Understanding the performance of multi-user multiple-input multiple-output (MU-MIMO) systems under imperfect channel state information at the transmitter (CSIT) remains a critical challenge in next-generation wireless networks. In this context, accurate statistical modeling of the signal-tointerference- plus-noise ratio (SINR) is essential for enabling tractable performance analysis of multi-user systems. This paper presents an improved statistical approximation of the SINR for downlink (DL) MU-MIMO systems with imperfect CSIT. The proposed model retains the analytical simplicity of existing approaches (e.g., Gamma-based approximations) while overcoming their limitations, particularly the underestimation of SINR variance. We evaluate the proposed approximation in the context of Rate-Splitting Multiple Access (RSMA)-enabled MIMO DL systems with outdated CSIT. The results demonstrate excellent accuracy across a wide range of system configurations, including varying

The core premise of AI debate as a scalable oversight technique is that it is harder to lie convincingly than to refute a lie, enabling the judge to identify the correct position. Yet, existing debate experiments have relied on datasets with ground truth, where lying is reduced to defending an incorrect proposition. This overlooks a subjective dimension: lying also requires the belief that the claim defended is false. In this work, we apply debate to subjective questions and explicitly measure large language models' prior beliefs before experiments. Debaters were asked to select their preferred position, then presented with a judge persona deliberately designed to conflict with their identified priors. This setup tested whether models would adopt sycophantic strategies, aligning with the judge's presumed perspective to maximize persuasiveness, or remain faithful to their prior beliefs. We implemented and compared two debate protocols, sequential and simultaneous, to evaluate potential systematic biases. Finally, we assessed whether models were more persuasive and produced higher-quality arguments when defending positions consistent with their prior beliefs versus when arguing against them. Our main findings show that models tend to prefer defending stances aligned with the judge persona rather than their prior beliefs, sequential debate introduces significant bias favoring the second debater, models are more persuasive when defending positions aligned with their prior beliefs, and paradoxically, arguments misaligned with prior beliefs are rated as higher quality in pairwise comparison. These results can inform human judges to provide higher-quality training signals and contribute to more aligned AI systems, while revealing important aspects of human-AI interaction regarding persuasion dynamics in language models.

Anatomical trees are critical for clinical diagnosis and treatment planning, yet their complex and diverse geometry make accurate representation a significant challenge. Motivated by the latest advances in large language models, we introduce an autoregressive method for synthesizing anatomical trees. Our approach first embeds vessel structures into a learned discrete vocabulary using a VQ-VAE architecture, then models their generation autoregressively with a GPT-2 model. This method effectively captures intricate geometries and branching patterns, enabling realistic vascular tree synthesis. Comprehensive qualitative and quantitative evaluations reveal that our technique achieves high-fidelity tree reconstruction with compact discrete representations. Moreover, our B-spline representation of vessel cross-sections preserves critical morphological details that are often overlooked in previous' methods parameterizations. To the best of our knowledge, this work is the first to generate blood vessels in an autoregressive manner. Code is available at this https URL.

Amortization systems are used widely in economy to generate payment schedules to repaid an initial debt with its interest. We present a generalization of these amortization systems by introducing the mathematical formalism of quantum mechanics based on vector spaces. Operators are defined for debt, amortization, interest and periodic payment and their mean values are computed in different orthonormal basis. The vector space of the amortization system will have dimension M, where M is the loan maturity and the vectors will have a SO(M) symmetry, yielding the possibility of rotating the basis of the vector space while preserving the distance among vectors. The results obtained are useful to add degrees of freedom to the usual amortization systems without affecting the interest profits of the lender while also benefitting the borrower who is able to alter the payment schedules. Furthermore, using the tensor product of algebras, we introduce loans entanglement in which two borrowers can correlate the payment schedules without altering the total repaid.

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.

