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A new concept of the molecular structure optimization method based on quantum dynamics computations is presented. Nuclei are treated as quantum mechanical particles, as are electrons, and the many-body wave function of the system is…
The flow of thin liquid films on inclined or vertical surfaces is one of immense importance, with applications spanning many types of process industries, due to the increased mass and heat transfer brought about by the presence of waves on…
The simulated self-assembly of molecular building blocks into functional complexes is a key area of study in computational biology and materials science. Self-assembly simulations of proteins using physically-motivated potentials for…
Currently it requires an artist to create 3D human avatars with realistic clothing that can move naturally. Despite progress on 3D scanning and modeling of human bodies, there is still no technology that can easily turn a static scan into…
In this lecture I give a brief review of low-dimensional few-body problems recently encountered in attempting a quantitative description of ultracold atoms and molecules confined in 2D and 1D optical lattices. Multi-channel nature of these…
In three-dimensional computational topology, the theory of normal surfaces is a tool of great theoretical and practical significance. Although this theory typically leads to exponential time algorithms, very little is known about how these…
A new approach to analyzing visual images is proposed, based on the idea of converting an optical image into a spatially varying pattern of polarized squeezed light, which is then used to produce a pattern of chiral edge currents in a thin…
Stochastic models of reaction-diffusion systems are important for the study of biochemical reaction networks where species are present in low copy numbers or if reactions are highly diffusion limited. In living cells many such systems…
Using methods of high performance computing, we have found indications that knotlike structures appear as stable finite energy solitons in a realistic 3+1 dimensional model. We have explicitly simulated the unknot and trefoil…
Geometric, topological and graph theory modeling and analysis of biomolecules are of essential importance in the conceptualization of molecular structure, function, dynamics, and transport. On the one hand, geometric modeling provides…
The realization of topological states of matter in ultracold atomic gases is currently the subject of intense experimental activity. Using a synthetic dimension, encoded in a non-spatial degree of freedom, can greatly simplify the…
Computational topology is an area that revisits topological problems from an algorithmic point of view, and develops topological tools for improved algorithms. We survey results in computational topology that are concerned with graphs drawn…
Quantum spin liquids, exotic phases of matter with topological order, have been a major focus of explorations in physical science for the past several decades. Such phases feature long-range quantum entanglement that can potentially be…
The protein folding problem must ultimately be solved on all length scales from the atomic up through a hierarchy of complicated structures. By analyzing the stability of the folding process using physics and mathematics, this paper shows…
The application of language models (LMs) to molecular structure generation using line notations such as SMILES and SELFIES has been well-established in the field of cheminformatics. However, extending these models to generate 3D molecular…
Molecular robotics is challenging, so it seems best to keep it simple. We consider an abstract molecular robotics model based on simple folding instructions that execute asynchronously. Turning Machines are a simple 1D to 2D folding model,…
Vision-language models (VLMs) achieve strong multimodal performance, yet how computation is organized across populations of neurons remains poorly understood. In this work, we study VLMs through the lens of neural topology, representing…
Deformable objects present a formidable challenge for robotic manipulation due to the lack of canonical low-dimensional representations and the difficulty of capturing, predicting, and controlling such objects. We construct compact…
In topological quantum computation, quantum information is stored in states which are intrinsically protected from decoherence, and quantum gates are carried out by dragging particle-like excitations (quasiparticles) around one another in…
Complex molecules and mesoscopic structures are naturally described by general networks of elementary building blocks and tight-binding is one of the simplest quantum model suitable for studying the physical properties arising from the…