Search results for "Combinatorics"

Chromatic sums for colorings avoiding monochromatic subgraphs

2015

Abstract Given graphs G and H, a vertex coloring c : V ( G ) → N is an H-free coloring of G if no color class contains a subgraph isomorphic to H. The H-free chromatic number of G, χ ( H , G ) , is the minimum number of colors in an H-free coloring of G. The H-free chromatic sum of G , Σ ( H , G ) , is the minimum value achieved by summing the vertex colors of each H-free coloring of G. We provide a general bound for Σ ( H , G ) , discuss the computational complexity of finding this parameter for different choices of H, and prove an exact formulas for some graphs G. For every integer k and for every graph H, we construct families of graphs, G k with the property that k more colors than χ ( …

Decremental 2- and 3-connectivity on planar graphs

1996

We study the problem of maintaining the 2-edge-, 2-vertex-, and 3-edge-connected components of a dynamic planar graph subject to edge deletions. The 2-edge-connected components can be maintained in a total ofO(n logn) time under any sequence of at mostO(n) deletions. This givesO(logn) amortized time per deletion. The 2-vertex- and 3-edge-connected components can be maintained in a total ofO(n log2n) time. This givesO(log2n) amortized time per deletion. The space required by all our data structures isO(n). All our time bounds improve previous bounds.

Unveiling the boost in the sandwich priming technique.

2021

The masked priming technique (which compares #####-house-HOUSE vs. #####-fight-HOUSE) is the gold-standard tool to examine the initial moments of word processing. Lupker and Davis showed that adding a pre-prime identical to the target produced greater priming effects in the sandwich technique (which compares #####-HOUSE-house-HOUSE vs #####-HOUSE-fight-HOUSE). While there is consensus that the sandwich technique magnifies the size of priming effects relative to the standard procedure, the mechanisms underlying this boost are not well understood (i.e., does it reflect quantitative or qualitative changes?). To fully characterise the sandwich technique, we compared the sandwich and standard t…

Optimal Mass Transport on Metric Graphs

2015

We study an optimal mass transport problem between two equal masses on a metric graph where the cost is given by the distance in the graph. To solve this problem we find a Kantorovich potential as the limit of $p$-Laplacian--type problems in the graph where at the vertices we impose zero total flux boundary conditions. In addition, the approximation procedure allows us to find a transport density that encodes how much mass has to be transported through a given point in the graph, and also provides a simple formula of convex optimization for the total cost.

Numerical study of blow-up in solutions to generalized Kadomtsev-Petviashvili equations

2013

We present a numerical study of solutions to the generalized Kadomtsev-Petviashvili equations with critical and supercritical nonlinearity for localized initial data with a single minimum and single maximum. In the cases with blow-up, we use a dynamic rescaling to identify the type of the singularity. We present a discussion of the observed blow-up scenarios.

Words

2015

Variances as order parameter and complexity measure for random Boolean networks

2005

Several order parameters have been considered to predict and characterize the transition between ordered and disordered phases in random Boolean networks, such as the Hamming distance between replicas or the stable core, which have been successfully used. In this work, we propose a natural and clear new order parameter: the temporal variance. We compute its value analytically and compare it with the results of numerical experiments. Finally, we propose a complexity measure based on the compromise between temporal and spatial variances. This new order parameter and its related complexity measure can be easily applied to other complex systems.

Localized potentials in electrical impedance tomography

2008

In this work we study localized electric potentials that have an arbitrarily high energy on some given subset of a domain and low energy on another. We show that such potentials exist for general L ∞ -conductivities in almost arbitrarily shaped subregions of a domain, as long as these regions are connected to the boundary and a unique continuation principle is satisfied. From this we deduce a simple, but new, theoretical identifiability result for the famous Calderon problem with partial data. We also show how to con- struct such potentials numerically and use a connection with the factorization method to derive a new non-iterative algorithm for the detection of inclusions in electrical imp…

The F-pure threshold of quasi-homogeneous polynomials

2018

Abstract Inspired by the work of Bhatt and Singh [3] we compute the F-pure threshold of quasi-homogeneous polynomials. We first consider the case of a curve given by a quasi-homogeneous polynomial f in three variables x , y , z of degree equal to the degree of xyz and then we proceed with the general case of a Calabi–Yau hypersurface, i.e. a hypersurface given by a quasi-homogeneous polynomial f in n + 1 variables x 0 , … , x n of degree equal to the degree of x 0 ⋯ x n .

k-Partite Graphs as Contexts

2018

International audience; In formal concept analysis, 2-dimensional formal contexts are bipar-tite graphs. In this work, we generalise the notions of context and concept to graphs that are not bipartite. We then study the complexity of the enumeration and identify the structure of the set of such concepts.