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# Visualization of spatial and temporal temperature distributions with magnetic particle imaging for liver tumor ablation therapy

## Abstract

Temperature-resolved magnetic particle imaging (MPI) represents a promising tool for medical imaging applications. In this study an approach based on a single calibration measurement was applied for highlighting the potential of MPI for monitoring of temperatures during thermal ablation of liver tumors. For this purpose, liver tissue and liver tumor phantoms embedding different superparamagnetic iron oxide nanoparticles (SPION) were prepared, locally heated up to 70 °C and recorded with MPI. Optimal temperature MPI SPIONs and a corresponding linear model for temperature calculation were determined. The temporal and spatial temperature distributions were compared with infrared (IR) camera results yielding quantitative agreements with a mean absolute deviation of 1 °C despite mismatches in boundary areas.

## Introduction

Minimal invasive treatment of hepatic tumors based on thermal ablation has become an important alternative to traditionally applied therapies, e.g. chemo- or radiation therapy or surgical resection, especially if surgery is associated with higher risk of complications1. Guidance of the thermal ablation process is commonly performed with ultrasound (US), fluoroscopy, computed tomography (CT) or magnetic resonance imaging (MRI)2. Whereas US, fluoroscopy and CT provide fast localization of liver tumor and guidance of ablation devices with adequate image contrast, a real-time measurement of the tissue temperatures induced by the thermal ablation processes is clinically only facilitated by MRI. Such temperature controlled interventional guidance enables a direct control of the induced tissue temperature distribution by the operator and consequently improves the safety and success of the therapy3,4. However, the availability of open MRI systems – required for these interventional applications – is quite limited. Higher financial investments are required and a combination of high spatial and temporal resolution is hampered by lower field strength (1T-1.5 T) compared to closed scanners (>3.0 T). Therefore, alternative fast and temperature-resolved imaging techniques are of high interest – such as magnetic particle imaging (MPI) which is characterized by frame rates of up to 46 frames/s. In principle, MPI scanners can be designed as open bore or even floating table systems5 allowing proper access to the investigated object – in the distant future possibly a patient. One promising concept proposed a setup for an open bore FFL MPI scanner without the need for mechanical rotation, where a comparable large field of view (FOV) can be scanned in a sufficient time span, which is needed for clinical usage6.

Magnetic particle imaging (MPI) was initially presented to measure in vivo distributions of superparamagnetic iron oxide nanoparticles (SPION) in cardiovascular applications with high temporal and spatial resolution7. MPI has rapidly developed and several other possible clinical and preclinical applications were presented, for instance: It was shown that MPI allows for preclinical stem cell tracking8,9. In the field of Neuroimaging MPI proved to be able to assess the hemodynamics of intracranial aneurysms10 and detect ischemic stroke in a mouse model with high sensitivity and high temporal resolution11. It has been shown suitable to detect small gut bleedings12 and to image pulmonary perfusion in small animal models13. MPI might be a useful tool for guiding catheter interventions by multicolored imaging14 and steering of interventional instruments15. Since the used particles are finally taken up by different organs, especially the mononuclear phagocytic system of the liver, MPI enables a direct visualization of healthy liver tissue16,17. The missing accumulation of these SPION in primary liver tumors18, e.g. hepato- or cholangiocellular carcinoma (HCC, CCA) or metastases, results in an indirect tumor imaging. In particular, tumors are causing signal gaps or drops in the measured particle distribution depending on the tumor structure and spatial MPI resolution. For instance, a heterogeneous tumor in the range of the spatial resolution could be overseen with MPI due to the partial particle uptake. Therefore, a second modality, e.g. CT or MRI either separately to the MPI or in a hybrid system19,20, must be used as an anatomical reference for reliable tumor detection21.

The magnetization dynamics of SPION applied in MPI depend significantly on temperature, which can be utilized for precise temperature measurements22. In first in vitro experiments, it was demonstrated that MPI allows simultaneous imaging of both, particle concentration and particle temperature distribution. For data reconstruction the multi-color approach was utilized and a temperature measurement precision of ± 0.5 °C was estimated23. Furthermore, MPI was evaluated for predicting the therapeutic effect of magnetic hyperthermia utilizing iron oxide nanoparticles. In in vivo experiments a strong correlation was found between the magnetically induced temperature rise and the average MPI value of the particle “hot spot”24.

In this study, we investigate the principle capability of MPI to monitor spatial and temporal temperature distributions in thermal liver tumor ablation therapies. The main challenge of thermal tumor ablation represents the tradeoff between sufficient tumor heating – destroying cancer cells reliably – and tolerable heating of healthy adjacent tissue – ensuring liver functionality. In this context, MPI can be applied to image the temperature distribution of healthy liver tissue surrounding tumors. Thus, MPI will provide direct temperature feedback to ensure adequate heating safety margins. In the case of thermal HCC ablation, tissue heating of at least 50–55 °C for 4–6 minutes – causing irreversible cellular damage – is recommended including a 0.5–1 cm thick safety margin around the HCC2. Herewith, an adequate destruction of microscopic invasions inside the healthy tissue is ensured. During thermal ablation, changes of the measured MPI particle distribution can be directly attributed to temperature changes, since the hepatic SPION distribution can be considered quasi-constant after the intravenous SPION injection and hepatic uptake process. Thus, MPI data reconstruction could be performed with one calibration measurement (system matrix) minimizing the calibration effort, e.g., required for multi-color temperature MPI25. In order to evaluate the temperature imaging capabilities of MPI in general and of this application in particular, MPI results of locally heated liver and liver tumor phantoms are compared with optical temperature (OT) sensor and infrared (IR) camera measurements.

## Materials and Methods

### Liver tumor ablation phantoms

The liver phantoms consist of MPI-suitable SPION embedded in denatured protein. For this purpose, the SPION were gently mixed with dissolved dried egg powder purchased from Sigma Aldrich (St. Louis, MO, USA) and heated in a water bath (80 °C) for 15 minutes. These phantoms represent healthy liver tissue after the specific uptake of SPION with respect to the particle aggregation and mobility status16. Corresponding phantoms representing tumorous liver tissue (see Fig. 1) were prepared from SPION-free and SPION-loaded denatured protein. Here, SPION-free areas simulate the missing accumulation of contrast agents in tumors.

Three different iron oxide multi-core nanoparticles were tested for their temperature imaging capabilities, whose composition benefits a quick and efficient liver SPION loading. Ferucarbotran (Resovist, Bayer Pharma AG, Berlin, Germany) was specifically developed for liver MRI investigations and is consequently characterized by rapid clearance from blood stream and predominant liver macrophage uptake26. It was successfully utilized in in vivo liver MPI experiments; however, image resolution appears to be suboptimal comparing ferucarbotran with MPI optimized SPION. Perimag nanoparticles purchased from micromod Partikeltechnologie GmbH (Rostock, Germany) are stabilized with dextran and exhibit hydrodynamic diameters of around 130 nm. They were optimized for MPI resulting in superior signal spectra27 enabling various biomedical imaging applications, e.g. cell tracking17. L93 represents a batch of MPI-optimized nanoparticles synthesized by Gunnar Schuetz from Bayer Pharma AG (Berlin, Germany) with dextran stabilization and average hydrodynamic diameter of 66 nm.

### Temperature-dependent MPS

The temperature dependence of the MPI signal spectra of the different SPION embedded in denatured protein were evaluated with a temperature controllable magnetic particle spectrometer (MPS)28. The setup comprises a one-dimensional alternating magnetic field excitation with a field amplitude and frequency of 12 mT and 25 kHz, respectively, resembling the performed MPI scans. The simultaneously recorded signal spectra were analyzed for sample temperatures ranging from 20 °C to 80 °C.

### Temperature MPI and reference

Temperature MPI was first evaluated with 100 µL samples containing the different SPIONs embedded in denatured protein. After identifying the most suitable SPION for temperature imaging, especially with respect to temperature sensitivity, (non-)tumorous liver phantoms containing the optimal SPION were prepared and investigated. The scans were performed with a preclinical MPI system (Philips Medical Systems DMC GmbH, Hamburg, Germany/Bruker BioSpin GmbH, Ettlingen Germany). It utilizes the field free point (FFP) approach scanning the field of view along 3D Lissajous trajectories. To guarantee stable system operation with respect to signal disturbances and cover an adequate FoV in the size range of a murine liver lobe while achieving an adequate spatial resolution and good signal-to-noise ratio (SNR), drive field amplitude and gradient strength were set to 12 mT and 1 Tm−1 (x-, y-direction)/2 Tm−1 (z-direction), respectively. Whereas the resulting FoV with a size of 24 × 24 × 12 mm³ for x-, y- and z-direction can be directly calculated, the spatial resolution and SNR strongly depend on the applied iron oxide nanoparticle system.

As temperature reference, the fiber optic temperature sensor TS5 (Optocon AG, Dresden, Germany) with temperature resolution of 0.1 °C and absolute accuracy of ±1 °C was utilized. In addition, the infrared camera Testo 885 (Testo SE & Co. KGaA, Lenzkirch, Germany) with temperature resolution of 0.1 °C and absolute accuracy of ±2 °C was used as reference for temperature images. With the corresponding 11° × 9° IR telephoto lens an image resolution of approximately 0.5 mm could be realized for the average object-to-camera distance of 0.75 m. For measurements, the camera was installed directly in front of the scanner’s bore opening, thus, imaging phantom surface temperatures in the y-z-plane. IR measurements were started prior to MPI measurements, time between start of IR and MPI data acquisition was measured and IR images recorded prior to the MPI data acquisition were excluded. Image registration between both modalities was performed manually assisted by phantom geometries visible in the IR images. Especially, the apparent temperature differences between the phantom and the surrounding environment (scanner bore) as well as the known phantom geometries enabled a reliable registration.

