Related papers: Single-Molecule Morphology of Topologically Digest…
DNA is an ideal candidate to organize matter on the nanoscale, primarily due to the specificity and complexity of DNA based interactions. Recent advances in this direction include the self-assembly of colloidal crystals using DNA grafted…
The unconstrained genomic DNA of bacteria forms a coil, which volume exceeds 1000 times the volume of the cell. Since prokaryotes lack a membrane-bound nucleus, in sharp contrast with eukaryotes, the DNA may consequently be expected to…
Within animals, oxygen exchange occurs within networks containing potentially billions of microvessels that are distributed throughout the animal's body. Innovative imaging methods now allow for mapping of the architecture and blood flows…
A theory is presented of DNA hairpins enclosed in a nanochannel. A hairpin becomes constrained as it approaches the wall of a channel which leads to an entropic force causing the hairpin to tighten. The free energy of the hairpin computed…
Blends of polymers of different topologies, such as ring and supercoiled, naturally occur in biology and often exhibit emergent viscoelastic properties coveted in industry. However, due to their complexity, along with the difficulty of…
Multiple scales coexist in complex networks. However, the small world property makes them strongly entangled. This turns the elucidation of length scales and symmetries a defiant challenge. Here, we define a geometric renormalization group…
Natural protein sequences that self-assemble to form globular structures are compact with high packing densities in the folded states. It is known that proteins unfold upon addition of denaturants, adopting random coil structures. The…
Networks are mathematical structures that are universally used to describe a large variety of complex systems such as the brain or the Internet. Characterizing the geometrical properties of these networks has become increasingly relevant…
We examine the conformations of a model for a short segment of closed DNA. The molecule is represented as a cylindrically symmetric elastic rod with a constraint corresponding to a specification of the linking number. We obtain analytic…
This paper introduces an adaptive convolutional neural network (CNN) architecture capable of automating various topology optimization (TO) problems with diverse underlying physics. The proposed architecture has an encoder-decoder-type…
We introduce an innovative, data-driven topological data analysis (TDA) technique for estimating the state spaces of dynamically changing functional human brain networks at rest. Our method utilizes the Wasserstein distance to measure…
Understanding the structural complexity and predictability of complex networks is a central challenge in network science. Although recent studies have revealed a relationship between compression-based entropy and link prediction…
Physical networks are made of nodes and links that are physical objects embedded in a geometric space. Understanding how the mutual volume exclusion between these elements affects the structure and function of physical networks calls for a…
Due to its longevity and enormous information density, DNA is an attractive medium for archival data storage. Thanks to rapid technological advances, DNA storage is becoming practically feasible, as demonstrated by a number of experimental…
We study complex networks formed by triangulations and higher-dimensional simplicial complexes representing closed evolving manifolds. In particular, for triangulations, the set of possible transformations of these networks is restricted by…
DNA frequently adopts liquid-crystalline conformations in both cells and viruses. The Oseen--Frank framework provides a powerful continuum description of these phases through three elastic moduli: splay ($K_1$), twist or cholesteric…
Segmentation in arthropod embryogenesis represents a well-known example of body plan diversity. Striped patterns of gene expression that lead to the future body segments appear simultaneously or sequentially in long and short germ-band…
At the core of high throughput DNA sequencing platforms lies a bio-physical surface process that results in a random geometry of clusters of homogenous short DNA fragments typically hundreds of base pairs long - bridge amplification. The…
Reinforced elastic sheets surround us in daily life, from concrete shell buildings to biological structures such as the arthropod exoskeleton or the venation network of dicotyledonous plant leaves. Natural structures are often highly…
As protein folding is a NP-complete problem, artificial intelligence tools like neural networks and genetic algorithms are used to attempt to predict the 3D shape of an amino acids sequence. Underlying these attempts, it is supposed that…