The feasibility to find stable BNF isomers with atomic arrangement other than the well-known octahedral Th-symmetry was explored. In this study, the number of homonuclear bonds in the modeled nanostructures was used as categorical parameter to describe and quantify the degree of structural order. The BNF without homonuclear bonds was identified as the most energetically favorable isomer. However, a variety of BNF arrays departing from Th-symmetry was determined as stable structures also. The calculated vibrational spectra suggest that isomers with chemical disorder can be identified by infrared spectroscopy. In general, formation of homonuclear bonds is possible meanwhile the entropy of the system increases, but at expense of cohesive energy. It is proposed that formation of phase-segregated regions stablishes an apparent limit to the number of homonuclear bonds in stable B12N12 fullerenes. It was found that formation of homonuclear bonds decreases substantially the chemical hardness of BNF isomers and generates zones with large charge density, which might act as reactive sites. Moreover, chemical disorder endows BNF isomers with a permanent electric dipole moment as large as 3.28 D. The obtained results suggest that by manipulating their chemical order, the interaction of BNF’s with other molecular entities can be controlled, making them potential candidates for drug delivery, catalysis and sensing.The effect of chemical order in the structural and physicochemical properties of B Additionally, a variety of BN nanostructures has been already synthetized, such as nanosheets, nanowires, nanotubes and fullerenes3. These nanosized polymorphs have been identified as promising materials for energy storage4, catalysis5, molecular sensing6, tribology7, heat transport8 and drug delivery9. Particularly, for those systems constituted by a few dozens of atoms, important efforts have been done to determine the effect of atomic arrangement in their functional properties. For example, in 1993 Jensen and Toftlund10 proposed several B12N12 conformational isomers based on their carbon counterparts, namely, monocyclic ring, graphite-like sheet and two fullerene structures. From computational ab initio calculations at the MP2/DZP level, they determined that among them, that with truncated octahedron symmetry (point group: Th) has the lowest total energy. This -fullerene has 14 faces generated by 36 covalent bonds between B and N atoms with sp2 hybridization. Six faces correspond to 4-membered rings (2B2N) and the other eight to 6-membered rings (3B3N). The B-N bond lengths belong in the range of 1.44–1.48 Å, being the overall size of the nanostructure around 0.4 nm. Several years later, Strout11 performed additional calculations using both Hartree-Fock and density functional theory (DFT) in local and gradient-corrected forms. Again, the octahedral Th-symmetry was identified as the most stable arrangement for B12N12 conformational isomers. In the late 90 s, Golberg et al.12 reported a method to obtain this kind of nanostructures using electron beam irradiation. Their B/N stoichiometric ratio was confirmed to be ∼1 by electron energy loss spectroscopy (EELS) and predicted octahedral symmetry was verified through high-resolution transmission electron microscopy (HRTEM).Boron nitride (BN) compound has gained huge attention because its high mechanical hardness, thermochemical stability, and electric and thermal conductivity. In bulk form, it crystallizes in hexagonal, cubic, rhombohedral and monoclinic structuresFor simplicity reasons, most theoretical models consider materials as defect-free systems, thus periodic and/or symmetrical atomic arrays are frequently used to study their properties. Nonetheless, at temperatures above 0 K, formation of defects debasing symmetry might occur spontaneously meanwhile the contribution to free energy due to entropy exceeds that of enthalpy. Under this condition, a large defect density may lead to substantial discrepancies between theoretical predictions and experimental measurements.14. In the case of the B12N12 fullerenes, although the octahedral Th-symmetry has been identified as the more energetically favorable atomic array, to the best of our knowledge, there is no direct evidence that discards formation of stable -fullerenes having homonuclear bonds (B-B and N-N) due to swapping B and N sites, i.e., isomers with some degree of chemical disorder. Because deeper understanding of chemical order may contribute to achieve fine-tuning of molecular functions, the aim of this study is to explore from a theoretical perspective the feasibility to find stable B12N12 -fullerene isomers with atomic arrangement other than the octahedral Th-symmetry, if so, quantify the effect of chemical order in their structural and physicochemical properties.Evidently, the role of chemical order in the physical and chemical properties become more preponderant as the size of the system decreases. For example, it has been demonstrated that the catalytic, optical and magnetic properties of bimetallic nanoparticles depend on whether their components are distributed is such manner to form mixing patterns or phase-separated arrangements12N12 -fullerene (BNF) having Th-symmetry. This B12N12 conformational isomer has no homonuclear bonds15. Hereafter, it is termed as the symmetric BNF isomer. When homonuclear bond restriction is discarded, the number of different arrangements is as large as ∼106. Clearly, a study of such population is intractable without a statistical approach. The methodology to select a representative sample was as follows. Initially, one thousand different BNF initial models (staring points) were generated using a regular truncated octahedron as template . B and N atoms were then placed at the apices randomly. The obtained arrangements were analyzed and organized considering the chemical order index σ as categorical attribute  and disordered (σ ≈ 0) mixtures from that systems with segregated phases (σ > 0). In our case, σ is also a measure of the number of homonuclear (B-B and N-N) and heteronuclear (B-N) bonds ratio. The chemical order index σ for the BNF isomers was defined as:nB-N, nB-B and nN-N are the number of B-N, B-B and N-N bonds, respectively. Since nB-B = nN-N = (36 − nB-N)/2, and defining nhomobonds = nB-B + nN-N, Eq. , the sample set was completed by adding them manually. Using this methodology, the initial BNF isomers set was constituted by 50 initial models distributed in 15 categories {x, σ, n} : {0, −1, 1}, {4, −0.78, 2}, {6, −0.67, 2}, {8, −0.56, 2}, {10, −0.44, 3}, {12, −0.33, 3}, {14, −0.22, 5}, {16, −0.11, 8}, {18, 0, 8}, {20, 0.11, 5}, {22, 0.22, 3}, {24, 0.33, 3}, {26, 0.44, 2}, {28, 0.56, 2} and {30, 0.67, 1}. For visualizing the whole set of BNF models please see Supplementary Table After, an appropriate number of isomers were randomly selected from each category to obtain a distribution that resembles that of the parent sample. Because models laying at the distribution tails have almost negligible probability to be generated through random process  basis set proposed by Pople et al.20 as implemented in the GAUSSIAN–09 package21. All the systems were considered as neutral in charge and having multiplicity M = 1 . Initially, an ultrafine integration grid and stringent convergence criterion (10−8 hartrees) were set for the total energy calculations. Then, atomic relaxation was conducted by setting the force convergence threshold at 10−6 hartrees bohr−1.The structural and physicochemical properties of the BNF isomers were studied by means of first principles calculations based on density functional theory (DFT) within the generalized gradient approximation (GGA). For this purpose, allab-initio molecular dynamic (MD) calculations using the atom density matrix propagation method (ADMP)24 