Phantom heating was achieved by sticking a straight copper wire in the phantom and keeping it inside the phantom during the MPI scan. The copper wire (diameter: 1 mm; length: 80 mm) was heated by eddy currents induced by the magnetic drive field29. Thus, phantom heating was directly linked to the MPI image acquisition process. The maximum temperatures in close vicinity (<3 mm) to the copper wire measured with reference sensor TS5 amounted to more than 80 °C. These temperatures represented a thermal equilibrium between heat generation by eddy currents and phantom cooling by system ventilation. In the MPI images no eddy current related artifacts were observed. Whereas the eddy current heating effect was beneficial for this study, it represents a serious safety issue in other MPI applications, e.g. in cardiovascular imaging of stents29.

The temperature MPI procedure consisted of the following steps: 1. The phantom with the copper wire was placed in the scanner’s bore according to the center of the FoV. 2. The corresponding temperature reference was positioned and a settling of the phantom temperature to the ambient temperature in the bore of (19 ± 1)°C was ensured to guarantee the same start conditions. 3. The MPI scan was started resulting in simultaneous sample heating and image acquisition. The latter was delayed (typically 25 s) due to the drive field startup process. The MPI scan time was set to reach thermal equilibrium – characterized by a temperature rise smaller than 0.5 °C/min.

MPI data reconstruction was adopted from previous investigations dealing with liver MPI16,21 utilizing a calibration measurement S (system matrix) linking the distribution of the particle iron concentration c and the measurement vector û:

$$Sc=\mathop{u}\limits^{\frown {}}.$$
(1)

In practice, a self-developed software framework30 programmed in the high-level general-purpose dynamic programming language Julia31 utilizing Kaczmarz’s algorithm and Tikhonov regularization32 was applied. The basic reconstruction procedure is explained in more detail by Knopp et al.33. Reconstruction parameters were chosen with respect to image signal-to-noise ratio: Regularization factor λ = 1 ∙ 10–3, number of iterations I = 6, signal-to-noise threshold SNR = 3 and number of averaged frames N = 500. The reconstruction of a MPI scan was performed with one system matrix measured on a cubic sample (3 × 3 × 3 mm³) filled with the corresponding SPION immobilized in denatured chicken white protein with a particle iron concentration of 100, 51.1 and 42.5 mM for ferucarbotran (Resovist), perimag and L93, respectively. The sample temperature was given by the average ambient temperature in the scanner’s bore.

MPI temperature images TMPI,t reflecting the spatial and temporal temperature distribution in SPION-loaded denatured protein – independent of the particle concentration – were calculated as follows:

$${{\boldsymbol{T}}}_{{\bf{M}}{\bf{P}}{\bf{I}},{\bf{t}}}=({\boldsymbol{MP}}{{\boldsymbol{I}}}_{{\bf{r}}{\bf{e}}{\bf{l}},{\bf{t}}}-1)\cdot {m}^{-1}+{{\boldsymbol{T}}}_{{\bf{M}}{\bf{P}}{\bf{I}},0}.$$
(2)

here, MPIrel,t represents the element-wise division of the MPI particle concentration c of time frame t by the initial particle concentration c0 – representing the first time frame of the image acquisition process. The element-wise division was performed for each element of c0 with a value larger than 0.1∙c(Fe) of the prepared phantom to ensure reliable signal analysis. Otherwise the element of MPIrel,t was excluded. In the following sections, the elements of MPIrel,t are referred to as relative MPI signal. Since the real particle concentrations in the phantoms were constant, changes of the elements of MPIrel,t could be directly linked to temperature changes via one single particle-dependent temperature coefficient m. In practice, m was based on temperature MPI scans of the chosen SPION immobilized in denatured protein and corresponding linear regressions (see results section: Temperature coefficient analysis). In order to calculate absolute temperature images the initial temperature distribution TMPI,0 was taken from IR camera reference measurements.

## Results

### Temperature-dependent MPS

Samples with SPION embedded in denatured protein and volumes of 150 μL were prepared for the temperature-dependent MPS measurements. The particle iron concentrations c(Fe) amounted to 50 mM for perimag and L93 as well as 100 mM for ferucarbotran in order to gain a sufficient signal strength. The measurement results, shown in Fig. 2, indicated different temperature MPI performances between the investigated SPION. In detail, the particles’ signal strengths differed – represented by the decay of the harmonics magnitudes. For instance, the harmonics magnitudes of ferucarbotran were characterized by the fastest decay. They dropped below the noise level at around 400 kHz limiting the signal analysis at higher frequencies. In contrast, the harmonics magnitudes of perimag and L93 were usable up to 600 kHz, although the particle iron concentration was only half of the concentration of ferucarbotran. Furthermore, different temperature-dependencies of the particles’ harmonics magnitudes could be observed. The dependence was strongest for L93 followed by perimag. For ferucarbotran, differences between the curves recorded at varying temperatures were hardly visible. Thus, the measured harmonics were normalized to the corresponding harmonics curve recorded at 20 °C. The illustration of these results as a function of frequency (second row) and temperature (third row) clarified the previously described temperature dependence. For perimag and L93, a nearly linear relation between magnitude and temperature was found, which could be approximated as constant between 200 kHz and 600 kHz. This was a prerequisite for a concentration-independent calculation of MPI temperature distributions according to Eq. (2).

### Temperature dependence of MPI signal

In Fig. 3a, a sample containing 100 µL denatured protein with embedded perimag particles (c(Fe) = 51.1 mM) and stuck copper wire is shown. Two similar samples containing ferucarbotran and L93 were prepared additionally. The samples were positioned in the center of the FoV together with temperature reference TS5 according to Fig. 3b. The results of the MPI temperature scans were reconstructed excluding signal components below 80 kHz due to filter instabilities of the MPI scanner. For each SPION, Fig. 3c illustrates the temperature dependence of the relative MPI signal, namely the element of MPIrel,t with the highest value in c0 as a function of temperature measured with reference TS5. These results support the temperature-dependent MPS measurements: an approximately linear relationship between signal and temperature was found, which was highest for L93 followed by perimag and ferucarbotran.

### Temperature coefficient analysis

Comparing the three SPION types, the first experimental results indicated that L93 was most suitable for temperature MPI in terms of harmonics magnitudes and signal temperature dependence. Perimag and ferucarbotran possessed reduced temperature dependencies. In the case of ferucarbotran, the dependence even changed over the whole investigated frequency range. Thus, the following temperature MPI measurements were performed with phantoms based on L93.

To calculate TMPI,t, the SPION-specific temperature coefficient m had to be determined. In principle, it was directly given by the linear slope of the corresponding curve in Fig. 3. It was assumed that m is independent of particle iron concentration if scan parameters and particle immobilization are unchanged. To verify that m and, consequently, TMPI,t are independent, the L93 dataset from Fig. 3 was reconstructed for different SNR thresholds ranging from 3 to 18. The increase of this reconstruction parameter reduced the frequency components considered for reconstruction due to the decay of the frequency components’ magnitudes with frequency and, thus, reflected the dependence of m on the given particle iron concentration. In comparison: A reduced particle iron concentration would also result in a reduced number of frequency components considered for reconstruction. Figure 4 demonstrates, that the temperature dependence of the relative MPI signal noticeably varied with SNR if signal frequency components below 220 kHz were considered for reconstruction. In contrast, comparable dependencies for varying SNR were found if these frequency components were not utilized in the reconstruction by setting the lower frequency threshold to 220 kHz. Only for SNR = 18, a clearly different non-linear behavior was observed. In this case, only seven frequency components were considered for reconstruction representing intolerable signal strength for temperature MPI.

For determination of an average m, the MPI scan with the L93 sample was carried out three times. Each time five reconstructions were computed with a lower frequency threshold of 220 kHz and a SNR threshold of 3, 6, 9, 12 or 15. Linear regressions were performed for each single reconstruction result yielding an average m of 0.01186 K−1 with a standard deviation of 0.00062 K−1. The root mean square of the deviation between these results and the linear model is 0.00294 K−1 representing an acceptable uncertainty for temperature calculations.

In order to identify possible spatial dependences of m comparable measurements were carried out with the heated L93 sample positioned 5 mm away from the FoV center in the positive and negative y- and z-direction. These directions represent the image plane of the following MPI images, which can be monitored by the reference IR camera. The temperature induced MPI signal changes of all positions show reasonable linear dependencies, see Fig. 5 (left image). Comparing all results with the linear model (average m determined at the central position) a root mean square deviation of 0.0051 K1 can be found. Performing linear fits on the dataset of each position, a maximal reduction by 10% (y-direction) and 3% (z-direction) is identified in comparison to m determined at the central position, see Fig. 5 (right image). This is still in an acceptable range for the current investigation.

### MPI temperature images

In order to analyze MPI temperature images, a cuboid phantom was prepared (see Fig. 6a). The particle iron concentration of embedded L93 SPION amounts to 12.8 mM. The cuboid side lengths of approximately 22 × 10 × 5 mm3 were chosen to guarantee a full coverage of the phantom by the FoV. The heating copper wire was centrally stuck into the phantom (red dot). The corresponding layer of the MPI image in Fig. 6b – representing the absolute particle concentration c0 – clearly reflects the phantoms cuboid geometry.

The MPI temperature change of the element marked with a red dot is plotted as a function of time in Fig. 6c. Here, a fast temperature rise of more than 8 °C is found within the first 100 s. After more than 200 s, the signal stabilizes 10 °C above the start temperature due to thermal equilibrium between heat generation and cooling. The change of the spatial MPI temperature distribution is shown in Fig. 6d for different time points. In detail, the appearance and expansion of a central temperature hot spot inside the phantom can be observed. However, also negative temperature changes appear at the phantom’s edges in y-direction.

