Explains isometric immersions and their applications.
problem Isometric immersions and their applications in math and physics.
method Historical overview and applications.
result Explains the importance and applications of isometric immersions.
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
169,341 papers · 148 categories
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48 results for “historical mathematics”
Invites readers to a mathematical journey with historical and contemporary mathematicians.
problem None explicitly stated, focuses on mathematical exploration.
method Exploration through historical and contemporary mathematicians, various mathematical concepts.
result Illustrates the interconnectedness of mathematics through historical and contemporary perspectives.
Historical note on unsolved complex structure existence problem.
problem Does have a complex structure?
method Historical overview and conference discussion.
result No definitive answer to the existence of complex structures on .
AI mirrors modern math's autonomous development, raising interpretive challenges.
problem AI's effectiveness in math mirrors historical autonomy of math.
method Analyzes historical evolution of modern mathematics and AI's role.
result AI's affinity with math's historical autonomy suggests interpretive limits.
Data describing historical economic growth are analysed. Included in the analysis is the world and regional economic growth. The analysis demonstrates that historical economic growth had a natural tendency to follow hyperbolic distributions. Parameters describing hyperbolic distributions have been determined. A search …
This article offers an introductory look at Khovanov homology and its historical context.
problem Classifying knot embeddings and understanding their homology.
method Expository presentation of Khovanov homology and its historical development.
result Introduction and popularization of knot theory and Khovanov homology in Colombia and Latin America.
Notes on angles and solid angles, in relation with Euler's memoir De mensura angulorum solidorummath.GT
This paper explores historical and philosophical aspects of angles and solid angles, inspired by Euler's work.
problem Understanding the historical context and philosophical implications of angles and solid angles.
method Historical review and analysis of mathematical and philosophical works.
result Questions raised by Euler about angles and solid angles are timeless and relevant to modern mathematics.
Mathematical properties of the historical GDP/cap distributions are discussed and explained. These distributions are frequently incorrectly interpreted and the Unified Growth Theory is an outstanding example of such common misconceptions. It is shown here that the fundamental postulates of this theory are contradicted …
The Prytz connectionsmath.DG
Mathematical analysis of Prytz planimeter using sub-Riemannian geometry.
problem Historical use of Prytz planimeter to approximate areas.
method Sub-Riemannian geometry and connections/horizontal lifts.
result Mathematical description and analysis of Prytz planimeter.
This talk reviews some mathematical and physical ideas related to the notion of dimension. After a brief historical introduction, various modern constructions from fractal geometry, noncommutative geometry, and theoretical physics are invoked and compared.
This paper surveys and classifies attribute-aware CF models.
problem Rating prediction with user and item attributes.
method Mathematical classification of attribute-aware CF models into four categories.
result Comprehensive comparison of effectiveness among different categories.
Quantum Field Theory and Differential Geometryphysics.pop-ph
We introduce the historical development and physical idea behind topological Yang-Mills theory and explain how a physical framework describing subatomic physics can be used as a tool to study differential geometry. Further, we emphasize that this phenomenon demonstrates that the interrelation between physics and mathem…
The paper gauges AGI's impact on GDP growth using mathematical metrics.
problem Determining the economic effect of AGI on GDP growth.
method Analysis of historical data, development of a new mathematical algorithm, regression analysis.
result There is a positive correlation between AGI growth and real GDP growth.
Survey of early moduli and Teichmüller space contributions.
problem Understanding the historical development of moduli and Teichmüller spaces.
method Historical review and explanation of mathematical ideas.
result Confirmation of Teichmüller's results by Ahlfors and Bers.
Galor's mysterious income growth rate is debunked, revealing data manipulation.
problem Mysterious sudden spurt in income per capita growth rate.
method Mathematical analysis of historical world economic growth data.
result The sudden spurt in income per capita growth rate is an artifact of data presentation.
Article reviews the history and development of probabilistic numerics.
problem Understanding the historical context and modern treatment of probabilistic numerics.
method Historical review and analysis of contributions from Sul'din and Larkin.
result Early ideas have matured and are now part of modern formal treatment.
