206570580
Sachs' Linkless Embedding Conjecture
Abstract We prove Sachs′ conjecture that a graph can be embedded in 3-space so that it contains no non-trivial link (in the sense of knot theory) if and only if it contains as a minor none of the seven graphs obtainable from K 6 by Y − Δ and Δ − Y exchanges. We also show the following: (i) A graph admits such a "linkless" embedding if and only if it admits a "panelled" embedding, one such that every circuit of the graph bounds a disc disjoint from the remainder of the graph. This was a conjecture of Bohme. (ii) An embedding is panelled if and only if for every subgraph, its complement in 3-space has free fundamental group. This extends a theorem of Scharlemann and Thompson, who proved it for planar graphs. (iii) If two panelled embeddings of the same graph are "different," that is, are not related by an orientation-preserving homeomorphism of the 3-space, then there is a subgraph which is a subdivision of K 5 or K 3, 3 such that the two induced embeddings of this subgraph are still different.
31141074
Petersen Family Minors
Abstract We show that the only graphs with certain connectivity and planarity properties are the Petersen graph and some other more trivial graphs. Then this is used to show that every graph with no minor in the Petersen family (the seven graphs that can be obtained from the Petersen graph by Y − Δ and Δ − Y exchanges) is either decomposable in some sense, or it is a 1-vertex extension of a planar graph, or it has high connectivity in a sense we can use, or it can be converted to one of these by Y − Δ and Δ − Y exchanges. This is a lemma for use in a subsequent paper, where we show that a graph has a "linkless" embedding in 3-space if and only if it has no minor in the Petersen family.
33726107
A menger-like property of tree-width: The finite case
The notion of tree-width was introduced by Robertson and Symour. A graph has tree-width ≦ w if it admits a tree-decomposition of tree-width ≦ w. We prove here that if G is finite and has tree-width ≦ w then it admits a tree-decomposition of tree-width ≦ w which satisfies a certain Menger-like condition. This result will be used in a future paper on well-quasi-ordering infinite graphs of bounded tree-width.
33773
An Agent-Based Optimal Bidding Function
Problems such as price volatility have been observed in electric power markets. Demand-side participation is often offered as a potential solution by promising to increase market efficiency when hockey-stick type offer curves are present. However, individual end-consumer will surely value electricity differently, which makes demand-side participation as a group and at a bus difficult. In this paper demand is categorized into two groups: one that highly values reliability and the other that does not. The two types are modeled separately and a new optimal bidding function is developed and tested based on this model.
37344904
Power System Bidding Tournaments for a Deregulated Environment
In this paper we describe certain tools for understanding and operating power systems in a deregulated environment. Many of the current models for this competitive market that employ an independent system operator (ISO) for controlling transmission, ensuring fair access and security, and providing a spot market for power will be studied. This centrally-dispatched power pool also ensures that generation meets demand based on bids submitted daily from independent generators (and from customers offering interruptible loads). Currently, most I S 0 bidding models allow only a single bid per day. In this paper, we present an asynchronous bidding scheme as a possible alternative. In particular, we examine the effects of including a feedback mechanism such that upon receiving generation levels from the ISO, independent generators (IGs) be allowed to modify their bid if they so desire. This competitive or ‘sequential’ bidding process should be allowed to take place each day for a predetermined period of time; in this way, IGs will have a chance to compete and hopefully optimize their profit margins. This paper also discusses the development tools necessary for examining the effects of different bidding processes on the I S 0 model and evaluating their capability of driving the market to an efJicient state of operation.
1283266
A guided clothoid spline
Abstract A method is described whereby a G 2 planar curve consisting of clothoid (Cornu spiral) segments, circular arcs and straight line segments is constructed. The curve passes through given points, is expressed parametrically, and has the attractive feature that the arc length and curvature are piecewise linear functions of the parameter. The given points through which the curve passes must be restricted somewhat so that a unique clothoid exists between each pair of points.
10283778
An Internet-based platform for testing generation scheduling auctions
The paper describes the uses and architecture of a network-centered computing-rich software platform called PowerWeb. PowerWeb was designed and built as a simulation environment for experimentally testing various power exchange auction markets through tournaments. It is designed to host simulations of a competitive "day-ahead" electric energy market in the content of a restructured electric power industry. The PowerWeb environment is meant to be flexible so as to accommodate different "rules of the game". The authors describe its interactive, distributed and Web-based character.
6233472
Underlying technical issues in electricity deregulation
This paper reports on the results of an attempt by the Power Systems Engineering Research Center (Pserc) and EPRI to determine the technical tools missing in currently unfolding electric power restructuring scenarios. Needed tools have been divided into the functional categories of generation, transmission and distribution. In each category, there seems to be a common need to interface existing technical tools with the new economic unbundling.