In Fig. 7a comparison of temperature MPI and IR camera results recorded on the L93 phantom from Fig. 6a is presented. In addition to images, line profiles are shown, which are marked in the images with black rectangles. The resolution of the original IR camera image was downsized to the MPI resolution to enable a representative image and line profile comparison. Whereas the relative MPI signal, as image and profile, showed a fair qualitative agreement with IR camera results, the MPI temperature image and the corresponding profiles yield good quantitative agreements. MPI data from two layers are presented for comparison. The top layer (MPI 1) is shown in the images. The bottom layer (MPI 2) represents the slice of the reconstructed MPI image stack directly below the top layer, thus, not visible for the IR camera. The resulting temperature deviations between IR camera and TMPI,t (line profiles) are illustrated in Fig. 7g with a maximum deviation of 3 °C at the phantom’s edges. TMPI,0 required for the calculation of TMPI,t was based on the IR camera image taken at the time of the first MPI frame. Since MPI data acquisition was delayed with respect to drive field start up (around 25 s), TMPI,0 does not represent the starting point of the heating process, which is characterized by a homogenous temperature distribution.

A test of the presented temperature MPI approach to locate heating throughout the whole phantom and FoV can be found in Fig. 8 illustrating a comparison similar to Fig. 7, but with a copper wire stuck laterally into the phantom. The temperature hot spot – either on the right or left side – is located correctly in the MPI temperature images. A quantitative comparison of line profiles – taken from the IR camera image and two layers of the MPI temperature image stack – shows an acceptable agreement between MPI and IR results. In this case, the temperature deviations of the line profiles amount to maximal 4.5 °C, again for temperatures located at the edges of the phantom. This experiment indicates - in agreement with our initial investigations – that the temperature coefficient m that we determined in the center has no strong spatial dependence.

The principle feasibility of MPI to monitor the temperature of healthy liver tissue surrounding tumors during thermal ablation therapies was evaluated with the phantom shown in Fig. 9a. The size of the denatured protein structure with embedded L93 (c(Fe) = 12.8 mM) is comparable to the previous phantoms. Inside the structure two SPION-free protein areas (white spots) can be found, representing two liver tumors with different sizes. At least the larger SPION-free liver tumor caused a clearly visible gap in the corresponding layer of the reconstructed MPI image, as demonstrated in Fig. 9b. This reflects MPI images recorded in small animal investigations10,20. A MPI scan without heating any tumor showed slight temperature changes in MPI and IR reference images (Fig. 9c,d). A separate and parallel heating of the tumors resulted in expected positive temperature changes around the tumors of up to 15 °C, which are in qualitative agreement with IR reference images (Fig. 9e–j). However, the exact temperature distribution of the MPI images differs from the expected results; for instance, some voxels show a significantly reduced temperature rise or even cooling.

## Discussion

The relative MPI signals of all investigated SPIONs showed an approximately linear relationship to temperature in the performed MPI scans, stated as positively temperature-dependent. This is partly contrary to previous investigations, for instance34, found a positive dependence for perimag and a negative one for ferucarbotran (Resovist). However, only one signal frequency component of liquid SPION suspensions was analyzed hampering a direct comparison of results, especially, when considering the frequency dependence of the temperature influence in the MPS results (Fig. 3). In general, the exact SPION structure and environment have a strong impact on the temperature dependence in MPI applications. In our case, the SPION immobilization with denatured protein blockades a free SPION rotation (Brownian relaxation process). Thus, the observed positive temperature dependence is dominated by the temperature dependence of the internal rotation of the SPIONs magnetization due to alternating magnetic fields (Néel relaxation process). This is in agreement with temperature-dependent MPS measurements comparing mobile (Brown) and immobile (Néel) SPION samples28. The relationship between SPIONs static magnetization and temperature is theoretically characterized by a negative dependence22 and, consequently, less relevant in our case.

The measured MPI temperature images agreed well with IR camera results. Induced hot spots were correctly located throughout the phantom and a mean absolute deviation of 1 °C was found in the performed comparisons shown in Figs. 7,8. Since IR cameras measure surface temperatures, MPI results from two different layers are shown. Here, no significant differences with respect to deviations between MPI and IR results could be seen. This indicates that a possible depth dependence of temperature is at least for these comparisons negligible.

The investigated temperature MPI approach benefits from a reduced calibration effort. An exact and constant sample temperature regulation for system matrix acquisition at different temperatures was not required enabling easier and quicker calibrations. However, most notably in the boundary areas of the particle distribution, MPI temperature images yielded less accuracy and even measured negative temperature changes. This apparent phantom cooling is physically not plausible, could not be identified with IR camera measurements and cannot be explained by the slight spatial dependence of m. In fact, it represents the main limitation of this MPI temperature imaging approach based on only one system matrix. We see two reasons for this. First of all, the regularized image reconstruction leads to non-local changes in the calculated particle concentration. In particular, if there is mismatch between the state of the particles in the system matrix and the actual measurements, we expect a non-zero residual. During image reconstruction the residual is minimized, which can lead to non-local artifacts. Consequently, a mismatch in the temperature in a specific location might lead to an artifact in another location. This issue will be partly addressed by the regularization but non-local artifacts will still appear for high temperature changes. Second, these negative temperature estimations primarily appear at the boundaries of the particle distribution where the MPI signal is already low. Consequently, these values are prone to a larger relative error which could increase the cooling. One way to handle the non-zero residual issue could be the usage of multi-color temperature MPI, which would use two or more system matrices at different temperatures and in turn allows integrating the temperature estimation directly into the reconstruction process in contrast to the pixel-wise post-processing strategy that we applied in this work.

In the case, that an optimized reconstruction strategy would solve the previously described limitation and to highlight the principle potential of magnetic nanoparticles as temperature probes in imaging, an uncertainty estimation is presented: Assuming MPI temperature monitoring of SPION-loaded tissue heated from a body temperature of 37 °C to 50 °C, following single uncertainties are considered for an exemplary estimation of the overall uncertainty of TMPI,t according to Eq. (2). The uncertainty of m from the temperature coefficient analysis is 0.00294 K-1. The uncertainties of the MPI images recorded at 37 °C and 50 °C, required for the calculation of MPIrel,t, are estimated at 0.4% of the MPI particle concentration of the corresponding image element. These values are based on the relative standard deviation of one central MPI image element taken from a 40 times repeated MPI scan of the L93 phantom from Fig. 6 without stuck copper wire. The uncertainty of the initial tissue temperature distribution TMPI,0 is expected to be around 1 °C, when assessing the core body temperature with a medical thermometer. Finally, propagation of error – applying linearization of Eq. (2) with first-order Taylor series expansion – yields a maximum uncertainty of 5 °C for a central MPI temperature image element. This result represents a fair accuracy for absolute temperature images, for instance, IR camera Testo 885 possesses an accuracy of ±2 °C. The sensitivity of MPI temperature images – characterizing the method’s capability to detect temperature changes – amounts to 0.8 °C for the described example. This result coincides with the signal variation identified in Fig. 6c.

The MPI voxel size of 3 × 3 × 3 mm3 represents a limitation for a murine liver, however, for a human thermal ablation therapy an adequate resolution. In fact, the limited FoV has to be enlarged for human applications. Upscaling MPI for human dimensions is possible in principle35,36 but a human sized scanner cannot be expected in the near future. Fortunately, the thermal response time of SPION to local temperature changes is faster than the utilized MPI scanner’s repetition time of approximately 21.54 ms and much faster than heat transfer in tissue37. Assuming an upscaled version of our scanner, half the gradient strength would still be sufficient for a 3 × 3 × 3 mm³ voxel size. Using the focus-field approach38, a scan of a 0.25 L volume per second with our preclinical system would be possible, still meeting clinical needs. Phantom heating induced by eddy currents seems not appropriate for clinical applications, since heating control is directly linked to temperature image acquisition possibly causing inadvertent tissue damage. In addition, tumor temperatures of even more than 100 °C can be found in thermal ablation therapies, which could hardly be realized with the copper wire approach. Thus, laser induced heating with optical fibers represents a proper solution. The application of radiofrequency or microwave ablation devices is likely hampered by electromagnetic interferences caused by the MPI field.

## Conclusion

The potential of MPI to monitor the temporal and spatial temperature distribution during thermal ablation of liver tumors was analyzed. The prepared phantoms based on denatured protein with embedded SPION were heated up to 70 °C yielding relative linear and positive temperature dependencies. For the optimal SPION, L93, a linear model was constructed to calculate MPI temperature images. Comparisons with simultaneously recorded IR camera measurements present good quantitative agreements with a mean absolute deviation of 1 °C. However, invalid phantom cooling is partly found most notably in the boundary areas of the particle distribution. This effect is most likely explained by non-local reconstruction artifacts and represents a limitation of the practical realization of this MPI temperature imaging approach. Nevertheless, the principle feasibility of MPI-guided liver tumor ablation could be demonstrated and the identified SPION temperature sensitivity resulted in acceptable uncertainties.

## Data availability

Most of the data generated or analyzed during this study are included in this published article, all source datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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## Acknowledgements

The authors acknowledge financial support by the Deutsche Forschungsgemeinschaft (DFG) within the collaborative research center (SFB) 841 and priority program (SPP) 1681 (LU800/4–3 and VI892/1–1), the DFG grant (KN 1108/2–1) and the grant (05M16GKA) of the Bundesministerium für Bildung und Forschung (BMBF).

