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The behaviour of elastic structures undergoing large deformations is the result of the competition between confining conditions, self-avoidance and elasticity. This combination of multiple phenomena creates a geometrical frustration that…
To compute robust 2D assembly plans, we present an approach that combines geometric planning with a deep neural network. We train the network using the Box2D physics simulator with added stochastic noise to yield robustness scores--the…
Neural models learn representations of high-dimensional data on low-dimensional manifolds. Multiple factors, including stochasticities in the training process, model architectures, and additional inductive biases, may induce different…
Practitioners prune neural networks for efficiency gains and generalization improvements, but few scrutinize the factors determining the prunability of a neural network the maximum fraction of weights that pruning can remove without…
The dynamical mechanism at the origin of the non-local rheology of dense granular flows is investigated trough discrete element simulations. We show that the influence of a shear band on the mechanical behavior of a distant zone is…
The problem of characterizing the structure of an elastic network constrained to lie on a frozen curved surface appears in many areas of science and has been addressed by many different approaches, most notably, extending linear elasticity…
A spatial scale-free network is introduced and studied whose motivation has been originated in the growing Internet as well as the Airport networks. We argue that in these real-world networks a new node necessarily selects one of its…
We studied the effects of spatial configuration on collective dynamics in a nearest-neighbour and diffusively coupled lattice of heterogeneous nodes. The networks contained nodes from two populations, which differed in their intrinsic…
The actin cytoskeleton is a key component in the machinery of eukaryotic cells, and it selfassembles out of equilibrium into a wide variety of biologically crucial structures. While the molecular mechanisms involved are well characterized,…
We consider a three-dimensional network of aqueous droplets joined by single lipid bilayers to form a cohesive, tissue-like material. The droplets in these networks can be programmed to have distinct osmolarities so that osmotic gradients…
The study of (minimally) rigid graphs is motivated by numerous applications, mostly in robotics and bioinformatics. A major open problem concerns the number of embeddings of such graphs, up to rigid motions, in Euclidean space. We capture…
We announce new results concerning the asymptotic behavior of the Betti numbers of higher rank locally symmetric spaces as their volumes tend to infinity. Our main theorem is a uniform version of the L\"uck Approximation Theorem…
A fundamental theory is presented for the mechanical response of polymer networks undergoing large deformation which seamlessly integrates statistical mechanical principles with macroscopic thermodynamic constitutive theory. Our formulation…
This article deals with the following simpler version of an open problem in system realization theory which has several important engineering applications: Given a collection of masses and a set of linear springs with a specified cost and…
Real-world networks process structured connections since they have non-trivial vertex degree correlation and clustering. Here we propose a toy model of structure formation in real-world weighted network. In our model, a network evolves by…
Polymer network models construct the constitutive relationships of a broader polymer network from the behavior of a single polymer chain (e.g. viscoelastic response to applied forces, applied electromagnetic fields, etc.). Network models…
In this paper, we study the probability that a dense network confined within a given geometry is fully connected. We employ a cluster expansion approach often used in statistical physics to analyze the effects that the boundaries of the…
We report simulation results on melts of entangled linear polymers confined in a free-standing thin film. We study how the geometric constraints imposed by the confinement alter the entanglement state of the system compared to the…
Plastic deformation of heterogeneous solid structures is often characterized by random intermittent local plastic events. On the mesoscale this feature can be represented by a spatially fluctuating local yield threshold. Here we study the…
Besides the chemical constituents, it is the lattice geometry that controls the most important material properties. In many interesting compounds, the arrangement of elements leads to pronounced anisotropies, which reflect into a varying…