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Causal learning is the cognitive process of developing the capability of making causal inferences based on available information, often guided by normative principles. This process is prone to errors and biases, such as the illusion of causality, in which people perceive a causal relationship between two variables despite lacking supporting evidence. This cognitive bias has been proposed to underlie many societal problems, including social prejudice, stereotype formation, misinformation, and superstitious thinking. In this research, we investigate whether large language models (LLMs) develop causal illusions, both in real-world and controlled laboratory contexts of causal learning and inference. To this end, we built a dataset of over 2K samples including purely correlational cases, situations with null contingency, and cases where temporal information excludes the possibility of causality by placing the potential effect before the cause. We then prompted the models to make statements or answer causal questions to evaluate their tendencies to infer causation erroneously in these structured settings. Our findings show a strong presence of causal illusion bias in LLMs. Specifically, in open-ended generation tasks involving spurious correlations, the models displayed bias at levels comparable to, or even lower than, those observed in similar studies on human subjects. However, when faced with null-contingency scenarios or temporal cues that negate causal relationships, where it was required to respond on a 0-100 scale, the models exhibited significantly higher bias. These findings suggest that the models have not uniformly, consistently, or reliably internalized the normative principles essential for accurate causal learning., Comment: 15 pages, 6 figures

Sycophancy refers to the tendency of a large language model to align its outputs with the user's perceived preferences, beliefs, or opinions, in order to look favorable, regardless of whether those statements are factually correct. This behavior can lead to undesirable consequences, such as reinforcing discriminatory biases or amplifying misinformation. Given that sycophancy is often linked to human feedback training mechanisms, this study explores whether sycophantic tendencies negatively impact user trust in large language models or, conversely, whether users consider such behavior as favorable. To investigate this, we instructed one group of participants to answer ground-truth questions with the assistance of a GPT specifically designed to provide sycophantic responses, while another group used the standard version of ChatGPT. Initially, participants were required to use the language model, after which they were given the option to continue using it if they found it trustworthy and useful. Trust was measured through both demonstrated actions and self-reported perceptions. The findings consistently show that participants exposed to sycophantic behavior reported and exhibited lower levels of trust compared to those who interacted with the standard version of the model, despite the opportunity to verify the accuracy of the model's output.

Given a bilinear (or sub-bilinear) operator $B$, we prove restricted weighted weak type inequalities of the form $$ ||B(f_1, f_2)||_{L^{p, \infty}(w_1^{p/p_1}w_2^{p/p_2})}\lesssim ||f_1||_{L^{p_1, 1}(w_1)}||f_2||_{L^{p_2, 1}(w_2)}, $$ whenever $B(f_1, f_2)= (T_1f_1) (T_2 f_2)$ is the product of two singular integral operators satisfying Dini conditions. Additionally, we also establish, as an application, the boundedness of a certain class of bounded variation bilinear Fourier multipliers solving a question posted in [Bilinear Fourier multipliers of bounded variation; Int. Math. Res. Not. (2023), no.24, 21943--21975 by Baena-Miret, Carro, Luque and Sanchez-Pascuala]., Comment: 14 pages

Illusions of causality occur when people develop the belief that there is a causal connection between two variables with no supporting evidence. This cognitive bias has been proposed to underlie many societal problems including social prejudice, stereotype formation, misinformation and superstitious thinking. In this research we investigate whether large language models develop the illusion of causality in real-world settings. We evaluated and compared news headlines generated by GPT-4o-Mini, Claude-3.5-Sonnet, and Gemini-1.5-Pro to determine whether the models incorrectly framed correlations as causal relationships. In order to also measure sycophantic behavior, which occurs when a model aligns with a user's beliefs in order to look favorable even if it is not objectively correct, we additionally incorporated the bias into the prompts, observing if this manipulation increases the likelihood of the models exhibiting the illusion of causality. We found that Claude-3.5-Sonnet is the model that presents the lowest degree of causal illusion aligned with experiments on Correlation-to-Causation Exaggeration in human-written press releases. On the other hand, our findings suggest that while mimicry sycophancy increases the likelihood of causal illusions in these models, especially in GPT-4o-Mini, Claude-3.5-Sonnet remains the most robust against this cognitive bias.

