moreover, those functions can be chosen not to attain their norm as functionals on the Lipschitz-free space over $M$. Second, we prove that for every infinite metric space $M$, neither the set of strongly norm-attaining Lipschitz functions on $M$ nor the union of its complement with zero is ever a linear space. Furthermore, we observe that the set consisting of Lipschitz functions which cannot be approximated by strongly norm-attaining ones and the zero element contains $\ell_\infty$ isometrically in all the known cases. Some natural observations and spaceability results are also investigated for Lipschitz functions that attain their norm in one way but do not in another, for several norm-attainment notions considered in the literature., Comment: 33 pages, 3 figures

Gr\"unbaum's equipartition problem asked if for any measure $\mu$ on $\mathbb{R}^d$ there are always $d$ hyperplanes which divide $\mathbb{R}^d$ into $2^d$ $\mu$-equal parts. This problem is known to have a positive answer for $d\le 3$ and a negative one for $d\ge 5$. A variant of this question is to require the hyperplanes to be mutually orthogonal. This variant is known to have a positive answer for $d\le 2$ and there is reason to expect it to have a negative answer for $d\ge 3$. In this note we exhibit measures that prove this. Additionally, we describe an algorithm that checks if a set of $8n$ in $\mathbb{R}^3$ can be split evenly by $3$ mutually orthogonal planes. To our surprise, it seems the probability that a random set of $8$ points chosen uniformly and independently in the unit cube does not admit such a partition is less than $0.001$.