Fluorescent in situ hybridization (FISH) has been extensively used in the past decades for the detection and localization of nucleic acid sequences or of the microorganisms themselves within samples. However, a mechanistic approach of the whole FISH process is still missing, and the main limiting steps for the hybridization to occur remain unclear. In here, FISH is approached as a particular case of a diffusion-reaction kinetics, where molecular probes move from the hybridization solution to the target RNA site within the cells. Based on literature models, the characteristic times taken by different molecular probes to diffuse across multiple cellular barriers, and the reaction time associated with the formation of the duplex molecular probe-RNA were estimated. Structural and size differences at the membrane level of bacterial and animal cells were considered. For bacterial cells, the limiting step for diffusion is likely to be the peptidoglycan layer (characteristic time of 2700-4524 s), whereas for animal cells the limiting step should be the diffusion of the probe through the bulk (1.8-5.0 s) followed by the diffusion through the lipid membrane (1 s). The information provided here may serve as a basis to optimize FISH protocols.

Plant negative density dependence is the result of interactions between plants themselves and between plants and the environment. We selected a succession series comprising early successional, mid-successional and late successional stages (Artemisia ordosica, Sophora alopecuroides and Stipa bungeana communities, respectively) in a semi-arid area. We investigated plant density and biomass and determined the nitrogen (N) and phosphorus (P) contents of each plant species in each of 225 quadrats, and we calculated the N and P contents of vegetation using biomass as a weighted coefficient. We found that the total plant density of the A. ordosica community increased with the increase in vegetation N:P ratio while the total plant density of the S. bungeana community decreased with the increase in vegetation N:P ratio, with the latter (late successional stage) community exhibiting negative density dependence. In the communities representing the early successional and mid-successional stages, the vertex coordinate of the quadratic function relationship between plant total density and vegetation N/P ratio was (16.6, 353.3); that is, if the N:P ratio of the vegetation was greater than 16.6, the community was characterized by negative density dependence. The analysis showed that the negative density dependence was due to P limitation. These findings reveal that the vegetation N:P ratio in a semi-arid region is the driver of negative density dependence.

Steel pipe dampers offer advantages such as a simple structure, low cost, high energy absorption and dissipation, consistent functionality under cyclic loading, and ductility. Dual-pipe dampers show improved performance over single pipe dampers in terms of strength. The current study focused on the structural performance of the dual-pipe system. The seismic performance of steel-framed structures having 4, 8, or 16 stories with either a simple moment frame or a braced frame equipped with pipe dampers were subjected to seismic loading and investigated using the finite element method. The performance of the models was examined by considering the base shear and lateral displacement of the roof as well as the von Mises distribution. The stress distribution caused by the plastic damage concentration increased in the pipe dampers in the 4- and 8-story models and the base shear decreased 50% in the 4-story models equipped with a pipe damper. The results showed that, in the 16-story models, the strength in the damping system should be designed in accordance with the other elements. In addition, the strength of the damping system can be increased by increasing the number of pipes and their thickness.

Herein a simple, compact quad-band circularly polarized monopole antenna is proposed for multisystem application. The monopole antenna is constructed via triple strip fed by the microstrip line, a ground plane on the reverse side of the substrate having a slotted square loop, and two stubs which are slotted employed transversely across the diagonal line on the square loop. This proposed antenna is simulated and fabricated to stimulate a number of resonances. Optimizations of the antenna design parameters combined the resonances, and thus obtained a wide multi impedance bandwidth (IBW). The measured multi IBW at S11<-10dB ranges from 4.63 – 5.47 GHz, 6.08 – 6.59 GHz, 8.26 – 9.59 GHz, 10.05- 10.42 GHz, and 11.81 – beyond 15 GHz. The simulated quad axial ratio bands are 217, 269, 223 and 564 MHz at centre frequencies (fc) of 5.3, 9.0, 12.1 and 13.8 GHz, correspondingly. Implemented antenna radiation features are also presented and deliberated.