as implemented in the GAUSSIAN–16 software25. For this purpose, the potential was determined “on-the-fly” at the HSE1PBE/6-31 G level of theory. MD-ADMP calculations were conducted with a step time of 0.2 fs, and intervals of 2.0 ps were considered for statistical analyses. The control of temperature was attained by velocity scaling at each step, and equations of motion were solved through the Verlet velocity algorithm26. The cohesive energy (Ecoh) for all isomers was determined as the average difference of energy per atom before and after getting bounded:The structural stability of the optimized models was verified by calculating their vibrational spectra within the harmonic approximation; non-imaginary frequency was used as stability criterion. Additionally, the kinetic stability of selected optimized isomers was further evaluated at room temperature by calculating propagation of nuclear centers and electron density through EB and EN are the energy of non-interacting boron and nitrogen atoms, respectively, and Etot is the total energy of the stable fullerene isomer (gas phase). Further characterization of the modeled systems was addressed by calculating the highest occupied molecular orbital (HOMO) energy εHOMO, the lowest unoccupied molecular orbital (LUMO) energy εLUMO, HOMO-LUMO gap energy εHOMO-LUMO, chemical hardness η, Mulliken electronegativity χ, dipole moment p, and molecular electrostatic potential (MEP) isosurfaces. According to Parr et al.27 and Zhan et al.28, η equals to εLUMO − εHOMO, and χ = −(εLUMO + εHOMO)/2, being the negative of the chemical potential μ (χ = −μ). Finally, the effect of chemical order in the charge distribution within the BNF isomers was studied by calculating p and MEP isosurfaces29.where 12 polytope and whose B-N, B-B and N-N bond lengths are within the range of ±10% the average value.Figure σ ≥ 0.33. Conversely, most of the optimized isomers with σ ≤ 0 have closed-shell structure and equal number of homonuclear bonds as the initial ones. Existence of several local minima implies that chemical disorder in B12N12 fullerenes does not necessary lead the system to an unstable state.A comparison of the number of homonuclear bonds before and after geometry optimization suggests that the minimum-energy path gets more biased as the number of homonuclear bonds increases. The latter can be interpreted as absence of local minima of the potential energy surface near the initial arrangements with et al.30 (−956.18558 hartrees) using the B3LYP functional along with the correlation-consistent double-zeta (cc-pVDZ) basis set. Additionally, Shevlin et al.31 estimated the cohesive energy of this fullerene in 7.30 eV/atom using a Perdew–Burke–Ernzerhof (PBE) functional, in agreement with the obtained value of 7.61 eV/atom. In the case of stable isomers with some degree of structural disorder, the total energy increases linearly with chemical order index. This behavior indicates that the energy difference among isomers resides mostly in the homonuclear bonds rather than structural stress. Since two homonuclear bonds (one B-B and one N-N) are formed at expense of two heteronuclear bonds, the total energy of the BNF must change in steps nearly to (EB-B + EN-N) − 2EB-N as σ increases. Under this reasoning, the magnitude of such discrete changes is estimated in 0.12 hartrees  each. It agrees with the reported dissociation enthalpies of B-N , B-B  and N-N  bonds32. Because thermal energy at room temperature is around 0.59 kcal mol−1 (gas phase), spontaneous reduction of the chemical order index in disordered BNF’s is not expected without an additional energy supply.Figure S, should increase progressively as σ approaches to zero (ΔS > 0). It agrees with the microscopic interpretation of entropy introduced by Boltzmann33, since the category with the largest number of different BNF arrangements corresponds to σ ≈ 0  chemical segregation is favored. These atomic arrays might be related to non-equilibrium states because the total energy of the system rises, but at the same time, it gets ordered, reducing its entropy; note that the number of different possible configurations decreases sharply as σ gets more positive. The previous arguments stablish an apparent limit to the number of homonuclear bonds in stable B12N12 fullerenes. In this sense, it is proposed that formation of homonuclear bonds can occur meanwhile the entropy of the system increases, but at expense of its cohesive energy.Lack of stable isomers with phase-segregated regions (numerous homonuclear bonds) and large total energy (low cohesive energy) can be understood from thermodynamic considerations. Assuming that the energy to generate homonuclear bonds were supplied as heat, the entropy of the system, see Fig. . HoweverεHOMO and εLUMO with σ of the different stable BNF isomers. In general, the frontier orbitals show an opposite behavior, in such a way that their energies approach as the chemical order index increases. The εHOMO-LUMO of the symmetric fullerene was calculated to be 6.67 eV, but it decays exponentiality up to an asymptotic value of ∼1 eV as σ increases. In agreement, Soltani et al.34 and Baei35 reported the εHOMO-LUMO of the symmetric B12N12 fullerene in 7.20 and 6.85 eV, respectively. These values indicate that this nanostructure behaves as an insulating material. Interestingly, formation of just a few homonuclear bonds induces an insulator-semiconductor transition. Since the εHOMO-LUMO of BNF isomers with σ > −1 readily trends to a similar value, it is proposed that the features of the HOMO and LUMO in disordered B12N12 fullerenes is determined mainly by the states associated to homonuclear bonds, rather than some specific atomic array. Figure Figure η) and electronegativity (χ) 27. This result indicates that this fullerene does not tend to form covalent bonds with other molecules. Nonetheless, chemical hardness decreases considerably due to formation of homonuclear bonds, and even lower values than that of molecular potassium (ηK2 < 2 eV)28 are calculated for isomers with intermediate chemical order index . It follows that, chemical disorder leads readily B12N12 fullerenes to be more liable to interact with their surroundings.An insight of the chemical behavior of the BNF isomers was elucidated from analyzing their chemical hardness . Seifert σ. For the symmetric fullerene, it was calculated to be 7.17 eV. The obtained χ values for the rest of isomers belong in the range of 6.47–7.62 eV . Therefore, the capacity to attract electrons by B12N12 fullerenes does not decrease due to chemical disorder.Conversely to chemical hardness, the electronegativity of the BNF isomers does not have an evident dependence with p) is a convenient observable, not just for describing the charge distribution, but to elucidate the interaction among chemical species through electrostatic and/or dipole-dipole attraction37. Figure Th-symmetry entails a null permanent dipole moment. Therefore, its interaction with other non-polar entities must be weak. Nonetheless, adsorption of low-electronegative sorbates through charge transfer mechanism or interaction with high polar molecules by induced dipole attraction still might be possible.Certainly, chemical interaction among molecular entities can be described in terms of their chemical hardness and electronegativity. Nonetheless, their interaction is mediated by the force filed generated by the spatial charge distribution within the system. In this regard, the magnitude of dipole moment . Nonetheless, it is worth noting that for some isomers having the same number of homonuclear bonds, their dipole moment can be six times as large as another analogous isomer. Moreover, the results suggest the range of p-values increases in size with σ. It could be just because the number of possible atomic