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This study examines the evolution of references to grain storage structures in medieval European charters, based on a quantitative and semantic analysis of the digitized CEMA (Cartae Europae Medii Aevi) corpus comprising more than 225,000 documents. The author applies text mining and distributional analysis methods to a lexicon of some forty terms designating storage locations (grangia, horreum, granarium, granica, etc.), cross-referencing these data with references to grain and analyzing their semantic contexts over the long term. The analysis reveals a paradigm shift between the early Middle Ages (decentralized, loosely regulated storage) and the 12th-13th centuries (centralization of storage by the ruling classes). Granaries became instruments of spatial polarization and social control, contributing to the accentuation of social domination in medieval Europe. This evolution was accompanied by a new conceptualization of storage, both material and spiritual.
Mathematicians have long been fascinated by the resolution of algebraic and Diophantine equations in search of integer or rational solutions. This article presents a list of thirty-three open problems in number theory, posed in the 13th century by Ibn al-Khawwām al-Baghdādī (Abdallāh ibn Muhammad ibn Muhammad al-Khawwām), extracted from his arithmetic treatise al-Fawāid al-Bahāiyya fī qawāid al-hisābiyya. We provide a historical and arithmetic analysis of these problems and their solutions, and, whenever possible, offer original solutions and bibliographic notes. This work situates these problems within the broader development of number theory.
The ThEdu series pursues the smooth transition from an intuitive way of doing mathematics at secondary school to a more formal approach to the subject in STEM education while favoring software support for this transition by exploiting the power of theorem-proving technologies. What follows is a brief description of how the present volume contributes to this enterprise. The 13th International Workshop on Theorem Proving Components for Educational Software (ThEdu'24), was a satellite event of the CADE29, part of IJCAR 2024, Nancy, France. ThEdu'24 was a vibrant workshop, with one invited talk by Jeremy Avigad (Carnegie Mellon University) and 14 submitted talks. An open call for papers was then issued and attracted 9 submissions. Eight of those submissions have been accepted by our reviewers. The resulting revised papers are collected in the present volume. The contributions in this volume are a faithful representation of the wide spectrum of ThEdu, ranging from those more focused on the automated deduction research, not losing track of the possible applications in an educational setting, to those focused on the applications, in educational settings, of automated deduction tools and m
The resolvent degree $\textrm{rd}_{\mathbb{C}}(n)$ is the smallest integer $d$ such that a root of the general polynomial $$f(x) = x^n + a_1 x^{n-1} + \ldots + a_n$$ can be expressed as a composition of algebraic functions in at most $d$ variables with complex coefficients. It is known that $\textrm{rd}_{\mathbb{C}}(n) = 1$ when $n \leqslant 5$. Hilbert was particularly interested in the next three cases: he asked if $\textrm{rd}_{\mathbb{C}}(6) = 2$ (Hilbert's Sextic Conjecture), $\textrm{rd}_{\mathbb{C}}(7) = 3$ (Hilbert's 13th Problem) and $\textrm{rd}_{\mathbb{C}}(8) = 4$ (Hilbert's Octic Conjecture). These problems remain open. It is known that $\textrm{rd}_{\mathbb{C}}(6) \leqslant 2$, $\textrm{rd}_{\mathbb{C}}(7) \leqslant 3$ and $\textrm{rd}_{\mathbb{C}}(8) \leqslant 4$. It is not known whether or not $\textrm{rd}_{\mathbb{C}}(n)$ can be $> 1$ for any $n \geqslant 6$. In this paper, we show that all three of Hilbert's conjectures can fail if we replace $\mathbb C$ with a base field of positive characteristic.
This volume contains the proceedings of DCM 2023, the 13th International Workshop on Developments in Computational Models held on 2 July 2023 in Rome, Italy. DCM 2023 was organised as a one-day satellite event of FSCD 2023, the 8th International Conference on Formal Structures for Computation and Deduction. The aim of this workshop is to bring together researchers who are currently developing new computation models or new features for traditional computation models, in order to foster their interaction, to provide a forum for presenting new ideas and work in progress, and to enable newcomers to learn about current activities in this area.
This volume contains the proceedings of the 13th International Symposium on Games, Automata, Logic and Formal Verification (GandALF 2022). The aim of GandALF 2022 symposium is to bring together researchers from academia and industry which are actively working in the fields of Games, Automata, Logics, and Formal Verification. The idea is to cover an ample spectrum of themes, ranging from theory to applications, and stimulate cross-fertilization.
