We generalize the class vectors found in neural networks to linear subspaces (i.e., points in the Grassmann manifold) and show that the Grassmann Class Representation (GCR) enables simultaneous improvement in accuracy and feature transferability. In GCR, e ...
A rank-adaptive integrator for the approximate solution of high-order tensor differential equations by tree tensor networks is proposed and analyzed. In a recursion from the leaves to the root, the integrator updates bases and then evolves connection tenso ...
Scaffold-based protein libraries are designed to be both diverse and rich in functional/folded proteins. However, introducing an extended diversity while preserving stability of the initial scaffold remains a challenge. Here we developed an original approa ...
Proteins, the central building blocks of life, play pivotal roles in nearly every biological function. To do so, these macromolecular structures interact with their surrounding environment in complex ways, leading to diverse functional behaviors. The predi ...
Proteins control nearly every facet of life on a molecular level. Proteins are formed from linear strings of amino acids, which fold into three-dimensional structures that can enact functions. Evolution has created highly efficient proteins in diverse fold ...
We propose a structured prediction approach for robot imitation learning from demonstrations. Among various tools for robot imitation learning, supervised learning has been observed to have a prominent role. Structured prediction is a form of supervised le ...
Structure determination of materials is key to understanding their physical properties. While single-crystal X-ray diffraction is the gold standard for structures displaying long-range order, many materials of interest are polycrystalline and/or disordered ...
Isogeometric analysis is a powerful paradigm which exploits the high smoothness of splines for the numerical solution of high order partial differential equations. However, the tensor-product structure of standard multivariate B-spline models is not well s ...
Reduced-order models are indispensable for multi-query or real-time problems. However, there are still many challenges to constructing efficient ROMs for time-dependent parametrized problems. Using a linear reduced space is inefficient for time-dependent n ...
Given a hyperelliptic hyperbolic surface S of genus g >= 2, we find bounds on the lengths of homologically independent loops on S. As a consequence, we show that for any lambda is an element of (0, 1) there exists a constant N(lambda) such that every such ...
The task of discovering equivalent entities in knowledge graphs (KGs), so-called KG entity alignment, has drawn much attention to overcome the incompleteness problem of KGs. The majority of existing techniques learns the pointwise representations of entiti ...
Tensor trains are a versatile tool to compress and work with high-dimensional data and functions. In this work we introduce the streaming tensor train approximation (STTA), a new class of algorithms for approximating a given tensor ' in the tensor train fo ...
