Related papers: Decoupled molecules with binding polynomials of bi…
Ultracold polar molecules in multilayered systems have been experimentally realized very recently. While experiments study these systems almost exclusively through their chemical reactivity, the outlook for creating and manipulating exotic…
Entanglement is crucial to many quantum applications including quantum information processing, simulation of quantum many-body systems, and quantum-enhanced sensing. Molecules, because of their rich internal structure and interactions, have…
An RNA molecule is structured on several layers. The primary and most obvious structure is its sequence of bases, i.e. a word over the alphabet {A,C,G,U}. The higher structure is a set of one-to-one base-pairings resulting in a…
We examine a class of geometric theorems on cyclic 2n-gons. We prove that if we take n disjoint pairs of sides, each pair separated by an even number of polygon sides, then there is a linear combination of the angles between those sides…
We show that for any set of n distinct points in the complex plane, there exists a polynomial p of degree at most n+1 so that the corresponding Newton map, or even the relaxed Newton map, for p has the given points as a super-attracting…
Molecular docking is an essential tool for drug design. It helps the scientist to rapidly know if two molecules, respectively called ligand and receptor, can be combined together to obtain a stable complex. We propose a new multi-objective…
Cells possess non-membrane-bound bodies, many of which are now understood as phase-separated condensates. One class of such condensates is composed of two polymer species, where each consists of repeated binding sites that interact in a…
We describe the entanglement of two indistinguishable delocalized spin-$\frac{1}{2}$ particles in the simplest spatial configuration of three spatial modes with the constraint that at most one particle occupy each mode. It is show that this…
Consider the $n$th degree polynomial equation, $X^n+A_{n-1}X^{n-1}+...+A_1X+A_0=0$ over the ring of 2 by 2 complex matrices. If this equation has more than ${2n \choose 2}$ solutions, then it has infinitely many solutions. We show here that…
We present a general criterion for entanglement of N indistinguishable particles decomposed into arbitrary s subsystems based on the unambiguous measurability of correlation. Our argument provides a unified viewpoint on the entanglement of…
Molecule representation learning is crucial for understanding and predicting molecular properties. However, conventional atom-centric models, which treat chemical bonds merely as pairwise interactions, often overlook complex bond-level…
Several convenient formulae for the entanglement of two indistinguishable delocalised spin-1/2 particles are introduced. This generalizes the standard formula for concurrence, valid only in the limit of localised or distinguishable…
Different types of ligands compete in binding to polymers with different consequences for the physical and chemical properties of the resulting complex. Here, we derive a general kinetic model for the competitive binding kinetics of…
We study the monodromy groups of compositions of two indecomposable polynomials. In particular, we show that such monodromy groups either fulfill a certain "largeness" property, or are in an explicit list of exceptions. Such largeness…
We utilise the two principles of decoupling introduced in [arXiv:2407.16108] to prove decoupling for two types of surfaces exhibiting radial symmetry. The first type are surfaces of revolution in $\mathbb R^n$ generated by smooth surfaces…
In this paper, we give sharp upper and lower bounds for the number of degenerate monic (and arbitrary, not necessarily monic) polynomials with integer coefficients of fixed degree $n \ge 2$ and height bounded by $H \ge 2$. The polynomial is…
Molecular Communications (MC) is a bio-inspired communication technique that uses molecules to transfer information among bio-nano devices. In this paper, we focus on the detection problem for biological MC receivers employing ligand…
The adhesion of biomembranes is mediated by the binding of membrane-anchored receptor and ligand proteins. The proteins can only bind if the separation between apposing membranes is sufficiently close to the length of the protein complexes,…
In this paper we obtain the first general multi-component solution to thermodynamic perturbation theory for the case that molecules can participate in cyclic double bonds. In contrast to previous authors, we do not restrict double bonding…
We derive a many-particle inseparability criterion for mixed states using the relation between single-mode and many-particle nonclassicalities. It works very well not only in the vicinity of the Dicke states, but also for the superposition…