*2.8. QTL Mapping of P. capsici Resistance and Candidate Gene Prediction*

QTL analysis was identified by r/QTL software using CIM methods [47,48]. The LOD score thresholds for evaluating the statistical significance of the QTL effects were established using 1000 permutations (*p* < 0.05). The predicted genes within the target QTL interval were determined by comparison with the annotated Zunla-1 and CM334 reference genomes (http://peppersequence.genomics.cn, accessed on: 20 January 2019). The function of genes identified in the candidate regions was manually determined by BLASTX (https://blast.ncbi.nlm.nih.gov/, accessed on: 20 January 2019). In addition, the predicted genes were further annotated based on KEGG (https://www.kegg.jp/kegg/, accessed on: 20 January 2019), COG (http://www.ncbi.nlm.nih.gov/COG/, accessed on: 20 January 2019), Swiss-Prot (http://www.ebi.ac.uk/uniprot/ accessed on: 20 January 2019), and NR (https://blast.ncbi.nlm.nih.gov/ accessed on: 20 January 2019) databases.


Preface

This Special Issue of *Coatings* is focused on the study of different photocatalyst-based coatings for developing self-cleaning, air-purifying and antibacterial properties. In this case, a wide variety of photocatalysts (TiO2, Si-TiO2, TiO2−*x*N*y*, Ag-TiO2, Mo-TiO2, ZnO, SnO2-Ag, Nb2O5 and C60 fullerene) were evaluated towards the removal of different molecules. Similarly, substrates such as glass, silica, sapphire, polycarbonate, aluminium, stainless steel, concrete and mortar were included in this issue. This information certainly contributes to a better understanding of the photocatalytic removal of different molecules (e.g., *Escherichia coli*, *Staphylococcus aureus*, resazuring, rhodamine B, methylene blue, Demeton-S, 2-chloroethyl phenyl sulfide (CEPS) and NO*x* (NO and NO2)) and the coating technologies required for such performances. Based on these interesting results, I encourage you to read through this Special Issue and use the valuable information provided therein to help us move forward in the exciting area of photocatalytic coatings for developing air-purifying, self-cleaning, and antimicrobial properties.

Anibal Maury-Ramirez *Guest Editor*

Chapter 1: Photocatalytic Removal of Microorganisms


**4. Conclusions**

Photoelectrochemical biosensors have shown a very recent development, which came later than other biosensors due to their higher complexity and difficulty to achieve. Nevertheless, they provide better performance with respect to background signal suppression and the ability to switch the sensor ON and OFF. Moreover, the larger number of components opens the door to tailor on-demand sensors that are not only better suited to specific applications than regular biosensors, but have also shown new ways to create and analyze a sensing signal. Future work will focus on new interfaces electrode-semiconductor and semiconductor-macrobiomolecule—where the optimization can be carried out—while increasing the sensitivity and selectivity of the sensor. Another research trend that allows the inclusion of light-dependent sensors is the selection of the excitation wavelength, which opens plenty of possibilities of multi-sensing platforms by a mere decomposition of white light.

**Author Contributions:** This review has been conceptualized by M.P. and M.d.B. The selection of articles to review was performed by M.P. and M.d.B. Writing and original draft preparation was performed by M.P., M.d.B. and G.L.-L. Editing was performed by M.P., M.d.B. and G.L.-L. Project administration was performed by M.P. and M.d.B. Funding acquisition was performed by M.P. and M.d.B. All authors have read and agreed to the published version of the manuscript.

**Funding:** M. del Barrio acknowledges funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 713366. G. Luna-López wishes to thank to "Comunidad de Madrid" and European Structural Funds for their financial support to FotoArt-CM project (S2018/NMT-4367). M. Pita thanks the Retos MCIU/AEI/FEDER, EU for funding project RTI2018-095090-B-I00.

**Conflicts of Interest:** The authors declare no conflict of interest.


**2.1 Study area**

*Resources of Water*

variations.

ity of water.

results of this meeting have been criticized by several scientific sectors because of their lack of ambition, so that it is valuable to continue making visible the importance of water resources studies and how they will be affected by future climate

In a national context, available water should not be a problem for Chile since it is one of the countries with the highest amounts of water per person [1]. From the year 1970 to 2000, Chile averaged an annual rainfall of 1006 mm (main input) and evapotranspiration of 311 mm as main output, so it has 695 mm of surplus [2]. In

Nonetheless, this significant global amount hides a great spatio-temporal variability depending on natural and socio-economic features of each region. A good example of this contrast between regions is the existing difference between the southern regions where water is abundant but people are few and the northern and central ones where population densities are too high in comparison to the availabil-

There are many situations in which natural conditions are combined with factors, such as economics, to give place to a long water crisis in Chile [3]. For example, if economic activities by sectors are considered, the largest user of water resources in Chile is agriculture, which consumes up to 75% of the water resources at a national scale [4]. This could be justified because it supplies water for an irrigated land of larger than 1 million ha, which is mostly located in the central zone of Chile [5]. Irrigated areas have significantly increased the use of water resources in the last

Among themselves, the crops of avocado (*Persea americana*) have increased 43% in terms of land surface during the last decades, Chile being the second producer country in the world. Avocado is indeed a species that records a water print of 715 l/kg exported, significantly higher than more traditional crops [6]. Most of the Chilean economy is based on natural resources, with a strong export-focused activity [7]. Despite this, in many regions of the country, the uncontrolled exploitation exceeds the actual availability of water resources. This has led to declare numerous

This situation could be even more worrying according to the effects of climate change foreseen by the scientific community. In the particular case of Chile, a reduction between 20 and 40% of total rainfall has been already reported [8]. Added to this, the lack of vegetation management in the upper areas of the watersheds and the elevation of the isotherms have increased water demand and reduced snow deposits, respectively, giving place to a strong decrease of river discharge. An intensive demand for water resources and a decrease in them requires knowing the water availability both in the present and in the future, in order to develop hydro-

Taking into account the abovementioned, this work is focused on the analysis of both the current and future water balance of each one of the administrative regions of Chile since they are the appropriated scale in which decisions on land planning should be made. The reasons of choice this scale work is twofold; on the one hand, Chile is divided into longitudinal regions easily assignable to climatic belts, and, on the other hand, they are the regional governments who are in charge of the regional administrations and consequently in charge of their land and water management. In addition, this research should be also useful to become aware of the upcoming effects of climate change, foreseen by reliable predictive models in every scenario (optimistic and pessimistic), that serve to discuss about the sustainability of many

decade. Besides, some products have increased the area for its cultivation.

logical plans to guarantee economic and environmental sustainability.

regions as depleted in both surface and groundwater [4].

of water susceptible to be

terms of storage, it has supposed to be more than 500 km3

used in human activities every year.

**10**

of the current human activities.

The study was carried out in the whole continental territory of Chile, excluding its islands and the Chilean Antarctic Territory. The size of the study area is 4270 km of distance from north to south and a width (from west to east) ranging from 90 to 445 km involving a great sort of different climate types (cold, temperate, Mediterranean, desert, and high mountain). The limits of the Continental Chile are Peru and Bolivia in the north, the Andes in the east, the Pacific Ocean in the west, and the Drake Passage in the south, Argentina being the country in whom Chile shares more kilometers of border.

This territory is inhabited by around 18 million people with a relatively high standard of living (according to the main macroeconomic indicators) within the context of Latin America. It is divided since 2017 into 16 regions, 56 provinces, and 346 communes. Each region has its own regional government headed by the intendant and the member of the Regional Council (elected every 4 years). These regions keep its original Roman number from I to XII following a gradient from north to south. The Metropolitan Region has the number XIII; and three new regions recently created have continued this tradition (**Figure 1**).

**Figure 1.** *Geographical distribution of the Chilean regions.*


4.  Generalization process

the LETKF analyses.