Ergonomic risk assessment is now, due to an increased awareness, carried out more often than in the past. The conventional risk assessment evaluation, based on expert-assisted observation of the workplaces and manually filling in score tables, is still predominant. Data analysis is usually done with a focus on critical moments, although without the support of contextual information and changes over time. In this paper we introduce ErgoExplorer, a system for the interactive visual analysis of risk assessment data. In contrast to the current practice, we focus on data that span across multiple actions and multiple workers while keeping all contextual information. Data is automatically extracted from video streams. Based on carefully investigated analysis tasks, we introduce new views and their corresponding interactions. These views also incorporate domain-specific score tables to guarantee an easy adoption by domain experts. All views are integrated into ErgoExplorer, which relies on coordinated multiple views to facilitate analysis through interaction. ErgoExplorer makes it possible for the first time to examine complex relationships between risk assessments of individual body parts over long sessions that span multiple operations. The newly introduced approach supports analysis and exploration at several levels of detail, ranging from a general overview, down to inspecting individual frames in the video stream, if necessary. We illustrate the usefulness of the newly proposed approach applying it to several datasets.

Metacognition is the concept of reasoning about an agent's own internal processes, and it has recently received renewed attention with respect to artificial intelligence (AI) and, more specifically, machine learning systems. This paper reviews a hybrid-AI approach known as "error detecting and correcting rules" (EDCR) that allows for the learning of rules to correct perceptual (e.g., neural) models. Additionally, we introduce a probabilistic framework that adds rigor to prior empirical studies, and we use this framework to prove results on necessary and sufficient conditions for metacognitive improvement, as well as limits to the approach. A set of future

We present a data-driven generative framework for synthesizing blood vessel 3D geometry. This is a challenging task due to the complexity of vascular systems, which are highly variating in shape, size, and structure. Existing model-based methods provide some degree of control and variation in the structures produced, but fail to capture the diversity of actual anatomical data. We developed VesselVAE, a recursive variational Neural Network that fully exploits the hierarchical organization of the vessel and learns a low-dimensional manifold encoding branch connectivity along with geometry features describing the target surface. After training, the VesselVAE latent space can be sampled to generate new vessel geometries. To the best of our knowledge, this work is the first to utilize this technique for synthesizing blood vessels. We achieve similarities of synthetic and real data for radius (.97), length (.95), and tortuosity (.96). By leveraging the power of deep neural networks, we generate 3D models of blood vessels that are both accurate and diverse, which is crucial for medical and surgical training, hemodynamic simulations, and many other purposes.

Lagrangian Neural Networks (LNNs) are a powerful tool for addressing physical systems, particularly those governed by conservation laws. LNNs can parametrize the Lagrangian of a system to predict trajectories with nearly conserved energy. These techniques have proven effective in unconstrained systems as well as those with holonomic constraints. In this work, we adapt LNN techniques to mechanical systems with nonholonomic constraints. We test our approach on some well-known examples with nonholonomic constraints, showing that incorporating these restrictions into the neural network's learning improves not only trajectory estimation accuracy but also ensures adherence to constraints and exhibits better energy behavior compared to the unconstrained counterpart.

In a recent work we have briefly introduced a new structural index for water that, unlike previous indicators, was devised specifically for generic contexts beyond bulk conditions, making it suitable for hydration and nanoconfinement settings. In this work we shall study this metric in detail, demonstrating its ability to reveal the existence of a fine-tuned interplay between local structure and energetics in liquid water. This molecular principle enables the establishment of an extended hydrogen bond network, while simultaneously allowing for the existence of network defects by compensating for uncoordinated sites. By studying different water models and different temperatures encompassing both the normal liquid and the supercooled regime, this molecular mechanism will be shown to underlie the two-state behavior of bulk water. Additionally, by studying functionalized self-assembled monolayers and diverse graphene-like surfaces, we shall show that this principle is also operative at hydration and nanoconfinement conditions, thus generalizing the validity of the two-liquids scenario of water to these contexts. This approach will allow us to define conditions for wettability, providing an accurate measure of hydrophobicity and a reliable predictor of filling and drying transitions. Hence, it might open the possibility of elucidating the active role of water in broad fields of biophysics and materials science. As a preliminary step, we shall study the hydration structure and hydrophilicity of graphene-like systems (parallel graphene sheets and carbon nanotubes) as a function of the confinement dimensionality. FOR A PROGRAMMING CODE TO IMPLEMENT V4s, PLEASE GO TO: this https URL

