Well-quasi-order proved for plane minors; polynomial-time algorithm for link diagrams.
problem Proving the well-quasi-order of plane minors and solving link diagrams.
method Sequence of vertex and edge deletions and contractions to prove well-quasi-order; polynomial-time algorithm for link diagrams.
result Well-quasi-order of plane minors established; polynomial-time algorithm for link diagrams.
Well-quasi-orders proved on embedded planar graphs.
problem Proving well-quasi-orders on embedded planar graphs.
method Careful analysis and extensions of classical methods for embedded minor relations.
result Embedded minor relations are well-quasi-orders on various classes of embedded planar graphs.
The paper is partially withdrawn: in its current form, Lemma 2.3 is false, so that our proof of Theorem A and Proposition B has an important gap. We were unable to fix it yet. Any help is most welcome. We prove that the restriction of surface minority to fiber surfaces of divides is a well-quasi-order. Here surface min…
Book covers tools for zeroth-order convex optimisation.
problem Zeroth-order convex optimisation.
method Cutting plane methods, interior point methods, continuous exponential weights, gradient descent, online Newton step.
result Improved existing bounds and algorithms.
This survey of some of the more topological aspects of the placement problem for complex curves in complex surfaces was originally published in L'Enseignement Mathematique 29 (1983). The present LaTeXed redaction corrects several typographical errors without, I hope, introducing new ones; some minor emendations and ref…
In this paper we consider minors of ribbon graphs (or, equivalently, cellularly embedded graphs). The theory of minors of ribbon graphs differs from that of graphs in that contracting loops is necessary and doing this can create additional vertices and components. Thus the ribbon graph minor relation is incompatible wi…
A new oversampling framework generates minority samples by perturbing majority classes.
problem Oversampling in imbalanced classification often neglects majority classes, leading to samples spread across the minority space.
method Introduces a counterfactual objective to generate new minority samples by perturbing majority samples.
result Generated minority samples are near the decision boundary and significantly outperform state-of-the-art methods.
Improves generation of minority samples using diffusion models.
problem Generating minority samples on low-density regions of a data manifold.
method Introduces minority guidance to focus diffusion models on minority samples.
result Significantly improves generation of high-quality minority samples.
Characterizes minor-minimal separating projective planar graphs and their generalizations.
problem Understanding projective planar graphs and their properties.
method Analyzing minors, embeddings, and specific link types.
result Partial characterization of minor-minimal separating projective planar graphs and their generalizations.
Every infinitely edge-connected graph has a minor of Farey graph or Tℵ0∗t.
problem Characterizing edge-connected graphs with specific minor properties.
method Analyzing the minor structure of infinitely edge-connected graphs.
result Infinitely edge-connected graphs contain Farey graph or Tℵ0∗t as a minor. Boost-and-Skip generates minority samples without guidance, faster and more effectively.
problem Generating minority samples in low-density regions of a data manifold.
method Boost-and-Skip approach with variance-boosted initialization and timestep skipping.
result Boost-and-Skip effectively promotes the emergence of underrepresented minority features.
Paper determines Assouad-Nagata dimension for all minor-closed metrics.
problem Understanding the Assouad-Nagata dimension of minor-closed metrics.
method Using edge-weighted graphs and edge-deletion/contraction to model minor-closed metrics, determining their Assouad-Nagata dimension.
result Determined the Assouad-Nagata dimension for every minor-closed metric.
The study combines graph-minors and metric spaces, answering some questions and conjectures.
problem Whether geodesic metric spaces without a fat H minor are quasi-isometric to graphs without H minor. method Combining graph-minors and coarse geometry, answering affirmatively for small H. result Affirmative answer for small H in the problem statement. In this paper we study the continuum time dynamics of a stock in a market where agents behavior is modeled by a Minority Game and a Grand Canonical Minority Game. The dynamics derived is a generalized geometric Brownian motion; from the Black & Scholes formula the calibration of both the Minority Game and the Grand Can…
We prove that the isoperimetric inequalities in the euclidean and hyperbolic plane hold for all euclidean, respectively hyperbolic, cone-metrics on a disk with singularities of negative curvature. This is a discrete analog of the theorems of Weil and Bol that deal with Riemannian metrics of curvature bounded from above…
This paper gives a critical account of the minority game literature. The minority game is a simple congestion game: players need to choose between two options, and those who have selected the option chosen by the minority win. The learning model proposed in this literature seems to differ markedly from the learning mod…
The complement of a non-separating planar graph contains a K_n minor.
problem Characterizing the structure of complements of planar graphs.
method Analyzing the structure of complements of non-separating planar graphs and using examples to illustrate hypotheses.
result The order 2n-3 is the lowest possible for a non-separating planar graph whose complement contains a K_n minor.
