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We present a comprehensive study of answer quality evaluation in Retrieval-Augmented Generation (RAG) applications using vRAG-Eval, a novel grading system that is designed to assess correctness, completeness, and honesty. We further map the grading of quality aspects aforementioned into a binary score, indicating an accept or reject decision, mirroring the intuitive "thumbs-up" or "thumbs-down" gesture commonly used in chat applications. This approach suits factual business contexts where a clear decision opinion is essential. Our assessment applies vRAG-Eval to two Large Language Models (LLMs), evaluating the quality of answers generated by a vanilla RAG application. We compare these evaluations with human expert judgments and find a substantial alignment between GPT-4's assessments and those of human experts, reaching 83% agreement on accept or reject decisions. This study highlights the potential of LLMs as reliable evaluators in closed-domain, closed-ended settings, particularly when human evaluations require significant resources., Comment: 13 pages, 8 figures, 12 tables

Perceptual aliasing and weak textures pose significant challenges to the task of place recognition, hindering the performance of Simultaneous Localization and Mapping (SLAM) systems. This paper presents a novel model, called UMF (standing for Unifying Local and Global Multimodal Features) that 1) leverages multi-modality by cross-attention blocks between vision and LiDAR features, and 2) includes a re-ranking stage that re-orders based on local feature matching the top-k candidates retrieved using a global representation. Our experiments, particularly on sequences captured on a planetary-analogous environment, show that UMF outperforms significantly previous baselines in those challenging aliased environments. Since our work aims to enhance the reliability of SLAM in all situations, we also explore its performance on the widely used RobotCar dataset, for broader applicability. Code and models are available at https://github.com/DLR-RM/UMF, Comment: Accepted submission to International Conference on Robotics and Automation (ICRA), 2024

This final degree project is devoted to study the topological classification of complex plane curves. These are subsets of $\mathbb{C}^2$ that can be described by an equation $f(x,y)=0$. Loosely speaking, curves are said to be equivalent in a topological sense whenever they are ambient homeomorphic, i.e., there exists an orientation-preserving homeomorphism of the ambient space carrying one curve to the other. The project's aim is to develop operative and clear conditions to determine whether two curves are equivalent. Curves will be shown to be decomposable into branches: sets that can be explicitly parametrised in the form $x=\phi(t), y=\psi(t)$. These parametric expressions will be analysed to extract a complete numerical invariant for the classification of branches: the Puiseux characteristic. The intermediate key result to lend this notion with topological weight is that a branch can be completely described through its associated knot, arising from the intersection of the branch with a small enough 3-sphere. The combination of these above-mentioned facts will then culminate in the project's most powerful result, which assures that two curves are equivalent if and only if their branches share the same Puiseux characteristics and intersection numbers., Comment: 84 pages

We study germs of hypersurfaces $(Y,0)\subset (\mathbb C^{n+1},0)$ that can be described as the image of $\mathscr A$-finite mappings $f:(X,S)\rightarrow (\mathbb C^{n+1},0)$ defined on an ICIS $(X,S)$ of dimension $n$. We extend the definition of the Jacobian module given by Fern\'andez de Bobadilla, Nu\~no-Ballesteros and Pe\~nafort-Sanchis when $X=\mathbb C^n$, which controls the image Milnor number $\mu_I(X,f)$. We apply these results to prove the case $n=2$ of the generalised Mond conjecture, which states that $\mu_I(X,f)\geq codim_{\mathscr A_e} (X,f)$, with equality if $(Y,0)$ is weighted homogeneous., Comment: 19 pages

In recent years there has been great progress in the use of machine learning algorithms to develop interatomic potential models. Machine-learned potential models are typically orders of magnitude faster than density functional theory but also orders of magnitude slower than physics-derived models such as the embedded atom method. In our previous work, we used symbolic regression to develop fast, accurate and transferrable interatomic potential models for copper with novel functional forms that resemble those of the embedded atom method. To determine the extent to which the success of these forms was specific to copper, here we explore the generalizability of these models to other face-centered cubic transition metals and analyze their out-of-sample performance on several material properties. We found that these forms work particularly well on elements that are chemically similar to copper. When compared to optimized Sutton-Chen models, which have similar complexity, the functional forms discovered using symbolic regression perform better across all elements considered except gold where they have a similar performance. They perform similarly to a moderately more complex embedded atom form on properties on which they were trained, and they are more accurate on average on other properties. We attribute this improved generalized accuracy to the relative simplicity of the models discovered using symbolic regression. The genetic programming models are found to outperform other models from the literature about 50% of the time in a variety of property predictions, with about 1/10th the model complexity on average. We discuss the implications of these results to the broader application of symbolic regression to the development of new potentials and highlight how models discovered for one element can be used to seed new searches for different elements.

Ultra-high-temperature ceramics (UHTCs) are optimal structural materials for applications that require extreme temperature resilience, resistance to chemically aggressive environments, wear, and mechanical stress. Processing UHTCs with laser-based additive manufacturing (AM) has not been fully realized due to a variety of obstacles. In this work, selective laser reaction sintering (SLRS) techniques were investigated for the production of near net-shape UHTC ceramics such as HfC, ZrC, TiC, HfN, ZrN, and TiN. Group IV transition metal and metal oxide precursor materials were chemically converted and reaction-bonded into layers of UHTCs using single-step selective laser processing in CH4 or NH3 gas that might be compatible with prevailing powder bed fusion techniques. Conversion of either metals (Hf, Zr and Ti) or metal oxides (HfO2, ZrO2, and TiO2) particles was first investigated to examine reaction mechanisms and volume changes associated with SLRS of single-component precursor systems. SLRS processing of metal or metal oxide alone produced near stoichiometric UHTC phases with yields up to 100 wt% total for carbides and nitrides. However, for single component precursors, gas-solid reactivity induced volumetric changes resulted in residual stresses and cracking in the product layer. To mitigate conversion-induced stresses, composite metal/metal oxide precursors were employed to compensate for the volume changes of either the metal (which expands during conversion) or the metal oxide precursor (which contracts)., Comment: 58 pages, 17 figures

