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For any fixed dimension $d \geq 3$ we construct a Nikodym set in $F_q^d$ of cardinality $q^d - (\frac{d-2}{\log 2} +1+o(1)) q^{d-1} \log q$ in the limit $q \to \infty$, when $q$ is an odd prime power. This improves upon the naive random construction, which gives a set of cardinality $q^d - (d-1+o(1)) q^{d-1} \log q$, and is new in the regime where $F_q$ has unbounded characteristic and $q$ not a perfect square. While the final proofs are completely human generated, the initial ideas of the construction were inspired by output from the tools \texttt{AlphaEvolve} and \texttt{DeepThink}. We also present a simple construction of Nikodym sets in $F_q^2$ for $q$ a perfect square that is a special case of known unital-based constructions, and matches the existing bounds of $q^2 - q^{3/2} + O(q \log q)$, assuming that $q$ is not the square of a prime $p \equiv 3 \pmod{4}$.
Human-robot collaboration in construction is often challenged by limited robot-to-human communication and the need to adapt to tolerance accumulation arising from material and assembly uncertainties. We present an adaptive human-robot collaborative workflow for masonry construction that addresses communication limitations and tolerance accumulation, demonstrated through a brickwork case study in which a robot places bricks while a human applies adhesive. This workflow is enabled by two complementary mechanisms: 1) an end-effector-mounted projector that provides spatially registered, just-in-time projection guidance for manual adhesive application, and 2) laser scanning for feedback-driven grasping and placement pose correction. Together, these mechanisms enable adjustment of human and robotic actions in response to material variability and accumulated assembly tolerances. Full-scale experiments across conventional running-bond and nonstandard configurations demonstrate that projection guidance improves adhesive application consistency and reduces application time, while laser-based correction maintains level courses and avoids collision-prone failures associated with open-loop exec
In this article, we give a construction of the (un-)stable motivic homotopy category of an algebraic stack in the spirit of Morel-Voevodsky. We prove that this new construction agrees with the stable motivic homotopy category defined by Chowdhury and D'Angelo. As an application, we extend Bachmann's spectral rigidity theorem to algebraic stacks. Moreover, we extend the construction of the framed motivic homotopy category to algebraic stacks and prove Hoyois' Reconstruction Theorem in this setting. Finally, we discuss an extension of the formalism of cocomplete coefficient systems à la Drew-Gallauer to algebraic stacks.
The construction industry has long explored robotics and computer vision, yet their deployment on construction sites remains very limited. These technologies have the potential to revolutionize traditional workflows by enhancing accuracy, efficiency, and safety in construction management. Ground robots equipped with advanced vision systems could automate tasks such as monitoring mechanical, electrical, and plumbing (MEP) systems. The present research evaluates the applicability of open-vocabulary vision-language models compared to fine-tuned, lightweight, closed-set object detectors for detecting MEP components using a mobile ground robotic platform. A dataset collected with cameras mounted on a ground robot was manually annotated and analyzed to compare model performance. The results demonstrate that, despite the versatility of vision-language models, fine-tuned lightweight models still largely outperform them in specialized environments and for domain-specific tasks.
The integration of Large Vision-Language Models (LVLMs) such as OpenAI's GPT-4 Vision into various sectors has marked a significant evolution in the field of artificial intelligence, particularly in the analysis and interpretation of visual data. This paper explores the practical application of GPT-4 Vision in the construction industry, focusing on its capabilities in monitoring and tracking the progress of construction projects. Utilizing high-resolution aerial imagery of construction sites, the study examines how GPT-4 Vision performs detailed scene analysis and tracks developmental changes over time. The findings demonstrate that while GPT-4 Vision is proficient in identifying construction stages, materials, and machinery, it faces challenges with precise object localization and segmentation. Despite these limitations, the potential for future advancements in this technology is considerable. This research not only highlights the current state and opportunities of using LVLMs in construction but also discusses future directions for enhancing the model's utility through domain-specific training and integration with other computer vision techniques and digital twins.