The influences of the initial states of HCl on the stereodynamics properties of the Ca+HCl reaction are investigated by utilizing the method based on the quasi-classical trajectory (QCT) theory and the analytical potential energy surface (APES). The orientation and alignment behaviors for the rotational angular momentum of the product, along with the generalized differential cross-section (PDDCS) dependent polarization, are employed to explore the stereodynamics properties. The initial rotational states of the HCl molecule impose a remarkable affection on the vector correlation distributions, regardless of the orientation, alignment, or PDDCS. The obvious forward or backward scattering, as well as the weak sideway scattering phenomena, are found for the different initial rotational states of the HCl molecule. The initial higher rotational-excited state of j=3 results in more obvious stereodynamics effects.

Tea is the second most consumed non-alcoholic beverage, only next to water. However, its production and qualities, including rich flavors and numerous health benefits, are often degraded by environmental stresses and contaminations with various agrochemicals. While most of tea quility-contributing secondary metabolites are synthesized in tea plant leaves, such as catechins, caffeine, volatiles, saponins, and theanine, primarily for defenses against biotic and abiotic stresses, few tea garden management measures have employed this tea plant innate innumity to enhance their tolerance against environmental stresses. This is partly due to the limited understanding of the biosynthesis and regulationof tea plant secondary metabolism. Given the importance of tea plant secondary metabolites for both tea flavors, health functions, and resistance against environmental stresses, study and in-depth understanding of the biosynthesis and environmental regulation of tea plant specialized metabolites are highly expected. Strategies developed from these studies would promote the production of safe and high quality teas. The review highlights relevant contexts of tea plant-environmental interaction at the secondary metabolism interfaces, particular their roles in enhancement of tea plant innate immunity and tea quality, so as to guide future research on genetic improvement of tea plants for safer food production and better human nutrition.

Rationale, aims and objectives; Magnetic resonance imaging (MRI) can be perceived as unpleasant even though the examination is noninvasive. Patients’ knowledge of the MRI procedure is usually scarce, which might enhance patient anxiety at the examination. The aims of this randomized single-blind placebo-controlled trial were to investigate the effects on anxiety and satisfaction with information of a standardized booklet on MRI compared to a placebo booklet delivered to adult patients prior to their first MRI examination. Method; The intervention group (n=95) received a standardized booklet prior to MRI, while the control group (n=102) received a placebo booklet in the same size and lay out but containing general information. The State Trait Anxiety Inventory (STAI) with supplementary questions from the Quality from the Patient’s Perspective questionnaire were used as the patient-reported outcome measures. Results; There was no significant difference in anxiety between the groups, either prior to MRI or during the examination, but those who received the placebo booklet were at higher risk of experiencing high anxiety prior to the MRI examination (odds ratio, 2.64; P=0.029). The intervention group was more satisfied with the information received (P=0.044), and a majority of participants in both groups (≥87%) considered it important to obtain information on the MRI procedure. Conclusion; Standardized written MRI information decreases the risk of experiencing high anxiety levels before MRI and improves patients’ satisfaction with the information. Further research is needed to investigate whether written information prior to MRI is beneficial not only from the patient perspective but if it can also be proven cost-effective.

