Analyzes properties of Hopf manifolds from analytic and metric perspectives.
problem Properties of Hopf manifolds
method Analytic and metric structure
result Reviews old and new properties of Hopf manifolds
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48 results for “analytic perspective”
GANs analyzed for performance and training issues.
problem Performance and training issues of GANs.
method SDE approximations for training GANs.
result Improved understanding of GANs through analytical perspectives.
Review of Gerber-Shiu function for practical actuarial science.
problem Difficulty in numerical approximation and statistical inference of Gerber-Shiu function.
method Comprehensive review of formulations, surplus processes, numerical methods, and statistical inference.
result Enhanced understanding and practical guide for Gerber-Shiu function.
In the present work we propose an original analytical model of coopetitive game. We try to apply this analytical model of coopetition - based on game theory and conceived at a macro level - to the Greek crisis, suggesting feasible solutions in a cooperative perspective for the divergent interests which drive the econom…
Unified geometric perspectives on PDEs, torsion invariants, and moduli theory.
problem Index theory and analytic torsion of nonlinear PDEs.
method Microlocal sheaf theory, factorization algebras, Spencer hypercohomology.
result Unified geometric perspectives on PDEs, torsion invariants, and moduli theory.
The Minority Game: a statistical physics perspectivecond-mat.dis-nn
A brief review is given of the minority game, an idealized model stimulated by a market of speculative agents, and its complex many-body behaviour. Particular consideration is given to analytic results for the model rather than discussions of its relevance in real-world situations.
Paper proves gluing formula for analytic torsions using Witten deformation for non-Morse functions.
problem Analyzing analytic torsions for non-Morse functions.
method Witten deformation, Mayer-Vietoris sequences, Vishik's theory of moving boundary problems.
result Novel, purely analytic proof of the gluing formula for analytic torsions.
Analyzes Kodaira-Iitaka dimension and multiplicity using intersection theory.
problem Understanding Kodaira-Iitaka dimension and multiplicity in analytic terms.
method Expresses dimensions and multiplicity in terms of intersection theory of plurisubharmonic envelopes.
result Introduces non-pluripolar numerical Kodaira-Iitaka dimension and shows it dominates the classical dimension.
Paper proposes a new method for learning business process representations.
problem Challenges in capturing all useful information in business process data.
method Combines Gramian Angular Fields and Convolutional Neural Networks for representation learning.
result Demonstrates effectiveness of the approach through visualization and multiple process prediction tasks.
Tensor completion is a problem of filling the missing or unobserved entries of partially observed tensors. Due to the multidimensional character of tensors in describing complex datasets, tensor completion algorithms and their applications have received wide attention and achievement in areas like data mining, computer…
Interactive model analysis, the process of understanding, diagnosing, and refining a machine learning model with the help of interactive visualization, is very important for users to efficiently solve real-world artificial intelligence and data mining problems. Dramatic advances in big data analytics has led to a wide …
Develops Lie-theoretic perspective on Hitchin's equations for cyclic G-Higgs bundles.
problem Analytic and geometric properties of harmonic maps.
method Lie-theoretic perspective on Hitchin's equations for cyclic G-Higgs bundles.
result Proves Dai-Li's conjecture on the monotonicity of the energy density and negative curvature conjecture for Coxeter cyclic G-Higgs bundles.
GNNs improve supply chain analytics with real-world benchmarks.
problem Limited research on applying GNNs to supply chain management.
method Conceptual discussions, detailed formulations, examples, mathematical definitions, and task guidelines.
result GNN-based models outperform other methods by 10-40% in various supply chain tasks.
Recently, deep learning has been advancing the state of the art in artificial intelligence to a new level, and humans rely on artificial intelligence techniques more than ever. However, even with such unprecedented advancements, the lack of explanation regarding the decisions made by deep learning models and absence of…
Leveraging Big Data Analytics in Healthcare Enhancement: Trends, Challenges and Opportunitiesstat.OT
Big data analytics improves healthcare through early detection and quality life.
problem Limited access to healthcare data hinders evidence-based decision-making.
method Analysis of healthcare data using various tools and techniques.
result Big data analytics enhances healthcare quality and patient outcomes.
Unified framework for comparing clusterings from information-theoretic and pair-counting perspectives.
problem Divergent evaluations of unsupervised models due to different clustering similarity measures.
method Developed an analytical framework that unifies pair-counting and information-theoretic clustering similarity measures.
result Unified framework clarifies when and why the two regimes diverge and provides a principled basis for selecting and interpreting clustering similarity measures.
