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.
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.
168,742 papers · 148 categories
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48 results for “mathematical problems”
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.
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.
Machine learning improves solving inverse problems and integrating data.
problem Solving complex inverse problems and integrating data effectively.
method Integrates machine learning techniques with inverse problems and data assimilation.
result Demonstrates machine learning's potential to enhance these fields.
Mathematical framework for minimum enclosing ball problem.
problem Determining the smallest sphere enclosing a set in d-dimensional space.
method Theoretical framework based on enclosing and partitioning theorems.
result Bounds and relations between circumradius, inradius, diameter, and width.
Mathematical reasoning---a core ability within human intelligence---presents some unique challenges as a domain: we do not come to understand and solve mathematical problems primarily on the back of experience and evidence, but on the basis of inferring, learning, and exploiting laws, axioms, and symbol manipulation ru…
A deep learning approach generates math word problems in multiple languages.
problem Template-based mechanisms for generating mathematical word problems lack customizability and creativity.
method Character Level Long Short Term Memory Network (LSTM) and POS tags are used to generate and resolve constraints in generated problems.
result The approach generates accurate math word problems in English and Sinhala with over 90% accuracy.
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.
This paper proposes a general duality framework for the problem of minimizing a convex integral functional over a space of stochastic processes adapted to a given filtration. The framework unifies many well-known duality frameworks from operations research and mathematical finance. The unification allows the extension …
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.
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.
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.
Mathematical Reinforcement Learning faces a 'Two-Hump' problem due to sparse rewards and a scarcity of intermediate 'hard-but-solvable' instances.
problem Mathematical search problems in Reinforcement Learning
method Novel data generation techniques and algorithmic enhancements
result Substantial performance improvements over previous baselines
This paper studies dynamic stochastic optimization problems parametrized by a random variable. Such problems arise in many applications in operations research and mathematical finance. We give sufficient conditions for the existence of solutions and the absence of a duality gap. Our proof uses extended dynamic programm…
Shapley values for feature importance lead to mathematical and practical issues.
problem Mathematical and practical issues with Shapley values for feature importance.
method Game-theoretic formulations of feature importance using Shapley values.
result Mathematical problems arise when using Shapley values for feature importance.
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.
Python module for RL trading in limit order books.
problem Training RL agents for algorithmic trading in limit order books.
method Model-based gym environments for reinforcement learning.
result Efficient RL training for trading problems.
The paper proves geometric properties of square tables and saddle surfaces.
problem The mathematical table problem from a geometric-topological perspective.
method Geometric-topological proofs on cylinder, saddle surfaces, and level sets of Fenn graphs.
result Zero-existence theorem on a cylinder, proving Fenn's square-table theorem under different boundary conditions.
We establish higher-order weighted Sobolev and Holder regularity for solutions to variational equations defined by the elliptic Heston operator, a linear second-order degenerate-elliptic operator arising in mathematical finance. Furthermore, given -smooth data, we prove -regularity of solutions up t…
The abstract discusses open problems in isoparametric theory.
problem Open problems in isoparametric theory.
method Survey and propose open problems.
result Discussion of open problems in isoparametric theory.
Deep learning finds mathematical equations from data.
problem Discovering underlying mathematical expressions from datasets.
method Uses a recurrent neural network to search for mathematical expressions and optimizes using a risk-seeking policy gradient.
result Outperforms existing methods in recovering exact symbolic expressions.
Novel tests for genetic independence in high-dimensional data.
problem Testing independence in genetics studies with many variables.
method Defining premetric structures on genetic data support spaces.
result Solid theoretical framework and computationally-efficient implementations.
Extends Itô's formula for path-dependent functions in finance.
problem Modeling and hedging of path-dependent financial options.
method Functional extension of Itô's formula for C^{0,1}-functions of continuous weak Dirichlet processes.
result Validates the hedging or superhedging problems for path-dependent options.
This article investigates a new gauge theoretic approach to Einstein's equations in dimension 4. Whilst aspects of the formalism are already explained in various places in the mathematics and physics literature, our first goal is to give a single coherent account of the theory in purely mathematical language. We then e…
Classically time is kept fixed for infinitesimal variations in problems in mechanics. Apparently, there appears to be no mathematical justification in the literature for this standard procedure. This can be explained canonically by unveiling the intrinsic mathematical structure of time in Lagrangian mechanics. Moreover…
The aim of this paper is to offer an overview of the most important applications of Jordan structures inside mathematics and also to physics, up-dated references being included. For a more detailed treatment of this topic see - especially - the recent book Iordanescu [364w], where sugestions for further developments ar…
LLMs will inevitably hallucinate due to their mathematical structure.
problem The inherent limitations of Large Language Models (LLMs).
method Analysis of LLMs using computational theory and Godel's Incompleteness Theorem.
result Hallucinations in LLMs are an inevitable feature, not just errors.
