this paper introduces a new approach to topology, based on category theory and universal algebra, and called categorically-algebraic (catalg) topology. it incorporates the most important settings of lattice-valued topology, including poslat topology of s.~e.~rodabaugh, $(l,m)$-fuzzy topology of t.~kubiak and a.~v{s}ostak, and $m$-fuzzy topology on $l$-fuzzy sets of c.~guido. moreover, its respe...

limited only by the rules that no region can shrink to a single point or cross through another region (4). If two knots can be wrangled into one another by a finite series of such deformations, we call them “equivalent.” For any knot in 3-dimensional space, we can draw an infinite number of equivalent knots on paper by applying our favorite deformations (1, 4). Therefore, even in this naughtily...

Biological systems exploit self-assembly to create complex structures whose arrangements are finely controlled from the molecular to mesoscopic level. We report an example of using fully synthetic systems that mimic two levels of self-assembly. We show the formation of vesicles using amphiphilic copolymers whose chemical nature is chosen to control both membrane formation and membrane-confined ...

The advent of high-throughput technologies and the concurrent advances in information sciences have led to a data revolution in biology. This revolution is most significant in molecular biology, with an increase in the number and scale of the “omics” projects over the last decade. Genomics projects, for example, have produced impressive advances in our knowledge of the information concealed int...