Coarse Graining of Data via Inhomogeneous Diffusion Condensation

Big data often has emergent structure that exists at multiple levels of abstraction, which are useful for characterizing complex interactions and dynamics of the observations. Here, we consider multiple levels of abstraction via a multiresolution geometry of data points at different granularities. To construct this geometry we define a time-inhomogeneous diffusion process that effectively condenses data points together to uncover nested groupings at larger and larger granularities. This inhomogeneous process creates a deep cascade of intrinsic low pass filters on the data affinity graph that are applied in sequence to gradually eliminate local variability while adjusting the learned data geometry to increasingly coarser resolutions. We provide visualizations to exhibit our method as a continuously-hierarchical clustering with directions of eliminated variation highlighted at each step. The utility of our algorithm is demonstrated via neuronal data condensation, where the constructed multiresolution data geometry uncovers the organization, grouping, and connectivity between neurons.Comment: 14 pages, 7 figure

Formation and Dissolution of Bacterial Colonies

Many organisms form colonies for a transient period of time to withstand environmental pressure. Bacterial biofilms are a prototypical example of such behavior. Despite significant interest across disciplines, physical mechanisms governing the formation and dissolution of bacterial colonies are still poorly understood. Starting from a kinetic description of motile and interacting cells we derive a hydrodynamic equation for their density on a surface. We use it to describe formation of multiple colonies with sizes consistent with experimental data and to discuss their dissolution.Comment: 3 figures, 1 Supplementary Materia

Harnessing fluctuations to discover dissipative evolution equations

This dataset contains the source codes for for the paper "Harnessing fluctuations to discover dissipative evolution equations". The code computes the macroscopic evolution operator associated with many-particle systems (hydrodynamic limit) from particle simulations. The method is based on fluctuation-dissipation theory and is described in the paper. A test case considered is the zero-range process.The zip file contains the code and a README fil

Molecular transport and flow past hard and soft surfaces: Computer simulation of model systems

The properties of polymer liquids on hard and soft substrates are investigated by molecular dynamics simulation of a coarse-grained bead-spring model and dynamic single-chain-in-mean-field (SCMF) simulations of a soft, coarse-grained polymer model. Hard, corrugated substrates are modelled by an FCC Lennard-Jones solid while polymer brushes are investigated as a prototypical example of a soft, deformable surface. From the molecular simulation we extract the coarse-grained parameters that characterise the equilibrium and flow properties of the liquid in contact with the substrate: the surface and interface tensions, and the parameters of the hydrodynamic boundary condition. The so-determined parameters enter a continuum description like the Stokes equation or the lubrication approximation.Comment: 41 pages, 13 figure

The Role of High-Dimensional Diffusive Search, Stabilization, and Frustration in Protein Folding

Proteins are polymeric molecules with many degrees of conformational freedom whose internal energetic interactions are typically screened to small distances. Therefore, in the high-dimensional conformation space of a protein, the energy landscape is locally relatively flat, in contrast to low-dimensional representations, where, because of the induced entropic contribution to the full free energy, it appears funnel-like. Proteins explore the conformation space by searching these flat subspaces to find a narrow energetic alley that we call a hypergutter and then explore the next, lower-dimensional, subspace. Such a framework provides an effective representation of the energy landscape and folding kinetics that does justice to the essential characteristic of high-dimensionality of the search-space. It also illuminates the important role of nonnative interactions in defining folding pathways. This principle is here illustrated using a coarse-grained model of a family of three-helix bundle proteins whose conformations, once secondary structure has formed, can be defined by six rotational degrees of freedom. Two folding mechanisms are possible, one of which involves an intermediate. The stabilization of intermediate subspaces (or states in low-dimensional projection) in protein folding can either speed up or slow down the folding rate depending on the amount of native and nonnative contacts made in those subspaces. The folding rate increases due to reduced-dimension pathways arising from the mere presence of intermediate states, but decreases if the contacts in the intermediate are very stable and introduce sizeable topological or energetic frustration that needs to be overcome. Remarkably, the hypergutter framework, although depending on just a few physically meaningful parameters, can reproduce all the types of experimentally observed curvature in chevron plots for realizations of this fold

Thermoosmosis of a near-critical binary fluid mixture: a general formulation and universal flow direction

We consider a binary fluid mixture, which lies in the one-phase region near the demixing critical point, and study its transport through a capillary tube linking two large reservoirs. We assume that short-range interactions cause preferential adsorption of one component on the tube's wall. The adsorption layer can become much thicker than the molecular size, which enables us to apply hydrodynamics based on a coarse-grained free-energy functional. For linear transport phenomena induced by gradients of the pressure, composition, and temperature along a cylindrical tube, we obtain the formulas of the Onsager coefficients to extend our previous results on isothermal transport, assuming the critical composition in the middle of each reservoir in the reference equilibrium state. Among the linear transport phenomena, we focus on thermoosmosis -- mass flow due to a temperature gradient. We explicitly derive a formula for the thermal force density, which is nonvanishing in the adsorption layer and causes thermoosmosis. This formula for a near-critical binary fluid mixture is an extension of the conventional formula for a one-component fluid, expressed in terms of local excess enthalpy. We predict that the direction of thermoosmotic flow of a mixture near the upper (lower) consolute point is the same as (opposite to) that of the temperature gradient, irrespective of which component is adsorbed on the wall. Our procedure would also be applied to dynamics of a soft material, whose mesoscopic inhomogeneity can be described by a coarse-grained free-energy functional.Comment: 46 pages, 7 figure

Evolution of non-uniformly seeded warm clouds in idealized turbulent conditions

We present a mean-field model of cloud evolution that describes droplet growth due to condensation and collisions and droplet loss due to fallout. The model accounts for the effects of cloud turbulence both in a large-scale turbulent mixing and in a microphysical enhancement of condensation and collisions. The model allows for an effective numerical simulation by a scheme that is conservative in water mass and keeps accurate count of the number of droplets. We first study the homogeneous situation and determine how the rain-initiation time depends on the concentration of cloud condensation nuclei (CCN) and turbulence level. We then consider clouds with an inhomogeneous concentration of CCN and evaluate how the rain initiation time and the effective optical depth vary in space and time. We argue that over-seeding even a part of a cloud by small hygroscopic nuclei, one can substantially delay the onset and increase the amount of precipitation