5,795 research outputs found
Distinguishing partitions of complete multipartite graphs
A \textit{distinguishing partition} of a group with automorphism group
is a partition of that is fixed by no nontrivial element of
. In the event that is a complete multipartite graph with its
automorphism group, the existence of a distinguishing partition is equivalent
to the existence of an asymmetric hypergraph with prescribed edge sizes. An
asymptotic result is proven on the existence of a distinguishing partition when
is a complete multipartite graph with parts of size and
parts of size for small , and large , . A key tool
in making the estimate is counting the number of trees of particular classes
Stochastically Stable Equilibria in Coordination Games with Multiple Populations
We investigate the equilibrium selection problem in n-person binary coordination games by means of adaptive play with mistakes (Young 1993). The size and the depth of a particular type of basins of attraction are found to be the main factors in determining the selection outcome. The main result shows that if a strategy has the larger basin of attraction, and if it is deep enough, then the strategy constitutes a stochastically stable equilibrium. The existence of games with multiple stochastically stable equilibria is an immediate consequence of the result. We explicitly address the qualitative difference between selection results in multi-dimensional stochastic evolution models and those in single dimensional models, and shed some light on the source of the difference.Equilibrium selection, stochastic stability, unanimity game, coordination game
Evidence for single top quark production at D0
The results of the first analysis to show evidence for production of single
top quarks are presented. Using 0.9 fb-1 of data collected with the D0 detector
at the Fermilab Tevatron, the analysis is performed in the electron+jets and
muon+jets decay modes, taking special care in modeling the large backgrounds,
applying a new powerful b-quark tagging algorithm and using three multivariate
techniques to extract the small signal in the data. The combined measured
production cross section is 4.8 +- 1.3 pb. The probability to measure a cross
section at this value or higher in the absence of a signal is 0.027%,
corresponding to a 3.5 standard deviation significance.Comment: 6 pages, 4 figures. Presented at 42nd Rencontres de Moriond on
Electroweak Interactions and Unified Theories, La Thuile, Italy, 10-17 Mar
200
Characterizing neuromorphologic alterations with additive shape functionals
The complexity of a neuronal cell shape is known to be related to its
function. Specifically, among other indicators, a decreased complexity in the
dendritic trees of cortical pyramidal neurons has been associated with mental
retardation. In this paper we develop a procedure to address the
characterization of morphological changes induced in cultured neurons by
over-expressing a gene involved in mental retardation. Measures associated with
the multiscale connectivity, an additive image functional, are found to give a
reasonable separation criterion between two categories of cells. One category
consists of a control group and two transfected groups of neurons, and the
other, a class of cat ganglionary cells. The reported framework also identified
a trend towards lower complexity in one of the transfected groups. Such results
establish the suggested measures as an effective descriptors of cell shape
Structural Node Embeddings with Homomorphism Counts
Graph homomorphism counts, first explored by Lov\'asz in 1967, have recently
garnered interest as a powerful tool in graph-based machine learning. Grohe
(PODS 2020) proposed the theoretical foundations for using homomorphism counts
in machine learning on graph level as well as node level tasks. By their very
nature, these capture local structural information, which enables the creation
of robust structural embeddings. While a first approach for graph level tasks
has been made by Nguyen and Maehara (ICML 2020), we experimentally show the
effectiveness of homomorphism count based node embeddings. Enriched with node
labels, node weights, and edge weights, these offer an interpretable
representation of graph data, allowing for enhanced explainability of machine
learning models.
We propose a theoretical framework for isomorphism-invariant homomorphism
count based embeddings which lend themselves to a wide variety of downstream
tasks. Our approach capitalises on the efficient computability of graph
homomorphism counts for bounded treewidth graph classes, rendering it a
practical solution for real-world applications. We demonstrate their
expressivity through experiments on benchmark datasets. Although our results do
not match the accuracy of state-of-the-art neural architectures, they are
comparable to other advanced graph learning models. Remarkably, our approach
demarcates itself by ensuring explainability for each individual feature. By
integrating interpretable machine learning algorithms like SVMs or Random
Forests, we establish a seamless, end-to-end explainable pipeline. Our study
contributes to the advancement of graph-based techniques that offer both
performance and interpretability
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