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The topology transition problem of transmission networks is becoming increasingly crucial with topological flexibility more widely leveraged to promote high renewable penetration. This paper proposes a novel methodology to address this…
Understanding crystal growth over arbitrary curved surfaces with arbitrary boundaries is a formidable challenge, stemming from the complexity of formulating non-linear elasticity using geometric invariant quantities. Solutions are generally…
Networks with underlying metric spaces attract increasing research attention in network science, statistical physics, applied mathematics, computer science, sociology, and other fields. This attention is further amplified by the current…
Synchronization in networks of coupled oscillators is known to be largely determined by the spectral and symmetry properties of the interaction network. Here we leverage this relation to study a class of networks for which the threshold…
Tensor network states provide an efficient class of states that faithfully capture strongly correlated quantum models and systems in classical statistical mechanics. While tensor networks can now be seen as becoming standard tools in the…
Both natural and engineered supply networks exhibit universal structural patterns, such as the formation of loops, yet the principles governing optimal structures remain unclear. These patterns can be interpreted as solutions of…
We use linear programming techniques to find points of absolute minimum over the unit sphere $S^{d}$ in $\mathbb R^{d+1}$ of the total potential of a point configuration $\omega_N\subset S^{d}$ which is a spherical $(2m-1)$-design contained…
The permutation symmetry of neurons in each layer of a deep neural network gives rise not only to multiple equivalent global minima of the loss function, but also to first-order saddle points located on the path between the global minima.…
The paper concerns the analysis of global minimizers of a Dirichlet-type energy functional defined on the space of vector fields $H^1(S,T)$, where $S$ and $T$ are surfaces of revolution. The energy functional we consider is closely related…
We consider the fundamental algorithmic problem of finding a cycle of minimum weight in a weighted graph. In particular, we show that the minimum weight cycle problem in an undirected n-node graph with edge weights in {1,...,M} or in a…
By dividing potential energy landscapes into basins of attractions surrounding minima and linking those basins that are connected by transition state valleys, a network description of energy landscapes naturally arises. These networks are…
In this note we prove that minimal networks enjoy minimizing properties for the length functional. A minimal network is, roughly speaking, a subset of $\mathbb{R}^2$ composed of straight segments joining at triple junctions forming angles…
Electromagnetic scattering and absorption by material particles is a fundamental physical problem with a broad range of applications, going from laboratory experiments, biology and material sciences, all the way up to environmental studies…
We consider the problem of balancing load items (tokens) in networks. Starting with an arbitrary load distribution, we allow nodes to exchange tokens with their neighbors in each round. The goal is to achieve a distribution where all nodes…
When a large collection of objects (e.g., robots, sensors, etc.) has to be deployed in a given environment, it is often required to plan a coordinated motion of the objects from their initial position to a final configuration enjoying some…
We propose a novel network measure of topological invariants, called small-worldness, for identifying topological phase transitions of quantum and classical spin models. Small-worldness is usually defined in the study of social networks…
This paper is about minimum cost constrained selection of inputs and outputs for generic arbitrary pole placement. The input-output set is constrained in the sense that the set of states that each input can influence and the set of states…
In this paper we numerically explore the convergence properties of the pseudo-Newtonian circular restricted problem of three and four primary bodies. The classical Newton-Raphson iterative scheme is used for revealing the basins of…
We present an efficient and robust numerical model for simulation of electrokinetic phenomena in porous networks over a wide range of applications including energy conversion, desalination, and lab-on-a-chip systems. Coupling between fluid…
Complex gene regulatory networks often display emergent simple behavior. Sometimes this simplicity can be traced to a nearly equivalent energy landscape, but not always. Here, we show how a topological theory for stochastic and biochemical…