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Measuring similarities/dissimilarities between atomic structures is important for the exploration of potential energy landscapes. However, the cell vectors together with the coordinates of the atoms, which are generally used to describe…
The short and intense pulses of the new X-ray free electron lasers, now operational or under construction, may make possible diffraction experiments on single molecule-sized objects with high resolution, before radiation damage destroys the…
Eukaryotic DNA is packaged into chromatin: one-dimensional arrays of nucleosomes separated by stretches of linker DNA are folded into 30-nm chromatin fibers which in turn form higher-order structures. Each nucleosome, the fundamental unit…
We present a quantitative measure of physical complexity, based on the amount of information required to build a given physical structure through self-assembly. Our procedure can be adapted to any given geometry, and thus to any given type…
We propose a technique, using interferometry of Bose-Einstein condensed alkali atoms, for the detection of sub-micron-range forces. It may extend present searches at 1 micron by 6 to 9 orders of magnitude, deep into the theoretically…
Protein structures can be encoded into binary sequences, these are used to define a Hamming distance in conformational space: the distance between two different molecular conformations is the number of different bits in their sequences.…
The high energy physics unfolding problem is an important statistical inverse problem in data analysis at the Large Hadron Collider (LHC) at CERN. The goal of unfolding is to make nonparametric inferences about a particle spectrum from…
This paper proposes a new mathematical framework that can be applied to biological problems such as analysis of the structures of proteins and protein complexes. In particular, it gives a new method for encoding the three-dimensional…
This work demonstrates that the convex hull of formation energies for solid compounds involving elements from hydrogen to uranium admits a remarkably simple description over the 92-dimensional space of chemical compositions, despite the…
The mode of action of proteins is to a large extent given by their ability to adopt different conformations. This is why imaging single biomolecules at atomic resolution is one of the ultimate goals of biophysics and structural biology. The…
The conformation space of cyclooctane, a ringlike organic molecule comprising eight carbon atoms, is a two-dimensional algebraic variety, which has been studied extensively for more than 90 years. We propose a cell structure representing…
The tilted-wave interferometer is a promising technique for the development of a reference measurement system for the highly accurate form measurement of aspheres and freeform surfaces. The technique combines interferometric measurements,…
Benzene, a hexagonal molecule with formula C$_6$H$_6$, is one of the most important aromatic hydrocarbons. Its structure arises from the $sp^{2}$ hybridization from which three in-plane $\sigma$-bonds are formed. A fourth $\pi$-orbital…
Improved understanding of charge-transport in single molecules is essential for harnessing the potential of molecules e.g. as circuit components at the ultimate size limit. However, interpretation and analysis of the large, stochastic…
We present a model, based on symmetry and geometry, for proteins. Using elementary ideas from mathematics and physics, we derive the geometries of discrete helices and sheets. We postulate a compatible solvent-mediated emergent pairwise…
Rapid determination of molecular structures can greatly accelerate workflows across many chemical disciplines. However, elucidating structure using only one-dimensional (1D) NMR spectra, the most readily accessible data, remains an…
Since the discovery of the fullerene C60, many very interesting structures have been proposed, such as Ti8C12, Au20, Au32, Au42, TM@Sin, Eu@Si20, B80, and B_{40}^{-/0}. Here, an exceptionally stable hollow cage containing 20 scandiums and…
The detection of fullerene molecules in a variety of astrophysical environments suggests that smaller dehydrogenated carbon molecules may also be present in these sources. One of these is planar C24 which has been shown to be more stable…
Starting with a similarity function between objects, it is possible to define a distance metric on pairs of objects, and more generally on probability distributions over them. These distance metrics have a deep basis in functional analysis,…
A novel approach for structure alignment is presented, where the key ingredients are: (1) An error function formulation of the problem simultaneously in terms of binary (Potts) assignment variables and real-valued atomic coordinates. (2)…