arXiv research

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.

Well-quasi-orders proved on embedded planar graphs.

Fewer obstructions for small graphs in knotless embedding.

This contains a list of (mostly very minor) corrections to the book Introduction to Symplectic Topology, Clarendon Press, Oxford, (1995), together with rewritten versions of two lemmas and some additional comments.

We present a new family of zero-field Ising models over $N$ binary variables/spins obtained by consecutive "gluing" of planar and $O(1)$-sized components and subsets of at most three vertices into a tree. The polynomial-time algorithm of the dynamic programming type for solving exact inference (computing partition func…

Study of hypersurfaces with specific expansion properties.

Researchers create metrics for Laplacian eigenfunctions with specific zero sets.

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

The abstract formulates and proves a categorification of Robertson's conjecture.

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.

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…

Current Deep Reinforcement Learning algorithms still heavily rely on handcrafted neural network architectures. We propose a novel approach to automatically find strong topologies for continuous control tasks while only adding a minor overhead in terms of interactions in the environment. To achieve this, we combine Neur…

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.

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

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

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

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…

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

The complement of a non-separating planar graph contains a K_n minor.

Consider a compact Riemannian manifold with boundary endowed with a magnetic field. A path taken by a particle of unit charge, mass, and energy is called a magnetic geodesic. It is shown that if everything is real-analytic, the topology, metric, and magnetic field are uniquely determined by the scattering relation of t…

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…

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.

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…

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.

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.

Extends ML fairness to handle minority groups over time.

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

Constructs positive energy representations from Toda equations Stokes data.

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

Study shows space writhe closely correlates with knot signature in polymers.

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

A new sampling method balances imbalanced data using gamma distribution.