The municipal solid waste system is a complex reverse logistic chain which comprises several optimisation problems. Although these problems are interdependent, i.e., the solution to one of the problems restricts the solution to the other, they are usually solved sequentially in the related literature because each is usually a computationally complex problem. We address two of the tactical planning problems in this chain by means of a Benders decomposition approach: determining the location and/or capacity of garbage accumulation points, and the design and schedule of collection routes for vehicles. Our approach manages to solve medium-sized real-world instances in the city of Bahía Blanca, Argentina, showing smaller computing times than solving a full MIP model.

In this article, we continue the study of tense symmetric Heyting algebras (or TSH-algebras). These algebras constitute a generalization of tense algebras. In particular, we describe a discrete duality for TSHalgebras bearing in mind the results indicated by E. Or lowska and I. Rewitzky in [E. Or lowska and I. Rewitzky, Discrete Dualities for Heyting Algebras with Operators, Fund. Inform. 81 (2007), no.1-3, 275-295.] for Heyting algebras. In addition, we introduce a propositional calculus and prove this calculus has TSH-algebras as algebraic counterpart. Finally, the duality mentioned above allowed us to show the completeness theorem for this calculus.

The first system of many-valued logic was introduced by J. Lukasiewicz, his motivation was of philosophical nature as he was looking for an interpretation of the concepts of possibility and necessity. Since then, plenty of research has been developed in this area. In 1968, when Gr.C. Moisil came across Zadeh's fuzzy set theory he found the motivation he had been looking for in order to legitimate the introduction and study of infinitely-valued Lukasiewicz algebras, so he defined \theta-valued Lukasiewicz algebras (or LM\theta-algebras, for short) (without negation), where \theta is the order type of a chain. In this article, our main interest is to investigate the principal and Boolean congruences and \theta-congruences on LM\theta-algebras. In order to do this we take into account a topological duality for these algebras obtained in (A.V. Figallo, I. Pascual, A. Ziliani, A Duality for \theta-Valued Lukasiewicz-Moisil Algebras and Aplicattions. J. LMult- Valued Logic & Soft Computing. Vol. 16, pp 303-322. (2010). Furthermore, we prove that the intersection of two principal ?-congruences is a principal one. On the other hand, we show that Boolean congruences are both principal congruences and \theta-congruences. This allowed us to establish necessary and sufficient conditions so that a principal congruence is a Boolean one. Finally, bearing in mind the above results, we characterize the principal and Boolean congruences on n-valued Lukasiewicz algebras without negation when we consider them as LM\theta-algebras in the case that \theta is an integer n, $n\geq 2$.

Background: Brain network models offer insights into brain dynamics, but the utility of model-derived bifurcation parameters as biomarkers remains underexplored. Objective: This study evaluates bifurcation parameters from a whole-brain network model as biomarkers for distinguishing brain states associated with resting-state and task-based cognitive conditions. Methods: Synthetic BOLD signals were generated using a supercritical Hopf brain network model to train deep learning models for bifurcation parameter prediction. Inference was performed on Human Connectome Project data, including both resting-state and task-based conditions. Statistical analyses assessed the separability of brain states based on bifurcation parameter distributions. Results: Bifurcation parameter distributions differed significantly across task and resting-state conditions (p < 0.0001 for all but one comparison). Task-based brain states exhibited higher bifurcation values compared to rest. Conclusion: Bifurcation parameters effectively differentiate cognitive and resting states, warranting further investigation as biomarkers for brain state characterization and neurological disorder assessment.

