The study proposes algorithms to minimize rating discordance in missing data.
problem Missing ratings in combined rating lists.
method Optimization models and algorithms that minimize total rating discordance.
result The proposed methods outperform state-of-the-art imputation methods in accuracy.
Advances neural tri-factorization for clustering and discordance analysis of multi-typed data.
problem Challenges in analyzing heterogeneous, multimodal relational data.
method Deep collective matrix tri-factorization for spectral clustering and cluster association learning.
result Demonstrates efficacy over previous non-neural approaches in clustering and discordance analysis.
New method finds local anomalies in time series by considering context information.
problem Finding anomalous subsequence in long time series is difficult.
method Introduces semantic discord, an approach that incorporates context information.
result Significantly outperforms state-of-the-art methods in locating anomalies.
Motivated by the sampling problems and heterogeneity issues common in high- dimensional big datasets, we consider a class of discordant additive index models. We propose method of moments based procedures for estimating the indices of such discordant additive index models in both low and high-dimensional settings. Our …
Ideas from deformation quantization applied to algebras with one generator lead to methods to treat a nonlinear flat connection. It provides us elements of algebras to be parallel sections. The moduli space of the parallel sections is studied as an example of bundle-like objects with discordant (sogo) transition functi…
Study uses sentiment analysis to predict cryptocurrency token returns in virtual reality.
problem Predicting cryptocurrency token returns in virtual reality economies.
method Used BERT for sentiment analysis and developed LSTM models integrating multi-modal features.
result Multi-modal model significantly outperforms price-only baseline in prediction accuracy.
The last decade has seen a flurry of research on all-pairs-similarity-search (or, self-join) for text, DNA, and a handful of other datatypes, and these systems have been applied to many diverse data mining problems. Surprisingly, however, little progress has been made on addressing this problem for time series subseque…
SDSR reconstructs species trees from genetic markers efficiently.
problem Challenges in reconstructing species trees from genetic data.
method Spectral divide-and-conquer approach based on graph theory.
result SDSR achieves up to 10-fold faster runtime with comparable accuracy.
New algorithm detects unique events in time series data.
problem Detecting anomalous events in unknown properties.
method Model-free, unsupervised detection using Temporal Outlier Factor (TOF).
result TOF outperforms traditional outlier detection methods.
Proposes an optimization framework for sparse robust subspace estimation.
problem Sparse robust one-dimensional subspace estimation.
method l1-norm regularization, linear relaxation, simple ratios, sorting techniques.
result Achieves global optimality for sparse robust subspace with polynomial time efficiency.
Supervised machine learning models boast remarkable predictive capabilities. But can you trust your model? Will it work in deployment? What else can it tell you about the world? We want models to be not only good, but interpretable. And yet the task of interpretation appears underspecified. Papers provide diverse and s…
We show how the problem of estimating conditional Kendall's tau can be rewritten as a classification task. Conditional Kendall's tau is a conditional dependence parameter that is a characteristic of a given pair of random variables. The goal is to predict whether the pair is concordant (value of 1) or discordant (val…
Study finds significant price declines and capital reallocation from centralized to decentralized exchanges after FTX collapse.
problem Quantifying trust dynamics and redistribution between centralized and decentralized exchanges.
method Interdisciplinary approach combining causal inference and computational text analysis.
result Significant price declines and capital reallocation from centralized to decentralized exchanges following the FTX collapse.
Optimizes choice sets to influence group decisions.
problem Maximizing agreement or disagreement in group decisions.
method Discrete choice modeling to develop optimization framework.
result Promoting a choice can be easier than encouraging consensus or discord.
Minimal networks minimize length and mass in certain configurations.
problem Finding minimal networks that minimize length and mass.
method Global and local calibrations to prove minimization properties.
result Minimal networks minimize mass and interfaces in partitions.
The study finds conditions for area-minimizing cones over submanifolds.
problem Conditions for area-minimizing cones over submanifolds.
method General configuration results for area-minimizing cones.
result Cone over the minimal product of submanifolds and spheres are area-minimizing.
