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BackgroundSpecific toxic compounds, such as polycyclic aromatic hydrocarbons (PAHs) and their metabolites, may affect the inhalation injury (INHI) grade, patients' status, and prognosis for recovery. This pilot prospective study aimed to: i) evaluate the suitability of bronchoalveolar lavage (BAL) for determination of PAHs in the LRT and of urine for determination of hydroxylated metabolites (OH-PAHs) in patients with INHI, ii) describe the dynamic changes in the levels of these toxic compounds, and iii) correlate these findings with clinical variables of the patients with INHI.MethodsThe BAL and urine samples from 10 patients with INHI were obtained on Days 1, 3, 5, 7, and 14 of hospitalization, if possible, and PAHs (BAL) and OH-PAHs (urine) were analyzed using chromatographic methods (GC-MS and HPLC).ResultsConcentrations of analyzed PAHs were in most cases and time points below the limit of quantification in BAL samples. Nine OH-PAHs were detected in the urine samples; however, their concentrations sharply decreased within the first three days of the hospitalization. On Day 14, the total amount of OH-PAHs in urine was higher in surviving patients with High-grade INHI (≥3) than in those with Low-grade INHI (ConclusionsBAL samples are not suitable for the analysis of PAHs. However, the OH-PAHs levels in urine can be measured reliably and were correlated with several clinical variables. Moreover, High-grade INHI was associated with higher total concentrations of OH-PAHs in urine.

Introduction: In this study, we aimed to characterise exposure to pyrethroids, organophosphates, and tebuconazole through multiple pathways in 110 parent–child pairs participating in the CELSPAC–SPECIMEn study. Methods: First, we estimated the daily intake (EDI) of pesticides based on measured urinary metabolites. Second, we compared EDI with estimated pesticide intake from food. We used multiple linear regression to identify the main predictors of urinary pesticide concentrations. We also assessed the relationship between urinary pesticide concentrations and organic and non-organic food consumption while controlling for a range of factors. Finally, we employed a model to estimate inhalation and dermal exposure due to spray drift and volatilization after assuming pesticide application in crop fields. Results: EDI was often higher in children in comparison to adults, especially in the winter season. A comparison of food intake estimates and EDI suggested diet as a critical pathway of tebuconazole exposure, less so in the case of organophosphates. Regression models showed that consumption per g of peaches/apricots was associated with an increase of 0.37% CI [0.23% to 0.51%] in urinary tebuconazole metabolite concentrations. Consumption of white bread was associated with an increase of 0.21% CI [0.08% to 0.35%], and consumption of organic strawberries was inversely associated (-61.52% CI [-79.34% to -28.32%]), with urinary pyrethroid metabolite concentrations. Inhalation and dermal exposure seemed to represent a relatively small contribution to pesticide exposure as compared to dietary intake. Conclusion: In our study population, findings indicate diet plays a significant role in exposure to the analysed pesticides. We found an influence of potential exposure due to spray drift and volatilization among the subpopulation residing near presumably sprayed crop fields to be minimal in comparison. However, the lack of data indicating actual spraying occurred during the critical 24-hour period prior to urine sample collection could be a significant contributing factor.

Quality communication between a teacher and a student or students contributes to the process of learning a foreign language. Communication in foreign language teaching is both a means of communication and the content of teaching. The model of willingness to communicate in a foreign language describes individual characteristics and situational variables that affect a pupil’s readiness to enter dialogue with another person at some point. The present study provides information on the process and results of scale adaptation Willingness to Communicate Inside the Classroom scale. The process of adaptation to Czech conditions includes the verification of content validity, construct validity, and the identification of a factor structure of the instrument. Using exploratory factor analysis (EFA) procedures in the JASP program 0.14.1. the suitability of the use of the originally designed scale was verified and a reduction from twenty-seven to eighteen items was proposed. The internal consistency of the Czech version of the Willingness to Communicate Inside the Classroom scale showed a sufficient Cronbach’s alpha coefficient of .82, thus we can assume that the tested scales show sufficient reliability.