Mathematical framework for transfer learning feasibility and transfer risk.
problem Theoretical analysis of transfer learning.
method Reformulated transfer learning as an optimization problem, introduced transfer risk concept.
result Demonstrated the potential and benefits of incorporating transfer risk in transfer learning evaluation.
We propose a simple mathematical model for unemployment. Despite its simpleness, we claim that the model is more realistic and useful than recent models available in the literature. A case study with real data from Portugal supports our claim. An optimal control problem is formulated and solved, which provides some non…
Mathematical advances needed for Digital Twins, differing from traditional models.
problem Foundational mathematical advances required for Digital Twins.
method Multi-scale, multi-physics modeling and coupling, different reliability criteria and uncertainty assessments.
result AI/ML methods can perform well in biomedical problems but fail in simple engineering systems.
New methods solve complex PDEs with mixed boundary conditions.
problem Solving inhomogeneous Robin type boundary value problems for linear PDEs.
method Odd and even Hilbert transforms.
result Non-standard solutions to various PDEs in finance, stochastic analysis, etc.
Mathematical models with time dependent parameters are of great interest in financial Mathematics because they capture real life scenarios in the financial market. In this study, via the Lie group technique, we analyse evolution-type equations with time dependent parameters and give the general symmetry structure of th…
We solve the problem of optimal stopping of a Brownian motion subject to the constraint that the stopping time's distribution is a given measure consisting of finitely-many atoms. In particular, we show that this problem can be converted to a finite sequence of state-constrained optimal control problems with additional…
We prove Transformers can learn diverse Gröbner bases.
problem Training Transformers for Gröbner basis computation.
method Prove generality of dataset generation algorithm; propose extended algorithm.
result Datasets are sufficiently general for diverse Gröbner bases learning.
Paper proposes a math-inspired L2O model for better generalization.
problem Overfitting and poor generalization of generic L2O models.
method Derived mathematical conditions for successful update rules and proposed a novel L2O model.
result Proposed model outperforms generic L2O models in out-of-distribution settings.
The Heston stochastic volatility process, which is widely used as an asset price model in mathematical finance, is a paradigm for a degenerate diffusion process where the degeneracy in the diffusion coefficient is proportional to the square root of the distance to the boundary of the half-plane. The generator of this p…
FX Market Volatilityq-fin.MF
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.
The main purpose of this paper is to formalize the modelling process, analysis and mathematical definition of corruption when entering into a contract between principal agent and producers. The formulation of the problem and the definition of concepts for the general case are considered. For definiteness, all calculati…
Prob2Vec embeds problems for adaptive tutoring, achieving high similarity accuracy.
problem Retrieve problems with similar mathematical concepts for adaptive tutoring.
method Hierarchical problem embedding algorithm (Prob2Vec) combining abstraction and embedding steps.
result 96.88% accuracy on problem similarity test, significantly outperforming state-of-the-art sentence embedding methods.
Deep learning models are growing, posing new mathematical challenges.
problem Mathematical challenges in training, inference, generalization, and optimization of deep models.
method Formal mathematical analysis and communication with mathematicians, statisticians, and computer scientists.
result A set of new mathematical challenges in deep learning.
Math proves deep learning unstable, despite stable neural networks existing.
problem Unstable neural networks in deep learning despite stable ones existing.
method Mathematical proof showing instability of current training procedures.
result Proven existence of stable and accurate neural networks with variable dimensions, but current algorithms cannot compute them.
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…
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 …
Mathematical framework for understanding attention in neural networks.
problem Lack of theoretical understanding of attention in neural networks.
method Proposes a measure-theoretic model of attention and interprets self-attention as a system of self-interacting particles.
result Shows that attention is Lipschitz-continuous under suitable assumptions.
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.
Mathematical study of learning long-term integration in linear RNNs.
problem How do linear recurrent neural networks learn to integrate over long timescales?
method Analytical study of linear RNNs trained to integrate white noise and damped oscillatory filters.
result Learning dynamics are described by low-dimensional effective equations for outlier eigenvalues.
Solves financial and non-financial problems using heat potentials.
problem Calibrating default boundaries, calculating default probabilities, and finding hitting time probabilities.
method Classical method of heat potentials, recently extended by the author.
result Successfully solved several financial and non-financial problems.
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.