We begin by considering certain analogues, in finite 3-dimensional affine spaces, of the ordinary cube. From the properties of these structures (as geometric lattices having point sets which are threefold Cartesian products) we derive the notion of an (abstract) finite cube. By studying the additional properties (including the properties of certain groups associated with the cube) of members of...

Despite a staggering technical progress in echocardiography, in daily clinical practice assessment of left ventricular (LV) ejection fraction (EF) is still often done in a rather inaccurate two-dimensional (2D) manner. Real-time three-dimensional echocardiography (RT3DE) provides a more representative realistic view of LV volumes, thereby being the Necker cube for the naive realism of 2D method...

Clathrin triskelions form polyhedral cages with hexagonal and pentagonal faces when dialyzed against suitable assembly buffers. However, when the buffer is made 12% saturated in ammonium sulfate and the dialysis is performed at 4 degrees C, clathrin polymerizes into cubes. The cube is constructed from eight triskelions with one at each corner. The edge length of the cube is approximately 45 nm,...

Algebraic attacks is a powerful type of attacks against LFSR-based stream ciphers. Solving large sparse linear equations Ax = b is needed for this attack. The traditional Gaussian elimination is not efficient for such matrix equations because of its cube run time complexity. Quadratic run time algorithms like Lanczos or Wiedemann Methods are the better for such large sparse matrices. We impleme...

We study the cube of type assignment systems, as introduced in [10]. This cube is obtained from Barendregt’s typed -cube [1] via a natural type erasing function E, that erases type information from terms. We prove that the systems in the former cube enjoy good computational properties, like subject reduction and strong normalization. We study the relationship between the two cubes, which leads ...

This paper proves the reconstruction conjecture for graphs which are isomorphic to the cube of a tree. The proof uses the reconstructibility of trees from their peripheral vertex deleted subgraphs. The main result follows from (i) characterization of the cube of a tree (ii) recognizability of the cube of a tree (iii) uniqueness of tree as a cube root of a graph G, except when G is a complete gr...

“Suppose a man born blind, and now adult, and taught by his touch to distinguish between a Cube, and a Sphere ..., so as to tell, when he felt one and t’other, which is the Cube, which the Sphere. Suppose then the Cube and Sphere placed on a Table, and the Blind Man to be made to see. Quære, whether by his sight, before he touched them, he could now distinguish, and tell, which is the Globe, wh...

“Suppose a man born blind, and now adult, and taught by his touch to distinguish between a Cube, and a Sphere..., so as to tell, when he felt one and t’other, which is the Cube, which the Sphere. Suppose then the Cube and Sphere placed on a Table, and the Blind Man to be made to see. Quære, whether by his sight, before he touched them, he could now distinguish, and tell, which is the Globe, whi...