arXiv research

We introduce a new cohomology theory for planar trivalent graphs with perfect matchings. The graded Euler characteristic of the cohomology is a one variable polynomial called the 2-factor polynomial that, if nonzero when evaluated at one, implies that the perfect matching is even and therefore the graph is 4-face color…

The paper refines 2-factor homology to a stable homotopy type for planar trivalent graphs with perfect matchings.

FMI uses matching to mimic interventions for causal feature learning.

The paper introduces a quantum state system to count perfect matchings in graphs.

New link polynomials linked to cluster theory.

OmniMatch algorithm perfectly matches graphs without edge correlation.

We give an algorithmic computation for the height of Kauffman's clock lattice obtained from a knot diagram with two adjacent regions starred and without crossing information specified. We show that this lattice is more familiarly the graph of perfect matchings of a bipartite graph obtained from the knot diagram by over…

This paper presents an algorithm to construct a weighted adjacency matrix of a plane bipartite graph obtained from a pretzel knot diagram. The determinant of this matrix after evaluation is shown to be the Jones polynomial of the pretzel knot by way of perfect matchings (or dimers) of this graph. The weights are Tutte'…

The paper characterizes discrete Morse functions on knot diagrams and generalizes a clock theorem.

Learning representations for counterfactual inference from observational data is of high practical relevance for many domains, such as healthcare, public policy and economics. Counterfactual inference enables one to answer "What if...?" questions, such as "What would be the outcome if we gave this patient treatment $t_…

Graph matching with feature vectors is solved using a two-layer graph neural network.

In recent work the author investigates perfect matchings of a bipartite graph obtained from a knot diagram and demonstrates that these correspond to discrete Morse functions on a 2-complex for the 2-sphere. This relationship is expounded below for the opposite audience: those who may be unfamiliar with knots.

Proves curvature of conference graphs and finds local matchings.

In this work an iterative algorithm based on unsupervised learning is presented, specifically on a Restricted Boltzmann Machine (RBM) to solve a perfect matching problem on a bipartite weighted graph. Iteratively is calculated the weights $w_{ij}$ and the bias parameters $θ= ( a_i, b_j)$ that maximize the energy funct…

GAN-based semi-supervised learning improves classifier generalization.

The paper connects knot theory and cluster algebras via dimer face polynomials.

We give polynomial-time algorithms for the exact computation of lowest-energy (ground) states, worst margin violators, log partition functions, and marginal edge probabilities in certain binary undirected graphical models. Our approach provides an interesting alternative to the well-known graph cut paradigm in that it …

Holographic principle matches deformed Liouville theory action.

This paper tackles matching two complete graphs with correlated edge weights in geometric models.

Paper tackles graph matching with partially correct seeds, improving performance guarantees.

Study reconstructs hidden perfect matchings in random graphs with specific edge weights.

Analysis of Vlasov plasma dynamics using matched pair Lie-Poisson formulation.

For a perfect Lie algebra $\mathfrak{h}$ we classify all Lie algebras containing $\mathfrak{h}$ as a subalgebra of codimension $1$. The automorphism groups of such Lie algebras are fully determined as subgroups of the semidirect product $\mathfrak{h} \ltimes (k^* \times {\rm Aut}_{\rm Lie} (\mathfrak{h}))$. In the non-…

The paper proposes multicalibration to improve matching in graphs with imperfect predictors.

We investigate triangulations of the two-dimensional sphere and torus with the faces properly colored white and black. We focus on matchings between white triangles and incident vertices. On the torus our objects are perfect pairings, whereas on the sphere this is only true after removing one triangle and its vertices.…

We describe a new optimization scheme for finding high-quality correlation clusterings in planar graphs that uses weighted perfect matching as a subroutine. Our method provides lower-bounds on the energy of the optimal correlation clustering that are typically fast to compute and tight in practice. We demonstrate our a…

Matching correlated VAR time series databases by recovering matching permutations.

The paper confirms a conjecture linking link bipyramid volume and Mahler measure.

The Penrose-Kauffman polynomial connects knot theory to graph coloring.

The study examines perfect fluid spacetimes and their properties.

We introduce a novel approach for training adversarial models by replacing the discriminator score with a bi-modal Gaussian distribution over the real/fake indicator variables. In order to do this, we train the Gaussian classifier to match the target bi-modal distribution implicitly through meta-adversarial training. W…

In his seminal 1951 paper "Extreme forms" Coxeter \cite{cox51} observed that for $n \ge 9$ one can add vectors to the perfect lattice $\sfA_9$ so that the resulting perfect lattice, called $\sfA_9^2$ by Coxeter, has exactly the same set of minimal vectors. An inhomogeneous analog of the notion of perfect lattice is tha…

The study examines properties of perfect fluid spacetimes in Einstein's theory.

Algorithm decides if pseudo-Anosov flows have perfect fits.

Paper proves a rigidity result for static perfect fluids.

Paper introduces $ρ$-Perfect to estimate model-human correlation in subjective datasets.

The notion of a locally continuously perfect group is introduced and studied. This notion generalizes locally smoothly perfect groups introduced by Haller and Teichmann. Next, we prove that the path connected identity component of the group of all homeomorphisms of a manifold is locally continuously perfect. The case o…

Joint matching over a collection of objects aims at aggregating information from a large collection of similar instances (e.g. images, graphs, shapes) to improve maps between pairs of them. Given multiple matches computed between a few object pairs in isolation, the goal is to recover an entire collection of maps that …

Study on static perfect fluid space-time geometry and boundary estimates.

We introduce the concept of hereditarily non uniformly perfect sets, compact sets for which no compact subset is uniformly perfect, and compare them with the following: Hausdorff dimension zero sets, logarithmic capacity zero sets, Lebesgue 2-dimensional measure zero sets, and porous sets. In particular, we give an exa…

Thompson sampling, a Bayesian method for balancing exploration and exploitation in bandit problems, has theoretical guarantees and exhibits strong empirical performance in many domains. Traditional Thompson sampling, however, assumes perfect compliance, where an agent's chosen action is treated as the implemented actio…

Uniformly perfect Morse boundaries characterize geometric properties of groups.

Study mapping class groups of infinite type surfaces with noncompact boundaries.

The property of perfectness plays an important role in the theory of Bayesian networks. First, the existence of perfect distributions for arbitrary sets of variables and directed acyclic graphs implies that various methods for reading independence from the structure of the graph (e.g., Pearl, 1988; Lauritzen, Dawid, La…

The paper explores uniform perfectness and centers in Morse boundaries.

Knowing when a graphical model is perfect to a distribution is essential in order to relate separation in the graph to conditional independence in the distribution, and this is particularly important when performing inference from data. When the model is perfect, there is a one-to-one correspondence between conditional…

The paper finds conditions for pseudosymmetric spacetimes to be perfect fluids.

New analysis shows FM learns underlying dynamical structure, not just trajectory replay.