Related papers: LeanBET: Formally-verified surface area calculatio…
We develop an invariant local theory of Lorentz surfaces in pseudo-Euclidean 4-space by use of a linear map of Weingarten type. We find a geometrically determined moving frame field at each point of the surface and obtain a system of…
An overall objective of energy efficiency in the built environment is to improve building and systems performances in terms of durability, comfort and economics. In order to predict, improve and meet a certain set of performance…
In this paper we consider a coupled bulk-surface PDE in two space dimensions. The model consists of a PDE in the bulk that is coupled to another PDE on the surface through general nonlinear boundary conditions. For such a system we propose…
We introduce BEDS (Bayesian Emergent Dissipative Structures), a formal framework for analyzing inference systems that must maintain beliefs continuously under energy constraints. Unlike classical computational models that assume perfect…
The evaluation of heuristic optimizers on test problems, better known as \emph{benchmarking}, is a cornerstone of research in multi-objective optimization. However, most test problems used in benchmarking numerical multi-objective black-box…
We present an algebraic method for solving the Bethe ansatz equations for the periodic totally asymmetric exclusion process (TASEP) with an arbitrary number of sites and particles. The Bethe ansatz equations are realized as an algebraic…
Depth completion from sparse LiDAR measurements and corresponding RGB images is a prerequisite for accurate 3D perception in robotic systems. Existing methods achieve high accuracy on standard benchmarks but rely on heavy backbone…
In this article we describe the formalisation of the Bruhat-Tits tree - an important tool in modern number theory - in the Lean Theorem Prover. Motivated by the goal of connecting to ongoing research, we apply our formalisation to verify a…
Predictive and real-time inference capability for the upstream separatrix electron density, $n_\text{e, sep}$, is essential for design and control of core-edge integrated plasma scenarios. In this study, both supervised and semi-supervised…
Data engineering pipelines are essential - albeit costly - components of predictive analytics frameworks requiring significant engineering time and domain expertise for carrying out tasks such as data ingestion, preprocessing, feature…
Large pre-trained language models have recently gained significant traction due to their improved performance on various down-stream tasks like text classification and question answering, requiring only few epochs of fine-tuning. However,…
Chain-of-Thought (CoT) prompting has become the de facto method to elicit reasoning capabilities from large language models (LLMs). However, to mitigate hallucinations in CoT that are notoriously difficult to detect, current methods such as…
Two prominent challenges in explainability research involve 1) the nuanced evaluation of explanations and 2) the modeling of missing information through baseline representations. The existing literature introduces diverse evaluation…
We present **Lean4PHYS**, a comprehensive reasoning framework for college-level physics problems in Lean4. **Lean4PHYS** includes *LeanPhysBench*, a college-level benchmark for formal physics reasoning in Lean4, which contains 200…
A NEMA performance evaluation was conducted on the new General Electric (GE) digital Omni Legend PET-CT system with 32-cm extended field-of-view. This study marks the introduction of the first-ever commercially available clinical digital…
Block copolymers provide a wonderful platform in studying the soft condensed matter systems. Many fascinating ordered structures have been discovered in bulk and confined systems. Among various theories, the self-consistent field theory…
Event Tree (ET) analysis is widely used as a forward deductive safety analysis technique for decision-making at the critical-system design stage. ET is a schematic diagram representing all possible operating states and external events in a…
Nowadays, machine learning (ML) plays a vital role in many aspects of our daily life. In essence, building well-performing ML applications requires the provision of high-quality data throughout the entire life-cycle of such applications.…
The Bidirectional Encoder Representations from Transformers (BERT) model has been radically improving the performance of many Natural Language Processing (NLP) tasks such as Text Classification and Named Entity Recognition (NER)…
To obtain the highest confidence on the correction of numerical simulation programs implementing the finite element method, one has to formalize the mathematical notions and results that allow to establish the soundness of the method.…