Generic system architecture for context-aware, distributed recommendation

In the existing literature on recommender systems, it is difficult to find an architecture for large-scale implementation. Often, the architectures proposed in papers are specific to an algorithm implementation or a domain. Thus, there is no clear architectural starting point for a new recommender system. This paper presents an architecture blueprint for a context-aware recommender system that provides scalability, availability, and security for its users. The architecture also contributes the dynamic ability to switch between single-device (offline), client-server (online), and fully distributed implementations. From this blueprint, a new recommender system could be built with minimal design and implementation effort regardless of the application.Electrical and Computer Engineerin

Martingales arising from minimal submanifolds and other geometric contexts

We consider a class of martingales on Cartan-Hadamard manifolds that includes Brownian motion on a minimal submanifold. We give sufficient conditions for such martingales to be transient, extending previous results on the transience of minimal submanifolds. We also give conditions for the almost sure convergence of the angular component (in polar coordinates) of a martingale in this class, including both the negatively pinched case (using earlier results on martingales of bounded dilation), and the radially symmetric case with quadratic decay of the upper curvature bound. Applied to minimal submanifolds, this gives curvature conditions on the ambient Cartan-Hadamard manifold under which any minimal submanifold admits a non-constant, bounded, harmonic function. Though our discussion is primarily motivated by minimal submanifolds, this class of martingales includes diffusions naturally associated to ancient solutions of mean curvature flow and to certain sub-Riemannian structures, and we briefly discuss these contexts as well. Our techniques are elementary, consisting mainly of comparison geometry and Ito's rule.Comment: Accepted version (some mistakes corrected from the previous), to appear in Illinois Journal of Mathematic

Loser Pays in Patent Examination

Many scholars and practitioners believe there are too many “weak” patents—those that should not have issued but somehow get approved by the U.S. Patent and Trademark Office (PTO). To the extent they exist, such patents unnecessarily tax real innovation and generate welfare losses for society. Some commentators have focused on the PTO’s failure to exclude weak patents, or the damage caused by these patents in litigation, often by patent trolls. But this scholarly discussion misses the point. The present Article argues that weak patents largely stem from a pricing problem: namely, a patent applicant pays higher patent fees when she succeeds (i.e., receives PTO approval) than when she fails (i.e., is rejected by the PTO). The Article explains why such pricing is precisely backwards, penalizing good patent applications instead of bad ones. It then proposes a novel remedy: import “loser pays” concepts from litigation into patent examination. By forcing unsuccessful patent applicants to pay more, a loser-pays system disincentivizes weak applications and improves application quality. The Article also describes how a loser-pays system could lower patent examiners’ burden and discourage continuation applications, both of which slow down patent examination. In doing so, the Article sketches out a new patent system that is at once more efficient and more effective in weeding out weak patents