Related papers: Cyclic Oritatami Systems Cannot Fold Infinite Frac…

Non-Hermitian systems exhibit interesting band structures, where novel topological phenomena arise from the existence of exceptional points at which eigenvalues and eigenvectors coalesce. One important open question is how this would…

Continuous linear dynamical systems are used extensively in mathematics, computer science, physics, and engineering to model the evolution of a system over time. A central technique for certifying safety properties of such systems is by…

Topological aspects of the geometry of DNA and similar chiral molecules have received a lot of attention, while the topology of their electronic structure is less explored. Previous experiments have revealed that DNA can efficiently filter…

In this paper, we present high-level overviews of tile-based self-assembling systems capable of producing complex, infinite, aperiodic structures known as discrete self-similar fractals. Fractals have a variety of interesting mathematical…

Two types of connected chord diagrams with chord endpoints lying in a collection of ordered and oriented real segments are considered here: the real segments may contain additional bivalent vertices in one model but not in the other. In the…

Existing state-of-the-art methods that take a single RNA sequence and predict the corresponding RNA secondary-structure are thermodynamic methods. These predict the most stable RNA structure, but do not consider the process of structure…

We prove the existence of fractal solutions to a class of linear ordinary differential equations.This reveals the possibility of chaos in the very short time limit of the evolution even of a linear one dimensional dynamical system.

Exact numerical methods and stochastic simulation methods are developed to study the force stretching single RNA issue on the secondary structure level in equilibrium. By computing the force-extension curves on the constant force and the…

When information is spatially repeated in self-similar fractal beam patterns, only a portion of the diffracted beam is needed to reconstruct the kernel data. What is unique to a fractal-encoding scheme is that the image demultiplexing…

We investigate fractal aspects of elliptical polynomial spirals; that is, planar spirals with differing polynomial rates of decay in the two axis directions. We give a full dimensional analysis of these spirals, computing explicitly their…

In this paper, we prove that in the abstract Tile Assembly Model (aTAM), an accretion-based model which only allows for a single tile to attach to a growing assembly at each step, there are no tile assembly systems capable of…

Quasicrystals are unique materials characterized by long-range order without periodicity. They are observed in systems such as metallic alloys, soft matter, and particle simulations. Unlike periodic crystals, which are invariant under…

Atomic orbitals underpin our understanding of electronic structure, providing intuitive descriptions of bonding, charge transfer, magnetism, and correlation effects. Despite their utility, an atomic basis that is adaptable, strictly…

The cornea provides the largest refractive power for the human visual system. Its stiffness, along with intraocular pressure (IOP), are linked to several pathologies, including keratoconus and glaucoma. Although mechanical tests can…

We formulate the RNA folding problem as an $N\times N$ matrix field theory. This matrix formalism allows us to give a systematic classification of the terms in the partition function according to their topological character. The theory is…

To study the elastic properties of rod-like DNA nanostructures, we perform long simulations of these structure using the oxDNA coarse-grained model. By analysing the fluctuations in these trajectories we obtain estimates of the bend and…

We describe new families of random fractals, referred to as "V-variable", which are intermediate between the notions of deterministic and of standard random fractals. The parameter V describes the degree of "variability" : at each…

Due to their dynamic properties such as irregular sampling rate and high-frequency sampling, Continuous Time Series (CTS) are found in many applications. Since CTS with irregular sampling rate are difficult to model with standard Recurrent…

We address the problem of analytically extracting a countable infinity of flat, non-dispersive bands in a periodic array of cells that comprise branching Vicsek geometries of higher and higher generations. Through a geometric construction,…

Fracton codes host unconventional topological states of matter and are promising for fault-tolerant quantum computation due to their large coding space and strong resilience against decoherence and noise. In this work, we investigate the…