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pro vyhledávání: '"Hall, H. P."'
Autor:
Abiad, Aida, Curtis, Bryan A., Flagg, Mary, Hall, H. Tracy, Lin, Jephian C. -H., Shader, Bryan
The inverse eigenvalue problem studies the possible spectra among matrices whose off-diagonal entries have their zero-nonzero patterns described by the adjacency of a graph $G$. In this paper, we refer to the $i$-nullity pair of a matrix $A$ as $(\op
Externí odkaz:
http://arxiv.org/abs/2310.13884
Autor:
Fallat, Shaun M., Hall, H. Tracy, Levene, Rupert H., Meyer, Seth A., Nasserasr, Shahla, Oblak, Polona, Šmigoc, Helena
If $G$ is a graph and $\mathbf{m}$ is an ordered multiplicity list which is realizable by at least one symmetric matrix with graph $G$, what can we say about the eigenvalues of all such realizing matrices for $\mathbf{m}$? It has sometimes been tempt
Externí odkaz:
http://arxiv.org/abs/2301.11073
Autor:
Cerro, G., Dasmahapatra, S., Day-Hall, H. A., Ford, B., Jain, S., Moretti, S., Shepherd-Themistocleous, C.
We present a new approach to jet definition alternative to clustering methods, such as the anti-$k_T$ scheme, that exploit kinematic data directly. Instead the new method uses kinematic information to represent the particles in a multidimensional spa
Externí odkaz:
http://arxiv.org/abs/2211.10164
The smallest possible number of distinct eigenvalues of a graph $G$, denoted by $q(G)$, has a combinatorial bound in terms of unique shortest paths in the graph. In particular, $q(G)$ is bounded below by $k$, where $k$ is the number of vertices of a
Externí odkaz:
http://arxiv.org/abs/2209.11307
In this article, we extend the notion of the Laplacian spread to simple directed graphs (digraphs) using the restricted numerical range. First, we provide Laplacian spread values for several families of digraphs. Then, we prove sharp upper bounds on
Externí odkaz:
http://arxiv.org/abs/2206.15410
We conjecture a new lower bound on the algebraic connectivity of a graph that involves the number of vertices of high eccentricity in a graph. We prove that this lower bound implies a strengthening of the Laplacian Spread Conjecture. We discuss furth
Externí odkaz:
http://arxiv.org/abs/2201.04225
The inverse eigenvalue problem of a graph studies the real symmetric matrices whose off-diagonal pattern is prescribed by the adjacencies of the graph. The strong spectral property (SSP) is an important tool for this problem. This note establishes th
Externí odkaz:
http://arxiv.org/abs/2112.11712
In 2020, Cameron et al. introduced the restricted numerical range of a digraph (directed graph) as a tool for characterizing digraphs and studying their algebraic connectivity. In particular, digraphs with a restricted numerical range of a single poi
Externí odkaz:
http://arxiv.org/abs/2106.00701
Autor:
Cerro, G., Dasmahapatra, S., Day-Hall, H. A., Ford, B., Moretti, S., Shepherd-Themistocleous, C. H.
We present a new approach to jet definition alternative to clustering methods, such as the anti-$k_T$ scheme, that exploit kinematic data directly. Instead the new method uses kinematic information to represent the particles in a multidimensional spa
Externí odkaz:
http://arxiv.org/abs/2104.01972
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