arXiv subjects

Justas Dauparas

Publications and source records attributed to Justas Dauparas.

8 recordsLinked to original sources

arXiv2021

Iterative SE(3)-Transformers

When manipulating three-dimensional data, it is possible to ensure that rotational and translational symmetries are respected by applying so-called SE(3)-equivariant models. Protein structure prediction is a prominent example of a task which displays these symmetries. Recent work in this area has successfully made use of an SE(3)-equivariant model, applying an iterative SE(3)-equivariant attention mechanism. Motivated by this application, we implement an iterative version of the SE(3)-Transformer, an SE(3)-equivariant attention-based model for graph data. We address the additional complications which arise when applying the SE(3)-Transformer in an iterative fashion, compare the iterative and single-pass versions on a toy problem, and consider why an iterative model may be beneficial in some problem settings. We make the code for our implementation available to the community.

cs.LG↗

arXiv2019

Unified framework for modeling multivariate distributions in biological sequences

Revealing the functional sites of biological sequences, such as evolutionary conserved, structurally interacting or co-evolving protein sites, is a fundamental, and yet challenging task. Different frameworks and models were developed to approach this challenge, including Position-Specific Scoring Matrices, Markov Random Fields, Multivariate Gaussian models and most recently Autoencoders. Each of these methods has certain advantages, and while they have generated a set of insights for better biological predictions, these have been restricted to the corresponding methods and were difficult to translate to the complementary domains. Here we propose a unified framework for the above-mentioned models, that allows for interpretable transformations between the different methods and naturally incorporates the advantages and insight gained individually in the different communities. We show how, by using the unified framework, we are able to achieve state-of-the-art performance for protein structure prediction, while enhancing interpretability of the prediction process.

q-bio.QM↗

arXiv2019

Self-organization of swimmers drives long-range fluid transport in bacterial colonies

Bacteria commonly live in structured communities that affect human health and influence ecological systems. Heterogeneous populations, such as motile and non-motile populations, often coexist in bacteria communities. Motile subpopulations in microbial communities are believed to be important to dispersal, quest for food, and material transport. However, except in circumstances where motile cells drive colony expansion (e.g. bacterial swarming), the physiological functions of motile subpopulations in bacterial communities are largely unclear. Here we discovered that motile cells in routinely cultured sessile colonies of peritrichously flagellated bacteria can self-organize into two adjacent, centimeter-scale motile rings surrounding the entire colony. The motile rings arise from spontaneous segregation of a homogeneous swimmer suspension that mimics a phase separation; the process is mediated by intercellular interactions and shear-induced depletion. As a result of this self-organization, cells drive fluid flows to circulate around the colony at a constant peak speed of approximately 30 microns per second, providing a stable and high-speed avenue for directed material transport at the macroscopic scale. These findings present a unique form of bacterial self-organization that influences population structure and material distribution in bacterial communities.

physics.bio-ph↗

arXiv2018

Depth and nonlinearity induce implicit exploration for RL

The question of how to explore, i.e., take actions with uncertain outcomes to learn about possible future rewards, is a key question in reinforcement learning (RL). Here, we show a surprising result: We show that Q-learning with nonlinear Q-function and no explicit exploration (i.e., a purely greedy policy) can learn several standard benchmark tasks, including mountain car, equally well as, or better than, the most commonly-used $ε$-greedy exploration. We carefully examine this result and show that both the depth of the Q-network and the type of nonlinearity are important to induce such deterministic exploration.

cs.LG↗

arXiv2018

Leading-order Stokes flows near a corner

Singular solutions of the Stokes equations play important roles in a variety of fluid dynamics problems. They allow the calculation of exact flows, are the basis of the boundary integral methods used in numerical computations, and can be exploited to derive asymptotic flows in a wide range of physical problems. The most fundamental singular solution is the flow's Green function due to a point force, termed the Stokeslet. Its expression is classical both in free space and near a flat surface. Motivated by problems in biological physics occurring near corners, we derive in this paper the asymptotic behaviour for the Stokeslet both near and far from a corner geometry by using complex analysis on a known double integral solution for corner flows. We investigate all possible orientations of the point force relative to the corner and all corner geometries from acute to obtuse. The case of salient corners is also addressed for point forces aligned with both walls. We use experiments on beads sedimenting in corn syrup to qualitatively test the applicability of our results. The final results and scaling laws will allow to address the role of hydrodynamic interactions in problems from colloidal science to microfluidics and biological physics.