Teaches advanced differential topology to master students with minimal background.
problem Teaching complex differential topology concepts to students with limited mathematical background.
method Cut-and-paste procedures, transversality, cobordism rings.
result Topics can be treated with 'bare hands' using simple mathematical tools.
Mathematical analysis shows Delisle-Euler map methods are optimal.
problem Comparing ancient and modern map drawing methods.
method Analyzing similarities and differences between ancient and modern map drawing methods.
result Delisle-Euler map methods are optimal among conical maps.
NeuTSFlow models continuous functions behind time series forecasting.
problem Forecasting treats time series as discrete sequences, ignoring their continuous nature.
method NeuTSFlow uses Neural Operators to learn the transition between historical and future function families.
result NeuTSFlow outperforms traditional methods in forecasting accuracy and robustness.
Historical income per capita data follow hyperbolic growth patterns.
problem Economic stagnation and Malthusian traps in historical data.
method Fitting hyperbolic distributions to GDP/capita and population data.
result Income per capita growth was monotonic and without transitions.
Study historical cholera epidemics and simulate long-term mortality impacts.
problem Long-term impacts of mortality shocks on longevity.
method Historical analysis of cholera epidemics and mathematical modeling of stochastic Individual-Based models.
result Simulated long-term mortality impacts following a mortality shock.
Residual networks' depth is mathematically equivalent to expanding an implicit ensemble size.
problem Understanding why deep residual networks are effective.
method Formal analysis of residual networks as ensembles of shallow models.
result Increasing network depth is equivalent to expanding the size of an implicit ensemble, revealing a hierarchical structure.
The importance of considering the volumes to analyze stock prices movements can be considered as a well-accepted practice in the financial area. However, when we look at the scientific production in this field, we still cannot find a unified model that includes volume and price variations for stock assessment purposes.…
Serendipity and strategy in rapid innovationphysics.soc-ph
Innovation is a mix of planned strategies and unexpected serendipity.
problem Understanding what drives innovation in organizations.
method Mathematical analysis of innovation as a search process for viable designs.
result Serendipity and strategic innovation are interconnected as the importance of component building blocks changes over time.
Tissot's indicatrix theory is foundational for quasiconformal mappings.
problem Understanding map distortions in geographical projections.
method Mathematical analysis of map projections and their distortions.
result Tissot's work laid the groundwork for quasiconformal mappings.
This paper corrects ReLU attribution and compares activation functions in deep learning.
problem Historical misattribution and performance comparison of activation functions.
method Historical tracing and empirical comparison of ReLU, Tanh, and Sigmoid across tasks.
result ReLU outperforms Sigmoid and Tanh in deep learning tasks.
Study Gram determinants in knot theory, focusing on a Möbius band determinant.
problem Closed formula for the Gram determinant of type .
method Survey of Gram determinants, focusing on a Möbius band determinant.
result Speculation on closed formula for Gram determinant.
New risk measures improve portfolio diversification and stability.
problem Concentration risk in traditional portfolio optimization methods.
method Equal-correlation portfolio strategy with mathematical optimization.
result Improved risk diversification and stable returns.
Predicts next actions in soccer possessions using path signatures.
problem Predicting next actions in soccer possessions with high accuracy.
method Leveraging path signatures to encode spatio-temporal structure of recent possessions, avoiding manual feature engineering.
result Our approach outperforms transformer-based benchmarks across various loss metrics and reduces computational cost.
The paper explores Wiener-Granger causality and its computational enhancements.
problem Analyzing causal relationships between time series data.
method Detailed overview of Granger causality, historical development, and computational advancements.
result Enhanced application of Granger causality in various fields.
The paper reviews historical and modern approaches to asset pricing probability measures.
problem Constructing or selecting probability measures for asset pricing.
method Historical review of various approaches including state price theory, martingale measures, and modern data-driven methods.
result Modern asset pricing involves constructing, transforming, or selecting probability measures to represent market prices.
A remarkable and elementary fact that a locally compact set F of Euclidean space is a smooth manifold if and only if the lower and upper paratangent cones to F coincide at every point, is proved. The celebrated von Neumann's result (1929) that a locally compact subgroup of the general linear group is a smooth manifold,…
Generative Networks outperform traditional methods in PiT ESG generation.
problem Generating economic scenarios quickly and flexibly for sudden changes.
method Comparison of nonparametric, parametric, and generative models.
result Conditional Variational Autoencoder (CVAE) performs best.