configurations growths significantly as σ approaches zero. In any case, it is evident that the magnitude of the permanent dipole moment generated by chemical disorder depends on the atomic arrangement. Further detail of its influence in the spatial distribution charge, and thus, the permanent dipole moment, can be obtained by calculating their MEP isosurfaces. Figure σ = −1), the charge density is symmetrically distributed around its mass center, being the electron density concentrated at the more electronegative nitrogen atoms. However, if two B-N pairs swap their sites (σ = −0.67), two analogous mononuclear groups resembling centered triangles are formed. Again, the N-group concentrates the electronic charge, and its position respect to the positive charged zone (B-group) determines the polar character of the fullerene. Since the positive and negative charged zones can be adjacent, but not overlapped, a non-zero dipole moment is a distinctive physicochemical feature of B12N12 fullerenes with some degree of chemical disorder. In this regard, large p-values seem to be related to formation of nitrogen rings . The latter explains the general relationship between p and σ observed in Fig. Certainly, the magnitude of  σ = −0.6, two anaσ = 0.11 (20 homonuclear bonds). The isomer with the smallest dipole moment is constituted by two incomplete nitrogen rings (1B5N) separated by a boron chain. Thus, the opposite position of these N-groups balances the negative charge around the mass center. Formation of 4-membered nitrogen rings are recognized in those isomers with intermediate dipole moment . In agreement with MEP isosurfaces, this geometrical feature matches with the largest positive charge density, and the resulting p-value is determined by its position respect to the largest B-group. Finally, the most polar isomer (p = 3.28 D) is characterized by a 6-membered nitrogen ring. Here, segregation of nitrogen atoms facilitates boron counterpart groups form at the opposite hemisphere of the fullerene structure. It follows, p increases notoriously.The likely correlation between the magnitude of the permanent dipole moment with some structural motif was confirmed by analyzing the atomic arrangement of several isomers with equal chemical order index. Figure 12N12 fullerenes could be identified by analyzing their Raman and/or infrared (IR) spectrum. Figure −1. It is attributed to symmetric stretching mode of N-B-N groups belonging to 4-memebered rings. Additionally, a weak band associated to wagging mode of 1B3N and 3B1N groups appears at 803 cm−1 36. In the case of isomers with chemical disorder, the latter results in an increasing number of infrared-active vibrational modes. It is proposed that this feature might be exploited through infrared spectroscopy as indicator of a fraction of isomers having some degree of structural disorder. In analogy to the symmetric BNF isomer, two groups of infrared bands are distinguished. The first corresponds to strong high-frequency modes , whereas the second to weaker low-frequency modes (800–200 cm−1). A systematic smearing towards lower frequencies are observed in both groups as σ increases. Several authors have suggested that low-frequency vibrational modes may be correlated with irreversible structural rearrangements of disordered systems near to the threshold of mechanical stability39. Thus, these transitions are associated to systems settled at local minima with low-potential energy barriers. In order to identify possible structural rearrangements of BNF isomers with chemical disorder towards Th symmetry or unstable states, the kinetic stability of the most stable ordered (σ = −1) and disordered  isomers was explored through ab-initio molecular dynamic trajectories at 300 K. Figure gab(r) of heteronuclear and homonuclear bonds were calculated under dynamic conditions  functions show a slight difference in the characteristic B−N bond length. It is determined that bonds constituting four-membered rings have lengths mainly retained in the range 1.40–1.60 Å, and those of six-membered rings belong in range 1.35–1.50 Å. When chemical disorder is present, the bond distances fall in the ranges 1.30–1.60 Å, 1.35–1.60 Å and 1.60–1.80 Å for B-N, N-N and B-B bonds, respectively. As can be noted, the dispersion of gab(r) functions increases with the number of homonuclear bonds. It suggests that kinetic stability of BNF isomers progressively decreases with chemical disorder, in agreement with the calculated cohesive energies.Since vibrational modes of materials are sensitive to the atomic arrangement, the corresponding vibrational spectrum can be considered as the fingerprint of each structure. In this sense, structural disorder in B12N12 -fullerene (BNF) isomers was studied from a theoretical perspective using density functional theory and molecular dynamic calculations. In agreement with previous reports, the octahedral Th-symmetry was identified as the most energetically favorable atomic arrangement; its cohesive energy was calculated to be around 7.6 eV/atom. However, a variety of stable BNF isomers having homonuclear bonds generated by chemical disorder were found also. In general, formation of homonuclear bonds is possible meanwhile the entropy of the system increases, although it occurs at expense of cohesive energy. Whereas the electronegativity of the BNF does not show an evident dependence with chemical order, its chemical hardness decreases considerably due to formation of homonuclear bonds, corresponding to the sites with large charge density. Conversely to the symmetric fullerene, the isomers with some degree of chemical disorder have an intrinsic electric dipole, which is favored by formation of large N- and B-rich moieties (4- or 6-membered rings). These changes in the physicochemical properties could make BNF’s with chemical disorder more liable to interact with their surroundings and be solubilized in polar media. Finally, it is proposed that using infrared spectroscopy is possible to identify whether a fraction of stoichiometric BNF present structural disorder by analyzing the number of bands in the range of 1,500–1,000 cm−1.The effect of chemical order in the structural and physicochemical properties of BSupplementary information


Cucumber selective breeding over recent decades has dramatically increased productivity and quality, but the genomic characterizations and changes associated with this breeding history remain unclear. Here, we analyzed the genome resequencing data of 56 artificially selected cucumber inbred lines that exhibit various phenotypes to detect trait-associated sequence variations that reflect breeding improvement. We found that the 56 cucumber lines could be assigned to group 1 and group 2, and the two groups formed a distinctive genetic structure due to the breeding history involving hybridization and selection. Differentially selected regions were identified between group 1 and group 2, with implications for genomic-selection breeding signatures. These regions included known quantitative trait loci or genes that were reported to be associated with agronomic traits. Our results advance knowledge of cucumber genomics, and the 56 selected inbred lines could be good germplasm resources for breeding. Cucumis sativus L.; 2n = 2x = 14) is generally considered to be an economically important vegetable crop worldwide1, as well as a well-characterized model for studying fleshy fruit development2. Cultivated cucumber varieties have evolved from their wild progenitors under natural and artificial selection4. The domestication of cucumber began ~3000 years ago, and since then, different breeding strategies have been used to produce desired characteristics in order to meet the demand for human nutrition and health5. However, it was reported that cucumber had a low