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We investigate stationary, spatially localized patterns in lattice dynamical systems that exhibit bistability. The profiles associated with these patterns have a long plateau where the pattern resembles one of the bistable states, while the…
Understanding collective properties of driven particle systems is significant for naturally occurring aggregates and because the knowledge gained can be used as building blocks for the design of artificial ones. We model self propelling…
We develop efficient ways to consider and correct for the effects of hidden units for the paradigmatic case of the inverse kinetic Ising model with fully asymmetric couplings. We identify two sources of error in reconstructing the…
We introduce a flexible framework for high-dimensional matrix estimation to incorporate side information for both rows and columns. Existing approaches, such as inductive matrix completion, often impose restrictive structure-for example, an…
Representation learning is central to graph machine learning, powering tasks such as link prediction and node classification. However, most graph embeddings are hard to interpret, offering limited insight into how learned features relate to…
The microscopic structure of several amorphous substances often reveals complex patterns such as medium- or long-range order, spatial heterogeneity, and even local polycrystallinity. To capture all these features, models usually incorporate…
Necessary and sufficient conditions are obtained for the infinitesimal rigidity of braced grids in the plane with respect to non-Euclidean norms. Component rectangles of the grid may carry 0, 1 or 2 diagonal braces, and the combinatorial…
The phase behavior of charged rods in the presence of inter-rod linkers is studied theoretically as a model for the equilibrium behavior underlying the organization of actin filaments by linker proteins in the cytoskeleton. The presence of…
The complex structure of a surface generated by the two-dimensional dynamical triangulation(DT) is determined by measuring the resistivity of the surface. It is found that surfaces coupled to matter fields have well-defined complex…
With this contribution, we give a complete and comprehensive framework for modeling the dynamics of complex mechanical structures as port-Hamiltonian systems. This is motivated by research on the potential of lightweight construction using…
Compound graphs are networks in which vertices can be grouped into larger subsets, with these subsets capable of further grouping, resulting in a nesting that can be many levels deep. In several applications, including biological workflows,…
A deformed differential calculus is developed based on an associative star-product. In two dimensions the Hamiltonian vector fields model the algebra of pseudo-differential operator, as used in the theory of integrable systems. Thus one…
The fluid-solid-electric dynamics of a flexible plate covered by interconnected piezoelectric patches in an axial steady flow are investigated using numerical simulations based on a reduced-order model of the fluid loading for slender…
Input-to-state stability (ISS) unifies the stability and robustness in one notion, and serves as a basis for broad areas of nonlinear control theory. In this contribution, we covered the most fundamental facts in the infinite-dimensional…
Network embedding is the process of learning low-dimensional representations for nodes in a network, while preserving node features. Existing studies only leverage network structure information and focus on preserving structural features.…
This paper proposes a framework to assess the stability of an ordinary differential equation which is coupled to a 1D-partial differential equation (PDE). The stability theorem is based on a new result on Integral Quadratic Constraints…
Colloidal particles that are confined to an interface such as the air-water interface are an example of a two-dimensional fluid. Such dispersions have been observed to spontaneously form cluster and stripe morphologies in certain systems…
Isolated oxygen impurities and fully oxidized structures of four stable two-dimensional (2D) SiS structures are investigated by {\em ab initio} density functional calculations. Binding energies of oxygen impurities for all the four 2D SiS…
Bayesian networks faithfully represent the symmetric conditional independences existing between the components of a random vector. Staged trees are an extension of Bayesian networks for categorical random vectors whose graph represents…
This paper considers the coupled problem of a three-dimensional elastic body and a two-dimensional plate, which are rigidly connected at their interface. The plate consists of a plane elasticity model along the longitudinal direction and a…