Related papers: Two-mode geometry controls multiscale organization…
Multiscale simulations facilitate the efficient exploration of large spatiotemporal scales in chemical and physical systems, yet particle-based simulations become prohibitively expensive at time and length scales beyond the molecular level.…
To better understand the overlapping modular organization of large networks with respect to flow, here we introduce the map equation for overlapping modules. In this information-theoretic framework, we use the correspondence between…
Neural networks have shown tremendous potential for reconstructing high-resolution images in inverse problems. The non-convex and opaque nature of neural networks, however, hinders their utility in sensitive applications such as medical…
We present a computer-assisted approach to coarse-graining the evolutionary dynamics of a system of nonidentical oscillators coupled through a (fixed) network structure. The existence of a spectral gap for the coupling network graph…
Scale-space representation has been popular in computer vision community due to its theoretical foundation. The motivation for generating a scale-space representation of a given data set originates from the basic observation that real-world…
We discuss the relationship between geometry, the renormalization group (RG) and gravity. We begin by reviewing our recent work on crossover problems in field theory. By crossover we mean the interpolation between different representations…
Motivated by performance optimization of large-scale graph processing systems that distribute the graph across multiple machines, we consider the balanced graph partitioning problem. Compared to the previous work, we study the…
We present a procedure to generate bipartite grids for simply connected domains in 2-D and 3-D of prescribed size and controlled regularity elements. The mesh elements $K$ of the triangulation satisfy $\zeta_{K} \leq C$ where $\zeta_{K}$ is…
The two-scale computational homogenization method is proposed for modelling of locally periodic fluid-saturated media subjected a to large deformation induced by quasistatic loading. The periodic heterogeneities are relevant to the…
Amortized optimization accelerates the solution of related optimization problems by learning mappings that exploit shared structure across problem instances. We explore the use of Scale Equivariant Graph Metanetworks (ScaleGMNs) for this…
Robust 3D representation learning forms the perceptual foundation of spatial intelligence, enabling downstream tasks in scene understanding and embodied AI. However, learning such representations directly from unposed multi-view images…
We address 2D floorplan reconstruction from 3D scans. Existing approaches typically employ heuristically designed multi-stage pipelines. Instead, we formulate floorplan reconstruction as a single-stage structured prediction task: find a…
We investigate static and dynamic topologies of a 2-mode real world university-industry cooperation network. Due to its large size and complex structure, we choose to use statistical proxies for this goal. Among the findings, we shall call…
We introduce a new notation for representing labeled regular bipartite graphs of arbitrary degree. Several enumeration problems for labeled and unlabeled regular bipartite graphs have been introduced. A general algorithm for enumerating all…
A model reduction technique based on an optimization principle is employed to coarse-grain inviscid, incompressible fluid dynamics in two dimensions. In this reduction the spectrally-truncated vorticity equation defines the microdynamics,…
We propose an efficient and robust iterative solution to the multi-object matching problem. We first clarify serious limitations of current methods as well as the inappropriateness of the standard iteratively reweighted least squares…
A discrete spatial lattice can be cast as a network structure over which spatially-correlated outcomes are observed. A second network structure may also capture similarities among measured features, when such information is available.…
Though commonly found in the real world, directed networks have received relatively less attention from the literature in which concerns their topological and dynamical characteristics. In this work, we develop a magnetic Laplacian-based…
Coarse-graining has become an area of tremendous importance within many different research fields. For molecular simulation, coarse-graining bears the promise of finding simplified models such that long-time simulations of large-scale…
Gradient-based methods successfully train highly overparameterized models in practice, even though the associated optimization problems are markedly nonconvex. Understanding the mechanisms that make such methods effective has become a…