A duality model of TCP and queue management algorithms

We propose a duality model of end-to-end congestion control and apply it to understanding the equilibrium properties of TCP and active queue management schemes. The basic idea is to regard source rates as primal variables and congestion measures as dual variables, and congestion control as a distributed primal-dual algorithm over the Internet to maximize aggregate utility subject to capacity constraints. The primal iteration is carried out by TCP algorithms such as Reno or Vegas, and the dual iteration is carried out by queue management algorithms such as DropTail, RED or REM. We present these algorithms and their generalizations, derive their utility functions, and study their interaction

University-Based Forestry Research and The Little Red Hen

Universities have three basic mission areas: service, teaching, and research. Through the service mission, many forest landowners participate in forestry extension programs and use university-based out reach materials and resources. Many forest landowners also recognize the teaching mission of universities by interacting regularly with forestry professionals who were trained through academic programs accredited by the Society of American Foresters. These two mission areas, service and teaching, have been and continue to be relevant to millions of forest landowners across the nation. But what about university-based forestry research? As a forestry dean and as current president of the National Association of University Forest Resources Programs, and (just as importantly) as a forest landowner, I\u27d like to address three key questions about forestry research, including what this has to do with The Little Red Hen

Convex Relaxation of Optimal Power Flow, Part I: Formulations and Equivalence

This tutorial summarizes recent advances in the convex relaxation of the optimal power flow (OPF) problem, focusing on structural properties rather than algorithms. Part I presents two power flow models, formulates OPF and their relaxations in each model, and proves equivalence relations among them. Part II presents sufficient conditions under which the convex relaxations are exact.Comment: Citation: IEEE Transactions on Control of Network Systems, 15(1):15-27, March 2014. This is an extended version with Appendices VIII and IX that provide some mathematical preliminaries and proofs of the main result

Convex Relaxation of Optimal Power Flow, Part II: Exactness

This tutorial summarizes recent advances in the convex relaxation of the optimal power flow (OPF) problem, focusing on structural properties rather than algorithms. Part I presents two power flow models, formulates OPF and their relaxations in each model, and proves equivalence relations among them. Part II presents sufficient conditions under which the convex relaxations are exact.Comment: Citation: IEEE Transactions on Control of Network Systems, June 2014. This is an extended version with Appendex VI that proves the main results in this tutoria

The Spectrum of the Partially Locked State for the Kuramoto Model

We solve a longstanding stability problem for the Kuramoto model of coupled oscillators. This system has attracted mathematical attention, in part because of its applications in fields ranging from neuroscience to condensed-matter physics, and also because it provides a beautiful connection between nonlinear dynamics and statistical mechanics. The model consists of a large population of phase oscillators with all-to-all sinusoidal coupling. The oscillators' intrinsic frequencies are randomly distributed across the population according to a prescribed probability density, here taken to be unimodal and symmetric about its mean. As the coupling between the oscillators is increased, the system spontaneously synchronizes: the oscillators near the center of the frequency distribution lock their phases together and run at the same frequency, while those in the tails remain unlocked and drift at different frequencies. Although this ``partially locked'' state has been observed in simulations for decades, its stability has never been analyzed mathematically. Part of the difficulty is in formulating a reasonable infinite-N limit of the model. Here we describe such a continuum limit, and prove that the corresponding partially locked state is, in fact, neutrally stable, contrary to what one might have expected. The possible implications of this result are discussed

Exactly Solvable Lattice Models with Crossing Symmetry

We show how to compute the exact partition function for lattice statistical-mechanical models whose Boltzmann weights obey a special "crossing" symmetry. The crossing symmetry equates partition functions on different trivalent graphs, allowing a transformation to a graph where the partition function is easily computed. The simplest example is counting the number of nets without ends on the honeycomb lattice, including a weight per branching. Other examples include an Ising model on the Kagome' lattice with three-spin interactions, dimers on any graph of corner-sharing triangles, and non-crossing loops on the honeycomb lattice, where multiple loops on each edge are allowed. We give several methods for obtaining models with this crossing symmetry, one utilizing discrete groups and another anyon fusion rules. We also present results indicating that for models which deviate slightly from having crossing symmetry, a real-space decimation (renormalization-group-like) procedure restores the crossing symmetry

Simulation comparison of RED and REM

We propose earlier an optimization based low control for the Internet called Random Exponential Marking (REM). REM consists of a link algorithm, that probabilistically marks packets inside the network, and a source algorithm, that adapts source rate to observed marking. The marking probability is exponential in a link congestion measure, so that the end-to-end marking probability is exponential in a path congestion measure. Because of the finer measure of congestion provided by REM, sources do not constantly probe the network for spare capacity, but settle around a globally optimal equilibrium, thus avoiding the perpetual cycle of sinking into and recovering from congestion. In this paper we compare the performance of REM with Reno over RED through simulation

Thermosensitivity of the lobster, Homarus americanus, as determined by cardiac assay

It is generally accepted that crustaceans detect, and respond to, changes in water temperature, yet few studies have directly addressed their thermosensitivity. In this investigation a cardiac assay was used as an indicator that lobsters (Homarus americanus) sensed a change in temperature. The typical cardiac response of lobsters to a 1-min application of a thermal stimulus, either warmer (n = 19) or colder (n = 17) than the holding temperature of 15 degrees C, consisted of a short bradycardia (39.5 +/- 8.0 s) followed by a prolonged tachycardia (188.2 +/- 10.7 s). Lobsters exposed to a range of rates of temperature change (0.7, 1.4, 2.6, 5.0 degrees C/min) responded in a dose-dependent manner, with fewer lobsters responding at slower rates of temperature change. The location of temperature receptors could not be determined, but lesioning of the cardioregulatory nerves eliminated the cardiac response. Although the absolute detection threshold is not known, it is conservatively estimated that lobsters can detect temperature changes of greater than 1 degree C, and probably as small as 0.15 degrees C. A comparison of winter and summer lobsters, both held at 15 degrees C for more than 4 weeks, revealed that although their responses to temperature changes were similar, winter lobsters (n = 18) had a significantly lower baseline heart rate (34.8 +/- 4.4 bpm) and a shorter duration cardiac response (174 s) than summer lobsters (n = 18; 49.9 +/- 5.0 bpm, and 320 s respectively). This suggests that some temperature-independent seasonal modulation of cardiac activity may be occurring