•We construct compact orientable surfaces the number of whose boundary components is one (called thickened graphs), which are used to synthesize DNA and polypeptide molecules.•We specifically give an ...algorithm to obtain thickened graphs by using two types of junctions: the 0-crossing junction (called τ-junction) and a special d(v)-crossing junction (called π-junction-junction), where d(v) is the degree of the vertex v at which the d(v)-crossing junction is to be placed.•We use 2-connected plane graphs (allowed to have multiple edges, and not have loops) instead of platforms seen as polyhedral graphs in biosynthesis.
The constructions of three-dimensional synthetic DNA and polypeptide structures with a single closed DNA strand and polypeptide chain are mathematically based on strong traces of polyhedral graphs. However, a method developed for constructing such a DNA and polypeptide structure may impose additional restrictions on the types of strong traces and polyhedral graphs. In this paper, we show that strong traces for certain 2-connected plane graphs (allowed to have multiple edges) can be obtained using thickened graphs (sometimes called ribbon graphs) constructed with only two types of junctions : 0-crossing junction and special d(v)-crossing junction (called π-junction), where d(v) is the degree of the vertex v at which the d(v)-crossing junction is to be placed. The π-junctions are only applicable to vertices with odd degrees (≥3). We characterize the 2-connected plane graphs to which our approach can be applied and provide a brief guideline for the implementation of our method. This approach provides the theory, as well as a set of candidates, for designing and constructing stable DNA and polypeptide molecules needing only a method capable of creating the 0-crossing and π-junctions in a 2-connected plane graph.
We establish the well-posedness of an initial-boundary value problem of mixed type for a stochastic nonlinear parabolic-hyperbolic equation on a space domain O=O′×O″ where a Neumann boundary ...condition is imposed on ∂O′×O″, the hyperbolic boundary, and a Dirichlet condition is imposed on O′×∂O″, the parabolic boundary. Among other points to be highlighted in our analysis of this problem we mention the new strong trace theorem for the special class of stochastic nonlinear parabolic-hyperbolic equations studied here, which is decisive for the uniqueness of the kinetic solution, and the new averaging lemma for the referred class of equations which is a vital part of the proof of the strong trace property. We also provide a detailed analysis of the approximate nondegenerate problems, which is also made here for the first time, as far as the authors know, whose solutions we prove to converge to the solution of our initial-boundary value problem.
We establish the well-posedness of the Neumann problem for stochastic conservation laws with multiplicative noise. As a crucial point in order to prove the uniqueness of the kinetic solution to the ...referred problem we establish a new strong trace theorem for stochastic conservation laws, which extends to the stochastic context the pioneering theorem by Vasseur. Existence of kinetic solutions is proved through the vanishing viscosity method and the detailed analysis of the corresponding stochastic parabolic problem is also made here for the first time, as far as the authors know.
This paper proposed new transient power quality disturbances (PQDs) detection using strong trace filter (STF). By appropriate filter model design, when there are stationary PQDs the STF works as the ...same as Kalman filter, while when there are transient disturbances the STF indicates each sudden change of the distorted waveform by the fading factor (FF). The FF can also reveal which parameter of the signal component is changing and its sensitivity to sudden change can be tuned by the soften factor easily to avoid noise influence. Besides, the STF is a small algorithm, which can be easily implemented on embedded system for real-time and time-varying detection. Both simulation and experiment suggest that the STF is a good solution for transient PQDs detection.
This paper proposed a parameterization power data compress using strong trace filter (STF) and dynamics (Dyn). The STF estimates the fundamental and harmonic component parameters. When there are only ...fundamental and harmonic components, the power data frame is compressed in parameter form. When there are other disturbances, the fading factors of STF and Dyn are used to recognize possible transient disturbances and interharmonics, respectively. By subtracting the fundamental and harmonic components, the residue of disturbances is coded by lifting wavelet transform (LWT). Then, the estimated parameters and LWT coefficients are used to reconstruct the power signal. The proposed method places emphasis on two important steps of parameterization power data compress and has a better performance than that of the related methods when the compress ratio is the same.
In 2013 a novel self-assembly strategy for polypeptide nanostructure design which could lead to significant developments in biotechnology was presented in Gradišar et al. (Nat Chem Bio 9:362–366,
...2013
). It was since observed that a polyhedron
P
can be realized by interlocking pairs of polypeptide chains if its corresponding graph
G
(
P
) admits a strong trace. It was since also demonstrated that a similar strategy can also be expanded to self-assembly of designed DNA (Kočar, Nat commun 7:1–8,
2016
). In this direction, in the present paper we characterize graphs which admit closed walk which traverses every edge exactly once in each direction and for every vertex
v
, there is no subset
N
of its neighbors, with
1
≤
|
N
|
≤
d
, such that every time the walk enters
v
from
N
, it also exits to a vertex in
N
. This extends Thomassen’s characterization (Thomassen, J Combin Theory Ser B 50:198–207,
1990
) for the case
d
=
1
.
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