Critical sets in parametric optimization

We deal with one-parameter families of optimization problems in finite dimensions. The constraints are both of equality and inequality type. The concept of a ‘generalized critical point’ (g.c. point) is introduced. In particular, every local minimum, Kuhn-Tucker point, and point of Fritz John type is a g.c. point. Under fairly weak (even generic) conditions we study the set∑ consisting of all g.c. points. Due to the parameter, the set∑ is pieced together from one-dimensional manifolds. The points of∑ can be divided into five (characteristic) types. The subset of ‘nondegenerate critical points’ (first type) is open and dense in∑ (nondegenerate means: strict complementarity, nondegeneracy of the corresponding quadratic form and linear independence of the gradients of binding constraints). A nondegenerate critical point is completely characterized by means of four indices. The change of these indices along∑ is presented. Finally, the Kuhn-Tucker subset of∑ is studied in more detail, in particular in connection with the (failure of the) Mangasarian-Fromowitz constraint qualification

Electroactive biofilms: new means for electrochemistry

This work demonstrates that electrochemical reactions can be catalysed by the natural biofilms that form on electrode surfaces dipping into drinking water or compost. In drinking water, oxygen reduction was monitored with stainless steel ultra-microelectrodes under constant potential electrolysis at )0.30 V/SCE for 13 days. 16 independent experiments were conducted in drinking water, either pure or with the addition of acetate or dextrose. In most cases, the current increased and reached 1.5–9.5 times the initial current. The current increase was attributed to biofilm forming on the electrode in a similar way to that has been observed in seawater. Epifluorescence microscopy showed that the bacteria size and the biofilm morphology depended on the nutrients added, but no quantitative correlation between biofilm morphology and current was established. In compost, the oxidation process was investigated using a titanium based electrode under constant polarisation in the range 0.10–0.70 V/SCE. It was demonstrated that the indigenous micro-organisms were responsible for the current increase observed after a few days, up to 60 mA m)2. Adding 10 mM acetate to the compost amplified the current density to 145 mA m)2 at 0.50 V/SCE. The study suggests that many natural environments, other than marine sediments, waste waters and seawaters that have been predominantly investigated until now, may be able to produce electrochemically active biofilm

Fuzzy Image Segmentation using Suppressed Fuzzy C-Means Clustering

Clustering algorithms are highly dependent on the features used and the type of the objects in a particular image. By considering object similar surface variations (SSV) as well as the arbitrariness of the fuzzy c-means (FCM) algorithm for pixellocation, a fuzzy image segmentation considering object surface similarity (FSOS) algorithm was developed, but it was unable to segment objects having SSV satisfactorily. To improve the effectiveness of FSOS in segmenting objects with SSV, thispaper introduces a new fuzzy image segmentation using suppressed fuzzy c-means clustering (FSSC) algorithm, which directly considers object SSV and incorporates the use of suppressed-FCM (SFCM) using pixel location. The algorithmalso perceptually selects the threshold within the range of human visual perception. Both qualitative and quantitative resultsconfirm the improved segmentation performance of FSSC compared with other algorithms including FSOS, FCM,possibilistic c-means (PCM) and SFCM for many different images

Kerr-Schild Symmetries

We study continuous groups of generalized Kerr-Schild transformations and the vector fields that generate them in any n-dimensional manifold with a Lorentzian metric. We prove that all these vector fields can be intrinsically characterized and that they constitute a Lie algebra if the null deformation direction is fixed. The properties of these Lie algebras are briefly analyzed and we show that they are generically finite-dimensional but that they may have infinite dimension in some relevant situations. The most general vector fields of the above type are explicitly constructed for the following cases: any two-dimensional metric, the general spherically symmetric metric and deformation direction, and the flat metric with parallel or cylindrical deformation directions.Comment: 15 pages, no figures, LaTe

The "Unromantic Pictures" of Quantum Theory

I am concerned with two views of quantum mechanics that John S. Bell called ``unromantic'': spontaneous wave function collapse and Bohmian mechanics. I discuss some of their merits and report about recent progress concerning extensions to quantum field theory and relativity. In the last section, I speculate about an extension of Bohmian mechanics to quantum gravity.Comment: 37 pages LaTeX, no figures; written for special volume of J. Phys. A in honor of G.C. Ghirard

On a recent proposal of faster than light quantum communication

In a recent paper, A.Y. Shiekh has discussed an experimental set-up which, in his opinion, should make possible faster-than-light communication using the collapse of the quantum wave function. Contrary to the many proposals which have been presented in the past, he does not resort to an entangled state of two systems but he works with a single particle in a superposition of two states - corresponding to its propagation in opposite directions - one of which goes through an appropriate interferometer. The possibility for an observer near the interferometer to introduce or not, at his free will, a phase shifter along one of the paths should allow to change instantaneously the probability of finding the particle in the far-away region corresponding to the other state of the superposition and, correspondingly, to change the intensity of a beam of particles reaching a distant observer. In this paper we show a flaw in the argument: once more, as it has been proved in full generality a long time ago, the process of wave packet reduction cannot be used for superluminal communication.Comment: 9 pages, LaTeX. Minor changes mad

Shedding Light on Diatom Photonics by means of Digital Holography

Diatoms are among the dominant phytoplankters in the worl's ocean, and their external silica investments, resembling artificial photonics crystal, are expected to play an active role in light manipulation. Digital holography allowed studying the interaction with light of Coscinodiscus wailesii cell wall reconstructing the light confinement inside the cell cytoplasm, condition that is hardly accessible via standard microscopy. The full characterization of the propagated beam, in terms of quantitative phase and intensity, removed a long-standing ambiguity about the origin of the light. The data were discussed in the light of living cell behavior in response to their environment