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# Identification and age-dependence of pteridines in bed bugs (Cimex lectularius) and bat bugs (C. pipistrelli) using liquid chromatography-tandem mass spectrometry

## Abstract

Determining the age of free-living insects, particularly of blood-sucking species, is important for human health because such knowledge critically influences the estimates of biting frequency and vectoring ability. Genetic age determination is currently not available. Pteridines gradually accumulate in the eyes of insects and their concentrations is the prevailing method. Despite of their stability, published extractions differ considerably, including for standards, for mixtures of pteridines and even for light conditions. This methodological inconsistency among studies is likely to influence age estimates severely and to hamper their comparability. Therefore we reviewed methodological steps across 106 studies to identify methodological denominators and results across studies. Second, we experimentally test how different pteridines vary in their age calibration curves in, common bed (Cimex lectularius) and bat bugs (C. pipistrelli). Here we show that the accumulation of particular pteridines varied between a) different populations and b) rearing temperatures but not c) with the impact of light conditions during extraction or d) the type of blood consumed by the bugs. To optimize the extraction of pteridines and measuring concentrations, we recommend the simultaneous measurement of more than one standard and subsequently to select those that show consistent changes over time to differentiate among age cohorts.

## Introduction

The development of an accurate methodology for determining the age of insects is a key technique to understanding many aspects of insect ecology, behaviour and effectiveness of pest control programmes. This particularly applies to blood-sucking, disease-transmitting insects where the age is an important parameter to predicting their biting frequency and hence vectoring ability1, as well as their fecundity2. Age-grading is also important in general evolutionary and ecological models that are based on insects, from individual to population level3,4. Finally, age-grading in insects has been important in veterinary and forensic medicine. Consequently, accurate methods for determining the age of adult insects in the field have gained considerable importance since the 60s of the 20th century3,5,6.

As all methods, currently available age-grading techniques also have limitations. Few genetic and cellular age markers exist and these, such as DNA methylation or telomere lengths, are related to cell division activity, and partially to age per se. Few markers are based on actual age, such as the circadian deposition of chitinous layers in cricket legs7,8,9,10. However, these circadian growth bands are visible till a certain age only and can vary with temperature8,11. Most markers indicate the accumulation of a marker with metabolic or other activity. For example, some markers are related to mandible abrasion with age and, therefore restricted to herbivorous insects12. Predictable anatomical changes in the reproductive system related to fertility changes, such as the accumulation of follicular relics and/or the appearance of ovarian tracheoles are also based on physiological age5,13,14. Finally, the standard method today appears to be a survey of the accumulation of fluorescent pigments in the eyes of insects15,16. It appears that most authors consider the deposition of pteridines as a chronological, rather than physiological age marker.

Most of the naturally occurring pteridines, called pterines, are the 2-amino-4-hydroxy derivatives17,18. Their stability allows for their long-term accumulation in the eye and minimal loss by decay19. Pteridines are poorly soluble in water, insoluble in non-polar organic solvents but soluble in strong acid or alkali. Other insect pigments, such as papiliochromes, anthocyanins and flavonoids are water-soluble20,21. The auto-chelating properties of pteridines result in high insolubility under normal physiological conditions and binding of the eye pteridines onto granules15. The pteridine content in both laboratory- and field-captured flies is typically a level of magnitude higher than the minimal detectable level and can be used to predict individual age in the laboratory population with high certainty22.

Pteridines have the advantage of being applicable to long-lived insects under different conditions and are measurable23. Found in the eyes, they are a group of fluorescent pigments derived from a pyrimidine-pyrazine ring structure. This structure is widely distributed in nature, being present in microorganisms, as well as plants and animals. In insects, pteridines have two important biological functions, i) as excretory products by inactivation of nitrogen metabolic wastes and ii) as pigments for signalling and screening15,24. While laboratory studies of individuals of known age indicate that pteridine levels increase linearly with age25,26,27 and are independent of sex28, pteridines are degradation products of purine metabolism and their accumulation may not be independent of physiological activity. Indeed, laboratory studies show pteridine levels to increase with rearing temperature29,30 and ambient light levels31,32.

A final difficulty in comparing the results of age-grading studies is that in addition to the biological variation outlined above, substantial differences exist between the protocols used. For example, many authors pooled the concentration of several pteridines in the eyes, even though their biosynthetic pathways are known to differ and they can convert into each other33. Protocols also differed with respect to whether pteridines were extracted only from eyes or the whole head. Further, the amount of light exposure during extractions34,35 and the duration of sample storage36 were often not mentioned. We feel that a systematic comparison of different approaches and protocols is useful and below provide such an overview. Based on this information, we experimentally test the effect of both biological as well as methodological conditions on the quantification of LC-MS/MS analyses of particular pteridines. Specifically, we examine the effects of the light-dark regime during extraction, extraction solvents and different insect body parts. We do so in groups of blood-sucking insects, bed bugs (Cimex lectularius) and bat bugs (C. pipistrelle), that vary in population genotype, diet and in rearing conditions.

## Results

### Review

The presence of specific pteridines in biological material was mentioned in 84 of 106 papers (79%), published between 1926 and 2019 (Figshare https://doi.org/10.6084/m9.figshare.11316473). These related to 44 different pteridines studied in 115 insect species from 32 families, however, some of them represented isomers (Supplementary Tables S1, S2). In 34% of publications the authors pooled pteridines, in 73% papers the authors worked with individual pteridines. At least one of the eight most intensely studied pteridines (6-biopterin, biopterin, erythropterin, isoxanthopterin, leucopterin, pterin, sepiapterin and xanthopterin) was mentioned in 67% of the publications. In 84% of the studied species, at least one of ten pteridines (8 mentioned above and two additional pteridines, i.e. 2-amino-4-hydroxypteridine and drosopterines) was described (Supplementary Table S1). Moreover, we found a lack of a consistent use of nomenclature for specific pteridines (Figshare https://doi.org/10.6084/m9.figshare.11316473). At least some of them are registered with the same CAS number (e.g. 492-10-4 with synonyms 7-methylxanthopterin and chrysopterine). This leads to that the same chemical compound was used under different trivial names in different studies (e. g. 2-amino-4-hydroxypteridine/pterin37,38, 7,8-dihydrobiopterin/deoxysepiapterin16,39, isoxantholumazine/violapterin18,40).

Previous studies listed 8 different extraction methods combined into at least 13 different protocols. The TRIS and ORG extraction solutions were used in 29 studies, hence other solutions were study-specific and used only a few times. In 75% of the papers, particular pteridines were compared against reference standards or literature. Commercially available standards were used in 61%, while in 39% of the studies, the extracted compounds were identified with the literature, i.e. comparing Rf values, spot colour or wavelengths. In 42.5% of studies, the samples were isolated in the dark or under red light. Isolation under reduced light intensity was mentioned in one study34 and 57% of studies did not specify any light conditions. Only one study tested how storage affected pteridine concentration36.

Only 39.6% (n = 42) of the papers focused on age-grading, while the majority of studies focused on the presence of different pteridines. These studies concerned 23 pteridines in 19 species from 15 families. In the context of age-grading, four analytical methods were commonly used, i.e. spectrofluorimetry (n = 35), HPLC (n = 8), thin layer chromatography (n = 5) and paper chromatography (n = 4). Pteridines for age-grading content were mainly extracted by TRIS (n = 15) and ORG (n = 14) solutions (see Methods). The most often studied body part was the head (n = 32).

### Optimization of LC-MS/MS method

#### Choice of extraction method

There were significant differences in pteridine concentrations among extraction methods (Kruskal-Wallis test: Bio: H2,26 = 9.91, p = 0.007; Iso: H2,26 = 9.10, p = 0.011; Leu: H2,25 = 15.55, p < 0.001). Follow-up tests have demonstrated a significant difference between ACID and ORG method in all three studied pteridines (Fig. 1a). The difference in the pteridine concentration extracted by ACID and TRIS method was significant for Leu and nearly significant for Bio and Iso. TRIS and ORG method did not differ with either pteridine.