New framework uses elliptic operators to study projective maps.
problem Understanding projective structures on Riemannian manifolds.
method Develops two elliptic operators of second and fourth order.
result Establishes a natural correspondence between analytical and geometric properties.
We present a new algorithm for approximate inference in probabilistic programs, based on a stochastic gradient for variational programs. This method is efficient without restrictions on the probabilistic program; it is particularly practical for distributions which are not analytically tractable, including highly struc…
Dropout regularizes against high-order interactions by canceling interaction rates.
problem Overfitting to high-order interactions in neural networks.
method Analyzes Dropout through the lens of interaction effects, showing how it effectively cancels out the probability of surviving interactions of different orders.
result Dropout regularizes against high-order interactions by effectively canceling out the probability of surviving interactions of different orders.
We prove that any steady solution to the real analytic Euler equations on a Riemannian 3-sphere must possess a periodic orbit bounding an embedded disc. One key ingredient is an extension of Fomenko's work on the topology of integrable Hamiltonian systems to a degenerate case involving stratified integrals. The result …
We study isometric maps between Teichmüller spaces and bounded symmetric domains in their intrinsic Kobayashi metric. From a complex analytic perspective, these two important classes of geometric spaces have several features in common but also exhibit many differences. The focus here is on recent results proved by the …
Study proposes explainable analytics for manufacturing process planning.
problem Improving data-driven decision-making in manufacturing.
method Combines process mining, machine learning, and XAI. Uses deep learning for prediction and Shapley values/ICE plots for explanations.
result Enhanced decision-making capabilities through local post-hoc explanations.
A new CoVaR framework integrates expert views using entropy pooling.
problem Risk assessment and spillover effects from diverse expert views.
method Entropy pooling method to integrate expert views and compute general CoVaR.
result General CoVaR shows linear relationships with expectations and differences in expectations, and nonlinear dependencies with variance, quantiles, and correlation.
Reinterprets quantization commutes with reduction using KK-theory.
problem Quantization commutes with reduction in geometric quantization.
method Uses KK-theory and recent formalism by Kasparov to simplify and clarify the index theoretic parts.
result Shows conceptual simplifications and clearer relationship to Ma-Tian-Zhang approach.
Geometrically studies Moore-Penrose inverse and polar decomposition continuity.
problem Continuity of Moore-Penrose inverse for perturbations by operator ideals.
method Geometric construction using essential codimension and Banach-Lie group action.
result Moore-Penrose inverse is a real analytic map between manifolds.
We show that any compact half-conformally flat manifold of negative type, with bounded energy, sufficiently small scalar curvature, and a non-collapsing assumption, has all betti numbers bounded. We show that this result is optimal from an analytic perspective by demonstrating singularity models that are 2-ended,…
In 1967, Japanese physicist Morikazu Toda published the seminal papers exhibiting soliton solutions to a chain of particles with nonlinear interactions between nearest neighbors. In the decades that followed, Toda's system of particles has been generalized in different directions, each with its own analytic, geometric,…
In this pedagogical study, carried out by adopting standard mathematical methods of nonlinear dynamics, we have presented some simple analytical models to understand terminal behaviour in industrial growth. This issue has also been addressed from a dynamical systems perspective, with especial emphasis on the concept of…
A Comprehensive Survey on Enterprise Financial Risk Analysis from Big Data and LLMs Perspectiveq-fin.RM
This paper surveys enterprise financial risk analysis from Big Data and LLMs perspectives.
problem Predicting future financial risk of enterprises.
method Systematic literature review of enterprise financial risk analysis approaches from Big Data and LLMs perspectives.
result Offers a holistic synthesis of research methods and key insights.
Analyzes metric spaces homeomorphic to manifolds, proving rigidity and inequalities.
problem Analyzing metric spaces homeomorphic to manifolds.
method Geometric and analytic approaches, proving existence of integral currents, establishing rigidity and inequalities.
result Metric manifolds admit non-trivial integral currents and satisfy isoperimetric inequalities.
Flat tori found non-isometric pairs with identical Laplace eigenvalues.
problem Finding the lowest dimension for isospectral non-isometric flat tori.
method Analytic, geometric, and number theoretic approaches.
result Schiemann resolved the isospectral problem for flat tori in the 1990s.
