The paper surveys mathematical results on filtration enlargement with financial examples.
problem Mathematical finance applications of filtration enlargement theory.
method Exhaustive survey and interpretation of key results from literature.
result Provides a compendium of known mathematical results for mathematical finance researchers.
Computer-generated proofs led to a mathematical result.
problem Discovering a mathematical result through computer-generated proofs.
method Combining computer-generated, human-readable proofs with mathematical abstraction.
result Abstracted lemma leading to an interesting mathematical result.
Thurston's influence on French math traced and problems solved.
problem Major problems in French math traced back to Thurston.
method Overview and survey of Thurston's influence and results.
result French math problems rooted in Thurston's work.
Lean 4 library formalizes mathematical finance, verifying over 200 theorems.
problem Formal verification of complex financial mathematics.
method Lean 4 proof assistant, Mathlib, BrownianMotion package, formal verification of over 200 theorems.
result Formal verification yields certified unification of known financial results.
Lean 4 library formalizes mathematical finance, verifying over 200 theorems.
problem Formal verification of complex financial mathematics.
method Lean 4 proof assistant, Mathlib, and BrownianMotion package.
result Formal verification yields certified unification of known results.
Advanced mathematical relativity course for math and physics students.
problem Mathematical foundations of general relativity.
method Comprehensive lecture notes covering advanced topics.
result Comprehensive coverage of mathematical relativity for advanced students.
TopicEq model generates equations and text from scientific papers.
problem Communicating ideas in scientific texts using both mathematics and text.
method Joint topic and equation generation model using correlated topic model and RNN.
result Joint model outperforms existing topic and equation models for scientific texts.
Mathematical general relativity reviewed.
problem Challenges in mathematical modeling of general relativity.
method Selected topics reviewed.
result Insights into mathematical models of general relativity.
Mathematical study shows post-hoc explanations are better than attention weights alone.
problem Understanding the internal behavior of attention-based models.
method Mathematical analysis of a simple attention-based architecture.
result Post-hoc explanations provide more useful insights than attention weights alone.
AI aids in mathematics research and problem-solving.
problem Complex mathematical problems and discoveries.
method Explains AI principles and diverse applications in math.
result AI assists in discovering patterns, proving theorems, and challenging conjectures.
This article reviews mathematical insights into neural networks and machine learning.
problem Understanding the success and subtleties of neural network-based machine learning.
method Rigorous mathematical analysis, numerical experiments, and simplified models.
result Identification of open problems in the field.
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.
Formalizes synthetic differential geometry in Lean.
problem Formalizing synthetic differential geometry in a proof assistant.
method Formalization of synthetic differential geometry with Lean and mathlib.
result Proves a Taylor theorem for functions of several variables.
Self-supervised skip-tree training improves mathematical reasoning in language models.
problem Improving logical reasoning in language models for formal mathematics.
method Self-supervised language modeling on mathematical formulas, skip-tree task.
result Models trained on skip-tree task outperform standard models in mathematical reasoning tasks.
Transformer models can solve complex math problems with less data.
problem Solving complex symbolic mathematics problems with limited data.
method Pretrain transformer models on language translation tasks and fine-tune for symbolic math.
result Pretrained transformer models achieve comparable accuracy to state-of-the-art models with less data.
This is a continuous work about the nonexistence of some complete metrics on the product of two manifolds studied by Tam-Yu [Asian Journal of Mathematics, 14(2010)]. Motivated by the result of Tossati [Comm.Anal.Geom. 15(2007)]. We generalize the corresponding results of Tam-Yu [Asian Journal of Mathematics, 14(2010)] …
Mathematical approach defines stability conditions for ML models.
problem Ensuring stability of machine learning models.
method Adopted topological and metric spaces theory to define stability.
result Stability of ML models depends on topological properties of classification sets.
Mathematical theory of super fiber bundles and connections developed.
problem Modeling anticommuting fermionic fields in mathematical physics.
method Detailed introduction to super fiber bundles, relative supermanifolds, and connections; construction of parallel transport map.
result Construction and comparison of parallel transport map with other methods in the literature.
This paper offers a mathematical introduction to GANs.
problem Understanding GANs from a mathematical perspective.
method Mathematical analysis of GANs.
result Provides clarity for math-oriented students.
Mathematical framework for differential machine learning in finance.
problem Theoretical assumptions in financial models and their impact on machine learning algorithms.
method Rigorous mathematical framework for differential machine learning in finance.
result Theoretical grounding enhances the predictive capabilities of neural networks in financial applications.
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.
Survey on AI math foundations, focusing on neural networks.
problem Lack of rigorous mathematical foundation for AI.
method Survey and discussion of theoretical directions in AI.
result Discussion of open problems in AI math.
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.
Mathematical model predicts international trade and global economy dynamics.
problem Understanding complex international trade and economy interactions.
method Developed a mathematical model for non-equilibrium processes in open systems.
result Predicted model accurately reflects international trade and economy.
Mathematical models reveal key factors for engaging Gen Z at work.
problem Understanding and improving engagement of Generation Z employees.
method Correlation and cluster analyses on engagement surveys.
result Clear responsibilities and challenging work are essential for Gen Z employees.
Higher topos theory applied to physics.
problem No specific problem stated.
method Exposition of higher topos theory.
result No specific key result mentioned.
