arXiv research

The paper is partially withdrawn: in its current form, Lemma 2.3 is false, so that our proof of Theorem A and Proposition B has an important gap.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…

We say that a $2$-dimensional CW complex is a multibranched surface if we remove all points whose open neighborhoods are homeomorphic to the $2$-dimensional Euclidean space, then we obtain a $1$-dimensional complex which is homeomorphic to a disjoint union of some $S^1$'s. We define the genus of a multibranched surface…

Study shows quasipositive fiber surfaces can't be well-ordered.

Paper studies asymptotic dimension and Assouad-Nagata dimension of graphs and surfaces.

Paper determines Assouad-Nagata dimension for all minor-closed metrics.

Well-quasi-orders proved on embedded planar graphs.

Graphs on surfaces have a 2-dimensional large scale structure.

Proves a quasi-order on fibre surfaces of positive braid links.

Extends diameter bounds for submanifolds with boundary and minor curvature restrictions.

Authors show that genus defects of Hopf arborescent links are decidable.

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.

Improves generation of minority samples using diffusion models.

Characterizes minor-minimal separating projective planar graphs and their generalizations.

Every infinitely edge-connected graph has a minor of Farey graph or $T_{\aleph_0}\ast t$.

Boost-and-Skip generates minority samples without guidance, faster and more effectively.

The study combines graph-minors and metric spaces, answering some questions and conjectures.

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…

Any surface can be foliated into equipotential hypersurfaces of the level sets. A current result is that the contours are the progressing wave fronts of a certain hyperbolic partial differential equation, a wave equation. It is connected with the gradient lines, as well as with a corresponding eikonal equation. The lev…

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…

Study of hypersurfaces with specific expansion properties.

We add two new 1-parameter families to the short list of known embedded triply periodic minimal surfaces of genus 4 in $\mathbb{R}^3$. Both surfaces can be tiled by minimal pentagons with two straight segments and three planar symmetry curves as boundary. In one case (which has the appearance of the CLP surface of Schw…

The complement of a non-separating planar graph 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…

This work is based on the approach developed by J.~Dorfmeister, F.~Pedit and H.~Wu [GANG and KITCS preprint, Report KITCS94-4-1] to construct maps $Φ:D\rightarrow R^3$, $D$ being the unit disk in $C$, whose images are surfaces of constant mean curvature. They start from certain meromorphic one forms, so called meromorp…

Model explains periodic trading in financial markets through game theory.

We show that the difference between the Seifert genus and the topological 4-genus of a prime positive braid knot is bounded from below by an affine function of the minimal number of strands among positive braid representatives of the knot. We deduce that among prime positive braid knots, the property of having such a g…

Overparameterized models can worsen minority group errors even when overall test error improves.

This paper classifies chiral graphs up to size 12.

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…

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.

We prove that every simple graph of order 12 which has minimum degree 6 contains a K_6 minor.

M2m method improves deep learning performance on class-imbalanced datasets.

AGGAN uses genetic algorithm with simulated annealing to generate minority class data.

We show that any self-complementary graph with $n$ vertices contains a $K_{\lfloor \frac{n+1}{2}\rfloor}$ 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.

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.

New proofs given for space curves with totally positive torsion.

Extends ML fairness to handle minority groups over time.

Decision trees can be biased towards minority class, contrary to belief.

Model shows how diversity on corporate boards influences decision-making and innovation.

Classifiers trained with class-imbalanced data are known to perform poorly on test data of the "minor" classes, of which we have insufficient training data. In this paper, we investigate learning a ConvNet classifier under such a scenario. We found that a ConvNet significantly over-fits the minor classes, which is quit…

New model explains neural collapse and limits on minority classes in imbalanced datasets.

A new sampling method balances imbalanced data using gamma distribution.

Graphs with fat minors have a limited large-scale structure.