• A
  • A
  • A
  • АБВ
  • АБВ
  • АБВ
  • A
  • A
  • A
  • A
  • A
Обычная версия сайта
  • RU
  • EN
  • HSE University
  • Publications
  • Articles
  • Generative geospatial modelling with geometric algebra
  • RU
  • EN
Расширенный поиск
Высшая школа экономики
Национальный исследовательский университет
Priority areas
  • business informatics
  • economics
  • engineering science
  • humanitarian
  • IT and mathematics
  • law
  • management
  • mathematics
  • sociology
  • state and public administration
by year
  • 2028
  • 2027
  • 2026
  • 2025
  • 2024
  • 2023
  • 2022
  • 2021
  • 2020
  • 2019
  • 2018
  • 2017
  • 2016
  • 2015
  • 2014
  • 2013
  • 2012
  • 2011
  • 2010
  • 2009
  • 2008
  • 2007
  • 2006
  • 2005
  • 2004
  • 2003
  • 2002
  • 2001
  • 2000
  • 1999
  • 1998
  • 1997
  • 1996
  • 1995
  • 1994
  • 1993
  • 1992
  • 1991
  • 1990
  • 1989
  • 1988
  • 1987
  • 1986
  • 1985
  • 1984
  • 1983
  • 1982
  • 1981
  • 1980
  • 1979
  • 1978
  • 1977
  • 1976
  • 1975
  • 1974
  • 1973
  • 1972
  • 1971
  • 1970
  • 1969
  • 1968
  • 1967
  • 1966
  • 1965
  • 1964
  • 1963
  • 1958
  • More
Subject
News
September 9, 2026
‘Balkan Hospitality Opens Doors: Studying Dialects on the Verge of Extinction
You cannot study spoken dialects from books. Instead, you need to go to a village, seek out its elders, and earn the trust of local residents before you can record hours of spontaneous stories. This is how Natalia Muravleva, Associate Professor at the Faculty of Humanities, conducts her research. Her internship in Serbia continued her long-standing study of dialects spoken by Macedonian settlers. In this interview, she discusses how diaspora cultural centres help researchers reach informants, why native speakers need to be interviewed only in their own language (otherwise, as she puts it, they may 'break'), and how a single field season helped her finalise her monograph. She also shares warm memories of autumn in Belgrade and of colleagues with whom grammar can be discussed in three languages at once.
September 9, 2026
Scientists Train Neural Network to Generate Process Plans from 3D Models
Researchers at the HSE FCS AI and Digital Science Institute have developed CAD2TechSpec, a framework that converts 3D models of mechanical parts into machining process plans—step-by-step instructions for machine tools. The solution aims to reduce the time required for the design and preparation of technical process documentation in mechanical engineering, aircraft manufacturing, and other high-tech industries. The study findings have been published in PeerJ Computer Science.
September 7, 2026
Biologists Discover 'Molecular Fingerprint' of Preeclampsia
Researchers at HSE University employed a new method to model hypoxia in placental cells during pregnancies complicated by preeclampsia and identified molecular markers of tissue hypoxia. Since hypoxia is one of the key mechanisms underlying preeclampsia, these findings are important for a more accurate and timely diagnosis of the disease and for the development of effective treatment methods. The paper has been published in Placenta.

 

Have you spotted a typo?
Highlight it, click Ctrl+Enter and send us a message. Thank you for your help!

Publications
  • Books
  • Articles
  • Chapters of books
  • Working papers
  • Report a publication
  • Research at HSE

?

Generative geospatial modelling with geometric algebra

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 2026. Vol. 384. No. 2326. Article 20250103.
Yu Z., Wang J., Wang Z., Liu Y., Shirokov D., Hildenbrand D., Yuan L.

The integration of data-driven and knowledge-driven approaches in generative geospatial modelling (GGM) is often hindered by their mathematical incompatibilities. Here, we propose a geometric algebra (GA)-based framework that employs a unified multi-vector representation to fuse heterogeneous data and diverse knowledge. The framework facilitates structured reasoning and hypothesis generation through a task-adaptable, five-stage cycle: representation, reasoning, generation, synthesis and computation. We illustrate this design through three case studies covering constrained trajectory reconstruction, typhoon intensity prediction and large language model-based GA code generation, which instantiate different components and implementation levels of the proposed framework. By offering a cohesive mathematical perspective, our work provides a conceptual and methodological framework for interpretable and
constraint-aware GGM. This article is part of the theme issue ‘Modern applications of geometric algebra’.

