Christology in the Epistle to the Hebrews: Martin Luther's Reception of John Chrysostom

Throughout the history of the Church, the Epistle to the Hebrews has been one of the most puzzling letters in the Canon, particularly regarding the implications of understanding the person of Jesus Christ. John Chrysostom, an important patristic writer, is acknowledged to have made significant contributions to the exegesis of this letter. Chrysostom's thought became the norm for traditional thinking and interpretation of this letter in the Middle Ages. Martin Luther's reception of Chrysostom's Homilies on Hebrews presents a unique interpretation that some scholars may describe as the "Reformation Discovery" on Hebrews. In tracing Luther's reception and appropriation of Chrysostom's exegesis of the letter to the Hebrews, there is a noticeable and significant shift in Christological interpretation. Whether or not these modifications were necessary is a matter of debate; however, they do reflect Luther's contextual and existential questions regarding faith, Christ and knowledge of God, which is evident in his Lectures on Hebrews.

STAIR: Practical AIMD Multirate Congestion Control

Existing approaches for multirate multicast congestion control are either friendly to TCP only over large time scales or introduce unfortunate side effects, such as significant control traffic, wasted bandwidth, or the need for modifications to existing routers. We advocate a layered multicast approach in which steady-state receiver reception rates emulate the classical TCP sawtooth derived from additive-increase, multiplicative decrease (AIMD) principles. Our approach introduces the concept of dynamic stair layers to simulate various rates of additive increase for receivers with heterogeneous round-trip times (RTTs), facilitated by a minimal amount of IGMP control traffic. We employ a mix of cumulative and non-cumulative layering to minimize the amount of excess bandwidth consumed by receivers operating asynchronously behind a shared bottleneck. We integrate these techniques together into a congestion control scheme called STAIR which is amenable to those multicast applications which can make effective use of arbitrary and time-varying subscription levels.

Smooth Multirate Multicast Congestion Control

A significant impediment to deployment of multicast services is the daunting technical complexity of developing, testing and validating congestion control protocols fit for wide-area deployment. Protocols such as pgmcc and TFMCC have recently made considerable progress on the single rate case, i.e. where one dynamic reception rate is maintained for all receivers in the session. However, these protocols have limited applicability, since scaling to session sizes beyond tens of participants necessitates the use of multiple rate protocols. Unfortunately, while existing multiple rate protocols exhibit better scalability, they are both less mature than single rate protocols and suffer from high complexity. We propose a new approach to multiple rate congestion control that leverages proven single rate congestion control methods by orchestrating an ensemble of independently controlled single rate sessions. We describe SMCC, a new multiple rate equation-based congestion control algorithm for layered multicast sessions that employs TFMCC as the primary underlying control mechanism for each layer. SMCC combines the benefits of TFMCC (smooth rate control, equation-based TCP friendliness) with the scalability and flexibility of multiple rates to provide a sound multiple rate multicast congestion control policy.