Mathematical Methods for the Analysis of Hierarchical Systems. 1. Problem Formulation, and Stochastic Algorithms for Solving Minimax and Multiobjective Problems

This is the first of two papers dealing with mathematical methods that can be used to analyze hierarchical systems. In this paper, the authors look at the situation that arises when certain decision-making powers are delegated to various elements within a hierarchical structure. It is found that these elements inevitably begin to operate in accordance with their own interests, which are not necessarily those of the system as a whole. Thus we have the problem of how to distribute the decision-making functions between the central body and the other parts of the system in such a way that the efficiency of the control system is maximized with respect to the global criterion. The authors take a game-theoretical approach to this problem. looking first at two-level hierarchical systems and using Germeyer's games as a model. They derive a number of methods for solving the problem thus formulated, and give some numerical results obtained using two of the resulting algorithms

Genomic variability in Potato virus M and the development of RT-PCR and RFLP procedures for the detection of this virus in seed potatoes

Potato virus M (PVM, Carlavirus) is considered to be one of the most common potato viruses distributed worldwide. Sequences of the coat protein (CP) gene of several Canadian PVM isolates were determined. Phylogenetic analysis indicated that all known PVM isolates fell into two distinct groups and the isolates from Canada and the US clustered in the same group. The Canadian PVM isolates could be further divided into two sub-groups. Two molecular procedures, reverse transcription - polymerase chain reaction (RT-PCR) and restriction fragment length polymorphism (RFLP) were developed in this study for the detection and identification of PVM in potato tubers. RT-PCR was highly specific and only amplified PVM RNA from potato samples. PVM RNAs were easily detected in composite samples of 400 to 800 potato leaves or 200 to 400 dormant tubers. Restriction analysis of PCR amplicons with MscI was a simple method for the confirmation of PCR tests. Thus, RT-PCR followed by RFLP analysis may be a useful approach for screening potato samples on a large scale for the presence of PVM

Salerno's model of DNA reanalysed: could solitons have biological significance?

We investigate the sequence-dependent behaviour of localised excitations in a toy, nonlinear model of DNA base-pair opening originally proposed by Salerno. Specifically we ask whether ``breather'' solitons could play a role in the facilitated location of promoters by RNA polymerase. In an effective potential formalism, we find excellent correlation between potential minima and {\em Escherichia coli} promoter recognition sites in the T7 bacteriophage genome. Evidence for a similar relationship between phage promoters and downstream coding regions is found and alternative reasons for links between AT richness and transcriptionally-significant sites are discussed. Consideration of the soliton energy of translocation provides a novel dynamical picture of sliding: steep potential gradients correspond to deterministic motion, while ``flat'' regions, corresponding to homogeneous AT or GC content, are governed by random, thermal motion. Finally we demonstrate an interesting equivalence between planar, breather solitons and the helical motion of a sliding protein ``particle'' about a bent DNA axis.Comment: Latex file 20 pages, 5 figures. Manuscript of paper to appear in J. Biol. Phys., accepted 02/09/0

An introduction to continuous optimization for imaging

International audienceA large number of imaging problems reduce to the optimization of a cost function , with typical structural properties. The aim of this paper is to describe the state of the art in continuous optimization methods for such problems, and present the most successful approaches and their interconnections. We place particular emphasis on optimal first-order schemes that can deal with typical non-smooth and large-scale objective functions used in imaging problems. We illustrate and compare the different algorithms using classical non-smooth problems in imaging, such as denoising and deblurring. Moreover, we present applications of the algorithms to more advanced problems, such as magnetic resonance imaging, multilabel image segmentation, optical flow estimation, stereo matching, and classification

STABILITY PROPERTIES OF THE GRADIENT PROJECTION METHOD WITH APPLICATIONS TO THE BACKPROPAGATION ALGORITHM

Convergence properties of the generalized gradient projection algorithm in the presence of data perturbations are investigated. It is shown that every trajectory of the method is attracted, in a certain sense, to an ?-stationary set of the problem, where ? depends on the magnitude of the perturbations. Estimates for the attraction sets of the iterates are given in the general (nonsmooth and nonconvex) case. In the convex case, our results imply convergence to an ?-optimal set. The results are further strengthened for weakly short and strong convex problems. Convergence of the parallel algorithm in the case of the additive objective function is established. One of the principal applications of our results is the stability analysis of the classical backpropagation algorithm for training artificial neural networks