The Conjugate Residual Method for Constrained Minimization Problems

International audienceThe method of conjugate gradients, a particular version of the general class of conjugate direction methods, was originally developed for solving a linear system of equations$$Ax = b,$$where $A$ is an $n \times n$ symmetric, positive definite matrix, $x$ is an unknown $n$-vector and $b$ is a fixed $n$-vector. The conjugate gradient method can be viewed as a descent procedure for the problem : Minimize$$(x , Ax) - 2(x, b);$$and through this viewpoint the method can be generalized so as to apply to the solution of general unconstrained minimization problems. For these general problems conjugate gradient methods are among the most effective first order descent procedures

Intermittent predictive control of an inverted pendulum

Intermittent predictive pole-placement control is successfully applied to the constrained-state control of a prestabilised experimental inverted pendulum

Turing's three philosophical lessons and the philosophy of information

In this article, I outline the three main philosophical lessons that we may learn from Turing's work, and how they lead to a new philosophy of information. After a brief introduction, I discuss his work on the method of levels of abstraction (LoA), and his insistence that questions could be meaningfully asked only by specifying the correct LoA. I then look at his second lesson, about the sort of philosophical questions that seem to be most pressing today. Finally, I focus on the third lesson, concerning the new philosophical anthropology that owes so much to Turing's work. I then show how the lessons are learned by the philosophy of information. In the conclusion, I draw a general synthesis of the points made, in view of the development of the philosophy of information itself as a continuation of Turing's work. This journal is © 2012 The Royal Society.Peer reviewe

Non-Centralized Navigation for Source Localization by Cooperative UAVs

In this paper, we propose a distributed solution to the navigation of a population of unmanned aerial vehicles (UAVs) to best localize a static source. The network is considered heterogeneous with UAVs equipped with received signal strength (RSS) sensors from which it is possible to estimate the distance from the source and/or the direction of arrival through ad-hoc rotations. This diversity in gathering and processing RSS measurements mitigates the loss of localization accuracy due to the adoption of low-complexity sensors. The UAVs plan their trajectories on-the-fly and in a distributed fashion. The collected data are disseminated through the network via multi-hops, therefore being subject to latency. Since not all the paths are equal in terms of information gathering rewards, the motion planning is formulated as a minimization of the uncertainty of the source position under UAV kinematic and anti-collision constraints and performed by 3D non-linear programming. The proposed analysis takes into account non-line-of-sight (NLOS) channel conditions as well as measurement age caused by the latency constraints in communication.Comment: 5 pages, 3 figures, conferenc

Risk and Utility in Portfolio Optimization

Modern portfolio theory(MPT) addresses the problem of determining the optimum allocation of investment resources among a set of candidate assets. In the original mean-variance approach of Markowitz, volatility is taken as a proxy for risk, conflating uncertainty with risk. There have been many subsequent attempts to alleviate that weakness which, typically, combine utility and risk. We present here a modification of MPT based on the inclusion of separate risk and utility criteria. We define risk as the probability of failure to meet a pre-established investment goal. We define utility as the expectation of a utility function with positive and decreasing marginal value as a function of yield. The emphasis throughout is on long investment horizons for which risk-free assets do not exist. Analytic results are presented for a Gaussian probability distribution. Risk-utility relations are explored via empirical stock-price data, and an illustrative portfolio is optimized using the empirical data.Comment: 10 pages, 1 figure, presented at 2002 Conference on Econophysics in Bali Indonesi

Drag-free and attitude control for the GOCE satellite

The paper concerns Drag-Free and Attitude Control of the European satellite Gravity field and steady-state Ocean Circulation Explorer (GOCE) during the science phase. Design has followed Embedded Model Control, where a spacecraft/environment discrete-time model becomes the realtime control core and is interfaced to actuators and sensors via tuneable feedback laws. Drag-free control implies cancelling non-gravitational forces and all torques, leaving the satellite to free fall subject only to gravity. In addition, for reasons of science, the spacecraft must be carefully aligned to the local orbital frame, retrieved from range and rate of a Global Positioning System receiver. Accurate drag-free and attitude control requires proportional and low-noise thrusting, which in turn raises the problem of propellant saving. Six-axis drag-free control is driven by accurate acceleration measurements provided by the mission payload. Their angular components must be combined with the star-tracker attitude so as to compensate accelerometer drift. Simulated results are presented and discusse

Methods of recycling of carbon-containing waste products

Рассмотрены вопросы утилизации отходов органических растворителей, лакокрасочных материалов и галогенсодержащих органических веществ. Исследованы разрядноимпульсные процессы двухстадийной переработки жидких углеродсодержащих отходов, включающей переработку образующихся газов. Показана возможность переработки твердых галогенсодержащих отходов в процессах самораспространяющегося высокотемпературного синтеза (СВС), инициируемого разрядным импульсом тока. Разрядноимпульный и СВС методы утилизации углеродсодержащих отходов целесообразно использовать для получения полезного продукта - углеродных наноматериалов.The problems of recycling of waste products of organic solvents, paint and varnish materials and halogen-containing compounds organic were considered. Pulse discharge processes for two-stage treatment of liquid carbon-containing waste products which includes recycling of forming gases were studied. The possibility of recycling of solid halogen-containing waste products in the process of self-propagating high-temperature synthesis (SHS), initiated by the pulse discharge current was shown. Effective regimes for processing of liquid carbon-containing waste products into carbon nanomaterials were determined. Pulse discharge and SHS methods of recycling of carbon-containing waste products can and should be used in the expedient production of industrially useful carbon nanomaterials

The Resonance Peak in Sr2_2RuO4_4: Signature of Spin Triplet Pairing

We study the dynamical spin susceptibility, $\chi({\bf q}, \omega)$, in the normal and superconducting state of Sr$_2$RuO$_4$. In the normal state, we find a peak in the vicinity of ${\bf Q}_i\simeq (0.72\pi,0.72\pi)$ in agreement with recent inelastic neutron scattering (INS) experiments. We predict that for spin triplet pairing in the superconducting state a {\it resonance peak} appears in the out-of-plane component of $\chi$, but is absent in the in-plane component. In contrast, no resonance peak is expected for spin singlet pairing.Comment: 4 pages, 4 figures, final versio

Analysis of the rebalancing frequency in log-optimal portfolio selection

In a dynamic investment situation, the right timing of portfolio revisions and adjustments is essential to sustain long-term growth. A high rebalancing frequency reduces the portfolio performance in the presence of transaction costs, whereas a low rebalancing frequency entails a static investment strategy that hardly reacts to changing market conditions. This article studies a family of portfolio problems in a Black-Scholes type economy which depend parametrically on the rebalancing frequency. As an objective criterion we use log-utility, which has strong theoretical appeal and represents a natural choice if the primary goal is long-term performance. We argue that continuous rebalancing only slightly outperforms discrete rebalancing if there are no transaction costs and if the rebalancing intervals are shorter than about one year. Our analysis also reveals that diversification has a dual effect on the mean and variance of the portfolio growth rate as well as on their sensitivities with respect to the rebalancing frequency