Related papers: Planar diagrams from optimization
To better understand the flows of ideas or information through social and biological systems, researchers develop maps that reveal important patterns in network flows. In practice, network flow models have implied memoryless first-order…
Mechanically bonded membranes of interlocked ring polymers are a significant generalization of conventional elastic sheets, where connectivity is provided by covalent bonding, and represent a promising class of topological meta-materials.…
Grid diagrams with their relatively simple mathematical formalism provide a convenient way to generate and model projections of various knots. It has been an open question whether these 2D diagrams can be used to model a complex 3D process…
Certain sequences of peptoid polymers (synthetic analogs of peptides) assemble into bilayer nanosheets via a nonequilibrium assembly pathway of adsorption, compression, and collapse at an air-water interface. As with other large-scale…
We suggest a new random model for links based on meander diagrams and graphs. We then prove that trivial links appear with vanishing probability in this model, no link $L$ is obtained with probability 1, and there is a lower bound for the…
The scattering function and radius of gyration of an ideal polymer network are calculated depending on the strength of the bonds that form the crosslinks. Our calculations are based on an {\it exact} theorem for the characteristic function…
Many topological data analysis (TDA) pipelines compute large collections of persistence diagrams, yet vectorizations and kernel methods discard the rank-induced implication relations among persistence intervals that are essential for…
Three-way data structures, characterized by three entities, the units, the variables and the occasions, are frequent in biological studies. In RNA sequencing, three-way data structures are obtained when high-throughput transcriptome…
We derive and analyze a novel approach for modeling and computing the mechanical relaxation of incommensurate 2D heterostructures. Our approach parametrizes the relaxation pattern by the compact local configuration space rather than real…
We study a simple solvable model describing the genesis of monomer sequences for hetero-polymers (such as proteins), as the result of the equilibration of a slow stochastic genetic selection process which is assumed to be driven by the…
Lateral microsegregation in a monolayer of a binary mixture of particles or macromolecules is studied by MD simulations in a generic model with the interacting potentials inspired by effective interactions in biological or soft-matter…
A coarse-graining strategy, previously developed for polymer solutions, is extended here to mixtures of linear polymers and hard-sphere colloids. In this approach groups of monomers are mapped onto a single pseudoatom (a blob) and the…
In biology, predicting RNA secondary structures plays a vital role in determining its physical and chemical properties. Although we have powerful energy models to predict them as well as parametric analysis to understand the models…
In this note, first the Recurrent Variational Approach (RVA) is introduced by using as example a non-trivial spin-model, the spin-1/2 antiferromagnetic two-leg-ladder. Then, a first application of this scheme to the electronic structure of…
The emergence of longer information-carrying and functional nucleotide polymers from random short strands was a major stepping stone at the dawn of life. But the formation of those polymers under temperature oscillation required some form…
We propose and solve a simple model describing secondary structure formation in random hetero-polymers. It describes monomers with a combination of one-dimensional short-range interactions (representing steric forces and hydrogen bonds) and…
We present a unified scaling theory for the dynamics of monomers for dilute solutions of semiflexible polymers under good solvent conditions in the free draining limit. Our theory encompasses the well-known regimes of mean square…
Branching architecture characterizes numerous systems, ranging from synthetic (hyper)branched polymers and biomolecules such as lignin, amylopectin, and nucleic acids to tracheal and neuronal networks. Its ubiquity reflects the many…
In this work we characterize the configurational space of a short chain of colloidal particles as function of the range of directional and heterogeneous isotropic interactions. The individual particles forming the chain are colloids…
The primary structure of a ribonucleic acid (RNA) molecule can be represented as a sequence of nucleotides (bases) over the alphabet {A, C, G, U}. The secondary or tertiary structure of an RNA is a set of base pairs which form bonds between…