Paper extends known α-minimizing hypercones using polynomial analysis.
problem Limitations in the class of known α-minimizing hypercones. method Sub-calibration methods and analysis of cubic and quartic polynomials.
result Significantly extended class of α-minimizing hypercones. We show the area-minimality property of all homogeneous area-minimizing hypercones in Euclidean spaces (classified by Lawlor) following Lawson's original idea in his 72' Trans. A.M.S. paper "The equivariant Plateau problem and interior regularity". Moreover, each of them enjoys (coflat) calibrations singular only at th…
Characterizes harmonic morphisms preserving minimal submanifolds and finds novel area-minimising hypercones.
problem Understanding harmonic morphisms and their relationship to minimal submanifolds.
method Characterization of harmonic morphisms as weakly horizontally conformal maps preserving minimal submanifold equations, derivation of reduction properties for other co-dimensions, application to find novel area-minimising hypercones.
result Novel family of degree 4 area-minimising hypercones in R^m, m≥32.
Study compares nodal sets of solutions to the Allen-Cahn equation.
problem Comparing nodal sets of solutions to the Allen-Cahn equation with conical asymptotics.
method Maximum principle for linearized operator on unbounded domains.
result Positive phase uniquely determines the solution and enforces global ordering.
The study proves that certain stable minimal hypersurfaces must be cylindrical.
problem Characterizing stable minimal hypersurfaces in Euclidean space.
method Analyzing the density at infinity and using stable area minimizing hypercone properties.
result Stable minimal hypersurfaces with specific conditions are cylindrical.
Rectifying curves on hypercones are geodesics, characterized in higher dimensions.
problem Characterizing rectifying curves in higher-dimensional spaces.
method Extending results from Chen (2017) to higher dimensions, using hypercones and hyperplanes.
result Rectifying curves on hypercones are geodesics, and these curves can be mapped to spherical curves in higher dimensions.
Extends isoparametric foliations and area-minimizing cones in product manifolds.
problem Generalizing isoparametric foliations and area-minimizing cones in SnimesSn. method Analyzes isoparametric foliations and area-minimizing cones, extending known results.
result Extends known area-minimizing cones to codimension-two cases, yielding infinitely many families of area-minimizing subcones.
We show that every area-minimizing hypercone and every oriented Lawlor cone in [Law91] can be realized as a tangent cone at a point of some homologically area-minimizing singular compact submanifold. In particular this generalizes the result of N. Smale [Sma99].
Smooths out complex shapes into simpler forms.
problem Transforming complex shapes into simpler, smooth forms.
method Perturbing minimizing hypercones and viscosity mean convex cones into smooth, properly embedded hypersurfaces.
result Properly embedded smooth minimizing hypersurfaces and self-expanders are achieved.
We prove that the density of a topologically nontrivial, area-minimizing hypercone with an isolated singularity must be greater than the square root of 2. The Simons' cones show that this is the best possible constant. If one of the components of the complement of the cone has nontrivial kth homotopy group, we prove a …
Paper constructs flows converging to cones and foliations.
problem Understanding mean curvature flow convergence to cones and foliations.
method Constructs a family of mean curvature flows converging to cones and foliations under specific conditions.
result Flow converges to area minimizing, strictly stable hypercone and Hardt-Simon foliation of the cone.
Construct locally minimizing (1,2)-clusters with prescribed asymptotic geometry.
problem Minimizing clusters with prescribed asymptotic geometry.
method Develop a refined construction using the Hardt-Simon foliation.
result Produce a countably infinite family of distinct locally minimizing clusters asymptotic to a singular area-minimizing hypercone.
Extends a Liouville theorem for stable minimal hypersurfaces.
problem Stable minimal hypersurfaces in cylindrical cones.
method Analyzes the density and foliation of minimal hypersurfaces.
result Shows that stable minimal hypersurfaces are cylindrical.
The paper studies canal hypersurfaces in Lorentz-Minkowski 4-space.
problem Characterizing canal hypersurfaces in Lorentz-Minkowski 4-space.
method Analyzing geometric invariants and conditions for canal hypersurfaces.
result Characterizations of canal hypersurfaces, including flatness and minimality conditions.
The study characterizes canal hypersurfaces in Euclidean spaces and their curvature properties.
problem Characterizing canal hypersurfaces in Euclidean spaces.
method Analyzing canal hypersurfaces in Euclidean n-space, focusing on E4, computing curvature properties, and proving specific cases.
result Flat canal hypersurfaces in Euclidean 4-space are only circular hypercylinders or circular hypercones, and minimal canal hypersurfaces are only generalized catenoids.