The biogeographical distribution of diversity among populations of threatened mammalian species is generally investigated through population genetics. However, intraspecific phenotypic diversity is rarely assessed beyond taxonomy-focused linear measurements or qualitative descriptions. Here, we use a technique widely used in the evolutionary sciences – geometric morphometrics – to characterize shape diversity in the skull of an endangered marsupial, the northern quoll, across its 5,000 km distribution range along the northern Australian coast. Skull shape is a proxy of feeding, behaviour, and phenotypic differentiation, allowing us to ask if populations can be distinguished and if patterns of variation indicate adaptability to changing environmental conditions. We analysed skull shape in 101 individuals across the four mainland populations and several islands. We assessed the contribution of population, size, sex, rainfall, temperature, and latitude/longitude to skull shape variation through Principal Components, Procrustes ANOVA, and variation partitioning analyses. Regardless of land area inhabited, northern quoll populations harbour similar amounts of broadly overlapping skull shape variation. Size predicted skull shape best, coinciding with braincase size variation and differences in the cheekbone shape. Size-adjusted population differences explained less variation with far smaller effect sizes, relating to changes in insertion areas of masticatory muscles, as well as the upper muzzle and incisor region. Climatic and geographic variables contributed little or nothing. Strikingly, the vast majority of shape variation - 76% - remained unexplained. Our results suggest a uniform within-species scope for shape variation, possibly due to phenotypic plasticity or allometric constraints. The lack of local adaptation indicates that cross-breeding between populations will not reduce local morphological skull (and probably general musculoskeletal) adaptation because none exists. However, the potential for heritable morphological variation (e.g. specialization to local diets) seems exceedingly limited. We conclude that 3D geometric morphometrics can provide a comprehensive, statistically rigorous phenomic contribution to genetics-based conservation studies.

Letter to the Editor, BJOG Exchange

Since December 2019, a new coronavirus (COVID-19) infection has rapidly become prevalent in central China [1]. On the basis of knowledge obtained from a previous coronavirus outbreak [2], pregnant women are believed to be susceptible to this virus. Once a maternal infection of 2019-nCoV is suspected or confirmed, childbirth becomes complicated and challenging. Efficient obstetric treatment is required, and is key to optimizing the prognosis for both mother and child. Care should be taken in determination of the timing of delivery, assessment of the indications for caesarean section, preparation of the delivery room to prevent infection, choice of the type of anesthesia, and newborn management.

Abstract: Objective: This study aimed to assess the cost-effectiveness of implementing NIPT screening for DS based on government-funded projects in China. Design: Decision analytical model. Setting: Fuyang City People’s Hospital (FCPH) in China. Population: 1,400 maternal women in FCPH for the period March to June 2019. Methods: An incremental cost-effectiveness ratio (ICER) was calculated from a societal perspective. Univariate sensitivity analysis measured the impact of the uptake rate of NIPT and the cost of NIPT, and probabilistic sensitivity analysis (PSA) also was conducted. Main outcome measures：The number of DS case detected. Results: NIPT age-related screening strategy (Strategy D) has the lowest ICER, with an ICER of USD 25,641.22 per additional DS case detected compared with second-trimester serum screening Strategy (Strategy A). Universal NIPT screening (Strategy E) was the most effective and showed more DS case detected compared with alternative strategies. However, it was also the most expensive strategy. Strategy E would not be cost-effective unless the unit cost of NIPT could be decreased to USD 57.00. PSA results indicated that, at willingness-to-pay threshold under USD 120,000.00, Strategy D is cost-effective compared with combined serum and NIPT screening (Strategy C, also the referred strategy in China). Conclusion: Compared with current referred screening strategy in China, age-related NIPT contingent screening performances better in cost-effectiveness analysis and safety, which should be recommended to pregnant women. While under the government-funded projects in China, universal NIPT screening is still not optimal. Lowering the price of NIPT is an effective measure to promote universal NIPT Strategy