This paper proposes a portfolio construction framework designed to remain robust under estimation error, non-stationarity, and realistic trading constraints. The methodology combines dynamic asset eligibility, deterministic rebalancing, and bounded multi-factor tilts applied to an equal-weight baseline. Asset eligibility is formalized as a state-dependent constraint on portfolio construction, allowing factor exposure to adjust endogenously in response to observable market conditions such as liquidity, volatility, and cross-sectional breadth. Rather than estimating expected returns or covariances, the framework relies on cross-sectional rankings and hard structural bounds to control concentration, turnover, and fragility. The resulting approach is fully algorithmic, transparent, and directly implementable. It provides a robustness-oriented alternative to parametric optimization and unconstrained multi-factor models, particularly suited for long-horizon allocations where stability and operational feasibility are primary objectives.
The fields of autonomous systems and robotics are receiving considerable attention in civil applications such as construction, logistics, and firefighting. Nevertheless, the widespread adoption of these technologies is hindered by the necessity for robust processing units to run AI models. Edge-AI solutions offer considerable promise, enabling low-power, cost-effective robotics that can automate civil services, improve safety, and enhance sustainability. This paper presents a novel Edge-AI-enabled drone-based surveillance system for autonomous multi-robot operations at construction sites. Our system integrates a lightweight MCU-based object detection model within a custom-built UAV platform and a 5G-enabled multi-agent coordination infrastructure. We specifically target the real-time obstacle detection and dynamic path planning problem in construction environments, providing a comprehensive dataset specifically created for MCU-based edge applications. Field experiments demonstrate practical viability and identify optimal operational parameters, highlighting our approach's scalability and computational efficiency advantages compared to existing UAV solutions. The present and future
Recent progress in deep learning and natural language processing has given rise to powerful models that are primarily trained on a cloze-like task and show some evidence of having access to substantial linguistic information, including some constructional knowledge. This groundbreaking discovery presents an exciting opportunity for a synergistic relationship between computational methods and Construction Grammar research. In this chapter, we explore three distinct approaches to the interplay between computational methods and Construction Grammar: (i) computational methods for text analysis, (ii) computational Construction Grammar, and (iii) deep learning models, with a particular focus on language models. We touch upon the first two approaches as a contextual foundation for the use of computational methods before providing an accessible, yet comprehensive overview of deep learning models, which also addresses reservations construction grammarians may have. Additionally, we delve into experiments that explore the emergence of constructionally relevant information within these models while also examining the aspects of Construction Grammar that may pose challenges for these models. T
In this thesis, a new approach for constructing subdivision algorithms for generalized quadratic and cubic B-spline subdivision for subdivision surfaces and volumes is presented. First, a catalog of quality criteria for these subdivision algorithms is developed, serving as a guideline for the construction process. The construction begins by generating the desired subdominant eigenvectors as the vertices of regular convex 3-polytopes for volumes using circle packings. Subsequently, these polytopes are utilized to construct a Colin-de-Verdiere-matrix for the generalized quadratic and a Colin-de-Verdiere-like matrix for the generalized cubic B-spline subdivision. These matrices are then adjusted using the matrix exponential to obtain subdivision matrices with the desired properties. All subdivision algorithms introduced in this paper empirically exhibit a subdominant eigenvalue of 1/2 with the desired algebraic and geometric multiplicity. For the quadratic case, this property can even be formally proven. Moreover, the corresponding eigenvectors form a convex polytope in the central region for the generalized quadratic B-spline subdivision algorithms, while for the generalized cubic B-
Construction robotics increasingly relies on natural language processing for task execution, creating a need for robust methods to interpret commands in complex, dynamic environments. While existing research primarily focuses on what tasks robots should perform, less attention has been paid to how these tasks should be executed safely and efficiently. This paper presents a novel probabilistic framework that uses sentiment analysis from natural language commands to dynamically adjust robot navigation policies in construction environments. The framework leverages Building Information Modeling (BIM) data and natural language prompts to create adaptive navigation strategies that account for varying levels of environmental risk and uncertainty. We introduce an object-aware path planning approach that combines exponential potential fields with a grid-based representation of the environment, where the potential fields are dynamically adjusted based on the semantic analysis of user prompts. The framework employs Bayesian inference to consolidate multiple information sources: the static data from BIM, the semantic content of natural language commands, and the implied safety constraints from
Argument structure constructions (ASCs) offer a theoretically grounded lens for analyzing second language (L2) proficiency, yet scalable and systematic tools for measuring their usage remain limited. This paper introduces the ASC analyzer, a publicly available Python package designed to address this gap. The analyzer automatically tags ASCs and computes 50 indices that capture diversity, proportion, frequency, and ASC-verb lemma association strength. To demonstrate its utility, we conduct both bivariate and multivariate analyses that examine the relationship between ASC-based indices and L2 writing scores.
