Uwe F. Mayer

The surface diffusion flow for immersed hypersurfaces

We show existence and uniqueness of classical solutions for the motion of immersed hypersurfaces driven by surface diusion. If the initial surface is embedded and close to a sphere, we prove that the solution exists globally and converges exponentially fast to a sphere. Furthermore, we provide numerical simulations showing the creation of singularities for immersed curves.

A numerical scheme for axisymmetric solutions of curvature-driven free boundary problems, with applications to the Willmore flow

We present a numerical scheme for axisymmetric solutions to curvature-driven moving boundary problems governed by a local law of motion, e.g. the mean curvature flow, the surface diffusion flow, and the Willmore flow. We then present several numerical experiments for the Willmore flow. In particular, we provide numerical evidence that the Willmore flow can develop singularities in finite time.

A numerical scheme for moving boundary problems that are gradient flows for the area functional

Many moving boundary problems that are driven in some way by the curvature of the free boundary are gradient flows for the area of the moving interface. Examples are the Mullins{Sekerka flow, the Hele-Shaw flow, flow by mean curvature, and flow by averaged mean curvature. The gradient flow structure suggests an implicit nite dierences approach to compute numerical solutions. The proposed numerical scheme will allow us to treat such free boundary problems in both IR 2 and IR 3 . The advantage of such an approach is the reusability of much of the setup for all of the dierent problems. As an example of the method, we compute solutions to the averaged mean curvature flow that exhibit the formation of a singularity.

Bootstrapped language identification for multi-site internet domains

We present an algorithm for language identification, in particular of short documents, for the case of an Internet domain with sites in multiple countries with differing languages. The algorithm is significantly faster than standard language identification methods, while providing state-of-the-art identification. We bootstrap the algorithm based on the language identification based on the site alone, a methodology suitable for any supervised language identification algorithm. We demonstrate the bootstrapping and algorithm on eBay email data and on Twitter status updates data. The algorithm is deployed at eBay as part of the back-office development data repository.

Self-Intersections for Willmore Flow

In this paper we consider the Willmore flow in three space dimensions. We prove that embedded surfaces can be driven to a self-intersection in finite time. This situation is in strict contrast to the behavior of hypersurfaces under the mean curvature flow, where the maximum principle prevents self-intersections, but very much analogous to the surface diffusion flow.

A Singular Example for the Averaged Mean Curvature Flow

An embedded curve is presented which under numerical simulation of the averaged mean curvature flow develops first a loss of embeddedness and then a singularity where the curvature becomes infinite, all in finite time. This leads to the conjecture that not all smooth embedded curves persist for all times under the averaged mean curvature flow.

Experimental design for solicitation campaigns

Data mining techniques are routinely used by fundraisers to select those prospects from a large pool of candidates who are most likely to make a financial contribution. These techniques often rely on statistical models based on trial performance data. This trial performance data is typically obtained by soliciting a smaller sample of the possible prospect pool. Collecting this trial data involves a cost; therefore the fundraiser is interested in keeping the trial size small while still collecting enough data to build a reliable statistical model that will be used to evaluate the remainder of the prospects.We describe an experimental design approach to optimally choose the trial prospects from an existing large pool of prospects. Prospects are clustered to render the problem practically tractable. We modify the standard D-optimality algorithm to prevent repeated selection of the same prospect cluster, since each prospect can only be solicited at most once.We assess the benefits of this approach on the KDD-98 data set by comparing the performance of the model based on the optimal trial data set with that of a model based on a randomly selected trial data set of equal size.

Loss of convexity for a modified Mullins–Sekerka model arising in diblock copolymer melts

Abstract. This modified (two-sided) Mullins–Sekerka model is a nonlocal evolution model for closed hypersurfaces, which appears as a singular limit of a modified Cahn-Hilliard equation describing micro-phase separation of diblock copolymer. Under this evolution the propagating interfaces maintain the enclosed volumes of the two phases. We will show by means of an example that this model does not preserve convexity in two space dimensions.

Canary in the e-Commerce Coal Mine: Detecting and Predicting Poor Experiences Using Buyer-to-Seller Messages

Reputation and feedback systems in online marketplaces are often biased, making it difficult to ascertain the quality of sellers. We use post-transaction, buyer-to-seller message traffic to detect signals of unsatisfactory transactions on eBay. We posit that a message sent after the item was paid for serves as a reliable indicator that the buyer may be unhappy with that purchase, particularly when the message included words associated with a negative experience. The fraction of a sellers message traffic that was negative predicts whether a buyer who transacts with this seller will stop purchasing on eBay, implying that platforms can use these messages as an additional signal of seller quality.

A unifying viewpoint of some clustering techniques using Bregman divergences and extensions to mixed data sets

We present a general viewpoint using Bregman divergences and exponential family properties that contains as special cases the three following algorithms: 1) exponential family principal component analysis (exponential PCA), 2) Semi-Parametric exponential family principal component analysis (SP-PCA) and 3) Bregman soft clustering. This framework is equivalent to a mixed data-type hierarchical Bayes graphical model assumption with latent variables constrained to a low-dimensional parameter subspace. We show that within this framework exponential PCA and SPPCA are similar to the Bregman soft clustering technique with the addition of a linear constraint in the parameter space. We implement the resulting modifications to SP-PCA and Bregman soft clustering for mixed (continuous and/or discrete) data sets, and add a nonparametric estimation of the point-mass probabilities to exponential PCA. Finally, we compare the relative performances of the three algorithms in a clustering setting for mixed data sets.