Eric Grosse

Nonobtuse triangulation of polygons

We show how to triangulate a polygon without using any obtuse triangles. Such triangulations can be used to discretize partial differential equations in a way that guarantees that the resulting matrix is Stieltjes, a desirable property both for computation and for theoretical analysis.A simple divide-and-conquer approach would fail because adjacent subproblems cannot be solved independently, but this can be overcome by careful subdivision. Overlay a square grid on the polygon, preferably with the polygon vertices at grid points. Choose boundary cells so they can be triangulated without propagating irregular points to adjacent cells. The remaining interior is rectangular and easily triangulated. Small angles can also be avoided in these constructions.

Repository mirroring

Distributed administration of network repositories demands a low-overhead procedure for cooperating repositories around the world to ensure they hold identical contents. Netlib has adopted some refinements on the widespread scheme of anonymous ftp and s-R. Checksum files and two small C programs give an easily maintained system that copes with communication breakdowns and subtle changes in repository contents. The packaging of these C programs inside a shell pipeline provides an explicit command stream that can readily be checked before execution. Protecting files, keeping logs, and so forth become effortless and reliable. The same tools, applied on a smaller scale, allow more people to participate in the editorial work of maintaining a high-quality repository, by eliminating the need for directly manipulating files at remote sites.

Multidimensional Additive Spline Approximation

We describe an adaptive procedure that approximates a function of many variables by a sum of (univariate) spline functions

Stable prehension with a multi-fingered hand

s_m

Cloud Computing Roundtable

of selected linear combinations

Protium, an infrastructure for partitioned applications

a_m \cdot x

Conformal mapping of circular arc polygons

of the coordinates \[ \phi (x) = \sum_{1 \leqq m \leqq M} {s_m ( a_m \cdot x)}. \] The procedure is nonlinear in that not only the spline coefficients but also the linear combinations are optimized for the particular problem. The sample need not lie on a regular grid, and the approximation is affine invariant, smooth, and lends itself to graphical interpretation. Function values, derivatives, and integrals are inexpensive to evaluate.

Network processors applied to IPv4/IPv6 transition

We study grasps by a robot hand with three spring-loaded fingers. In two dimensions, the hand can grasp any polygon stably. That is, the grip is at a local minimum of the potential energy function defined by the springs of the fingers, ignoring friction. Surprisingly, under some conditions an equilibrium grasp on a circle is unstable even with respect to translation. In three dimensions, the hand can grasp and lift any cylindrical surface with a polygonal cross-section. In contrast we show that a hand with finger angles fixed at 120°, as proposed by Hanafusa and Asada, generally can not achieve a two-dimensional stable grip in the absence of friction.

Stable prehension with three fingers

As part of this special issue on cloud computing, guest editors Iván Arce and Anup Ghosh put together a roundtable discussion so readers can hear about cloud computing security from those who are on the front lines, providing services and looking at the real-world threats and requirements from the market.

Aspects of Computational Circuit Analysis

Remote access feels different from local access. The major issues are consistency (machines vary in GUIs, applications, and devices) and responsiveness (the user must wait for network and server delays), Protium attacks these by partitioning programs into local viewers that connect to remote services using application-specific protocols. Partitioning allows viewers to be customized to adapt to local features and limitations. Services are responsible for maintaining long-term state. Viewers manage the user interface and use state to reduce communication between viewer and service, reducing latency whenever possible. System infrastructure sits between the viewer and service, supporting replication, consistency, session management, and multiple simultaneous viewers. The prototype system includes an editor, a draw program, a PDF viewer, a map database, a music jukebox, and windowing system support. It runs on servers, workstations, PCs, and PDAs under Plan 9, Linux, and Windows; services and viewers have been written in C, Java, and Concurrent ML.