We prove that every simple graph of order 12 which has minimum degree 6 contains a K_6 minor.
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48 results for “simple minors”
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.
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.
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.
New graph shows edge deletion/contraction doesn't always result in intrinsically linked graphs.
problem Edge operations in intrinsically knotted graphs don't always produce intrinsically linked graphs.
method Presented a new intrinsically knotted graph.
result Edge operations in intrinsically knotted graphs don't always result in intrinsically linked graphs.
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…
We discuss a simple model based on the Minority Game which reproduces the main stylized facts of anomalous fluctuations in finance. We present the analytic solution of the model in the thermodynamic limit and show that stylized facts arise only close to a line of critical points with non-trivial properties. By a simple…
We introduce a simple extension of the minority game in which the market rewards contrarian (resp. trend-following) strategies when it is far from (resp. close to) efficiency. The model displays a smooth crossover from a regime where contrarians dominate to one where trend-followers dominate. In the intermediate phase,…
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 …
Non-equilibrium statistical mechanics of Minority Gamescond-mat.dis-nn
In this paper I give a brief introduction to a family of simple but non-trivial models designed to increase our understanding of collective processes in markets, the so-called Minority Games, and their non-equilibrium statistical mathematical analysis. Since the most commonly studied members of this family define disor…
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.
Optimizes portfolios using CPT utility via convex optimization.
problem Maximizing CPT utility in portfolio selection.
method Minorization-maximization (MM) algorithm and convex-concave (CC) procedure.
result Problems can be solved globally and efficiently.
Exploring Deep Neural Networks via Layer-Peeled Model: Minority Collapse in Imbalanced Trainingcs.LG
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.
We prove that if the minors of degree of a Sobolev map are smooth then the map is smooth, when are not both even. We use this result to derive a simple, self-contained proof of the famous Liouville theorem for conformal maps, under the weakest possible regularity assumptions, i…
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…
We characterise positive braid links with positive Seifert form via a finite number of forbidden minors. From this we deduce a one-to-one correspondence between prime positive braid links with positive Seifert form and simply laced Dynkin diagrams, as well as a simple classification of alternating positive braid knots.
Paper examines fairness of data augmentation methods, finding vanilla Mixup outperforms Fair Mixup.
problem Improving fairness in classification models with limited minority data.
method Uses multicalibration to rigorously evaluate and improve data augmentation methods for classification fairness.
result Vanilla Mixup outperforms Fair Mixup and baseline methods in fairness and accuracy, especially with small minority groups.
We propose an analytically tractable variation of the minority game in which rational agents use probabilistic strategies. In our model, agents choose between two alternatives repeatedly, and those who are in the minority get a pay-off 1, others zero. The agents optimize the expectation value of their discounted fu…
Ensembling DNNs improves minority group performance, leading to fairness.
problem Improving subgroup performances in DNN classifiers.
method Simple homogeneous ensembling of DNNs.
result Fairness naturally emerges from ensembling, improving minority group performance.
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.
The paper explores how deep generative models can improve performance on imbalanced datasets.
problem Imbalanced datasets lead to poor classifier performance and misleading evaluation metrics.
method The paper studies deep generative models for oversampling minority classes in imbalanced tabular data.
result Deep generative models can improve performance on imbalanced classification tasks, but require different under- and oversampling ratios.
Planar Legendrian graphsmath.GT
We prove two results on the classification of trivial Legendrian embeddings of planar graphs. First, the oriented Legendrian ribbon and rotation invariant are a complete set of invariants. Second, if is 3-connected or contains as a minor, then the unique t…
The resolution and calibration of pure spectra of minority components in measurements of chemical mixtures without prior knowledge of the mixture is a challenging problem. In this work, a combination of band target entropy minimization (BTEM) and target partial least squares (T-PLS) was used to obtain estimates for sin…
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.
We study a variation of the minority game. There are N agents. Each has to choose between one of two alternatives everyday, and there is reward to each member of the smaller group. The agents cannot communicate with each other, but try to guess the choice others will make, based only the past history of number of peopl…
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 .
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 as a minor.
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 minor are quasi-isometric to graphs without minor.
method Combining graph-minors and coarse geometry, answering affirmatively for small .
result Affirmative answer for small 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…
Robust cancer screening model using pre-trained ensembles for biomarkers.
problem Detecting early-stage cancer, especially in hard-to-diagnose cases like pancreatic cancer.
method Meta-trained Hyperfast model for robust classification, combined with ensembling of XGBoost and LightGBM.
result Achieved highest AUC of 0.9929 and robust performance on imbalanced datasets.
Bayesian framework improves minority class performance in class-imbalanced data.
problem Class imbalance in predictive toxicology models.
method Weighted likelihood approach modifying likelihood function weights inversely proportional to class proportions.
result Improves balanced accuracy and sensitivity for minority class (toxic compounds).
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.
An Adaptive Oversampling Learning Method for Class-Imbalanced Fault Diagnostics and Prognosticscs.LG
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…
Anomalous fluctuations in Minority Games and related multi-agent models of financial marketsphysics.soc-ph
We review the recent approaches to modelling financial markets based on multi-agent systems. After a brief summary of the basic stylised facts observed in real-market time-series we discuss some simple agent-based systems which are currently used to model financial markets. One of the most prominent examples is here th…
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…
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.
Bayesian model uses simple functions to forecast macroeconomic data.
problem Forecasting large datasets in macroeconomics with complex nonlinear relationships.
method Sum of simple two-component location mixtures, logistic function threshold, conjugate priors.
result Accurate point and density forecasts in US macroeconomic aggregates.
Statistical and Multifractal Properties of the Time Series Generated by a Modified Minority Gamephysics.soc-ph
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…
Weighted Classification Cascades for Optimizing Discovery Significance in the HiggsML Challengestat.ML
We introduce a minorization-maximization approach to optimizing common measures of discovery significance in high energy physics. The approach alternates between solving a weighted binary classification problem and updating class weights in a simple, closed-form manner. Moreover, an argument based on convex duality sho…
Dynamical Minority Games in Futures Exchange Marketsphysics.soc-ph
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…
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.
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.
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 vertices contains a minor. We derive topological properties of self-complementary graphs.
Imbalanced data classification problem has always been a popular topic in the field of machine learning research. In order to balance the samples between majority and minority class. Oversampling algorithm is used to synthesize new minority class samples, but it could bring in noise. Pointing to the noise problems, thi…
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.