We tackle the problem of multi-task learning with copula process. Multivariable prediction in spatial and spatial-temporal processes such as natural resource estimation and pollution monitoring have been typically addressed using techniques based on Gaussian processes and co-Kriging. While the Gaussian prior assumption…
Unified interpretation of sub-Riemannian Gauss-Bonnet theorem for surfaces in 3D contact manifolds.
problem Proving a sub-Riemannian Gauss-Bonnet theorem for surfaces in 3D contact manifolds.
method Measure-theoretic perspective, focusing on singular measures and characteristic points.
result Unified interpretation of previous results and natural geometric conditions for the theorem.
A method for ranking items using distance-based learning from positive and unlabeled data.
problem Learning to rank items without an analytic description of what constitutes a good ranking.
method Combining representations using an integer linear program for ranking items based on nominations.
result The method is effective in simulation and real data examples, especially when supervision is light.
FLORAS uses orthogonal sequences for SISO FL, offering both DP and convergence guarantees.
problem Privacy-preserving wireless federated learning in SISO systems.
method Leverages orthogonal sequences to eliminate CSIT requirement and provide DP guarantees.
result FLORAS achieves a smooth tradeoff between convergence rate and DP levels.
Develops Weil bundles over \( p \)-adic manifolds for arithmetic geometry.
problem Connecting differential calculus and arithmetic geometry over \( p \)-adic fields.
method Systematic theory of Weil bundles, developing analytic structures.
result Establishes canonical analytic structures on Weil bundles and their cohomological comparison.
A Bornological Perspective on the Representability of Derived Moduli Stacks of Solutions to PDEsmath.AG
New theory proves representability of PDE solutions without complex machinery.
problem Proving representability of PDE solutions using traditional methods is difficult.
method Developed a new model of derived differential geometry using -bornological rings.
result Representability of derived moduli stacks of PDE solutions naturally follows from an Artin-Lurie style theorem.
Study inert and ambiguous classes in modular group using combinatorial methods.
problem Counting inert and ambiguous conjugacy classes in modular group.
method Purely combinatorial approach using word length in free product representation.
result Exact counting formulas and asymptotic growth rates for inert and ambiguous classes.
Inferring Volatility in the Heston Model and its Relatives -- an Information Theoretical Approachq-fin.ST
Stochastic volatility models describe asset prices as driven by an unobserved process capturing the random dynamics of volatility . Here, we quantify how much information about can be inferred from asset prices in terms of Shannon's mutual information . This motivates a careful nume…
This paper explores how NLP enhances insurance data analysis.
problem Traditional insurance data limitations and need for alternative data.
method Application of NLP techniques to transform and analyze unstructured text data.
result NLP techniques improve insurance data analysis and risk assessment.
Given a matrix , a linear feasibility problem (of which linear classification is a special case) aims to find a solution to a primal problem or a certificate for the dual problem which is a probability distribution . Inspired by the continued importance of "large-margin cla…
Bayesian interpretation of deep ensembles improves uncertainty quantification.
problem Improving uncertainty estimation in deep learning models.
method Viewing deep ensembles as an approximate Bayesian method and specifying corresponding assumptions.
result Improved approximation leads to larger epistemic uncertainty, potentially more reliable predictions.
We give a combinatorial description of the Legendrian contact homology algebra associated to a Legendrian link in or any connected sum , viewed as the contact boundary of the Weinstein manifold obtained by attaching 1-handles to the 4-ball. In view of the surgery formula for symplec…
Analyzes multi-day stock returns, showing linear volatility and mean dependence.
problem Linear dependence of volatility and mean in accumulated stock returns.
method Modified Jones-Faddy skew t-distribution analysis.
result Linear dependence of volatility and mean on the number of days of accumulation.
Every year at the United Nations, member states deliver statements during the General Debate discussing major issues in world politics. These speeches provide invaluable information on governments' perspectives and preferences on a wide range of issues, but have largely been overlooked in the study of international pol…
Ridge regression reveals surprising high-dimensional behaviors via random matrix theory.
problem Understanding power-law scalings in high-dimensional regression models.
method Random matrix theory and free probability.
result Analytic formulas for training and generalization errors derived from -transform.
Cluster analysis of very high dimensional data can benefit from the properties of such high dimensionality. Informally expressed, in this work, our focus is on the analogous situation when the dimensionality is moderate to small, relative to a massively sized set of observations. Mathematically expressed, these are the…
Bayesian graph contrastive learning improves uncertainty quantification for graph analytics.
problem Uncertainty quantification for node representations in graph contrastive learning.
method Proposes a Bayesian framework to learn stochastic encoders representing nodes as distributions, providing uncertainty estimates.
result Significant improvement in performance on benchmark datasets compared to existing methods.