the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Scaled Kendrick Mass Defect Analysis for Improved Visualization of Atmospheric Mass Spectral Data
Mitchell W. Alton
Harald Stark
Manjula R. Canagaratna
Eleanor C. Browne
Abstract. Mass spectrometry is an important analytical technique within the field of atmospheric chemistry. Owing to advances in instrumentation, particularly with regards to mass resolving power and instrument response factors (sensitivities), hundreds of different mass-to-charge (m/z) signals are routinely measured. This large number of detected ions creates challenges for data visualization. Furthermore, assignment of chemical formulas to these ions is time-consuming and increases in difficulty at the higher m/z ranges. We present a technique called scaled Kendrick mass defect (SKMD) analysis to facilitate the visualization and peak identification processes for typical atmospheric organic (and to some extent inorganic) compounds. SKMD is related to the previously proposed resolution enhanced Kendrick mass defect (REKMD). SKMD introduces a tunable integer scaling factor into the mass defect equation that effectively contracts or expands the mass scale. The SKMD transformation maintains the horizontal alignment of ion series related by integer multiples of the chosen base unit that is characteristic of Kendrick mass defect analysis. However, the tunable integer acts to alter the mass defect spacing between different homologue ion series. As a result, the entire mass defect range (-0.5 to 0.5) is more effectively used simplifying data visualization and facilitating chemical formula assignment. We describe the mechanism of this transformation and discuss base unit and scaling factor selections appropriate for compounds typically found in atmospheric measurements. We present an open-source graphical user interface (GUI) for calculating and visualizing SKMD analysis results within the Igor Pro Environment.
- Preprint
(1644 KB) -
Supplement
(903 KB) - BibTeX
- EndNote
Mitchell W. Alton et al.
Status: closed
-
CC1: 'Comment on egusphere-2022-1319: mass excess', Marc Gonin, 13 Dec 2022
There is an error in nomenclature in this paper. This concerns the quantity "mass defect" that is used in a way which is not in line with the usual scientific definition.
mass defect:
- is the difference between the masses of the free elementary particles and the bound elementary particles of a nucleus, and atom or a molecule.
- it is always positive and never negative
- it represents the binding energy by E = mc2
- see https://en.wikipedia.org/wiki/Nuclear_binding_energy
mass excess:
- is the difference between the mass and the nucleon number x Da (= nominal mass) of nuclei, atoms or molecules
- it is positive for atoms with low binding energies per nucleon, and negative for atoms with high binding energies per nucleon.
- https://en.wikipedia.org/wiki/Mass_excess
- conceptually, if a defect is large the mass must be small, the excess must be small
The quantity you refering to is therefore mass excess, not mass defect.
Mass spectrometrists have a long history in getting this wrong. It is now even wrong in textbooks and reference materials. However, in my opinion this should not serve as an excuse to accept this faulty nomenclature. Mass defect and mass excess are caused by nuclear physics and therefore mass spectrometrists should accept and use their nomenclature.
It is not helpful if every branch of science developes their own jargon. This hinders mutual undertstanding and promotes the view of science as isolated ivory towers. Science is under large critizism today, and we should not promote critizism by using sloppy nomenclature. Scientific rigor is the only answer to this criticism.
Citation: https://doi.org/10.5194/egusphere-2022-1319-CC1 - AC1: 'Author response to all comments', Eleanor Browne, 19 Mar 2023
-
CC2: 'Comment on egusphere-2022-1319: mass vs mas/charge', Marc Gonin, 13 Dec 2022
When discussing mass excess or mass defect, the quantitiy mass should be used in the plots, not the quantity mass/charge. This in spite of mass spectrometers measuring mass/charge. The relevant quantity in these discussions is mass.
Citation: https://doi.org/10.5194/egusphere-2022-1319-CC2 -
RC2: 'Reply on CC2', Thierry Fouquet, 06 Jan 2023
Dear Marc,
why would you recommend using "mass" instead of "m/z" as x-axis ? Kendrick "mass defects" (or fractional mass) are calculated from m/z, and using m/z reveals the charge state of ion series at a glance. Using mass implies that the mass spectral data are pre-processed for charge deconvolution which is not error-free, especially with a QTOF resolving power.