By method ACID we obtained the highest concentrations of pteridines but also the highest variation. The problem of ORG method was that two immiscible phases were produced after the addition of NaOH. Because the TRIS method showed no immiscible liquid phases and had a relatively small standard deviation, we used TRIS as the standard solvent for all experiments reported below.

#### Storage mode of biological material before extraction

There was no significant difference in pteridine concentration between samples frozen at −20 °C and stored in 70% ethanol extracted with the TRIS method (Fig. 1b, Supplementary Table S3).

#### Internal standard

IS reduced the variability of measured pteridine concentration because it removed the variability caused by the detection fluctuation of the machine during analyses (Fig. 2). The use of IS decreased variability by 10% for Leu (SD decreased from 0.465 to 0.229) and by 40% for Bio (SD decreased from 2.033 to 0.748). Because of that we used IS for all experiments reported below.

#### Stability of samples over time

The changes in the concentration of pteridines in the extract stored in the freezer for 14 days were up to 26% in samples spiked by pteridines mixture to a concentration 50 and 100 ng/mL and up to 36% in samples spiked to a concentration of 5 ng/mL (Table 1). However, the changes in concentrations are mostly non-significant (Table 1), the analyses of extract should be realized as soon as possible after extraction, to minimize errors in the analyses of individual analytes.

#### Accuracy

The accuracy of the LC-MS/MS method was evaluated as recovery in percent (RE%) of the amount of target analyte added into the sample. The average of all pteridine RE values for samples spiked to 100 ng/mL was 116%, for sample spiked to 50 ng/mL was 95%, for samples spike to 5 ng/mL was 96% (see more in Table 2). Whereas the standard error usually does not exceed the threshold of 5%, the variance of measured concentration is generally insignificant (Table 2).

#### Light condition during the pteridine extraction

There was no significant difference in variance or the mean pteridine concentration (Fig. 3a) between protocols using extraction under normal laboratory light or dark conditions. Therefore, the more error-prone extraction in dark was not used.

#### Localization of pteridines in the head parts

Compared to whole head extracts, Bio, Iso and Leu were mostly stored in the eyes of bed bugs (ANOVA test: Bio: F2,13 = 8.25, p = 0.005; Iso: F2,13 = 11.73, p = 0.001; Leu: F2,13 = 4.73, p = 0.029) but Pte was clearly present also in the head cuticle (Pte: F2,13 = 3.09, p = 0.08) (Fig. 3b). The post-hoc tests revealed that this was due to a strong difference between the pteridine concentration of the head cuticle and of the whole head.

#### Head size effect on pteridine concentration

Head dimensions (eye width, head width, intraocular space dorsally) had no significant effect at all on pteridine concentration for Bio, Iso or Leu (t-test: all F3,28 < 0.01, all p > 0.05). Therefore, no body size correction was necessary.

#### Rearing conditions effect on the pteridine deposition

We found a positive effect of temperature on the deposition of pteridines during the rearing of bed bugs (Fig. 4a). The light-regime had no significant effect on the deposition of Bio and Iso but a slight positive effect in 12 h/12 h L:D on Leu concentration (Fig. 4b).

#### Selection of pteridines for age-grading

Based on all previous methodical steps, Iso seems to be the most useful pteridine for age-grading in bed bugs. We excluded Bio because of large differences in the slope between BL populations (Table 3) and Pte based on different trends between lineages of Clec (Supplementary Figure S1). We also excluded Leu. Although Leu has positive trends in all studied populations, it could tend to overestimate the age due to a flatter slope of the regression curve (Table 3).

#### Verification of calibration curves with blind samples

Blind samples split into three age cohorts did not reveal significant differences in pteridine concentrations between 2nd and the other two age cohorts (Table 4). Therefore, we omitted the middle cohort and verified the correct grouping of blind samples from the youngest and the eldest cohort for all three pteridines separately (Table 5). When we compared the slopes of regression lines based on blind samples and calibration curves based on laboratory-reared bed bugs (see below “Assay of laboratory-reared C. lectularius and C. pipistrelli of known age”), it seemed that only the slopes of Iso were similar (Table 4), which reinforced our decision from the previous step to include Iso. When we split samples from the middle age cohort to the youngest or eldest age cohorts by K-means analysis, the presumption of increasing pteridine concentrations held (Mann-Whitney U test: Bio: Z = −2.57, Iso: Z = −2.76, Leu: Z = −3.06, all: p < 0.01).

### Assay of laboratory-reared C. lectularius and C. pipistrelli of known age

We calculated calibration curves of Iso and Leu for Clec BL and Clec HL (by combining the results of the two appropriate populations) and for Cpip (Table 3). The concentration of both pteridines significantly and linearly increased with age for bugs of all populations, though in Leu with a lower slope (Table 3).

The concentration of both pteridines was strongly affected by age cohort (GLS: Iso: F1,336 = 394.10, Leu: F1,347 = 373.60, p < 0.001), and the linear relationship between concentration and age differed in slope between lineages (GLS: Iso: F2,336 = 50.26, Leu: F2,347 = 12.97, both p < 0.001). The Iso accumulation rate of BL significantly differed from that of HL (partial t-test: t342 = −9.48, p < 0.001) and Cpip (partial t-test: t342 = −7.71, p < 0.001) but not between HL and Cpip (partial t-test: t342 = 0.30, p > 0.05). Leu accumulation rate of Cpip was different from both lineages of Clec (partial t-test: BL: t353 = 5.09, HL: t353 = 21.09, p < 0.001) that did not differ from each other (partial t-test: t353 = 0.08, p > 0.05).

### Assay of field-sampled bed bugs C. lectularius

Based on calibration curves from laboratory-reared Clec lineages (at 27 °C), individuals from Loukov (BL) varied in age by approximately 155 days. The calculated age cohorts varied from 0.6 to 11.1 (mean=4.7 cohort, n = 30). Krakow (HL) individuals differed by up to 2 age cohorts, i.e. 25 days, ranging from −9.6 to −7.8 age cohort (mean = −9.1 cohort, n = 20) (Fig. 5). The negative predicted age of Krakow females was almost certainly an effect of the high temperature in the laboratory model (27°C), which will not be reached in human settlements. Using the 23°C prediction curve from laboratory-reared Clec BL females at 23 °C, produced an age range of 4 cohorts (approx. 50 days) with a mean of 2.7 and ranging from 1.6 to 5.9 cohorts.

## Discussion

### Review

We identified that the literature seems to vary widely in the methods used to analyse pteridines, and this was true regardless of whether or not there was an application in age-grading. Variation especially existed in the method of pteridine extractions, the process of identification of different pteridine compounds and the use of internal standards.

In the studies we reviewed, we identified a lack of a consistent use of trivial nomenclature for specific pteridines. Older studies using paper chromatography as well as newer studies using more modern methods, especially in biological journals, used different trivial names for same chemical compound. Based on the literature review we have developed and here presented a reliable LC-MS/MS method to quantify four bioactive pteridines (Bio, Iso, Leu and Pte) simultaneously in bed bug heads. We also show this assay to be suitable to monitor pteridines in wild and laboratory-reared bed bugs. These results have implications for future researchers aiming to optimise their age determination protocols and for the application of the pteridine method to age-grade insects in the wild.

### Optimization of extraction, storage and LC-MS/MS methods

One of the first methodological complications one encounters is the extraction of pteridines from biological material. Alkaline or acid extractions are usually used because many pteridines are pH sensitive and decompose readily at a defined pH41. The use of very low pH conditions, usually pH ~ 3, can often lead to ring cleavage42, while below pH 8.8 Iso and Leu are eluted43. Our results showed that the ACID method, which was used for extraction in only two studies, provides the highest concentrations of pteridines, but with a high among sample variation in concentrations.

