Abstract. We study the inverse problem of determining a finite weighted graph [Formula: see text] from the source-to-solution map on a vertex subset [Formula: see text] for heat equations on graphs, where the time variable can be either discrete or continuous. We prove that this problem is equivalent to the discrete version of the inverse interior spectral problem, provided that there does not exist a nonzero eigenfunction of the weighted graph Laplacian vanishing identically on [Formula: see text]. In particular, we consider inverse problems for discrete-time random walks on finite graphs. We show that under a novel geometric condition (called the Two-Points Condition), the graph structure and the transition matrix of the random walk can be uniquely recovered from the distributions of the first passing times on [Formula: see text], or from the observation on [Formula: see text] of one realization of the random walk.

Removing hard drives from a data center may expose sensitive data, such as encryption keys or passwords. To prevent exposure, data centers have security policies in place to physically secure drives in the system, and securely delete data from drives that are removed. Despite advances in security technology and best practices, implementation of these security measures is often done incorrectly. We anticipate that physical security will fail, and fixing the issue after the failure is costly and ineffective.

We present Flicker, an infrastructure for executing security-sensitive code in complete isolation while trusting as few as 250 lines of additional code. Flicker can also provide meaningful, fine-grained attestation of the code executed (as well as its inputs and outputs) to a remote party. Flicker guarantees these properties even if the BIOS, OS and DMA-enabled devices are all malicious. Flicker leverages new commodity processors from AMD and Intel and does not require a new OS or VMM. We demonstrate a full implementation of Flicker on an AMD platform and describe our development environment for simplifying the construction of Flicker-enabled code.