Study of colored triangulations linked to symmetric groups.
problem Enumeration of permutations up to conjugation.
method Analysis of checker triangulated surfaces and their Belyi data.
result Links between triangulations and infinite symmetric groups.
Random hyperbolic surfaces have nearly optimal spectral gaps.
problem Proving the nearly optimal spectral gap conjecture for random Belyi surfaces.
method Using the Brooks-Makover model, the authors show a spectral gap greater than 1/4 - c/log(n).
result A random hyperbolic surface in the Brooks-Makover model has a spectral gap greater than 1/4 - c/log(n).
New results on plane graphs linked to rational functions.
problem Existence problems for plane graphs with specific degree conditions.
method Recent results on the Hurwitz existence problem.
result Description of Belyi functions corresponding to such graphs.
Random surfaces' diameter grows logarithmically with size.
problem Estimating the diameter of random hyperbolic surfaces.
method Uniform gluing of triangles, compactification, asymptotic analysis.
result The diameter is asymptotic to 2logn. Every open Riemann surface can be triangulated with equilateral triangles.
problem The structure and triangulation of Riemann surfaces.
method Constructing a holomorphic branched covering to the Riemann sphere and glueing together equilateral triangles.
result Every open Riemann surface can be equilaterally triangulated.
Maximal automorphisms found for complex projective structures.
problem Maximizing automorphisms in complex projective structures.
method Analyzing Fuchsian uniformizations and Galois Belyi curves.
result Fuchsian uniformizations of Hurwitz surfaces achieve maximal automorphisms.
Brooks and Makover introduced an approach to studying the global geometric quantities (in particular, the first eigenvalue of the Laplacian, injectivity radius and diameter) of a ``typical'' compact Riemann surface of large genus based on compactifying finite-area Riemann surfaces associated with random cubic graphs; b…
We give a list of Heun equations which are Picard-Fuchs associated to families of algebraic varieties. Our list is based on the classification of families of elliptic curves with four singular fibers done by Herfurtner. We also show that pullbacks of hypergeometric functions by rational Belyi functions with restricted …
Explicit solutions to the Riemann-Hilbert problem will be found realising some irreducible non-rigid local systems. The relation to isomonodromy and the sixth Painleve equation will be described. Keywords: Riemann-Hilbert problem, Painleve equations, algebraic solutions, Heun equations, tetrahedral/octahedral group, tr…
We define a new Hurwitz problem which is essentially a small core of the simple Hurwitz problem. The corresponding Hurwitz numbers have simpler formulae, satisfy effective recursion relations and determine the simple Hurwitz numbers. We also apply this idea of finding a smaller simpler enumerative problem to orbifold H…
Brooks and Makover introduced an approach to random Riemann surfaces based on associating a dense set of them - Belyi surfaces - with random cubic graphs. In this paper, using Bollobas model for random regular graphs, we examine the topological structure of these surfaces, obtaining in particular an estimate for the ex…
Random hyperbolic surfaces have low Cheeger constants.
problem Estimating Cheeger constants of random hyperbolic surfaces.
method Modeling random hyperbolic surfaces using ideal triangles and analyzing their Cheeger constants.
result Generic hyperbolic surfaces have Cheeger constants less than 3/2π + ε.
Let Λ be a collection of partitions of a positive integer d of the form (a1,⋯,ap),(b1,⋯,bq),(m1+1,1,⋯,1),⋯,(ml+1,1,⋯,1), where (m1,⋯,ml) is a partition of p+q−2>0. We prove that there exists a rational function on the Riemann sphere C with …
If all but two vertices of a triangulated sphere have degrees divisible by k, then the exceptional vertices are not adjacent. This theorem is proved for k=2 with the help of the coloring monodromy. For k=3,4,5 colorings by the vertices of platonic solids have to be used. With a coloring monodromy one can asso…
In this paper, we address the following question: What does a typical compact Riemann surface of large genus look like geometrically? We do so by constructing compact Riemann surfaces from oriented 3-regular graphs. The set for such Riemann surfaces is dense in the space of all compact Riemann surfaces, namely Belyi su…
New approach finds minima of geodesic lengths for non-uniform fillings.
problem Finding minima of geodesic length functions for non-uniform fillings.
method Elementary optimization for 4-regular topological fillings, analysis of fat graphs and optimization techniques.
result Minima of geodesic length functions are found to be at triangle surfaces in both analyzed classes of non-uniform fillings.
