The historical value of Cantor's work, and also of set theory, both in its naive and axiomatic phases, are undeniable. This article, however, carries out a critical reading of Cantorian theory and, to a large extent, of axiomatic set theory, and connects the analysis with some hints for ongoing discussion in mathematics, physics and epistemology. Inconsistencies and contradictions, in key points of the theory, are highlighted: actual infinity, equal treatment, for most aspects, of infinite and finite sets, infinite plurality and hierarchy of uncountable sets, faultiness of diagonal method. Some of these critical issues have been incorporated, with differences between various versions, into axiomatic theory, which failed to complete the program of providing secure and well-defined foundations for mathematics, which, however, does not appear to suffer from poor health. Mathematicians did not care much about failure of various foundationalist schools, they continued, and it was the best choice, to dedicate themselves to mathematical practice. With the crisis of foundations and with concomitant physical revolutions, the loss of many certainties has occurred, however, the research perspective ends up reversing into an extraordinary open horizon, in mathematics and in borderlands between logic, physics, philosophy and mathematics.
Table reasoning requires models to jointly perform semantic understanding and precise numerical operations. Most existing methods rely on a single-turn reasoning paradigm over tables which suffers from context overflow and weak numerical sensitivity. To address these limitations, we previously proposed TableMind as a tuning-based autonomous programmatic agent that simulates human-like interaction within a lightweight large language model (LLM). TableMind internalizes planning, action, and reflection through a two-stage training strategy involving supervised fine-tuning (SFT) on filtered high-quality data and reinforcement learning (RL) via a multi-perspective reward and the Rank-Aware Policy Optimization (RAPO) algorithm. While TableMind establishes a solid foundation for programmatic agents, the inherent stochasticity of LLMs remains a critical challenge that leads to hallucinations. In this paper, we extend this foundation to TableMind++ by introducing a novel uncertainty-aware inference framework to mitigate hallucinations. Specifically, we propose memory-guided plan pruning to retrieve historical trajectories for validating and filtering out logically flawed plans to address epistemic uncertainty. To ensure execution precision, we introduce confidence-based action refinement which monitors token-level probabilities to detect and self-correct syntactic noise for aleatoric uncertainty mitigation. Finally, we employ dual-weighted trajectory aggregation to synthesize a robust consensus from multiple reasoning paths. Extensive experiments on diverse benchmarks demonstrate that TableMind++ consistently outperforms previous baselines and proprietary models to validate the effectiveness of integrating autonomous training with uncertainty quantification. Our code is available.
Eliott Thomas, Mickael Coustaty, Aurelie Joseph
et al.
Extracting tables from documents is a critical task across various industries, especially on business documents like invoices and reports. Existing systems based on DEtection TRansformer (DETR) such as TAble TRansformer (TATR), offer solutions for Table Detection (TD) and Table Structure Recognition (TSR) but face challenges with diverse table formats and common errors like incorrect area detection and overlapping columns. This research introduces RAPTOR, a modular post-processing system designed to enhance state-of-the-art models for improved table extraction, particularly for product tables. RAPTOR addresses recurrent TD and TSR issues, improving both precision and structural predictions. For TD, we use DETR (trained on ICDAR 2019) and TATR (trained on PubTables-1M and FinTabNet), while TSR only relies on TATR. A Genetic Algorithm is incorporated to optimize RAPTOR's module parameters, using a private dataset of product tables to align with industrial needs. We evaluate our method on two private datasets of product tables, the public DOCILE dataset (which contains tables similar to our target product tables), and the ICDAR 2013 and ICDAR 2019 datasets. The results demonstrate that while our approach excels at product tables, it also maintains reasonable performance across diverse table formats. An ablation study further validates the contribution of each module in our system.
6G is the next-generation intelligent and integrated digital information infrastructure, characterized by ubiquitous interconnection, native intelligence, multi-dimensional perception, global coverage, green and low-carbon, native network security, etc. 6G will realize the transition from serving people and people-things communication to supporting the efficient connection of intelligent agents, and comprehensively leading the digital, intelligent and green transformation of the economy and the society. As the core support system for mobile communication network, 6 6G BSS need to integrate with new business models brought about by the development of the next-generation Internet and IT, upgrade from "network-centric" to "business and service centric" and "customer-centric". 6G OSS and BSS systems need to strengthen their integration to improve the operational efficiency and benefits of customers by connecting the digital intelligence support capabilities on both sides of supply and demand. This paper provides a detailed introduction to the overall vision, potential key technologies, and functional architecture of 6G BSS systems. It also presents an evolutionary roadmap and technological prospects for the BSS systems from 5G to 6G.
Vooral mensen van buiten het vakgebied associëren auditing doorgaans met een specifieke verschijningsvorm van toetsend onderzoek, of dat nu terecht is of niet. Kenmerkend voor dat type onderzoek is dat een praktijksituatie wordt geconfronteerd met een norm, om zo tot een oordeel te kunnen komen. Zo’n nogal beperkte en begrensde interpretatie van de auditprofessie doet natuurlijk geen recht aan de beroepspraktijk, waarin gelukkig vaak ook (en steeds meer) ruimte is voor heel andere typen onderzoek. Tegelijkertijd vormt dit beeld wel een mooi referentiepunt voor vragen, aan de hand waarvan een grensverkenning is uit te voeren in het domein van de sociale wetenschappen om (de beeldvorming rond) het vakgebied te verrijken.