NN activation.

i�m,j�m, k�m ¼ yo

ðm ¼ 1, 2, …, MÞ

8 < :

jÞ

2 þ zp � yo

process and also adds positive flags in the observation mask.

k � �2

> i , yo j , yo

ijk ð Þ 6 � γ r2 ijk þX 6

0 ð Þ if there is no observation

where byo is the weighted observation, M is the number of discrete layers considered around

Each observation's influence computed on a certain grid point is a new location, hereafter referred to as pseudo-observation, which adds values to the three input vectors to NN training

Then, the grid points to be considered in MLP-DA analysis are greater than grid points considered to LETKF analysis, although these calculations are made without interference on LETKF system. The back-propagation algorithm stops the training process using the criteria cited at item 6 above (Section 3), after obtaining the best set of weights; it is a function of smallest error between the MPL-NN analysis and the target analysis (e.g., when the root mean square error between the calculated output and the input target vector is less than 10�5

learning process is the same for each MLP of the set of 30 NN and takes about 15 min to get the fixed weights before the MLP-DA data assimilation cycle or generalization process of

The training is performed with combined data from January, February, and March of 1982, 1983, and 1984, and in generalization process, MLP-DA is able to perform analyses similar to

The generalization process is indeed the data assimilation process. The MLP-DA results a global analysis field. The MLP-DA activation is entering by input values (only 6 hours forecast and observations) at each grid point once, with no data used in the training process. The input vectors are done at grid model point, where it is marked (by positive flag mask) with observation or pseudo-observation (Eq. 10). The procedure is the same for all NN but one NN for each region, and each prognostic variable has own connection weights. All NNs have one hidden layer, with the same number of neurons for all regions. The regional grid points are put in the global domain to make the analysis field after generalization process of the MLP-DA, e.g., the activation of 30 NN results a global analysis. The regional division is only for inputting each

1 if there is observation; and : γnew ¼ γold þ 1 � �

kÞ is the coordinate of the observation, and γ is a counter of grid points with

l¼1 αl yo

i�m,j�m, k�m r2 ijk

, where (xp, yp, zp) is coordinate of the grid point, and

kÞ. If γ = 6, there is no influence to be considered.

(10)

). The

The input and output values of prognostic variables (ps, u, v, T, and q) are processed on grid model points for time integrations to an intermittent forecasting and analysis cycle. Taking into account the pseudo-observation (Eq. 10), two grid layers (M = 2) around a given observation are considered.

The results show the comparison of analysis fields, generated by the MLP-DA, the LETKF, and the true model fields. The global surface pressure fields (at 11 January 1985 1800 UTC) and differences between the analyses are shown in Figure 4. The analysis fields and the differences between both assimilation, for 11 January 1985 at 1800 UTC at 950 and 500 hPa are also shown, for at 18 UTC at levels 950 hPa (near surface) and 500 hPa are also shown, for T, u, v, and q meteorological global fields, in Figures 5–10. These results show that the application of MLP-DA, as an assimilation system, generates analyses similar to those calculated by the LETKF system. Sub-figure (d) from Figures 5–10 shows very small differences between the MLP-DA and LETKF analyses. The difference field of absolute temperature (K) at 500 hPa is about 3 degrees; and the difference field of humidity at 950 hPa is about 0.002 kg/kg.

Figure 4. Surface pressure (PS) [Pa]—Jan/11/1985 at 18 UTC (a) LETKF analysis, (b) ANN analysis, (c) true model, and (d) differences analysis.

Figure 5. Absolute temperature (T) [K] Fi-950 hPa, Jan/11/1985 at 18 UTC. (a) LETKF analysis, (b) ANN analysis, (c) true model, and (d) differences analysis.

Figure 6. Absolute temperature (T) [K] at 500 hPa—Jan/11/1985 at 18 UTC (a) LETKF analysis, (b) ANN analysis, (c) true model, and (d) differences analysis.

Figure 7. Zonal wind component (u) [m/s] at 500 hPa—Jan/11/1985 at 18 UTC. (a) LETKF analysis, (b) ANN analysis, (c) true model, and (d) differences analysis.

Data Assimilation by Artificial Neural Networks for an Atmospheric General Circulation Model http://dx.doi.org/10.5772/intechopen.70791 279

Figure 8. Meridional wind component (v) [m/s] fields at 500 hPa—Jan/11/1985 at 18 UTC (a) LETKF analysis, (b) ANN analysis, (c) true model, and (d) differences analysis.

Figure 5. Absolute temperature (T) [K] Fi-950 hPa, Jan/11/1985 at 18 UTC. (a) LETKF analysis, (b) ANN analysis, (c) true

Figure 6. Absolute temperature (T) [K] at 500 hPa—Jan/11/1985 at 18 UTC (a) LETKF analysis, (b) ANN analysis, (c) true

Figure 7. Zonal wind component (u) [m/s] at 500 hPa—Jan/11/1985 at 18 UTC. (a) LETKF analysis, (b) ANN analysis,

model, and (d) differences analysis.

278 Advanced Applications for Artificial Neural Networks

model, and (d) differences analysis.

(c) true model, and (d) differences analysis.

Monthly average of absolute temperature analyses fields was obtained. The field of differences between the analyses (LETKF and MLP-DA) for data assimilation cycles is shown in Figure 11. The differences are slightly larger in some regions, such as the northeast regions of North America and South America.

The root mean square error (RMSE) of the absolute temperature analyses related to true model is calculated by fixing a point at longitude (87 W) for all latitude points. Figure 12 shows the temperature RMSEs for the entire period of the assimilation cycle (January 1985). Subfigure (a) for Figure 12 shows the RMSE of the LETKF analysis by line and the RMSE of the MLP-DA analysis by circles; and subfigure (b) for Figure 12 shows the differences between LETKF and MLP-DA analyses RMSE. The differences are less than 103 .

Figure 9. Specific humidity (q) at 950 hPa—Jan/11/1985 at 18 UTC (a) LETKF analysis, (b) ANN analysis, (c) true model, and (d) differences analysis.

Figure 10. Specific humidity (q) at 950 hPa—Jan/11/1985 at 18 UTC (a) LETKF analysis, (b) ANN analysis, (c) true model, and (d) differences analysis.

Figure 11. Differences field of the average of absolute temperature MLP-DA analysis and LETKF analysis for the assimilation cycle.

Figure 12. Meridional root mean square error for entire period of the assimilation cycles. RMSE analyses to the "true" state to (a) the errors of the LETKF analysis (line) and the errors of MLP-DA analysis (circles) to the absolute temperature at 500 hPa. (b) Differences of RMSE analyses.

#### 4.1. Computer performance

Several aspects of modeling stress computational systems and push the capability requirements. These aspects include increased grid resolution, the inclusion of improved physics processes and concurrent execution of earth-system components, and coupled models (ocean circulation and environmental prediction, for example).

Often, real-time necessities define capability requirements. In data assimilation, the computational requirements become much more challenging. Observations from Earth-orbiting satellites in operational numerical prediction models are used to improve weather forecasts. However, using the amount of satellite data increases the computational effort. As a result, there is a need for an assimilation method able to compute the initial field for the numerical model in the operational window time to make a prediction. At present, most of the NWP centers find it difficult to assimilate all the available data because of computational costs and the cost of transferring huge amounts of data from the storage system to the main computer memory.

The data assimilation cycle has a recent forecast and the observations as the inputs for assimilation system. The described MLP-DA system produced an analysis to initiate the actual cycle. This time simulation experiment is for January 1985 (28 days). There were 2075 observations inserted at runs of 0600 and 1800 UTC for surface variables, and 12,035 observations inserted at runs of 0000 and 1200 UTC for all upper layer variables.

The LETKF data assimilation cycle initiates running the ensemble forecasts with the SPEEDY model, and each analysis produced to each member at the latter LETKF cycle to result 30 (members) 6-hour forecasts; the second step is to compute the average of those forecasts. After, with a set of observations and the mean forecast, the LETKF system is performed. The LETKF cycle results one analysis to each member for the ensemble and one average field of the ensemble analyses. The MLP-DA data assimilation cycle is composed by the reading of 6-hour forecast of SPEEDY model from latter cycle and reading the set of observations to the cycle time, the division of input vectors, the activation of MLP-DA, and the assembly of output vectors to a global analysis field.