We study existence and uniqueness of a transmission problem in simply connected domains in the plane with data in weighted Lebesgue spaces by first investigating solvability results of a related novel problem associated to a homeomorphism in the real line and domains given by the upper and lower half planes. Our techniques are based on the use of conformal maps and Rellich identities for the Hilbert transform, and are motivated by previous works concerning the Dirichlet, Neumann and Zaremba problems., Comment: 26 pages, 4 figures

We prove Hilbert transform identities involving conformal maps via the use of Rellich identity and the solution of the Neumann problem in a graph Lipschitz domain in the plane. We obtain as consequences new $L^2$-weighted estimates for the Hilbert transform, including a sharp bound for its norm as a bounded operator in weighted $L^2$ in terms of a weight constant associated to the Helson-Szeg\"o theorem., Comment: 15 pages, 2 figures

We prove optimal Lipschitz regularity of solutions to Poisson's equation with measure data supported on a $C^{1,\operatorname{Dini}}$ interface and with $C^{0,\operatorname{Dini}}$ density. We achieve this by deriving pointwise gradient estimates on the interface, further showing the piecewise differentiability of solutions up to this surface. Our approach relies on perturbation arguments and estimates for the Green's function of the Laplacian. Additionally, we provide sharp counterexamples highlighting the minimality of our assumptions., Comment: Improved the presentation of the main results, adding Corollary 1.4, two appendices, and references. To appear in Comm. Partial Differential Equations

In the recent years, the interest in electric direct current (DC) technologies (such as converters, batteries, electric vehicles, etc.) is increasing due to its potential on energy efficiency and sustainability. However, the vast majority of electric systems and networks are based on alternating current (AC), as they also have certain advantages regarding cost-effective transport and robustness. In this paper, an AC/DC optimal power flow method for hybrid microgrids and several key performance indicators (KPIs) for its techno-economic assessment are presented. The combination of both calculations allows users to clearly determine the viability of their hybrid microgrids. AC/DC networks have been modelled considering their most common elements. For the power flow method, a polynomial optimisation is formulated considering four different objective functions: the minimisation of energy losses, voltage deviation and operational costs, and also the maximisation of the microgrid generation. The power flow method and the techno-economic analysis have been implemented in Python and validated in the Centro de Desarrollo de Energ\'ias Renovables (CEDER) demonstrator for TIGON. The results show that the calculated power flow variables and the ones measured at CEDER are practically the same. In addition, the KPIs have been obtained and compared for four operating scenarios: baseline, no battery, battery flexibility and virtual battery (VB) flexibility. The last one result in the most profitable option.

We study a two-phase parabolic free boundary problem motivated by the jump of conductivity in composite materials that undergo a phase transition. Each phase is governed by a heat equation with distinct thermal conductivity, and a transmission-type condition is imposed on the free interface. We establish strong regularity properties of the free boundary: first, we prove that flat free boundaries are $C^{1,\alpha}$ by means of a linearization technique and compactness arguments. Then we use the Hodograph transform to achieve higher regularity. To this end, we prove a new Harnack-type inequality and develop the Schauder theory for parabolic linear transmission problems., Comment: 34 pages, 2 figures; slightly improved Section 8

The main goal of this paper is to provide a complete characterization of the weak-type boundedness of the Hardy-Littlewood maximal operator, $M$, on weighted Lorentz spaces $\Lambda^p_u(w)$, whenever $p>1$. This solves a problem left open in \cite{crs:crs}. Moreover, with this result, we complete the program of unifying the study of the boundedness of $M$ on weighted Lebesgue spaces and classical Lorentz spaces, which was initiated in the aforementioned monograph., Comment: 7 pages

We prove a pointwise estimate for the decreasing rearrangement of $Tf$, where $T$ is any sublinear operator satisfying the weak-type boundedness $$ T:L^{p,1}(\mu) \to L^{p,\infty}(\nu), \quad \forall p: 1

We shall prove pointwise estimates for the decreasing rearrangement of $Tf$, where $T$ covers a wide range of interesting operators in Harmonic Analysis such as operators satisfying a Fefferman-Stein inequality, the Bochner-Riesz operator, rough operators, sparse operators, Fourier multipliers, etc. In particular, our main estimate is of the form $$ (Tf)^*(t) \leq C\left( \frac 1t\int_0^tf^*(s)\,ds + \int_t^\infty \left( 1 + \log\frac st \right)^{- 1}\varphi \left(1 + \log\frac st \right) f^*(s)\,\frac{ds}s \right), $$ where $\varphi$ is determined by the Muckenhoupt $A_p$-weight norm behaviour of the operator., Comment: 23 pages

We prove the Lorentz-Shimogaki and Boyd theorems for the spaces $\Lambda^p_u(w)$. As a consequence, we give the complete characterization of the strong boundedness of $H$ on these spaces in terms of some geometric conditions on the weights $u$ and $w$, whenever $p>1$. For these values of $p$, we also give the complete solution of the weak-type boundedness of the Hardy-Littlewood operator on $\Lambda^p_u(w)$., Comment: 20 pages, 2 figures

