When working with diagrams in visual environments like graphical diagram editors, diagrams have to be represented by an internal model. Graphs and hypergraphs are well-known concepts for such internal models. This paper shows how hypergraphs can be uniformly used for a wide range of different diagram types where hyperedges are used to represent diagram components as well as spatial relationship...

Sketching, i.e., drawing diagrams by hand and directly on the screen, is gaining popularity, as it is a comfortable and natural way to create and edit diagrams. Hand drawing is inherently imprecise, and often sloppy. As a consequence, when processing hand drawn diagrams with a computer, ambiguities arise: it is not always clear what part of the drawing is meant to represent what component. Reso...

DiaGen is a specification method, which is primarily based on a hypergraph grammar, and a tool that allows to automatically generate diagram editors from such a specification. Generated editors are free-hand editors, but with an automatic, constraint-based layout for correct diagrams. A hypergraph parser checks diagram correctness and makes it possible to translate diagrams into some user-defin...

Using multimodal neuroimaging data to characterize brain network is currently an advanced technique for Alzheimer’s disease(AD) Analysis. Over recent years the community has made tremendous progress in study of resting-state functional magnetic resonance imaging (rs-fMRI) derived from blood-oxygen-level-dependent (BOLD) signals and Diffusion Tensor Imaging (DTI) white matter fiber tractography....

Recently, graph neural networks have attracted great attention and achieved prominent performance in various research fields. Most of those algorithms assumed pairwise relationships objects interest. However, many real applications, the between are higher-order, beyond a formulation. To efficiently learn deep embeddings on high-order graph-structured data, we introduce two end-to-end trainable ...

Let $nin mathbb{N}$. An additive map $h:Ato B$ between algebras $A$ and $B$ is called $n$-Jordan homomorphism if $h(a^n)=(h(a))^n$ for all $ain A$. We show that every $n$-Jordan homomorphism between commutative Banach algebras is a $n$-ring homomorphism when $n < 8$. For these cases, every involutive $n$-Jordan homomorphism between commutative C-algebras is norm continuous.

for a given hypergraph $h$ with chromatic number $chi(h)$ and with no edge containing only one vertex, it is shown that the minimum number $l$ for which there exists a partition (also a covering) ${e_1,e_2,ldots,e_l}$ for $e(h)$, such that the hypergraph induced by $e_i$ for each $1leq ileq l$ is $k$-colorable, is $lceil log_{k} chi(h) rceil$.

let $mathcal {a} $ and $mathcal {b} $ be c$^*$-algebras. assume that $mathcal {a}$ is of real rank zero and unital with unit $i$ and $k>0$ is a real number. it is shown that if $phi:mathcal{a} tomathcal{b}$ is an additive map preserving $|cdot|^k$ for all normal elements; that is, $phi(|a|^k)=|phi(a)|^k $ for all normal elements $ainmathcal a$, $phi(i)$ is a projection, and there exists a posit...

A graph homomorphism is an edge preserving vertex mapping between two graphs. Locally constrained homomorphisms are those that behave well on the neighborhoods of vertices — if the neighborhood of any vertex of the source graph is mapped bijectively (injectively, surjectively) to the neighborhood of its image in the target graph, the homomorphism is called locally bijective (injective, surjecti...

Graph homomorphism has been studied intensively. Given an m ×m symmetric matrix A, the graph homomorphism function is defined as