The paper studies deformations of singular minimal hypersurfaces in dimensions 7 and above.
problem The behavior of singular minimal hypersurfaces in dimensions 7 and above.
method Analyzes the local behavior of minimal hypersurfaces under perturbations and convergence of families of hypersurfaces.
result Existence and smoothness of nearby minimal hypersurfaces under perturbations, uniqueness of homological minimization, and existence of Jacobi fields.
Minimal surfaces in 3-sphere created by reflections from polygons, with new examples based on pentagons.
problem Constructing minimal surfaces in 3-sphere using reflections.
method Minimal n-gon solves free boundary problem; curvature lines combinatorics investigated. result New examples of minimal reflection surfaces based on pentagons.
Study on minimal surfaces in a 3D space with 2m-norm.
problem Characterizing minimal surfaces in a specific geometric space.
method Examining translation, homothetical, and separable minimal surfaces.
result New insights into minimal surfaces in a 3D space with 2m-norm.
Some elementary considerations are presented concerning Catenoids and their stability, separable minimal hypersurfaces, minimal surfaces obtainable by rotating shapes, determinantal varieties, minimal tori in S3, the minimality in Rnk of the ordered set of k orthogonal equal-length n-vectors, and U(1)-invariant minimal…
Study counts minimal surfaces in curved 3D spaces, finding hyperbolic space minimizes area.
problem Counting minimal surfaces in negatively curved 3-manifolds.
method Introduced an asymptotic quantity to count area-minimizing surfaces and showed minimization by hyperbolic metric.
result Hyperbolic metric minimizes the quantity of area-minimizing surfaces in negatively curved 3-manifolds.
Proves unique continuation for area minimizing currents.
problem Ensuring area minimizing currents match minimal surfaces.
method Analyzes infinite order contact between currents and minimal surfaces.
result Currents and minimal surfaces coincide in a neighborhood.
New inequality helps map stability in minimal surfaces.
problem Stability of minimal surfaces in Rn. method Developing new inequalities and perspectives on minimal surfaces.
result Reproves instability of classical minimal surfaces like Enneper.
Minimal submanifolds in spheres can be produced via Clifford type minimal products, and their Morse indices and nullities are calculated.
problem Understanding the properties of minimal submanifolds in spheres via Clifford products.
method Analyzing the first eigenfunctions and Morse indices of minimal products of minimal submanifolds.
result The Morse index and nullity of the minimal product are calculated and shown for specific cases.
Round balls minimize liquid drop model volumes ≤ 1.
problem Minimizing volumes in liquid drop models.
method Proved uniqueness of minimizers for small volumes.
result Round balls uniquely minimize volumes ≤ 1.
Minimal generating sets of Reidemeister moves identified and classified.
problem Classifying minimal generating sets of Reidemeister moves.
method Determined minimal generating sets, provided classifications, and identified candidates.
result 12 out of 16 candidates for minimal generating sets were proven minimal.
The paper creates symmetrical discrete minimal nets using Schwarz reflection.
problem Creating symmetrical discrete minimal nets.
method Extending Schwarz reflection principle to discrete minimal surfaces.
result Global examples of discrete minimal nets with high symmetry.
In this paper, we prove that every conformal minimal immersion of a compact bordered Riemann surface M into a minimally convex domain D⊂R3 can be approximated, uniformly on compacts in M˚=M∖bM, by proper complete conformal minimal immersions M˚→D. We also obtain a …
We prove that there are no minimal hypersurfaces properly immersed in any region of the Euclidean space bounded by unstable minimal cones. We also prove the analogous result for r-minimal hypersurfaces.
New minimal surfaces grow area very quickly.
problem Understanding minimal surfaces with rapid area growth.
method Examples of minimal immersions in Euclidean space.
result Proper minimal surfaces with rapid area growth found.