We study the boundedness of the Hilbert transform $H$ and the Hilbert maximal operator $H^*$ on weighted Lorentz spaces $\Lambda^p_u(w)$. We start by giving several necessary conditions that, in particular, lead us to the complete characterization of the weak-type boundedness of both $H$ and $H^*$, whenever $u\in A_1$. For the strong-type case, we also get the characterization of both operators when $p>1$. Applications to the case of Lorentz spaces $L^{p,q}(u)$ are presented., Comment: 17 pages

We characterize the weak-type boundedness of the Hilbert transform $H$ on weighted Lorentz spaces $\Lambda^p_u(w)$, with $p>0$, in terms of some geometric conditions on the weights $u$ and $w$ and the weak-type boundedness of the Hardy-Littlewood maximal operator on the same spaces. Our results recover simultaneously the theory of the boundedness of $H$ on weighted Lebesgue spaces $L^p(u)$ and Muckenhoupt weights $A_p$, and the theory on classical Lorentz spaces $\Lambda^p(w)$ and Ari\~no Muckenhoupt weights $B_p$., Comment: 19

One of the main challenges in simultaneous localization and mapping (SLAM) is real-time processing. High-computational loads linked to data acquisition and processing complicate this task. This article presents an efficient feature extraction approach for mapping structured environments. The proposed methodology, weighted conformal LiDAR-mapping (WCLM), is based on the extraction of polygonal profiles and propagation of uncertainties from raw measurement data. This is achieved using conformal M bius transformation. The algorithm has been validated experimentally using 2-D data obtained from a low-cost Light Detection and Ranging (LiDAR) range finder. The results obtained suggest that computational efficiency is significantly improved with reference to other state-of-the-art SLAM approaches.

Recently, GaAsSb/GaAsN type II short-period superlattices (SLs) have been proposed as suitable structures to be implemented in the optimal design of monolithic multi-junction solar cells. However, due to strong surface Sb segregation, experimental Sb composition profiles differ greatly from the nominal square-wave design. In this work, the improvement of the interface quality of these SLs in terms of compositional abruptness and surface roughness has been evaluated by implementing different growth interruption times under Sb4/As4 (soaking) and As4 (desorption) overpressure conditions before and after the growth of GaAsSb layers, respectively. The combined effects of both processes enhance Sb distribution, achieving squarer compositional profiles with reduced surface roughness interfaces. It has been found that the improvement in compositional abruptness is quantitatively much higher at the lower interface, during soaking, than at the upper interface during desorption. Conversely, a larger decrease in surface roughness is achieved at the upper interface than at the lower interface. Fitting of the Sb segregation profiles using the 3-layer kinetic fluid model has shown that the increase in Sb incorporation rate is due to the decrease in segregation energy, presumably to changes in the surface reconstruction of the floating layer at the surface., Comment: 7 pages, 5 figures

The accuracy of neural networks has greatly improved across various domains over the past years. Their ever-increasing complexity, however, leads to prohibitively high energy demands and latency in von Neumann systems. Several computing-in-memory (CIM) systems have recently been proposed to overcome this, but trade-offs involving accuracy, hardware reliability, and scalability for large models remain a challenge. Additionally, for some CIM designs, the activation movement still requires considerable time and energy. This paper explores the combination of algorithmic optimizations for ternary weight neural networks and associative processors (APs) implemented using racetrack memory (RTM). We propose a novel compilation flow to optimize convolutions on APs by reducing their arithmetic intensity. By leveraging the benefits of RTM-based APs, this approach substantially reduces data transfers within the memory while addressing accuracy, energy efficiency, and reliability concerns. Concretely, our solution improves the energy efficiency of ResNet-18 inference on ImageNet by 7.5x compared to crossbar in-memory accelerators while retaining software accuracy., Comment: To be presented at DATE24

All industries are trying to leverage Artificial Intelligence (AI) based on their existing big data which is available in so called tabular form, where each record is composed of a number of heterogeneous continuous and categorical columns also known as features. Deep Learning (DL) has constituted a major breakthrough for AI in fields related to human skills like natural language processing, but its applicability to tabular data has been more challenging. More classical Machine Learning (ML) models like tree-based ensemble ones usually perform better. This paper presents a novel DL model using Graph Neural Network (GNN) more specifically Interaction Network (IN), for contextual embedding and modelling interactions among tabular features. Its results outperform those of a recently published survey with DL benchmark based on five public datasets, also achieving competitive results when compared to boosted-tree solutions.