## Author information

Authors

### Contributions

J.S. Performing experiments, data analysis, writing the manuscript. J.D. Preparing figures, performing the experiments, statistical analysis, writing the manuscript. M.G.K. Programming and providing software for data analysis and analyzed data. C.J. Performing experiments. G.A. Providing MPI- and MRI scanner facility and medical background. T.K. Programming, providing software and knowledge for image reconstruction and image analysis. M.M. Image reconstruction, image analysis. S.D. and F.L. Performing the experiments at TU Braunschweig, data analysis, preparing figures. H.I. Study design, study supervision and resource management, initial idea, writing the manuscript. All authors reviewed the manuscript.

### Corresponding author

Correspondence to J. Salamon.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Rights and permissions

Reprints and Permissions

Salamon, J., Dieckhoff, J., Kaul, M.G. et al. Visualization of spatial and temporal temperature distributions with magnetic particle imaging for liver tumor ablation therapy. Sci Rep 10, 7480 (2020). https://doi.org/10.1038/s41598-020-64280-1

• Accepted:

• Published:

• DOI: https://doi.org/10.1038/s41598-020-64280-1

• ### Ex vivo magnetic particle imaging of vascular inflammation in abdominal aortic aneurysm in a murine model

• Dilyana B. Mangarova
• Julia Brangsch
• Marcus R. Makowski

Scientific Reports (2020)