We illustrated that the usage of different extraction methods leads to large variability among samples and even the absence of some compounds after physical separation during liquid chromatography. Many authors solve this problem by jointly analysing more pteridines, but this way they do not reveal which compounds they have in a sample36,44,45,46. In such studies, the authors rely only on the fluorescence excitation wavelength of all analytes. In the studies where standards are not applied, the authors can only use the emission wavelengths, Rf values or colours from paper chromatography published for specific pteridines, which can be expected in their biological samples47,48. Therefore, the publication of pooled concentrations can lead to misinterpretation when evaluating the change in concentration over time, e.g. in age-grading. We confirm that the direct comparison of the wavelengths of the standards and peaks found in the samples, as included in most studies from the last two decades, is the most appropriate method (e.g. Tomic-Carruthers et al16., Tornero et al49.).

The extraction procedure is time-consuming and usually complicates the design of the experiments. In our study, the number of samples needed to produce calibration curves was impossible to dissect and measure within one day by one person. Therefore, we performed stability tests of pteridines in aqueous TRIS extracts comparing analyses of such extracts i) immediately after addition of known concentration of standards and ii) after 14 days storage of these samples in the freezer at −20 °C. Our results showed a decrease in concentrations of pteridines. This is consistent with previously published findings50. Therefore, the analyses of extracts should be realized as soon as possible after extraction. It seems that this recommendation has intuitively already been considered. Most studies (93% of researched papers) extracted new samples just before measurement and only in six studies samples were stored. If pre-analysis storage should be necessary, we recommend precise statements of the freezing conditions, in fact more precise than in current practice.

The light conditions of the sample analysis have been suggested a critical step in the extraction process29. Our results show that the extraction of pteridines requiring crushing the eye in a micro-tissue grinder in the dark was complicated and attracted a high error rate. Pteridines were below the detection limit or absent completely in many samples, caused by the unsuccessful disruption of the eye. Our successful dark extractions showed similar concentrations of Bio, Iso and Leu as extraction during laboratory light. Therefore, our results suggest instead that dark extraction may not be necessary34.

Pteridines can occur in three oxidation states with different stability51. Many authors mentioned different sensitivity in fluorescence detection of pteridines arising from their oxidation properties, among others also from the sensitivity to light52,53. At neutral pH, reduced forms are easily oxidized by molecular oxygen giving rise to stable fluorescent forms. A wide range of techniques (pre–treatments) and sample matrices are available to oxidize any residual reduced pteridines in order to facilitate the analysis by using more stable and more fluorescent, oxidized forms49. Most of the reviewed studies draw attention to pteridines with multiple oxidation states that are labile to heat, light, and auto-oxidation. The currently used published standard protocols31,54 should therefore, be augmented by more detailed description of the extraction methods.

### Distribution of pteridines in the body

Conventional wisdom has it that pteridines are found in the eyes only. We did not detect different pteridine concentrations in the eyes and whole head capsule, as the majority of pteridines was included in bed bug eyes. However, recently it was found that the pteridine biosynthesis pathway has been co-opted in the embryo to produce various pteridines in the antennae and legs55. This might explain non-significant difference of Pte between head cuticle and whole head capsule. It is possible, that generally the occurrence of pteridine in the specific parts of the body of the chosen model organism is important. Also, it is not always possible to dissect exactly the same amount of tissue from each individual. For example, eye preparation is complicated especially in small model organisms and extends the light exposure time. Therefore for the determination of differences in age-grading, we used only Bio, Iso and Leu stored in the eyes of bed bugs, while Pte are probably present also in the head cuticle.

We did not find higher pteridine concentrations in larger heads, similarly as Robson et al.56 for Drosophila serrata. Since the differences among bed bug cohorts are represented by the slope of the calibration curves, not by the positive/negative trend itself, an effect of the body size on the speed of pteridine accumulation cannot be excluded. In general, body size is connected to eye morphology, but the interaction between visual signalling and body size is not straight-forward; visual signalling species with smaller eyes showed a greater increase in maximum facet diameter than visual signalling species with larger eyes57. An increase in the facet diameter improves the eye’s sensitivity by improving photon capture58. Thus, differences in facet diameter within the wood ant compound eye are presumably connected with different requirements on the sensitivity and resolution of different eye regions when constrained by resources and space available58. Therefore, the morphology of the insect eye does not show a direct link between eye size, its function and pteridine accumulation.

### Other parameters affecting pteridine concentrations

Pteridines have a different accumulation rate with regard to several environmental factors, such as light, temperature, food etc.59 or physiological aspects, such as metabolic activity60. In our experiment, pteridine accumulation significantly increased with higher rearing temperatures. This positive effect of temperature on the pteridine accumulation has also been found in Stomoxys calcitrans54 and in Musca domestica32. Adult Drosophila developing at 27 °C showed greater head capsule fluorescence than adult flies developing at 17 °C32. These differences persisted for 15 days32.

Diet is another factor that can affect the concentration of pteridines in the eyes. For example, the changes in pooled concentrations of six pteridines showed a characteristic pattern of increased and/or decreased amounts in response to dietary levels61. Even though we did not directly test the effect of diet in our study, we would like to highlight the potential importance of diet when applying laboratory results to age-grading in wild populations. However, because the pteridine concentrations in Cpip (feeding on bat blood) were more similar to Clec HL (feeding on human blood) rather than Clec BL (that also feed on bat blood), it is clear that Cimex pteridine concentrations are not affected by bat or human blood per se.

### Age-dependence of pteridines in wild populations

It seems doubtful that pteridines are general indicators of chronological age, given their variation with temperature and between populations. Concentrations of pteridines usually correlate positively with the age of an individual27,62. However, first of all, it is unlikely that the deposition of pteridines is independent of metabolic activity. Second, the relationship with age does not apply to all pteridines. We showed that the concentration of Iso and Leu correlates positively with the age of the bed bugs (Table 3), while the concentration of Pte even decreased, but only in two HL populations and Cpip (Supplementary Figure S1). We only used females in our experiments but note that males and females can even show opposite patterns63. The concentrations of xanthopterin decreased markedly in the heads of males and females with increasing moth age, while those of Pte decreased more slowly and Bio remained largely unchanged in both sexes.

For two wild populations, we applied age-grading estimated based on concentrations of pteridines obtained from laboratory populations. The Loukov (BL) population, had a very large variations in age structure. That corresponds well to the fact that we not only found juveniles, but also very old females, which survived the winter in bat roosts. In contrast, for human-associated bugs (Krakow) we estimated a very low age, formally even reaching negative values. This finding can be expected for HL because bed bug control actions are likely to reduce average age in infestations. These actions are apparently not carried out in bat roosts. Bed bug individuals in human settlements can be expected to develop in temperatures less than 27 °C, the temperature of our calibration curves. Assuming a room temperature of 23 °C, easily expected in human dwellings, the negative age values disappear. A low age of a bedbug population is, of course, expected with bed bug control actions, which are not carried out in bat roosts.

Although the method of liquid chromatography of pteridines is often used for age-grading in insect, it still has restrictions. Our research showed that the calibration curves based on individuals bred under standard conditions are specific not only for taxonomic species, but also showed differences between populations, indicating other, yet unknown intrinsic factors that affect different pteridine accumulation between populations. In wild populations, we can expect even greater deviations, where the temperature and availability of food are significant factors as well14,32.

## Conclusion

We confirmed that after optimization of the extraction method, LC-MS/MS can be successfully used to determine the age in individual bed bugs based on different concentrations of pteridines. However, we recommend, before preparing the calibration curves, to thoroughly test the characteristics of the pteridine standards, the feasibility of methodical procedures, in particular the extraction of pteridines from biological material, and not to rely too much on completeness of published protocols. It is advisable to ensure that enough different standards are available to exclude pteridines that do not show the necessary trend among age cohorts of the model taxon. Our results indicate limits in the age-grading using pteridine concentrations in wild samples calibrated on the laboratory model. Based on pteridine concentrations estimating age with days accuracy is not possible, therefore we recommend working with age cohorts.