Study minima of geodesic lengths for specific curves on surfaces.
problem Finding the shortest geodesic paths on surfaces.
method Using curves related to dessins d'enfants and Grothendieck-Belyi surfaces.
result Minima of geodesic lengths are achieved on Riemann surfaces defined over number fields.
The paper calculates spectral determinants for two complex surfaces.
problem Calculating spectral determinants for complex surfaces.
method Closed explicit formulas, multiplicative relations, Belyi maps, and constant-curvature spheres.
result Spectral determinants of the Bolza surface and Klein quartic are calculated.
Proposes RSP model for efficient big data analysis.
problem Efficiently partitioning big data sets for analysis.
method Random sample partition (RSP) data model and block-level sampling.
result RSP data blocks can estimate statistics and build models equivalent to whole data set.
Data preprocessing improves data quality for robust data mining.
problem Noisy and incomplete data hinders data mining models.
method Overview of data cleaning, transformation, and preprocessing methods.
result Preprocessing significantly affects data mining model performance.
A new method for handling imbalanced big data using ensembles and smart data.
problem Imbalanced data distribution in big data scenarios.
method Smart Data driven Decision Trees Ensemble (SD_DeTE) methodology.
result SD_DeTE outperforms Random Forest in handling imbalanced binary classification problems in big data.
Prevents sensitive data generation in diffusion models using labeled and unlabeled data.
problem Generating sensitive data in diffusion models using unlabeled data.
method Positive-Unlabeled Diffusion Models, approximating ELBO with labeled and unlabeled data.
result Prevents the generation of sensitive data without compromising image quality.
Study reveals Data Shapley's inconsistent performance in data selection tasks.
problem Inconsistency of Data Shapley's performance in data selection across different settings.
method Hypothesis testing framework and identification of utility functions.
result Data Shapley's performance is no better than random selection without specific constraints.
Survey on data collection challenges in machine learning.
problem Data scarcity and need for labeled data in machine learning.
method Comprehensive study of data acquisition, labeling, and improvement techniques.
result Identification of research challenges in data collection.
PRRO generates synthetic tabular data that improves SL performance and class distribution.
problem Low SL utility of synthetic data due to class imbalance and overlooked data relationships.
method Data pruning and column reordering to optimize SL utility.
result Synthetic data generated with PRRO enhances predictive performance and class distribution.
Defines data science as a natural ecosystem with challenges and missions.
problem Challenges and missions in data science due to 5D complexities and data life cycle phases.
method Systemic and data-centric view of data science as a fusion of data universe and its challenges, formalizing a general-purpose architecture.
result Essential data science as a natural ecosystem integrating specific disciplines and high-impact applications.
Synthetic data enhances analytics but requires careful volume management.
problem Accuracy of statistical methods on synthetic data vs. raw data.
method Synthetic Data Generation for Analytics framework using tabular diffusion models.
result Error rate decreases with more synthetic data but may stabilize or increase.
Data science redefines causal inference from observational data, classifying tasks into description, prediction, and counterfactual prediction.
problem Widespread misunderstandings about data science's role in causal inference from observational data.
method Organizing data science tasks into three classes: Description, prediction, and counterfactual prediction (including causal inference).
result The necessity of subject-matter expert knowledge for causal analyses in data science.
This paper evaluates how dirty data affects data mining and machine learning results.
problem Negative impacts of dirty data on data mining and machine learning results.
method Experimental comparison of missing, inconsistent, and conflicting data on classification and clustering algorithms.
result Guidelines for algorithm selection and data cleaning based on experimental findings.
DPASF stream preprocesses Big Data streams efficiently.
problem Efficient preprocessing of streaming Big Data.
method Implemented six preprocessing algorithms in Apache Flink.
result Preprocessing improves data accuracy in streaming Big Data.
This paper introduces C-DSL to improve data mining outcomes by considering context.
problem Data collection ambiguities, data imbalance, hidden biases, lack of domain info, and data incompleteness.
method Developed Context-Driven Data Science Lifecycle (C-DSL) to address data quality issues.
result Tangible improvements to data mining outcomes were achieved through C-DSL.