The algebraic form of Hilbert's 13th Problem asks for the resolvent degree $\text{rd}(n)$ of the general polynomial $f(x) = x^n + a_1 x^{n-1} + \ldots + a_n$ of degree $n$, where $a_1, \ldots, a_n$ are independent variables. The resolvent degree is the minimal integer $d$ such that every root of $f(x)$ can be obtained in a finite number of steps, starting with $\mathbb C(a_1, \ldots, a_n)$ and adjoining algebraic functions in $\leq d$ variables at each step. Recently Farb and Wolfson defined the resolvent degree $\text{rd}_k(G)$ of any finite group $G$ and any base field $k$ of characteristic $0$. In this setting $\text{rd}(n) = \text{rd}_{\mathbb C}(S_n)$, where $S_n$ denotes the symmetric group. In this paper we define $\text{rd}_k(G)$ for every algebraic group $G$ over an arbitrary field $k$, investigate the dependency of this quantity on $k$ and show that $\text{rd}_k(G) \leq 5$ for any field $k$ and any connected group $G$. The question of whether $\text{rd}_k(G)$ can be bigger than $1$ for any field $k$ and any algebraic group $G$ over $k$ (not necessarily connected) remains open.
We develop the theory of resolvent degree, introduced by Brauer \cite{Br} in order to study the complexity of formulas for roots of polynomials and to give a precise formulation of Hilbert's 13th Problem. We extend the context of this theory to enumerative problems in algebraic geometry, and consider it as an intrinsic invariant of a finite group. As one application of this point of view, we prove that Hilbert's 13th Problem, and his Sextic and Octic Conjectures, are equivalent to various enumerative geometry problems, for example problems of finding lines on a smooth cubic surface or bitangents on a smooth planar quartic.
General expressions are given for Chern forms up to the 13th order in curvature in terms of simple polynomial concomitants of the curvature 2-form for n-dimensional differentiable manifolds having a general linear connection.
This volume contains the proceedings of the 13th International Workshop on Verification of Infinite-State Systems (INFINITY 2011). The workshop was held in Taipei, Taiwan on October 10, 2011, as a satellite event to the 9th International Symposium on Automated Technology for Verification and Analysis (ATVA). The INFINITY workshop aims at providing a forum for researchers who are interested in the development of formal methods and algorithmic techniques for the analysis of systems with infinitely many states, and their application in automated verification of complex software and hardware systems.
We summarize the talks presented at the QG4 session (loop quantum gravity: cosmology and black holes) of the 13th Marcel Grossmann Meeting held in Stockholm, Sweden.
This volume contains a selection of papers presented at LFMTP 2018, the 13th international Workshop on Logical Frameworks and Meta-Languages: Theory and Practice (LFMTP), held on July 7, 2018, in Oxford, UK. The workshop was affiliated with the 3rd international conference on Formal Structures for Computation and Deduction (FSCD) within the 7th Federated Logic Conference (FLoC).
The magnitude of the biotic enhancement of weathering (BEW) has profound implications for the long-term carbon cycle. The BEW ratio is defined as how much faster the silicate weathering carbon sink is under biotic conditions than under abiotic conditions at the same atmospheric pCO2 level and surface temperature. Thus, a 13th hypothesis should be considered in addition to the 12 outlined by Brantley...(2011) regarding the geobiology of weathering: The BEW factor and its evolution over geological time can be inferred from meta-analysis of empirical and theoretical weathering studies. Estimates of the global magnitude of the BEW are presented, drawing from lab, field, watershed data and models of the long-term carbon cycle, with values ranging from one to two orders of magnitude.
This note is purely expository. In the course of the Kolmogorov-Arnold solution of Hilbert's 13th problem on superpositions there appeared the notion of basic embedding. A subset K of R^2 is basic if for each continuous function f:K->R there exist continuous functions g,h:R->R such that f(x,y)=g(x)+h(y) for each point (x,y) in K. We present descriptions of basic subsets of the plane (with a proof) and description of graphs basically embeddable into the plane (solutions of Arnold's and Sternfeld's problems). We present some results and open problems on the smooth version of the property of being basic. This note is accessible to undergraduates and could be an interesting easy reading for mature mathematicians. The two sections can be read independently on each other.
