Correction: Meyer-Plath et al. A Practicable Measurement Strategy for Compliance Checking Number Concentrations of Airborne Nano- and Microscale Fibers. Atmosphere 2020, 11, 1254

Asmus Meyer-Plath; Daphne Bäger; Nico Dziurowitz; Doris Perseke; Barbara Katrin Simonow; Carmen Thim; Daniela Wenzlaff; Sabine Plitzko

doi:10.3390/atmos13020202

The authors wish to make the following corrections to this paper [1]:

1.

We missed noticing a flaw in Table 4 that resulted from an incorrect input value (25 nm instead of 20 nm) in the second row. Please replace:

Table 4. Number of pixels and images to acquire for analyzing 0.5 mm² or 0.5 mm²/5 = 0.1 mm² filter area. Image numbers of currently hardly or not yet manageable workload are marked in grey.

	$Filter Area to Analyze : 0.5 {mm}^{2}$			$Filter Area to Analyze : 0.1 {mm}^{2}$
Pixel Size s	Pixels to Acquire P_x ⋅ P_y	Images à 1280 × 960 Pixel	Images à 5120 × 3840 Pixel	Pixels to Acquire P_x ⋅ P_y	Images à 1280 × 960 Pixel	Images à 5120 × 3840 Pixel
$100 nm$	$0.05 \times 10^{9}$	$41$	$3$	$0.01 \times 10^{9}$	$8$	$1$
$20 nm$	$1.3 \times 10^{9}$	$651$	$41$	$0.16 \times 10^{9}$	$130$	$8$
$10 nm$	$5.0 \times 10^{9}$	$4069$	$254$	$1.0 \times 10^{9}$	$814$	$51$
$8.3 nm$	$7.3 \times 10^{9}$	$5907$	$369$	$1.5 \times 10^{9}$	$1181$	$74$
$5.0 nm$	$20 \times 10^{9}$	16,276	$1017$	$4.0 \times 10^{9}$	$3255$	$203$
$2.5 nm$	$80 \times 10^{9}$	65,104	$4069$	$16 \times 10^{9}$	13,021	$814$
$1.0 nm$	$500 \times 10^{9}$	406,901	25,431	$100 \times 10^{9}$	81,380	$5086$

Since the values resulting for the pixel size of 20 nm are of special relevance throughout the paper, we would like to correct them as follows.

Table 4. Number of pixels and images to acquire for analyzing 0.5 mm² or 0.5 mm²/5 = 0.1 mm² filter area. Image numbers of currently hardly or not yet manageable workloads are marked in grey.

	$Filter Area to Analyze : 0.5 {mm}^{2}$			$Filter Area to Analyze : 0.1 {mm}^{2}$
Pixel Size s	Pixels to Acquire P_x ⋅ P_y	Images à 1280 × 960 Pixel	Images à 5120 × 3840 Pixel	Pixels to Acquire P_x ⋅ P_y	Images à 1280 × 960 Pixel	Images à 5120 × 3840 Pixel
$100 nm$	$0.05 \times 10^{9}$	$41$	$3$	$0.01 \times 10^{9}$	$8$	$1$
$20 nm$	$1.3 \times 10^{9}$	$1017$	$64$	$0.25 \times 10^{9}$	$203$	$13$
$10 nm$	$5.0 \times 10^{9}$	$4069$	$254$	$1.0 \times 10^{9}$	$814$	$51$
$8.3 nm$	$7.3 \times 10^{9}$	$5907$	$369$	$1.5 \times 10^{9}$	$1181$	$74$
$5.0 nm$	$20 \times 10^{9}$	16,276	$1017$	$4.0 \times 10^{9}$	$3255$	$203$
$2.5 nm$	$80 \times 10^{9}$	65,104	$4069$	$16 \times 10^{9}$	13,021	$814$
$1.0 nm$	$500 \times 10^{9}$	406,901	25,431	$100 \times 10^{9}$	81,380	$5086$

2.

The horizontal separators of Table 5 before and after “Objects to Be Counted as WHO-Analogue Fibers” were removed. This disimproves the readability of the table since this text is a header for the second part of the table, as is the text “Objects Not to Be Counted as WHO-Analogue Fibers” is a header for the first part of the table. A suggestion for the new layout with two additional horizontal lines is shown subsequently. Please replace:

Table 5. Categories for categorizing respirable particles according to morphology, exemplified by example images. The length of the scale bar is 2 µm.