New minimal surfaces found with Cantor ends in convex domains.
problem Finding complex structures for minimal surfaces with Cantor ends.
method Proving existence of complete minimal surfaces with Cantor ends in minimally convex domains.
result Existence of a Cantor set whose complement forms a complete minimal surface.
Study on minimal hypersurfaces in a special normed space.
problem Characterizing minimal hypersurfaces in a specific normed space.
method Investigate translation and separable minimal hypersurfaces.
result New insights into the properties of minimal hypersurfaces.
Minimal surfaces help compare geometric shapes.
problem Comparing different geometric shapes.
method Applications of minimal surfaces.
result New insights into geometric comparisons.
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.
Proves minimal crossing diagrams for specific spatial graphs.
problem Proving minimal crossing diagrams for spatial graphs.
method Analyzing adequate diagrams and replacing vertices and edges.
result All 1-vertex spatial graphs with adequate diagrams have minimal crossing number.
Minimal partitions with minimal perimeter found in metric spaces.
problem Finding minimal partitions with minimal perimeter in metric spaces.
method Existence proof and regularity analysis of minimal domains.
result Existence and regularity of minimal partitions in various metric spaces.
The paper studies minimal submanifolds with specific curvature properties in Euclidean space.
problem Minimal submanifolds with (n−2)-umbilical properties in Euclidean space. method Established a correspondence and developed a Weierstrass type method for local parametrization.
result Minimal, generic, (n−2)-umbilic submanifolds are (n−2)-rotational and have a parametric description. This paper solves minimal surface equations near Hardt-Simon foliations.
problem Minimal surfaces near Hardt-Simon foliations.
method Uses gluing methods to construct minimal surfaces.
result Constructs minimal surfaces over Hardt-Simon surfaces and near quadratic cones.
This paper proves all Pfaffian varieties are area-minimizing except hypersurfaces.
problem Proving area-minimizing property of Pfaffian varieties.
method Analyzing families of minimal real matrix varieties and proving area-minimizing property.
result All Pfaffian varieties are area-minimizing except hypersurfaces.
This paper finds all prime alternating knots with minimal warping degree two.
problem Finding knots with minimal warping degree.
method Examined all prime alternating knots and determined those with minimal warping degree two.
result All prime alternating knots with minimal warping degree two were identified.
Minimal graphs over simply connected domains grow at most exponentially.
problem Growth of minimal graphs over simply connected domains with boundary values 0.
method Analyzing solutions to the minimal surface equation.
result Minimal graphs have at most exponential growth.
Study area minimizing currents in conformal cones, solving Dirichlet problems.
problem Area minimizing currents in conformal cones.
method Minimizing problem of area functionals, Dirichlet problem of minimal surface equations.
result Existence and uniqueness of area minimizing currents in a wide class of conformal manifolds.
Paper proves stable minimal surfaces in 3D are flat.
problem Understanding stable minimal surfaces in 3D.
method Analyzes quadratic area growth and stability conditions.
result Stable minimal Plateau surfaces in 3D are flat.
Study minimal surfaces in Kropina 3D space, finding only planes as minimal translation surfaces.
problem Characterizing minimal surfaces in Kropina 3D space.
method Solving partial differential equations to characterize minimal surfaces.
result Only planes are minimal translation surfaces in Kropina 3D space.
Classifies minimal submanifolds in complex hyperbolic spaces.
problem Identifying minimal submanifolds in complex hyperbolic spaces.
method Classification based on extrinsic homogeneity.
result Classification of minimal extrinsically homogeneous submanifolds.
In this paper, by constructing area-nonincreasing retractions, we prove area-minimizing properties of some cones over minimal embeddings of R-spaces.
Cone structures over minimal products can't be calibrated smoothly.
problem Calibrating cones over minimal products with smooth calibrations.
method Extending a key result from [Zha26], showing obstruction.
result Cone structures over minimal products cannot be calibrated by smooth calibrations.
Survey of minimal genus problem progress.
problem Finding the smallest genus surface in 3-manifolds.
method Survey and review of existing research.
result Summarizes recent advancements in the minimal genus problem.