Paper proves minimal surfaces near quadratic cones have specific smooth structure.
problem Characterize minimal surfaces near quadratic cones.
method Analyzes n-varifolds in the unit ball close to a minimizing quadratic cone. result Singularities modeled on these cones determine the local structure of nearby minimal surfaces.
The paper studies stability and minimizing properties of higher codimensional surfaces in Euclidean space.
problem Stability and minimizing properties of higher codimensional surfaces in Euclidean space.
method Analyzes surfaces associated with the weighted area-functional and proves stability and minimization properties under specific conditions.
result Minimal cones with globally flat normal bundles are f-stable, and highly singular determinantal varieties and Pfaffian varieties are f-minimizing. Efficient private matrix analysis algorithms for recent variants.
problem Private analysis of recent matrix updates.
method Identifying sufficient conditions on positive semidefinite matrices.
result First efficient differentially private algorithms for various matrix analysis tasks.
This paper introduces compositional data analysis for financial ratios, improving industry-level analysis.
problem Statistical issues with standard financial ratios at industry level.
method Compositional data analysis techniques for financial ratios.
result Improved analysis of financial ratios using compositional data methods.
In this dissertation, the main goal is visualisation of financial time series. We expect that visualisation of financial time series will be a useful auxiliary for technical analysis. Firstly, we review the technical analysis methods and test our trading rules, which are built by the essential concepts of technical ana…
Paper combines geometry and time-series analysis for spatiotemporal data.
problem Multivariate time-series data from multiple sensors.
method Combines manifold learning, Riemannian geometry, and spectral analysis.
result Proposes Riemannian multi-resolution analysis (RMRA) for dynamic mode extraction.
In this paper the exact linear relation between the leading eigenvectors of the modularity matrix and the singular vectors of an uncentered data matrix is developed. Based on this analysis the concept of a modularity component is defined, and its properties are developed. It is shown that modularity component analysis …
Paper uses dynamic analysis to detect malware with PHMMs.
problem Malware detection using static and dynamic analysis techniques.
method Hidden Markov Models (HMMs) and Profile Hidden Markov Models (PHMMs) trained on API call sequences.
result PHMMs outperform HMMs in malware detection.
This paper investigates to identify the requirement and the development of machine learning-based mobile big data analysis through discussing the insights of challenges in the mobile big data (MBD). Furthermore, it reviews the state-of-the-art applications of data analysis in the area of MBD. Firstly, we introduce the …
Interactive DR framework for comparing datasets.
problem Limited flexibility in existing DR methods for comparative analysis.
method Unified linear comparative analysis (ULCA) with interactive optimization and visualization.
result ULCA and optimization algorithm improve comparative analysis efficiency and flexibility.
This paper reviews R packages for automating data analysis tasks.
problem Time-consuming Exploratory Data Analysis in large, noisy data sets.
method Systematic review of 12 R packages for autoEDA.
result Identifies automated tasks and areas for future development.
Improves transparency of deep neural networks through feature and consistency analysis.
problem Black-box nature of deep learning inference limits transparency for safety-critical systems.
method Structural and linguistic feature analysis, consistency analysis.
result 75% of human workers found input data and results consistent, 70% found inference and results consistent.
Proposes a method to optimize class mean preservation in kernel-based feature spaces.
problem Optimizing the selection of kernel subspace for better performance.
method Component analysis method for kernel-based dimensionality reduction that optimally preserves class mean distances.
result Discriminant analysis version of the proposed method provides insights into feature space properties.
Combines topological and geometric approaches to data analysis.
problem Understanding when and how geometric objects intersect.
method Connects topological and geometric concepts of curvature.
result Reconceptualizes curvature and links it to hyperconvexity.
Proposes a multivariate regression model for better analysis of multiple datasets.
problem Insufficient performance of single-dataset analysis in integrative studies.
method Sparse estimation for variable and group selection, alternating direction method of multipliers algorithm.
result Demonstrated improved performance through simulations and real data analysis.
New method uses topological data analysis to study stock market crashes.
problem Characterizing and predicting stock market crashes.
method Topological data analysis, persistence landscape, dynamic time series analysis.
result Demonstrates effectiveness of new method for Flash Crash characterization and prediction.