The MLP-DA runtime measurement initiates after reading the 6-hour forecast of SPEEDY model from latter cycle and the set of observations. The time of generalization includes the division of observation and prediction fields into regions, and the execution of the various trained networks by gathering all regions in a global analysis. It initiates after reading the mean 6-hours forecast of SPEEDY model and the set of observations. The LETKF time includes the results of 30 analyses and one mean ensemble analysis. The comparison in Table 1 is the data assimilation cycles for the same observations points and the same model resolution to the same time simulations. LETKF and MLP-DA executions are performed independently. Considering the total execution time of those 112 cycles simulated, the computational performance of the MLP-DA data assimilation is better than that obtained with the LETKF approach. These results show that the computational efficiency of the NN for data assimilation to the SPEEDY model, for the adopted resolution, is 90 times faster and produces analyses of the same quality (Table 1). Considering only the analyses execution time of those 112 data assimilation processes simulated, the computational efficiency of MLP-DA is 421 times faster than LETKF process. Table 2 shows the mean execution time of each element to one cycle of the LETKF data assimilation method (ensemble forecast and analysis) and the MLP-DA method (model forecast and analysis). The computational efficiency of one MLP-DA execution keeps the relationship about speed-up, comparing with one LETKF execution (421 times faster). Details for this experiment can be found in Ref. [6].

4.1. Computer performance

at 500 hPa. (b) Differences of RMSE analyses.

and (d) differences analysis.

280 Advanced Applications for Artificial Neural Networks

assimilation cycle.

Several aspects of modeling stress computational systems and push the capability requirements. These aspects include increased grid resolution, the inclusion of improved physics

Figure 12. Meridional root mean square error for entire period of the assimilation cycles. RMSE analyses to the "true" state to (a) the errors of the LETKF analysis (line) and the errors of MLP-DA analysis (circles) to the absolute temperature

Figure 10. Specific humidity (q) at 950 hPa—Jan/11/1985 at 18 UTC (a) LETKF analysis, (b) ANN analysis, (c) true model,

Figure 11. Differences field of the average of absolute temperature MLP-DA analysis and LETKF analysis for the

Table 1. Total running time of 112 cycles of complete data assimilation (analysis and forecasting).

Table 2. Mean time of one execution (hour:min:sec:lll).


*4.2.1 SLE and renal involvement*

The revised American College of Rheumatology (ACR) 1997 criteria specifies that a patient can be diagnosed with SLE if 4 of 11 criteria are met at any interval of observation (**Table 2**). Renal involvement can be considered if patient developed proteinuria of >0.5/day or appearance of cellular cast (red cells, haemoglobin, granular, tubular or mixed) [57]. The 2012 Systemic Lupus International Collaborating Clinics (SLICC) criteria divided SLE features into 11 clinical and 6 immunologic criteria, where SLE can be fulfilled by a) biopsy-proven LN in presence of ANA or anti-DNA antibodies or b) meeting ≥4 of 17 criteria, with at least 1 criterion from each division [58].

European League Against Rheumatism (EULAR)/ACR published a new set of criteria for SLE diagnosis in 2019 [58]. It employs the strategy that ANA must be positive for the diagnosis to be considered, followed by 10 domains with different individual weightage; diagnosis can be made if total score reaches 10 points, again with renal involvement carrying a high weight between 4 and 10 depending on the renal manifestations (**Table 2**) [59].


Within-group comparisons to assess the pre-post effect of the twelve sessions separately for each group revealed a significant difference in the parents' rating of the FBB-ADHS only for the NIRS-group (*z* = −2.25, *p* = 0.024, *r* = −0.531, see **Table 5** and **Figure 8**). A trend for a lower FBB-ADHS score was observed for the EEG-group (*z* = −1.90, *p* = 0.058, *r* = −0.447) and the EMGgroup (*z* = −1.84, *p* = 0.066, *r* = −0.434).

Comparing the three groups in the differences of parents' ratings of the FBB-ADHS (post test 1 values minus pretest values), there were no significant differences between the groups (NIRS: *Mdn* = −0.65, *IQR* = −1.03 − −0.11; EEG: *Mdn* = −0.60, *IQR* = −1.06 – 0.03; EMG: *Mdn* = −0.20, *IQR* = −0.38–0.04; *H*(2) = 2.72, *p* = 0.256).

### **DISCUSSION**

In this pilot study NIRS-neurofeedback as a new method of neurofeedback training for children with ADHD was investigated. Hemodynamic brain activity in the dorsolateral prefrontal cortex was measured and fed back. Children should learn to gain control over their brain activity in 12 training sessions and 3 weeks of transfer exercises. Primary outcome was the effect on ADHD symptoms rated by parents. Teachers' ratings of symptoms as well as ratings of associated behavioral symptoms by parents and teachers, self-rated quality of life and performance in a computer based attention task were assessed. In addition, a comparison with two other feedback methods (EEG, EMG) was carried out.

### **NIRS -NEUROFEEDBACK—EFFECTS AND FEASIBILITY**

As primary outcome, parents' ratings of ADHD symptoms in the NIRS-group were significantly reduced 4 weeks and 6 months after the training. Teachers' ratings of ADHD symptoms showed a significant reduction 4 weeks after the end of treatment. Attention and impulsivity in the computer based attention test TAP improved significantly (Go/NoGo: speed,

Mdn = median, IQR = interquartile range, r = effect size, bold = significant at α ≤ 0.05, FBB-ADHS = Rating scale for ADHD.

variability, commissions; Flexibility: variability, commissions). According to these results, NIRS-neurofeedback might be as effective in reducing the main symptoms of ADHD, as it was shown before in randomized controlled studies for EEGneurofeedback (e.g., Gevensleben et al., 2009; Meisel et al., 2013).

The effect size for the parents' ratings of ADHD symptoms in the NIRS-group was high for pre-post comparison (*r* = −0.587). This is comparable to effect-sizes of EEGneurofeedback as reported in the meta-analysis of Arns et al. (2009). Here, high effect sizes for inattention and impulsivity and medium effect sizes for hyperactivity in pre-post designs of EEG-neurofeedback-studies were observed. With larger sample sizes in NIRS-neurofeedback, a differentiated analysis of effects on symptom groups (inattention, impulsivity, hyperactivity) could be conducted, allowing detailed comparisons with effect sizes of EEG-neurofeedback.

The general question of feasibility of NIRS-neurofeedback for children with ADHD can be answered by taking into account different variables. On the one hand, the technical implementation was possible; on the other hand, children and parents accepted the procedure. All nine children took part in all twelve sessions. At the beginning of each training session, motivation was rated on a 4-point smiley scale (1 = totally motivated, 2 = quite motivated, 3 = not much motivated, 4 = not motivated at all). The mean motivation over all sessions and children was high (*M* = 1.51; *sd* = 0.89). Parents rated their satisfaction with the training on a six-item scale 4 weeks and 6 months after the training. They were asked to rate satisfaction with the training, satisfaction with the trainer, empathy of the trainer, trust in the training, trust in the competence of the trainer and recommendation of the training on a 7-point scale (endpoints: 0 = not at all, 7 totally). The mean of parent satisfaction 4 weeks and 6 months after training was high (post test 2: *M* = 5.48, *sd* = 0.58, follow-up test: *M* = 5.57, *sd* = 0.57). Additionally, parents were asked for adverse side effects in relation to measurement and training at all measurement points. No serious adverse events were documented. Two children reported to have had transient headaches directly after some of the training sessions, possibly caused by the fixation of the probe set. In conclusion, NIRS-neurofeedback seems to be a feasible and accepted intervention for children with ADHD.

### **COMPARISON WITH EEG-NEUROFEEDBACK AND EMG-FEEDBACK AND FUTURE DIRECTIONS**

The NIRS-group showed a significant reduction of ADHD symptoms in parents' ratings after twelve training sessions. A trend towards decreased ADHD symptoms was observed for

the EEG- and the EMG-group. In the between group comparison there were no significant differences in symptom reduction. Despite the matching, the three groups differed significantly in some of the initial values of clinical impairment (quality of life and associated behavioral problems).

