Domain-specific quantitative reasoning remains a major challenge for large language models (LLMs), especially in fields requiring expert knowledge and complex question answering (QA). In this work, we propose Expert Question Decomposition (EQD), an approach designed to balance the use of domain knowledge with computational efficiency. EQD is built on a two-step fine-tuning framework and guided by a reward function that measures the effectiveness of generated sub-questions in improving QA outcomes. It requires only a few thousand training examples and a single A100 GPU for fine-tuning, with inference time comparable to zero-shot prompting. Beyond its efficiency, EQD outperforms state-of-the-art domain-tuned models and advanced prompting strategies. We evaluate EQD in the financial domain, characterized by specialized knowledge and complex quantitative reasoning, across four benchmark datasets. Our method consistently improves QA performance by 0.6% to 10.5% across different LLMs. Our analysis reveals an important insight: in domain-specific QA, a single supporting question often provides greater benefit than detailed guidance steps.

Symmetry, a fundamental concept to understand our environment, often oversimplifies reality from a mathematical perspective. Humans are a prime example, deviating from perfect symmetry in terms of appearance and cognitive biases (e.g. having a dominant hand). Nevertheless, our brain can easily overcome these imperfections and efficiently adapt to symmetrical tasks. The driving motivation behind this work lies in capturing this ability through reinforcement learning. To this end, we introduce Adaptive Symmetry Learning (ASL), a model-minimization actor-critic extension that addresses incomplete or inexact symmetry descriptions by adapting itself during the learning process. ASL consists of a symmetry fitting component and a modular loss function that enforces a common symmetric relation across all states while adapting to the learned policy. The performance of ASL is compared to existing symmetry-enhanced methods in a case study involving a four-legged ant model for multidirectional locomotion tasks. The results show that ASL can recover from large perturbations and generalize knowledge to hidden symmetric states. It achieves comparable or better performance than alternative methods in most scenarios, making it a valuable approach for leveraging model symmetry while compensating for inherent perturbations.

A new paradigm for data-driven, model-agnostic new physics searches at colliders is emerging, and aims to leverage recent breakthroughs in anomaly detection and machine learning. In order to develop and benchmark new anomaly detection methods within this framework, it is essential to have standard datasets. To this end, we have created the LHC Olympics 2020, a community challenge accompanied by a set of simulated collider events. Participants in these Olympics have developed their methods using an R&D dataset and then tested them on black boxes: datasets with an unknown anomaly (or not). This paper will review the LHC Olympics 2020 challenge, including an overview of the competition, a description of methods deployed in the competition, lessons learned from the experience, and implications for data analyses with future datasets as well as future colliders.

Perception and prediction modules are critical components of autonomous driving systems, enabling vehicles to navigate safely through complex environments. The perception module is responsible for perceiving the environment, including static and dynamic objects, while the prediction module is responsible for predicting the future behavior of these objects. These modules are typically divided into three tasks: object detection, object tracking, and motion prediction. Traditionally, these tasks are developed and optimized independently, with outputs passed sequentially from one to the next. However, this approach has significant limitations: computational resources are not shared across tasks, the lack of joint optimization can amplify errors as they propagate throughout the pipeline, and uncertainty is rarely propagated between modules, resulting in significant information loss. To address these challenges, the joint perception and prediction paradigm has emerged, integrating perception and prediction into a unified model through multi-task learning. This strategy not only overcomes the limitations of previous methods, but also enables the three tasks to have direct access to raw sensor data, allowing richer and more nuanced environmental interpretations. This paper presents the first comprehensive survey of joint perception and prediction for autonomous driving. We propose a taxonomy that categorizes approaches based on input representation, scene context modeling, and output representation, highlighting their contributions and limitations. Additionally, we present a qualitative analysis and quantitative comparison of existing methods. Finally, we discuss future research directions based on identified gaps in the state-of-the-art.

A C++ library for sensitivity analysis of optimisation problems involving ordinary differential equations (ODEs) enabled by automatic differentiation (AD) and SIMD (Single Instruction, Multiple data) vectorization is presented. The discrete adjoint sensitivity analysis method is implemented for adaptive explicit Runge-Kutta (ERK) methods. Automatic adjoint differentiation (AAD) is employed for efficient evaluations of products of vectors and the Jacobian matrix of the right hand side of the ODE system. This approach avoids the low-level drawbacks of the black box approach of employing AAD on the entire ODE solver and opens the possibility to leverage parallelization. SIMD vectorization is employed to compute the vector-Jacobian products concurrently. We study the performance of other methods and implementations of sensitivity analysis and we find that our algorithm presents a small advantage compared to equivalent existing software.