Selective laser reaction sintering techniques (SLRS) techniques were investigated for the production of near net-shape non-oxide ceramics including SiC, Si$_3$N$_4$, and HfC/SiC composites that might be compatible with prevailing powder bed fusion additive manufacturing processes. Reaction bonded layers of covalent ceramics were produced using in-situ reactions that occur during selective laser processing and layer formation. During SLRS, precursor materials composed of metal and/or metal oxide powders were fashioned into powder beds for conversion to non-oxide ceramic layers. Laser-processing was used to initiate simultaneous chemical conversion and local interparticle bonding of precursor particles in CH4 or NH3 gases. Several factors related to the reaction synthesis process (precursor chemistry, gas-solid and gas-liquid synthesis mechanisms, precursor vapor pressures) were investigated in relation to resulting microstructures and non-oxide yields. Results indicated that the volumetric changes which occurred during in-situ conversion of single component precursors negatively impacted the surface layer microstructure. To circumvent the internal stresses and cracking that accompanied the conversion of Si or Hf (that expands upon conversion) or SiO$_x$ (that contracts during conversion), optimized ratios of the precursor constituents were used to produce near isovolumetric conversion to the product phase. The results demonstrate that under appropriate processing conditions and precursor selection, the formation of near net-shape SiC and SiC composites might be achieved through single-step AM-compatible techniques., Comment: 31 pages, 11 figures

In this brief White Paper we glance over the studies carried out so far by the CMS Collaboration in the field of conventional and exotic hadron spectroscopy. We highlight the most relevant scientific achievements and discuss the future perspectives of this engagement., Comment: 6 pages

In this paper we estimate the first-order sensitivity index of random variables within a model by reconstructing the embedding manifold of a two-dimensional cloud point. The model assumed has p predictors and a continuous outcome Y . Our method gauges the manifold through a Vietoris-Rips complex with a fixed radius for each variable. With this object, and using the area and its symmetric reflection, we can estimate an index of relevance for each predictor. The index reveals the geometric nature of the data points. Also, given the method used, we can decide whether a pair of non-correlated random variables have some structural pattern in their interaction.

The propagation of infectious diseases and its impact on individuals play a major role in disease dynamics, and it is important to incorporate population heterogeneity into efforts to study diseases. As a simplistic but illustrative example, we examine interactions between urban and rural populations in the dynamics of disease spreading. Using a compartmental framework of susceptible--infected--susceptible ($\mathrm{SI\widetilde{S}}$) dynamics with some level of immunity, we formulate a model that allows nonlinear reinfection. We investigate the effects of population movement in the simplest scenario: a case with two patches, which allows us to model movement between urban and rural areas. To study the dynamics of the system, we compute a basic reproduction number for each population (urban and rural). We also compute steady states, determine the local stability of the disease-free steady state, and identify conditions for the existence of endemic steady states. From our analysis and computational experiments, we illustrate that population movement plays an important role in disease dynamics. In some cases, it can be rather beneficial, as it can enlarge the region of stability of a disease-free steady state.

The length and time scales of atomistic simulations are limited by the computational cost of the methods used to predict material properties. In recent years there has been great progress in the use of machine learning algorithms to develop fast and accurate interatomic potential models, but it remains a challenge to develop models that generalize well and are fast enough to be used at extreme time and length scales. To address this challenge, we have developed a machine learning algorithm based on symbolic regression in the form of genetic programming that is capable of discovering accurate, computationally efficient manybody potential models. The key to our approach is to explore a hypothesis space of models based on fundamental physical principles and select models within this hypothesis space based on their accuracy, speed, and simplicity. The focus on simplicity reduces the risk of overfitting the training data and increases the chances of discovering a model that generalizes well. Our algorithm was validated by rediscovering an exact Lennard-Jones potential and a Sutton Chen embedded atom method potential from training data generated using these models. By using training data generated from density functional theory calculations, we found potential models for elemental copper that are simple, as fast as embedded atom models, and capable of accurately predicting properties outside of their training set. Our approach requires relatively small sets of training data, making it possible to generate training data using highly accurate methods at a reasonable computational cost. We present our approach, the forms of the discovered models, and assessments of their transferability, accuracy and speed.

The use of synthetic data generated by Generative Adversarial Networks (GANs) has become quite a popular method to do data augmentation for many applications. While practitioners celebrate this as an economical way to get more synthetic data that can be used to train downstream classifiers, it is not clear that they recognize the inherent pitfalls of this technique. In this paper, we aim to exhort practitioners against deriving any false sense of security against data biases based on data augmentation. To drive this point home, we show that starting with a dataset consisting of head-shots of engineering researchers, GAN-based augmentation "imagines" synthetic engineers, most of whom have masculine features and white skin color (inferred from a human subject study conducted on Amazon Mechanical Turk). This demonstrates how biases inherent in the training data are reinforced, and sometimes even amplified, by GAN-based data augmentation; it should serve as a cautionary tale for the lay practitioners., Comment: 6 pages, 6 figures

We derived a geometric goodness-of-fit index, similar to $R^2$ using topological data analysis techniques. We build the Vietoris-Rips complex from the data-cloud projected onto each variable. Estimating the area of the complex and their domain, we create an index that measures the emptiness of the space with respect to the data. We made the analysis with an own package called TopSA (Topological Sensitivy Analysis).