Fundamental Study of the Fill-in Minimization Problem

In this paper the fill-in minimization problem which arises at the application of the sparse matrix method for a large sparse set of linear equations is discussed from the graph-theoretic viewpoint and also through the numerical experiments. Therefore, this investigation consists of two parts, and in the former part the author shows, at first, that the elimination process of a sparse matrix is equivalently replaced to the vertex eliminations for a graph obtained from the matrix, and by use of some concepts in the theory of graph he proves that the vertex elimination process for the minimum fill-in is equivalent to the vertex eliminations for vertices in each subgraph which is obtained by the appropriate dissection of whole graph, and that there are only two types of vertex eliminations through the process. This results in the proposal of a new model of the vertex elimination process. The latter part of this investigation is used for the verification of the results from the theoretic investigation. Through the numerical experiments he concludes that the new model of the vertex elimination process is valid, at least, for a graph like a regular finite element mesh. Furthermore, he shows that this model coincides with Nested Dissection Method which can give the minimum value of fill-in, at present

A caffeine-sensitive membrane electrode: Previous misleading report and present approach

Although a previous study [S.S.M. Hassan, M.A. Ahmed, M.M. Saoudi, Anal. Chem. 57 (1985) 1126] had shown that a caffeine-sensitive electrode made with picrylsulfonate and 1-octanol as a cation-exchanger and a solvent mediator, respectively, had a wide working pH range (5.5-9.5) and exhibited a Nernstian response, we could not find such response in this electrode. The present result was reasonable, because the pK, value of caffeinium ion was reported to be around 0.7 and the neutral form of caffeine was predominant in the pH range examined. Thus, we reinvestigated the response characteristics of a caffeine electrode, taking into consideration the pKa value, and constructed a new electrode with a combination of the lipophilic cation-exchanger, tetrakis[3,5-bis(2-methoxyhexafluoro-2-propyl)phenyl]borate (HFPB), and the solvent mediator with high degree of dielectric constant, 2-fluoro-2'-nitrodiphenyl ether (FNDPE). This electrode showed a pH-dependent response to caffeinium ion and gave a detection limit of 50 mu M with a slope of 55 mV per concentration decade at pH 2. The use of other solvent mediators was less effective than that of FNDPE. The electrode was applied for the determination of caffeine in some central stimulants

Human Models for Human-Robot Interaction

This paper discusses various human models required in human-robot interaction study. Good human models are critical for robots to realize effective interactions. For example, human behavior model is necessary to choose appropriate cost functions to determine robot actions that are comfortable for humans. We will present several case studies that attempt to model the human physiology and behavior, as well as their application to humanoid and character control

Weak value amplification in a shot-noise limited interferometer

We study the weak-value amplification (WVA) in a phase measurement with an optical interferometer in which shot noise limits the sensitivity. We compute the signal and the shot noise including the full-order interaction terms of the WVA, and show that the shot-noise contribution to a phase shift in a pointer variable is always larger than the final variance of the pointer variable. This yields difference in estimating noise level up to a factor of 1.5. To clarify an advantage for practical uses of the WVA, we discuss signal-to-noise ratio and its optimization in the presence of the shot noise.Comment: 6 pages, 4 figure