Citation: https://doi.org/10.5194/egusphere-2022-1319-RC2 - AC1: 'Author response to all comments', Eleanor Browne, 19 Mar 2023
-
RC2: 'Reply on CC2', Thierry Fouquet, 06 Jan 2023
-
RC1: 'Comment on egusphere-2022-1319', Thierry Fouquet, 06 Jan 2023
Apologies for being late with my comments, I had trouble submitting my post.
I read this article with great interest and did appreciate its form and the application of Kendrick analyses for a new type of mass spectral data and unusual instrument. I also acknowledge the efforts of the Authors to try finding differences between their proposed “scaled Kendrick mass defect” SKMD and the existing “REKMD” or “traditional” Kendrick analysis. If I strongly support new applications of this easy and powerful data processing/visualization tool and its implementation in more programs, I am nonetheless circumspect about the added value of the SKMD formula justifying the introduction of a new name and a seemingly new concept. Based on my comments below, I do strongly recommend not to try adding a new term to a long list of wrongly named methods but keep using either “REKMD” (also wrongly named, but published before) or better simply “Kendrick analysis”, and shift the focus of this draft from the differentiation SKMD / REKMD which is non-existent to the application of the Kendrick analysis to their unusual data, providing examples of ion series assignments, separation of ion series of interest from congested mass spectra, deisotoping, binary comparisons, ….
1) The formula of “SKMD” look different from the formula(s) of “REKMD” proposed in the original article, but this notation KM=m/z*x/R has already been reported in J Mass Spectrom. 2019;54:933–947 (doi: /doi.org/10.1002/jms.4480), sadly not cited by the Authors.
2) The case x=1 in the formula KM=m/z*x/R has already been explained in the same article, and named “remainders” by several Authors (e.g. Anal Chem. 2019;91(10):6479â6486 or Anal Chem. 2018;90(14):8716â8718). The only change introduced by this preprint would then be the range of values 1<x<2/3R, and x>2R. Looking at the plot ΔSKMD and ΔREKMD in the Supporting Information (Fig S1), it seems that the expansions provided by SKMD are already achieved by REKMD in its linearity range. I have not been convinced by the examples of x=4 and x=40 (not truly REKMD in terms of range of divisors) in terms of gain of visualization / separation as compared to the other plots (x=17, 20, 24) which are truly REKMD. Can the Authors find a case where values of x <2/3R or >2R provide a truly unique separation capability not achievable by REKMD with integer or non-integer x ? I haven't found any case myself yet.
3) The formula KM=m/z*x/R is still fundamentally a traditional Kendrick change of basis as proposed by Kendrick a while ago, simply choosing x instead of round(R) as the new reference mass. The formula KM=m/z*round(R)/R is a basic “rule of three”, setting the mass of R at an integer value round(R) to define a new reference instead of the IUPAC convention m(12C)=12, re-calculating other mass accordingly. In the SKM formula, the Authors choose to set the mass of 16O (or other moieties) at 2, or 6, or 40 or any integer instead of 16 to define a new mass scale. The concept does not vary from what Kendrick proposed, so does this really deserve a new name ? I do agree that the same question should have been raised when the concept of REKMD has been introduced. That is the reason why I am strongly in favor of calling the whole method a "Kendrick analysis" with no other mention.
m(/z) 16O IUPAC = 15.9949 --> m(/z) 16O Kendrick base = 16
m(/z) IUPAC --> rule of three --> m(/z) Kendrick base = m/(z) IUPAC *16/15.9949
m(/z) 16O IUPAC = 15.9949 --> m(/z) 16O Kendrick base = x
m(/z) IUPAC --> rule of three --> m(/z) Kendrick base = m/(z) IUPAC *x/15.9949
4) REKMD and its latest variations as reported in detail in the same article J Mass Spectrom. 2019;54:933–947 takes the charge state of the ions into account (simply adding an integer to the formula to cancel z) so it is applicable for multiply charged ions, while SKMD in its current form would deal with singly charged ions only. More importantly, this additional integer in the formula of KM also made possible the generation of an infinite number of Kendrick plots with a pseudo continuous coverage of expansions using non-integer x (ie nearly 0 step between expansions allowing the finest tune to separate series) while SKMD does only provide fixed expansions varying linearly with a step dictated by the value of R itself, and no finer control available (the larger R, the larger the step).
