Self-complementary graphs have complete minors.
problem Finding complete minors in self-complementary graphs.
method Analyzing topological properties of self-complementary graphs.
result Self-complementary graphs contain minors.
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48 results for “minor properties”
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.
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…
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.
The paper is partially withdrawn: in its current form, Lemma 2.3 is false, so that our proof of Theorem A and Proposition B has an important gap.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…
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 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.
Fewer obstructions for small graphs in knotless embedding.
problem Finite obstructions for knotless embedding of small graphs.
method Analysis of graph minor obstructions and knotless embedding.
result There are only three obstructions for size 23 graphs, significantly fewer than previously known.
We show that the 20 graph Heawood family, obtained by a combination of triangle-Y and Y-triangle moves on , is precisely the set of graphs of at most 21 edges that are minor minimal for the property not --apex. As a corollary, this gives a new proof that the 14 graphs obtained by triangle-Y moves on are t…
The study defines and analyzes multibranched surfaces and their minors, proving genus inequalities.
problem Understanding the genus of multibranched surfaces and their minors.
method Defining multibranched surfaces, calculating genus, and proving genus inequalities.
result Upper bounds for the genus of multibranched surfaces are derived.
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 and .
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.
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.
Planar Legendrian graphsmath.GT
Classifies trivial Legendrian embeddings of planar graphs.
problem Classifying trivial Legendrian embeddings of planar graphs.
method Proves two results using invariants and minor properties.
result Unique trivial embedding is Legendrian simple for certain planar graphs.
We show that the 14 graphs obtained by moves on K_7 constitute a complete list of the minor minimal intrinsically knotted graphs on 21 edges. We also present evidence in support of a conjecture that the 20 graph Heawood family, obtained by a combination of and mo…
Dynamics of multi-frequency minority gamescond-mat.dis-nn
The dynamics of minority games with agents trading on different time scales is studied via dynamical mean-field theory. We analyze the case where the agents' decision-making process is deterministic and its stochastic generalization with finite heterogeneous learning rates. In each case, we characterize the macroscopic…
New bounds on knot genus for positive braids.
problem Understanding the genus difference in positive braids.
method Analyzing the Seifert genus and 4-genus with respect to the number of strands.
result Characterizing knots with specific genus differences by forbidden minors.
The study examines six variations of apex graphs and their planar properties.
problem Characterizing apex, edge apex, and contraction apex graphs.
method Defined and analyzed six variations of apex graphs, using the Graph Minor Theorem and determining obstruction graphs.
result Found at least 36, 55, and 82 obstruction graphs for apex, edge apex, and contraction apex respectively.
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…
MimosaNet prevents model stealing by making neural networks sensitive to weight changes.
problem Neural networks are vulnerable to model stealing due to robustness to minor parameter changes.
method Develops a method to create a sensitive version of a trained neural network.
result The sensitive network produces the same responses but is highly sensitive to weight changes, preventing model stealing.
New invariant links graph structure to tropical curve properties.
problem Understanding graph and curve minor structures.
method Defined Ceresa-Zharkov class for graphs, related to tropical curves.
result Ceresa-Zharkov class is zero for hyperelliptic graphs.
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.
New framework reduces strategic manipulation cost for minority groups in fair classification.
problem Strategic manipulation disparities in fair classification.
method Constrained optimization framework that constructs classifiers to reduce strategic manipulation cost for minority groups.
result Empirically, the approach reduces strategic manipulation cost for minority groups over multiple real-world datasets.
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…
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.
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.
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.
Paper analyzes stability and forgetting in score-based generative models.
problem Understanding the stability and long-time behavior of generative models.
method Quantitative bounds on sampling error using stability and forgetting properties of the Markov chain.
result Provides practical consequences of stability and contraction mechanism in sampling.
Matrix sketching balances class sizes for better supervised classification performance.
problem Class imbalance in supervised classification leads to poor performance.
method Matrix sketching using random projections to rebalance class sizes.
result Rebalanced classes improve classification performance, especially for minority classes.
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…
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 Minority Game framework was recently generalized to account for the possibility that agents adapt not only through strategy selection but also by diversifying their response according to the kind of dynamical regime, or the risk, they perceive. Here we study the effects of this mechanism in different information st…
An Adaptive Oversampling Learning Method for Class-Imbalanced Fault Diagnostics and Prognosticscs.LG
A new method improves fault diagnostics and prognostics for class-imbalanced data.
problem Class imbalance in industrial fault diagnostics and prognostics.
method EWMOTE: EM-based Weighted Minority Oversampling TEchnique.
result EWMOTE achieves better performance on binary and multi-class imbalance learning tasks.
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.
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.
The search for more realistic modeling of financial time series reveals several stylized facts of real markets. In this work we focus on the multifractal properties found in price and index signals. Although the usual Minority Game (MG) models do not exhibit multifractality, we study here one of its variants that does.…
We give several versions of local and global inverse mapping theorem for tame non necessarily smooth, mappings. Here tame mapping means a mapping which is subanalytic or, more generally, definable in some o-minimal structure. Our sufficient conditions are formulated in terms of various properties (convexity, positivity…
Study of hypersurfaces with specific expansion properties.
problem Existence and properties of hypersurfaces with prescribed null expansion.
method Adapted Eichmair's Perron approach for existence.
result Topology theorem for hypersurfaces with prescribed null expansion.
We present a comprehensive study of utility function of the minority game in its efficient regime. We develop an effective description of state of the game. For the payoff function $g(x)=\sgn (x)$ we explicitly represent the game as the Markov process and prove the finitness of number of states. We also demonstrate bou…
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.
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…
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.
Characterizes 3D embeddability of certain 2D complexes via excluded minors.
problem Characterizing embeddability of specific 2D complexes in 3-space.
method Using Kuratowski-type characterisation via excluded minors.
result Answers Lovász, Pardon, and Wagner's questions about embeddability.
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.
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.