We present a cubical type theory based on the Cartesian cube category (faces, degeneracies, symmetries, diagonals, but no connections or reversal) with univalent universes, each containing Π, Σ, path, identity, natural number, boolean, pushout, and glue (equivalence extension) types. The type theory includes a syntactic description of a uniform Kan operation, along with judgemental equality rul...

The structure of N,N'-bis(2-hydroxybenzylidene)-2,2-dimethyl-1,3-propanediamine, C19H22N2O2, has been studied at low temperature (120K) by means of single-crystal X-ray diffraction. Solving the structure shows an orthorhombic unit cell, with P212121 space group, Z = 4, a = 6.1046 (4) Å, b = 15.8349 (11)</e...

background drug design against human immunodeficiency virus type 1 (hiv-1) integrase through its mechanistic study is of great interest in the area in biological research. the main obstacle in this area is the absence of the full-length crystal structure for hiv-1 integrase to be used as a model. a complete structure, similar to hiv-1 of a prototype foamy virus integrase in complex with dna, in...

Cohomology groups and the cohomology ring of threedimensional (3D) objects are topological invariants that characterize holes and their relations. Cohomology ring has been traditionally computed on simplicial complexes. Nevertheless, cubical complexes deal directly with the voxels in 3D images, no additional triangulation is necessary. This could facilitate efficient algorithms for the computat...

Ehrenborg noted that all tilings of a bipartite planar graph are encoded by its cubical matching complex and claimed this is collapsible. We point out to an oversight in his proof explain why these complexes can be the disjoint union two or more collapsible complexes. also prove links suspensions up homotopy. Furthermore, we extend definition graphs not necessarily bipartite, show either contra...

K Maps are generally and ideally , thought to be simplest form for obtaining solution of Boolean equations.Cubical Representation of Boolean equations is an alternate pick to incur a solution, otherwise to be meted out with Truth Tables, Boolean Laws and different traits of Karnaugh Maps. Largest possible kcubes that exist for a given function are equivalent to its prime implicants. A technique...