Extreme low-data fine-grained classification is common in expert domains where labeling is expensive, yet practitioners still need principled guidance for selecting pretrained encoders. We study emerald inclusion grading with a custom dataset of labeled images across three classes and ask: under matched backbone capacity, how does pretraining objective affect downstream representation quality? We compare four frozen ViT-B/16 encoders trained with supervised classification, contrastive learning (SigLIP2), masked reconstruction (MAE), and self-distillation (DINOv3), and evaluate them with leave-one-out cross-validation using linear and nonlinear probes. To control statistical noise in the low-N regime, we use permutation testing (N=1000) on macro one-vs-rest AUC. Supervised and contrastive encoders provide the strongest linear separability (logistic AUC: 0.768 and 0.735; SVM AUC: 0.739 and 0.697), while MAE improves under nonlinear probes (XGBoost AUC: 0.713). We find that DINOv3 underperforms across probe families in this domain. These results support a practical recommendation for extreme low-data FGVC: prioritize margin-enforcing pretraining objectives when data scarcity restricts
This study presents an efficient transformer-based question-answering (QA) model optimized for deployment on a 13th Gen Intel i7-1355U CPU, using the Stanford Question Answering Dataset (SQuAD) v1.1. Leveraging exploratory data analysis, data augmentation, and fine-tuning of a DistilBERT architecture, the model achieves a validation F1 score of 0.6536 with an average inference time of 0.1208 seconds per question. Compared to a rule-based baseline (F1: 0.3124) and full BERT-based models, our approach offers a favorable trade-off between accuracy and computational efficiency. This makes it well-suited for real-time applications on resource-constrained systems. The study includes systematic evaluation of data augmentation strategies and hyperparameter configurations, providing practical insights into optimizing transformer models for CPU-based inference.
Robotic grasping is a fundamental skill across all domains of robot applications. There is a large body of research for grasping objects in table-top scenarios, where finding suitable grasps is the main challenge. In this work, we are interested in scenarios where the objects are in confined spaces and hence particularly difficult to reach. Planning how the robot approaches the object becomes a major part of the challenge, giving rise to methods for joint grasp and motion planning. The framework proposed in this paper provides 20 benchmark scenarios with systematically increasing difficulty, realistic objects with precomputed grasp annotations, and tools to create and share more scenarios. We further provide two baseline planners and evaluate them on the scenarios, demonstrating that the proposed difficulty levels indeed offer a meaningful progression. We invite the research community to build upon this framework by making all components publicly available as open source.
Nowadays, the rapid growth of Deep Neural Network (DNN) architectures has established them as the defacto approach for providing advanced Machine Learning tasks with excellent accuracy. Targeting low-power DNN computing, this paper examines the interplay of fine-grained error resilience of DNN workloads in collaboration with hardware approximation techniques, to achieve higher levels of energy efficiency. Utilizing the state-of-the-art ROUP approximate multipliers, we systematically explore their fine-grained distribution across the network according to our layer-, filter-, and kernel-level approaches, and examine their impact on accuracy and energy. We use the ResNet-8 model on the CIFAR-10 dataset to evaluate our approximations. The proposed solution delivers up to 54% energy gains in exchange for up to 4% accuracy loss, compared to the baseline quantized model, while it provides 2x energy gains with better accuracy versus the state-of-the-art DNN approximations.
Phishing attacks remain a critical cybersecurity threat. Attackers constantly refine their methods, making phishing emails harder to detect. Traditional detection methods, including rule-based systems and supervised machine learning models, either rely on predefined patterns like blacklists, which can be bypassed with slight modifications, or require large datasets for training and still can generate false positives and false negatives. In this work, we propose a multi-agent large language model (LLM) prompting technique that simulates debates among agents to detect whether the content presented on an email is phishing. Our approach uses two LLM agents to present arguments for or against the classification task, with a judge agent adjudicating the final verdict based on the quality of reasoning provided. This debate mechanism enables the models to critically analyze contextual cue and deceptive patterns in text, which leads to improved classification accuracy. The proposed framework is evaluated on multiple phishing email datasets and demonstrate that mixed-agent configurations consistently outperform homogeneous configurations. Results also show that the debate structure itself is
An AI design framework was developed based on three core principles, namely understandability, trust, and usability. The framework was conceptualized by synthesizing evidence from the literature and by consulting with experts. The initial version of the AI Explainability Framework was validated based on an in-depth expert engagement and review process. For evaluation purposes, an AI-anchored prototype, incorporating novel explainability features, was built and deployed online. The primary function of the prototype was to predict the postpartum depression risk using analytics models. The development of the prototype was carried out in an iterative fashion, based on a pilot-level formative evaluation, followed by refinements and summative evaluation. The System Explainability Scale (SES) metric was developed to measure the influence of the three dimensions of the AI Explainability Framework. For the summative stage, a comprehensive usability test was conducted involving 20 clinicians, and the SES metric was used to assess clinicians` satisfaction with the tool. On a 5-point rating system, the tool received high scores for the usability dimension, followed by trust and understandabili