In atmospheric fatigue, intrinsic threshold stress intensity, Kth, far from being a material constant, varies significantly. It is controlled by a certain computable, load-history sensitive, near-tip residual stress, s*, that appears to moderate crack-tip diffusion kinetics and thereby determines Kth, the incremental K required for an open crack to extend by fatigue. This demands reconsideration of the relationship between near-threshold crack growth rates and applied effective stress intensity range, DKeff. Its practical implementation requires considerations of Linear Hysteretic Fracture Mechanics (LHFM). LHFM is applied to translate applied K, to near-tip cyclic inelastic stress-strain response. A procedure is described to separate intrinsic threshold stress intensity from ‘extrinsic’ component for a known DKth, obtained by conventional means. This opens the way to engineering application of the vast amount of available legacy fatigue threshold data obtained on long cracks by load shedding techniques. The new relationships permit extension of fracture mechanics considerations to short cracks including defects in additive manufactured materials and naturally forming cracks in components over high-cycle and very high-cycle (HCF/VHCF) regimes. Most importantly, the new approach permits handling near-threshold fatigue response both under constant amplitude as well as under variable-amplitude loading, representative of actual service conditions. It also permits re-interpretation of test data obtained by the so-called cyclic R-curve and compression-compression pre-cracking techniques.

Adenylate Kinase (ADK) catalyzes the reversible interconversion between cytoplasmic nucleotides that is essential for energy homeostasis. We performed several Molecular Dynamics simulations on ADK, containing metal ions Mg+2 and Zn+2. The dynamics of the enzyme were computed on the ion-free structure, and the structures containing individual ions. RMSD and Rg data demonstrate that the coordination of Zn+2 does not significantly affect the overall stability of the enzyme. Decreasing the overall dynamics of the enzyme in the presence of both metal ions was explained by the cooperativity between the stabilizing interactions of metal ions. The high RMSF value of a specific segment in the presence of both ions, demonstrates that a fine balance between the conformational stability and local structural dynamics may be involved in the regulation of the enzyme catalysis. It was also concluded that the orientation of the structural domains is affected by the simultaneous presence of both ions.

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Resistance to insecticides in the mosquito Anopheles gambiae s.l can jeopardize malaria vector control strategies in Africa. Previous studies have shown that the agricultural use of pesticides, particularly for cotton protection, contributes to the selection of insecticide resistance of malaria vector mosquitoes. Our study aimed at assessing the impact of three cotton pests control strategies in different ecological settings (conventional, organic and transgenic cotton growing areas) on the i) susceptibility to insecticides (Permethrin and Deltamethrin (pyrethroids), DDT (organochlorine), Bendiocarb (carbamate), chlorpyriphos-methyl (organophosphate) tested on the main malaria vectors and ii) frequencies of kdr L1014F, during rainy season of 2008, 2009, 2013 and 2014 in Burkina Faso, West Africa. From 2008 to 2014, a reduction in susceptibility to all insecticides except chlorpyriphos-methyl was detected in most populations of An. gambiae s.l from the three cotton growing areas. The frequency of kdr-w mutations varied depending on localities and species within the An. gambiae complex, but we found no relationship between the cotton pest control strategy and the frequency of kdr-w or, otherwise with phenotypic resistance evaluated from bioassays. The implementation of organic cotton and Bt transgenic cotton programs in certain areas of Burkina Faso does not change the insecticide resistance status of An. gambiae s.l. populations in the region concerned. These results confirm the worrying status of insecticide multi-resistance of the main malaria vector mosquito species in Burkina Faso.

Loss-of-function mutations in the COL2A1 gene were recently described as a cause of type II collagenopathy, a major subgroup of genetic skeletal diseases. However, the pathogenic mechanisms associated with COL2A1 mutations remain unclear, and there are few large-mammal models of these diseases. In this study, we established a swine model carrying COL2A1 mutations using CRISPR/Cas9 and somatic cell nuclear transfer technologies. Animals mutant for COL2A1 exhibited severe skeletal dysplasia characterized by shortened long bones, abnormal vertebrae, depressed nasal bridge, and cleft palate. Importantly, COL2A1 mutant piglets suffered tracheal collapse, which was almost certainly the cause of their death shortly after birth. In conclusion, we have demonstrated for the first time that overt and striking skeletal dysplasia occurring in human patients can be recapitulated in large transgenic mammals. This model underscores the importance of employing large animals as models to investigate the pathogenesis and potential therapeutics of skeletal diseases.

