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We study a data-dependent notion of diffusion-model generalization: when a model does not memorize the training set, where do its generated samples go relative to the geometry induced by the data? To answer this, we introduce a…
Random feature ridge regression is often analyzed in the high-dimensional regime under the homogeneous sampling model $x_i=\Sigma^{1/2}x_i'$, where the vectors $x_i'$ have iid entries and the same covariance matrix $\Sigma$ is shared by all…
The main chain dihedral angles play an important role to decide the protein conformation. The native states of a protein can be regard as an ensemble of a lot of similar conformations, in different conformations the main chain dihedral…
We derive and study a theoretical description for single file diffusion, i.e., diffusion in a one dimensional lattice of particles with hard core interaction. It is well known that for this system a tagged particle has anomalous diffusion…
Properties of a contact process in continuum for a system of two type particles one type of which is independent are considered. We study dynamics of the first and second order correlation functions, their asymptotics and dependence on…
Length scales are determined that govern the behavior at small separations of the correlations of fluid-particle acceleration, viscous force, and pressure gradient. The length scales and an associated universal constant are quantified on…
We look at the new two-particle Bose-Einstein correlation (BEC) function accompanied by the color-electric flux model which can explain the "ridge" behavior in enhanced angular correlation between two identical pions at very broad rapidity…
Failure of amorphous materials is characterized by the emergence of dissipation. The connection between particle dynamics, dissipation, and overall material rheology, however, has still not been elucidated. Here, we take a new approach…
Autonomous robotics is critically affected by the robustness of its scene understanding algorithms. We propose a two-axis pipeline based on polarization indices to analyze dynamic urban scenes. As robots evolve in unknown environments, they…
We study the two-dimensional (2D) shear flow of amorphous solids within variants of an elastoplastic model, paying particular attention to spatial correlations and time fluctuations of, e.g., local stresses. The model is based on the local…
We study non-linear phenomena in double barrier heterostructures. Systems in 3D under the effect of an external magnetic field along the current and 1D systems are analyzed. Non-linearities are reflected in the I-V characteristic curve as…
I study the effect of length polydispersity in the surface phase diagram of hard rods interacting with a hard wall. The properly extended interface Gibbs-Duhem equation for a polydisperse system allows us to predict the behaviour of the…
A phase diagram for a one dimensional fiber bundle model is constructed with a continuous variation in two parameters guiding dynamics of the model: strength of disorder and system size. We monitor the successive events of fiber rupture in…
Complex network theory provides an elegant and powerful framework to statistically investigate different types of systems such as society, brain or the structure of local and long-range dynamical interrelationships in the climate system.…
The two-particle short-range correlation functions in rapidity, azimuthal angle and transverse momentum, following from the decay of statistical clusters are evaluated and discussed.
Optimization of fluid transport in the slime mold Physarum polycephalum has been the subject of several modeling efforts in recent literature. Existing models assume that the tube adaptation mechanism in P. polycephalum's tubular network is…
The random-cluster model, a correlated bond percolation model, unifies a range of important models of statistical mechanics in one description, including independent bond percolation, the Potts model and uniform spanning trees. By…
A novel decomposition technique is used to extract the centrality dependence of di-jet properties and yields from azimuthal correlation functions obtained in Au+Au collisions at $\sqrt{s_{_{\rm NN}}}$=200 GeV. The width of the near-side jet…
Via event driven molecular dynamics simulations and experiments, we study the packing fraction and shear-rate dependence of single particle fluctuations and dynamic correlations in hard sphere glasses under shear. At packing fractions above…
Particles transported in fluid flows, such as cells, polymers, or nanorods, are rarely spherical. In this study, we numerically and theoretically investigate the dispersion of an initially localized patch of passive elongated Brownian…