Early transition detection

Wavelets are very useful for applications that require local and multi-scale information. In this chapter an application of the discrete wavelet transform is discussed where these properties are used for online detection of transitions in time series. This method named Early Transition Detection is demonstrated on data from a chemical sensor array. 

In this chapter it will be demonstrated how wavelets can be used in data analysis by discussing a specific data set from a chemical sensor array. The data is a time series where each point in time belongs to a certain unknown class and needs to be classified. It will be discussed what problems arise when a common classifier like SIMCA [I] or Nearest Neighbour [2] is used. Further, it will be shown that an extended classifier named Early Transition Detection (ETD) [3] can be used to overcome these problems. For the construction of the ETD classifier the Discrete Wavelet Transform (DWT) is used. It will be shown that the DWT provides an expedient tool to solve this problem. 

Early Transition Detection is an extension of common static classification methods like SIMCA or Nearest Neighbour in order to enable these methods to process time-dependent data in some cases. ETD is useful e.g. for the... 

M. Marth, D. Maier, J. Honerkamp, M. Rupprecht and J. Goschnick, Early Transition Detection - a dynamic extension to common classification methods, Chemometrics and Intelligent Laboratory System 43 (1998), 123-133. 

The stereochemistry of the resulting cyclopropane product (.s vn vs anti) was rationalized from a kinetic study which implicated an early transition state with no detectable intermediates. Approach of the alkene substrate perpendicular to the proposed carbene intermediate occurs with the largest alkene substituent opposite the carbene ester group. This is followed by rotation of the alkene as the new C—C bonds begin to form. The steric effect of the alkene substituent determines... 

As intuitively deduced, coordinating Y and Z must be removed or displaced in order for alkenes to coordinate and form an alkene tr-complex (Scheme 2). Since these intermediates, Cp 2MR(alkene), have never been observed in any detectable amounts for early transition metal-mediated polymerization, several chelate model systems have been devised (Figure 3). 

Early optically detected microwave transition linewidth studies (Pratt and Broida, 1969) suggested that CN A2II(u = 10) —> B2E+(u = 0) collision-induced transitions through perturbed levels occur at gas-kinetic collision rates, faster than pure rotational relaxation. The pressure dependence of chemiluminescence in the Ba + N2O system also implied BaO b3II(u = 10) —> A1E+(u = 1) collisional transfer through spectroscopic doorways (Field, et al., 1974). 

The terminal hydride (1) is the most common type. In these species, the M-H distance is close to the sum of the Covalent Radii. Neutron diffraction gives this distance reliably, but X-ray methods, because they detect electron density and not the nuclear positions, underestimate the M-H distance by about 0.1 A. It is not uncommon for the H to escape detection entirely by X-ray methods as a result of the proximity of the metal, always a strong diffractor of X rays. Typical M-H distances are 1.45 to 1.6 A for first-row elements, 1.6 to 1.7 A for the second row, and 1.65 to 1.75 A for the third row actinides have M-H distances near 2 A. Early transition metals have M-H distances about 0.1A longer than do late metals. Electron diffraction methods have been used for volatile carbonyl hydrides such as HMn(CO)s, HCo(CO)4, and H2Fe(CO)4 for the Mn compound, the e-diffraction and n-diffraction Mn-H bond lengths are in good agreement. 

The present evidence on these points comes from published work (8)of Moodie, Schofield and their group at the University of Exeter. They have studied the nitration of pseudocumene and have shown that there is about a 9 1 selectivity of attack on positions 5 and 6 provided that one makes the reasonable assumption that any ipso-attack is not followed by rearrangement under the chosen conditions. Both positions are reactive enough to achieve the limiting rate and have similar steric requirements. This deduction rules out the explanation in terms of early transition states of the positionally oriented type and also precludes the possibility of detectable positionally oriented intermediates prior to the Wheland intermediates. It means that there must be a common intermediate prior to Wheland intermediate formation, but the extent of intramolecular selectivity is certainly not sufficient to make it necessary to postulate any attractive interaction in this intermediate. 

