Each crumpled 4-cube is a closed 4-cell-complement

The Splitting Number of the 4-Cube

The splitting number of a graph G consists in the smallest positive integer k 0, such that a planar graph can be obtained from G by k splitting operations, such operation replaces v by two nonadjacent vertices v1 and v2, and attaches the neighbors of v either to v1 or to v2. One of the most useful graphs in computer science is the n{cube. Dean and Richter devoted an article to proving that the ...

OCT-4 Is a Good Predictive Biomarker for Local Recurrence in Head and Neck Basal Cell Carcinoma

Background and Aim: Basal cell carcinoma (BCC) is considered to be the most common malignancy in humans and occurs primarily in the skin especially in the head and neck region. Considering the high recurrence rate of the tumor, finding a marker for prediction of recurrence is very important. Cancer stem cells are a small subpopulation in the tumors that are related to tumorigenesis and recurren...

Closed 2-cell embeddings of 4 cross-cap embeddable graphs

The strong embedding conjecture states that every 2-connected graph has a closed 2-cell embedding in some surface , i . e . an embedding that each face is bounded by a circuit in the graph . A graph is called k -crosscap embeddable if it can be embedded in the surface of non-orientable genus k . We confirm the strong embedding conjecture for 5-crosscap embeddable graphs . As a corollary , every...

The Complement of a D-Tree is Pure Shellable

Cube-4 - A Scalable Architecture for Real-Time Volume Rendering

We present Cube-4, a special-purpose volume rendering architecture that is capable of rendering high-resolution (e.g., 10243) datasets at 30 frames per second. The underlying algorithm, called slice-parallel ray-casting, uses tri-linear interpolation of samples between data slices for parallel and perspective projections. The architecture uses a distributed interleaved memory, several parallel ...