The Gross-Neveu model is a quantum field theory model of Dirac fermions in two dimensions with a quartic interaction term. Like Yang-Mills theory in four dimensions, the model is scaling critical (i.e. renormalizable but not super-renormalizable) and asymptotically free (i.e. its short-distance behavior is governed by the free theory). We give a new construction of the massive Euclidean Gross-Neveu model in infinite volume. The distinctive feature of the construction is that it does not involve cluster expansion, discretization of phase-space or a tree expansion ansatz and is based solely on the renormalization group flow equation. We express the Schwinger functions of the Gross-Neveu model in terms of the effective potential and construct the effective potential by solving the flow equation using the Banach fixed point theorem. Moreover, we construct a random field in the probability space of the free field such that its moments coincide with the Schwinger functions of the Gross-Neveu model. This is the first construction of a strong coupling between the free and interacting fields for a scaling-critical QFT. Since we use crucially the fact that fermionic fields can be represented
Information retrieval and question answering from safety regulations are essential for automated construction compliance checking but are hindered by the linguistic and structural complexity of regulatory text. Many queries are multi-hop, requiring synthesis across interlinked clauses. To address the challenge, this paper introduces BifrostRAG, a dual-graph retrieval-augmented generation (RAG) system that models both linguistic relationships and document structure. The proposed architecture supports a hybrid retrieval mechanism that combines graph traversal with vector-based semantic search, enabling large language models to reason over both the content and the structure of the text. On a multi-hop question dataset, BifrostRAG achieves 92.8% precision, 85.5% recall, and an F1 score of 87.3%. These results significantly outperform vector-only and graph-only RAG baselines, establishing BifrostRAG as a robust knowledge engine for LLM-driven compliance checking. The dual-graph, hybrid retrieval mechanism presented in this paper offers a transferable blueprint for navigating complex technical documents across knowledge-intensive engineering domains.
In this chapter, we argue that it is highly beneficial for the contemporary construction grammarian to have a thorough understanding of the strong relationship between the research fields of construction grammar and artificial intelligence. We start by unravelling the historical links between the two fields, showing that their relationship is rooted in a common attitude towards human communication and language. We then discuss the first direction of influence, focussing in particular on how insights and techniques from the field of artificial intelligence play an important role in operationalising, validating and scaling constructionist approaches to language. We then proceed to the second direction of influence, highlighting the relevance of construction grammar insights and analyses to the artificial intelligence endeavour of building truly intelligent agents. We support our case with a variety of illustrative examples and conclude that the further elaboration of this relationship will play a key role in shaping the future of the field of construction grammar.
Based on the Wronski determinant, we propose the construction of linearly independent and orthogonal functions in any Hilbert function space. The method requires only an initial function from the space of functions under consideration, that satisfies mild conditions, and emerges as a generalization of the Gram-Schmidt process. Two applications are considered, including solutions to ordinary differential equations and the construction of basis functions. We also present a conjecture that connects the latter two concepts, which leads to the introduction of the Wronski basis.