5) REKMD or its variations has already been implemented - but not called as such - in numerous programs, free or commercial, such as MZMine2, MSRepeatFinder, SpectraScope, Kendo, or Mass Mountaineer not to mention in simple Excel spreadsheets. These programs do not mention any REKMD but simply incorporate the divisor “x” which can be changed by the user. It is a wonderful idea to keep implementing the Kendrick analysis with all its variations in other programs, but would that require to use a new name and a seemingly new concept which in fact produces the same results as those already reported ? Would it be clearer for users to have a tool called “Kendrick analysis” with no S or RE or no mass defect (cf last comment below), but simply this "x" textbox to play with the change of basis and expansions ?
6) As a last reason not to introduce another (S)KMD term, and as pointed out by one reader of the community in his comment, several Authors strongly recommend not to use the “KMD” term anymore. The values we are dealing with are not mass defects – and not mass excess either – but fractional mass calculated with no a priori knowledge about the ions. This point has been greatly explained by the Authors in this preprint, as opposite to other plots such as Van Krevelen diagrams which require the elemental composition of ions to be known prior to their generation. The calculation of true mass defect/excess ALSO requires the elemental composition of the ions to be known. The y-values of Kendrick plots are computed a) without knowing the compositions of the ions but only their m/z, and b) are comprised between -0.5 and 0.5 (or -1 and 0, or 0 and 1) regardless of m due to the aliasing of the formula m-round(m) (or floor or ceiling) while the mass defect/excess would keep increasing/decreasing with the number of atoms in a molecule above or below (-)0.5
Citation: https://doi.org/10.5194/egusphere-2022-1319-RC1 - AC1: 'Author response to all comments', Eleanor Browne, 19 Mar 2023
-
RC3: 'RC2', Anonymous Referee #2, 31 Jan 2023
General Comments:
Overall, I think that this manuscript provides a valuable demonstration of a “Kendrick analysis” (using terminology from RC1) that can be applied to complex mass spectrometry data (in this case a VOCUS-PTRTOFMS) without knowledge of the ion elemental composition to improve data visualization towards assisting in ion assignment, revealing chemical homologues, and potential chemical trends. The manuscript is generally well-written and straightforward, thoughtful about introducing KMD, REKMD, and SKMD, and definitely proves through the figures the potential for using effective scaling for allowing greater insight into atmospheric chemical measurements (e.g. the separation of nominally odd/even IUPAC mass ions into odd nitrogen containing or no/even nitrogen containing formulas). That being said, I agree with RC1’s concerns that the main formulation of SKM/SKMD not truly being novel per prior publication in Fouquet (2019) necessitates reframing how the manuscript is presented/worded. After this, I still see the manuscript being publishable and of interest to the atmospheric measurement community for bringing attention to a potentially valuable data processing method for the torrent of mass spectrometric data being collected in recent times.
Specific Comments:
- Line 172: the introduced term “reduced fraction” representing X/RIUPAC is not the most intuitive given values of X (as exampled in the cases of X=20, 24, 40) with RIUPAC as 16O results in expanding the mass scale instead of contraction—this seems more like a scaling factor whether enlarged or reduced. Consider changing this term and revising throughout the rest of the discussion.
- Line 303: The text would be enhanced to include more information such as the caption for Figure 7. That is, explain here that these points in Fig. 7a are not just simply omitted in Fib. 7b, but they would not appear in Fig. 7b because they would not fall within the SKMD range after m/z transformation.
- Lines 241, Line 251, Line 296: By using “REKMD” in these section headings, it signals to the reader that co-authors intend SKMD to be a sub-method/type of REKMD, yet the language earlier in text introducing SKMD as a concept makes it seem that it should be distinct as it is used in the analyses in these sections. Thus, I would have expected these section titles to be “SKMD” instead of “REKMD”. Given the comments from RC1 on nomenclature/reframing the paper generally as a “Kendrick analysis,” just be consistent with the chosen framing in the revised version.
- General comment on Figures 3, 4, 5: For further connection with text and enforcing of how mass defect analysis allows for visualization of homologous series, it would be helpful for labels on the figures pointing out the chemical families and their generic chemical formulations if possible.
Technical Corrections:
- It would be helpful perhaps in Fig. S1 to include vertical lines associated with the bounds of X presented in Eq. (7), which brings more focus to the linearity and equivalency of the two methods within those bounds.
- Figure 2 captions for c and d have inconsistent X values with those in subpanels of figure. Caption text for c) should have X = 24, d) should have X = 20.
- Line 148: Extra space before period should be deleted.
- Line 180: Change “result” to “results”.