The paper presents an algorithm to determine discreteness of certain groups.
problem Determining discreteness of specific groups generated by parabolic transformations.
method Algorithmic approach based on historical mathematical paradigms.
result Equivalence of different approaches to the discreteness problem.
The h-principle helps solve complex geometric problems.
problem Solving complex geometric problems using the h-principle.
method Developed from the Oka-Grauert principle and Gromov's theory, the h-principle is applied to Oka manifolds and maps.
result Recent developments and applications of the h-principle in complex analysis and geometry.
Synthetic data can be used to ask more questions and accelerate discovery with provable validity guarantees.
problem Valid inference with synthetic data
method Task exchangeability
result Provable validity guarantees for synthetic data inference
Unified HS and related methods with explicit modeling assumptions.
problem Lack of clear assumptions in HS methods for Value-at-Risk.
method Explicitly defined parametric model for asset returns and extraction of innovation process.
result HS and related methods require more assumptions than commonly acknowledged.
In Lorentzian manifolds of any dimension the concept of causal tensors is introduced. Causal tensors have positivity properties analogous to the so-called ``dominant energy condition''. Further, it is shown how to build, from ANY given tensor , a new tensor quadratic in and ``positive'', in the sense that it is …
Proposes SAHP for better Hawkes process modeling.
problem Predicting occurrence patterns of event sequences.
method Leverages self-attention to modify Hawkes process intensity function.
result Demonstrates effectiveness on real-world datasets.
The thesis examines stochastic calculus in option pricing with logistic models and numerical methods.
problem Exploring the application of stochastic calculus in option pricing.
method Monte-Carlo Simulation and machine learning algorithms.
result Insights from Peter Carr and Lorenzo Torricelli's convex duality in continuous models.
Enhanced Black-Scholes model for option pricing with stochastic volatility and interest rate variability.
problem Improving option pricing accuracy in volatile financial markets.
method Extended Black-Scholes model using finite difference method and LSTM machine learning.
result Finite difference method outperforms LSTM in computational efficiency but not in accuracy.
ArtificialReplay improves data efficiency in bandits using historical data.
problem Data inefficiency in warm-starting bandit algorithms.
method ArtificialReplay, a meta-algorithm for incorporating historical data into any bandit algorithm.
result ArtificialReplay uses only a fraction of historical data compared to a full warm-start approach, achieving identical regret.
We present and discuss a stochastic model of financial assets dynamics based on the idea of an inverse renormalization group strategy. With this strategy we construct the multivariate distributions of elementary returns based on the scaling with time of the probability density of their aggregates. In its simplest versi…
Analogical Deep Research: Retrieving and Integrating Historical Analogies for Foresight Analysiscs.CL
ADR helps LLMs find and use historical analogies for foresight analysis.
problem LLMs struggle to find relevant historical analogies due to surface-level matching.
method Proposes CANA framework with mechanism alignment and cross-analogy confirmation.
result CANA improves historical analogy generation by up to 10%.
A new method to estimate local volatility from high-frequency data.
problem Quantitative trading risk management needs a better way to estimate volatility.
method Realized local volatility surface estimated via high-frequency data and Bayesian nonparametric estimation.
result The method can capture counterfactual volatility and improve risk management.
Boosts models to detect synchronisation between EEG and EMG data.
problem Understanding the functional relationship between EEG and EMG during emotion episodes.
method Applied historical function-on-function regression models with gradient boosting algorithm.
result Improved models for detecting synchronisation in bioelectrical signals.
Proposes dynamic borrowing method for historical data in clinical trials.
problem Insufficient statistical power in rare and pediatric disease clinical trials.
method Dynamic borrowing method based on frequentist approach using similarity measures.
result Demonstrates usefulness of dynamic borrowing in reanalyzing clinical trial data.
Talk 1: Open problems in knot theory that everyone can try to solve. Knot theory is more than two hundred years old; the first scientists who considered knots as mathematical objects were A.Vandermonde (1771) and C.F.Gauss (1794). However, despite the impressive grow of the theory, there are simply formulated but funda…