NIRS-neurofeedback was effective in the reduction of the main symptoms of ADHD and possibly more time-effective in comparison to EEG-neurofeedback. However, this interpretation has to be confirmed, due to the fact that differences in improvement after the 12 sessions did not reach significance, and that the initial values in quality of life and associated behavioral symptoms of the groups differed. Moreover, a completed intervention was compared with two uncompleted interventions, based on the assumption of a more rapid improvement with NIRS neurofeedback, and the sample sizes were small. For future studies, sample sizes have to be enlarged and a randomized controlled design is mandatory. NIRS-neurofeedback could enlarge the treatment options for ADHD, with the possible advantage of being a shorter intervention in comparison to EEG-neurofeedback. The analysis of NIRS-data throughout the training will hopefully allow conclusions as regards to the learning of self-regulation and number of sessions needed. Birbaumer et al. (2013) assume that faster learning of self-regulation of blood oxygenation in comparison to neuroelectricity is associated with the sensoric input processed for the vascular system allowing a faster development of an adequate response. Future studies should analyze the differences in the protocols and learning curves of NIRS- and EEG-neurofeedback to gain more insights into the underlying mechanisms of self-regulation. As regards to the different velocity of the feedback signals one might speculate that a slower signal facilitates learning. In the absence of any study investigating this issue it should be noted for future research.

As a limitation it has to be taken into account, that medication could have a distorting effect on the results: seven of nine children in each group received a medication with methylphenidate during the training. The effects of medication were not assessable in this study. It might be possible, that symptom reduction only occurs in less impaired children or because medication allows a better training. Larger sample sizes, subgroups with medicated and unmedicated children are necessary to control for effects of medication. As an example, results of the multicenter study (comparison of EEG- and EMG-feedback), show that effects of neurofeedback were independent of medication (Holtmann et al., 2014c) and the relationship between symptom severity and outcome is inverse.

Whether NIRS-neurofeedback can be implemented as a stand-alone or part of a multimodal treatment of ADHD will only be answered after studies with a corresponding design. A combination of different interventions according to individual forming of problems is another field of future research in the treatment of ADHD. A multi-center stepped care study dealing with severity-adapted combined interventions including SCP-neurofeedback will be conducted in Germany from February 2015 (ESCAlife: Evidence-based, Stepped Care of ADHS along the life-span)1 . Results could give a hint on additional effects of neurofeedback and medication.

NIRS-neurofeedback is a promising intervention for children with ADHD and can enlarge the range of options for a treatment of ADHD. Future studies should focus on randomized controlled designs. Especially the comparison with EEG-neurofeedback, and with its final rather than its intermediate outcome, is necessary to further support the assumption that NIRS-neurofeedback needs fewer sessions for comparable symptom reduction. It would also be important to clarify whether longer NIRS-neurofeedback training (i.e., with more than 12 sessions) yields further clinical improvement. For further development of NIRS-neurofeedback the identification of other possible feedback regions based on the growing number of NIRS-studies with children with ADHD is required. The prefrontal cortex plays a central role in ADHD. However, involving a greater database and identifying target regions according to symptomatology could lead to an evidencebased adaption of feedback protocols for individualized treatment of ADHD.

### **ACKNOWLEDGMENTS**

We strongly thank the children with ADHD, their parents and teachers for participating in this study. Additionally, we thank Ramona Taeglich, Judith Kittel and Raphaela Kuemmerle for their assistance and the involved staff of IZKS Mainz for providing data from the multicentric neurofeedback study. This work is based on the PhD dissertation of Anna-Maria Marx (Neurofeedback mittels Nah-Infrarot-Spektroskopie als Behandlungsmöglichkeit für Kinder mit einer Aufmerksamkeitsdefizit/Hyperaktivitätsstörung, University of Tuebingen, 2014). It was supported by the Bernstein Computational Neuroscience Program of the German Federal Ministry of Education and Research (Grant number: 01GQ0831). The multicenter study which provided the data of the SCPand EMG-feedback groups was supported by the German Research Foundation (Deutsche Forschungsgemeinschaft [DFG] HO 2503/4-1, BI 195/69-1). We acknowledge support by the Deutsche Forschungsgemeinschaft and the Open Access Publishing Fund of the University of Tuebingen.

### **REFERENCES**

1Project description: http://akip.uk-koeln.de/forschung-publikation/forsch ungsprojekte/fg\_esca\_06\_2014\_weg.pdf [14.09.2014]

computer interface system," in *Foundations of Augmented Cognition. Neuroergonomics and Operational Neuroscience*, eds D. D. Schmorrow et al. (Berlin Heidelberg: Springer Verlag), 699–708.

**Conflict of Interest Statement**: Anna-Maria Marx, Adrian Furdea, Yvonne Fuchsenberger, Holger Gevensleben, Daniel Brandeis, Ann-Christine Ehlis and Andreas J. Fallgatter declare no commercial or financial relationships that could be construed as a potential conflict of interest. Ute Strehl was paid for public speaking by Novartis, Medice, Neuroconn, the German Society for Biofeedback and Akademie König und Müller. Martin Holtmann served in an advisory or consultancy role for Lilly, Shire and Bristol-Myers Squibb, and received conference attendance support or was paid for public speaking by Bristol-Myers Squibb, Janssen-Cilag, Lilly, Medice, Neuroconn, Novartis and Shire. Christine M. Freitag received one time speaker's fees by Ely Lilly and Shire over the last 3 years. Tobias Banaschewski served in an advisory or consultancy role for Hexal Pharma, Lilly, Medice, Novartis, Otsuka, Oxford outcomes, PCM scientific, Shire and Viforpharma. He received conference attendance support and conference support or received speaker's fee by Lilly, Medice, Novartis and Shire. He is/has been involved in clinical trials conducted by Lilly, Shire and Viforpharma. The present work is unrelated to the above grants and relationships. Prof. Rothenberger is member of an advisory board and speakers' bureau of Lilly, Shire, Medice and Novartis. He got research and travel support and an educational grant from Shire and research support from the German Research Society. Where applicable, the above mentioned authors declare that the present work is unrelated to the above mentioned grants and relationships.

### *Received: 30 September 2014; accepted: 11 December 2014; published online: 07 January 2015*.

*Citation: Marx A-M, Ehlis A-C, Furdea A, Holtmann M, Banaschewski T, Brandeis D, Rothenberger A, Gevensleben H, Freitag CM, Fuchsenberger Y, Fallgatter AJ and Strehl U (2015) Near-infrared spectroscopy (NIRS) neurofeedback as a treatment for children with attention deficit hyperactivity disorder (ADHD)—a pilot study. Front. Hum. Neurosci. 8:1038. doi: 10.3389/fnhum.2014.01038*

*This article was submitted to the journal Frontiers in Human Neuroscience*.

*Copyright © 2015 Marx, Ehlis, Furdea, Holtmann, Banaschewski, Brandeis, Rothenberger, Gevensleben, Freitag, Fuchsenberger, Fallgatter and Strehl. This is an openaccess article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution and reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms*.

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These results indicate that the CIEDE2000 shows greater difference between the swatches from the cross-polarised workflow. The extent of the colour difference is in the perceptible range (>1) to the observer, which suggests an incremental improvement in the ability to distinguish between the colour of the surface characteristics of the metal item using the cross-polarised workflow.

It may be that this variation in colour is due to the deterioration or change to the gilt-finished ormolu surface. If this is the case, this comparison illustrates the ability to better differentiate between the areas where the finish is intact, document its present condition and better record any further changes.

**Fig. 12.** Comparison between unpolarised (left) and cross-polarised (right) diffuse albedo texture maps for item DC351. Swatches A and B (for both images) are sampled from identical locations and represent averaged colour values for identical areas on both maps.

A further observation is the presence of fine particulate matter on the item surface, e.g., dust, lint, etc. Typically, this matter can collect on an item depending on storage, or more likely, display conditions. As shown in Fig. 13, the presence of this is immediately obvious in the cross-polarised image texture and the derived specular map. This is due to the highly diffuse characteristics of the particulate matter. This is nearly indistinguishable in the unpolarised (i.e., typical) approach due to the occluding glare of the reflective surface from the lighting conditions. The ability to detect this could be valuable for fine-level assessment of condition, for example, of items before and after public display (where it may be exposed to uncontrolled environmental conditions), or before and after the item returns from a loan.

