Moment-Based Relaxation of the Optimal Power Flow Problem

The optimal power flow (OPF) problem minimizes power system operating cost subject to both engineering and network constraints. With the potential to find global solutions, significant research interest has focused on convex relaxations of the non-convex AC OPF problem. This paper investigates ``moment-based'' relaxations of the OPF problem developed from the theory of polynomial optimization problems. At the cost of increased computational requirements, moment-based relaxations are generally tighter than the semidefinite relaxation employed in previous research, thus resulting in global solutions for a broader class of OPF problems. Exploration of the feasible space for test systems illustrates the effectiveness of the moment-based relaxation.Comment: 7 pages, 4 figures. Abstract accepted, full paper in revie

Modular Frobenius manifolds and their invariant flows

The space of Frobenius manifolds has a natural involutive symmetry on it: there exists a map $I$ which send a Frobenius manifold to another Frobenius manifold. Also, from a Frobenius manifold one may construct a so-called almost dual Frobenius manifold which satisfies almost all of the axioms of a Frobenius manifold. The action of $I$ on the almost dual manifolds is studied, and the action of $I$ on objects such as periods, twisted periods and flows is studied. A distinguished class of Frobenius manifolds sit at the fixed point of this involutive symmetry, and this is made manifest in certain modular properties of the various structures. In particular, up to a simple reciprocal transformation, for this class of modular Frobenius manifolds, the flows are invariant under the action of $I\,.

Solution of Optimal Power Flow Problems using Moment Relaxations Augmented with Objective Function Penalization

The optimal power flow (OPF) problem minimizes the operating cost of an electric power system. Applications of convex relaxation techniques to the non-convex OPF problem have been of recent interest, including work using the Lasserre hierarchy of "moment" relaxations to globally solve many OPF problems. By preprocessing the network model to eliminate low-impedance lines, this paper demonstrates the capability of the moment relaxations to globally solve large OPF problems that minimize active power losses for portions of several European power systems. Large problems with more general objective functions have thus far been computationally intractable for current formulations of the moment relaxations. To overcome this limitation, this paper proposes the combination of an objective function penalization with the moment relaxations. This combination yields feasible points with objective function values that are close to the global optimum of several large OPF problems. Compared to an existing penalization method, the combination of penalization and the moment relaxations eliminates the need to specify one of the penalty parameters and solves a broader class of problems.Comment: 8 pages, 1 figure, to appear in IEEE 54th Annual Conference on Decision and Control (CDC), 15-18 December 201

Knizhnik-Zamolodchikov-type equations for gauged WZNW models

We study correlation functions of coset constructions by utilizing the method of gauge dressing. As an example we apply this method to the minimal models and to the Witten 2D black hole. We exhibit a striking similarity between the latter and the gravitational dressing. In particular, we look for logarithmic operators in the 2D black hole.Comment: 24 pages, latex, no figures. More discussion of logarithmic operators was adde

Using Narrow Band Photometry to Detect Young Brown Dwarfs in IC348

We report the discovery of a population of young brown dwarf candidates in the open star cluster IC348 and the development of a new spectroscopic classification technique using narrow band photometry. Observations were made using FLITECAM, the First Light Camera for SOFIA, at the 3-m Shane Telescope at Lick Observatory. FLITECAM is a new 1-5 micron camera with an 8 arcmin field of view. Custom narrow band filters were developed to detect absorption features of water vapor (at 1.495 microns) and methane (at 1.66 microns) characteristic of brown dwarfs. These filters enable spectral classification of stars and brown dwarfs without spectroscopy. FLITECAM's narrow and broadband photometry was verified by examining the color-color and color-magnitude characteristics of stars whose spectral type and reddening was known from previous surveys. Using our narrow band filter photometry method, it was possible to identify an object measured with a signal-to-noise ratio of 20 or better to within +/-3 spectral class subtypes for late-type stars. With this technique, very deep images of the central region of IC348 (H ~ 20.0) have identified 18 sources as possible L or T dwarf candidates. Out of these 18, we expect that between 3 - 6 of these objects are statistically likely to be background stars, with the remainder being true low-mass members of the cluster. If confirmed as cluster members then these are very low-mass objects (~5 Mjupiter). We also describe how two additional narrow band filters can improve the contrast between M, L, and T dwarfs as well as provide a means to determine the reddening of an individual object.Comment: 43 pages, 17 figures. Accepted for publication in the Astrophysical Journal 27 June 200

Entangled resource for interfacing single- and dual-rail optical qubits

Today's most widely used method of encoding quantum information in optical qubits is the dual-rail basis, often carried out through the polarisation of a single photon. On the other hand, many stationary carriers of quantum information - such as atoms - couple to light via the single-rail encoding in which the qubit is encoded in the number of photons. As such, interconversion between the two encodings is paramount in order to achieve cohesive quantum networks. In this paper, we demonstrate this by generating an entangled resource between the two encodings and using it to teleport a dual-rail qubit onto its single-rail counterpart. This work completes the set of tools necessary for the interconversion between the three primary encodings of the qubit in the optical field: single-rail, dual-rail and continuous-variable.Comment: Published in Quantu

Lateral Line Analogue Aids Vision in Successful Predator Evasion for the Brief Squid, Lolliguncula Brevis

Cephalopods have visual and mechanoreception systems that may be employed to sense and respond to an approaching predator. While vision presumably plays the dominant role, the importance of the lateral line analogue for predator evasion has not been examined in cephalopods. To test the respective roles of vision and the lateral line analogue, brief squid, Lolliguncula brevis, were observed in the presence of summer flounder, Paralichthys dentatus, under light and dark conditions with their lateral line analogue intact and ablated. Hair cell ablation was achieved through a pharmacological technique used for the first time on a cephalopod. The proportion of predator-prey interactions survived was significantly higher in the light non-ablated and light ablated groups compared with the dark ablated group. The mean number of interactions survived varied across treatment groups with the light non-ablated group having significantly more success than the light ablated, dark non-ablated and dark ablated groups. These findings demonstrate that although vision is the primary sense, the lateral line analogue also contributes to predator evasion in squid