Business, Business mathematics. Commercial arithmetic. Including tables, etc.
Elena Khasanova, Pooja Hiranandani, Shayna Gardiner
et al.
For agents at a contact centre receiving calls, the most important piece of information is the reason for a given call. An agent cannot provide support on a call if they do not know why a customer is calling. In this paper we describe our implementation of a commercial system to detect Purpose of Call statements in English business call transcripts in real time. We present a detailed analysis of types of Purpose of Call statements and language patterns related to them, discuss an approach to collect rich training data by bootstrapping from a set of rules to a neural model, and describe a hybrid model which consists of a transformer-based classifier and a set of rules by leveraging insights from the analysis of call transcripts. The model achieved 88.6 F1 on average in various types of business calls when tested on real life data and has low inference time. We reflect on the challenges and design decisions when developing and deploying the system.
A permutation of the integers avoiding monotone arithmetic progressions of length $6$ was constructed in (Geneson, 2018). We improve on this by constructing a permutation of the integers avoiding monotone arithmetic progressions of length $5$. We also construct permutations of the integers and the positive integers that improve on previous upper and lower density results. In (Davis et al. 1977) they constructed a doubly infinite permutation of the positive integers that avoids monotone arithmetic progressions of length $4$. We construct a doubly infinite permutation of the integers avoiding monotone arithmetic progressions of length $5$. A permutation of the positive integers that avoided monotone arithmetic progressions of length $4$ with odd common difference was constructed in (LeSaulnier and Vijay, 2011). We generalise this result and show that for each $k\geq 1$, there exists a permutation of the positive integers that avoids monotone arithmetic progressions of length $4$ with common difference not divisible by $2^k$. In addition, we specify the structure of permutations of $[1,n]$ that avoid length $3$ monotone arithmetic progressions mod $n$ as defined in (Davis et al. 1977) and provide an explicit construction for a multiplicative result on permutations that avoid length $k$ monotone arithmetic progressions mod $n$.
This article has studied a full truckload transportation problem in the context of an empty return scenario, particularly an order selection and vehicle routing problem with full truckload, multiple depots and time windows (SFTMDVRPTW). The aim is to develop a solution where a set of truck routes serves a subset of selected transportation demands from a number of full truckload orders to maximize the total profit obtained from those orders. Each truck route is a chain of selected demands to serve, originating at a departure point and terminating at an arriving point of trucks in a way that respects the constraints of availability and time windows. It is not mandatory to serve all orders, and only the profitable ones are selected. In this study, we have formulated the SFTMDVRPTW as a mixed-integer linear programming (MILP) model. Finally, Computational results are conducted on a new data set that contains thirty randomly generated problem instances ranging from 16 to 30 orders using the CPLEX software. The findings prove that our model has provided good solutions in a reasonable time.
Analysis, Business mathematics. Commercial arithmetic. Including tables, etc.
Juan Pablo Orejuela Cabrera, Milton Alexander Londoño, Vivian Lorena Chud Pantoja
School bus routing problem is widely studied, however, social elements such as the interaction between children traveling on the same route have not been considered so far. In this way, this article has as its main objective to propose a methodology to solve the school bus routing problem, including affinity as a strategy to increase positive interrelationships between children, and with this, support in bullying situations during school trips. The methodology includes two stages, assigning children to vehicles considering affinities and defining vehicle routes. The main contribution is the consideration of affinity in the process of forming the groups of children that will be taken on the bus, evidencing a balance in the affinity of the groups. Additionally, from the methodological point of view, the integration of a modified group technology algorithm and a new assignment model are proposed that simplify the classic quadratic assignment problem. Consideration of affinity in school bus routing generates benefits from a social point of view.
Analysis, Business mathematics. Commercial arithmetic. Including tables, etc.
Alistair P. Barros, Arthur H. M. ter Hofstede, Henderik A. Proper
The workflow concept, proliferated through the recently emergent computer supported cooperative work (CSCW) systems and workflow systems, advances information systems (IS) implementation models by incorporating aspects of collaboration and coordination in business processes. Under traditional implementation models, applications are partitioned into discrete units of functionality, with (typically) operational procedures used to describe how human and computerised actions of business processes combine to deliver business services. In this paper, a number of essential modelling concepts and features for business transaction workflows are developed.