#### **3.3 Wood**

As a natural, organic material, wood can vary hugely in its visual characteristics. Its use for cultural artefacts is usually accompanied by different decorative and/or protective finishes that can include the use of pigments in paint application, varnishes and waxes, that can all alter its reflective properties. Fundamental differences such as softwoods versus hardwoods can govern many aspects of the visual appearance. Whilst items made from bare or natural wood might have a visually consistent presentation for the wood substrate, as an assembly an item might include metallic fixings or other inorganic materials. Like ceramics, wood is a dielectric material. Cross-polarised light has also been used for specific research applications into wood related to enhancing tree-ring inspection (Gärtner et al. 2015).

**Fig. 13.** Comparison between excerpts of item DC351 image texture maps showing diffuse albedo (unpolarised, left), diffuse albedo (cross-polarised, centre) and specular albedo (right).

### **Stirling Head (STC022)**

Item description: "*Oak roundel, part of a series of carvings that decorated the ceiling of the King's Presence Chamber at Stirling Castle. The pose and costume in this Head appears in contemporary paintings of flamboyant noblemen. He is shown wearing an elaborate and stylish quilted doublet. The Stirling Heads are constructed of 3 panels, originally only secured by glue. The great majority of the Heads, however, are in part constructed in 2 ply, an additional board or block having been placed over the middle board to enable the carver to model the central portion of the medallion in high relief. Nail holes are apparent in the borders which indicate the way in which the Heads were fixed to the ceiling.*" Item dimensions: diameter 762mm. (HES, Vernon Collections Management System, 'Object - STC022' accessed 25/10/21).

*Discussion and Interpretation*

Initially the specular map results are apparent across the entire surface of the Oak roundel. A subtle, consistent level of reflectance can be observed from the specular map in Fig. 14(C). Areas of obvious occlusion and a reduction in specular response from surface geometry can be found for carved recessed details, such as the figure's mouth, fingers and details of the clothing. This can be compared with the normal map in Fig. 14(B), showing a geometric correlation to these details.

Figure 15 compares an unpolarised photograph with a cross-polarised photograph, showing the veiling effect of the specular response for the underlying wood tone. Whilst the specular response does not appear to affect the legibility of wood grain, it does occlude the surface colour of the wood, particularly around the specular highlight in the image centre.

**Fig. 14.** Stirling Head - Detailed area excerpt of UV texture sheet maps in the following order left-to-right: (A) Diffuse albedo; (B) tangent-space surface normal; (C) specular albedo. Assession number STC022.

**Fig. 15.** Split image showing side-by-side results for photographs of item STC022 from (A) the cross-polarised setup (top half) and (B) unpolarised photograph (bottom half).

The 'figure' of wood (often simplified, or referred to, as 'grain') is a key feature of the material's appearance. It can provide key diagnostic information for inspection purposes, both in terms of identifying wood species and the orientation of the surface from cutting (Hoadley 2000, p. 25). Figure 16 illustrates an example wherein the characteristics of this figure can be seen. Initially there appear to be few differences between the crosspolarised and unpolarised results, however the specular albedo map and surface normal map reveal that the undulations of the surface geometry caused by the carved wood surface interacting with the figure of the wood to affect the reflectance characteristics. The specular map clearly captures the recesses and raised areas in detail, allowing more accurate visualisation and interrogation of the surfaces in the captured data.

**Fig. 16.** Comparison of item STC022 between excerpts from the diffuse albedo (cross-polarised, left), diffuse albedo (unpolarised, centre-left), specular albedo (difference product, centre-right) and tangent-space surface normal (right).

It was unclear from the outset of the project whether there would be an appreciable benefit from using the cross-polarised workflow for a wooden item. The possible benefits demonstrated above should be weighed against the increased fieldwork/data capture and processing time. This is particularly true for sensitive organic items that may normally be stored in a protective environment.

### **4 Conclusion**

Structure from Motion photogrammetry has become widely embraced as a powerful and flexible 3D data capture technique. However, as indicated in this paper more complex materials, surfaces and items can hinder robust and consistent results. The technique has seen development within the realm of computer imaging and rendering, which has driven more sophisticated modes of data capture and visualisation. However, best practices and guidance for geospatial application of photogrammetry is still primarily focussed on recording 'diffuse' surfaces within a measurable survey tolerance. This often neglects the rich and spatially varied material characteristics seen across cultural heritage that are able to be represented through sophisticated material shaders.

While not unlike a typical photogrammetry workflow, this cross-polarised method of capture provides information about cultural heritage artefacts that another technique could miss. Indeed, in some cases imperfections on the surface that are only revealed with these methods change the appearance of an object entirely.

More than improving the visualisation of artefacts, there are potential conservation applications in using richer material shaders and a greater depth of surface information, including:

The workflow described here is far more involved that the standard approach to single camera photogrammetry, extending the time required during both data capture and processing stages. That said, these results are promising when applied to documenting complex objects that are a challenge to capture using unpolarised light workflows. The improvements to the quality of image textures and the 3D data captured for these objects has been identified and explored for these cultural heritage artefacts. These items are exemplars of complex surfaces with varied materials, and spatially varied reflective properties. The work described here has established a foundation for further research in creating a standardised cross-polarised workflow in a heritage context in the future.

### **Appendix**

### **References**

**Open Access** This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

### **Author Index**

**A** Anagnostopoulos, Christos-Nikolaos 65

### **B**

Basiakoulis, Alexandros 103 Blersch, Daniel 34 Brumana, R. 77

**C** Chatzistamatis, Stamatis 65 Cliffen, Harriet 103

**E** E.Tsekouras, George 65 Efstathiou, Kyriakos 103 Efstathiou, Marianna 103

**F** Fröhlich, Christoph 34 Frost, Adam 131

**G** Georgiou, Rafaella 103 **H**

Haynes, Ronald 50 Held, Christoph 34

**I** Ioannides, Marinos 1

**J** Joncic, Nenad 103

**M** Mettenleiter, Markus 34 Millan, Elina Rodriguez 131 Mirashrafi, Sophia 131

**P** Patias, Petros 1

**S** Sánchez, Clara Molina 131

**V** Vacas-Madrid, David 131

**W**

Wilson, Lyn 131


5.1. Formulation of balances for NaOH (C, V) ) Br2 (C0, V0) system

#### 5.1.1. Approach II to GEB

Note that V0 mL of the titrand D composed of Br2 (N01)+H2O (N02) is titrated with V mL of titrant T composed of NaOH (N03)+H2O (N04). For the V0 + V mL of the D + T mixture, with the set of the species completed by Na+1 (N11, n11).

The balances can be formulated as follows:

$$\begin{aligned} f\_1 &= f(\mathbb{H}):\\ 2N\_1 + N\_2(1+2n\_2) + N\_3(1+2n\_3) + N\_4(1+2n\_4) + 2N\_5n\_5 + N\_6(1+2n\_6) + 2N\_7n\_7 + 8N\_8n\_8\\ 2N\_1 + 2N\_9n\_9 + 2N\_{10}n\_{10} + N\_{11}(1+2n\_{11}) &= 2N\_{02} + N\_{03} + 2N\_{04} \end{aligned}$$

(37)

$$\begin{aligned} f\_2 &= f(\mathbf{O}):\\ N\_1 + N\_2 n\_2 &+ N\_3(1+n\_3) + N\_4(3+n\_4) + N\_5(3+n\_5) + N\_6(1+n\_6) + N\_7(1+n\_7) + N\_8 n\_8 \\ &+ N\_9 n\_9 + N\_{10} n\_{10} + N\_{11}(1+n\_{11}) = N\_{02} + N\_{03} + N\_{04} \end{aligned} \tag{38}$$

$$f\_0 = \text{ChB}: \qquad N\_2\text{-N}\_3\text{-N}\_5\text{-N}\_7\text{-N}\_9\text{-N}\_{10} + N\_{11} = \text{ 0} \tag{39}$$

$$-f\_3 = -f(\text{Na}): \qquad \text{N}\_{03} = \text{N}\_{11} \tag{40}$$

$$f\_4 = f(\text{Br}):\qquad \text{N}\_4 + \text{N}\_5 + \text{N}\_6 + \text{N}\_7 + \text{ 2N}\_8 + \text{3N}\_9 + \text{N}\_{10}\text{-2N}\_{01} = 0\tag{41}$$