text:
# C. Sean Burns: Notebook

### Site Tools

 blog:reading-robert-k-merton-matthew-effect [2017/03/07 08:48]seanburns created blog:reading-robert-k-merton-matthew-effect [2017/03/07 08:54]seanburns 2019/06/04 09:44 seanburns 2017/03/07 08:54 seanburns 2017/03/07 08:48 seanburns created 2019/06/04 09:44 seanburns 2017/03/07 08:54 seanburns 2017/03/07 08:48 seanburns created Last revision Both sides next revision Line 3: Line 3: **date: 2013-10-23 13:14** **date: 2013-10-23 13:14** - Some notes on reading "The Matthew Effect in Science" in [The + Some notes on reading "The Matthew Effect in Science" in //The Sociology of Science: Theoretical and Empirical Investigations// ((http://www.worldcat.org/oclc/817893417)) by Robert K. Merton. - Sociology of Science: Theoretical and Empirical + - Investigations](http://www.worldcat.org/oclc/817893417) by Robert + - K. Merton. + **Note:** Recognition: **Note:** Recognition: - > Some time ago it was noted that graded awards in the realm of + > Some time ago it was noted that graded awards in the realm of science are distributed principally in the coin of recognition accorded by fellow scientists (p. 439). - > science are distributed principally in the coin of recognition + - > accorded by fellow scientists (p. 439). + Two key points: Two key points: - - the award is recognition + - the award is recognition - - the award is *given by* "fellow scientists" + - the award is //given by// "fellow scientists" - The obvious question is whether recognition that is awarded by + The obvious question is whether recognition that is awarded by those outside the institution of science is worth more or less. - those outside the institution of science is worth more or less. + - **Note:** "The 41st chair" (pp. 440-441). Those who have made + **Note:** "The 41st chair" (pp. 440-441). Those who have made highly significant scientific contributions but who will never receive the highest honors. - highly significant scientific contributions but who will never + - receive the highest honors. + - > History serves as an appellate court, ready to reverse the + > History serves as an appellate court, ready to reverse the judgments of the lower courts, which are limited by the myopia of contemporaneity. But in greater part, the phenomenon of the forty-first chair is an artifact of having a fixed number of places available at the summit of recognition. Moreover, when a particular generation is rich in achievements of a high order, it follows from the rule of fixed numbers that some whose accomplishments rank as high as those actually given the award will be excluded from the honorific rank (p. 441). - > judgments of the lower courts, which are limited by the myopia + - > of contemporaneity. But in greater part, the phenomenon of the + - > forty-first chair is an artifact of having a fixed number of + - > places available at the summit of recognition. Moreover, when a + - > particular generation is rich in achievements of a high order, + - > it follows from the rule of fixed numbers that some whose + - > accomplishments rank as high as those actually given the award + - > will be excluded from the honorific rank (p. 441). + All the participants in this system are aware of the 41st chair. All the participants in this system are aware of the 41st chair. Line 40: Line 24: **Note:** The never ending pursuit, the *way station*: **Note:** The never ending pursuit, the *way station*: - > What appears from below to be the summit becomes, in the + > What appears from below to be the summit becomes, in the experience of those who have reached it, only another way station. The scientist's peers and other associates regard each of his scientific achievements as only the prelude to new and greater achievements. Such social pressures do not often permit those those who have climbed the rugged mountains of scientific achievement to remain constant (p. 442). - > experience of those who have reached it, only another way + - > station. The scientist's peers and other associates regard each + - > of his scientific achievements as only the prelude to new and + - > greater achievements. Such social pressures do not often permit + - > those those who have climbed the rugged mountains of scientific + - > achievement to remain constant (p. 442). + - Are those scientists who are highlighted by social media, and by + Are those scientists who are highlighted by social media, and by non-scientists, feel the same pressure? Do they feel that greater expectations are placed on this, because of this medium? - non-scientists, feel the same pressure? Do they feel that greater + - expectations are placed on this, because of this medium? + **Note:** Class structure and the reward system: **Note:** Class structure and the reward system: - > Without deliberate intent on the part of any group, the reward + > Without deliberate intent on the part of any group, the reward system thus influences the "class structure" of science by providing a stratified distribution of chances, among scientists, for enlarging their role as investigators (p. 443). - > system thus influences the "class structure" of science by + - > providing a stratified distribution of chances, among + - > scientists, for enlarging their role as investigators (p. 443). + And: And: - > There is thus a continuing interplay between the status system, + > There is thus a continuing interplay between the status system, based on honor and esteem, and the class system, based on differential life-chances, which locates scientists in differing positions within the opportunity structure of science (p. 443). - > based on honor and esteem, and the class system, based on + - > differential life-chances, which locates scientists in differing + - > positions within the opportunity structure of science (p. 443). + Does social media influence a class structure too? Does social media influence a class structure too? - **Note:** The retroactive judgment implies that earlier work can + **Note:** The retroactive judgment implies that earlier work can function as an investment for a future payoff. Even though the payoff at the time may be null or a cost. - function as an investment for a future payoff. Even though the + - payoff at the time may be null or a cost. + See (short quoting now, see text for full marked passages): See (short quoting now, see text for full marked passages): Line 86: Line 54: **Note:** In sum: **Note:** In sum: - > the Matthew effect consists of the accruing of greater + > the Matthew effect consists of the accruing of greater increments of recognition ... (p. 446). - > increments of recognition ... (p. 446). + **Note:** The "Eccliesiasticus components" (p. 447). **Note:** The "Eccliesiasticus components" (p. 447). - > But it has other implications for the development of science, + > But it has other implications for the development of science, and we must shift our angle of theoretical vision in order to identify them (p. 447). - > and we must shift our angle of theoretical vision in order to + - > identify them (p. 447). + **Note:** Science and scholarly communication: **Note:** Science and scholarly communication: - > the standpoint of science conceived of as a system of + > the standpoint of science conceived of as a system of communication (p. 447). - > communication (p. 447). + - **Note:** *am* it seems to me, doesn't really change the system. + **Note:** //am// it seems to me, doesn't really change the system. It only seems to augment and strengthen it. In this sense, it does not seem so revolutionary. - It only seems to augment and strengthen it. In this sense, it does + - not seem so revolutionary. + - --- + ---- **Note:** Proceeds to discuss science as the communication of science. **Note:** Proceeds to discuss science as the communication of science. - > But it $Matthew effect$ has other implications for the + > But it [Matthew effect] has other implications for the development of science, and we must shift our angle of theoretical vision in order to identify them (p. 447) - > development of science, and we must shift our angle of + - > theoretical vision in order to identify them (p. 447) + - --- + ---- - **Note:** There's no science w/o the communication of science. The + **Note:** There's no science w/o the communication of science. The reporting of science is the scientific enterprise. - reporting of science is the scientific enterprise. + - > from the standpoint of science conceived of as a system of + > from the standpoint of science conceived of as a system of communication (p. 447). - > communication (p. 447). + **Note:** More of a side note about scholars' reading habits: **Note:** More of a side note about scholars' reading habits: - > It has been found, for example, that only about half of 1 + > It has been found, for example, that only about half of 1 percent of the articles published in journals of chemistry are read by any other one chemist (p. 448). - > percent of the articles published in journals of chemistry are + - > read by any other one chemist (p. 448). + And, for those that read: And, for those that read: - > The American Psychological Association study found that from 15 + > The American Psychological Association study found that from 15 to 23 percent of the psychologist-readers' behaviors in selecting articles were based on the identity of the authors (p. 449). - > to 23 percent of the psychologist-readers' behaviors in + - > selecting articles were based on the identity of the authors (p. + - > 449). + - See footnote 24 on p. 449 for reference to the Coles' study. + See footnote 24 on p. 449 for reference to the Coles' study. Here's the reference, from footnote 23: - Here's the reference, from footnote 23: + - > 23\. S. Cole and J. R. Cole, "Visibility and the Structural + > 23. S. Cole and J. R. Cole, "Visibility and the Structural Bases of Observability in Science," a paper presented before the American Sociological Association, August 1967, and developed further in their *Social Stratification in Science* (p. 448). - > Bases of Observability in Science," a paper presented before the + - > American Sociological Association, August 1967, and developed + - > further in their *Social Stratification in Science* (p. 448). + - **Note:** This is the *genius* of some researchers / scientists + **Note:** This is the *genius* of some researchers/scientists who use social media effectively. Whether their research is original, scientific, rigorous, or etc. hardly matters. Rather, it's their ability and determination to aggressively communicate their messages that has been the cornerstone of their achievement. - who use social media effectively. Whether their research is + - original, scientific, rigorous, or etc. hardly matters. Rather, + - it's their ability and determination to aggressively communicate + - their messages that has been the cornerstone of their achievement. + - The question is whether the content of their message has been + The question is whether the content of their message has been "socially validated." The use of social media by researchers whose research has not been socially validated can highlight an ability - "socially validated." The use of social media by researchers whose + that ends up abusing and causing harm to the institution of science. It is the communication of valid science that needs to be aggressive. - research has not been socially validated can highlight an ability + - that ends up abusing and causing harm to the institution of + - science. It is the communication of valid science that needs to be + - aggressive. + - All this highlights those odd cases where a junior researcher's + All this highlights those odd cases where a junior researcher's esteem becomes greater than the senior researcher's, even before the research has been socially validated. - esteem becomes greater than the senior researcher's, even before + - the research has been socially validated. + - > But, for science to be advanced, it is not enough that fruitful + > But, for science to be advanced, it is not enough that fruitful ideas be originated or new experiments developed or new problems formulated or new methods instituted. The innovations must be effectively communicated to others. That, after all, is what we mean by a *contribution* to science--something given to the common fund of knowledge. In the end, then, science is a socially shared and socially validated body of knowledge. For the development of science, only work work that is effectively perceived and utilized by other scientists, then and there, matters (p. 450). - > ideas be originated or new experiments developed or new problems + - > formulated or new methods instituted. The innovations must be + - > effectively communicated to others. That, after all, is what we + - > mean by a *contribution* to science--something given to the + - > common fund of knowledge. In the end, then, science is a + - > socially shared and socially validated body of knowledge. For + - > the development of science, only work work that is effectively + - > perceived and utilized by other scientists, then and there, + - > matters (p. 450). + Then, in the next paragraph: Then, in the next paragraph: - > Looking at the Matthew effect from this perspective, we have + > Looking at the Matthew effect from this perspective, we have noted the distinct possibility that contributions made by scientists of considerable standing are the most likely to enter promptly and widely into the communication networks of science, and so to accelerate its development (p. 450). - > noted the distinct possibility that contributions made by + - > scientists of considerable standing are the most likely to enter + - > promptly and widely into the communication networks of science, + - > and so to accelerate its development (p. 450). + - Junior researchers, by effective use of social media, are then + Junior researchers, by effective use of social media, are then capable of **bootstrapping** their standing w/o at first really contributing knowledge. At least, that's the possibility. - capable of **bootstrapping** their standing w/o at first really + - contributing knowledge. At least, that's the possibility. + **Note:** The focalizing effect: **Note:** The focalizing effect: - > It required a Freud, for instance, to focus the attention of + > It required a Freud, for instance, to focus the attention of many psychologists upon a wide array of ideas which, as has been shown elsewhere (see footnote 29), had in large part also been hit upon by various other scientists. Such focalizing may turn out to be a distinctive function of eminent men and women of science (p. 452). - > many psychologists upon a wide array of ideas which, as has been + - > shown elsewhere (see footnote 29), had in large part also been + - > hit upon by various other scientists. Such focalizing may turn + - > out to be a distinctive function of eminent men and women of + - > science (p. 452). + More: More: - > It is no so much that these great men of science pass on their + > It is no so much that these great men of science pass on their techniques, methods, information, and theory to novices working with them. More consequently, they convey to their associates the norms and values that govern significant research. Often in their later years, or after their death, this personal influence becomes routinized, in the fashion described by Max Weber for other fields of human activity. Charisma becomes institutionalized, in the forms of schools of thought and research establishments (pp. 452-453) - > techniques, methods, information, and theory to novices working + - > with them. More consequently, they convey to their associates + - > the norms and values that govern significant research. Often in + - > their later years, or after their death, this personal influence + - > becomes routinized, in the fashion described by Max Weber for + - > other fields of human activity. Charisma becomes + - > institutionalized, in the forms of schools of thought and + - > research establishments (pp. 452-453) + And: And: - > the importance of problem-*finding*, not only problem-solving. + > the importance of problem-//finding//, not only problem-solving. - Sometimes these norms and values are based not on significant + Sometimes these norms and values are based not on significant research but on the **bootstrapping** ability to get one's self into the proper arena in a very substantial way. - research but on the **bootstrapping** ability to get one's self + - into the proper arena in a very substantial way. + - But, the above in more detail, as it pertains to the *aesthetics* + But, the above in more detail, as it pertains to the //aesthetics// of the scientific institution: - of the scientific institution: + - > The role of outstanding scientists in influencing younger + > The role of outstanding scientists in influencing younger associates is repeatedly emphasized in the interviews with laureates. Almost invariably they lay great emphasis on the importance of problem-*finding*, not only problem-solving. They uniformly express the strong conviction that what matters most in their work is a developing sense of taste, of judgment, in seizing upon problems that are of fundamental importance (p. 453). - > associates is repeatedly emphasized in the interviews with + - > laureates. Almost invariably they lay great emphasis on the + - > importance of problem-*finding*, not only problem-solving. They + - > uniformly express the strong conviction that what matters most + - > in their work is a developing sense of taste, of judgment, in + - > seizing upon problems that are of fundamental importance (p. + - > 453). + - And this is the *aesthetics of science*. See the line, middle of + And this is the //aesthetics of science//. See the line, middle of paragraph, about the "expansion of taste" as well as "attitude." - paragraph, about the "expansion of taste" as well as "attitude." + - But the aesthetic of problem-finding is intertwined with the + But the aesthetic of problem-finding is intertwined with the basic, hard-work of doing science. Social media's affordances lets someone **bootstrap** past the hard-work, at least hypothetically. It deflates the aesthetic. The recent no-named movement represents a postmodern aesthetic based on a topsy-turvy lack of hard scientific work and lots of rhetoric. This is post-science, if not - basic, hard-work of doing science. Social media's affordances lets + - someone **bootstrap** past the hard-work, at least hypothetically. + - It deflates the aesthetic. The recent no-named movement represents + - a post-modern aesthetic base on a topsy-turvy lack of hard + - scientific work and lots of rhetoric. This is post-science, if not + just post-modern. just post-modern. And: And: - > Certain aspects of their character also play a part. With few + > Certain aspects of their character also play a part. With few exceptions, these are men of exceptional ego strength (p. 453). - > exceptions, these are men of exceptional ego strength (p. 453). + And: And: - > Their self-assurance finds varied expression within the context + > Their self-assurance finds varied expression within the context of science as a social institution. That institution, as we know, includes a norm calling for autonomous and critical judgment about one's own work of others (p. 453). - > of science as a social institution. That institution, as we + - > know, includes a norm calling for autonomous and critical + - > judgment about one's own work of others (p. 453). + And: And: - > They exhibit a great capacity to tolerate frustration in their + > They exhibit a great capacity to tolerate frustration in their work, absorbing repeated failures without manifest psychological damage (p. 453). - > work, absorbing repeated failures without manifest psychological + - > damage (p. 453). + - **Note:** Then the entire middle paragraph on page 455. Specially + **Note:** Then the entire middle paragraph on page 455. Specially this part: - this part: + - > Outstanding scientists tend to develop an immunity to *insanabile + > Outstanding scientists tend to develop an immunity to //insanabile scribendi cacoēthes// (the itch to publish) (p. 455). - > scribendi cacoēthes* (the itch to publish) (p. 455). + - And the next sentence, which I separate just to emphasize the + And the next sentence, which I separate just to emphasize the notion of //merely extensive//: - notion of *merely extensive*: + - > Since they prefer their published work to be significant and + > Since they prefer their published work to be significant and fruitful rather than **merely extensive**, their contributions are apt to matter [emphasis added] (p. 455). - > fruitful rather than **merely extensive**, their contributions + - > are apt to matter $emphasis added$ (p. 455). + - **Note:** Whether this is still true; that is, whether effective + **Note:** Whether this is still true; that is, whether effective social media campaigns can *bootstrap* the Matthew effect: - social media campaigns can *bootstrap* the Matthew effect: + - > After all, scientists do not begin by being eminent..." (p. + > After all, scientists do not begin by being eminent..." (p. 456). - > 456). + - **Note:** On the bias towards eminence and violating the norm of + **Note:** On the bias towards eminence and violating the norm of universalism: - universalism: + - > When the Matthew effect is thus transformed into an idol of + > When the Matthew effect is thus transformed into an idol of authority, it violates the norm of universalism embodied in the institution of science and curbs the advancement of knowledge (p. 457). - > authority, it violates the norm of universalism embodied in the + - > institution of science and curbs the advancement of knowledge + - > (p. 457). + - **Note:** It's not just that the richer get richer, Merton points + **Note:** It's not just that the richer get richer, Merton points out, it's also that the poor get poorer. There is a finite amount of scholarly wealth or currency, so to speak. - out, it's also that the poor get poorer. There is a finite amount + - of scholarly wealth or currency, so to speak. + - > This is expressed in the principle of cumulative advantage that + > This is expressed in the principle of cumulative advantage that operates in many systems of social stratification to produce the same result: the rich get richer at a rate that makes the poor become relatively poorer (p. 457). - > operates in many systems of social stratification to produce the + - > same result: the rich get richer at a rate that makes the poor + - > become relatively poorer (p. 457). + - Thus, real world problems for certain institutions to climb to the + Thus, real world problems for certain institutions to climb to the top (unless they can //bootstrap// themselves, perhaps): - top (unless they can *bootstrap* themselves, perhaps): + - > These social processes of social selection that deepen the + > These social processes of social selection that deepen the concentration of top scientific talent create extreme difficulties for any efforts to counteract the institutional consequences of the Matthew principle in order to produce new centers of scientific excellence (p. 458). - > concentration of top scientific talent create extreme + - > difficulties for any efforts to counteract the institutional + - > consequences of the Matthew principle in order to produce new + - > centers of scientific excellence (p. 458). + * categories: * categories:

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## LaTeX forum ⇒ Texmaker and TeXstudio ⇒ TexMaker / Miktex : problem with the package mychemistry Topic is solved

Information and discussion about Texmaker, an integrated LaTeX environment for several platforms, and the related TeXstudio
jobic2005
Posts: 5
Joined: Tue Oct 02, 2012 2:16 pm

### TexMaker / Miktex : problem with the package mychemistry

Hi,
I use TexMaker Editor with the MikTex distribution (OS Windows XP)
I want to write document dealing with chemistry for my course (Newman Molecular Representation).
In that way, I want to use Mychemistry and chemmacros packages.
To practise these packages, I have copied the following code in TexMaker (attached document test.tex) : I found this code at the mychemistry page (following adress : http://www.mychemistry.eu/2011/05/chemmacros-nearly-there/.)