Research target: Mathematics Computer Science
Language: English
Full text
DOI
Text on another site
Keywords: geometric algebraGEOGRAPHICAL INFORMATION SYSTEM artificial intelligencegenerative geospatial modelling
Publication based on the results of:
Кватернионы, геометрические алгебры и приложения (2026)
Similar publications
On phase-lock area parquet in a special slow-fast limit of model of Josephson junction.
Glutsyuk A., / Series arXiv "math". 2026.
B.Josephson (Nobel Prize, 1973) predicted a tunnelling effect for a system of two superconductors separated by a narrow dielectric (such a system is called Josephson junction): existence of a supercurrent through it and equations governing it. The overdamped Josephson junction is modeled by the family of differential equations on the 2-torus, dθdτ=1ω(cosθ+B+Acosτ), which is known as ...
Added: September 8, 2026
On exotic rationally integrable dual billiards I. Complex geometry and type of dynamics.
Glutsyuk A., / Series arXiv "math". 2026.
A planar dual billiard is a planar curve γ equipped with a family (σP)|P∈γ of projective involutions of the projective lines LP tangent to γ at P that fix P. A dual billiard is called rationally integrable, if there exists a rational function R(x,y) of two variables (called first integral) whose restriction to each tangent ...
Added: September 8, 2026
Dynamical systems on torus related to general Heun equations: phase-lock areas and constriction breaking
Alexandrov A., Glutsyuk A., Journal of Differential Equations 2026 Vol. 465 Article 114178
The overdamped Josephson junction in superconductivity theory can be modeled by the family of dynamical systems on the torus, which is known as the RSJ model. This family admits an equivalent description by a family of second-order differential equations: special double confluent Heun equations. In the present paper, we construct two new families of dynamical systems on ...
Added: September 8, 2026
On rationally integrable planar dual and projective billiards
Glutsyuk A., Inventiones Mathematicae 2026 Vol. 245 P. 977–1058
A caustic of a strictly convex planar bounded billiard is a smooth curve whose tangent lines are reflected from the billiard boundary to its tangent lines. The famous Birkhoff Conjecture, studied by many mathematicians, states that if the billiard boundary has an inner neighborhood foliated by closed caustics, then it is an ellipse. In the paper we study ...
Added: September 8, 2026
Анализ согласованности голосования стран ЕАЭС и ОДКБ в ГА ООН с помощью иерархической кластеризации
Вохминцев И. В., Вестник международных организаций: образование, наука, новая экономика 2026 Т. 21 № 2
The EAEU and the CSTO are Russia’s principal regional international organisations. Understanding, assessing, and analysing the foreign-policy positions of the countries that belong to them is a matter of the state’s national interests. This determines the purpose of the study: to identify the level and the form of cohesion in the voting of EAEU and ...
Added: September 7, 2026
Rational p-adic Hodge theory for d-de Rham-proper stacks
Prikhodko Artem, Kubrak D., Compositio Mathematica 2026 Vol. 162 No. 6 P. 1377–1438
In this follow-up paper we show that smooth Hodge-proper stacks over O𝐾 are ℚ𝑝-locally acyclic: namely the natural map between étale ℚ𝑝-cohomology of the algebraic and Raynaud generic fibers is an equivalence. This establishes the ℚ𝑝-case of general conjectures made in D. Kubrak and A. Prikhodko [p-adic Hodge theory for Artin stacks, Mem. Amer. Math. ...
Added: September 7, 2026
Lower Bounds on the Measure of the Support of Positive and Negative Parts of Trigonometric Polynomials
Ismailov A., Constructive Approximation 2026
The measure of the positivity set {x ∈ [0; 2π] | f (x) > 0} of a trigonometric polynomial f  is bounded from below by the Motzkin density. We generalize the bound to polynomials in several variables and almost periodic functions. We then use these generalizations to extend known results on Taikov’s problem. ...
Added: September 7, 2026
Pupillometry and autonomic nervous system responses to cognitive load and false feedback: an unsupervised machine learning approach
Alshanskaia E., Portnova G., Liaukovich K. et al., Frontiers in Neuroscience 2024 Vol. 18
Added: September 7, 2026
Oil Spill Segmentation in SAR Data Using ViT-UNet: Performance and Practical Insights
Зуенко Д. О., Trofimova E., Хайдарова И., IEEE Access 2026 Vol. 14 P. 121339–121357
Oil spill segmentation in Synthetic Aperture Radar (SAR) images is limited by noisy annotations in publicly available datasets and by architectural choices that interact with label quality in opposing directions. First, we introduce a manually refined version of the Deep-SAR Oil Spill (SOS) dataset, in which 36.25% of masks are corrected for false positives, missed ...