Macrophyte productivity supports the littoral food web in fresh waters where widespread active CO2 concentrating mechanisms (CCMs) allow their productivity to be maintained despite potential inorganic carbon limitation. We studied HCO3- acquisition, the most common CCM in macrophytes, in the freshwater monocot Ottelia alismoides and showed that the external carbonic anhydrase (CA) inhibitor acetazolamide (AZ) decreases the affinity for CO2 uptake and prevents HCO3- use. The anion exchanger (AE)/solute carrier (SLC) type HCO3- transporters inhibitor 4,4’-diisothio-cyanatostilbene-2,2’-disulfonate (DIDS), has a smaller effect on CO2 uptake but also prevents HCO3- use. Analysis of transcripts showed that putative αCA-1 and SLC4 HCO3- transporters are unaffected by acclimation of leaves to different CO2, in agreement with physiological measurements showing a constitutive HCO3- use. Therefore, it is likely that αCA-1 and SLC4 HCO3- transporters are the targets of AZ and DIDS, respectively. Altogether, these results are consistent with acquisition of HCO3- based on co-diffusion of CO2 and HCO3- through the boundary layer, conversion of HCO3- to CO2 at the plasmalemma by αCA-1 and in addition, transport of HCO3- across the plasmalemma by SLC4 transporters. A model of these processes has been produced that can be used to test inorganic carbon uptake in future experiments.

Protein modification by aldehydes has been generally associated with aging and onset of various chronic and cardiovascular diseases. The characteristics of bovine serum albumin (BSA) incubated with three dien-aldehydes (trans, trans-2,4-heptadienal, trans, trans-2,4-nonadienal, trans, trans-2,4-decadienal) of different chain lengths at different concentrations were examined. The results were as follows: loss of the amino group and increased carbonyl value were indicative of BSA side chain damage by these three unsaturated aldehydes. Sodium dodecyl sulfate-polyacrylamide gel electrophoresis results showed that all the three aldehydes led to formation of BSA aggregation; the most significant effect was observed for heptadienal. Changes in intrinsic fluorescence and surface hydrophobic value of BSAs indicated that aldehydes modified protein structures of BSAs. Moreover, the three aldehydes used in this experiment caused BSAs to form yellowish-brown adducts and fluorescent lipofuscin. The heptadienal-BSA adducts exhibited increased ultraviolet–visible (UV-Vis) absorbance at 270-280 nm and 300-400 nm, similar to the two other aldehyde-BSA adducts. We also examined the correlation between the various oxidation parameters and the concentration of modifiers. Strong correlations were observed between formation of protein-bound carbonyls, the retention ratio of free amino content, maximum UV-Vis absorption value, and concentration of aldehydes. Finally, Principal component analysis (PCA) analysis was conducted on oxidation parameters and the comprehensive effect of these parameters on BSA modification. In general, greater BSA damage was observed when incubated with aldehydes with shorter chain length at higher concentration.

Rice bran as a by-product of rice processing can be used to produce oil. The main objective of this study was to select appropriate enzymes for aqueous enzymatic extraction (AEE) and evaluated the quality of rice bran oil (RBO) obtained by AEE and solvent extraction (SE). In addition, the microstructure of rice bran before and after different extraction processes were also observed. The results showed that Alcalase 2.4L was the most effective in releasing RBO. Moreover, iodine value and saponification value in the AEE-extracted oil (AEEO) were found to be higher than the SE-extracted oil (SEO). AEEO with lower acid value and peroxide value was considered to be a high quality and the content of wax and phospholipid in AEEO were lower, which could simplify the refining steps. Additionally, AEEO exhibited a higher content of unsaturated fatty acids (76.31%), vitamin E (1004.42 mg/kg), sterols (7749.44 mg/100 g), squalene (2962.56 mg/kg) and oryzanol (2.43%). In comparison to the SEO, AEEO was found to have lower crystallization and melting points. Scanning electron microscope (SEM) results showed the destruction of cell walls and the decrease of substances in the cell by AEE. In general, the results of this study showed improvement in the quality of the AEEO and provided necessary data support for green extraction of RBO in food industry.

