Decomposition of Geometric Set Systems and Graphs

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Fairness of decision-making algorithms is an increasingly important issue. In this paper, we focus on spectral clustering with group fairness constraints, where every demographic group is represented in each cluster proportionally as in the general populat ...

We prove the non-planarity of a family of 3-regular graphs constructed from the solutions to the Markoff equation x2 + y2 + z2 = xyz modulo prime numbers greater than 7. The proof uses Euler characteristic and an enumeration of the short cycles in these gr ...

We examine the connection of two graph parameters, the size of a minimum feedback arcs set and the acyclic disconnection. A feedback arc set of a directed graph is a subset of arcs such that after deletion the graph becomes acyclic. The acyclic disconnecti ...

Let F be a family of n pairwise intersecting circles in the plane. We show that the number of lenses, that is convex digons, in the arrangement induced by F is at most 2n - 2. This bound is tight. Furthermore, if no two circles in F touch, then the geometr ...

Orthogonal group synchronization is the problem of estimating n elements Z(1),& mldr;,Z(n) from the rxr orthogonal group given some relative measurements R-ij approximate to Z(i)Z(j)(-1). The least-squares formulation is nonconvex. To avoid its local minim ...

A polyhedral graph is a 3-connected planar graph. We find the least possible order p(k, a) of a polyhedral graph containing a k-independent set of size a for all positive integers k and a. In the case k =1 and a even, we prove that the extremal graphs are ...

When can a unimodular random planar graph be drawn in the Euclidean or the hyperbolic plane in a way that the distribution of the random drawing is isometry-invariant? This question was answered for one-ended unimodular graphs in Benjamini and Timar, using ...

In data-parallel optimization of machine learning models, workers collaborate to improve their estimates of the model: more accurate gradients allow them to use larger learning rates and optimize faster. In the decentralized setting, in which workers commu ...

Graph machine learning offers a powerful framework with natural applications in scientific fields such as chemistry, biology and material sciences. By representing data as a graph, we encode the prior knowledge that the data is composed of a set of entiti ...

A graph H is a minor of a second graph G if G can be transformed into H by two operations: 1) deleting nodes and/or edges, or 2) contracting edges. Coarse-grained reconfigurable array (CGRA) application mapping is closely related to the graph minor problem ...

We study the limit behaviour of sequences of non-convex, vectorial, random integral functionals, defined on W1,1, whose integrands are ergodic and satisfy degenerate linear growth conditions. The latter involve suitable random, scale-dependent weight-funct ...

The set of finite binary matrices of a given size is known to carry a finite type AA bicrystal structure. We first review this classical construction, explain how it yields a short proof of the equality between Kostka polynomials and one-dimensional sums t ...

We present two open-source Python packages: "electron spectro-microscopy"(espm) and "electron microscopy tables"(emtables). The espm software enables the simulation of scanning transmission electron microscopy energy-dispersive X-ray spectroscopy datacubes ...

We prove that for any triangle-free intersection graph of n axis-parallel line segments in the plane, the independence number alpha of this graph is at least alpha n/4+ohm(root n). We complement this with a construction of a graph in this class satisfying ...

We approach the graph generation problem from a spectral perspective by first generating the dominant parts of the graph Laplacian spectrum and then building a graph matching these eigenvalues and eigenvectors. Spectral conditioning allows for direct model ...

An integer linear program is a problem of the form max{c^T x : Ax=b, x >= 0, x integer}, where A is in Z^(n x m), b in Z^m, and c in Z^n. Solving an integer linear program is NP-hard in general, but there are several assumptions for which it becomes fixed ...

Transition from fossils to renewables is leading to radical societal changes. Shifting the capital from fossils to renewables is commonly accompanied with political concerns, such as energy autonomy, domestic employment etc. Despite a decreasing trend in r ...

We study experiment design for unique identification of the causal graph of a system where the graph may contain cycles. The presence of cycles in the structure introduces major challenges for experiment design as, unlike acyclic graphs, learning the skele ...

Non-convex constrained optimization problems have become a powerful framework for modeling a wide range of machine learning problems, with applications in k-means clustering, large- scale semidefinite programs (SDPs), and various other tasks. As the perfor ...

Superoxide radicals (O-2(center dot-)) have been suggested as an important chain carrier in the radical chain reaction that promotes ozone (O-3) decomposition to hydroxyl radicals ((OH)-O-center dot) during ozonation. However, due to the difficulty in meas ...

Decomposition of Geometric Set Systems and Graphs

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Accelerating Spectral Clustering under Fairness Constraints

Non-planarity of Markoff graphs mod p

The connection of the acyclic disconnection and feedback arc sets - On an open problem of Figueroa et al

A Note on Lenses in Arrangements of Pairwise Intersecting Circles in the Plane

BENIGN LANDSCAPES OF LOW-DIMENSIONAL RELAXATIONS FOR ORTHOGONAL SYNCHRONIZATION ON GENERAL GRAPHS

Independence numbers of polyhedral graphs

A full characterization of invariant embeddability of unimodular planar graphs

Beyond Spectral Gap: The Role of the Topology in Decentralized Learning

Equivariant Neural Architectures for Representing and Generating Graphs

GRAMM: Fast CGRA Application Mapping Based on A Heuristic for Finding Graph Minors

Stochastic homogenization of degenerate integral functionals with linear growth

Duality and bicrystals on infinite binary matrices

espm: A Python library for the simulation of STEM-EDXS datasets

ON THE INDEPENDENCE NUMBER OF INTERSECTION GRAPHS OF AXIS-PARALLEL SEGMENTS

SPECTRE: Spectral Conditioning Helps to Overcome the Expressivity Limits of One-shot Graph Generators

Results on Sparse Integer Programming and Geometric Independent Sets

Where is the money ? A decomposition of monetary flows behind fossil fuels

A Unified Experiment Design Approach for Cyclic and Acyclic Causal Models

Augmented Lagrangian Methods for Provable and Scalable Machine Learning

Evaluation of the role of superoxide radical as chain carrier for the formation of hydroxyl radical during ozonation