Humanoid robots are made to resemble humans but their locomotion abilities are far from ours in terms of agility and versatility. When humans walk on complex terrains, or face external disturbances, they combine a set of strategies, unconsciously and efficiently, to regain stability. This paper tackles the problem of developing a robust omnidirectional walking framework, which is able to generate versatile and agile locomotion on complex terrains. The Linear Inverted Pendulum Model and Central Pattern Generator concepts are used to develop a closed-loop walk engine, which is then combined with a reinforcement learning module. This module learns to regulate the walk engine parameters adaptively, and generates residuals to adjust the robot's target joint positions (residual physics). Additionally, we propose a proximal symmetry loss function to increase the sample efficiency of the Proximal Policy Optimization algorithm, by leveraging model symmetries and the trust region concept. The effectiveness of the proposed framework was demonstrated and evaluated across a set of challenging simulation scenarios. The robot was able to generalize what it learned in unforeseen circumstances, displaying human-like locomotion skills, even in the presence of noise and external pushes.

This paper investigates the extension of lattice-based logics into modal languages. We observe that such extensions admit multiple approaches, as the interpretation of the necessity operator is not uniquely determined by the underlying lattice structure. The most natural interpretation defines necessity as the meet of the truth values of a formula across all accessible worlds -- an approach we refer to as the \textitnormal interpretation. We examine the logical properties that emerge under this and other interpretations, including the conditions under which the resulting modal logic satisfies the axiom K and other common modal validities. Furthermore, we consider cases in which necessity is attributed exclusively to formulas that hold in all accessible worlds.

In today's data-driven ecosystems, ensuring data integrity, traceability and accountability is important. Provenance polynomials constitute a powerful formalism for tracing the origin and the derivations made to produce database query results. Despite their theoretical expressiveness, current implementations have limitations in handling aggregations and nested queries, and some of them and tightly coupled to a single Database Management System (DBMS), hindering interoperability and broader applicability. This paper presents a query rewriting-based approach for annotating Structured Query Language (SQL) queries with provenance polynomials. The proposed methods are DBMS-independent and support Select-Projection-Join-Union-Aggregation (SPJUA) operations and nested queries, through recursive propagation of provenance annotations. This constitutes the first full implementation of semiring-based theory for provenance polynomials extended with semimodule structures. It also presents an experimental evaluation to assess the validity of the proposed methods and compare the performance against state-of-the-art systems using benchmark data and queries. The results indicate that our solution delivers a comprehensive implementation of the theoretical formalisms proposed in the literature, and demonstrates improved performance and scalability, outperforming existing methods.

We propose a new dynamic SIR model that, in contrast with the available model on time scales, is biological relevant. For the new SIR model we obtain an explicit solution, we prove the asymptotic stability of the extinction and disease-free equilibria, and deduce some necessary conditions for the monotonic behavior of the infected population. The new results are illustrated with several examples in the discrete, continuous, and quantum settings.

Maximum Distance Separable (MDS) convolutional codes are cha- racterized through the property that the free distance meets the generalized Singleton bound. The existence of free MDS convolutional codes over Z p r was recently discovered in [26] via the Hensel lift of a cyclic code. In this paper we further investigate this important class of convolutional codes over Z p r from a new perspective. We introduce the notions of p-standard form and r- optimal parameters to derive a novel upper bound of Singleton type on the free distance. Moreover, we present a constructive method for building general (non necessarily free) MDS convolutional codes over Z p r for any given set of parameters.