Data-driven fault diagnostics and prognostics suffers from class-imbalance problem in industrial systems and it raises challenges to common machine learning algorithms as it becomes difficult to learn the features of the minority class samples. Synthetic oversampling methods are commonly used to tackle these problems b…
Simple graphs with 12 nodes and 6 neighbors always have a 6-node subgraph.
problem Finding a specific subgraph in simple graphs.
method Proving every graph of order 12 with minimum degree 6 contains a K_6 minor.
result Simple graphs of order 12 and minimum degree 6 contain K_6 minors.
Divide knots and links, defined by A'Campo in the singularity theory of complex curves, is a method to present knots or links by real plane curves. The present paper is a continuation of the author's previous result that every knot in the major subfamilies of Berge's lens space surgery (i.e., knots yielding a lens spac…
Model explains periodic trading in financial markets through game theory.
problem Understanding periodic trading activities in financial markets.
method Mean-field liquidation game with major-minor players.
result Existence and uniqueness of Nash equilibrium established.
Overparameterized models can worsen minority group errors even when overall test error improves.
problem Overparameterization exacerbates spurious correlations, harming minority groups.
method Simulations and experiments on image datasets, theoretical analysis of linear models.
result Subsampling the majority group can achieve low minority error in overparameterized models.
This paper classifies chiral graphs up to size 12.
problem Understanding the chirality of simple graphs to predict molecular behavior.
method Classifying minor minimal intrinsically chiral graphs among simple graphs of size up to 12.
result Complete set of minor minimal graphs for intrinsic properties of chiral molecules.
In this paper it was developed a modification of the known multiagent model Minority Game, designed to simulate the behavior of traders in financial markets and the resulting price dynamics on the abstract resource. The model was implemented in the form of software. The modified version of Minority Game was investigate…
We introduce the minority game theory for two kinds of the Korean treasury bond (KTB) in Korean futures exchange markets. Since we discuss numerically the standard deviation and the global efficiency for an arbitrary strategy, our case is found to be approximate to the majority game. Our result presented will be compar…
GenSample uses genetic algorithms to improve minority class classification in imbalanced datasets.
problem Poor classification performance on minority class in imbalanced datasets.
method GenSample uses genetic algorithms to oversample minority class, considering difficulty and performance improvement.
result GenSample achieved the highest F-Score on 8 out of 9 real-world imbalanced datasets.
We list more than 200 new examples of minor minimal intrinsically knotted graphs and describe many more that are intrinsically knotted and likely minor minimal.
M2m method improves deep learning performance on class-imbalanced datasets.
problem Class imbalance in labeled training datasets causes deep neural networks to generalize poorly to minority classes.
method Augment less-frequent classes by translating samples from more-frequent classes.
result Significantly improves generalization on minority classes compared to existing methods.
AGGAN uses genetic algorithm with simulated annealing to generate minority class data.
problem Overcoming class imbalance in minority class data.
method AGGAN combines genetic algorithm and simulated annealing to train GANs on scarce minority class data.
result AGGAN effectively generates minority class data distributions from limited samples.
We show that any self-complementary graph with n vertices contains a K⌊2n+1⌋ minor. We derive topological properties of self-complementary graphs.
LoRAS improves model performance on imbalanced datasets by better oversampling the minority class.
problem Imbalanced datasets lead to poor model performance, especially for the majority class.
method Localized Random Affine Shadowsampling (LoRAS) to oversample minority class data.
result LoRAS generates better ML models in terms of F1-Score and Balanced accuracy compared to SMOTE and its extensions.
Framework learns to transform majority to minority samples for balanced classification.
problem Imbalanced classification leading to biased predictions.
method Minimizes MMD and uses triplet loss for global alignment and boundary awareness.
result Consistent improvements over classical and generative baselines in AUROC, G-mean, F1-score, and MCC.