Objects Not to Be Counted as WHO-Analogue Fibers

	Not fiber-shaped agglomerates with $L / D < 3$

Short individual fibers with $L < 5 µ m$ and $L / D > 3$	Short fiber-shaped agglomerates with $L < 5 µ m$ and $L / D > 3$
Objects to Be Counted as WHO-Analogue Fibers

Long individual fibers with $L \geq 5 µ m$ and $D < 3 µ m$ and $L / D > 3$	Long fiber-shaped agglomerates with and $L \geq 5 µ m$ , $D < 3 µ m$ and $L / D > 3$

with

Table 5. Categories for categorizing respirable particles according to morphology, exemplified by example images. The length of the scale bar is 2 µm.

Objects Not to Be Counted as WHO-Analogue Fibers

	Not fiber-shaped agglomerates with $L / D < 3$

Short individual fibers with $L < 5 µ m$ and $L / D > 3$	Short fiber-shaped agglomerates with $L < 5 µ m$ and $L / D > 3$
Objects to Be Counted as WHO-Analogue Fibers

Long individual fibers with $L \geq 5 µ m$ and $D < 3 µ m$ and $L / D > 3$	Long fiber-shaped agglomerates with and $L \geq 5 µ m$ , $D < 3 µ m$ and $L / D > 3$

3.

In Table 11, we preferred if the header text “Workflow” was centered relative to the left column and the text “Sec.” centered relative to the right column that contains Section numbers. Please replace:

Table 11. Data evaluation workflow schematized as Nassi-Shneiderman-like diagram.

with

Table 11. Data evaluation workflow schematized as Nassi-Shneiderman-like diagram.

4.: The symbol $p_{H}^{s}$ in Equation (11) was corrupted. Please replace:

$α \overset{!}{\geq} p \frac{S}{H} (\hat{N}) = \sum_{k = 0}^{\hat{N}} \overset{\overset{P (k; H_{S})}{⏞}}{\frac{H_{S}^{k}}{k!} e^{- H_{S}}} \overset{α = p_{H}^{S}}{\Rightarrow} H_{S} (\hat{N}; α) = \frac{1}{2} F_{χ^{2}}^{- 1} (1 - α; 2 (\hat{N} + 1)) .$

(11)

with

$α \overset{!}{\geq} p_{H}^{S} (\hat{N}) = \sum_{k = 0}^{\hat{N}} \overset{\overset{P (k; H_{S})}{⏞}}{\frac{H_{S}^{k}}{k!} e^{- H_{S}}} \overset{α = p_{H}^{S}}{\Rightarrow} H_{S} (\hat{N}; α) = \frac{1}{2} F_{χ^{2}}^{- 1} (1 - α; 2 (\hat{N} + 1)) .$

(11)

5.

In Table A2, the letter “alpha” was incorrectly replaced by the letter “mu”. The symbol “alpha” stands for significance level throughout the text. The same applies to

\hat{N}

which was replaced with (non-hat, non-italics) N. Please replace:

Table A2. Upper and lower limits of twin hypothesis testing for Frequentist (L_T and H_T) and Bayesian theorem (L_G) probability intervals as calculated from Equations (A5), (A6) and (A12) for

\hat{N}

observed fibers and a significance level of μ = 5%. Gray areas indicate fiber counts with relatively large intervals.

Table A2. Upper and lower limits of twin hypothesis testing for Frequentist (L_T and H_T) and Bayesian theorem (L_G) probability intervals as calculated from Equations (A5), (A6) and (A12) for

\hat{N}

observed fibers and a significance level of μ = 5%. Gray areas indicate fiber counts with relatively large intervals.

Probability Interval Limits and Relative Errors for N Observed Fibers and μ = 5% Significance
δH_T	460%	260%	190%	130%	84%	65%	43%	32%	22%	17%
H_T	5.6	7.2	8.8	11.7	18.4	24.7	42.8	65.9	122	176
$\hat{N}$	1	2	3	5	10	15	30	50	100	150
L_T	0	0.2	0.6	1.6	4.8	8.4	20.2	37.4	81.4	127.0
δL_T	97%	88%	79%	68%	52%	44%	33%	26%	19%	15%
L_G	0.2	0.6	1.1	2.2	5.5	9.1	21.1	38.0	82.3	127.9
δL_G	76%	69%	64%	56%	45%	39%	30%	24%	18%	15%

with

Table A2. Upper and lower limits of twin hypothesis testing for Frequentist (L_T and H_T) and Bayesian theorem (L_G) probability intervals as calculated from Equations (A5), (A6) and (A12) for

\hat{N}

observed fibers and a significance level of α = 5%. Gray areas indicate fiber counts with relatively large intervals.

Table A2. Upper and lower limits of twin hypothesis testing for Frequentist (L_T and H_T) and Bayesian theorem (L_G) probability intervals as calculated from Equations (A5), (A6) and (A12) for

\hat{N}

observed fibers and a significance level of α = 5%. Gray areas indicate fiber counts with relatively large intervals.