Accurate dynamic models are crucial for many robotic applications. Traditional approaches to deriving these models are based on the application of Lagrangian or Newtonian mechanics. Although these methods provide a good insight into the physical behaviour of the system, they rely on the exact knowledge of parameters such as inertia, friction and joint flexibility. In addition, the system is often affected by uncertain and nonlinear effects, such as saturation and dead zones, which can be difficult to model. A popular alternative is the application of Machine Learning (ML) techniques - e.g., Neural Networks (NNs) - in the context of a "black-box" methodology. This paper reports on our experience with this approach for a real-life 6 degrees of freedom (DoF) manipulator. Specifically, we considered several NN architectures: single NN, multiple NNs, and cascade NN. We compared the performance of the system by using different policies for selecting the NN hyperparameters. Our experiments reveal that the best accuracy and performance are obtained by a cascade NN, in which we encode our prior physical knowledge about the dependencies between joints, complemented by an appropriate optimisation of the hyperparameters.

We propose a constraint-based algorithm, which automatically determines causal relevance thresholds, to infer causal networks from data. We call these topological thresholds. We present two methods for determining the threshold: the first seeks a set of edges that leaves no disconnected nodes in the network; the second seeks a causal large connected component in the data. We tested these methods both for discrete synthetic and real data, and compared the results with those obtained for the PC algorithm, which we took as the benchmark. We show that this novel algorithm is generally faster and more accurate than the PC algorithm. The algorithm for determining the thresholds requires choosing a measure of causality. We tested our methods for Fisher Correlations, commonly used in PC algorithm (for instance in \cite{kalisch2005}), and further proposed a discrete and asymmetric measure of causality, that we called Net Influence, which provided very good results when inferring causal networks from discrete data. This metric allows for inferring directionality of the edges in the process of applying the thresholds, speeding up the inference of causal DAGs.

Inductive Conformal Prediction (ICP) is a set of distribution-free and model agnostic algorithms devised to predict with a user-defined confidence with coverage guarantee. Instead of having point predictions, i.e., a real number in the case of regression or a single class in multi class classification, models calibrated using ICP output an interval or a set of classes, respectively. ICP takes special importance in high-risk settings where we want the true output to belong to the prediction set with high probability. As an example, a classification model might output that given a magnetic resonance image a patient has no latent diseases to report. However, this model output was based on the most likely class, the second most likely class might tell that the patient has a 15% chance of brain tumor or other severe disease and therefore further exams should be conducted. Using ICP is therefore way more informative and we believe that should be the standard way of producing forecasts. This paper is a hands-on introduction, this means that we will provide examples as we introduce the theory.

As already mentioned by Lawvere in his 1973 paper, the characterisation of Cauchy completeness of metric spaces in terms of representability of adjoint distributors amounts to the idempotent-split property of an ordinary category when the governing symmetric monoidal-closed category is changed from the extended real half-line to the category of sets. In this paper, for any commutative quantale $\mathcal{V}$, we extend these two characterisations of Lawvere-style completeness to $\mathcal{V}$-normed categories, thus replacing $[0,\infty]$ and $\mathsf{Set}$ more generally by the category $\mathsf{Set}{/\!\!/}\mathcal{V}$ of $\mathcal{V}$-normed sets. We also establish improvements of recent results regarding the normed convergence of Cauchy sequences in two important $\mathcal{V}$-normed categories.

The rapid depletion of fossil fuel resources and environmental concerns has given awareness on generation of renewable energy resources. Among the various renewable resources, hybrid solar and wind energy seems to be promising solutions to provide reliable power supply with improved system efficiency and reduced storage requirements for stand-alone applications. This paper presents a feasibility assessment and optimum size of photovoltaic (PV) array, wind turbine and battery bank for a standalone hybrid Solar/Wind Power system (HSWPS) at remote telecom station of Nepal at Latitude (27{\deg}23'50") and Longitude (86{\deg}44'23") consisting a telecommunication load of Very Small Aperture Terminal (VSAT), Repeater station and Code Division Multiple Access Base Transceiver Station (CDMA 2C10 BTS). In any RES based system, the feasibility assessment is considered as the first step analysis. In this work, feasibility analysis is carried through hybrid optimization model for electric renewables (HOMER) and mathematical models were implemented in the MATLAB environment to perform the optimal configuration for a given load and a desired loss of power supply probability (LPSP) from a set of systems components with the lowest value of cost function defined in terms of reliability and levelized unit electricity cost (LUCE). The simulation results for the existing and the proposed models are compared. The simulation results shows that existing architecture consisting of 6.12 kW KC85T photovoltaic modules, 1kW H3.1 wind turbine and 1600 Ah GFM-800 battery bank have a 36.6% of unmet load during a year. On the other hand, the proposed system includes 1kW *2 H3.1 Wind turbine, 8.05 kW TSM-175DA01 photovoltaic modules and 1125 Ah T-105 battery bank with system reliability of 99.99% with a significant cost reduction as well as reliable energy production.

