Topological properties of flat electroencephalography’s state space

The integrable state function of delta interaction on an infinite line is constrained to a ring of finite circumference. The state function remains consistent with the Bethe ansatz, but in a multiply connected state space. The constants of integration of the integrable state function are roots of a transcendental equation determined by the topological properties of this multiply connected space.

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Strictifying and taming directed paths in Higher Dimensional Automata

Mathematical Structures in Computer Science ◽

10.1017/s0960129521000128 ◽

2021 ◽

Vol 31 (2) ◽

pp. 193-213

Author(s):

Martin Raussen

Keyword(s):

State Space ◽

Algebraic Topology ◽

Computational Topology ◽

Topological Properties ◽

Engineering Communication ◽

Higher Dimensional ◽

Directed Paths

AbstractDirected paths have been used by several authors to describe concurrent executions of a program. Spaces of directed paths in an appropriate state space contain executions with all possible legal schedulings. It is interesting to investigate whether one obtains different topological properties of such a space of executions if one restricts attention to schedulings with “nice” properties, e.g. involving synchronisations. This note shows that this is not the case, i.e. that one may operate with nice schedulings without inflicting any harm. Several of the results in this note had previously been obtained by Ziemiański in Ziemiański (2017. Applicable Algebra in Engineering, Communication and Computing28 497–525; 2020a. Journal of Applied and Computational Topology4 (1) 45–78). We attempt to make them accessible for a wider audience by giving an easier proof for these findings by an application of quite elementary results from algebraic topology; notably the nerve lemma.

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Electron Microscopy of Nucleic Acids

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100051529 ◽

1974 ◽

Vol 32 ◽

pp. 302-303

Author(s):

Norman Davidson

Keyword(s):

Electron Microscopy ◽

Nucleic Acids ◽

Basic Protein ◽

Molecular Biologist ◽

Topological Properties ◽

Protein Film ◽

Polynucleotide Chain

The basic protein film technique for mounting nucleic acids for electron microscopy has proven to be a general and powerful tool for the working molecular biologist in characterizing different nucleic acids. It i s possible to measure molecular lengths of duplex and single-stranded DNAs and RNAs. In particular, it is thus possible to as certain whether or not the nucleic acids extracted from a particular source are or are not homogeneous in length. The topological properties of the polynucleotide chain (linear or circular, relaxed or supercoiled circles, interlocked circles, etc. ) can also be as certained.

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