species diversity due to narrow bottlenecks3; therefore, the breeding of new cucumber varieties that require low inputs and are environmentally sustainable will probably still be challenging in the future.Cucumber  are used to detect genetic variations that underlie many important and complex traits in plants21. To date, some loci or genes have been identified by genomic studies in cucumber with large natural populations23. However, very few studies have identified loci or genomic regions in populations exposed to long-term artificial selection.Traditionally, the breeding of cucumber germplasm was accomplished simply by selecting lines with desirable characteristics for propagation, while the new methodology has accompanied the development of high-volume parallel genotyping and sequencing technologies, for instance, genomic selectionIn recent decades, we focused on breeding elite cucumbers with outstanding phenotypes by crossing excellent Asian and European germplasm and performing artificial selection. On the one hand, we aimed to combine desirable agronomic traits from Asian and Eurasian lines in the progenies. On the other hand, we always selected the seeds from healthy plants and removed the disease-infected plants; therefore, most of the lines performed well in the field and were free of disease infection. As a result of long-term selection, we obtained 56 elite cucumber lines that retained phenotypic diversity. In this case, we would like to know the genomic characterizations and changes associated with this breeding history and the potential of our breeding materials.3. The data from our 56 lines revealed specific selected regions related to breeding efforts, and these selected regions were associated with the agronomic performance of cucumber varieties and harbored many reportedly important genes.Here, we resequenced the 56 cucumber lines and found that their genetic background was significantly different from that previously reported for 115 cucumber lines24 , which has a background similar to that of East Asian (EA) cucumber lines, and group 2 (G2), which has the Eurasian (EU) background (Supplementary Table https://www.ncbi.nlm.nih.gov/)3. Resequencing of the 56 selected lines generated a total of 1.6 billion paired-end reads, with an average depth of ~18× and coverage of 98.4%  were identified , Indian wild (INW) and Xishuangbanna (XSBN) groups  was used, the G1, G2, EA, EU, IND, INW, and XSBN groups were assigned to independent clusters ups Fig. , which w= 2 Fig. . Within sis Fig. . When thers Fig. . However. 3 Fig. . In addi32 model and the seven populations, we detected that G1 and G2 were phylogenetically similar to the EA population, and the migration edge signaled introgression of EU into G1 and G2, especially to G2  with increasing physical distance between SNPs was calculated by combining the 115 publicly available lines. The results indicated that both G1 and G2 cucumbers exhibited higher LD than previously reported for the 115 lines  for the G1, G2, EA, EU, IND, INW, and XSBN lines were 1.56 × 10−3, 1.71 × 10−3, 1.37 × 10−3, 2.26 × 10−3, 4.25 × 10−3, 9.27 × 10−3, and 1.37 × 10−3, respectively . The high LD and low π values confirmed that G1 and G2 are highly artificially selected populations.Increased linkage disequilibrium (LD) and reduced nucleotide diversity are expected in artificial selection linesnes Fig. , suggestely Fig. . The π v36. However, wild species of Cucumis are important as potential genetic sources for breeding37; INW is the origin population of cucumber and thus harbors higher genomic diversity than XSBN  between G1 and G2, as well as the composite likelihood ratio (CLR)38 to identify genomic regions differentially selected within each group. The FST value highlighted 89 signature sites that were distributed on chromosomes 1–6 and were significantly selected between G1 and G2  than the EA, EU, and INW groups .15. At least 5 μg of genomic DNA was prepared from a single plant of each accession for sequencing, and a library was constructed with an insert size of ~300–350 bp for all of the lines, following the manufacturer’s instructions .Genomic DNA was extracted as previously described46 after trimming low-quality reads by using Trimmomatic47. Picard tools (https://broadinstitute.github.io/picard/) was employed for the removal of PCR duplicates and realignment of indel regions. Generated files in Binary Alignment Map (BAM) format were used to call single nucleotide polymorphisms (SNPs) via the HaplotypeCaller function of Genome Analysis Toolkit  with default parameters48.The paired-end reads were aligned against the 9930 cucumber reference genome using the MEM algorithm implemented in BWA software48. The genotype calls were then improved by imputing and phasing the polymorphism dataset with Beagle 4.1 software based on genotype likelihoods49. Finally, the effects of SNPs were predicted with SnpEff 4.3 software50.To obtain high-quality SNPs, a hard filtering step was performed by following the GATK Best Practices recommendations51 were used to calculate pairwise matrixes for the construction of a principal component analysis (PCA) plot and neighbor-joining tree, respectively. In addition, the ADMIXTURE (version 1.3.0) tool53 was employed to estimate individual ancestry by setting the K-value from 2 to 7. Nucleotide diversity measured by the π value for each population was estimated by using VCFtools54 with a 50 kb window and 5 kb sliding steps. In addition, the decay of linkage disequilibrium (LD) with physical distance between SNPs was calculated and visualized by using PopLDdecay software55. Furthermore, TreeMix-1.1232 was used to model the genetic drift of genome-wide allele frequency data to infer population splitting and mixing. The standard errors of migration proportions were calculated by using the “-se” option. Migration edges (with the “-m” option) were added gradually from 0 to 5.We further thinned the SNP dataset by using the following rules: (1) core chromosomes (“--chr 1–7”); (2) minor allele frequency > 0.05; (3) missing values <10%; (4) a Hardy-Weinberg equilibrium test (“--hwe 0.001”); and (5) pruning SNPs by “--indep-pairwise 50 10 0.1”. Two parameters (“--pca” and “--distance-matrix”) in PLINK software56, which decomposed locus-population FST coefficients into a population-specific component  and a locus-specific component  using logistic regression. A positive α value suggests diversifying selection, whereas a negative value indicates balancing or purifying selection. A q-value <0.05, analogous to the p value but used under multiple testing, was used to indicate significance. BayeScan software56 was run under the default parameters. To detect regions under complete selection within the population, the SweeD program was employed to calculate the composite likelihood ratio (CLR)57, which identifies regions with significant deviations from the neutral site frequency spectrum (SFS). We set the top 1% as a significance threshold. Finally, the overlapping regions detected by FST and the CLR were identified as having signatures of selection. Gene Ontology (GO) annotations were assigned using AgriGO for cucumber (http://systemsbiology.cau.edu.cn).The difference in allele frequency between the G1 and G2 groups was estimated with BayeScan software (version 2.0)Suplementary figuresThe list of cucumber lines sampled in this studyD statistic and numbers of ABBA, BABA sitesRegions under selection in the 56 inbred linesGenes under selection in the 56 inbred linesGO analisis for selected genes


