相关论文: A Central Partition of Molecular Conformational Sp…

We present a three-dimensional graph convolutional network (3DGCN), which predicts molecular properties and biochemical activities, based on 3D molecular graph. In the 3DGCN, graph convolution is unified with learning operations on the…

Decomposition spaces are a class of function spaces constructed out of well-behaved coverings and partitions of unity of a set. The structure of the covering of the set determines the properties of the decomposition space. Besov spaces,…

Molecular shape and geometry dictate key biophysical recognition processes, yet many graph neural networks disregard 3D information for molecular property prediction. Here, we propose a new contrastive-learning procedure for graph neural…

We detail the application of bounding volume hierarchies to accelerate second-virial evaluations for arbitrary complex particles interacting through hard and soft finite-range potentials. This procedure, based on the construction of…

We study the problem of computing the homology of the configuration spaces of a finite cell complex $X$. We proceed by viewing $X$, together with its subdivisions, as a subdivisional space--a kind of diagram object in a category of cell…

The Partition function of two Hard Spheres in a Hard Wall Pore is studied appealing to a graph representation. The exact evaluation of the canonical partition function, and the one-body distribution function, in three different shaped pores…

Various non-trivial spaces are becoming popular for embedding structured data such as graphs, texts, or images. Following spherical and hyperbolic spaces, more general product spaces have been proposed. However, searching for the best…

Predicting the structure of multi-protein complexes is a grand challenge in biochemistry, with major implications for basic science and drug discovery. Computational structure prediction methods generally leverage pre-defined structural…

We derive the equations of motion for a planar rigid body of circular shape moving in a 2D perfect fluid with point vortices using symplectic reduction by stages. After formulating the theory as a mechanical system on a configuration space…

Molecular design requires systematic and broadly applicable methods to extract structure-property relationships. The focus of this study is on learning thermodynamic properties from molecular-liquid simulations. The methodology relies on an…

Models of folding of a triangular lattice embedded in a discrete space are studied as simple models of the crumpling transition of fixed-connectivity membranes. Both the case of planar folding and three-dimensional folding on a…

We have developed a symmetry-adapted modeling procedure for molecules and crystals. By using the completeness of multipoles to express spatial and time-reversal parity-specific anisotropic distributions, we can generate systematically the…

The lattice of intersections of reflecting hyperplanes of a complex reflection group W may be considered as the poset of 1-eigenspaces of the elements of W. In this paper we replace 1 with an arbitrary eigenvalue and study the topology and…

Analysis on fractals is a growing field, with hints of potential for widespread applicability across all of STEM. One of the most heavily researched type of fractals are the nested fractals, fractal shapes defined by virtue of being made of…

The two pillars of Algebraic topology - Homology and homotopy theory rely on the availability of basic building blocks called cells. Cells take the form of simplexes, and have properties such as faces, sub-cells, convexity and…

During cell migration, cells become polarized, change their shape, and move in response to various internal and external cues. Cell polarization is defined through the spatio-temporal organization of molecules such as PI3K or small GTPases,…

We introduce combinatorial types of arrangements of convex bodies, extending order types of point sets to arrangements of convex bodies, and study their realization spaces. Our main results witness a trade-off between the combinatorial…

We investigate the behavior of colloidal suspensions with different volume fractions confined between parallel walls under a range of steady shears. We model the particles using molecular dynamics (MD) with full hydrodynamic interactions…

In this paper, we propose an efficient clustering technique to solve the problem of clustering in the presence of obstacles. The proposed algorithm divides the spatial area into rectangular cells. Each cell is associated with statistical…

Computational methods that operate on three-dimensional molecular structure have the potential to solve important questions in biology and chemistry. In particular, deep neural networks have gained significant attention, but their…