As composites of constant, (co)product, identity, and powerset functors, Kripke polynomial functors form a relevant class of $\mathsf{Set}$-functors in the theory of coalgebras. The main goal of this paper is to expand the theory of limits in categories of coalgebras of Kripke polynomial functors to the context of quantale-enriched categories. To assume the role of the powerset functor we consider "powerset-like" functors based on the Hausdorff $\mathsf{V}$-category structure. As a starting point, we show that for a lifting of a $\mathsf{SET}$-functor to a topological category $\mathsf{X}$ over $\mathsf{Set}$ that commutes with the forgetful functor, the corresponding category of coalgebras over $\mathsf{X}$ is topological over the category of coalgebras over $\mathsf{Set}$ and, therefore, it is "as complete" but cannot be "more complete". Secondly, based on a Cantor-like argument, we observe that Hausdorff functors on categories of quantale-enriched categories do not admit a terminal coalgebra. Finally, in order to overcome these "negative" results, we combine quantale-enriched categories and topology \emph{à la} Nachbin. Besides studying some basic properties of these categories, we investigate "powerset-like" functors which simultaneously encode the classical Hausdorff metric and Vietoris topology and show that the corresponding categories of coalgebras of "Kripke polynomial" functors are (co)complete.

The giant mutually connected component (GMCC) of an interdependent or multiplex network collapses with a discontinuous hybrid transition under random damage to the network. If the nodes to be damaged are selected in a targeted way, the collapse of the GMCC may occur significantly sooner. Finding the minimal damage set which destroys the largest mutually connected component of a given interdependent network is a computationally prohibitive simultaneous optimization problem. We introduce a simple heuristic strategy -- Effective Multiplex Degree -- for targeted attack on interdependent networks that leverages the indirect damage inherent in multiplex networks to achieve a damage set smaller than that found by any other non computationally intensive algorithm. We show that the intuition from single layer networks that decycling (damage of the $2$-core) is the most effective way to destroy the giant component, does not carry over to interdependent networks, and in fact such approaches are worse than simply removing the highest degree nodes.

We propose a novel dynamical model for blood alcohol concentration that incorporates $\psi$-Caputo fractional derivatives. Using the generalized Laplace transform technique, we successfully derive an analytic solution for both the alcohol concentration in the stomach and the alcohol concentration in the blood of an individual. These analytical formulas provide us a straightforward numerical scheme, which demonstrates the efficacy of the $\psi$-Caputo derivative operator in achieving a better fit to real experimental data on blood alcohol levels available in the literature. In comparison to existing classical and fractional models found in the literature, our model outperforms them significantly. Indeed, by employing a simple yet non-standard kernel function $\psi(t)$, we are able to reduce the error by more than half, resulting in an impressive gain improvement of 59 percent.

The Transiting Exoplanet Survey Satellite (TESS) has detected thousands of exoplanet candidates since 2018, most of which have yet to be confirmed. A key step in the confirmation process of these candidates is ruling out false positives through vetting. Vetting also eases the burden on follow-up observations, provides input for demographics studies, and facilitates training machine learning algorithms. Here we present the TESS Triple-9 (TT9) catalog -- a uniformly-vetted catalog containing dispositions for 999 exoplanet candidates listed on ExoFOP-TESS, known as TESS Objects of Interest (TOIs). The TT9 was produced using the Discovery And Vetting of Exoplanets pipeline, DAVE, and utilizing the power of citizen science as part of the Planet Patrol project. More than 70% of the TOIs listed in the TT9 pass our diagnostic tests, and are thus marked as true planetary candidates. We flagged 144 candidates as false positives, and identified 146 as potential false positives. At the time of writing, the TT9 catalog contains ~20% of the entire ExoFOP-TESS TOIs list, demonstrates the synergy between automated tools and citizen science, and represents the first stage of our efforts to vet all TOIs. The DAVE generated results are publicly available on ExoFOP-TESS.