Language acquisition in infants is driven by on-going neural plasticity that is acutely sensitive to environmental acoustic cues. Recent studies showed that attention-based experience with non-linguistic, temporally-modulated auditory stimuli sharpens cortical responses. A previous ERP study from this laboratory showed that interactive auditory experience via behavior-based feedback (AEx), over a 6-week period from 4- to 7-months-of-age, confers a processing advantage, compared to passive auditory exposure (PEx) or maturation alone . Here, we provide a follow-up investigation of the underlying neural oscillatory patterns in these three groups. In AEx infants, Standard stimuli with invariant frequency (STD) elicited greater Theta-band (4–6 Hz) activity in Right Auditory Cortex (RAC), as compared to NC infants, and Deviant stimuli with rapid frequency change (DEV) elicited larger responses in Left Auditory Cortex (LAC). PEx and NC counterparts showed less-mature bilateral patterns. AEx infants also displayed stronger Gamma (33–37 Hz) activity in the LAC during DEV discrimination, compared to NCs, while NC and PEx groups demonstrated bilateral activity in this band, if at all. This suggests that interactive acoustic experience with non-linguistic stimuli can promote a distinct, robust and precise cortical pattern during rapid auditory processing, perhaps reflecting mechanisms that support fine-tuning of early acoustic mapping. PlasticRecent event-related potential (ERP) research from our lab suggests that early, targeted acoustic experience can enhance and accelerate the maturation of temporal processing in typically-developing infants . In an aKey mechanistic questions arise from these results, including where in the brain these changes take place and what neurophysiological mechanisms support these modifications. Classical analysis of scalp-recorded ERP data blur such response features because the peak latency and amplitude of channel-based ERP data sum across space, frequency, phase and magnitude . DetermiThe onset of an auditory stimulus resets the phase of neuronal oscillations in auditory cortex, which often co-occurs with the discharge of an action potential. Event-related oscillations in the mature system have been characterized by two phenomena: nested phase-locking and asymmetry of temporal processing. In nested phase-locking, evoked oscillations in the lower frequency bands of Delta and Theta synchronize to the slower temporal dynamics sound such as the speech envelope  while faOur previous studies show that tone and phoneme discrimination in infancy evoke activity in both Theta and Gamma bands , but the2Methods for recording and analysis in the current study follow those in previous publications from our laboratory . Abbrevi2.1m = 18.2 weeks, SD = 0.77) and then followed longitudinally to 7-months-of-age . The Active Experience group  participated in operantly-conditioned feedback-modulated auditory training  and served as “naïve”, cross-sectional, maturational controls .This study was conducted in accordance with the Declaration of Helsinki. Informed consent, approved by the Institutional Review Board of our university, was obtained from all parents before study participation. Parents were compensated for their time, and infants received a toy after the visit. A total of forty-nine infants participated in this study. Infants were from monolingual English families with no reported family history of specific language impairment or of dyslexia, learning disability, attention deficit disorder, pervasive developmental disorder, or autism in either the nuclear or extended family . Before the first testing session, each infant was randomly assigned to one of three groups . Fig. 1Aing e.g.  between 2.2Infants in the AEx group visited the lab once a week for six consecutive weeks between 4 and 7 months of age. Each session lasted approximately 20 min with infant active engagement lasting about 8 min. The AEx group participated in a go/no-go (G/N-G) operantly-conditioned looking task designed to train an association between an auditory stimulus and the onset of a video reward . The pro2.3Infants in the PEx group also visited the lab once a week for six consecutive weeks between 4 and 7 months of age. Each session lasted 20 min as the infant sat comfortably in an infant seat placed on a chair equidistant between left and right speakers in a sound-attenuated and electrically shielded sound booth . The PEx group was exposed to the same stimuli as the AEx group. However, there was no response-contingent reward for PEx infant looking behavior . Sounds were presented free-field while the infant was silently entertained with puppets/silent toys to maintain alertness. Two blocks of stimuli were presented in random order at each session, 10 min at 40 ms ISI and 10 min at 70 ms ISI. This condition was designed to increase spectrotemporal processing efficiency through passive background auditory exposure.2.4Infants in both groups were presented with three different types of paired acoustic stimuli, as follows: weeks 1 and 2, complex tones ; weeks 3 and 4, bandpass noise ; and weeks 5 and 6: simple sweeps .2.51 = 800 Hz, F02 = 1200 Hz). Presentation of DEV stimuli was pseudo-randomized with at least three and no more than 12 STD pairs presented before each DEV pair. All stimuli were presented using E-Prime software  amplified  to a calibrated level of 56.1 dB sound pressure level (SPL). Sounds were presented in free-field to the infants via left and right speakers which were attached to opposite walls of a sound-attenuated and electrically-shielded sound booth .70 ms complex tone pairs were presented in a passive oddball paradigm using a blocked design with an inter-stimulus interval of 70 ms and an inter-trial interval of 915 ms B. Each tInfants were seated on their caregiver’s lap in a comfortable chair, positioned with its center equidistant (30 inches) from the face of each speaker. An experimenter, present in the room, engaged the infant’s attention with a silent puppet show or other silent toys to help minimize their movement. Age-appropriate movies or cartoons were also played silently on a video monitor in front of the children. High-density EEG data were recorded from a 128-channel geodesic sensor, vertex-referenced net using an EGI  recording system. The EEG was sampled at 250 Hz and bandpass filtered online at 0.1–100 Hz. For visualization of the net application and EEG recording with infants, see . Stimulu2.6EEG data were processed according to previously published parameters using BESA 5.3 Research , EEGLAB , ERPLAB 2.7The surface ERP was transformed into brain source activity, using BESA’s MRI co-registration and source montage approach . First, 2.8Instantaneous amplitude and phase to a three-step complex demodulation algorithm was applied to the continuous data in source space. Frequencies between 2 and 50 Hz were analyzed in 50 ms time bins, relative to a baseline pre-stimulus epoch of −100 to 0 ms . The demt-test between groups per data point. Second, the t-test values were submitted to parameter-free permutation testing, in combination with what is referred to as “data clustering”, in order to reduce type I error via multiple comparisons . Results of this analysis are described below and an example cluster is illustrated in Mathematically, the time-frequency computation yields two 3-D matrices, for ITPL and TSE values, per participant . In order to obtain meaningful values for our planned statistical comparisons, we performed a data-driven, three-step analysis using these matrices. First, we detected regions of significant TSE and ITPL differences for the DEV response using BESA Statistics 1.0  software. This program calculates a preliminary Student's Statistical analysis of the time-frequency matrices yielded three significant time-frequency clusters (p < 0.05):(1) Theta ITPL from 4 to 6 Hz over 150–250 ms, (2) Theta TSE from 3 to 7 Hz over 50–450 ms, and (3) Gamma TSE from 33 to 37 Hz over 200–500 ms. Individual means used in subsequent analyses were derived from