Proposes using probabilistic models for privacy-preserving synthetic data.
problem Designing high-quality synthetic data for privacy preservation.
method Formulate the problem through probabilistic modelling, choosing a model for the data.
result Statistical discoveries can be reliably reproduced from synthetic data.
Unlabeled data helps stop active learning better than labeled data.
problem Reducing the need for manual annotation in text classification.
method Compared stopping methods based on labeled, unlabeled, and training data.
result Stopping methods using unlabeled data are more effective.
New test ensures quality of shared data in machine learning.
problem Ensuring quality of external data in machine learning tasks.
method Distribution-free two-sample testing procedures grounded in conformal outlier detection.
result Identifies valuable external data agents for model personalization.
Paper creates fair synthetic data ensuring equal predictions across sensitive attributes.
problem Ensuring fair predictions across sensitive attributes in synthetic data.
method Equalizing target probability distributions across sensitive attributes in synthetic data generation.
result Synthetic data provides strong fair predictions, equal across all thresholds.
A new method classifies multiple correlated data streams simultaneously.
problem Classifying multiple correlated data streams in practical scenarios.
method Double-Coupling Support Vector Machines (DC-SVM) considers both internal and external correlations.
result The proposed method outperforms traditional methods on artificial and real-world data streams.
This paper improves neural machine translation training by selecting and denoising data.
problem Reduces negative impact of noisy data on neural machine translation training.
method Measures and selects domain data, applies denoising curriculum using online data selection.
result Significant effectiveness for training on noisy data.
DPA preserves data distribution in reduced dimensions.
problem Loss of data distribution in dimension reduction.
method DPA combines encoder and decoder to match data distribution.
result DPA successfully reconstructs data distribution.
Framework captures missing data in sparse data sets.
problem Capturing missing data in extremely sparse data sets.
method Coupled compound Poisson factorization with stochastic variational inference.
result Explicitly modeling missing data improves results in clustering, prediction, and matrix factorization.
Efficient synthetic data generation improves model performance on tabular data.
problem Improving model robustness and performance with scarce or low-quality data.
method Hardness characterization to identify high-value training points, generating synthetic data only from these points.
result Synthetic data generated from hardest points outperforms non-targeted methods on tabular datasets.
For most problems in science and engineering we can obtain data sets that describe the observed system from various perspectives and record the behavior of its individual components. Heterogeneous data sets can be collectively mined by data fusion. Fusion can focus on a specific target relation and exploit directly ass…
DAERNN models censored data using neural networks with data augmentation.
problem Handling censored data in expectile regression.
method Data augmentation based Expectile Regression Neural Networks (ERNNs).
result DAERNN outperforms existing censored ERNNs methods and achieves comparable predictive performance to fully observed data.
This paper quantifies uncertainty in Data Shapley using statistical inference.
problem Uncertainty in data valuation due to dynamic data distribution.
method Established relationship with U-statistics and quantified uncertainty using statistical inference.
result Confidence intervals for Data Shapley estimations are provided.
Generative Adversarial Networks create time series data from images.
problem Generating realistic time series data from images.
method Wasserstein GANs with gradient penalty for stability, synthesizing sinusoidal, PPG, and ECG data.
result Successfully generated time series data using image-based GANs.
DCoM uses deep neural networks to detect semantic data types from raw column values.
problem Detecting semantic data types from dirty and unseen data.
method DCoM employs multi-input NLP-based deep neural networks trained on 686,765 data columns.
result DCoM outperforms existing methods significantly on 78 different semantic data types.
Model refines coarse spatial data using diverse auxiliary data sets.
problem Tackles the challenge of refining coarse spatial data with varying auxiliary data granularities.
method Proposes a probabilistic model using Gaussian processes to hierarchically incorporate auxiliary data sets of various granularities.
result Can effectively refine coarse-grained spatial data using auxiliary data sets of different granularities.
GANs generate training data for machine learning tasks.
problem Imbalanced data sets and sensitive information.
method Generative Adversarial Networks (GANs) to create artificial training data.
result A Decision Tree classifier trained on GAN-generated data achieved similar or better accuracy and recall than on original data.
Task-agnostic data valuation without validation requirements.
problem Valuing data without specific task assumptions.
method Estimating data diversity and relevance through queries without raw data.
result Estimates capture the diversity and relevance of seller's data for the buyer.