## Materials and methods

### Literature review

To identify the most commonly used and most suitable pteridines, we reviewed the existing body of literature using Google Scholar, Web of Science and the following keywords: pteridine AND insect AND method. This literature review yielded 139 studies but not all of them were based on suitable methodological steps. From the remaining 106 papers we conducted a detailed analysis of the pteridine extraction methods used and the pteridines found in insect (online Figshare dataset, https://doi.org/10.6084/m9.figshare.11316473).

### The study system

Bed bugs (Cimex lectularius) (Clec) are well-known human parasites that can also be associated with bats. Human-associated and bat-associated bed bugs, henceforth called human lines (HL) and bat lines (BL), are two separate genetic lineages that may eventually diverge into two different species64. We also examined a closely related species, Cimex pipistrelli64,65, henceforth called the bat bug, that is only associated with bats. Both species belong to the Cimicidae (Insecta: Hemiptera) and exclusively live on the blood of either bats or humans, are nocturnal. They can live for up to one year and experience different temperature ranges12.

### Insect origins and culture conditions

Clec BL bugs were collected at two nursery colonies of mouse-eared bats (Myotis myotis) roosting under roofs of the churches in Hanušovice and Raškov (North Moravia, Czech Republic), arbitrarily called BAT1 and BAT2. Bat bugs (Cpip) were collected from colonies of M. myotis roosting under the roof of the castle in Luhačovice (south Moravia, Czech Republic). All bugs were cultured in incubators at 23 ± 1 °C and 27 ± 1 °C in (see below) complete dark at 70% relative humidity. They were fed weekly on bat blood using the protocol of Wawrocka and Bartonička66. Bats were fed ad libitum with a mixed diet consisting of crickets (Acheta spp.) and mealworms (Tenebrio molitor) and, after experiments, returned to the colony. All the protocols are carried out according to relevant guidelines and regulations. Experimental procedures were approved by the Ethical Committee of the Masaryk University (No. 1/2018). All bats were captured, handled and temporarily kept in captivity under the licence issued by the South Moravian Regional Authority (Permit JMK 24451/2013 and 63761/2017). TB is authorised to handle free-living bats under the Certificate of Competency No. CZ01297 (§17, law No 246/1992), No. 922/93-OOP/2884/93 and 137/06/38/MK/E/07 of the Ministry of Environment of the Czech Republic.

Clec HL bugs were sourced from two lab cultures at Bayreuth University, Germany which were originally collected in Budapest, Hungary and London, United Kingdom, arbitrarily called HUM1 and HUM2. They were maintained in an incubator at 27 ± 1 °C in either complete darkness or a 12 h/12 h L:D light regime, at 70% relative humidity. They were fed weekly on human blood (conserved by CPDA; obtained from Faculty Hospital Bohunice, Brno with permission to use it for research purposes) using the protocol by Aak and Rukke67.

To control for age, newly eclosed adults of the respective populations were taken from the stock cultures for the experimental trials (for details see below “Assay of laboratory-reared C. lectularius and C. pipistrelli of known age”). Methodological steps were tested on same-aged adult females from BAT1. All samples were freeze-killed and stored at −20 °C until chemical extractions and analyses were conducted.

### Sample preparation

Bed bugs were decapitated and the head capsules extracted immediately using a microscalpel. Each bed bug head was homogenized separately in a glass 25–100 μL micro-tissue grinder (P-LAB, Czech Republic) with 50 μL of buffer and the suspension was transferred to a 1.5 mL Eppendorf vial. To ensure that all parts of the head capsule were removed and to maximize the amount of transferred pteridine, 50 μL of buffer were added three times into the micro-tissue grinder and transferred to the suspension. The amount of buffer in the vial was supplemented according to the extraction method TRIS29 or ORG31 or ACID68 (see Supplementary methods). Vials with a suspension were left standing in the ultrasound for approximately 2 hours. During this period, the ultrasound was turned on three times for 15 min (at the beginning, after 1 hour and at the end). After that, the suspension was centrifuged for 5 min at 6000 r.p.m. The 0.5 mL of supernatant was transferred into a sealed dark glass vial and stored at −20 °C until the LC-MS/MS analysis was conducted. The head capsule was homogenized and transferred under normal light conditions, all other extraction steps were conducted in the dark.

### Pteridine standards

Based on our literature review (see Results), we chose 6-biopterin, isoxanthopterin, leucopterin and pterin as standards for liquid chromatography-tandem mass spectrometry (LC-MS/MS). They were selected from 44 potential pteridines (Supplementary Table S1) because they were tested on the largest number of insect families. Moreover, isoxanthopterin and leucopterin were found in other families of Heteroptera and we expected to be present in bed bugs as well. Erythropterin was excluded because no manufacturer of the standard was found. The name of 6-biopterin was used instead of simple biopterin due to the same CAS number. For optimization of methodological steps and to establish calibration curves for age-grading we used 6-biopterin (Bio, CAS number: 22150–76–1) and isoxanthopterin (Iso, CAS 529-69-1) obtained from Sigma Aldrich Corporation (St Louis, MO, U.S.A.), leucopterin (Leu, CAS 492-11-5) and pterin (Pte, CAS 2236-60-4) from Schircks Laboratories (Switzerland).

The stock solutions of pteridine standards were prepared by dissolving 4 mg of each pteridine in 10 mL water solution comprising 0.1% (w/v) dithiothreitol and 40 mmol/L ammonium hydroxide (DTT solution). Then, we mixed appropriate volume of each pteridine stock solution and DTT solution to obtain a concentration of 10 µg/mL. From this mixed stock solution, we prepared calibration standards by serial dilution in acetonitrile.

### LC-MS/MS analysis

Liquid chromatograph Agilent 1290 Infinity II Series (Agilent Technologies, Santa Clara, CA was used for separation of mixture of target pteridines. Separation was realised using the chromatographic column Luna NH2 (100 Å 150 ×2.0 mm 3μm, Phenomenex, USA) at column temperature 30 °C; the volume injected sample was 5 µl69. Mobile phase for binary gradient elution consisted from (A): twice demineralized water containing 0.1% (v/v) formic acid and 10 mmol/L ammonium acetate and (B): acetonitrile containing 0.1% (v/v) formic acid. The gradient elution started at 15% (A) + 85% (B) and changed in 0-5 min interval of analyses from 85% (B) to 80% (B). Then in 5-6 min interval changed from 80% (B) to 85% (B) with a subsequent equilibration step of 85% (B) to 11 min. The flow rate of mobile phase was 0.4 mL/min. The Agilent 6495 Triple Quadrupole (Agilent Technologies, Santa Clara, CA) operating in the ESI-negative SRM mode was used for MS/MS analysis. Two MS/MS transitions of each pteridine were used for quantitative LC-MS/MS analyses. The conditions of triple quadrupole instrument optimised for analyses of pteridines were as follows: drying gas temperature 290 °C, drying gas flow 11 L/min, nebulizer gas pressure 45 psi, sheath gas temperature 350 °C, sheath gas flow 10 L/min, capillary voltage 3 500 V70. SRM transition of MS/MS analyses of pteridines are summarized in Table 6. The fragment ion with the highest abundance of each pteridine precursor was used for the quantification of the respective analyte. The fragment ion with the second highest abundance was used to confirm the presence of the respective analyte.

A method of internal standard calibration was used for the final quantification of the target compounds in the respective extract. Calibration curves were constructed in the concentration range 1.0-100 ng/mL of each pteridine using an internal standard of 6,7-dimethyl-5,6,7,8-tetrahydropterine hydrochloride at a concentration of 30 ng/mL. Instrumental limits of quantification (mean LOQ = 5 µg per injection) were determined from the concentration of individual standards giving an analyte to noise ratio of MS/MS detection of 10:1.

Individual steps in optimization of LC-MS/MS method are described in supplementary materials (section S1).

### Assay of laboratory-reared C. lectularius and C. pipistrelli of known age

Using the optimized LC-MS/MS protocol, we determined the association between the pteridine concentration, and the female age in bed/bat bugs that differ genetically (i.e., population, lineage, or species). We examined the five stock populations described above (2 Clec BL and HL populations each, reared at 27 °C, and one population of Cpip reared at 23 °C). Seven females were taken at 11–13 time points (cohorts) after eclosion till day 249. Sampling was spaced from 7 to 17 days, the last two (oldest) cohorts were 42 days apart.

