15,160 research outputs found
A Cycle-Based Formulation and Valid Inequalities for DC Power Transmission Problems with Switching
It is well-known that optimizing network topology by switching on and off
transmission lines improves the efficiency of power delivery in electrical
networks. In fact, the USA Energy Policy Act of 2005 (Section 1223) states that
the U.S. should "encourage, as appropriate, the deployment of advanced
transmission technologies" including "optimized transmission line
configurations". As such, many authors have studied the problem of determining
an optimal set of transmission lines to switch off to minimize the cost of
meeting a given power demand under the direct current (DC) model of power flow.
This problem is known in the literature as the Direct-Current Optimal
Transmission Switching Problem (DC-OTS). Most research on DC-OTS has focused on
heuristic algorithms for generating quality solutions or on the application of
DC-OTS to crucial operational and strategic problems such as contingency
correction, real-time dispatch, and transmission expansion. The mathematical
theory of the DC-OTS problem is less well-developed. In this work, we formally
establish that DC-OTS is NP-Hard, even if the power network is a
series-parallel graph with at most one load/demand pair. Inspired by Kirchoff's
Voltage Law, we give a cycle-based formulation for DC-OTS, and we use the new
formulation to build a cycle-induced relaxation. We characterize the convex
hull of the cycle-induced relaxation, and the characterization provides strong
valid inequalities that can be used in a cutting-plane approach to solve the
DC-OTS. We give details of a practical implementation, and we show promising
computational results on standard benchmark instances
Optimal fluctuations and the control of chaos.
The energy-optimal migration of a chaotic oscillator from one attractor to another coexisting attractor is investigated via an analogy between the Hamiltonian theory of fluctuations and Hamiltonian formulation of the control problem. We demonstrate both on physical grounds and rigorously that the Wentzel-Freidlin Hamiltonian arising in the analysis of fluctuations is equivalent to Pontryagin's Hamiltonian in the control problem with an additive linear unrestricted control. The deterministic optimal control function is identied with the optimal fluctuational force. Numerical and analogue experiments undertaken to verify these ideas demonstrate that, in the limit of small noise intensity, fluctuational escape from the chaotic attractor occurs via a unique (optimal) path corresponding to a unique (optimal) fluctuational force. Initial conditions on the chaotic attractor are identified. The solution of the boundary value control problem for the Pontryagin Hamiltonian is found numerically. It is shown that this solution is approximated very accurately by the optimal fluctuational force found using statistical analysis of the escape trajectories. A second series of numerical experiments on the deterministic system (i.e. in the absence of noise) show that a control function of precisely the same shape and magnitude is indeed able to instigate escape. It is demonstrated that this control function minimizes the cost functional and the corresponding energy is found to be smaller than that obtained with some earlier adaptive control algorithms
Promote-IT: An efficient Real-Time Tertiary-Storage Scheduler
Promote-IT is an efficient heuristic scheduler that provides QoS guarantees for accessing data from tertiary storage. It can deal with a wide variety of requests and jukebox hardware. It provides short response and confirmation times, and makes good use of the jukebox resources. It separates the scheduling and dispatching functionality and effectively uses this separation to dispatch tasks earlier than scheduled, provided that the resource constraints are respected and no task misses its deadline. To prove the efficiency of Promote-IT we implemented alternative schedulers based on different scheduling models and scheduling paradigms. The evaluation shows that Promote-IT performs better than the other heuristic schedulers. Additionally, Promote-IT provides response-times near the optimum in cases where the optimal scheduler can be computed
On the Anticipatory Aspects of the Four Interactions: what the Known Classical and Semi-Classical Solutions Teach us
The four (electro-magnetic, weak, strong and gravitational) interactions are
described by singular Lagrangians and by Dirac-Bergmann theory of Hamiltonian
constraints. As a consequence a subset of the original configuration variables
are {\it gauge variables}, not determined by the equations of motion. Only at
the Hamiltonian level it is possible to separate the gauge variables from the
deterministic physical degrees of freedom, the {\it Dirac observables}, and to
formulate a well posed Cauchy problem for them both in special and general
relativity. Then the requirement of {\it causality} dictates the choice of {\it
retarded} solutions at the classical level. However both the problems of the
classical theory of the electron, leading to the choice of solutions, and the regularization of quantum field
teory, leading to the Feynman propagator, introduce {\it anticipatory} aspects.
The determination of the relativistic Darwin potential as a semi-classical
approximation to the Lienard-Wiechert solution for particles with
Grassmann-valued electric charges, regularizing the Coulomb self-energies,
shows that these anticipatory effects live beyond the semi-classical
approximation (tree level) under the form of radiative corrections, at least
for the electro-magnetic interaction.Comment: 12 pages, Talk and "best contribution" at The Sixth International
Conference on Computing Anticipatory Systems CASYS'03, Liege August 11-16,
200
Virtual Biquandles
In the present paper, we describe new approaches for constructing virtual
knot invariants. The main background of this paper comes from formulating and
bringing together the ideas of biquandle (Kauffman and Radford) the virtual
quandle (Manturov), the ideas of quaternion biquandles by Roger Fenn and Andrew
Bartholomew, the concepts and properties of long virtual knots (Manturov), and
other ideas in the interface between classical and virtual knot theory. In the
present paper we present a new algebraic construction of virtual knot
invariants, give various presentations of it, and study several examples.
Several conjectures and unsolved problems are presented throughout the paper
- …