Understanding complex collaboration processes is essential for the success of construction projects. However, there is still a lack of efficient methods for timely collection and analysis of collaborative networks. Therefore, an integrated framework consisting three parts, namely, system updating for data collection, data preprocessing, and social network analysis, is proposed for the twinning and mining collaborative network of a construction project. First, a system updating strategy for automatic data collection is introduced. Centrality measures are then utilized to identify key players, including hubs and brokers. Meanwhile, information sharing frequency (ISF) and association rule mining are introduced to discover collaborative patterns, that is, frequently collaborating users (FCUs) and associations between information flows and task levels. Finally, the proposed framework is validated and demonstrated in a large-scale project. The results show that key players, FCUs, and associations between information flows and task levels were successfully discovered, providing a deep understanding of collaboration and communication for decision-making processes. This research contributes
The Grothendieck construction is a fundamental link between indexed categories and opfibrations. This work is a detailed study of the Grothendieck construction over a small tight bipermutative category in the context of Cat-enriched multicategories, with applications to inverse K-theory and pseudo symmetric E-infinity-algebras. The ordinary Grothendieck construction over a small category C is a 2-equivalence that sends a C-indexed category to an opfibration over C. We show that the Grothendieck construction over a small tight bipermutative category D is a pseudo symmetric Cat-multifunctor that is generally not a Cat-multifunctor in the symmetric sense. When the projection to D is taken into account, we prove that the Grothendieck construction over D lifts to a non-symmetric Cat-multiequivalence whose codomain is a non-symmetric Cat-multicategory with small permutative opfibrations over D as objects. As applications we show that inverse K-theory, from Gamma-categories to small permutative categories, is a pseudo symmetric Cat-multifunctor but not a Cat-multifunctor in the symmetric sense. It follows that inverse K-theory preserves algebraic structures parametrized by non-symmetric a
In Part I we constructed the Quantum Mechanics of a charged unitary entity and prescribed the form in which such a particle interacts with other charged particles and matter in general. In this second part we extend the description to the hydrogen atom testing the correctness and accuracy of the general description. The relation between electron and proton in the atom is described systematically in a construction that is free from analogies or ad-hoc derivations and it supersedes conventional Quantum Mechanics (whose equations linked to measurements can be recovered). We briefly discuss why the concept of isolation built in Schrödinger's time evolution is not acceptable and how it immediately results in the well known measurement paradoxes of quantum mechanics. We also discuss the epistemic grounds of the development as well as those of conventional Quantum Mechanics.
We provide a construction method for biharmonic submanifolds in cohomogeneity one manifolds. In particular, we give new examples of biharmonic submanifolds and study the normal index of these submanifolds. We use this strategy to construct metrics on the sphere admitting biharmonic non-minimal hypersurfaces with three distinct principal curvatures. Finally, we perform a similar study of $r$-harmonic submanifolds of cohomogeneity one manifolds.
This report introduces the 1st place winning solution for the Autonomous Driving Challenge 2023 - Online HD-map Construction. By delving into the vectorization pipeline, we elaborate an effective architecture, termed as MachMap, which formulates the task of HD-map construction as the point detection paradigm in the bird-eye-view space with an end-to-end manner. Firstly, we introduce a novel map-compaction scheme into our framework, leading to reducing the number of vectorized points by 93% without any expression performance degradation. Build upon the above process, we then follow the general query-based paradigm and propose a strong baseline with integrating a powerful CNN-based backbone like InternImage, a temporal-based instance decoder and a well-designed point-mask coupling head. Additionally, an extra optional ensemble stage is utilized to refine model predictions for better performance. Our MachMap-tiny with IN-1K initialization achieves a mAP of 79.1 on the Argoverse2 benchmark and the further improved MachMap-huge reaches the best mAP of 83.5, outperforming all the other online HD-map construction approaches on the final leaderboard with a distinct performance margin (>