### Assay of field-sampled bed bugs C. lectularius

To test the age distribution in the wild, we obtained snapshot (one time point) samples from two populations that did not belong to the study populations. In June 2018, Clec BL females were collected in a bat nursery colony in Loukov (northeast Bohemia, Czech Republic; n = 30) and in May 2011, Clec HL was collected in an apartment building in Krakow (Poland; n = 20). To predict the ages of field-sampled females, the marginal models of pteridine concentration of Clec lineages reared at 27 °C

$$(Concentratio{n}_{ij}={\alpha }_{i}+\beta Cohor{t}_{j}+{\varepsilon }_{ij},)$$
(1)

were modified to form the predictive equations for individual age of wild bed bugs from different lineages (Table 3).

### Statistical analysis

All statistical analyses were performed using R 3.6.171 using the packages nlme72 and ggplot273, only K-means clustering analysis was made in STATISTICA74.

All data were tested for normal distribution using Shapiro-Wilk test and for homogeneity of variances using Levene’s test. In order to determine the extraction method efficiency, a Kruskal-Wallis test with following non-parametric post-hoc comparisons were performed. The difference between storage modes of biological material before extraction, the light effect during extraction, the temperature and light-regime effect during rearing were tested using two-sample t-tests. The importance of internal standard use was verified by Wilcoxon matched-pairs signed-ranks test. The sample stability over time was tested by paired t-test. To detect the localization of pteridines in head parts and head size effect on pteridine concentration, one-way ANOVA with post-hoc comparisons using Scheffé's method was used.

To verify the established calibration curves, pteridine concentrations of blind samples were grouped based on K-means clustering analysis (the initial cluster centres were computed using the method of sorting distances and taking observations at constant intervals). The relation between age and pteridine concentration in blind samples was described using a linear regression model and the differences between age cohorts were tested by Kruskal-Wallis test with the following non-parametric post-hoc comparisons or with Mann-Whitney U test.

The association between pteridine concentration and female age was conducted using general least squares (GLS) regression and a partial t-test testing homogeneity of the slope:

$$Concentratio{n}_{ijk}=\alpha +Lineag{e}_{k}+{\beta }_{k}Cohor{t}_{j}+{\varepsilon }_{ijk},$$
(2)

where age cohort (Cohort) was treated as a continuous variable, lineage (Lineage) was a fixed factor, subscripts i, j and k refer to lineage and age cohort of the particular individual, α represented the intercept of pteridine concentration, β the slope of the relationship between age and pteridine concentration and ε residuals. Lineage was replaced by population to test differences between populations.

## Data availability

All relevant data are within the paper as Supporting Information files (Tables S1-3 and Figure S1) and in dataset repository Figshare https://doi.org/10.6084/m9.figshare.11316473.

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## Acknowledgements

Tomáš Bartonička, Jana Křemenová and Ondřej Balvín were supported by GACR grant (T.B., J.K., O.B. No. 18–08468 J) and Masaryk University (J.K. MUNI/A/1436/2018). Oliver Otti and Klaus Reinhardt were supported by a grant from the German Research Foundation (OT 521/4-1; KR 1666/4-1).

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T.B., K.R., O.O., O.B. and Z.Š. conceived the idea and designed the experiment. J.K., T.B., M.P., Z.Š. and O.O. carried out the experiment. T.B., J.K. and Z.Š. performed the bioinformatics and statistical analysis. T.B., J.K., and Z.Š. interpreted the results and wrote the manuscript. All authors read and approved of the final manuscript.

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Correspondence to Jana Křemenová.

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Křemenová, J., Balvín, O., Otti, O. et al. Identification and age-dependence of pteridines in bed bugs (Cimex lectularius) and bat bugs (C. pipistrelli) using liquid chromatography-tandem mass spectrometry. Sci Rep 10, 10146 (2020). https://doi.org/10.1038/s41598-020-66919-5