physics.flu-dyn↗

arXiv2018

Helical micropumps near surfaces

Recent experiments proposed to use confined bacteria in order to generate flows near surfaces. We develop a mathematical and a computational model of this fluid transport using a linear superposition of fundamental flow singularities. The rotation of a helical bacterial flagellum induces both a force and a torque on the surrounding fluid, both of which lead to a net flow along the surface. The combined flow is in general directed at an angle to the axis of the flagellar filament. The optimal pumping is thus achieved when bacteria are tilted with respect to the direction in which one wants to move the fluid, in good agreement with experimental results. We further investigate the optimal helical shapes to be used as micropumps near surfaces and show that bacterial flagella are nearly optimal, a result which could be relevant to the expansion of bacterial swarms.

physics.bio-ph↗

arXiv2017

Ice Shelves as Floating Channel Flows of Viscous Power-Law Fluids

We explain the force balance in flowing marine ice sheets and the ice shelves they often feed. Treating ice as a viscous shear-thinning power law fluid, we develop an asymptotic (late-time) theory in two cases $-$ the presence or absence of contact with sidewalls. The solution without sidewalls is a simple generalisation of that found by Robison (JFM, 648, 363), allowing us to obtain the equilibrium grounding line thickness using a simple computer model and to get an analytic approximation. For laterally confined shelves, we obtain an asymptotic theory valid for long shelves and define when this is. Our theory is based on the velocity profile across the channel being a generalised version of Poiseuille flow, which works when lateral shear dominates the force balance. We conducted experiments using a laboratory model for ice. This was an aqueous suspension of $0.5\%$ mass concentration xanthan, yielding $n \approx 3.8$ (similar to ice). Our theories agreed extremely well with our experiments for all relevant parameters (front position, thickness profile, lateral velocity profile, longitudinal velocity gradient and grounding line thickness). This strongly suggests that we have understood the dominant force balance in both types of ice shelf. In the real world, ice tongues are unlikely to rapidly disintegrate but can be shortened until they no longer exist, at which point the sheet becomes unstable and ultimately the grounding line should retreat above sea level. Prior to that point, the flow of ice into it should not be speeded up and the grounding line should also not retreat, assuming that only oceanic conditions change. However, laterally confined ice shelves experience significant buttressing. If removed, this leads to a rapid speedup of the sheet and a much smaller equilibrium grounding line thickness. Something similar may have occurred to the Larsen B ice shelf.

physics.flu-dyn↗

arXiv2016

Flagellar flows around bacterial swarms

Flagellated bacteria on nutrient-rich substrates can differentiate into a swarming state and move in dense swarms across surfaces. A recent experiment measured the flow in the fluid around an Escherichia coli swarm (Wu, Hosu and Berg, 2011 Proc. Natl. Acad. Sci. USA 108 4147). A systematic chiral flow was observed in the clockwise direction (when viewed from above) ahead of the swarm with flow speeds of about $10~μ$m/s, about 3 times greater than the radial velocity at the edge of the swarm. The working hypothesis is that this flow is due to the action of cells stalled at the edge of a colony that extend their flagellar filaments outwards, moving fluid over the virgin agar. In this work we quantitatively test his hypothesis. We first build an analytical model of the flow induced by a single flagellum in a thin film and then use the model, and its extension to multiple flagella, to compare with experimental measurements. The results we obtain are in agreement with the flagellar hypothesis. The model provides further quantitative insight into the flagella orientations and their spatial distributions as well as the tangential speed profile. In particular, the model suggests that flagella are on average pointing radially out of the swarm and are not wrapped tangentially.

physics.bio-ph↗