A survey on sampling and probe methods for inverse problems

The goal of the review is to provide a state-of-the-art survey on sampling and probe methods for the solution of inverse problems. Further, a configuration approach to some of the problems will be presented. We study the concepts and analytical results for several recent sampling and probe methods. We will give an introduction to the basic idea behind each method using a simple model problem and then provide some general formulation in terms of particular configurations to study the range of the arguments which are used to set up the method. This provides a novel way to present the algorithms and the analytic arguments for their investigation in a variety of different settings. In detail we investigate the probe method (Ikehata), linear sampling method (Colton-Kirsch) and the factorization method (Kirsch), singular sources Method (Potthast), no response test (Luke-Potthast), range test (Kusiak, Potthast and Sylvester) and the enclosure method (Ikehata) for the solution of inverse acoustic and electromagnetic scattering problems. The main ideas, approaches and convergence results of the methods are presented. For each method, we provide a historical survey about applications to different situations.

A numerical study of the probe method

The goal of this work is the numerical realization of the probe method suggested by Ikehata for the detection of an obstacle D in inverse scattering. The main idea of the method is to use probes in the form of point source (., z) with source point z to define an indicator function (I) over cap (z) which can be reconstructed from Cauchy data or far. eld data. The indicator function boolean AND (I) over cap (z) can be shown to blow off when the source point z tends to the boundary aD, and this behavior can be used to find D. To study the feasibility of the probe method we will use two equivalent formulations of the indicator function. We will carry out the numerical realization of the functional and show reconstructions of a sound-soft obstacle.

Unification of the probe and singular sources methods for the inverse boundary value problem by the no-response test

In this article, we use the no-response test idea, introduced in Luke and Potthast (2003) and Potthast (Preprint) and the inverse obstacle problem, to identify the interface of the discontinuity of the coefficient gamma of the equation del (.) gamma(x)del + c(x) with piecewise regular gamma and bounded function c(x). We use infinitely many Cauchy data as measurement and give a reconstructive method to localize the interface. We will base this multiwave version of the no-response test on two different proofs. The first one contains a pointwise estimate as used by the singular sources method. The second one is built on an energy (or an integral) estimate which is the basis of the probe method. As a conclusion of this, the probe and the singular sources methods are equivalent regarding their convergence and the no-response test can be seen as a unified framework for these methods. As a further contribution, we provide a formula to reconstruct the values of the jump of gamma(x), x is an element of partial derivative D at the boundary. A second consequence of this formula is that the blow-up rate of the indicator functions of the probe and singular sources methods at the interface is given by the order of the singularity of the fundamental solution.

Eddy current testing system with scanning probe head having parallel and normal sensing coils

An eddy current testing system consists of a multi-sensor probe, a computer and a special expansion card and software for data-collection and analysis. The probe incorporates an excitation coil, and sensor coils; at least one sensor coil is a lateral current-normal coil and at least one is a current perturbation coil.

Eddy current testing program with scanning probe head having parallel and normal sensing coils

An eddy current testing system consists of a multi-sensor probe, computer and a special expansion card and software for data collection and analysis. The probe incorporates an excitation coil, and sensor coils; at least one sensor coil is a lateral current-normal coil and at least one is a current perturbation coil.

Redefinition of the kilogram, ampere, kelvin and mole: a proposed approach to implementing CIPM recommendation 1 (CI-2005)

The International System of Units (SI) is founded on seven base units, the metre, kilogram, second, ampere, kelvin, mole and candela corresponding to the seven base quantities of length, mass, time, electric current, thermodynamic temperature, amount of substance and luminous intensity. At its 94th meeting in October 2005, the International Committee for Weights and Measures (CIPM) adopted a recommendation on preparative steps towards redefining the kilogram, ampere, kelvin and mole so that these units are linked to exactly known values of fundamental constants. We propose here that these four base units should be given new definitions linking them to exactly defined values of the Planck constant h, elementary charge e, Boltzmann constant k and Avogadro constant NA, respectively. This would mean that six of the seven base units of the SI would be defined in terms of true invariants of nature. In addition, not only would these four fundamental constants have exactly defined values but also the uncertainties of many of the other fundamental constants of physics would be either eliminated or appreciably reduced. In this paper we present the background and discuss the merits of these proposed changes, and we also present possible wordings for the four new definitions. We also suggest a novel way to define the entire SI explicitly using such definitions without making any distinction between base units and derived units. We list a number of key points that should be addressed when the new definitions are adopted by the General Conference on Weights and Measures (CGPM), possibly by the 24th CGPM in 2011, and we discuss the implications of these changes for other aspects of metrology.

A family of promoter probe vectors incorporating autofluorescent and chromogenic reporter proteins for studying gene expression in Gram-negative bacteria

A series of promoter probe vectors for use in Gram-negative bacteria has been made in two broad-host-range vectors, pOT (pBBR replicon) and pJP2 (incP replicon). Reporter fusions can be made to gfpUV, gfprnut3.1, unstable gfpmut3.1 variants (LAA, LVA, AAV and ASV), gfp+, dsRed2, dsRedT3, dsRedT4, mRFP1, gusA or lacZ. The two vector families, pOT and pJP2, are compatible with one another and share the same polylinker for facile interchange of promoter regions. Vectors based on pJP2 have the advantage of being ultra-stable in the environment due to the presence of the parABCDE genes. As a confirmation of their usefulness, the dicarboxylic acid transport system promoter (dctA(p)) was cloned into a pOT (pRU1097)- and a pJP2 (pRU1156)-based vector and shown to be expressed by Rhizobium leguminosarum in infection threads of vetch. This indicates the presence of dicarboxylates at the earliest stages of nodule formation.