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text: Example: hands-on exercise $$\PageIndex{1}\label{he:proprelat-01}$$. Nonetheless, it is possible for a relation to be neither reflexive nor irreflexive. Therefore, $$R$$ is antisymmetric and transitive. hands-on exercise $$\PageIndex{6}\label{he:proprelat-06}$$, Determine whether the following relation $$W$$ on a nonempty set of individuals in a community is reflexive, irreflexive, symmetric, antisymmetric, or transitive: $a\,W\,b \,\Leftrightarrow\, \mbox{a and b have the same last name}. Exercise $$\PageIndex{5}\label{ex:proprelat-05}$$. • Is Rfun irreflexive? Many students find the concept of symmetry and antisymmetry confusing. Discrete Mathematics Properties of Binary Operations with introduction, sets theory, types of sets, set operations, algebra of sets, multisets, induction, relations, functions and algorithms etc. Relations Properties of Binary Relations Binary Relation A … However, for some authors and in everyday usage, orders are more commonly irreflexive, so that "John is taller than Thomas" does not include the possibility that John and Thomas are the same height. Solved programs: » CSS For the relation in Problem 9 in Exercises 1.1, determine which of the five properties are satisfied. The Logic of Compound Statements: Logical Form and Logical Equivalence, Conditional Statements, Valid and Invalid Arguments Would like to know why those are the answers below. The two most important classes of relations in math are order relations (antisymmetric and transitive) and equivalence relations (reflexive, symmetric and transitive). The relation is reflexive, symmetric, antisymmetric, and transitive. » DBMS » SEO Given any relation $$R$$ on a set $$A$$, we are interested in five properties that $$R$$ may or may not have. Therefore, R will be called a relation on X. » Certificates In this article, we will learn about the relations and the properties of relation in the discrete mathematics. In other words, a binary relation from A to B is a set T of ordered pairs where the first element of each ordered pair comes from A and the second element comes from B . Relations are subsets of two given sets. For each of the following relations on $$\mathbb{N}$$, determine which of the five properties are satisfied. Using this observation, it is easy to see why $$W$$ is antisymmetric. $$V_1=\{(x,y)\mid xy>0\}$$ $$V_2=\{(x,y)\mid x-y$$ … CS 441 Discrete mathematics for CS M. Hauskrecht Properties of relations Definition (irreflexive relation): A relation R on a set A is called irreflexive if (a,a) R for every a A. 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For each of the following relations on $$\mathbb{Z}$$, determine which of the five properties are satisfied. relations and their properties in discrete mathematics ppt, In discrete mathematics, we call this map that Mary created a graph. Since $$(2,3)\in S$$ and $$(3,2)\in S$$, but $$(2,2)\notin S$$, the relation $$S$$ is not transitive. Discrete Mathematics. Hence, these two properties are mutually exclusive. \nonumber$ Thus, if two distinct elements $$a$$ and $$b$$ are related (not every pair of elements need to be related), then either $$a$$ is related to $$b$$, or $$b$$ is related to $$a$$, but not both. Browse other questions tagged discrete-mathematics elementary-set-theory proof-explanation relations problem-solving or ask your own question. Discrete numeric function. The relation $$R$$ is said to be antisymmetric if given any two. Since $$\sqrt{2}\;T\sqrt{18}$$ and $$\sqrt{18}\;T\sqrt{2}$$, yet $$\sqrt{2}\neq\sqrt{18}$$, we conclude that $$T$$ is not antisymmetric. We find that $$R$$ is. Exercise $$\PageIndex{8}\label{ex:proprelat-08}$$. For each relation in Problem 1 in Exercises 1.1, determine which of the five properties are satisfied. It is obvious that $$W$$ cannot be symmetric. Exercise $$\PageIndex{10}\label{ex:proprelat-10}$$, Exercise $$\PageIndex{11}\label{ex:proprelat-11}$$. It is easy to check that $$S$$ is reflexive, symmetric, and transitive. \nonumber\]. Example 2: •Rfun on A = {1,2,3,4} defined as: •Rfun = {(1,2),(2,2),(3,3)}. Nobody can be a child of himself or herself, hence, $$W$$ cannot be reflexive. Properties: A relation R is reflexive if there is loop at every node of directed graph. Define a relation $$S$$ on $${\cal T}$$ such that $$(T_1,T_2)\in S$$ if and only if the two triangles are similar. Aptitude que. & ans. Exercises for Discrete Maths Discrete Maths Teacher: Alessandro Artale ... Science Free University of Bozen-Bolzano Disclaimer. » SQL A relation R is irreflexive if there is no loop at any node of directed graphs. The reflexive property and the irreflexive property are mutually exclusive, and it is possible for a relation to be neither reflexive nor irreflexive. © https://www.includehelp.com some rights reserved. Watch the recordings here on Youtube! » C A relation from a set $$A$$ to itself is called a relation on $$A$$. If $$b$$ is also related to $$a$$, the two vertices will be joined by two directed lines, one in each direction. More specifically, we want to know whether $$(a,b)\in \emptyset \Rightarrow (b,a)\in \emptyset$$. Properties of relations in math. Symmetric if $$M$$ is symmetric, that is, $$m_{ij}=m_{ji}$$ whenever $$i\neq j$$. Define the relation $$R$$ on the set $$\mathbb{R}$$ as $a\,R\,b \,\Leftrightarrow\, a\leq b. Since $$(a,b)\in\emptyset$$ is always false, the implication is always true. Let $${\cal T}$$ be the set of triangles that can be drawn on a plane. For instance, the incidence matrix for the identity relation consists of 1s on the main diagonal, and 0s everywhere else. Relations Properties of Binary Relations B5.2 Properties of Binary Relations Malte Helmert, Gabriele R oger (University of Basel)Discrete Mathematics in Computer Science October 7, 2020 7 / 14 B5. Again, it is obvious that $$P$$ is reflexive, symmetric, and transitive. The contrapositive of the original definition asserts that when $$a\neq b$$, three things could happen: $$a$$ and $$b$$ are incomparable ($$\overline{a\,W\,b}$$ and $$\overline{b\,W\,a}$$), that is, $$a$$ and $$b$$ are unrelated; $$a\,W\,b$$ but $$\overline{b\,W\,a}$$, or. \nonumber$ Determine whether $$R$$ is reflexive, irreflexive, symmetric, antisymmetric, or transitive. » Kotlin Define a relation $$P$$ on $${\cal L}$$ according to $$(L_1,L_2)\in P$$ if and only if $$L_1$$ and $$L_2$$ are parallel lines. » Embedded C \nonumber\] Determine whether $$U$$ is reflexive, irreflexive, symmetric, antisymmetric, or transitive. » DS More precisely, $$R$$ is transitive if $$x\,R\,y$$ and $$y\,R\,z$$ implies that $$x\,R\,z$$. The relation $$R$$ is said to be symmetric if the relation can go in both directions, that is, if $$x\,R\,y$$ implies $$y\,R\,x$$ for any $$x,y\in A$$. Unit: Details: I: Introduction: Variables, The Language of Sets, The Language of Relations and Function Set Theory: Definitions and the Element Method of Proof, Properties of Sets, Disproofs, Algebraic Proofs, Boolean Algebras, Russell’s Paradox and the Halting Problem. For example, $$5\mid(2+3)$$ and $$5\mid(3+2)$$, yet $$2\neq3$$. » Content Writers of the Month, SUBSCRIBE Math151 Discrete Mathematics (4,1) Relations and Their Properties By: Malek Zein AL-Abidin DEFINITION 1 Let A and B be sets. » Feedback For the relation in Problem 7 in Exercises 1.1, determine which of the five properties are satisfied. \nonumber\]. We conclude that $$S$$ is irreflexive and symmetric. hands-on exercise $$\PageIndex{4}\label{he:proprelat-04}$$. » Java Interview que. Example $$\PageIndex{2}\label{eg:proprelat-02}$$, Consider the relation $$R$$ on the set $$A=\{1,2,3,4\}$$ defined by $R = \{(1,1),(2,3),(2,4),(3,3),(3,4)\}. A binary relation from A to B is a subset of A × B . Exercise $$\PageIndex{6}\label{ex:proprelat-06}$$. » JavaScript » CS Organizations » Python For the relation in Problem 8 in Exercises 1.1, determine which of the five properties are satisfied. Submitted by Prerana Jain, on August 17, 2018. » C++ Discrete Mathematics Relations and Functions H. Turgut Uyar Ay¸seg¨ul Gen¸cata Yayımlı Emre Harmancı 2001-2016 2. Hence, $$T$$ is transitive. Relations. \nonumber$, hands-on exercise $$\PageIndex{5}\label{he:proprelat-05}$$, Determine whether the following relation $$V$$ on some universal set $$\cal U$$ is reflexive, irreflexive, symmetric, antisymmetric, or transitive: $(S,T)\in V \,\Leftrightarrow\, S\subseteq T. \nonumber$, Example $$\PageIndex{7}\label{eg:proprelat-06}$$, Consider the relation $$V$$ on the set $$A=\{0,1\}$$ is defined according to $V = \{(0,0),(1,1)\}. A similar argument shows that $$V$$ is transitive. » Contact us https://www.tutorialspoint.com/.../discrete_mathematics_relations.htm Web Technologies: \nonumber$ Determine whether $$T$$ is reflexive, irreflexive, symmetric, antisymmetric, or transitive. We have $$(2,3)\in R$$ but $$(3,2)\notin R$$, thus $$R$$ is not symmetric. \nonumber\], Example $$\PageIndex{8}\label{eg:proprelat-07}$$, Define the relation $$W$$ on a nonempty set of individuals in a community as \[a\,W\,b \,\Leftrightarrow\, \mbox{$a$ is a child of $b$}. There’s something like 7 or 8 other types of relations. Here, we shall only consider relation called binary relation, between the pairs of objects. Partially ordered sets and sets with other relations have applications in several areas. Exercise $$\PageIndex{7}\label{ex:proprelat-07}$$. The following are some examples of the equivalence relation: Join our Blogging forum. Exercise $$\PageIndex{1}\label{ex:proprelat-01}$$. My book doesn't do a good job explaining. Topics 1 Relations Introduction Relation Properties Equivalence Relations 2 Functions Introduction Pigeonhole Principle Recursion 4. Antisymmetric if every pair of vertices is connected by none or exactly one directed line. Exercise $$\PageIndex{4}\label{ex:proprelat-04}$$. Since $$(1,1),(2,2),(3,3),(4,4)\notin S$$, the relation $$S$$ is irreflexive, hence, it is not reflexive. More: Reflexive if every entry on the main diagonal of $$M$$ is 1. » News/Updates, ABOUT SECTION Indeed, whenever $$(a,b)\in V$$, we must also have $$a=b$$, because $$V$$ consists of only two ordered pairs, both of them are in the form of $$(a,a)$$. A relation is any association or link between elements of one set, called the domain or (less formally) the set of inputs, and another set, called the range or set of outputs. Example $$\PageIndex{3}\label{eg:proprelat-03}$$, Define the relation $$S$$ on the set $$A=\{1,2,3,4\}$$ according to \[S = \{(2,3),(3,2)\}. Some people mistakenly refer to the range as the codomain(range), but as we will see, that really means the set of all possible outputs—even values that the relation does not actually use. • Answer: No. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. & ans. If it is irreflexive, then it cannot be reflexive. It is clearly symmetric, because $$(a,b)\in V$$ always implies $$(b,a)\in V$$. » Ajax For more information contact us at info@libretexts.org or check out our status page at https://status.libretexts.org. Gen¸Cata Yayımlı Emre properties of relations in discrete mathematics 2001-2016 2 of ordered pairs of objects in a set X then D ( )! { 8 } \label { ex: proprelat-09 } \ ) Problem 3 in 1.1..., between the pairs of X and y are used to represent relation of vertices is connected none. Nobody can be a child of himself or herself, hence, \ ( T\ ) symmetric... 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text:
# Multiple list comparison Python