Purpose: The purpose of this paper is to contribute to the debate as to whether collaboration in coworking spaces contributes to firm innovativeness and impacts the business models of organizations in a positive manner. Methodology: This paper includes primary data from 75 organizations in 17 coworking spaces and uses quantitative research methods. The methodology includes multiple statistical methods, such as principal component analysis, correlation analysis as well as linear and binary regression analysis. Results: The results show a positive interrelation between collaboration and innovation, indicating that coworkers are able to improve their innovative capabilities by making use of strategic partnerships in coworking spaces. Further, this study shows that business models are significantly affected by the level of collaboration in coworking spaces, which suggests that coworking is a promoting force for business model development or business model innovation. Contributions: The paper contributes to management literature and represents the first empirical investigations which focuses on the effects of collaboration on a firm-level in coworking spaces. Practical implications: The results indicate that organizations in coworking spaces should embrace a collaborative mindset and should actively seek out collaborative alliances and partnerships, as doing such is shown to increase their innovativeness and/or develop their business model. Future Research: Future research should focus on the antecedents of collaboration or could investigate the effects of collaboration in coworking spaces on a community level.
A practical algorithm to compute the fundamental domain of an arithmetic Fuchsian group was given by Voight, and implemented in Magma. It was later expanded by Page to the case of arithmetic Kleinian groups. We combine and improve on parts of both algorithms to produce a more efficient algorithm for arithmetic Fuchsian groups. This algorithm is implemented in PARI/GP, and we demonstrate the improvements by comparing running times versus the live Magma implementation.
This chapter provides an overview of the different Artificial Intelligence (AI) systems that are being used in contemporary digital tools for Mathematics Education (ME). It is aimed at researchers in AI and Machine Learning (ML), for whom we shed some light on the specific technologies that are being used in educational applications; and at researchers in ME, for whom we clarify: i) what the possibilities of the current AI technologies are, ii) what is still out of reach and iii) what is to be expected in the near future. We start our analysis by establishing a high-level taxonomy of AI tools that are found as components in digital ME applications. Then, we describe in detail how these AI tools, and in particular ML, are being used in two key applications, specifically AI-based calculators and intelligent tutoring systems. We finish the chapter with a discussion about student modeling systems and their relationship to artificial general intelligence.
The research deals with application of the LEAN principles to business processes of a typical IT company. The paper discusses LEAN principles amplifying advantages and shortcomings of their application. The authors suggest use of the LEAN principles as a tool to identify improvement potential for IT company's business processes and work-flow efficiency. During a case study the implementation of LEAN principles has been exemplified in business processes of a particular Latvian IT company. The obtained results and conclusions can be used for meaningful and successful application of LEAN principles and methods in projects of other IT companies.
Yara Rizk, Abhishek Bhandwalder, Scott Boag
et al.
Business process automation is a booming multi-billion-dollar industry that promises to remove menial tasks from workers' plates -- through the introduction of autonomous agents -- and free up their time and brain power for more creative and engaging tasks. However, an essential component to the successful deployment of such autonomous agents is the ability of business users to monitor their performance and customize their execution. A simple and user-friendly interface with a low learning curve is necessary to increase the adoption of such agents in banking, insurance, retail and other domains. As a result, proactive chatbots will play a crucial role in the business automation space. Not only can they respond to users' queries and perform actions on their behalf but also initiate communication with the users to inform them of the system's behavior. This will provide business users a natural language interface to interact with, monitor and control autonomous agents. In this work, we present a multi-agent orchestration framework to develop such proactive chatbots by discussing the types of skills that can be composed into agents and how to orchestrate these agents. Two use cases on a travel preapproval business process and a loan application business process are adopted to qualitatively analyze the proposed framework based on four criteria: performance, coding overhead, scalability, and agent overlap.
In this paper, we propose a novel privacy-preserving machine learning scheme with encrypted images, called EtC (Encryption-then-Compression) images. Using machine learning algorithms in cloud environments has been spreading in many fields. However, there are serious issues with it for end users, due to semi-trusted cloud providers. Accordingly, we propose using EtC images, which have been proposed for EtC systems with JPEG compression. In this paper, a novel property of EtC images is considered under the use of z-score normalization. It is demonstrated that the use of EtC images allows us not only to protect visual information of images, but also to preserve both the Euclidean distance and the inner product between vectors. In addition, dimensionality reduction is shown to can be applied to EtC images for fast and accurate matching. In an experiment, the proposed scheme is applied to a facial recognition algorithm with classifiers for confirming the effectiveness of the scheme under the use of support vector machine (SVM) with the kernel trick.
Recommender Systems are nowadays successfully used by all major web sites (from e-commerce to social media) to filter content and make suggestions in a personalized way. Academic research largely focuses on the value of recommenders for consumers, e.g., in terms of reduced information overload. To what extent and in which ways recommender systems create business value is, however, much less clear, and the literature on the topic is scattered. In this research commentary, we review existing publications on field tests of recommender systems and report which business-related performance measures were used in such real-world deployments. We summarize common challenges of measuring the business value in practice and critically discuss the value of algorithmic improvements and offline experiments as commonly done in academic environments. Overall, our review indicates that various open questions remain both regarding the realistic quantification of the business effects of recommenders and the performance assessment of recommendation algorithms in academia.
This article surveys recent literature by Parsons, McGee, Shapiro and others on the significance of categoricity arguments in the philosophy of mathematics. After discussing whether categoricity arguments are sufficient to secure reference to mathematical structures up to isomorphism, we assess what exactly is achieved by recent `internal' renditions of the famous categoricity arguments for arithmetic and set theory.