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  1. Abstract

    In active matter systems, deformable boundaries provide a mechanism to organize internal active stresses. To study a minimal model of such a system, we perform particle-based simulations of an elastic vesicle containing a collection of polar active filaments. The interplay between the active stress organization due to interparticle interactions and that due to the deformability of the confinement leads to a variety of filament spatiotemporal organizations that have not been observed in bulk systems or under rigid confinement, including highly-aligned rings and caps. In turn, these filament assemblies drive dramatic and tunable transformations of the vesicle shape and its dynamics. We present simple scaling models that reveal the mechanisms underlying these emergent behaviors and yield design principles for engineering active materials with targeted shape dynamics.

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  2. Knowledge graph (KG) representation learning aims to encode entities and relations into dense continuous vector spaces such that knowledge contained in a dataset could be consistently represented. Dense embeddings trained from KG datasets benefit a variety of downstream tasks such as KG completion and link prediction. However, existing KG embedding methods fell short to provide a systematic solution for the global consistency of knowledge representation. We developed a mathematical language for KG based on an observation of their inherent algebraic structure, which we termed as Knowledgebra. By analyzing five distinct algebraic properties, we proved that the semigroup is the most reasonable algebraic structure for the relation embedding of a general knowledge graph. We implemented an instantiation model, SemE, using simple matrix semigroups, which exhibits state-of-the-art performance on standard datasets. Moreover, we proposed a regularization-based method to integrate chain-like logic rules derived from human knowledge into embedding training, which further demonstrates the power of the developed language. As far as we know, by applying abstract algebra in statistical learning, this work develops the first formal language for general knowledge graphs, and also sheds light on the problem of neural-symbolic integration from an algebraic perspective. 
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  3. Were astronauts forced to land on the surface of Mars using manual control of their vehicle, they would not have familiar gravitational cues because Mars’ gravity is only 0.38 g. They could become susceptible to spatial disorientation, potentially causing mission ending crashes. In our earlier studies, we secured blindfolded participants into a Multi-Axis Rotation System (MARS) device that was programmed to behave like an inverted pendulum. Participants used a joystick to stabilize around the balance point. We created a spaceflight analog condition by having participants dynamically balance in the horizontal roll plane, where they did not tilt relative to the gravitational vertical and therefore could not use gravitational cues to determine their position. We found 90% of participants in our spaceflight analog condition reported spatial disorientation and all of them showed it in their data. There was a high rate of crashing into boundaries that were set at ± 60 ° from the balance point. Our goal was to see whether we could use deep learning to predict the occurrence of crashes before they happened. We used stacked gated recurrent units (GRU) to predict crash events 800 ms in advance with an AUC (area under the curve) value of 99%. When we prioritized reducing false negatives we found it resulted in more false positives. We found that false negatives occurred when participants made destabilizing joystick deflections that rapidly moved the MARS away from the balance point. These unpredictable destabilizing joystick deflections, which occurred in the duration of time after the input data, are likely a result of spatial disorientation. If our model could work in real time, we calculated that immediate human action would result in the prevention of 80.7% of crashes, however, if we accounted for human reaction times (∼400 ms), only 30.3% of crashes could be prevented, suggesting that one solution could be an AI taking temporary control of the spacecraft during these moments. 
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  4. Abstract An active Brownian particle is a minimal model for a self-propelled colloid in a dissipative environment. Experiments and simulations show that, in the presence of boundaries and obstacles, active Brownian particle systems approach nontrivial nonequilibrium steady states with intriguing phenomenology, such as accumulation at boundaries, ratchet effects, and long-range depletion interactions. Nevertheless, theoretical analysis of these phenomena has proven difficult. Here, we address this theoretical challenge in the context of non-interacting particles in two dimensions, basing our analysis on the steady-state Smoluchowski equation for the one-particle distribution function. Our primary result is an approximation strategy that connects asymptotic solutions of the Smoluchowski equation to boundary conditions. We test this approximation against the exact analytic solution in a 2D planar geometry, as well as numerical solutions in circular and elliptic geometries. We find good agreement so long as the boundary conditions do not vary too rapidly with respect to the persistence length of particle trajectories. Our results are relevant for characterizing long-range flows and depletion interactions in such systems. In particular, our framework shows how such behaviors are connected to the breaking of detailed balance at the boundaries. 
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  5. null (Ed.)
    Active nematics are a class of far-from-equilibrium materials characterized by local orientational order of force-generating, anisotropic constitutes. Traditional methods for predicting the dynamics of active nematics rely on hydrodynamic models, which accurately describe idealized flows and many of the steady-state properties, but do not capture certain detailed dynamics of experimental active nematics. We have developed a deep learning approach that uses a Convolutional Long-Short-Term-Memory (ConvLSTM) algorithm to automatically learn and forecast the dynamics of active nematics. We demonstrate our purely data-driven approach on experiments of 2D unconfined active nematics of extensile microtubule bundles, as well as on data from numerical simulations of active nematics. 
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