- Line 278: Add period after “respectively.”
- Figure S4: Add panel labels to figure
References:
RC 1: https://doi.org/10.5194/egusphere-2022-1319-RC1
Fouquet, TNJ. The Kendrick analysis for polymer mass spectrometry. J Mass Spectrom. 2019; 54: 933– 947.
Citation: https://doi.org/10.5194/egusphere-2022-1319-RC3 - AC1: 'Author response to all comments', Eleanor Browne, 19 Mar 2023
Status: closed
-
CC1: 'Comment on egusphere-2022-1319: mass excess', Marc Gonin, 13 Dec 2022
There is an error in nomenclature in this paper. This concerns the quantity "mass defect" that is used in a way which is not in line with the usual scientific definition.
mass defect:
- is the difference between the masses of the free elementary particles and the bound elementary particles of a nucleus, and atom or a molecule.
- it is always positive and never negative
- it represents the binding energy by E = mc2
- see https://en.wikipedia.org/wiki/Nuclear_binding_energy
mass excess:
- is the difference between the mass and the nucleon number x Da (= nominal mass) of nuclei, atoms or molecules
- it is positive for atoms with low binding energies per nucleon, and negative for atoms with high binding energies per nucleon.
- https://en.wikipedia.org/wiki/Mass_excess
- conceptually, if a defect is large the mass must be small, the excess must be small
The quantity you refering to is therefore mass excess, not mass defect.
Mass spectrometrists have a long history in getting this wrong. It is now even wrong in textbooks and reference materials. However, in my opinion this should not serve as an excuse to accept this faulty nomenclature. Mass defect and mass excess are caused by nuclear physics and therefore mass spectrometrists should accept and use their nomenclature.
It is not helpful if every branch of science developes their own jargon. This hinders mutual undertstanding and promotes the view of science as isolated ivory towers. Science is under large critizism today, and we should not promote critizism by using sloppy nomenclature. Scientific rigor is the only answer to this criticism.
Citation: https://doi.org/10.5194/egusphere-2022-1319-CC1 - AC1: 'Author response to all comments', Eleanor Browne, 19 Mar 2023
-
CC2: 'Comment on egusphere-2022-1319: mass vs mas/charge', Marc Gonin, 13 Dec 2022
When discussing mass excess or mass defect, the quantitiy mass should be used in the plots, not the quantity mass/charge. This in spite of mass spectrometers measuring mass/charge. The relevant quantity in these discussions is mass.
Citation: https://doi.org/10.5194/egusphere-2022-1319-CC2 -
RC2: 'Reply on CC2', Thierry Fouquet, 06 Jan 2023
Dear Marc,
why would you recommend using "mass" instead of "m/z" as x-axis ? Kendrick "mass defects" (or fractional mass) are calculated from m/z, and using m/z reveals the charge state of ion series at a glance. Using mass implies that the mass spectral data are pre-processed for charge deconvolution which is not error-free, especially with a QTOF resolving power.
Citation: https://doi.org/10.5194/egusphere-2022-1319-RC2 - AC1: 'Author response to all comments', Eleanor Browne, 19 Mar 2023
-
RC2: 'Reply on CC2', Thierry Fouquet, 06 Jan 2023
-
RC1: 'Comment on egusphere-2022-1319', Thierry Fouquet, 06 Jan 2023
Apologies for being late with my comments, I had trouble submitting my post.
I read this article with great interest and did appreciate its form and the application of Kendrick analyses for a new type of mass spectral data and unusual instrument. I also acknowledge the efforts of the Authors to try finding differences between their proposed “scaled Kendrick mass defect” SKMD and the existing “REKMD” or “traditional” Kendrick analysis. If I strongly support new applications of this easy and powerful data processing/visualization tool and its implementation in more programs, I am nonetheless circumspect about the added value of the SKMD formula justifying the introduction of a new name and a seemingly new concept. Based on my comments below, I do strongly recommend not to try adding a new term to a long list of wrongly named methods but keep using either “REKMD” (also wrongly named, but published before) or better simply “Kendrick analysis”, and shift the focus of this draft from the differentiation SKMD / REKMD which is non-existent to the application of the Kendrick analysis to their unusual data, providing examples of ion series assignments, separation of ion series of interest from congested mass spectra, deisotoping, binary comparisons, ….