Five-valued Nelson algebras are those satisfying the condition: $((x\to z)\to y)\to(((y \to x)\to y)\to y)=1$. We give alternative equations defining these algebras, and determine the structure and number of elements of the free five-valued Nelson algebra with a finite number of free generators.

Experimental data on thin films of cylinder-forming block copolymers (BC) -- free-standing BC membranes as well as supported BC films -- strongly suggest that the local orientation of the BC patterns is coupled to the geometry in which the patterns are embedded. We analyze this phenomenon using general symmetry considerations and numerical self-consistent field studies of curved BC films in cylindrical geometry. The stability of the films against curvature-induced dewetting is also analyzed. In good agreement with experiments, we find that the BC cylinders tend to align along the direction of curvature at high curvatures. At low curvatures, we identify a transition from perpendicular to parallel alignment in supported films, which is absent in free standing membranes. Hence both experiments and theory show that curvature can be used to manipulate and align BC patterns.

In this article, we continue the study of monadic distributive lattices (or m-lattices) which are a natural generalization of monadic Heyting algebras, introduced by Monteiro and Varsavsky and developed exhaustively by Bezhanishvili. First, we extended the duality obtained by Cignoli for Q-distributive lattices to m-lattices. This new duality allows us to describe in a simple way the subdirectly irreducible algebras in this variety and in particular, to characterize the finite ones. Next, we introduce the category mKF whose objects are monadic augmented Kripke frames and whose morphisms are increasing continuous functions verifying certain additional conditions and we prove that it is equivalent to the one obtained above. Finally, we show that the category of perfect augmented Kripke frames given by Bezhanishvili for monadic Heyting algebras is a proper subcategory of mKF.

Dynamic Stochastic General Equilibrium (DSGE) models are nowadays a crucial quantitative tool for policy-makers. However, they did not emerge spontaneously. They are built upon previously established ideas in Economics and relatively recent advancements in Mathematics. This essay provides a comprehensive coverage of their history, starting from the pioneering Neoclassical general equilibrium theories and eventually reaching the New Neoclassical Synthesis (NNS). In addition, the mathematical tools involved in formulating a DSGE model are thoroughly presented. I argue that this history has a mixed nature rather than an absolutist or relativist one, that the NNS may have emerged due to the complementary nature of New Classical and New Keynesian theories, and that the recent adoption and development of DSGE models by central banks from different countries has entailed a departure from the goal of building a universally valid theory that Economics has always had. The latter means that DSGE modeling has landed not without loss of generality.

The Coherent Neutrino-Nucleus Interaction Experiment (CONNIE) is taking data at the Angra 2 nuclear reactor with the aim of detecting the coherent elastic scattering of reactor antineutrinos with silicon nuclei using charge-coupled devices (CCDs). In 2019 the experiment operated with a hardware binning applied to the readout stage, leading to lower levels of readout noise and improving the detection threshold down to 50 eV. The results of the analysis of 2019 data are reported here, corresponding to the detector array of 8 CCDs with a fiducial mass of 36.2 g and a total exposure of 2.2 kg-days. The difference between the reactor-on and reactor-off spectra shows no excess at low energies and yields upper limits at 95% confidence level for the neutrino interaction rates. In the lowest-energy range, 50-180 eV, the expected limit stands at 34 (39) times the standard model prediction, while the observed limit is 66 (75) times the standard model prediction with Sarkis (Chavarria) quenching factors.

Here we initiate an investigation of the equational classes of m-symmetric algebras endowed with two tense operators. These varieties is a generalization of tense algebras. Our main interest is the duality theory for these classes of algebras. In order to do this, we require Urquart's duality for Ockham algebras and Goldblatt's duality for bounded distributive lattice with operations. The dualities enable us to describe the lattices of congruences on tense m-symmetric algebras.