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Coarse-grained models are a core computational tool in theoretical chemistry and biophysics. A judicious choice of a coarse-grained model can yield physical insight by isolating the essential degrees of freedom that dictate the…
The Gradient Boosted Tree (GBT) algorithm is one of the most popular machine learning algorithms used in production, for tasks that include Click-Through Rate (CTR) prediction and learning-to-rank. To deal with the massive datasets…
Coarse-graining (CG) of molecular simulations simplifies the particle representation by grouping selected atoms into pseudo-beads and drastically accelerates simulation. However, such CG procedure induces information losses, which makes…
A polycrystalline graphene consists of perfect domains tilted at angle {\alpha} to each other and separated by the grain boundaries (GB). These nearly one-dimensional regions consist in turn of elementary topological defects, 5-pentagons…
Adiabatic quantum computation has recently attracted attention in the physics and computer science communities, but its computational power was unknown. We describe an efficient adiabatic simulation of any given quantum algorithm, which…
Exploiting symmetries and invariance in data is a powerful, yet not fully exploited, way to achieve better generalisation with more efficiency. In this paper, we introduce two graph network architectures that are equivariant to several…
For the interpolation of graph signals with generalized shifts of a graph basis function (GBF), we introduce the concept of positive definite functions on graphs. This concept merges kernel-based interpolation with spectral theory on graphs…
State estimation is highly critical for accurately observing the dynamic behavior of the power grids and minimizing risks from cyber threats. However, existing state estimation methods encounter challenges in accurately capturing power…
Generalized balance tournament packings (GBTPs) extend the concept of generalized balanced tournament designs introduced by Lamken and Vanstone (1989). In this paper, we establish the connection between GBTPs and a class of codes called…
We give a combinatorial condition for the existence of efficient, LP-based FPT algorithms for a broad class of graph-theoretical optimisation problems. Our condition is based on the notion of biased graphs known from matroid theory.…
Graph neural networks (GNNs) have received tremendous attention due to their power in learning effective representations for graphs. Most GNNs follow a message-passing scheme where the node representations are updated by aggregating and…
We develop a multiscale patch scheme for studying the system level characteristics of heterogeneous functional graded beams. The algorithm computes the detailed beam dynamics on the microscale, but only in small patches of the beam domain,…
Conformal transformations of a Euclidean (complex) plane have some kind of completeness (sufficiency) for the solution of many mathematical and physical-mathematical problems formulated on this plane. There is no such completeness in the…
We extend the construction of so-called encapsulated global summation-by-parts operators to the general case of a mesh which is not boundary conforming. Owing to this development, energy stable discretizations of nonlinear and variable…
A generalized Gaussian process model (GGPM) is a unifying framework that encompasses many existing Gaussian process (GP) models, such as GP regression, classification, and counting. In the GGPM framework, the observation likelihood of the…
Generalized belief propagation (GBP) has proven to be a promising technique for approximate inference tasks in AI and machine learning. However, the choice of a good set of clusters to be used in GBP has remained more of an art then a…
Machine learning on graphs, especially using graph neural networks (GNNs), has seen a surge in interest due to the wide availability of graph data across a broad spectrum of disciplines, from life to social and engineering sciences. Despite…
The good performance of the GW approximation for band-structure calculations in solids was long taken as a sign that the sum of self-energy diagrams is converged and that all omitted terms are small. However, with modern computational…
Modeling physical systems is an essential skill for a control engineer, since it enables to achieve a deep understanding of their dynamic behavior and, consequently, the development of effective control strategies. The first part of this…
In the past decade, several multi-resolution representation theories for graph signals have been proposed. Bipartite filter-banks stand out as the most natural extension of time domain filter-banks, in part because perfect reconstruction,…