within these cluster boundaries .2.9A series of ANOVA models were conducted to assess the typical maturational changes from 4 to 7-months of age as well as the effects of auditory exposure over and above that of maturation on LAC and RAC peak latency and amplitude (P1 and N1/N2*) as well as time frequency measures . Least Significant Difference (LSD) correction was used for multiple comparisons.33.14M = 9.5%; MNC = 9.2%; MPEx = 9.7%, MAEx = 9.1%), and slightly higher in the DEV condition . Residual Variance of the two-dipole model fitting was less than 10% for the STD P1 peak , PEx (3Biii) and AEx infants (3Biv).3.23.2.1F = 20.91, p < 0.001. To assess age-related changes in the peak latency and amplitude of LAC and RAC source waveforms, mixed-design ANOVAs with age  as a between-subjects factor and source  and condition  as within-subjects factors were conducted with P1 and N1/N2* measures. The test of P1 latency revealed a main effect of age, F = 28.71, p < 0.001, and main effects of source for amplitude, F = 10.83, p < 0.010. As expected, the N2*, which appears in the DEV condition only, had a shorter latency when compared to the N1 from the STD condition, at both ages  = 7.150, p = 0.011, source, F = 5.027, p = 0.032Maturation of frequency magnitude and phase-coherence over Left and Right auditory cortex was tested with the 2 × 2 × 2 mixed-design ANOVAs for F = 26.461, p < 0.001, suggesting that the phase synchrony maturation from 4 to 7 months is different for STD and DEV stimuli. Theta ITPL for 4- and 7-month-olds and illustrates that Theta ITPL decreases with age and is smaller at 7 months only in the DEV condition, and particularly in the RAC. Frequency change in the DEV condition elicits greater phase coherence in the RAC, compared to the LAC, particularly at 4 months of age. Thus it appears that the difference in maturation between conditions is largely due to the fact that RAC activity to DEV stimuli is very large at 4 months and then decreases in amplitude and shows bilateral activation at 7 months.and condition, 3.33.3.1F = 38.897, p < 0.001 and amplitude − = 8.531, p = 0.006. The N2* latency from the DEV condition was earlier and smaller as compared to the N1 from the STD condition for all three groups  x 2  × 2  ANOVAs on P1 and N1/N2* latency and amplitude measures. Tests of N1/N2* revealed main effects of condition for latency e groups .3.3.2Theta TSE, F = 9.825, p < 0.001. Two significant interaction effects in the simple ANOVAs were observed. First, the 2  by 3  ANOVA was significant for Theta TSE in the STD condition, F = 5.187, p = 0.009, suggesting a difference in lateralization across groups. Mean values, presented in F = 6.422, p = 0.004), suggesting that the response to STD and DEV stimuli differed across groups. The means in The mixed-design ANOVA for frequency magnitude and phase-coherence over Left and Right auditory cortex was used to assess source and condition differences across the 3 groups. A significant three-way interaction of group by source  by condition  was observed for had larger responses to the STD stimuli in the LAC. Thus, it appears that sounds that do not change in frequency are processed in the right hemisphere in AEx infants, whereas sounds that change in frequency are processed in the left. Gamma TSE magnitude yielded a significant group by source by condition interaction effect, F = 5.121 p = 0.010. A significant between-subjects effect was observed for Gamma TSE in the DEV condition in the 2  by 3  ANOVA, F = 4.721, p = 0.014), suggesting a group difference in the left hemisphere during DEV processing. In post-hoc comparisons of Gamma TSE in the LAC, only AEx and NC means differed significantly in the DEV condition  with PEX means falling between the other two groups  and DEV  conditions. No differences were observed between LAC and RAC in NC or PEx infants. Following examination of main effects, post-hoc paired 4The major findings of this study include: (1) increased speed of event-related source sensory response (P1 latency) and decreased Theta phase stability (ITPL) as a function of maturation from 4- to 7-months in NC infants; (2) the N2* peak on the deviant wave was shown to index specific modulation of frequency discrimination responses for both 4- and 7-month-old infants; and (3) changes in Theta and Gamma oscillatory dynamics emerged in the AEx group when compared to both PEx and NC groups.4.1P1 peak latencies from LAC and RAC sources decreased over maturation from 4- to 7-months in the naïve group in line with previous data showing faster sensory responses with increasing age . Source Theta ITPL was observed over the same time window as the P1 peak (i.e. 150–250 ms). Because ITPL is a measure of phase stability, the observed decrease in Theta ITPL suggests that as infants mature, processing efficiency and automatization may increase and thus less phase synchronization might be required to process auditory signals.If latency changes were associated with a decline in synaptic density, there should also be a decrease in peak amplitude, reflecting the response of a smaller number of active neurons. Although no significant peak amplitude differences were seen across maturation, a decrease in 4.2The N2* component of the DEV response is of prime interest as it marks the beginning of the discrimination response and has been shown to be a robust infant predictor of later language outcomes . In Bena4.3Overall the AEx infants displayed more robust and precise acoustic mapping in Theta- and Gamma-band frequencies for both automatic sound processing and detection of rapid frequency change. Because this response is less clear in PEx and NC infants, we suggest that active engagement is an important catalyst for auditory plasticity at this age. This notion is akin to a multidimensional view of lateralization, which may vary over developmental epochs  and matuOur results also show that AEx infants show greater RAC response to STDs in the Theta band and greater LAC response to DEV stimuli in the Gamma band, as compared to NC infants. PEx infants do not differ from either AEx or NCs, and their mean values fall between the two groups for both conditions. These findings are compatible with the Asymmetric Sampling in Time theory AST,  which poOne hypothesis as to how this might be accomplished is related to the representation of spectral and temporal acoustic characteristics. Several lines of research have demonstrated lateralization of auditory processing based on spectral and temporal stability. In adults, rapid temporal dynamics, such as seen in speech sounds, are processed primarily in LAC and dense spectral dynamics in the RAC . In our The Gamma finding supports our conclusion of a “more mature pattern” of processing in AEx infants on several fronts. First, only the AEx group shows coherent activity in the Gamma range see . In NC a4.4The idea of attention-driven short- and long-term brain plasticity is not new. It has been proposed that even short-term auditory training with attentional modulation can retune neurons to segregate relevant sounds . Repeate5Our results show that interactive auditory experience is associated with changes in oscillatory encoding and acoustic cortical mapping. We suggest that the ability of a child’s brain to automatically process and differentiate rapidly-changing acoustic cues may index neuronal maturation. Acoustic experience during the time when infants are constructing cortical maps for language appears to promote more mature oscillatory and lateralized patterns of rapid auditory processing and frequency discrimination. Further investigation is needed to determine longer-term outcomes of early interactive experience, and to directly test experience-dependent relationships among tone-pairs, speech encoding and language outcomes.None.