Then we formulate the linear combinations:

In further sections, we formulate the balances for redox systems containing one, two or three electron-active elements in redox systems (aqueous media), where the complete set of expressions for independent equilibrium constants interrelating concentrations of different species is involved. We start our considerations from the systems with one electron-active element involved with disproportionation and symproportionation [5, 13, 15, 16, 19]. These properties are appropriate for the elements that form compounds and species at three or more oxidation degrees. In particular, bromine (Br) forms the species on five oxidation degrees (–1, –1/3, 0, 1, 5), see Figure 1, e.g. 0 (for Br2) and 1 (for HBrO or NaBrO) e (–1, 5). There are possible transitions between different bromine species, associated with changes of the oxidation states

HBrO3, BrO3 -

dis-

sym-

HBrO, BrO-

Br2 Br3 - Br -

Note that V0 mL of the titrand D composed of Br2 (N01)+H2O (N02) is titrated with V mL of titrant T composed of NaOH (N03)+H2O (N04). For the V0 + V mL of the D + T mixture, with the

2N1 þ N2ð1 þ 2n2Þ þ N3ð1 þ 2n3Þ þ N4ð1 þ 2n4Þ þ 2N5n5 þ N6ð1 þ 2n6Þ þ 2N7n7 þ 8N8n8

(37)

of this element, see Figure 1.

5.1.1. Approach II to GEB

f 1 ¼ fðHÞ :

5. Disproportionating systems

5

20 Redox - Principles and Advanced Applications

1 0

Figure 1. Schemes of disproportionation and symproportionation within bromine species [5].

set of the species completed by Na+1 (N11, n11).

The balances can be formulated as follows:

5.1. Formulation of balances for NaOH (C, V) ) Br2 (C0, V0) system

þ 2N9n9 þ 2N10n10 þ N11ð1 þ 2n11Þ ¼ 2N02 þ N03 þ 2N04

$$f\_{12} = 2 \cdot f(\mathbf{O}) - f(\mathbf{H}): \qquad -\mathbf{N}\_2 + \mathbf{N}\_3 + 5\mathbf{N}\_4 + 6\mathbf{N}\_5 + \mathbf{N}\_6 + 2\mathbf{N}\_7 = \mathbf{N}\_{03} \tag{42}$$

$$f\_{012} = f\_{12} + f\_0 : \quad \quad \quad \quad \quad 5(N\_4 + N\_5) + N\_6 + N\_7 - N\_9 - N\_{10} + N\_{11} = 0 \tag{43}$$

$$f\_{0123} = f\_{12} + f\_0 - f\_3 \ : \qquad \quad \quad \quad \quad 5(\text{N}\_4 + \text{N}\_5) + \text{N}\_6 + \text{N}\_7 - \text{N}\_9 - \text{N}\_{10} = \ 0 \tag{44}$$

$$f\_{01234} = (f\_{0123} + f\_4)/2 : \qquad \Im(\mathcal{N}\_4 + \mathcal{N}\_5) + \mathcal{N}\_6 + \mathcal{N}\_7 + \mathcal{N}\_8 + \mathcal{N}\_9 = \mathcal{N}\_{01} \tag{45}$$

For comparative purposes, we formulate also the linear combination ZBr∙f3 – f0123

$$(\mathbf{Z\_{Br}} - \mathbf{5})(\mathbf{N\_4} + \mathbf{N\_5}) + (\mathbf{Z\_{Br}} - \mathbf{5})(\mathbf{N\_6} + \mathbf{N\_7}) + 2\mathbf{Z\_{Br}}\mathbf{N\_8} + (\mathbf{3Z\_{Br}} + \mathbf{1})\mathbf{N\_9} + (\mathbf{Z\_{Br}} + \mathbf{1})\mathbf{N\_{10}} = 2\mathbf{Z\_{Br}}\mathbf{N\_{01}}\tag{46}$$

where ZBr = 35 is the atomic number for bromine (Br).

All the linear combinations (42)–(46) are not reducible to identity, 0 = 0; in the simplest case, we have six constituents (species, components) involved in f0123 (Eq. (44)). Eqs. (42)–(46) are equivalent forms of GEB, expressed in terms of particular constituents (components, species). To express them in terms of molar concentrations, we apply the relations: (1a) and C0∙V0 = 103 ∙N01/NA, CV = 103 ∙N03/NA. In this way, we consider the titration of V0 mL of Br2 (C0 mol/L) solution with V mL of C mol/L NaOH solution added up to a defined point of the titration. In particular, from Eq. (46), we have the balance for GEB

$$\begin{aligned} \left(\text{Z}\_{\text{Br}} - \text{5}\right) \left(\text{HBrO}\_{3}\text{I} + \left[\text{BrO}\_{3}^{-1}\right]\text{I}\right) + \left(\text{Z}\_{\text{Br}} - \text{1}\right) \left(\text{HBrO}\text{I} + \left[\text{BrO}^{-1}\right]\text{I}\right) + 2\text{Z}\_{\text{Br}}\left[\text{Br}\_{2}\right] \\ + \left(\text{3Z}\_{\text{Br}} + \text{1}\right) \left[\text{Br}\_{3}^{-1}\right] + \left(\text{Z}\_{\text{Br}} + \text{1}\right) \left[\text{Br}^{-1}\right] &= 2\text{Z}\_{\text{Br}}\text{C}\_{0}V\_{0}/(V\_{0} + V) \end{aligned} \tag{46a}$$

completed by the balances for ChB, CB(Br) and CB(Na):

$$-\left[\mathbf{H}^{+1}\right]-\left[\mathbf{OH}^{-1}\right]+\left[\mathbf{Na}^{+1}\right]-\left[\mathbf{BrO}\_{3}^{-1}\right]-\left[\mathbf{BrO}^{-1}\right]-\left[\mathbf{Br}\_{3}^{-1}\right]-\left[\mathbf{Br}^{-1}\right]=\mathbf{0}\tag{46b}$$

$$\begin{aligned} \left[ \text{HBrO}\_3 \right] + \left[ \text{BrO}\_3^{-1} \right] + \left[ \text{HBrO} \right] + \left[ \text{BrO}^{-1} \right] + 2\left[ \text{Br}\_2 \right] + 3\left[ \text{Br}\_3^{-1} \right] + \left[ \text{Br}^{-1} \right] - 2\text{C}\_0 \text{V}\_0 / (\text{V}\_0 + \text{V}) = 0 \end{aligned} \tag{46c}$$

$$\left[\mathrm{Na}^{+1}\right] = \mathrm{CV}/(V\_0 + V) \tag{46d}$$

#### 5.1.2. Approach I to GEB

The (optional) formulas for GEB, expressed by Eqs. (42)–(46), were obtained according to approach II to GEB, based on pr-GEB = 2∙f(O) – f(H). In this section, we apply the approach I to GEB, known also as the 'short' version of GEB, where prior knowledge of oxidation numbers of all elements in the system is assumed/required.

In the NaOH (C, V) ) Br2 (C0, V0) system considered in Section 4.2, bromine is the only electron-active element, considered as the carrier of its own, bromine electrons. One atom of Br has ZBr bromine electrons, and then one molecule of Br2 has 2ZBr bromine electrons, i.e. N01 molecules of Br2 involve 2ZBr∙N01 bromine electrons. The oxidation degree x of an atom in simple species, such as ones formed here by bromine, is calculated on the basis of known oxidation degrees: +1 for H and –2 for O and external charge of this species. Then for HBrO3, we have, by turns: 1∙1+1∙x + 3∙(–2) = 0 ) x = 5; for BrO3 �1 : 1∙x + 3∙(–2) = –1 ) x = 5; for HBrO: 1∙1+1∙x + 1∙(–2) = 0 ) x = 1, etc.

