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Real-world learning tasks often encounter uncertainty due to covariate shift and noisy or inconsistent labels. However, existing robust learning methods merge these effects into a single distributional uncertainty set. In this work, we…
Binomial data with unknown sizes often appear in biological and medical sciences and are usually overdispersed. All previous methods used parametric models and only considered overdispersion due to the variation of sizes. The proposed…
In a bearing state, touching spheres (disks in two dimensions) roll on each other without slip. Here we frustrate a system of touching spheres by imposing two different bearing states on opposite sides and search for the configurations of…
We use a new version of the reversible Parking Lot Model to study the compaction of vibrated polydisperse media. The particle sizes are distributed according to a truncated power law. We introduce a self-consistent desorption mechanism with…
Transport properties of three-dimensional self-affine rough fractures are studied by means of an effective-medium analysis and numerical simulations using the Lattice-Boltzmann method. The numerical results show that the effective-medium…
We show that the class of conditional distributions satisfying the coarsening at Random (CAR) property for discrete data has a simple and robust algorithmic description based on randomized uniform multicovers: combinatorial objects…
A modern aircraft may require on the order of thousands of custom shims to fill gaps between structural components in the airframe that arise due to manufacturing tolerances adding up across large structures. These shims are necessary to…
In this work, we study the well-posedness of certain sparse regularized linear regression problems, i.e., the existence, uniqueness and continuity of the solution map with respect to the data. We focus on regularization functions that are…
In this chapter we report on the measurements of the overlap distribution of the replica symmetry breaking solution in complex disordered systems. After a general introduction to the problem of the experimental validation of the Parisi…
One-point time-series measurements limit the observation of three-dimensional fully developed turbulence to one dimension. For one-dimensional models, like multiplicative branching processes, this implies that the energy flux from large to…
Seismological and geodetic observations of fault zones reveal diverse slip dynamics, scaling, and statistical laws. Existing mechanisms explain some but not all of these behaviors. We show that incorporating an off-fault damage…
Photonic crystals with a sufficiently high refractive index contrast display partial or full band gaps. However, imperfections in the metamaterial cause light scattering and extinction of the interfering propagating waves. Positive as well…
We consider the morphology of two dimensional cracks observed in experimental results obtained from paper samples and compare these results with the numerical simulations of the random fuse model (RFM). We demonstrate that the data obey…
We analyze the large scale structure and fluctuations of jammed packings of size disperse spheres, produced in a granular experiment as well as numerically. While the structure factor of the packings reveals no unusual behavior for small…
A recent work of Abbasi et al. [FOCS 2023] introduced the notion of $\varepsilon$-scatter dimension of a metric space and showed a general framework for efficient parameterized approximation schemes (so-called EPASes) for a wide range of…
In this work we have studied the optical properties of disordered photonic structures, in which we have controlled the distribution of the random layer thickness. Such structures are characterized by an alternation of high and low…
Assessing the significance of alignment scores of optimally aligned DNA or amino acid sequences can be achieved via the knowledge of the score distribution of random sequences. But this requires obtaining the distribution in the…
Modeling spatial overdispersion requires point processes models with finite dimensional distributions that are overdisperse relative to the Poisson. Fitting such models usually heavily relies on the properties of stationarity, ergodicity,…
The ratio of two consecutive level spacings has emerged as a very useful metric in investigating universal features exhibited by complex spectra. It does not require the knowledge of density of states and is therefore quite convenient to…
Homogeneous random fractals form a probabilistic extension of self-similar sets with more dependencies than in random recursive constructions. For such random fractals we consider mean values of the Lipschitz-Killing curvatures of their…