A Majorization-Minimization Approach to Design of Power Transmission Networks

We propose an optimization approach to design cost-effective electrical power transmission networks. That is, we aim to select both the network structure and the line conductances (line sizes) so as to optimize the trade-off between network efficiency (low power dissipation within the transmission network) and the cost to build the network. We begin with a convex optimization method based on the paper ``Minimizing Effective Resistance of a Graph'' [Ghosh, Boyd \& Saberi]. We show that this (DC) resistive network method can be adapted to the context of AC power flow. However, that does not address the combinatorial aspect of selecting network structure. We approach this problem as selecting a subgraph within an over-complete network, posed as minimizing the (convex) network power dissipation plus a non-convex cost on line conductances that encourages sparse networks where many line conductances are set to zero. We develop a heuristic approach to solve this non-convex optimization problem using: (1) a continuation method to interpolate from the smooth, convex problem to the (non-smooth, non-convex) combinatorial problem, (2) the majorization-minimization algorithm to perform the necessary intermediate smooth but non-convex optimization steps. Ultimately, this involves solving a sequence of convex optimization problems in which we iteratively reweight a linear cost on line conductances to fit the actual non-convex cost. Several examples are presented which suggest that the overall method is a good heuristic for network design. We also consider how to obtain sparse networks that are still robust against failures of lines and/or generators.Comment: 8 pages, 3 figures. To appear in Proc. 49th IEEE Conference on Decision and Control (CDC '10

Analog hardware for detecting discontinuities in early vision

The detection of discontinuities in motion, intensity, color, and depth is a well-studied but difficult problem in computer vision [6]. We discuss the first hardware circuit that explicitly implements either analog or binary line processes in a deterministic fashion. Specifically, we show that the processes of smoothing (using a first-order or membrane type of stabilizer) and of segmentation can be implemented by a single, two-terminal nonlinear voltage-controlled resistor, the “resistive fuse”; and we derive its current-voltage relationship from a number of deterministic approximations to the underlying stochastic Markov random fields algorthms. The concept that the quadratic variation functionals of early vision can be solved via linear resistive networks minimizing power dissipation [37] can be extended to non-convex variational functionals with analog or binary line processes being solved by nonlinear resistive networks minimizing the electrical co-content. We have successfully designed, tested, and demonstrated an analog CMOS VLSI circuit that contains a 1D resistive network of fuses implementing piecewise smooth surface interpolation. We furthermore demonstrate the segmenting abilities of these analog and deterministic “line processes” by numerically simulating the nonlinear resistive network computing optical flow in the presence of motion discontinuities. Finally, we discuss various circuit implementations of the optical flow computation using these circuits

Optical Flow and Surface Interpolation in Resistive Networks: Algorithms and Analog VLSI Chips

To us, and to other biological organisms, vision seems effortless. We open our eyes and we "see" the world in all its color, brightness, and movement. Flies, frogs, cats, and humans can all equally well perceive a rapidly changing environment and act on it. Yet, we have great difficulties when trying to endow our machines with similar abilities. In this article, we describe recent developments in the theory of early vision that led from the formulation of the motion problem as an ill-posed one to its solution by minimizing certain "cost" functions. These cost or energy functions can be mapped onto simple analog and digital resistive networks. For instance, as detailed in this chapter, we can compute the optical flow by injecting currents into resistive networks and recording the resulting stationary voltage distribution at each node. These networks, which are implemented in subthreshold, analog, complementary metal oxide semiconductor (CMOS) very large scale integrated (VLSI) circuits, are very attractive for their technological potential

Theoretical Developments in Electromagnetic Induction Geophysics with Selected Applications in the Near Surface

Near-surface applied electromagnetic geophysics is experiencing an explosive period of growth with many innovative techniques and applications presently emergent and others certain to be forthcoming. An attempt is made here to bring together and describe some of the most notable advances. This is a difficult task since papers describing electromagnetic induction methods are widely dispersed throughout the scientific literature. The traditional topics discussed herein include modeling, inversion, heterogeneity, anisotropy, target recognition, logging, and airborne electromagnetics (EM). Several new or emerging techniques are introduced including landmine detection, biogeophysics, interferometry, shallow-water electromagnetics, radiomagnetotellurics, and airborne unexploded ordnance (UXO) discrimination. Representative case histories that illustrate the range of exciting new geoscience that has been enabled by the developing techniques are presented from important application areas such as hydrogeology, contamination, UXO and landmines, soils and agriculture, archeology, and hazards and climat

VLSI analogs of neuronal visual processing: a synthesis of form and function

This thesis describes the development and testing of a simple visual system fabricated using complementary metal-oxide-semiconductor (CMOS) very large scale integration (VLSI) technology. This visual system is composed of three subsystems. A silicon retina, fabricated on a single chip, transduces light and performs signal processing in a manner similar to a simple vertebrate retina. A stereocorrespondence chip uses bilateral retinal input to estimate the location of objects in depth. A silicon optic nerve allows communication between chips by a method that preserves the idiom of action potential transmission in the nervous system. Each of these subsystems illuminates various aspects of the relationship between VLSI analogs and their neurobiological counterparts. The overall synthetic visual system demonstrates that analog VLSI can capture a significant portion of the function of neural structures at a systems level, and concomitantly, that incorporating neural architectures leads to new engineering approaches to computation in VLSI. The relationship between neural systems and VLSI is rooted in the shared limitations imposed by computing in similar physical media. The systems discussed in this text support the belief that the physical limitations imposed by the computational medium significantly affect the evolving algorithm. Since circuits are essentially physical structures, I advocate the use of analog VLSI as powerful medium of abstraction, suitable for understanding and expressing the function of real neural systems. The working chip elevates the circuit description to a kind of synthetic formalism. The behaving physical circuit provides a formal test of theories of function that can be expressed in the language of circuits