1) The formula of “SKMD” look different from the formula(s) of “REKMD” proposed in the original article, but this notation KM=m/z*x/R has already been reported in J Mass Spectrom. 2019;54:933–947 (doi: /doi.org/10.1002/jms.4480), sadly not cited by the Authors.
2) The case x=1 in the formula KM=m/z*x/R has already been explained in the same article, and named “remainders” by several Authors (e.g. Anal Chem. 2019;91(10):6479â6486 or Anal Chem. 2018;90(14):8716â8718). The only change introduced by this preprint would then be the range of values 1<x<2/3R, and x>2R. Looking at the plot ΔSKMD and ΔREKMD in the Supporting Information (Fig S1), it seems that the expansions provided by SKMD are already achieved by REKMD in its linearity range. I have not been convinced by the examples of x=4 and x=40 (not truly REKMD in terms of range of divisors) in terms of gain of visualization / separation as compared to the other plots (x=17, 20, 24) which are truly REKMD. Can the Authors find a case where values of x <2/3R or >2R provide a truly unique separation capability not achievable by REKMD with integer or non-integer x ? I haven't found any case myself yet.
3) The formula KM=m/z*x/R is still fundamentally a traditional Kendrick change of basis as proposed by Kendrick a while ago, simply choosing x instead of round(R) as the new reference mass. The formula KM=m/z*round(R)/R is a basic “rule of three”, setting the mass of R at an integer value round(R) to define a new reference instead of the IUPAC convention m(12C)=12, re-calculating other mass accordingly. In the SKM formula, the Authors choose to set the mass of 16O (or other moieties) at 2, or 6, or 40 or any integer instead of 16 to define a new mass scale. The concept does not vary from what Kendrick proposed, so does this really deserve a new name ? I do agree that the same question should have been raised when the concept of REKMD has been introduced. That is the reason why I am strongly in favor of calling the whole method a "Kendrick analysis" with no other mention.
m(/z) 16O IUPAC = 15.9949 --> m(/z) 16O Kendrick base = 16
m(/z) IUPAC --> rule of three --> m(/z) Kendrick base = m/(z) IUPAC *16/15.9949
m(/z) 16O IUPAC = 15.9949 --> m(/z) 16O Kendrick base = x
m(/z) IUPAC --> rule of three --> m(/z) Kendrick base = m/(z) IUPAC *x/15.9949
4) REKMD and its latest variations as reported in detail in the same article J Mass Spectrom. 2019;54:933–947 takes the charge state of the ions into account (simply adding an integer to the formula to cancel z) so it is applicable for multiply charged ions, while SKMD in its current form would deal with singly charged ions only. More importantly, this additional integer in the formula of KM also made possible the generation of an infinite number of Kendrick plots with a pseudo continuous coverage of expansions using non-integer x (ie nearly 0 step between expansions allowing the finest tune to separate series) while SKMD does only provide fixed expansions varying linearly with a step dictated by the value of R itself, and no finer control available (the larger R, the larger the step).
5) REKMD or its variations has already been implemented - but not called as such - in numerous programs, free or commercial, such as MZMine2, MSRepeatFinder, SpectraScope, Kendo, or Mass Mountaineer not to mention in simple Excel spreadsheets. These programs do not mention any REKMD but simply incorporate the divisor “x” which can be changed by the user. It is a wonderful idea to keep implementing the Kendrick analysis with all its variations in other programs, but would that require to use a new name and a seemingly new concept which in fact produces the same results as those already reported ? Would it be clearer for users to have a tool called “Kendrick analysis” with no S or RE or no mass defect (cf last comment below), but simply this "x" textbox to play with the change of basis and expansions ?