It is known that, due to the fact that $L^{1, \infty}$ is not a Banach space, if $(T_j)_j$ is a sequence of bounded operators so that $$ T_j:L^1\longrightarrow L^{1, \infty}, $$ with norm less than or equal to $||T_j||$ and $\sum_j ||T_j||<\infty$, nothing can be said about the operator $T=\sum_j T_j$. This is the origin of many difficult and open problems. However, if we assume that $$ T_j:L^1(u)\longrightarrow L^{1, \infty}(u), \qquad \forall u\in A_1, $$ with norm less than or equal to $\varphi(||u||_{A_1})||T_j||$, where $\varphi$ is a nondecreasing function and $A_1$ the Muckenhoupt class of weights, then we prove that, essentially, $$ T:L^1(u) \longrightarrow L^{1, \infty}(u), \qquad \forall u\in A_1. $$ We shall see that this is the case of many interesting problems in Harmonic Analysis.

In this paper we study a mathematical model that represents the concentration polarization and osmosis effects in a reverse osmosis cross-flow channel with porous membranes at some of its boundaries. The fluid is modeled using the Navier-Stokes equations and Darcy's law is used to impose the momentum balance on the membrane. The scheme consist of a conforming finite element method with the velocity-pressure formulation for the Navier-Stokes equations, together with a primal scheme for the convection-diffusion equations. The Nitsche method is used to impose the permeability condition across the membrane. Several numerical experiments are performed to show the robustness of the method. The resulting model accurately replicates the analytical models and predicts similar results to previous works. It is found that the submerged configuration has the highest permeate production, but also has the greatest pressure loss of all three configurations studied.

Bundling is a pervasive strategy in telecommunications markets. Due to the great success obtained at Spanish Telco market, this article analyzes the impacts of the introduction of convergent bundling on that market. This commercial strategy has caused major changes in the market, both from the point of view of demand and its own structure. From the demand-side, we analyze how product bundling has produced a substantial reduction on effective prices in the sector, and by means of technological diffusion models, we show that bundling is the main factor of Fixed Broadband development, along with FTTH networks deployments, in contrast with stand-alone product marketing scenarios. Pay TV inclusion and hard-bundling strategies at communications packages has motivated the greatest growth of this product in the history of this market. Regarding market structure, the introduction of convergent bundling has led to a consolidation in the market, increasing the concentration around the main convergent players

The production of vector mesons in deep inelastic scattering is an interesting yet scarsely explored channel to study the transverse spin structure of the nucleon and the related phenomena. The COMPASS collaboration has performed the first measurement of the Collins and Sivers asymmetries for inclusively produced $\rho^0$ mesons. The analysis is based on the data set collected in deep inelastic scattering in $2010$ using a $160\,\,\rm{GeV}/c$ $\mu^+$ beam impinging on a transversely polarized $\rm{NH}_3$ target. The $\rho^{0}$ mesons are selected from oppositely charged hadron pairs, and the asymmetries are extracted as a function of the Bjorken-$x$ variable, the transverse momentum of the pair and the fraction of the energy $z$ carried by the pair. Indications for positive Collins and Sivers asymmetries are observed.

We report on a measurement of Spin Density Matrix Elements (SDMEs) in hard exclusive $\rho ^0$ meson muoproduction at COMPASS using 160~GeV/$c$ polarised $ \mu ^{+}$ and $ \mu ^{-}$ beams impinging on a liquid hydrogen target. The measurement covers the kinematic range 5.0~GeV/$c^2$ $< W <$ 17.0~GeV/$c^2$, 1.0 (GeV/$c$)$^2$ $< Q^2 <$ 10.0 (GeV/$c$)$^2$ and 0.01 (GeV/$c$)$^2$ $< p_{\rm{T}}^2 <$ 0.5 (GeV/$c$)$^2$. Here, $W$ denotes the mass of the final hadronic system, $Q^2$ the virtuality of the exchanged photon, and $p_{\rm{T}}$ the transverse momentum of the $\rho ^0$ meson with respect to the virtual-photon direction. The measured non-zero SDMEs for the transitions of transversely polarised virtual photons to longitudinally polarised vector mesons ($\gamma^*_T \to V^{ }_L$) indicate a violation of $s$-channel helicity conservation. Additionally, we observe a dominant contribution of natural-parity-exchange transitions and a very small contribution of unnatural-parity-exchange transitions, which is compatible with zero within experimental uncertainties. The results provide important input for modelling Generalised Parton Distributions (GPDs). In particular, they may allow one to evaluate in a model-dependent way the role of parton helicity-flip GPDs in exclusive $\rho ^0$ production.