Four prospective studies include patients with vitamin B12 deficiency related to the aforementioned etiologies, except veganism or vegetarianism. The systematic present review documents that oral vitamin B12 replacement, at a daily dose of 1000 μg (1 mg), was adequate to normalize serum vitamin B12 levels and cure main clinical manifestations related to vitamin B12 deficiency, in GI disorders, and thus, with safety profile. For nasal vitamin B12 treatment, only one preliminary study was available. We conclude that oral vitamin B12 is an effective alternative to intramuscular vitamin B12 . Oral vitamin B12 treatment avoids the discomfort, contraindication (in patients with anticoagulation), and cost of monthly injections.The objective of this review is to provide an update on the effectiveness of oral and nasal vitamin B12  treatment in gastrointestinal (GI) disorders. Relevant articles were identified by PubMed and Google Scholar systematic search, from January 2010 and June 2018, and through hand search of relevant reference articles. Additional studies were obtained from references of identified studies, the Cochrane Library and the ISI Web of Knowledge. Data gleaned from reference textbooks and international meetings were also used, as was information gleaned from commercial sites on the web and data from CARE B12 research group. For oral vitamin B12 treatment, 4 randomized controlled trials (vs. intramuscular), 4 narrative and 4 systematic reviews, and 13 prospective studies fulfilled our inclusion criteria. These studies concerned patients with vitamin B12 deficiency related to: food-cobalamin malabsorption ( Gastrointestinal (GI) disorders affect millions of people of all ages . They arNevertheless in this setting, new routes of B12 replacement, particularly nasal and oral, have been developed . In factThis systematic review summarizes the current knowledge on the efficacy and safety of oral and nasal B12  treatment in patients with cobalamin deficiency related to GI disorders.Helicobacter pylori”, “atrophic gastritis”, “inflammatory bowel disease”, “exocrine pancreatic insufficiency”, “oral vitamin B12 therapy”, “oral cobalamin therapy”, “oral vitamin B12 treatment”, “oral cobalamin treatment”, “nasal vitamin B12 therapy”, and “nasal cobalamin therapy”; restrictions included: English- or French-language publications; published from 1 January 2010, to 1 July 2018; human subjects; adults and elderly subjects, clinical trials, review articles or guidelines.A systematic literature search was performed on the PubMed database of the US National Library of Medicine and on Scholar Google. We searched for articles published between January 2010 and June 2018, using the following key words or associations: “gastrointestinal disorders”, “vitamin B12 deficiency”, “cobalamin deficiency”, “Biermer’s disease”, “pernicious anemia”, “gastrectomy”, “food-cobalamin malabsorption”, “Additional studies were obtained from references of identified studies, the Cochrane Library and the ISI Web of Knowledge. Data gleaned from international meetings were also used, as information gleaned from commercial sites on the web. American Society of Hematology educational books, textbooks of hematology and internal medicine were also used, as was information gleaned from international meetings and from commercial web sites.All of the English and French abstracts were reviewed by at least two senior researchers from our research team .We reviewed 413 references, which yielded 115 potentially relevant papers . Forty-f- For oral vitamin B12 treatmentn = 6), Biermer’s disease (n = 3), veganism or vegetarianism (n = 1), total gastrectomy after Roux-en-Y gastric bypass (n = 2), and Crohn’s disease (n = 1). Four prospective studies include patients with B12 deficiency related to the aforementioned etiologies, except veganism or vegetarianism. All these studies included adults and elderly patients.Four prospective randomized controlled trials (vs. intramuscular vitamin B12 treatment) ,8,9,10, - For nasal vitamin B12 replacementOnly one preliminary well-documented study of nasal B12 treatment was available in elderly patients .Four prospective randomized controlled studies comparing oral B12 vs. intramuscular (I.M.) B12 replacement have well-documented the efficacy and safety of oral B12 as a curative treatment  7,8,9,1,19,10. Ip < 0.001. The difference was even greater at four months: 1005 ± 595 vs. 325 ± 165 pg/mL. Four of the 18 patients in the oral group and 4 of the 15 in the I.M. group had a neurological response with a marked improvement or clearing of paresthesia, ataxia, or memory loss.In a first study, Kuzminski et al., in a prospective randomized trial including 38 patients, reported improvement of hematological parameters and B12 levels , after four months of oral cyanocobalamin replacement using a much higher dose )  [7]. In p < 0.0001), but authors did not analyze difference between both groups. Both groups reported improvements of cognitive functions, sensory neuropathy, and vibration sense, but there was no statistical significant difference between both groups.Bolaman et al., in a prospective randomized trial of 60 patients, also reported significant improvement of hematological parameters and B12 levels (mean improvement: +140.9 pg/mL), after three months of daily 1000 µg of oral cyanocobalamin treatment  8]. In . In 8]. In a controlled, randomized, multicenter, parallel, non-inferiority clinical trial (OB12 study) lasting one year, a preliminary analysis gives a glimpse that the oral route for B12 replacement may be as effective and safe and administered at a lower cost than the I.M. route (ongoing study)  9]. Thi. Thi9]. In another randomized, parallel-group, double-blind, dose-finding trial, Eussen et al. showed that the lowest dose of oral cyanocobalamin required to normalize mild B12 deficiency is more than 200 times the recommended dietary allowance of approximately 3 µg daily  per day)  10]. Ap. Ap10]. It is to note that the effect of oral B12 treatment in patients presenting with ‘severe’ neurological manifestations  has not yet been adequately documented in these studies . Thus unTo our knowledge, only two of the aforementioned trials studied oral B12 replacement reported data on adverse events, with two of such adverse events  in one study in the group of oral vitamin B12 ,8.The first evidence-based analysis by the Vitamin B12 Cochrane Group in 2005 , as wellIn this setting, the Cochrane Group concludes that: “daily oral replacement may be as effective as I.M. administration in obtaining short term hematological and neurological responses in vitamin B12 deficient patients” . The revThe second evidence based-analysis from the same aforementioned group in 2018 confirms their previous analysis . In factH. pylori, long-term ingestion of proton pump inhibitors, chronic alcoholism, and partial and exocrine pancreatic insufficiency . Af. Af21]. p < 0.0000003 compared with baseline). Eight patients had increased hemoglobin levels, with a mean