But when I compile, I get the error message that you can see in the attached document Log File.pdf and message.jpg.

Screen shot of TexMaker error message
message.jpg (303.78 KiB) Viewed 12030 times

I can't solve the problem...please, thank you for helping me.
Jobic (France)
Attachments
LOG FILE.pdf
Log message provide by TexMaker
test.tex
Tex document for testing the chemmacros and mhchem packages

Tags:

cgnieder
Site Moderator
Posts: 1993
Joined: Sat Apr 16, 2011 7:27 pm
Hi jobic,

Welcome to the LaTeX community!

I would bet you have an outdated TeX distribution. chemmacros relies on up to date versions of the l3kernel and l3packages. You should try to update your system.

BTW: the code I posted on the site you've linked is outdated, too. It uses deprecated commands (like \Rcip), or the macros have changed in how they take their arguments (like \ox). Try the examples of the documentation (chemmacros) instead. (I should mention it there, I guess...)

Regards
Last edited by cgnieder on Tue Oct 02, 2012 3:28 pm, edited 2 times in total.
site moderator & package author

jobic2005
Posts: 5
Joined: Tue Oct 02, 2012 2:16 pm
You are right, my packages were outdated (I can't understand with the Miktex Update Manager didn't detect it.
I have updated the three files l3kernel, l3experimental and l3packages : downloaded and extracted in the Miktex folder.

I have run refresh FNDB in Miktex Setting

And I have only keep the following lines in attached file: test.tex

But I still get an error message :
1. ("C:\Program Files\MiKTeX 2.9\tex\latex\chemmacros\chemmacros.sty"
3. Type X to quit or <RETURN> to proceed,
4. or enter new name. (Default extension: sty)
5. Enter file name:
6. ! Emergency stop.
8. l.30 \RequirePackage
9. { tikz , mathtools , environ , scrlfile , etoolbox , bm }
10. *** (cannot \read from terminal in nonstop modes)
11. Here is how much of TeX's memory you used:
12. 11866 strings out of 493921
13. 241034 string characters out of 3147210
14. 272705 words of memory out of 3000000
15. 15029 multiletter control sequences out of 15000+200000
16. 3940 words of font info for 15 fonts, out of 3000000 for 9000
17. 841 hyphenation exceptions out of 8191
18. 56i,1n,52p,304b,53s stack positions out of 5000i,500n,10000p,200000b,50000s
19. ! ==> Fatal error occurred, no output PDF file produced!

Regards
Jobic
Attachments
test.tex
Last edited by cgnieder on Tue Oct 02, 2012 11:36 pm, edited 1 time in total.

cgnieder
Site Moderator
Posts: 1993
Joined: Sat Apr 16, 2011 7:27 pm
If xfrac is missing you still don't have the up to date versions since it is part of the l3packages.

I'm no MiKTeX user so I can't advise you there but I've read more than once about update problems with MiKTex both in this forum and elsewhere.

Regards
site moderator & package author

jobic2005
Posts: 5
Joined: Tue Oct 02, 2012 2:16 pm
Hi,
I have found xfrac.dtx and xfrac.ins in the l3packages...where can I found xfrac.sty ?
Here is the limit of my knowledge...
thank you
Jobic
Attachments
l3packages.jpg (57.67 KiB) Viewed 12019 times

jobic2005
Posts: 5
Joined: Tue Oct 02, 2012 2:16 pm
Hi,
I succed in generating the xfrac.sty (and the other file.sty) by using the cmd console of windows. I have run twice "latex l3.ins" which is located in the l3kernel, then I have run xfrac.ins twice ...then I copied it in the folder l3packages...
but I still get error message (LOG FIL1.pdf)
I don't understand, I get a test.pdf but It is unreadable...(have a look... on the attached file)
Jobic
Attachments
test.pdf
LOG FIL1.pdf

cgnieder
Site Moderator
Posts: 1993
Joined: Sat Apr 16, 2011 7:27 pm
Instead of updating packages manually - which is tricky as you've noticed and bears the danger of getting packages aut of sync - you should use the update manager. I know MiKTeX has one. And you've probably need to refresh the database as well. A forum or web search should give you hints how to do both tasks.

Regards
site moderator & package author

cgnieder
Site Moderator
Posts: 1993
Joined: Sat Apr 16, 2011 7:27 pm
site moderator & package author

localghost
Site Moderator
Posts: 9204
Joined: Fri Feb 02, 2007 12:06 pm
It can't do any harm to read the relevant part of the MiKTeX Manual (Chapter 4 - Maintenance). Start the MiKTeX Package Manager (MPM), synchronize the package repository database and then install the LaTeX3 related packages (see attachment). Get used to keeping your TeX distribution up to date. LaTeX packages are under continuous development.

Best regards and welcome to the board
Thorsten
Attachments
The MiKTeX Package Manager (Admin) with the list of available packages.
MPM(Admin)-Repository-Synchronize.png (41.46 KiB) Viewed 12010 times
LaTeX Community Moderator

¹ System: openSUSE 42.2 (Linux 4.4.52), TeX Live 2016 (vanilla), TeXworks 0.6.1

jobic2005
Posts: 5
Joined: Tue Oct 02, 2012 2:16 pm
Hi,
Sorry not to have answered to the comments done by localghost and cgnieder because I was busy (teaching).
Following what you notice concerning Miktex, I have read the MikTex Manual then I have uninstalled Miktex and re-installed it in order to get a "clean" packages installation.
Result : it nearly works !...
Actually, in the newmantest.tex file, TexMaker compile the entire file but the line in comment (line 11,17,24,37,42).
But cgnieder has mentionned that a few commands were outdated in this example. I have tried commands from the http://texdoc.net/texmf-dist/doc/latex/chemmacros/chemmacros_en.pdf and it looks fine. I get some problems but I am not worried about them because the document is compiled : these are not packages problems (the orbitals representation on page 41 of the english version : the compilation works and the lines 10 using chemfig package produce a wrong picture. But I have not worked on the origin of the problem).

Now, with the chemmacros tuto, I should succeed in using the chemmacros packages. It looks really powerfull.
For me, the conclusion is that I have to maintain Miktex carefully...
I really thank you for your help. Sorry for my english...
regards,
Jobic2005
Attachments
newmantest.tex


text:
Autotools detect YAML library

I have been updating my build tools to optionally use autotools (autoconfig/automake/libtool etc.).

As part of this change I have written a couple of M4 macros. This not being something I have done before, any input is appreciated on style or if things can be done better.

This macro checks to see if the YAML libraries are installed:

AC_DEFUN([AX_FUNC_THOR_USE_YAML],
[
AC_ARG_WITH(
[yamlroot],
AS_HELP_STRING([--with-yamlroot=<location>], [Directory of YAML_ROOT])
)
AC_ARG_ENABLE(
[yaml],
AS_HELP_STRING([--disable-yaml], [Disable yaml serializsation])
)
AS_IF(
[test "x$enable_yaml" != "xno"], ORIG_LDFLAGS="${LDFLAGS}"
if test "${with_yamlroot}" != ""; then LDFLAGS="$LDFLAGS -L$with_yamlroot/lib" fi AC_CHECK_LIB( [yaml], [yaml_parser_initialize], [ AC_DEFINE([HAVE_YAML], 1, [When on Yaml Serialization code will be compiled]) with_yamllib=-lyaml ], [AC_MSG_ERROR([ Error: Could not find libyaml You can solve this by installing libyaml see http://pyyaml.org/wiki/LibYAML Alternately specify install location with: --with-yamlroot=<location of yaml installation> If you do not want to use yaml serialization then it can be disabled with: --disable-yaml ], [1])] ) LDFLAGS="${ORIG_LDFLAGS}"
)
])

If YAML is detected, then no problems. If the configure script cannot find them, the error message is generated with three options:

1. Disable the use of YAML
2. Provide the location where YAML is installed (not default)
3. Instructions on how to install

This is a very archaic (and silly) way of testing flags:

    [test "x$enable_yaml" != "xno"],  You can write simpler as:  [test "$enable_yaml" != no],

This can be simplified:

    if test "${with_yamlroot}" != ""; then  To just:  if test "${with_yamlroot}"; then

I also find it odd to use sometimes $this_style and sometimes ${that_style}. I prefer less typing (especially the shift key for }), so the first, simpler style. The only time I use braces is when appending some text directly after the variable would break the script, for example in situations like this:

authtype=...  # something
# broken, not using the $authtype variable #modpath=/usr/libexec/apache2/mod_$authtype_dbd.so
# good
modpath=/usr/libexec/apache2/mod_\${authtype}_dbd.so


text:
## The Cycle Embedding Problem

• Given two hypergraphs, representing a fine and a coarse "layer", and a cycle cover of the nodes of the coarse layer, the cycle embedding problem (CEP) asks for an embedding of the coarse cycles into the fine layer. The CEP is NP-hard for general hypergraphs, but it can be solved in polynomial time for graphs. We propose an integer rogramming formulation for the CEP that provides a complete escription of the CEP polytope for the graphical case. The CEP comes up in railway vehicle rotation scheduling. We present computational results for problem instances of DB Fernverkehr AG that justify a sequential coarse-first-fine-second planning approach.