WOTBoost improves minority class accuracy in imbalanced datasets.
problem Imbalanced datasets lead to low accuracy in minority class classification.
method Combines weighted oversampling and boosting techniques.
result WOTBoost achieves best G mean and highest AUC score on multiple datasets.
We demonstrate that minority mechanisms arise in the dynamics of markets because of effects of price impact; accordingly the relative importance of minority and delayed majority mechanisms depends on the frequency of trading. We then use minority games to illustrate that a vanishing price return auto-correlation functi…
Two new minor minimal intrinsically chiral graphs identified.
problem Identifying intrinsically chiral graphs in molecular structures.
method Analyzing graph symmetry and embedding properties.
result Found two new minor minimal intrinsically chiral graphs Γ7 and Γ8. Extends ML fairness to handle minority groups over time.
problem Limitations of existing fairness criteria.
method Performative Distributionally Robust Optimization.
result Improves fairness for minority groups over time.
Decision trees can be biased towards minority class, contrary to belief.
problem Bias in decision trees towards minority class in imbalanced datasets.
method Critical evaluation of past literature, specific conditions analysis, tree-fitting adjustments, and post-hoc calibration methods.
result Decision trees can be biased towards minority class under specific conditions, not always towards majority.
Model shows how diversity on corporate boards influences decision-making and innovation.
problem Understanding dynamics of diversity and innovation in corporate boards.
method Developed a dynamic model calibrated with empirical data of firm and board networks.
result Homophily and visibility biases shape the trajectory towards equality in corporate boards.
Paper proposes a DAE algorithm to improve credit card fraud detection.
problem Imbalanced data classification problem in credit card fraud detection.
method Proposes a denoising autoencoder neural network (DAE) algorithm to oversample and denoise minority class samples.
result Improves classification accuracy of minority class samples in imbalanced datasets.
New model explains neural collapse and limits on minority classes in imbalanced datasets.
problem Understanding and predicting performance limits of deep learning models on imbalanced datasets.
method Layer-Peeled Model, a nonconvex optimization program isolating top layers and applying constraints.
result Reveals a new phenomenon called Minority Collapse that limits deep learning models on minority classes.
A new sampling method balances imbalanced data using gamma distribution.
problem Imbalanced class distribution in data causes bias in classification algorithms.
method Intelligent resampling of minority class instances via gamma distribution.
result The proposed method outperforms existing techniques on 12 out of 24 datasets.
PCA minor projection is most sensitive to distributional changes in bivariate data.
problem Detecting sparse distributional changes in high-dimensional data.
method Proved that the minor projection of PCA-rotated data is most sensitive to distributional changes defined by Hellinger distance.
result The minor projection is the most sensitive to sparse distributional changes in high-dimensional data.
Graphs with fat minors have a limited large-scale structure.
problem Understanding the large-scale structure of graphs excluding certain minors.
method Introduced the concept of Baker-treewidth and used it to prove asymptotic dimension bounds.
result Every hereditary class of bounded-degree graphs excluding some graph as a fat minor has asymptotic dimension at most 2.
In this paper, we present a simple stock market model (the market game) which incorporates, as ab initio dynamics delayed majority dynamics, according to which agents (with heterogeneous strategies and price expectations) are rewarded if their actions at time t are the actions of the majority of agents at time t+1. We …
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.
Develops variational framework for LQG risk-sensitive MFGs with major-minor interactions.
problem Risk-sensitive optimal control in LQG systems with major-minor interactions.
method Variational approach, nonlinear necessary and sufficient condition of optimality, equivalent risk-neutral measure, Markovian closed-loop best-response strategies.
result Derives optimal control strategies for LQG risk-sensitive MFGs with major-minor interactions, establishing Nash and ε-Nash equilibria. The paper analyzes how minority group imbalance affects neural network performance.
problem The impact of minority group imbalance on neural network performance.
method Formulated group imbalance problem with Gaussian Mixture Model, quantified sample complexity, convergence rate, and testing performance.
result Increasing the minority group fraction does not necessarily improve the generalization performance of the minority group.
The paper extends logistic regression for unbounded majority classes and derives asymptotic properties.
problem Infinitely imbalanced logistic regression inference.
method Derive a second order expansion for slope parameter under unbounded majority class.
result The second order term converges to a normal distribution with a variance depending only on the minority class's mean.