Modified rare earth semiconductor oxide as a new nucleotide probe

Recent rapid developments in biological analysis, medical diagnosis, pharmaceutical industry, and environmental control fuel the urgent need for recognition of particular DNA sequences from samples. Currently, DNA detection techniques use radiochemical, enzymatic, fluorescent, or electrochemiluminescent methods; however, these techniques require costly labeled DNA and highly skilled and cumbersome procedure, which prohibit any in-situ monitoring. Here, we report that hybridization of surface-immobilized single-stranded oligonucleotide on praseodymium oxide (evaluated as a biosensor surface for the first time) with complimentary strands in solution provokes a significant shift of electrical impedance curve. This shift is attributed to a change in electrical characteristics through modification of surface charge of the underlying modified praseodymium oxide upon hybridization with the complementary oligonucelotide strand. On the other hand, using a noncomplementary single strand in solution does not create an equivalent change in the impedance value. This result clearly suggests that a new and simple electrochemical technique based on the change in electrical properties of the modified praseodymium oxide semiconductor surface upon recognition and transduction of a biological event without using labeled species is revealed.

Insights into redox cycling of sulfur and iron in peatlands using high-resolution diffusive equilibrium thin film (DET) gel probe sampling

High spatial resolution vertical profiles of pore-water chemistry have been obtained for a peatland using diffusive equilibrium in thin films (DET) gel probes. Comparison of DET pore-water data with more traditional depth-specific sampling shows good agreement and the DET profiling method is less invasive and less likely to induce mixing of pore-waters. Chloride mass balances as water tables fell in the early summer indicate that evaporative concentration dominates and there is negligible lateral flow in the peat. Lack of lateral flow allows element budgets for the same site at different times to be compared. The high spatial resolution of sampling also enables gradients to be observed that permit calculations of vertical fluxes. Sulfate concentrations fall at two sites with net rates of 1.5 and 5.0nmol cm− 3 day− 1, likely due to a dominance of bacterial sulfate reduction, while a third site showed a net gain in sulfate due to oxidation of sulfur over the study period at an average rate of 3.4nmol cm− 3 day− 1. Behaviour of iron is closely coupled to that of sulfur; there is net removal of iron at the two sites where sulfate reduction dominates and addition of iron where oxidation dominates. The profiles demonstrate that, in addition to strong vertical redox related chemical changes, there is significant spatial heterogeneity. Whilst overall there is evidence for net reduction of sulfate within the peatland pore-waters, this can be reversed, at least temporarily, during periods of drought when sulfide oxidation with resulting acid production predominates.

Mechatronic design of a high frequency probe for haptic interaction

Current force feedback, haptic interface devices are generally limited to the display of low frequency, high amplitude spatial data. A typical device consists of a low impedance framework of one or more degrees-of-freedom (dof), allowing a user to explore a pre-defined workspace via an end effector such as a handle, thimble, probe or stylus. The movement of the device is then constrained using high gain positional feedback, thus reducing the apparent dof of the device and conveying the illusion of hard contact to the user. Such devices are, however, limited to a narrow bandwidth of frequencies, typically below 30Hz, and are not well suited to the display of surface properties, such as object texture. This paper details a device to augment an existing force feedback haptic display with a vibrotactile display, thus providing a means of conveying low amplitude, high frequency spatial information of object surface properties. 1. Haptics and Haptic Interfaces Haptics is the study of human touch and interaction with the external environment via touch. Information from the human sense of touch can be classified in to two categories, cutaneous and kinesthetic. Cutaneous information is provided via the mechanoreceptive nerve endings in the glabrous skin of the human hand. It is primarily a means of relaying information regarding small-scale details in the form of skin stretch, compression and vibration.

Evaluation of the environmental specificity of fluorescence in situ hybridization (FISH) using fluorescence-activated cell sorting (FACS) of probe (PSE1284)-positive cells extracted from rhizosphere soil

We explicitly tested for the first time the ‘environmental specificity’ of traditional 16S rRNAtargeted fluorescence in situ hybridization (FISH) through comparison of the bacterial diversity actually targeted in the environment with the diversity that should be exactly targeted (i.e. without mismatches) according to in silico analysis. To do this, we exploited advances in modern Flow Cytometry that enabled improved detection and therefore sorting of sub-micron-sized particles and used probe PSE1284 (designed to target Pseudomonads) applied to Lolium perenne rhizosphere soil as our test system. The 6-carboxyfluorescein (6-FAM)-PSE1284-hybridised population, defined as displaying enhanced green fluorescence in Flow Cytometry, represented 3.51±1.28% of the total detected population when corrected using a nonsense (NON-EUB338) probe control. Analysis of 16S rRNA gene libraries constructed from Fluorescence Activated Cell Sorted (FACS) -recovered fluorescent populations (n=3), revealed that 98.5% (Pseudomonas spp. comprised 68.7% and Burkholderia spp. 29.8%) of the total sorted population was specifically targeted as evidenced by the homology of the 16S rRNA sequences to the probe sequence. In silico evaluation of probe PSE1284 with the use of RDP-10 probeMatch justified the existence of Burkholderia spp. among the sorted cells. The lack of novelty in Pseudomonas spp. sequences uncovered was notable, probably reflecting the well-studied nature of this functionally important genus. To judge the diversity recorded within the FACS-sorted population, rarefaction and DGGE analysis were used to evaluate, respectively, the proportion of Pseudomonas diversity uncovered by the sequencing effort and the representativeness of the Nycodenz® method for the extraction of bacterial cells from soil.