6) As a last reason not to introduce another (S)KMD term, and as pointed out by one reader of the community in his comment, several Authors strongly recommend not to use the “KMD” term anymore. The values we are dealing with are not mass defects – and not mass excess either – but fractional mass calculated with no a priori knowledge about the ions. This point has been greatly explained by the Authors in this preprint, as opposite to other plots such as Van Krevelen diagrams which require the elemental composition of ions to be known prior to their generation. The calculation of true mass defect/excess ALSO requires the elemental composition of the ions to be known. The y-values of Kendrick plots are computed a) without knowing the compositions of the ions but only their m/z, and b) are comprised between -0.5 and 0.5 (or -1 and 0, or 0 and 1) regardless of m due to the aliasing of the formula m-round(m) (or floor or ceiling) while the mass defect/excess would keep increasing/decreasing with the number of atoms in a molecule above or below (-)0.5
Citation: https://doi.org/10.5194/egusphere-2022-1319-RC1 - AC1: 'Author response to all comments', Eleanor Browne, 19 Mar 2023
-
RC3: 'RC2', Anonymous Referee #2, 31 Jan 2023
General Comments:
Overall, I think that this manuscript provides a valuable demonstration of a “Kendrick analysis” (using terminology from RC1) that can be applied to complex mass spectrometry data (in this case a VOCUS-PTRTOFMS) without knowledge of the ion elemental composition to improve data visualization towards assisting in ion assignment, revealing chemical homologues, and potential chemical trends. The manuscript is generally well-written and straightforward, thoughtful about introducing KMD, REKMD, and SKMD, and definitely proves through the figures the potential for using effective scaling for allowing greater insight into atmospheric chemical measurements (e.g. the separation of nominally odd/even IUPAC mass ions into odd nitrogen containing or no/even nitrogen containing formulas). That being said, I agree with RC1’s concerns that the main formulation of SKM/SKMD not truly being novel per prior publication in Fouquet (2019) necessitates reframing how the manuscript is presented/worded. After this, I still see the manuscript being publishable and of interest to the atmospheric measurement community for bringing attention to a potentially valuable data processing method for the torrent of mass spectrometric data being collected in recent times.
Specific Comments:
- Line 172: the introduced term “reduced fraction” representing X/RIUPAC is not the most intuitive given values of X (as exampled in the cases of X=20, 24, 40) with RIUPAC as 16O results in expanding the mass scale instead of contraction—this seems more like a scaling factor whether enlarged or reduced. Consider changing this term and revising throughout the rest of the discussion.
- Line 303: The text would be enhanced to include more information such as the caption for Figure 7. That is, explain here that these points in Fig. 7a are not just simply omitted in Fib. 7b, but they would not appear in Fig. 7b because they would not fall within the SKMD range after m/z transformation.
- Lines 241, Line 251, Line 296: By using “REKMD” in these section headings, it signals to the reader that co-authors intend SKMD to be a sub-method/type of REKMD, yet the language earlier in text introducing SKMD as a concept makes it seem that it should be distinct as it is used in the analyses in these sections. Thus, I would have expected these section titles to be “SKMD” instead of “REKMD”. Given the comments from RC1 on nomenclature/reframing the paper generally as a “Kendrick analysis,” just be consistent with the chosen framing in the revised version.
- General comment on Figures 3, 4, 5: For further connection with text and enforcing of how mass defect analysis allows for visualization of homologous series, it would be helpful for labels on the figures pointing out the chemical families and their generic chemical formulations if possible.
Technical Corrections:
- It would be helpful perhaps in Fig. S1 to include vertical lines associated with the bounds of X presented in Eq. (7), which brings more focus to the linearity and equivalency of the two methods within those bounds.
- Figure 2 captions for c and d have inconsistent X values with those in subpanels of figure. Caption text for c) should have X = 24, d) should have X = 20.
- Line 148: Extra space before period should be deleted.
- Line 180: Change “result” to “results”.
- Line 278: Add period after “respectively.”
- Figure S4: Add panel labels to figure
References:
RC 1: https://doi.org/10.5194/egusphere-2022-1319-RC1
Fouquet, TNJ. The Kendrick analysis for polymer mass spectrometry. J Mass Spectrom. 2019; 54: 933– 947.
Citation: https://doi.org/10.5194/egusphere-2022-1319-RC3 - AC1: 'Author response to all comments', Eleanor Browne, 19 Mar 2023
Mitchell W. Alton et al.
Model code and software
SKMD panel Mitchell Alton, Harald Stark, Eleanor Browne https://github.com/BrowneLab/SKMD_Panel.git
Mitchell W. Alton et al.
Viewed
| HTML | XML | Total | Supplement | BibTeX | EndNote | |
|---|---|---|---|---|---|---|
| 451 | 200 | 25 | 676 | 53 | 9 | 8 |
- HTML: 451
- PDF: 200
- XML: 25
- Total: 676
- Supplement: 53
- BibTeX: 9
- EndNote: 8
Viewed (geographical distribution)
| Country | # | Views | % |
|---|
| Total: | 0 |
| HTML: | 0 |
| PDF: | 0 |
| XML: | 0 |
- 1