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The definition of complexity through Statistical Complexity Measures (SCM) has recently seen major improvements. Mostly, effort is concentrated in measures on time series. We propose a SCM definition for spatial dynamical systems. Our…
Classical multi-scale methods involving two spatial scales face significant challenges when simulating heterogeneous structures with complicated three-scale spatial configurations. This study proposes an innovative higher-order three-scale…
Numerical modeling of hydraulic fracturing is complicated when a fracture reaches a stress barrier. For high barriers, it may require changing of a computational scheme. Despite there are examples of modeling propagation through barriers,…
The global topology of the Universe can affect long-range gravitational forces via boundary conditions. Detailed studies of non-trivial topologies require simulations that natively adopt such geometries. Cosmological $N$-body simulations…
We derive the expressions for configurational forces in Kohn-Sham density functional theory, which correspond to the generalized variational force computed as the derivative of the Kohn-Sham energy functional with respect to the position of…
Traditional member-based two-step design approaches included in current structural codes for steel structures, as well as more recent system-based direct-design alternatives, require building rigorous structural reliability frameworks for…
Symmetries are fundamental to dynamical processes in complex networks such as cluster synchronization, which have attracted a great deal of current research. Finding symmetric nodes in large complex networks, however, has relied on…
We introduce the Structured Sparsity Specification (S$^3$), an algebraic framework for defining, composing, and implementing structured sparse patterns. S$^3$ specifies sparsity through three components: a View that reshapes the tensor via…
The interaction between a turbulent convective boundary layer (CBL) and the underlying land surface is an important research problem in the geosciences. In order to model this interaction adequately, it is necessary to develop tools which…
Variables adapted to the quantum dynamics of spherically symmetric models are introduced, which further simplify the spherically symmetric volume operator and allow an explicit computation of all matrix elements of the Euclidean and…
The statistical properties of dynamically triangulated manifolds (DT mfds) in terms of the geodesic distance have been studied numerically. The string susceptibility exponents for the boundary surfaces in three-dimensional DT mfds were…
In this paper we consider a semitetrad covariant decomposition of spherically symmetric spacetimes and find a governing hyperbolic equation of the Gaussian curvature of two dimensional spherical shells, that emerges due to the…
The structural cohesion model is a powerful theoretical conception of cohesion in social groups, but its diffusion in empirical literature has been hampered by operationalization and computational problems. In this paper we start from the…
In additive manufacturing, the fabrication sequence has a large influence on the quality of manufactured components. While planning of the fabrication sequence is typically performed after the component has been designed, recent…
The coherence attribute is one of the most commonly used attributes in seismic interpretation. In this paper, we propose building on the recently introduced Generalized Tensor-based Coherence (GTC) attribute to make it directionally…
Spatial transcriptomics measures the expression of thousands of genes in a tissue sample while preserving its spatial structure. This class of technologies has enabled the investigation of the spatial variation of gene expressions and their…
We describe a skeletonization of the spherical harmonic connection problem that reduces the storage and pre-computation to superoptimal complexities at the cost of increasing the execution time by the modest multiplicative factor of…
Evaluating conjunctive queries and solving constraint satisfaction problems are fundamental problems in database theory and artificial intelligence, respectively. These problems are NP-hard, so that several research efforts have been made…
In this paper we present a mixed projection- and density-based topology optimization approach. The aim is to combine the benefits of both parametrizations: the explicit geometric representation provides specific controls on certain design…
Multi-sector capacity expansion models play a crucial role in energy planning by providing decision support for policymaking in technology development. To ensure reliable support, these models require high technological, spatial, and…