I have some code that has three lists, and it then checks the index of the second list against the index of the first as long as the first list has six elements. The code will then append to the third list if part of a string matches in the index of the first list. If the string does not match, it will append a message. I am hoping to find a better, more Pythonic way of writing my algorithm. Here is my code:

L1 = ["first = 1st","second = 2nd","third = 3rd","fourth = 4th","sixth = 6th",
"first = A","second = B","third = C","fifth = E","sixth = F",
"second = W","third = X","fourth = Y","fifth = Z","sixth = AA","first = BB"]
L2 = ["first","second","third","fourth","fifth","sixth"]
L3 = []

#Used in case a list has less than six elements
if len(L1) % 6 != 0:
L1.append("Missing_Data")

c = 0
for i in L1:
cont = True
while cont:
if L2[c] in i:
L3.append(i.split("= ")[-1])
c += 1
if c < len(L2):
cont = False
else:
c = 0
cont = False
else:
L3.append("Missing_Data")
c += 1
if c < len(L2):
continue
else:
c = 0
break

This code works for what I want it to do but I think its too long. Any help in making this code more Pythonic would be greatly appreciated. Thanks in advance.

• Can you show the output for the example and explain a bit more how it relates to the input? I'd prefer not having to read the code in order to try to understand what the task is that it's supposed to do. Not least because it wouldn't be the first time that people post actually wrong code, in which case we can't deduce the task from the code. – superb rain Sep 17 at 13:41

My review of your current code is easy to summarize: It's too darn complicated and makes my head hurt. But don't feel bad, because you're in great company. First attempts are often like that – even for people who have been doing this for a long time.

What, specifically, makes it hard to understand? Algorithmic complexity: nested loops and conditionals, breaks, managing list indexes, and so forth. Whenever you perceive that type of complexity, it often helps to consider whether a more powerful data structure would simplify the situation (I'm using "data structure" in a very broad sense). In the rewrite offered below, we will use a special iterable that allows us to peek at the next value without actually consuming it every time. That one change drastically simplifies the bookkeeping inside the main loop, and it also simplifies how we append the needed remainder of missing values after we exit the loop.

# This is a third party library that is worth knowing about.
from more_itertools import peekable

# Your data, aligned so we can see what is going on.
xs = [
'first = 1st', 'second = 2nd', 'third = 3rd', 'fourth = 4th',              'sixth = 6th',
'first = A',   'second = B',   'third = C',                   'fifth = E', 'sixth = F',
'second = W',   'third = X',   'fourth = Y',   'fifth = Z', 'sixth = AA',
'first = BB',
]

ys = ['first', 'second', 'third', 'fourth', 'fifth', 'sixth']

# Python has a builtin concept for missing data. Use it if you can.
# If you cannot, define a constant.
MISSING = None

# The results we want.
# When you ask a question, it's a good idea to provide this.
EXPECTED = [
'1st',     '2nd',     '3rd',     '4th',     MISSING,   '6th',
'A',       'B',       'C',       MISSING,   'E',       'F',
MISSING,   'W',       'X',       'Y',       'Z',       'AA',
'BB',      MISSING,   MISSING,   MISSING,   MISSING,   MISSING
]

# We will use a peekable iterable for both the Xs and the Ys.
xit = peekable(xs)
yit = None
results = []

# Process all Xs to build the results.
# A Y is consumed each time, and we get a fresh Ys iterable as needed.
# We consume an X only when current X and Y agree.
while xit:
yit = yit or peekable(ys)
x = xit.peek()
y = next(yit)
val = next(xit).split('= ')[-1] if y in x else MISSING
results.append(val)

# The results should always contain a full cycle of Ys.
results.extend(MISSING for _ in yit)

# Check.
print(results == EXPECTED)

• This is wonderful @FMc! I'm going to do more research on more_itertools to learn more about it. Using your code would drop the original by 13 lines. Cheers! – Hellyeah Sep 17 at 19:00
if c < len(L2):
continue
else:
c = 0
break

Since continue always happens at the end of a loop, you can reverse these conditions, to make it shorter.

if c >= len(L2):
c = 0
break

now you don't need else since anything else than the break condition will continue automatically.

Higher up where you set cont = False, you could use break instead as far as I can tell. That removes the need for cont altogether so you can just do while True:

• I tried this and it works! Thank you for the insight. – Hellyeah Sep 17 at 14:42

I'm mostly answering on SO so my answer might not be following PEP8 or other guidelines but I tried to make a version of your code that is easier to see what's going on, without ifs, breaks, continues and having a smaller line count:

length = len(L2)
missing = 'Missing_Data'
index = -1

for item in L1:
key,value = item.split(' = ')
current = L2.index(key)
no_missing = (current-index)%length-1 # get number of missing elements
L3 += [missing] * no_missing # append this many of the missing value
L3.append(value) # append current value
index = current

L3 += [missing] * (length-index-1) # fill rest of list with missing elements


text:
# Mill (grinding)

A mill is a device, often a structure, machine or kitchen appliance, that breaks solid materials into smaller pieces by grinding, crushing, or cutting. Such comminution is an important unit operation in many processes. There are many different types of mills and many types of materials processed in them. Historically mills were powered by hand or by animals (e.g., via a hand crank), working animal (e.g., horse mill), wind (windmill) or water (watermill). In modern era, they are usually powered by electricity.

Other names A tabletop hammer mill Grinding mill Grinding Mortar and pestleExpellerExtruder

The grinding of solid materials occurs through mechanical forces that break up the structure by overcoming the interior bonding forces. After the grinding the state of the solid is changed: the grain size, the grain size disposition and the grain shape.

Milling also refers to the process of breaking down, separating, sizing, or classifying aggregate material (e.g. mining ore). For instance rock crushing or grinding to produce uniform aggregate size for construction purposes, or separation of rock, soil or aggregate material for the purposes of structural fill or land reclamation activities. Aggregate milling processes are also used to remove or separate contamination or moisture from aggregate or soil and to produce "dry fills" prior to transport or structural filling.

Grinding may serve the following purposes in engineering:

• increase of the surface area of a solid
• manufacturing of a solid with a desired grain size
• pulping of resources

## Grinding laws

In spite of a great number of studies in the field of fracture schemes there is no formula known which connects the technical grinding work with grinding results. Mining engineers, Peter von Rittinger, Friedrich Kick and Fred Chester Bond independently developed equations relating produced equations to relate the needed grinding work to the grain size produced and a fourth engineer, R.T.Hukki suggested that these three equations might each describe a narrow range of grain sizes and proposed uniting them along a single curve describing what has come to be known as the Hukki relationship.[1][2][3]

In stirred mills, the Hukki relationship does not apply and instead, experimentation has to be performed to determine any relationship.[4]

To evaluate the grinding results the grain size disposition of the source material (1) and of the ground material (2) is needed. Grinding degree is the ratio of the sizes from the grain disposition. There are several definitions for this characteristic value:

• Grinding degree referring to grain size d80
${\displaystyle Z_{d}={\frac {d_{80,1}}{d_{80,2}}}\,}$
Instead of the value of d80 also d50 or other grain diameter can be used.
• Grinding degree referring to specific surface
${\displaystyle Z_{S}={\frac {S_{v,2}}{S_{v,1}}}={\frac {S_{m,2}}{S_{m,1}}}\,}$
The specific surface area referring to volume Sv and the specific surface area referring to mass Sm can be found out through experiments.
• Pretended grinding degree
${\displaystyle Z_{a}={\frac {d_{1}}{a}}\,}$
The discharge die gap a of the grinding machine is used for the ground solid matter in this formula.

## Grinding machines

In materials processing a grinder is a machine for producing fine particle size reduction through attrition and compressive forces at the grain size level. See also crusher for mechanisms producing larger particles. In general, grinding processes require a relatively large amount of energy; for this reason, an experimental method to measure the energy used locally during milling with different machines was recently proposed.[5]

### Autogenous mill

Autogenous or autogenic mills are so-called due to the self-grinding of the ore: a rotating drum throws larger rocks of ore in a cascading motion which causes impact breakage of larger rocks and compressive grinding of finer particles. It is similar in operation to a SAG mill as described below but does not use steel balls in the mill. Also known as ROM or "Run Of Mine" grinding.