BackgroundThe impact of the urban environment on human health is a contemporary subject of environmental research. Air pollution is often considered a leading environmental driver. However, a plethora of other factors within the urban exposome may be involved. At the same time, the resolution of spatial data is also an important facet to consider. Generally, systematic tools for accurate health risk assessment in the urban environment are missing or are not implemented.MethodsThe long-term impact of air quality (PM10, PM2.5, NO2, benzene, and SO2) on respiratory and cardiovascular health was assessed with a log-linear model. We used the most accurate health data in high city scale spatial resolution over the period 2010 to 2018. Selected external exposome parameters were also included in the analysis.ResultsStatistically significant associations between air pollution and the health of the urban population were found. The strongest association was between benzene and the incidence of bronchitis in the adult population [RR 1.552 95% CI (1.415–1.704) per 0.5 μg/m3 change in benzene concentration]. A similar relation was observed between NO2 and the same health condition [RR 1.483 95% CI (1.227–1.792) per 8.9 μg/m3 of change in NO2]. Other weaker associations were also found between asthma in children and PMs, NO2, or benzene. Cardiovascular-related hospitalizations in the general population were linked with NO2 [RR 1.218 95% CI (1.119–1.325) per 9.7 μg/m3 change in NO2]. The remaining pollutants were slightly less but still significantly associated with cardiovascular-related hospitalizations.ConclusionOur findings are mostly highly statistically significant (p ≤ 0.001) and are in line with current literature on the adverse effects of air pollution on the human population. The results highlight the need for continual improvements in air quality. We propose the implementation of this approach as a systematic tool for the investigation of possible health risks over a long period of time. However, further research involving other variables is an essential step toward understanding the complex urban exposome and its implications for human health. An increase in data spatial resolution is especially important in this respect as well as for improving city health risk management.

This study evaluated the environmental genotoxic load of mountain and alpine habitats of Slovak mountains caused by the total mixture of air pollutants at 69 sites using the phytoindicator Pinus mugo. The level of overall genotoxicity was determined by pollen grain abortion assay. This shows that the test is sensitive enough to detect contamination from more distant sources, including long-range transboundary pollutants. It extends the applicability of this test to mountain environments. Soil and plant samples (pollen, one-two year old needles) were collected during a three-year growing period (2011–2013). The study identified source regions of pollutants by assessments at different altitudes and slope exposures. The highest genotoxicity was found in the Little Fatra Mts. on Suchy Mt., with pollen abortivity 3.52 % which represented a 23.5 times higher genotoxic load than at the control site. Samples from mountain peaks showed a higher genotoxicity in 2012 than in 2011 on most mountains. A gradual increase of pollen abortivity and needle Pb content (one year old) with increasing altitude was found in the vertical transect in Belian Tatras. The influence of subsoil type was analysed; higher genotoxicity and Pb content in soil and needles were found on limestone subsoil (Sivy vrch Mt.) and higher values of needle Cd were on granite (Brestova Mt.). The highest Pb and Cd concentrations in needles were measured in the Great Fatra Mts. on Krizna Mt. situated between highly-industrialized areas. The other mountain ranges with the high loading by Pb, Cd were Chocske vrchy Mts. and Low Tatra Mts. The lead content increased with needle age, but the correlation between soil Pb and needle Pb was not confirmed. The positive correlation between soil Pb and abortivity was found only at mountain peaks. The results showed a significant impact of both local industrial and transboundary sources of pollutants. Based on the results, the studied Slovak mountains were not strongly burdened by Pb, Cd and an overall mixture of air pollutants. This methodological approach may contribute to the assessment of urban exposome by comparing the external exposure in urban environment of big cities with background - mountain areas, where the only possible source is long-range transport.