### Additional Services

Author: Ralf Borndörfer, Marika Karbstein, Julika Mehrgahrdt, Markus Reuther, Thomas Schlechte In Proceedings Operations Research Proceedings 2014 465 472 2016 urn:nbn:de:0297-zib-52788 http://dx.doi.org/10.1007/978-3-319-28697-6_65

$Rev: 13581$


text:
[This article was first published on From the Bottom of the Heap - R, and kindly contributed to R-bloggers]. (You can report issue about the content on this page here)
Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.

There are lots of choices for fitting generalized linear mixed effects models within R, but if you want to include smooth functions of covariates, the choices are limited. One option is to fit the model using gamm() from the mgcv ???? or gamm4() from the gamm4 ????, which use lme() (nlme ????) or one of lmer() or glmer() (lme4 ????) under the hood respectively. The problem with doing things that way is that you get PQL fitting for non-Gaussian models (????) and the range of families for handling non-Gaussian responses is quite limited, especially compared with the extended families now available with gam(). brms ???? is a good option if you don’t want to do everything by hand, but the MCMC can be slow. Instead, we could use the equivalence between smooths and random effects and use gam() or bam() from mgcv. In this post I’ll show you how to do just that.

## Smooths as random effects

The sorts of smooths we fit in mgcv are (typically) penalized smooths; we choose to use some number of basis functions (k), which sets an upper limit on the complexity — wiggliness — of the smooth, and then we estimate parameters for the model by maximizing a penalized log-likelihood. The log-likelihood of the model is a measure of the fit (or lack there of), while the penalty helps us avoid fitting overly complex smooths.

In the sorts of models that can be fitted in mgcv, the penalty is a function of the model coefficients, (), and a penalty matrix1, which we write as (). The penalty then is (^{} ). The penalty matrix measures the wiggliness of each basis function (on the diagonal), and how the wiggliness of one basis function affects the wiggliness of another (the off diagonals). Just as the () scale the individual basis functions, they also scale penalty values in the penalty matrix; if you were to choose large weights for the most wiggly basis functions, the overall penalty (^{} ) would increase by a lot more than if we used smaller weights for those really wiggly functions.

The penalty then acts to shrink the estimates of () away from the values they would take if we weren’t doing a penalized fit and were instead fixing the wiggliness of the smooth at the maximum value dictated by (k). Put another way, the penalty shrinks the estimates for () towards zero.

Random effects also involve shrinkage. With a random effect we’re trying to model subject specific effects (subject-specific intercepts, or subject-specific “slopes” of covariates) without having to explicitly estimate a fixed effect parameter for each subject’s intercept or covariate effect. Instead we think of the subject-specific intercepts or “slopes” as coming from distribution, typically a Gaussian distribution, with mean 0 and some variance that is to be estimated. The larger this random effect variance, the greater the variation among subject-specific intercepts, “slopes” etc. The smaller the random effect variance, the closer to zero the estimated effects are pulled. As a result, random effects shrink to, varying degrees, the estimated subject-specific effects, and how much they do that is related to the random effect variance.

If I abuse all standards of notation and represent the estimated random effects with (), you might get the feeling that perhaps there is some link between whats happening when we estimate random effects shrinking the () towards zero, and the penalty applied to smooths that shrinks the () towards zero. If you did, you’d be right, there is. And if so, there must be a penalty matrix that we can write down for a random effect — if we assume that each random intercept or “slope” is a basis function, the penalty matrix () is a simple diagonal matrix, one row and column per subject, with a constant value on the diagonal (and zeroes everywhere else):

To complete the picture, when we fit a GAM, we’re maximising the penalised log-likelihood over both the model parameters () and a smoothness parameter, (). It’s () that actually controls how much price we pay for the wiggliness penalty as we add ( ^{} ) to the log-likelihood. It turns out that the variance of the random effect is equal to the scale parameter (the residual variance (^{2}_{}) in a Gaussian model for example) divided by ().

This link between smooths and random effects is really cool; not only are we able to estimate smooths and GAMs using the machinery of mixed effects models, we can also estimate random effects using all the penalized spline machinery available for GAMs in mgcv.

OK, so that was all really hand-wavy and skipped over a lot of math and theory2, but I hope it gives you the intuition you need to understand how random effects are represented as smooths, through the identity penalty matrix.

## Fitting random effects with mgcv

So much for the theory, let’s see how this all works in practice.

By way of an example, I’m going to use a data set from a study on the effects of testosterone on the growth of rats from Molenberghs and Verbeke (2000), which was analysed in Fahrmeir et al. (2013), from were I also obtained the data. In the experiment, 50 rats were randomly assigned to one of three groups; a control group or a group receiving low or high doses of Decapeptyl, which inhibits testosterone production. The experiment started when the rats were 45 days old and starting with the 50th day, the size of the rat’s head was measured via an X-ray image. You can download the data here.

For the example, we’ll use the following packages

We’ll also need the development version of the gratia ????, which we can install with the remotes ???? (if you don’t have that installed, install it first)

We load the data — ignore the warning about new names as we deleted that column anyway

Next we need to prepare the data for modelling. The variable transf_time is the main covariate of interest. It relates to the age of the rats in days via the transformation

[(1 + ( - 45) / 10)]

where () is the time variable in the data set. We also need to convert the group variable to a factor with useful levels to create a treatment variable and we convert subject — an identifier for each individual rat — a factor

The number of observations per rat is variable, with only 22 of the 50 rats having the complete seven measurements by day 110

so there’ll be no averaging the response within subjects and doing an ANOVA.

Before we fit the models an explore how to work with random effects in mgcv, we’ll plot the data

The model fitted in Fahrmeir et al. (2013) is

[y_{ij} = 0 + {0i} + 1 L_i t{ij} + 2 H_i t{ij} + 3 C_i t{ij} + {1i} t{ij} + _{ij}]

where

• (_0) is the population mean of the response at the start of the treatment
• (L_i), (H_i), (C_i) are dummy variables encoding for each treatment group
• (_{0i}) is the rat-specific mean (random intercept)
• ({qi} t{ij}) is the rat-specific effect of transf_time (random slope)

If this isn’t very clear — it took me a little while to grok what this meant and translate it to R speak — note that each of (_1), (_2), and (_3) are associated with an interaction between the dummy variable coding for the treatment and the time variable. So we have a model with an intercept and three interaction terms with no main effects.

In lmer() we can fit this model with (ignore the singular fit warning for now)

If you’re not familiar with this model specification for the random effects, it specifies uncorrelated random effects for the subject-specific means (random intercept; (1 | subject)) and the subject_specific effects of transf_time (random slope; (0 + transf_time | subject)). The 0 in the formula for the latter suppresses the (random) intercept as we already included that as a separate term.

The reason we’re fitting uncorrelated random effects is because that’s all mgcv can fit; there’s no way to encode a covariance term between the two random effects.

The equivalent model fitted using gam() is

Note:

1. we specify two separate random effect smooths, one per random term,
2. we indicate that the smooth should be a random effect with bs = ‘re’,
3. any grouping variables must be coded as a factor — that’s why we converted subject (which is an integer vector) to a factor right after importing the data.

Let’s compare the fixed effect terms; first for the lmer() version

and for the gam() version

which are close enough.

Next let’s look at the estimated variances of the random effect terms. First for the lmer() model:

and now for the gam() model

Apart from being as close for the differences not to matter, we should also note that the variance for the rat-specific effect of transf_time is effectively 0. This is likely the cause of the singular fit warning from lmer(). The lower_ci and upper_ci variables indicate the limits of a 95% confidence interval on the standard deviation of each variance component; the coverage can be controlled via the coverage argument to variance_comp(). The confidence interval for the rat-specific time effect variance is huge, again indicating that there really isn’t much variation at all in this component.

Here we used the variance_comp() function from gratia to extract the variance components, which expresses the random effects as their equivalent variance components that you’d see in a mixed model output. variance_comp() is a simple wrapper to mgcv::gam.vcomp(), which is doing all the hard work, but variance_comp() suppresses the annoying printed output produced by gam.vcomp() and returns the variance components as a tibble.

You can see a nicer version of the variance components for lmer() by printing the whole summary() but it produces a lot of output; the bit we are interested in just now is in the section labelled Random effects:

One of the nice things about the output from the gam() model is that the summary() contains a test for the random effects

This test is due to Wood (2013). It is based on a likelihood ratio test and uses a reference distribution that is appropriate for testing a null hypothesis that is on the boundary of the parameter space (the null, that the variance is 0, is on the lower boundary of possible values for the parameter — you can’t have a negative variance!)

There is little evidence in support of the rat-specific time effects, reflecting what we saw when we looked at the variance components above.

If we look at the estimated degrees of freedom (EDF; the edf column) for each of the “smooths” we see the shrinkage in action. The Ref.df column contains the maximum degrees of freedom for each term, used in the calculation of the p value. The rat-specific mean distances — the s(subject) term — have only been shrunk a little to an EDF of ~43.7. In contrast, the EDF for the rat-specific effects of time has been shrunk to effectively zero.