Operation of a ball mill

### Ball mill

A typical type of fine grinder is the ball mill. A slightly inclined or horizontal rotating cylinder is partially filled with balls, usually stone or metal, which grind material to the necessary fineness by friction and impact with the tumbling balls. Ball mills normally operate with an approximate ball charge of 30%. Ball mills are characterized by their smaller (comparatively) diameter and longer length, and often have a length 1.5 to 2.5 times the diameter. The feed is at one end of the cylinder and the discharge is at the other. Ball mills are commonly used in the manufacture of Portland cement and finer grinding stages of mineral processing. Industrial ball mills can be as large as 8.5 m (28 ft) in diameter with a 22 MW motor,[6] drawing approximately 0.0011% of the total world's power (see List of countries by electricity consumption). However, small versions of ball mills can be found in laboratories where they are used for grinding sample material for quality assurance.

The power predictions for ball mills typically use the following form of the Bond equation:[7]

${\displaystyle E=10W\left({\frac {1}{\sqrt {P_{80}}}}-{\frac {1}{\sqrt {F_{80}}}}\right)\,}$

where

• E is the energy (kilowatt-hours per metric or short ton)
• W is the work index measured in a laboratory ball mill (kilowatt-hours per metric or short ton)
• P80 is the mill circuit product size in micrometers
• F80 is the mill circuit feed size in micrometers.

### Buhrstone mill

Another type of fine grinder commonly used is the French buhrstone mill, which is similar to old-fashioned flour mills.

### High pressure grinding rolls

A high pressure grinding roll, often referred to as HPGRs or roller press, consists out of two rollers with the same dimensions, which are rotating against each other with the same circumferential speed. The special feeding of bulk material through a hopper leads to a material bed between the two rollers. The bearing units of one roller can move linearly and are pressed against the material bed by springs or hydraulic cylinders. The pressures in the material bed are greater than 50 MPa (7,000 PSI). In general they achieve 100 to 300 MPa. By this the material bed is compacted to a solid volume portion of more than 80%.

The roller press has a certain similarity to roller crushers and roller presses for the compacting of powders, but purpose, construction and operation mode are different.

Extreme pressure causes the particles inside of the compacted material bed to fracture into finer particles and also causes microfracturing at the grain size level. Compared to ball mills HPGRs achieve a 30 to 50% lower specific energy consumption, although they are not as common as ball mills since they are a newer technology.

A similar type of intermediate crusher is the edge runner, which consists of a circular pan with two or more heavy wheels known as mullers rotating within it; material to be crushed is shoved underneath the wheels using attached plow blades.

### Pebble mill

A rotating drum causes friction and attrition between rock pebbles and ore particles. May be used where product contamination by iron from steel balls must be avoided. Quartz or silica is commonly used because it is inexpensive to obtain.

### Rod mill

A rotating drum causes friction and attrition between steel rods and ore particles.[citation needed] But note that the term 'rod mill' is also used as a synonym for a slitting mill, which makes rods of iron or other metal. Rod mills are less common than ball mills for grinding minerals.

The rods used in the mill, usually a high-carbon steel, can vary in both the length and the diameter. However, the smaller the rods, the larger is the total surface area and hence, the greater the grinding efficiency[8]

Principle of SAG Mill operation

### SAG mill

SAG is an acronym for semi-autogenous grinding. SAG mills are autogenous mills that also use grinding balls like a ball mill. A SAG mill is usually a primary or first stage grinder. SAG mills use a ball charge of 8 to 21%.[9][10] The largest SAG mill is 42' (12.8m) in diameter, powered by a 28 MW (38,000 HP) motor.[11] A SAG mill with a 44' (13.4m) diameter and a power of 35 MW (47,000 HP) has been designed.[12]

Attrition between grinding balls and ore particles causes grinding of finer particles. SAG mills are characterized by their large diameter and short length as compared to ball mills. The inside of the mill is lined with lifting plates to lift the material inside the mill, where it then falls off the plates onto the rest of the ore charge. SAG mills are primarily used at gold, copper and platinum mines with applications also in the lead, zinc, silver, alumina and nickel industries.

### Tower mill

Tower mills, often called vertical mills, stirred mills or regrind mills, are a more efficient means of grinding material at smaller particle sizes, and can be used after ball mills in a grinding process. Like ball mills, grinding (steel) balls or pebbles are often added to stirred mills to help grind ore, however these mills contain a large screw mounted vertically to lift and grind material. In tower mills, there is no cascading action as in standard grinding mills. Stirred mills are also common for mixing quicklime (CaO) into a lime slurry. There are several advantages to the tower mill: low noise, efficient energy usage, and low operating costs.

Table top hammer mill

### Vertical shaft impactor mill (VSI mill)

A VSI mill throws rock or ore particles against a wear plate by slinging them from a spinning center that rotates on a vertical shaft. This type of mill uses the same principle as a VSI crusher.

## Types of grinding mills

• Windmill, wind powered
• Watermill, water powered
• Horse mill, animal powered
• Ship mill, floats near a river bank or bridge
• Arrastra, simple mill for grinding and pulverizing (typically) gold or silver ore.
• Roller mill, an equipment for the grinding or pulverizing of grain and other raw materials using cylinders
• Stamp mill, a specialized machine for reducing ore to powder for further processing or for fracturing other materials
• A place of business for making articles of manufacture. The term mill was once in common use for a factory because many factories in the early stages of the Industrial Revolution were powered by a watermill, but nowadays it is only used in a few specific contexts; e.g.,

## References

1. ^ Lynch, A.J.; Rowland, C.A. (2005). "Chapter 2. The Science and the Scientists". The History of Grinding. Society for Mining, Metallurgy, and Exploration. ISBN 978-0-87335-238-3. Retrieved 2022-10-04.
2. ^ A. Jankovic; H. Dundar; R. Mehta‡ (March 2010). "Relationships between comminution energy and product size for a magnetite ore" (PDF). The Journal of the Southern African Institute of Mining and Metallurgy. 110.{{cite journal}}: CS1 maint: date and year (link)
3. ^ Hukki, R.T. (1961). "Proposal for Solomonic settlement between theories of Rittinger, Kick,and Bond". scribd.com.
4. ^ Thomas, A; Filippov, L.O. (1999). "Fractures, fractals and breakage energy of mineral particles". International Journal of Mineral Processing. 57 (4): 285. doi:10.1016/S0301-7516(99)00029-0.
5. ^ Baron, M.; Chamayou, A.; Marchioro, L.; Raffi, J. (2005). "Radicalar probes to measure the action of energy on granular materials" (PDF). Advanced Powder Technology. 16 (3): 199. doi:10.1163/1568552053750242.
6. ^ "ABB". ABB Communications. ABB Communications.
7. ^ Mineral Beneficiation – The Third Theory of Comminution – Document Summary. Onemine.org. Retrieved on 2010-10-09.
8. ^ Wills, B.A. (2006). Mineral Processing Technology: An Introduction to the Practical Aspects of Ore Treatment and Mineral Recovery. Vol. 7th ed. Amsterdam, Boston, MA. p. 157. ISBN 0750644508.
9. ^ Strohmayr, S. and Valery, W. Jr. SAG mill circuit optimisation at Ernest Henry Mining. ResearchGate.net
10. ^ Mular, Andrew L.; Halbe, Doug N.; Barratt, Derek J. (2002). Mineral Processing Plant Design, Practice, and Control: Proceedings. SME. pp. 2369–. ISBN 978-0-87335-223-9. Retrieved 26 October 2012.
11. ^ van de Vijfeijken, Maarten (October 2010). "Mills and GMDs" (PDF). International Mining: 30.
12. ^ Gearless mill drives. abb.com