Quantum cohomology connects quantum physics with classical math.
problem Quantum cohomology's relevance in modern mathematics.
method Informal review and discussion of connections.
result Quantum cohomology still has significant relevance in mathematics.
These notes grew out of a lecture course on mathematical methods of classical physics for students of mathematics and mathematical physics at the master's level. Also, physicists with a strong interest in mathematics may find this text useful as a resource complementary to existing textbooks on classical physics. Topic…
A new deterministic method for symbolic regression finds mathematical expressions from data.
problem Finding mathematical expressions from datasets efficiently and reliably.
method Deterministic growth of simple expressions until they fit the data.
result Results are as good as other Machine Learning methods but in lower computational time.
Overview of Thurston's work in math.
problem None explicitly stated, focuses on Thurston's contributions.
method Presentation of significant results.
result Impact of Thurston's work on mathematics.
Riemann's mathematical papers contain many ideas that arise from physics, and some of them are motivated by problems from physics. In fact, it is not easy to separate Riemann's ideas in mathematics from those in physics. Furthermore, Riemann's philosophical ideas are often in the background of his work on science. The …
Graph neural networks can perform approximate reasoning in latent space for mathematical statements.
problem Can neural networks perform steps of approximate reasoning in a fixed dimensional latent space?
method Design and conduct an experiment using graph neural networks to predict rewrite-success of mathematical statements in a latent space.
result Graph neural networks can make non-trivial predictions about rewrite-success of statements in latent space.
Improves recommender systems using mathematical principles.
problem Accuracy and speed of recommender systems.
method Explains and analyzes mathematical principles and algorithms.
result Describes the strengths and weaknesses of mathematical distance methods.
Abstracts Higgs bundles without diving into geometry.
problem Understanding Higgs bundles without geometry.
method Informal linear algebra approach.
result Anticipates deeper structure in Higgs bundles moduli space.
This paper evaluates neural models' mathematical reasoning abilities.
problem Evaluating neural models' capability in solving mathematical problems.
method Developed a task suite of mathematics problems, analyzed two sequence-to-sequence architecture classes.
result Notable differences in models' ability to solve and generalize mathematical problems.
Paper examines two methods for FX market volatility modeling.
problem FX market volatility modeling problem.
method Classical econometric GCH and mathematical approaches (SSA, dynamical systems stability analysis).
result Both mathematical tools show promising results in FX market volatility modeling.
These lecture notes review the topological string theory and its applications to mathematics and physics. They expand on material presented at the Takagi Lectures of the Mathematical Society of Japan on 21 June 2008 at Department of Mathematics, Kyoto University.
Attribute-aware CF models aims at rating prediction given not only the historical rating from users to items, but also the information associated with users (e.g. age), items (e.g. price), or even ratings (e.g. rating time). This paper surveys works in the past decade developing attribute-aware CF systems, and discover…
In mathematical finance a popular approach for pricing options under some Levy model is to consider underlying that follows a Poisson jump diffusion process. As it is well known this results in a partial integro-differential equation (PIDE) that usually does not allow an analytical solution while numerical solution bri…
Classifies 85 tie knots into mathematical categories.
problem Classifying and understanding the mathematical properties of tie knots.
method Formal language and sequence of moves to describe tie knots, classification based on knot theory.
result Proves that any tie knot is prime and alternating.
This study optimizes crypto-market trading conditions without assuming convexity.
problem Optimizing crypto-market trading conditions without convexity.
method Rigorous mathematical analysis of constant function market makers under quasilinear trade functions.
result Quasilinear trade functions can replicate convex functions' robustness against arbitrage.
Investigates the effects of nondominated sets of probability measures in robust models of finance.
problem Uncertainty in financial models due to multiple possible probability measures.
method Analyzes various results from mathematical finance literature under the assumption of nondominated sets of probability measures.
result Many classical results in robust models do not hold when the set of measures is nondominated.
A tribute to Norbert A'Campo's life and mathematics.
problem None explicitly stated in the abstract.
method None explicitly stated in the abstract.
result No specific key result mentioned.
Jones Polynomial shows unity in math.
problem No specific problem stated.
method Discussion of Jones Polynomial.
result Illustrates unity between different mathematical fields.
Mathematical framework for language models processes text and predicts next tokens.
problem Understanding and optimizing the performance of large language models.
method Describes encoding, prediction models, learning from data, and deployment of LLMs.
result Demonstrates remarkable empirical successes and provides a platform for further research.
Optimal binning method for numeric targets using mathematical programming.
problem Optimizing the discretization of numeric variables for classification.
method Mathematical programming formulation for binary, continuous, and multi-class targets with constraints.
result Convex mixed-integer programming formulations for all target types.
LLMs struggle with arithmetic tasks unless they use high numerical precision.
problem Improving arithmetical reasoning capabilities of LLMs.
method Theoretical analysis and empirical experiments on numerical precision.
result LLMs require high numerical precision to efficiently handle arithmetic tasks.
Recent years have seen noteworthy progress in the mathematical formulation of quantum field theory and perturbative string theory. We give a brief survey of these developments. It serves as an introduction to the more detailed collection "Mathematical Foundations of Quantum Field Theory and Perturbative String Theory".