Added: September 7, 2026
Конечные последовательности и перестановки, ими порождаемые
Kucheryavyy P., Математические заметки 2026 Т. 2026 № 120 С. 380–401
В работе изучаются перестановки, возникающие при упорядочивании по возрастанию дробных долей произведений элементов фиксированной целочисленной последовательности на вещественный параметр. Исследуется количество различных перестановок, которые можно получить таким образом при изменении этого параметра от нуля до единицы. ...
Added: September 7, 2026
Scalable machine learning approach to disordered s-wave superconductors
Неверов В. Д., Красавин А. В., Vagov A. et al., Physical Review B: Condensed Matter and Materials Physics 2026 Vol. 113 P. 1–6
We develop a neural network approach to solve the self-consistent Bogoliubov-de Gennes equations in strongly disordered s-wave superconductors. The method accurately reproduces inhomogeneous gap distributions and generalizes to system sizes far larger than those used in training. It reduces computational scaling from O(N6 ) to O(N2), enabling quantitative analysis of percolation phenomena and the superconductor-insulator ...
Added: September 5, 2026
On the rate of Gaussian approximation for online linear regression problems
Sheshukova M., Durmus A., Khusainov M. et al., Statistics 2026 P. 1–25
In this paper, we consider the problem of Gaussian approximation for the online linear regression task. We derive the corresponding rates for the setting of a constant stepsize and study the explicit dependence of the convergence rate on the problem dimension d and quantities related to the design matrix. When the number of iterations n is known in advance, ...
Added: September 4, 2026
Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence (UAI), PMLR Volume 337, 17-21 August 2026, KIT, Amsterdam, the Netherlands
Proceedings of Machine Learning Research , 2026.
Added: September 4, 2026
Банки и экосистемы
Бровкина Н. Е., Терновская Е. П., Мешкова Е. И. et al., В кн.: Банк в современной экономикеКн. Банк в современной экономике.: М.: КноРус, 2026. С. 127–147.
Banks are the central link in the national financial market and the economy as a whole. The share of bank assets in the asset structure of the Russian financial market, despite a slight decline, remains dominant relative to other participants, reaching 80%. Russian banks are multifaceted. On the one hand, they provide working capital financing, long-term ...
Added: September 3, 2026
Относительные аналитические законы взаимности
Осипов Д.В., Математический сборник 2026 Т. 217 № 9 С. 130–146
Изучаются законы взаимности, связанные с комплексными линейными расслоениями на расслоениях на ориентируемые окружности. В частности, доказывается следующий закон взаимности. Пусть B – комплексное многообразие и πi:Mi→B – расслоение на ориентируемые окружности, где индекс i пробегает конечное множество. Пусть Li и Ni – комплексные линейные расслоения на каждом многообразии Mi. Закон взаимности утверждает, что сумма всех элементов (πi)∗(c1(Li)∪c1(Ni)), где (πi)∗ – ...
Added: September 3, 2026
Tokyo Sympathy Tower by Qudan Rie: The Tower of Babel of Our Days and the Birth of the “New Human”
Borkina A., Russian Japanology Review 2026 Vol. 9 No. 1 P. 30–48
The article examines the novel by Japanese writer Qudan Rie Tokyo Sympathy Tower, which was awarded the prestigious Akutagawa Literary Prize in 2024. The award sparked a wide discussion due to the writer’s use of generative artificial intelligence in her work, which not only suggested some ideas, but also became the prototype for one of ...
Added: September 2, 2026
Explicit Formula for Inverse and Determinant in Geometric Algebras over Seven-dimensional Vector Spaces
Abdulkhaev K., Shirokov D., , in: 10th International Workshop, ENGAGE 2025, Hong Kong, China, July 14, 2025, Proceedings. Empowering Novel Geometric Algebra for Graphics and Engineering, (LNCS, volume 16510)Vol. 16510.: Cham: Springer, 2026. P. 189–200.
In this paper, we present an explicit formula for the inverse and determinant in geometric (Clifford) algebras over vector spaces of dimension . We generalize the concept of conjugation to basis conjugation operations, allowing us to express the determinant formula independently of any specific algebra isomorphism. This construction provides a practical computational tool for determining invertibility ...
Added: August 13, 2026
ASEAN and the Resolution of the South China Sea Issue: Assessing Digital Limitations
Kanaev E., Southeast Asia: Actual Problems of Development 2026 Vol. 2 No. 2(71) P. 11–22