The oxidation number is the net charge resulting from the presence of charge carriers, inherently involved in an atom: protons in nuclei and orbital electrons, expressed in elementary charge units—as +1 for protons and –1 for electrons. The number y of bromine electrons in one molecule of HBrO3 is calculated from the formula: ZBr∙(+1) + y∙(–1) = 5, i.e., bromine in HBrO3 involves y = ZBr – 5 bromine electrons, etc. On this basis, we state that [15]

Balancing the bromine electrons, we get Eq. (46), and then Eq. (46a), considered as the GEB obtained immediately from the approach I to GEB; this proves the equivalency of approaches I and II to GEB.

#### 5.1.3. Preparation of an algorithm and computer program

Let us refer again to balances (46a)–(46d) interrelating concentrations [Xi zi] of the species Xi zi with the total concentrations C0, C of indicated components of the system. In this place, one should distinguish between the terms equation and equality. The term equation is related here

Table 1. Equilibrium data related to different bromine species.

½Naþ1

numbers of all elements in the system is assumed/required.

we have, by turns: 1∙1+1∙x + 3∙(–2) = 0 ) x = 5; for BrO3

5.1.3. Preparation of an algorithm and computer program

Let us refer again to balances (46a)–(46d) interrelating concentrations [Xi

The (optional) formulas for GEB, expressed by Eqs. (42)–(46), were obtained according to approach II to GEB, based on pr-GEB = 2∙f(O) – f(H). In this section, we apply the approach I to GEB, known also as the 'short' version of GEB, where prior knowledge of oxidation

In the NaOH (C, V) ) Br2 (C0, V0) system considered in Section 4.2, bromine is the only electron-active element, considered as the carrier of its own, bromine electrons. One atom of Br has ZBr bromine electrons, and then one molecule of Br2 has 2ZBr bromine electrons, i.e. N01 molecules of Br2 involve 2ZBr∙N01 bromine electrons. The oxidation degree x of an atom in simple species, such as ones formed here by bromine, is calculated on the basis of known oxidation degrees: +1 for H and –2 for O and external charge of this species. Then for HBrO3,

The oxidation number is the net charge resulting from the presence of charge carriers, inherently involved in an atom: protons in nuclei and orbital electrons, expressed in elementary charge units—as +1 for protons and –1 for electrons. The number y of bromine electrons in one molecule of HBrO3 is calculated from the formula: ZBr∙(+1) + y∙(–1) = 5, i.e., bromine in HBrO3

N4 species HBrO3∙n4H2O involve (ZBr – 5)∙N4 bromine electrons;

N6 species HBrO∙n6H2O involve (ZBr – 1)∙N6 bromine electrons;

N8 species Br2∙n8H2O involve 2ZBr∙N8 bromine electrons;

∙n5H2O involve (ZBr– 5)∙N5 bromine electrons;

∙n7H2O involve (ZBr – 1)∙N7 bromine electrons;

∙n9H2O involve (3ZBr + 1)∙N9 bromine electrons;

∙n10H2O involve (ZBr + 1)∙N10 bromine electrons;

Balancing the bromine electrons, we get Eq. (46), and then Eq. (46a), considered as the GEB obtained immediately from the approach I to GEB; this proves the equivalency of approaches I

N01 molecules of Br2 involved 2ZBr∙N01 bromine electrons.

with the total concentrations C0, C of indicated components of the system. In this place, one should distinguish between the terms equation and equality. The term equation is related here

involves y = ZBr – 5 bromine electrons, etc. On this basis, we state that [15]

�1

5.1.2. Approach I to GEB

22 Redox - Principles and Advanced Applications

1∙1+1∙x + 1∙(–2) = 0 ) x = 1, etc.

and II to GEB.

N5 species BrO3

N7 species BrO�1

N9 species Br3

N10 species Br�1

�1

�1

� ¼ CV=ðV0 þ VÞ (46d)

: 1∙x + 3∙(–2) = –1 ) x = 5; for HBrO:

zi] of the species Xi

zi

to the balance where at least two species are involved; these species are interrelated by expressions for the corresponding equilibrium constants values (Table 1). Such a requirement is fulfilled by Eqs. (46a)–(46c), whereas in Eq. (46d) we have concentration of one species; at any V value, [Na+1] is a number (not variable) and, as such, it enters immediately ChB (Eq. (46b)).

From the interrelations obtained on the basis of equilibrium data [56] collected in Table 1 we have

$$\begin{aligned} \left[\text{H}^{+}\right] &= 10^{-\text{pH}}; \ \left[\text{OH}^{-1}\right] = 10^{\text{pH}-14}; \ \left[\text{BrO}\_{3}^{-1}\right] = 10^{\text{ÁA}(\text{E}-1.45)-\text{pBr}+\text{éF}};\\ \left[\text{BrO}^{-1}\right] &= 10^{2\text{A}(\text{E}-0.76)-\text{pBr}+2\text{pH}-28}; \ \left[\text{Br}\_{2}\right] = 10^{2\text{A}(\text{E}-1.05)-2\text{pBr}}; \ \left[\text{Br}\_{3}^{-1}\right] = 102^{\text{A}(\text{E}-1.05)-2\text{pBr}}; \end{aligned} \tag{47}$$
  $\left[\text{HBrO}\right] = 10^{0.7-\text{pH}}$   $\left[\text{BrO}\_{3}^{-1}\right]; \ \left[\text{HBrO}\right] = 10^{8.6-\text{pH}} \cdot \left[\text{BrO}^{-1}\right]$

where the uniformly defined (scalar) variables: E, pH and pBr, forming a vector x = (E, pH, pBr)T , are involved; A∙E = – log[e–1 ], pH = –log[H+1], pBr = –log[Br–1 ]. All the variables are in the exponents of the power for 10 in [e–1 ] = 10-AE, [H+1] = 10-pH, [Br–1 ] = 10-pBr. The number of the (independent) variables equals to the number of equations, K = 2 + 1 = 3; this ensures a unique solution of the equations, at a pre-set C0, C and V0 values, and the V-value at which the calculations are realized, at a defined step of the calculation procedure, according to iterative computer program presented below.

Computer program for the NaOH\_Br2 system

```
function F = NaOH_Br2(x)
global V C0 V0 C yy
   E = x(1);
   pH = x(2);
   pBr = x(3);
   H = 10^(-pH);
   Kw = 10^-14;
```
pKw = 14; OH = Kw/H; A = 16.92; Br = 10^-pBr; ZBr = 35; Br2=Br^2\*10^(2\*A\*(E-1.087)); Br3=Br^3\*10^(2\*A\*(E-1.05)); BrO=Br\*10^(2\*A\*(E-0.76)+2\*pH-2\*pKw);

BrO3=Br\*10^(6\*A\*(E-1.45)+6\*pH);

HBrO=10^8.6\*H\*BrO;

HBrO3=10^0.7\*H\*BrO3;

Na=C\*V/(V0+V);

F = [%Charge balance

(H-OH+Na-Br-Br3-BrO-BrO3);

%Concentration balance for Br

(Br+3\*Br3+2\*Br2+HBrO+BrO+HBrO3+BrO3-2\*C0\*V0/(V0+V));

%Electron balance

((ZBr+1)\*Br+(3\*ZBr+1)\*Br3+2\*ZBr\*Br2+(ZBr-1)\*(HBrO+BrO)…

+(ZBr-5)\*(HBrO3+BrO3)-2\*ZBr\*C0\*V0/(V0+V))];

yy(1)=log10(Br);

```
yy(2)=log10(Br3);
```

```
yy(3)=log10(Br2);
```

```
yy(4)=log10(HBrO);
```

```
yy(5)=log10(BrO);
```

```
yy(6)=log10(HBrO3);
```

```
yy(7)=log10(BrO3);
```

```
yy(8)=log10(Na);
```
end

5.1.4. Preparation of the computer program for NaOH (C, V) ) HBrO (C0, V0) system

Modification of the computer program makes it possible to carry out calculations for other systems associated with bromine, e.g. for the system NaOH (C, V) ) HBrO (C0, V0). In this case, the changes are made in the following lines:

Computer program for the NaOH\_HBrO system

Function F = NaOH\_HBrO(x)

—

pKw = 14;

A = 16.92;

ZBr = 35;

OH = Kw/H;

Br = 10^-pBr;