The EDFs for smooths can be extracted from a fitted model with edf()

To plot the estimated time effects for each rat, we need to produce a new data frame with values of the range of transf_time for each rat, and include the relevant treatment value for the rat also. We do this with expand() and nesting() from the tidyr ????.

which we then use to predict from the model

which gives us something we can plot easily with ggplot

We can also compare the fitted curves with the observed data

A simpler model, which drops the rat-specific effects of transf_time is

[y_{ij} = 0 + {0i} + 1 L_i t{ij} + 2 H_i t{ij} + 3 C_i t{ij} + _{ij}]

which drops the ({qi} t{ij}) term, excluding the rat-specific time effects from the model.

As we should now expected, the two models have estimated variance components that are essentially equivalent. First for the lmer() fit:

and now for the gam() version

We could use the anova() method for “gam” fits but for fully penalized terms like random effects, the test isn’t very good and p values can be badly biased. Wood (2017, p. 315) says of the test “As expected, the test if clearly useless for comparing models differing in [their] random effect structure.” So, maybe give this one a miss.

Using AIC() to compare the models is also an option:

AIC clearly favours the simpler model as the fits of the two models are essentially the same. Note that because the EDF of the s(subject, transf_time) was so close to zero, we don’t pay much of a penalty for including this term in the model, and hence the AICs of the two models are very similar (typically we’d expect that where two models have the same fit, the AIC for the more complex one would be the larger value).

Note that the AIC computed for the gam() model is a conditional AIC, where the likelihood is of all model coefficients set to their maximum penalized likelihood estimates. The AIC for an lmer() fit is a marginal AIC, where all the penalized coefficients are viewed as random effects and integrated out of the joint density of the response and random effects.

The conditional AIC for the gam() fit would be anti-conservative, especially so in the case of models containing random effects. The upshot of that is that the conditional AIC would typically choose a model with a random effects structure that isn’t in the true model if no steps were taking to account for smoothness parameter selection in the EDF calculation. The AIC() method for gam() fits applies a suitable correction to the model EDF to account for smoothness parameter selection, resulting in an information criterion that has mostly good properties.

We need parametric = FALSE here because at the time of writing there is a bug in the code that handles parametric fixed effects.

## It’s not all good news

It all seems a little too good to be true, doesn’t it! We have a way to fit models with random effects that works well, allows for tests of random effect terms against a null of 0 variance, and which allows us to use all the extended families that gam() allows including some complex distributional model families.

Well, as they say, there is no free lunch; the main issue with fitting random effects as smooths within gam() fits is to do with efficiency. lmer() and glmer() use very efficient algorithms for fitting the model, including the use of sparse matrices for the model terms. Because gam() fits need the full penalty matrix for each random effect, and gam() currently doesn’t use any sparse matrices for efficient computation, gam() fits are going to get very slow as the number of random effects increases: the larger the number of subjects (levels) the slower things will get. The same will happen the greater the number of complex random effect terms you include the model.

Basically, if you have random effects with many hundreds or thousands of levels (subjects), expect the time it takes to fit your gam() to increase dramatically, and expect the memory usage to increase markedly too.

Also, running summary() on a model with random effects with many levels or lots of random effects terms is also going to be slow: the test for the random effect terms is quite computationally expensive. If you are mostly interested in the other model terms, setting the re.test argument to FALSE will skip the tests for random effects (and other terms with zero dimension null space), allowing the summary for the other terms to be computed quickly.

## Fin

In this post I showed how random effects can be represented as smooths and how to use them practically in in gam() models. I hope you found it useful. If you have any comments or questions, let me know them in the comments below.

### References

Fahrmeir, L., Kneib, T., Lang, S., and Marx, B. (2013). Regression: Models, methods and applications. Springer Berlin Heidelberg doi:10.1007/978-3-642-34333-9.

Molenberghs, G., and Verbeke, G. (2000). Linear mixed models for longitudinal data. Springer, New York, NY doi:10.1007/978-1-4419-0300-6.

Wood, S. N. (2013). A simple test for random effects in regression models. Biometrika 100, 1005–1010. doi:10.1093/biomet/ast038.

Wood, S. N. (2017). Generalized Additive Models: An introduction with R, second edition. CRC Press.

1. or matrices; smooths can have multiple penalty matrices that are stacked block-diagonally in (). For simplicity’s sake I’m just going to assume a single penalty matrix.↩


text:
#### need solution for rd sharma maths class 12 chapter determinants exercise 5.5 question 3

Answer: $x = -7k, y = 8k, z = 13k$, where $k \in R$

Hint: : If $\left | A \right |= 0$, then the system has an infinite number of solutions.

Given:

$3x+y+z=0$

$x - 4y + 3z = 0$

$2 x + 5y - 2z = 0$

Solution:

The above linear equations can be represented in matrix form i.e.

$A = \begin{bmatrix} 3 & 1 & 1\\ 1& -4 & 3\\ 2& 5& -2 \end{bmatrix}, X = \begin{bmatrix} x\\ y\\ z\end{bmatrix}, B = \begin{bmatrix} 0\\ 0\\ 0\end{bmatrix}$

Now,

$\left | A \right | = \begin{vmatrix} 3 & 1& 1\\ 1 & -4 &3 \\ 2& 5& -2 \end{vmatrix}$

$= 3(8 -15) -1(-2 -6) + 1(5+8)$

$= 3(-7) + 8 +15$

$= - 21 + 21$

$= 0$

So, the system of equations has non – trivial solutions.

Consider, first two equation and put z = k

$3 x + y = -k$

$x - 4y = -3k$

Now, By Crammer’s rule:

$x = \frac{D_{1}}{D} = \frac{\begin{vmatrix} -k & 1\\ -3k & -4 \end{vmatrix}}{\begin{vmatrix} 3&1 \\ 1& -4 \end{vmatrix}} = \frac{7k}{-13} = \frac{-7k}{13}$

$y = \frac{D_{2}}{D} = \frac{\begin{vmatrix} 3 & -k\\ 1 & -3k \end{vmatrix}}{\begin{vmatrix} 3&1 \\ 1& -4 \end{vmatrix}} = \frac{-8k}{-13} = \frac{8k}{13}$

$x=\frac{-7k}{13}, y = \frac{8k}{13}$  and $z=k$

or $x = -7k$, $y = 8k$ and $z = 13k$, where $k \in R$

It will satisfy the third equation.

Hence, $x = -7k$, $y = 8k$ and $z = 13k$, where $k \in R$


text:
## Pacific Journal of Mathematics

### Classification of algebraic surfaces with sectional genus less than or equal to six. I. Rational surfaces.

Elvira Laura Livorni

#### Article information

Source
Pacific J. Math., Volume 113, Number 1 (1984), 93-114.

Dates
First available in Project Euclid: 8 December 2004

https://projecteuclid.org/euclid.pjm/1102709380

Mathematical Reviews number (MathSciNet)
MR745598

Zentralblatt MATH identifier
0573.14013

Subjects
Primary: 14J26: Rational and ruled surfaces
Secondary: 14J10: Families, moduli, classification: algebraic theory

#### Citation

Livorni, Elvira Laura. Classification of algebraic surfaces with sectional genus less than or equal to six. I. Rational surfaces. Pacific J. Math. 113 (1984), no. 1, 93--114. https://projecteuclid.org/euclid.pjm/1102709380

#### References

• [A+F] A. Andreotti and T. Frankel, The Lefschetz theorem on hyperplane sections, Ann. of Math., 69 (1959), 713-717.
• [Ba] H. F. Baker,Principles of Geometry, V, CambridgeUniversityPress,1933.
• [Bo] R. Bott, On a theorem of Lefschetz, Michigan Math. J., 6, 211-216.
• [Fu] T. Fujita, On the structure of polarized varieties with -genera zero, J. Fac. Sci. Univ. Tokyo,22 (1975),103-115.
• [G-f H] P. A. Griffiths and J. Harris, Residues and zero cycles on algebraic varieties, Ann. of Math., 108(1978), 461-555.
• [Ha] R. Hartshorne, Algebraic Geometry, Springer-Verlag,New York, 1977.
• [Io] P. Ionescu, An enumerationof all smoothprojective varieties of degree5 and 6, Preprint, Series in Mathematics Nr. 74/1981.
• [N] M. Nagata, On rational surfaces I, Mem. Coll. Sci. Kyoto, (A) 32 (1960), 351-370.
• [R] L. Roth, On theprojective classificationof surfaces, Proc. London Math. Soc, (2)42(1937), 142-170.
• [Sa] B. Saint-Donat, On PetriJs analysis of the linear system of quadrics through a canonicalcurve, Math. Ann.,206 (1973),157-175.
• [Sk] F. Sakai, Semi-stablecurves on algebraic surfaces and logarithmic pluricanoni- cal maps, Sonderforschungsbereich Theoritische Mathematik 40, Universitat Bonn.
• [S4-R] J. G. Semple and L. Roth, Introduction to Algebraic Geometry, Clarendon Press, Oxford, 1949.
• [So] A. J. Sommese,Hyperplane sections of projective surfaces I--The adjunction mapping, Duke Math. J.,46 No. 2(1979).
• [So] A. J. Sommese, On the minimality of hyperplane sections of projective threefolds, J. Reine Angew. Math., 329 (1981), 16-41.

• Elvira Laura Livorni. Classification of algebraic surfaces with sectional genus less than or equal to six. {II}. Ruled surfaces with {${\r dim}\,\phi\sb {K\sb Xøtimes L}(X)=1$}. II [MR 88d:14023] Canad. J. Math. 38 1986 5 1110--1121.
• Elvira Laura Livorni. Classification of algebraic surfaces with sectional genus less than or equal to six. {III}. Ruled surfaces with {${\r dim}\phi\sb {K\sb Xøtimes L}(X)=2$}. III [MR 88d:14024] Math. Scand. 59 1986 1 9--29.