The most common food using hemp (Cannabis sativa L.) is hempseed oil (HSO) because it is a rich source of nutrients and not nutrients with nutritional and functional beneficial effects for human body. Harvesting time can affect the quality of HSO, consequently the aim of this study was to evaluate the composition of lipid fraction, fatty acids, tocopherols and sterols, during ripening. Two cultivars, Futura 75 and Carmagnola, were collected at three ripening stages during August and September 2015 and their lipid composition was determined by analytical techniques. Among the fatty acid identified, the linoleic acid was the preponderant, followed by oleic, α-linolenic and palmitic acid. Linoleic:α-linolenic acid and polyunsaturated:saturated fatty acid ratios decreased and increased, respectively, in both varieties with ripening. γ-tocopherol was the preponderant tocopherol identified, Futura 75 showed the highest content in the middle of maturation while Carmagnola at the beginning. β-sitosterol was the predominant sterol identified in both varieties, followed by campesterol, Δ5-avenasterol, stigmasterol and Δ7-stigmasterol. Total sterol content increased and decreased with ripening in Futura 75 and Carmagnola, respectively. The study confirms that ripening stage affects the quality of hempseed oil, important parameter to consider for hemp seed producers.

In this study neutralized and bleached canola oil, deodorized according to the Central Composite Design consisting 30 experiments with differing levels of deodorization temperature, pressure, stripping steam rate and time parameters. Free fatty acid (FFA) content, oxidation stability index (OSI), peroxide value (PV), total polar compounds (TPC), tintometric redness, fatty acid composition of every deodorized canola oil sample was measured. Deodorization parameters were optimized using only responses with good model fit by aiming lowest free fatty acid and trans-linolenic acid (tr-C18:3) contents and highest OSI value and polyunsaturated fatty acid (PUFA) content via Response Surface Methodology. Optimum temperature, pressure, stripping steam, and time were predicted as 228.8°C, 1.4mBar, 1.25 gr/min and 80 minutes, respectively and the optimization model has predicted the FFA level to be 0.044%, OSI as 10.65h, tr-C18:3 content as 0.21% and PUFA content as 30.50%. Results of the validation experiments at this optimum point were close to the those predicted and the relative differences between predicted and validation results were within the variance coefficients of each model. Temperature and time of deodorization were found significantly effective on trans isomerization of linolenic acid on ANOVA, therefore the reaction rate constants of tr-C18:3 formation and cis-linolenic acid (cis-C18:3) degradation were calculated together with Arrhenius’ equation constants using graphical method. Cis-C18:3 degradation rate was higher than that of tr-C18:3 formation showing; besides isomerization, different decomposition mechanisms took place for possibly not only for linolenic acid but also for all polyunsaturated fatty acids of canola oil during deodorization.

During Qingjinju processing, a large quantity of seeds is produced as agro-industrial waste. However, these seeds contain oil that may be a potential source of valuable compounds. This work describes the physicochemical properties, nutrient substances, and volatile compounds of Qingjinju seed oils obtained using different extraction methods. The main volatile compounds of Qingjinju seed oils were esters, aldehydes, hydrocarbons, acids, and alcohols. The seven major volatile compounds were found across all extraction techniques. The extraction methods were found to influence the quality of Qingjinju seed oils. Solvent extraction oils possessed superior physicochemical properties, such as lower acid and peroxide values and were lighter in color. Screw press extraction and supercritical CO2 extraction oils contained more nutrient substances, such as limonin and nomilin. These findings suggest that varying the extraction technique can prepare Qingjinju seed oils for targeted applications in the food, cosmetic, detergent, and pharmaceutical industries.