The author focuses on a strengthening digital component in the evolution of the South China Sea issue in the context of ASEAN’s evolving approach to the deepening contradictions and its policy in the digital field. On outlining ASEAN’s policy on the South China Sea issue, the author proceeds to exploring the digital agenda of ASEAN’s ...
Added: July 30, 2026
Artificial Intelligence in Courts, Arbitration and Issues of “Hallucinations”
Klementiev A., Kasatkina A., Legal Issues in the Digital Age 2026 Vol. 7 No. 2 P. 40–60
The article examines specific aspects of artificial (machine) intelligence in dispute resolution in state and arbitration courts . Drawing on legal research methods and data from artificial intelligence science, the authors propose a significant obstacle to its application in the legal sphere is the so-called “hallucination problem,” i .e ., the generation of false data by machine intelligence programs ...
Added: July 14, 2026
Проникновение искусственного интеллекта в жизненный цикл разработки программного обеспечения: эмпирический анализ рынка труда
Stoyanova O., Окусков И. С., Бизнес-информатика 2026 Т. 20 № 2 С. 81–93
The integration of artificial intelligence (AI) into information technologies is reshaping competency requirements for IT specialists. However, AI competency penetration into the early phases of the Software Development Life Cycle (SDLC) – requirements analysis and planning – remains underexplored. Existing studies either rely on static competency models lacking empirical validation or analyze the labor market ...
Added: July 5, 2026
Сегодня: четыре мегатренда клиентоцентричности
Selskiy A., Snegirev A., Колбин Е. И. et al., В кн.: Цифровая клиентоцентричность. Как современные технологии помогают компаниям и государству сделать шаг навстречу потребителям.: М.: ИСИЭЗ ВШЭ, 2026. Гл. 2 С. 71–142.
The second chapter of the monograph analyzes the current megatrends of customer centricity, shaped by digital technologies and transforming the approaches of companies and government bodies to customer and citizen engagement. Based on semantic big data analysis (using the iFORA system) and expert interviews, the authors identify four key megatrends. The first megatrend, proactive engagement and personalization, describes ...
Added: June 26, 2026
Искусственный интеллект на рабочем месте: современное состояние исследований в социальных науках
Talakauskas D., Пути России. Журнал cоциальных и этнографических исследований 2026 Т. 4 № 3 С. 44–67
An increasing number of organizations are implementing artificial intelligence (AI) technologies into various business processes, and the number of publications addressing aspects of AI’s application in the workplace is growing rapidly. Given the uncertainty surrounding the effects of AI implementation on the labor market, the time lag associated with its integration, and the novelty and ...
Added: June 24, 2026
Book Review: The Eye of the Master: A Social History of Artificial Intelligence
Kosmarsky A., Напреенко И. В., Journal of Cultural Economy 2026 P. 1–4
Added: June 23, 2026
Социальное программирование как методологический инструмент сетевой самоорганизации: проблемы и тенденции (материалы «круглого стола»)
Pruzhinin B. I., Afanasov N., Буданов В. Г. et al., Вопросы философии 2026 № 5 С. 5–35
In December 2025, the Institute of Philosophy of the Russian Academy of Sciences hosted an international roundtable on the topic “Social Programming as a Methodological Tool of Network Self-Organization: Problems and Trends”. The roundtable was organized by the journal “Voprosy Filosofii” and representatives of the research project No. 25-28-00707, “Social Programming as a Problem of Network ...
Added: June 18, 2026
  • About
  • About
  • Key Figures & Facts
  • Sustainability at HSE University
  • Faculties & Departments
  • International Partnerships
  • Faculty & Staff
  • HSE Buildings
  • HSE University for Persons with Disabilities
  • Public Enquiries
  • Studies
  • Admissions
  • Programme Catalogue
  • Undergraduate
  • Graduate
  • Exchange Programmes
  • Summer University
  • Summer Schools
  • Semester in Moscow
  • Business Internship
  • Research
  • International Laboratories
  • Research Centres
  • Research Projects
  • Monitoring Studies
  • Conferences & Seminars
  • Academic Jobs
  • Yasin (April) International Academic Conference on Economic and Social Development
  • Media & Resources
  • Publications by staff
  • HSE Journals
  • Publishing House
  • iq.hse.ru: commentary by HSE experts
  • Library
  • Economic & Social Data Archive
  • Video
  • HSE Repository of Socio-Economic Information
  • HSE1993–2026
  • Contacts
  • Copyright
  • Privacy Policy
  • Site Map
Edit