Free ${\cal N}=4$ Super Yang-Mills theory (in the large $N$ limit) is dual to an, as yet, intractable closed string theory on $AdS_5\times S^5$. We aim to implement open-closed string duality in this system and thereby recast the free field correlation functions as amplitudes in $AdS$. The basic strategy is to implement this duality directly on planar field theory correlation functions in the worldline (or first quantised) formulation. The worldline loops (remnants of the worldsheet holes) close to form tree diagrams. These tree diagrams are then to be manifested as tree amplitudes in $AdS$ by a change of variables on the worldline moduli space (i.e. Schwinger parameter space). Restricting to twist two operators, we are able to carry through this program for two and three point functions. However, it appears that this strategy can be implemented for four and higher point functions as well. An analogy to electrical networks is very useful in this regard.

background

Introductory circuit theory

From free fields to AdS

A history of equivalent circuit modeling of acoustic structures is presented. This is followed by a tutorial development of their use to represent piezoelectric (PE) and piezomagnetic (PM) plate transducers and bimorph cantilever beams for the purpose of facilitating transition of modern micro/nanotechnology creations to practical sensor, actuator, and transducer applications. Circuit approximations of various types are derived from the more general networks.

Modeling piezoelectric and piezomagnetic devices and structures via equivalent networks

This paper develops a framework using mechanical multi-port networks to study the performance capabilities and constraints in vehicle suspensions. We seek to understand the set of dynamic responses which are achievable for both passive and active systems. To this end, we view a suspension system as a mechanical multi-port network and draw on concepts from electrical circuits such as passivity and reciprocity. We identify necessary conditions on the external behaviour of a quarter-car model for the suspension to be capable of passive realisation, and thereby establish that several behaviours or force laws cannot be implemented without an internal power source. We study the number of available degrees of freedom (i.e., independently specifiable impedances) in the quarter-, half- and full-car cases.

Performance limitations and constraints for active and passive suspensions : a mechanical multi-port approach

Given a large graph and a query node, finding its k-nearest-neighbor (kNN) is a fundamental problem. Various random walk based measures have been developed to measure the proximity (similarity) between nodes. Existing algorithms for the random walk based top-k proximity search can be categorized as global and local methods based on their search strategies. Global methods usually require an expensive precomputing step. By only searching the nodes near the query node, local methods have the potential to support more efficient query. However, most existing local search methods cannot guarantee the exactness of the solution. Moreover, they are usually designed for specific proximity measures. Can we devise an efficient local search method that applies to different measures and also guarantees result exactness? In this paper, we present FLoS (Fast Local Search), a unified local search method for efficient and exact top-k proximity query in large graphs. FLoS is based on the no local optimum property of proximity measures. We show that many measures have no local optimum. Utilizing this property, we introduce several simple operations on transition probabilities, which allow developing lower and upper bounds on the proximity. The bounds monotonically converge to the exact proximity when more nodes are visited. We further show that FLoS can also be applied to measures having local optimum by utilizing relationship among different measures. We perform comprehensive experiments to evaluate the efficiency and applicability of the proposed method.

methods

Fast and unified local search for random walk based k-nearest-neighbor query in large graphs

The generalized method of time and transfer constants is introduced. It can be used to determine the transfer function to the desired level of accuracy in terms of time and transfer constants of first-order systems using exclusively low frequency calculations. This method can be used to determine the poles and zeros of circuits with both inductors and capacitors. An inductive proof of this generalized method is given which subsumes special cases, such as methods of zero- and infinite-value time constants. Several important and useful corollaries of this method are discussed and several examples are analyzed.

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Introductory circuit theory

Citations

From free fields to AdS

Modeling piezoelectric and piezomagnetic devices and structures via equivalent networks

Performance limitations and constraints for active and passive suspensions : a mechanical multi-port approach

Fast and unified local search for random walk based k-nearest-neighbor query in large graphs

Generalized Time- and Transfer-Constant Circuit Analysis

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