Probability Interval Limits and Relative Errors for $\hat{N}$ Observed Fibers and α = 5% Significance
δH_T	460%	260%	190%	130%	84%	65%	43%	32%	22%	17%
H_T	5.6	7.2	8.8	11.7	18.4	24.7	42.8	65.9	122	176
$\hat{N}$	1	2	3	5	10	15	30	50	100	150
L_T	0	0.2	0.6	1.6	4.8	8.4	20.2	37.4	81.4	127.0
δL_T	97%	88%	79%	68%	52%	44%	33%	26%	19%	15%
L_G	0.2	0.6	1.1	2.2	5.5	9.1	21.1	38.0	82.3	127.9
δL_G	76%	69%	64%	56%	45%	39%	30%	24%	18%	15%

6.: In Appendix A.3, are the two hyperlinks broken since the text of the adjacent line was not included when creating the link. They must read:
● https://functions.wolfram.com/GammaBetaErf/InverseGammaRegularized3 (accessed on 23 December 2021)
● https://functions.wolfram.com/webMathematica/FunctionEvaluation.jsp?name=InverseGammaRegularized3 (accessed on 23 December 2021)

7.: Equation (A7) was corrupted with respect to the exponent $k$ , the letter $\hat{N},$ the exponent $e^{- H_{S}}$ and $H_{S}$ in the under-bracket. Please replace:

$\overset{p_{H}^{S} (N) = α}{\overset{︷}{\sum_{k = 0}^{\hat{N}} \frac{H_{S^{k}}}{k!} e^{- N_{S}}}} + \underset{C L (L_{G} \leq N \leq H_{T} ∣ \hat{N})}{\underset{︸}{\int_{0}^{H_{S}} \overset{G (N; \hat{N})}{\overset{︷}{\frac{N^{\hat{N}}}{\hat{N}!} e^{- N}}} d N}} = 1 .$

(A7)

with

$\overset{p_{H}^{S} (\hat{N}) = α}{\overset{︷}{\sum_{k = 0}^{\hat{N}} \frac{H_{S}^{k}}{k!} e^{- H_{S}}}} + \underset{C L (0 \leq N \leq H_{S} ∣ \hat{N})}{\underset{︸}{\int_{0}^{H_{S}} \overset{G (N; \hat{N})}{\overset{︷}{\frac{N^{\hat{N}}}{\hat{N}!} e^{- N}}} d N}} = 1 .$

(A7)
7.: Equation (A11) was corrupted with respect to the sign in $e^{- H_{T}}$ and the non-captital exponent symbol $k$ . Please replace

$\overset{p_{H}^{T} (\hat{N}) = \frac{α}{2}}{\overset{︷}{\sum_{k = 0}^{\hat{N}} \frac{{H_{T}}^{K}}{k!} e^{H_{T}}}} + \underset{C L (L_{G} \leq N \leq H_{T} ∣ \hat{N})}{\underset{︸}{\int_{L_{G}}^{H_{T}} \overset{G (N; \hat{N})}{\overset{︷}{\frac{N^{\hat{N}}}{\hat{N}!} e^{- N}}} d N}} + \overset{= : p_{L}^{G} (\hat{N}) = \frac{α}{2}}{\overset{︷}{\sum_{k = \hat{N} + 1}^{\infty} \frac{{L_{G}}^{K}}{k!} e^{- L_{G}}}} = 1$

(A11)

with

$\overset{p_{H}^{T} (\hat{N}) = \frac{α}{2}}{\overset{︷}{\sum_{k = 0}^{\hat{N}} \frac{{H_{T}}^{k}}{k!} e^{- H_{T}}}} + \underset{C L (L_{G} \leq N \leq H_{T} ∣ \hat{N})}{\underset{︸}{\int_{L_{G}}^{H_{T}} \overset{G (N; \hat{N})}{\overset{︷}{\frac{N^{\hat{N}}}{\hat{N}!} e^{- N}}} d N}} + \overset{= : p_{L}^{G} (\hat{N}) = \frac{α}{2}}{\overset{︷}{\sum_{k = \hat{N} + 1}^{\infty} \frac{{L_{G}}^{k}}{k!} e^{- L_{G}}}} = 1$

(A11)

The authors would like to apologize for any inconvenience caused to the readers by these changes.

Reference

Meyer-Plath, A.; Bäger, D.; Dziurowitz, N.; Perseke, D.; Simonow, B.K.; Thim, C.; Wenzlaff, D.; Plitzko, S. A Practicable Measurement Strategy for Compliance Checking Number Concentrations of Airborne Nano- and Microscale Fibers. Atmosphere 2020, 11, 1254. [Google Scholar] [CrossRef] [Scilit]

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