If there exists a partition of V ( G ) into p convex sets we say that G is p-convex. We prove that it is N P-complete to decide whether a graph G is p-convex for a fixed integer p ≥ 2. We show that every connected chordal graph is p-convex, for 1 ≤ p ≤ n. We also...
04 DANIEL MCGINNIS_ A FAMILY OF CONVEX SETS IN THE PLANE SATISFYING THE ( 4 , 3 ) - 42:56 BENJAMIN SCHRAEN_ AROUND THE CLASSICALITY OF P-ADIC AUTOMORPHIC FORMS 56:22 ABHISHEK SAHA_ QUANTUM UNIQUE ERGODICITY FOR SAITO-KUROKAWA LIFTS 59:38 JASMIN MATZ_ EQUIDISTRIBUTION IN AUTOMORPHIC ...
CONVEX TRANSLATES 1:00:05 FLOER-THEORETIC FILTRATION OF PAINLEVÉ HITCHIN SPACES 1:14:25 CROSSING NUMBERS OF CROSSING-CRITICAL GRAPHS 1:00:15 CANONICAL RESULTS IN RAMSEY THEORY 1:03:39 ALMOST OPTIMAL PACKINGS OF EQUAL SPHERES IN DIMENSIONS 8 AND 24 1:31:23 IDEAL-THEORETIC STUDY OF CRITICAL ...
However, they are not ideal for large data sets due to dimensionality. The low-density areas as noise make the algorithms based on this clustering method unable to detect intrinsic cluster structure common in real-life data. There is also the problem of cluster border detection because there is...
choice() # sets of closed switches in unsafe power flows >>> tl.draw(closed_switches)New configuration must be one of the safe flows, and must be realized with least switch operations. We put a score (edge weight) on a new switch status if it is inconsistent with the current status, ...
In this work, we identify three desiderata for graph-rewiring: (i) reduce over-squashing, (ii) respect the locality of the graph, and (iii) preserve the sparsity of the graph. We highlight fundamental trade-offs that occur between spatial and spectral rewiring techniques; while the former ...
Machine learning plays an increasingly important role in many areas of chemistry and materials science, being used to predict materials properties, accelerate simulations, design new structures, and predict synthesis routes of new materials. Graph neural networks (GNNs) are one of the fastest growing ...
sets the graph constraint parameterλto characterize the spatial relationships and dependences in the low-dimensional embeddingZ. Subsequently, GraphPCA infers the embedding matrixZby integrating both spatial locationSand gene expression informationXby solving a non-convex optimization problem with graph ...
Zhang, Convex sets in graphs. Congr. Numer. 136, 19–32 (1999) MathSciNet MATH Google Scholar G. Chartrand, P. Zhang, On the chromatic dimension of a graph. Congr. Numer. 145, 97–108 (2000) MathSciNet MATH Google Scholar G. Chartrand, P. Zhang, The theory and applications of...
However, in practice, the types of cost functions and constraints allowed by the communication format are usually restricted to functions that facilitate the dispatch problem’s solution (e.g. (4)). In contrast, the actual costs and constraints (2b) may be strongly non-convex. Therefore, the...