ABSTRACT We consider a ’Fekih-Ahmed’ transform based on a single equation which is probably a coincidence. MAIN Consider the series expansion for the reciprocal Gamma function {\Gamma(z)} = ^\infty a_n z^n = z + \gamma z^2 + \left({2} - {12}\right)z^3 + \cdots According to the Wikipedia page (Reciprocal gamma function) there is an integral formula for these coefficients due to Fekih-Ahmed: a_n = {\pi n!}\int_0^\infty e^{-t}\Im[(\log(t)-i\pi)^n]dt excellent, looks interesting. Let’s draw analogy from the Mellin transform, and the definition of the Gamma function \Gamma(z) = \int_0^\infty e^{-t}t^{z-1} dt both of these equations have an e−t, the integral domain is the same and both relate to Gamma functions. We also note the presence of the term $$ \chi(n) = {n!} $$ which is critical in the Ramanujan master theorem allowing us to express the Mellin transform of a function with expansion $$ f(x) = ^\infty \chi(k)\phi(k)x^k $$ as [f](s) = \int_0^\infty x^{s-1}f(x) \; dx = \Gamma(s)\phi(-s) where possible. Based on this we absorb the coefficient in the definition and define the Fekih-Ahmed transform as [f](n) = \int_0^\infty f(x) \Im[(\log(t)-i\pi)^n] {\pi} and allow functions to be defined by g(x) = ^\infty \chi(k)[f](k)x^k namely {\Gamma(z)} = ^\infty \chi(k)[e^{-x}](k) z^k Put into words: “The gamma function is Mellin transform of e−x, the function whose alternating exponential coefficient is 1.” and “The alternating exponential coefficient of the reciprocal gamma function is the Fekih-Ahmed transform of e−x”. This is not quite symmetric, but there seems to be a rough interplay between the concepts. Let’s explore further... EXAMPLES It seems that $$ {n!}\left[{(x+1)^k}\right](n) = {(k-1)!}, n<k $$ we are in sketchy territory for inserting random functions into the transform, as we are trying to match up terms from series expansions and from the integral evaluations. It will be more productive to take a series expansion of a related function such as $$ {\Gamma(z)\Gamma(z+1)} = z+ 2 \gamma z^2 + \cdots $$ and work out the contents of the FA transform that match this, perhaps it will be a simple function: Following the logic of Mellin transforms, it might be best to explore hypergeometric type arguments. For example the inverse Mellin transform of Γ(s)² is $$ ^{-1}[\Gamma(s)^2](x) = 2K_0(2\sqrt(x)) $$ so we consider $$ g(x) = ^\infty \left[2K_0(2)\right](k+1) z^k = 1 + 2\gamma z + 2\gamma^2 z^2 + {3}z^3 + {3}z^4 + \cdots = A + B + C + \cdots $$ which seems to have a component of $$ A = ^\infty {n!}\gamma^n z^n = e^{2 \gamma z} $$ this seems to be the right kind of language to describe these expansions. We can inspect in more detail the meaning of the term in the integral. In terms of a probability distribution or similar: $$ [f](1)}{1!} = \int_0^\infty f(x) dx $$ the n = 1 term is the normalization. $$ [f](2)}{2!} = \int_0^\infty -\log(x) f(x) dx $$ the n = 2 term is the expectation of the ’negative log’. $$ [f](3)}{3!} = \int_0^\infty (\log(t)^2/2-\zeta(2)) f(x) dx $$ $$ [f](4)}{4!} = \int_0^\infty (\zeta(2)\log(x) - \log(t)^3/6) f(x) dx $$ The coefficients appear to be A109447, $$ ... $$

The comment by Gamisch (2020) draws the attention of users of the R-package RPANDA (Morlon et al. 2016) on situations when properly interpreting the results of linear diversification dependencies requires caution. Here we provide clarifications to help users interpreting their results when using any type of functional diversification dependencies with time or the environment.