相关论文: Strong Traces Model of Self-Assembly Polypeptide S…
In $2013$ a novel self-assembly strategy for polypeptide nanostructure design which could lead to significant developments in biotechnology was presented in [Design of a single-chain polypeptide tetrahedron assembled from coiled-coil…
For a graph $G$ and $E \subseteq E(G)$, $E$-restricted strong trace is a closed walk which traverses every edge from $E$ once in each direction and every other edge twice in the same direction. In addition, every time a strong trace come to…
Recently designed biomolecular approaches to build single chain polypeptide polyhedra as molecular origami nanostructures have risen high interest in various double traces of the underlying graphs of these polyhedra. Double traces are walks…
Experiments have reached a monumental capacity for designing and synthesizing microscopic particles for self-assembly, making it possible to precisely control particle concentrations, shapes, and interactions. However, more physical insight…
Peptides are recognized for their varied self-assembly behaviors, forming a wide array of structures and geometries, such as spheres, fibers, and hydrogels, each presenting a unique set of material properties. The functionalities of these…
A parallel $d$-stable trace is a closed walk which traverses every edge of a graph exactly twice in the same direction and for every vertex $v$, there is no subset $X \subseteq N(v)$ with $1 \leq |N| \leq d$ such that every time the walk…
Peppytides is a coarse-grained, accurate, physical model of the polypeptide chain. I have shared instructions to make your own polypeptide chain and STL files of Peppytides in MAKE magazine in Jan 2014 issue. However, Peppytides involves a…
Multilevel self-assembly involving small structured groups of nano-particles provides new routes to development of functional materials with a sophisticated architecture. Apart from the inter-particle forces, the geometrical shapes and…
Graphs as a type of data structure have recently attracted significant attention. Representation learning of geometric graphs has achieved great success in many fields including molecular, social, and financial networks. It is natural to…
Self-assembling peptides (SAPs) have the ability to spontaneously assemble into ordered nanostructures enabling the manufacture of "designer" nanomaterials. The reversible molecular association of SAPs has been shown to offer great promise…
In recent experiments [T. Basta et al., Proc. Natl. Acad. Sci. U.S.A. 111, 670 (2014)] lipids and membrane proteins were observed to self-assemble into membrane protein polyhedral nanoparticles (MPPNs) with a well-defined polyhedral protein…
Electronically-active organic molecules have demonstrated great promise as novel soft materials for energy harvesting and transport. Self-assembled nanoaggregates formed from $\pi$-conjugated oligopeptides composed of an aromatic core…
This paper develops a structural theory of unique shortest paths in real-weighted graphs. Our main goal is to characterize exactly which sets of node sequences, which we call path systems, can be realized as unique shortest paths in a graph…
DNA self-assembly is an important tool that has a wide range of applications such as building nanostructures, the transport of target virotherapies, and nano-circuitry. Tools from graph theory can be used to encode the biological process of…
Self-assembly in the laboratory can now yield `information-rich' nanostructures in which each component is of a distinct type and has a defined spatial position. Ensuring the thermodynamic stability of such structures requires…
Self-assembling peptides (SAPs) have shown to offer great promise in therapeutics and have the ability to undergo self-assembly and form ordered nanostructures. However SAP gels are often associated with inherent weak and transient…
Highly connected and yet sparse graphs (such as expanders or graphs of high treewidth) are fundamental, widely applicable and extensively studied combinatorial objects. We initiate the study of such highly connected graphs that are, in…
Persistence diagrams (PDs), often characterized as sets of death and birth of homology class, have been known for providing a topological representation of a graph structure, which is often useful in machine learning tasks. Prior works rely…
In real-world systems, the relationships and connections between components are highly complex. Real systems are often described as networks, where nodes represent objects in the system and edges represent relationships or connections…
We study the graphs formed from instances of the stable matching problem by connecting pairs of elements with an edge when there exists a stable matching in which they are matched. Our results include the NP-completeness of recognizing…