Moseley P, Williams DE (1989) Gas sensors based on oxides of early transition meteds. Polyhedron 8 1615-1618 Mosley PT, Norris J, Williams DE (eds) (1991) Techniques and mechanisms in gas sensing. Adam Hilger, New York Moulson AJ, Herbert JM (1990) Electroceramics materieils, properties, applications. Chapman and Hall, London Mukundan R, Brosha E, Brown D, Garzon F (1999) Ceria-electrolyte-based mixed potential sensors for the detection of hydrocarbons and carbon monoxide. Electrochem Soc Lett 2(8) 412-414 MuUa IS, Ramgir NS, Hwang YK, Chang J-S (2004) Semiconductor tin oxide gas sensors from bulk to thin films. J Ind Eng Chem 10(7) 1242-1256... 

Some other expectations of the nowadays practice is the development of analytical devices that are able to monitor in real time in vivo parameters. In this case electrochemical biosensors have played an important significant role in the transition towards point-of-care diagnostic devices. Such electrical devices are extremely useful for dehvering the diagnostic information in a fast, simple, and low-cost fashion in coimection with compact (handheld) analyzers. Such modem electrochemical bioaffinity, DNA, or immunosensors have been developed with remarkable sensitivity essential for early cancer detection. ... 

However, with the advent of lasers, the teclmique of laser-induced fluorescence (LIF) has probably become the single most popular means of detennining product-state distributions an early example is the work by Zare and co-workers on Ba + FLT (X= F, Cl, Br, I) reactions [25]. Here, a tunable laser excites an electronic transition of one of the products (the BaX product in this example), and the total fluorescence is detected as a... 

Caekelbergh et al. calculated the direct costs of HIV/AIDS in Belgium from the health care pay perspective. On the basis of 150 patients, they determined the costs of antiretrovirals, outpatient and inpatient resource use for the year 2005. They realize that the costs strongly depend on the CD4- - T-cell count, that is, the annual costs per patient are on average about US 2,900 for a patient with a CD4+ T-cell count >500, US 3,200 (CD4 351-500), US 8,650 (CD4 210-350), US 16,600 (CD4 101-200), US 31,300 (CD4 51-100), and US 49,400 (CD4 0-50), respectively. Consequently, the early detection of an HIV-infection as well as proper management that prohibits disease transition is of high cost-importance. 

Mossbauer spectroscopy is particularly suitable to study ST since (1) the spectral parameters associated with the HS and LS states of iron(II) clearly differ and (2) the time-scale of the technique ( 10 s) allows the detection of the separate spin states in the course of the transition. Typically, Mossbauer spectra of HS iron(II) show relatively high quadrupole splitting (AEq 2-3 mm s ) and isomer shift (3 1 mm s ), while for LS iron(II), these parameters are generally smaller (AEq < 1 mm s 3 < 0.5 mm s ). Among the early applications of Mossbauer spectroscopy to study ST phenomena in iron(II) complexes is the work of Dezsi et al. [7] on [Fe (phen)2(NCS)2] (phen = 1,10-phenanthroline) as a function of temperature (Fig. 8.2). The transition from the HS ( 12) state (quadrupole doublet of outer two lines with AEq 3 mm s ) to the LS CAi) state (quadrupole... 

During our early experiments on chemical gels, when first observing the intermediate state with the self-similar spectrum, Eq. 1-5, we simply called it viscoelastic transition . Then, numerous solvent extraction and swelling experiments on crosslinking samples showed that the viscoelastic transition marks the transition from a completely soluble state to an insoluble state. The sol-gel transition and the viscoelastic transition were found to be indistinguishable within the detection limit of our experiments. The most simple explanation for this observation was that both phenomena coincide, and that Eqs. 1-1 and 1-5 are indeed expressions of the LST. Modeling calculations of Winter and Cham-bon [6] also showed that Eq. 1-1 predicts an infinite viscosity (see Sect. 4) and a zero equilibrium modulus. This is consistent with what one would expect for a material at the gel point. 

---