Br2=Br^2\*10^(2\*A\*(E-1.087)); Br3=Br^3\*10^(2\*A\*(E-1.05));

24 Redox - Principles and Advanced Applications

BrO=Br\*10^(2\*A\*(E-0.76)+2\*pH-2\*pKw);

BrO3=Br\*10^(6\*A\*(E-1.45)+6\*pH);

(H-OH+Na-Br-Br3-BrO-BrO3); %Concentration balance for Br

(Br+3\*Br3+2\*Br2+HBrO+BrO+HBrO3+BrO3-2\*C0\*V0/(V0+V));

((ZBr+1)\*Br+(3\*ZBr+1)\*Br3+2\*ZBr\*Br2+(ZBr-1)\*(HBrO+BrO)…

+(ZBr-5)\*(HBrO3+BrO3)-2\*ZBr\*C0\*V0/(V0+V))];

HBrO=10^8.6\*H\*BrO; HBrO3=10^0.7\*H\*BrO3;

F = [%Charge balance

%Electron balance

yy(1)=log10(Br); yy(2)=log10(Br3); yy(3)=log10(Br2);

yy(4)=log10(HBrO); yy(5)=log10(BrO);

yy(6)=log10(HBrO3); yy(7)=log10(BrO3); yy(8)=log10(Na);

end

Na=C\*V/(V0+V);

(Br+3\*Br3+2\*Br2+HBrO+BrO+HBrO3+BrO3-C0\*V0/(V0+V));

—

+(ZBr-5)\*(HBrO3+BrO3)-(ZBr-1)\*C0\*V0/(V0+V))];

—

#### 5.1.5. Graphical presentation of the data and discussion

The systems considered here are characterized by distinctly marked jumps in E and pH values (Figures 2A and B) at the vicinity of the equivalence points, occurring at Φeq1 = 1 for NaOH (C, V) ! HBrO (C0, V0) (system I), and at Φeq2 = 2 for NaOH (C, V) ! Br2 (C0, V0) (system II), see Table 2 [15, 16].

Reactions occurred in the systems I and II can be formulated from the analysis of the respective speciation diagrams. As results from Figure 2C, the disproportionation reaction in the system I occurs according to the scheme

$$\text{\textbulletBr}\_2 + \text{\textbulletOH}^{-1} = \text{BrO}\_3^{-1} + \text{5Br}^{-1} + \text{3H}\_2\text{O} \tag{48}$$

i.e. Φeq = 2 ) CVeq1 = 2C0V0. After crossing the equivalent point, the main products of this disproportionation reaction are Br�1 and BrO3 �1 , not Br�1 and BrO�1 corresponding to the reaction

$$\text{Br}\_2 + 2\text{OH}^{-1} = \text{BrO}^{-1} + \text{Br}^{-1} + \text{H}\_2\text{O} \tag{49}$$

with the same stoichiometry, 3 : 6 = 1 : 2. From detailed calculations at Φ = 2.5, i.e. at an excess of NaOH added, we find [BrO3 �1 ]/[BrO�1 ] = 10�2.574/10�6.7584 = 1.53∙104 , i.e. efficiency of the reaction (48) is more than 4 orders of magnitude greater than the efficiency of reaction (49).

Scheme of Br2 disproportionation affected by NaOH (C) can also be calculated [16]. At Φ = 2.5, we have [BrO3 �1 ]/[Br�1 ] = 10�2.574/10�1.875 = 10�0.699 = 0.2 = 1:5, i.e. at an excess of NaOH added (see Figure 2c), the disproportionation occurs mainly according to the scheme indicated by reaction (48) from the products side.

Figure 2. (A) pH = pH(Φ) and (B) E = E(Φ) relationships plotted for the systems I and II, and the related speciation diagrams for the systems: I (C) and II (D).

In the system II, disproportionation of HBrO affected by NaOH (C) added according to the titrimetric mode is presented in Figure 2D [16]. The [Br1 ]/[BrO3 1 ] ratio equals: 102.2553/ 102.5563 at Φ = 2.0; 102.2730/102.5740 at Φ = 2.5, i.e. 100.3010 = 2 = 2:1, corresponding to the stoichiometric ratio of products of this reaction. As results from Figure 2C, the disproportionation, at an excess of NaOH added, occurs mainly according to reaction 3HBrO + 3OH1 = 2Br1 + BrO3 1 + 3H2O (stoichiometry 3:3 = 1:1), resulting from half reactions: HBrO + 2e1 + H+1 = Br1 + H2O, HBrO – 4e1 + 2H2O = BrO3 1 + 5H+1, and 3H+1 + 3OH1 = 3H3O. The

Table 2. The sets of rounded (Φ, pH, E) values taken from the vicinity of the equivalence points; V0 = 100, C0 = 0.01, C = 0.1.

(Φ, pH, E) values from the close vicinity of the corresponding equivalence points on the curves in Figures 2A and B are collected in Table 2. The Br2 solution is acidic, as results, e.g. from the ChB (Eq. (29a)): at [Na+1]=0(Φ = 0) we have [H+1] – [OH�1 ] = [BrO3 �1 ]+[BrO�1 ]+[Br3 �1 ]+[Br�1 ] > 0, i.e. [H+1] > [OH�1 ]; this inequality is also obtained from Eq. (42), at N03 = 0: [H+1] – [OH�1 ] = 5[HBrO3]+6[BrO3 �1 ] + [HBrO] + 2[BrO�1 ] > 0. Br2 is an acid with a strength comparable to that of acetic acid; at C0 = 0.01, pH equals 3.40 for Br2 and 3.325 for CH3COOH (pK1 = 4.65). Disproportionation of Br2 occurs initially to a small extent (several %), according to the scheme Br2 + OH�1 = HBrO + Br�1 , compare with [57].

In C0 = 0.01 mol/L HBrO solution, more than 90% HBrO disproportionates occur according to the reaction 5HBrO = BrO3 �1 + 2Br2 + 2H2O+H+1; at V = 0, we have [Br2] = 10�2.4406, [BrO3 �1 ] = 10�2.7442, i.e. [Br2]/[BrO3 �1 ] = 100.3036 ≈ 2, which confirms this stoichiometry of the reaction. The H+1 ions formed in this reaction acidify the solution significantly: at C0 = 0.01 and V = 0, we have pH = 2.74, although HBrO itself is a relatively weak acid.

The numerical values of the concentrations given here are taken from the corresponding files with results of iterative calculations.


**About the Editors**

## **David Tyfield**

David Tyfield is Professor in Sustainable Transitions and Political Economy at the Lancaster Environment Centre (LEC), Lancaster University, and Associate Director of Lancaster's Centre for Mobilities Research (CeMoRe). His research focuses on sustainable transition, especially urban e-mobility and associated infrastructures, including 'ecological civilisation' in China, which he has been studying since 2007. His latest book is *Liberalism 2.0 and the Rise of China: Global Crisis, Innovation, Urban Mobility* (Routledge, 2018) and he is a co-editor of *Mobilities* journal.

## **Rebecca Willis**

Rebecca Willis is a Professor in Energy & Climate Governance at Lancaster Environment Centre, where she leads the Climate Citizens project. In 2020 she was an Expert Lead for Climate Assembly UK, the Citizens' Assembly established by the UK Parliament. Rebecca is a Trustee of the New Economics Foundation and an adviser to the National Lottery's Climate Action Fund. Previously, she was a research fellow for the IGov project at the University of Exeter, investigating energy governance. She features on the Woman's Hour Our Planet Power List which highlights 30 women making an impact by helping to protect our planet. Her book, '*Too Hot To Handle? The democratic challenge of climate change*' was published by Bristol University Press in March 2020.

## **Andy Yuille**

Andy Yuille is a Senior Research Associate in the Lancaster Environment Centre. His research focuses on the interfaces between different knowledges, experiences and practices, in particular relating to environmental decision-making. He is interested in how environmental problems are brought into being, how different human and non-human elements of 'the problem' come to be related in specific ways, and how different relations that might prove less problematic can be brought about. He combines 15 years' experience of influencing public decision-making through working with NGOs, community groups and public-private partnerships, with an academic approach informed by Science and Technology Studies and the idea of public sociology.