A short proof of the middle-levels theorem, Discrete Analysis 2018:8, 12 pp. Let $n$ be a positive integer, and define a bipartite graph where one vertex set consists of all subsets of $\{1,2,\dots,2n+1\}$ of size $n$, the other consists of all subsets of size $n+1$, and we join a set $A$ of size $n$ to a set $B$ of size $n+1$ if and only if $A\subset B$. The following innocent looking question was an open problem for a long time: does this graph contain a Hamilton cycle? That is, can we find a sequence of sets $A_1,B_1,\dots,A_N,B_N$ (where $N=\binom{2n+1}n$) such that each set of size $n$ or $n+1$ appears exactly once, and such that $A_1$ is contained in $B_1$, which contains $A_2$, which is contained in $B_2$, and so on all the way up to $B_N$, which contains $A_1$? For very small values of $n$, one can find Hamilton cycles, and one can even imagine that one is finding them in a potentially systematic way, but in the end all patterns seem to evaporate. One difficulty is that it can be shown that in any Hamilton cycle, each of the $2n+1$ possible edge directions must occur the same number of times. This means that if one tries to use a solution to the $n-1$ case to build a Hamilton cycle for the $n$ case, one will have to chop it up into exponentially many pieces. (This is in sharp contrast with the case of the entire $n$-dimensional cube, where one can easily prove that it contains a Hamilton cycle by taking two parallel Hamilton cycles in copies of an $(n-1)$-dimensional cube, removing an edge from the first and the corresponding edge from the second, and adding two linking edges to form a single Hamilton cycle.) Another approach that one might imagine attempting to use is a probabilistic one, perhaps creating most of a Hamilton cycle randomly and then making a few adjustments at the end in order to complete it. But this kind of argument also runs into problems: the constraints are not too severe to start with, but the more of the cycle one constructs, the stronger they become, and without a clever idea one gets stuck long before completing a cycle. In 2014 the problem, by then over 30 years old, was solved by Torsten Mütze [1], one of the authors of this paper, using a long and technical (and constructive) argument. This paper gives a much shorter and simpler argument that avoids nearly all the technicalities of the first argument and thereby makes Mütze's remarkable result truly accessible for the first time. Very roughly, the idea behind the proof is to begin by finding a certain special collection $\mathcal C$ of vertex-disjoint cycles that includes all vertices. If there were only one cycle in the collection, we would be done, but since that is not the case, we have to join them together. This is done by using an auxiliary collection of 6-cycles: if a 6-cycle intersects the union of two cycles $C_1,C_2$ in a particular way, then the symmetric difference of all three cycles is a single cycle that visits the same vertices as $C_1$ and $C_2$. The authors prove various lemmas about the cycles in $\mathcal C$ and the 6-cycles, which they then use to prove that this process can be continued until there is just one cycle left. (The reason 6-cycles are used, rather than 4-cycles as in the case of the complete cube, is brutally simple: it is easy to check that the middle-layers graph does not contain any 4-cycles.) The proof gives rise to an efficient algorithm for actually finding Hamilton cycles in the middle-layers graph. If you are curious to see what the cycles look like, the algorithm can be run online on [this web page](http://page.math.tu-berlin.de/~muetze/cos/middle.html). [1] Torsten Mütze, _Proof of the middle levels conjecture_, Proc. London Math. Soc. *112* (2016), pp. 677-713. Also available at [arXiv:1404.4442](https://arxiv.org/abs/1404.4442)

Graphs and Algorithms

Graphs and Algorithms

Given a family $\{u_i,v_i\}_{i=1}^k$ of pairwise distinct vertices of the $n$-dimensional hypercube $Q_n$ such that the distance of $u_i$ and $v_i$ is odd and $k \leq n-1$, there exists a family $\{P_i\}_{i=1}^k$ of paths such that $u_i$ and $v_i$ are the endvertices of $P_i$ and $\{V(P_i)\}_{i=1}^k$ partitions $V(Q_n)$. This holds for any $n \geq 2$ with one exception in the case when $n=k+1=4$. On the other hand, for any $n \geq 3$ there exist $n$ pairs of vertices satisfying the above condition for which such a family of spanning paths does not exist. We suggest further generalization of this result and explore a relationship to the problem of hamiltonicity of hypercubes with faulty vertices.