In this paper, we enumerate the parameter matrices of all perfect $2$-colorings of the Platonic graphs consisting of the tetrahedral graph, the cubical graph, the octahedral graph, the dodecahedral graph, and  the icosahedral graph.

Many techniques for tracking based on gradient descent cannot follow objects as they undergo large movements or deformation. On the other hand, multi-hypothesis trackers capable of handling such behavior are computationally expensive. The standard graph cut technique offers a middle ground, quickly capturing objects anywhere in the image; however, because of its global nature, it is prone to ca...

Disorders of the Central Nervous System (CNS) are worldwide causes of morbidity and mortality. In order to further investigate the nature of the CNS research, we generate from an initial reference a controlled vocabulary and ontological tree structure for this vocabulary, and then apply the vocabulary in an analysis of the past ten years of abstracts (n = 10,468) from a major neuroscience journ...

A service is designed to interact with other services. If the service interaction is stateful and asynchronous, the interaction protocol can become quite complex. A service may be able to interact with a lot of possible partner services, one partner or no partner at all. Having no partner surely is not intended by the designer. But the stateful interaction between services can be formalized and...

a signed graph (marked graph) is an ordered pair $s=(g,sigma)$$(s=(g,mu))$, where $g=(v,e)$ is a graph called the underlyinggraph of $s$ and $sigma:erightarrow{+,-}$$(mu:vrightarrow{+,-})$ is a function. for a graph $g$, $v(g),e(g)$ and $c(g)$ denote its vertex set, edge set and cut-vertexset, respectively. the lict graph $l_{c}(g)$ of a graph $g=(v,e)$is defined as the graph having vertex set ...

Abstract Student-centered active learning pedagogies improve outcomes and increase the engagement of underrepresented groups. Implementing such requires interactive tools for students to manipulate inputs use outputs construct knowledge. This work introduces worksheets teaching about atmospheric aerosol cloud physics describes toolchain create deliver content. The material is appropriate upper-...

Causal Emotion Entailment aims to identify causal utterances that are responsible for the target utterance with a non-neutral emotion in conversations. Previous works limited thorough understanding of conversational context and accurate reasoning cause. To this end, we propose Knowledge-Bridged Interaction Network (KBCIN) commonsense knowledge (CSK) leveraged as three bridges. Specifically, con...

Network sampling is an indispensable tool for understanding features of large complex networks where it practically impossible to search over the entire graph. In this paper, we develop a framework statistical inference counting network motifs, such as edges, triangles and wedges, in widely used subgraph model, each vertex sampled independently, induced by vertices observed. We derive necessary...

let $g$ be a group. the order graph of $g$ is the (undirected)graph $gamma(g)$,those whose vertices are non-trivial subgroups of $g$ and two distinctvertices $h$ and $k$ are adjacent if and only if either$o(h)|o(k)$ or $o(k)|o(h)$. in this paper, we investigate theinterplay between the group-theoretic properties of $g$ and thegraph-theoretic properties of $gamma(g)$. for a finite group$g$, we s...

The family of all independent k-sets a graph containing fixed vertex v is called star and its center. Stars are interesting for their relation to Erdős–Ko–Rado graphs. Hurlbert Kamat conjectured that in trees the largest stars centered leaves. This conjecture was disproven independently by Baber, Borg, Feghali, Johnson, Thomas. In this paper we introduce tool bound size at certain vertices We u...