Analyzes stock trends and e-commerce user behavior using Twitter data.
problem Understanding the relationship between stock prices, stock news, and e-commerce user behavior.
method Cross-domain analysis using Hadoop, Hive, and Tableau on three datasets.
result Identified correlations between stock sentiment, stock trends, and e-commerce user behavior.
Genetic programming optimizes Gaussian kernels for better sentiment analysis.
problem Improving accuracy of sentiment analysis in text.
method Genetic Programming applied to evolve more effective Gaussian kernels.
result The evolved kernels outperform traditional Gaussian Processes in sentiment analysis.
Analyzes changes in cryptocurrency market structure.
problem Understanding shifts in cryptocurrency market dynamics.
method Structural change analysis techniques.
result Identifies key structural changes in the market.
Study analyzes Disney stock market performance using machine learning.
problem Forecasting stock market performance of Disney.
method Exploratory data analysis, feature engineering, model selection (linear regression).
result Linear regression model performed best.
This study analyzes data science vocabulary changes over 13 years.
problem Understanding evolution of data science terms over time.
method Exploratory Data Analysis, Latent Semantic Analysis, Latent Dirichlet Analysis, N-grams Analysis.
result Identified new vocabulary and its incorporation into scientific literature.
FinSphere improves stock analysis quality with AI and expert-curated data.
problem Lack of objective evaluation metrics and depth in stock analysis by FinLLMs.
method Developed AnalyScore, curated Stocksis dataset, and FinSphere AI agent.
result FinSphere outperforms general and domain-specific LLMs in generating high-quality stock analysis reports.
Random forest identifies key features for diagnosing machine faults.
problem Identifying specific factors causing machine faults.
method Gaussian mixture model clustering, spectrum analysis, random forest classification.
result Identified significant features for different machine states.
This study examines whether PCA can effectively identify nitrogen pollution sources in rivers.
problem Identifying pollution sources in rivers for effective environmental management.
method Principal Component Analysis and its modifications, along with Independent Component Analysis and Factor Analysis, are applied to nitrogen pollution source identification.
result PCA and related techniques can be powerful tools for uncovering nitrogen pollution sources in rivers.
We present a unifying framework which reduces the construction of probabilistic component analysis techniques to a mere selection of the latent neighbourhood, thus providing an elegant and principled framework for creating novel component analysis models as well as constructing probabilistic equivalents of deterministi…
Paper introduces probabilistic methods to approximate archetypal analysis, reducing complexity.
problem Inherent computational complexity of archetypal analysis limits its practical applicability.
method Two preprocessing techniques: dimensionality reduction and representation cardinality reduction, using probabilistic geometry.
result The method effectively reduces scaling and provides near-optimal solutions for prediction errors.
DeepCAM learns convolutional dictionaries for image processing.
problem Processing high-dimensional signals like images efficiently.
method Introduces a Deep Convolutional Analysis Dictionary Model (DeepCAM) using convolutional dictionaries.
result DeepCAM achieves performance comparable to other methods on single image super-resolution.
Improved LDA method for better classification and dimensionality reduction.
problem Improving linear discriminant analysis for better classification performance.
method Integrates spectrally-corrected covariance matrix and regularized discriminant analysis.
result SRLDA has a linear classification global optimal solution under spiked model assumption.
CDVI improves variational inference for survival analysis by considering censoring mechanisms.
problem Challenges in applying variational methods to survival data, especially the dependence on censoring.
method Censor-dependent variational inference (CDVI) tailored for latent variable models in survival analysis.
result Significant improvements in estimating individual survival distributions.
Prototypal analysis is introduced to overcome two shortcomings of archetypal analysis: its sensitivity to outliers and its non-locality, which reduces its applicability as a learning tool. Same as archetypal analysis, prototypal analysis finds prototypes through convex combination of the data points and approximates th…
Survey on spectral embeddings for data analysis.
problem None explicitly stated in the abstract.
method Presentation of spectral embeddings from Riemannian geometry to data analysis.
result Survey of spectral embeddings and their applications.
Improved analysis of UCBVI algorithm with better empirical performance.
problem Improving the UCBVI algorithm's performance and understanding its bounds.
method Refined analysis of UCBVI algorithm with improved bonus terms and regret analysis.
result Improving multiplicative constants in UCBVI bounds enhances empirical performance.
Reduces survival analysis to common regression tasks.
problem Applying standard machine learning tools to survival analysis.
method Various reduction techniques to simplify survival analysis.
result Benchmark analysis shows improved predictive performance.