increase of 2.45 g/dL; p < 0.01. All 10 patients had decreased mean erythrocyte cell volume . Three patients (one-third) experienced clinical improvements (secondary criteria).The aforementioned results were also observed in a population of patients presenting with Biermer’s disease . In thisn = 40), with the median serum B12 level of 1193 pg/mL after three months of oral B12 replacement .,27.26,27The CARE B12 group had also documented the long-term efficacy of oral B12 treatment ), with a median follow up of 2.5 years, in a population of 22 patients with well-established cobalamin deficiency  28]. Th. Th28]. n = 40), Del Bo’ C et al. studied in a randomized controlled trial the effect of two different sublingual dosages of B12 on cobalamin nutritional status .,40.14,40H. pylori infection until the germ eradication is documented; or by supplemented pancreatic exocrine failure [In this context, ongoing oral B12 replacement may be necessary until any associated GI disorders are corrected, if possible: e.g., by halting the ingestion of the offending medication or alcoholism; by treating  failure . This ma failure .In our opinion, patients with B12 deficiency who are symptomatic have severe neurological deficits or have critically low blood levels of B12 should be treated with I.M. B12 replacement. This is to ensure rapid replenishment of body stores to prevent irreversible consequences of the cobalamin deficiency. Subsequently, patients may be able to convert to oral replacement with close monitoring .This alternative route of replacement had been developed and proposed as a way of avoiding the discomfort, inconvenience, and cost of monthly injections (with the need of a nurse) ,30. In pTo date, the oral B12 treatment regimen is not yet formally approved. Further studies should include testing the efficacy of different molecules  and dosages. In this setting, it may be important to study the knowledge and practices of doctors/health-care workers with regard to oral B12 replacement for patients with documented cobalamin deficiency.To date, recent developments in conjunction with nanomedicine for the co-administration of drugs with lipid compounds have been reported to enhance lymphatic transport . These tSublingual administration of vitamin B12 (placing the vitamin beneath the tongue for one to two minutes) is another promising way of administration which has been studied historically  and whic


In this paper, we give some reverse-types of Ando’s and Hölder–McCarthy’s inequalities for positive linear maps, and positive invertible operators. For this purpose, we use a recently improved Young inequality and its reverse. I; also A is positive, and A is positive invertible. For A and the A and I. A linear map Φ on J and all Let a, b and The well-known Young inequality says that, for positive real numbers entclass1pt{minimaroven in –16 and troven in  obtained(i)for (ii)for  where Zhao et al.  obtained(i)for (ii)for  wherex.Sababheh et al. , 16 estat-weighted arithmetic, geometric, and harmonic means of operators A, B are defined by Let For positive real numbers eader to , 12, 20 ity see , 17)..\documenA and any unit vector The Hölder–McCarthy’s inequality says that for any positive operator . Furuta  showed tIn this paper, we establish a reverse of Ando’s inequality for positive  linear maps and positive definite matrices by using an inequality due to Sababheh. We obtain some reverses of the matrix Hölder and Cauchy–Schwarz inequalities and a reverse of inequality  for \docWe use the properties of inner product and the inequalities obtained in  and 19]19].To prove our first result, we need the following lemmas.Letbe positive definite matrices andThenwhereFor shown in  for posiLetbe positive invertible operators and(i)Ifthen(ii)IfthenwhereandLetbe positive definite matrices and(i)Ifthen(ii)IfthenwhereandBy using functional calculus and numerical inequalities in , 16, we For shown in  for posiLetbe positive invertible operators and(i)Ifthen(ii)IfthenwhereandNow, we obtain a reverse of Ando’s inequality for positive invertible operators as follows.Letbe positive invertible operators, Φ be a positive linear map and(i)Ifthen(ii)IfthenwhereandThe proof of inequality  is similA and B by Let ualities  and 9),,\documenmentclass2pt{minimSimilarly for entclass1pt{minimaLetbe positive invertible operators, Φ be a positive linear map and(i)Ifthen(ii)ifthenwhereandWe want to establish some inequalities for positive invertible operators.Letbe positive invertible. Ifand Φ, Ψ are two unital positive linear maps, then for any unit vector(i)for(ii)forwhereThe proof of part (ii) is similar to the proof of part (i). Thus we only prove (i).k, s, we haves in for(ii)forwherek and any unit vector A, we haveThe proof of part (ii) is similar to the proof of part (i). Thus we just prove (i). For any positive real number Letbe positive, Φ be a unital positive linear map andThen for any unit vector(i)for(ii)forwhereLetting In the next result, we obtain a refinement of inequality  for \docLetbe positive operator andbe a unit vector. Then, forwe havewheret with If we replace In this section, we prove some difference reverse-types of the Hölder and Cauchy–Schwarz inequalities.Letbe positive invertible and(i)Ifthen(ii)IfthenwhereandTaking ualities  and 18)\documentSince the function mentclasspt{minima(i)If (ii)If If for positive operators mentclasspt{minimaA, B and In , the Tsamentclasspt{minimaLetbe positive invertible and(i)Ifthen(ii)IfthenApplying Theorem B be a non-invertible operator and We can present our results for non-invertible operators; see . It is a


Background: The Frank-Starling curve is the basis of hemodynamics. Changes in cardiac output (CO) caused by central venous pressure (CVP) are the most important concerns in the treatment of critically ill patients.Objectives: To explore the use of CVP and its relevant mechanisms with respect to CO in the clinic.Methods: A total of 134 patients with circulatory shock were retrospectively included and analyzed. Hemodynamic data were recorded and analyzed at PICCO initiation and 24 h after PICCO. Data regarding 28-day mortality and renal function were also collected.Results: The patients were divided into a CVP↑+ CO↑ group (n = 23), a CVP↑+ CO↓ group (n = 29), a CVP↓+ CO↑ group (n = 44), and a CVP↓+ CO↓ group (n = 38) based on values at PICCO initiation and 24 h after PICCO. Post- hoc tests showed that the CVP↓+ CO↑ group had a higher 28-day survival than the other groups . In terms of hemodynamic characteristics, the CVP↓+ CO↑ group had a lower cardiac function index (CFI) (4.1 ± 1.4/min) and higher extravascular lung water index (EVLWI) (11.0 ± 4.7 ml/kg) at PICCO initiation. This group used more cardiotonic drugs  and had a negative fluid balance  24 h after PICCO than the other three groups. Cardiotonic drug use and dehydration treatment were associated with increased CFI  and reduced ELVWI . Renal function tests showed that SCr and BUN levels in the CVP↓+ CO↑ group were significantly improved .Conclusions: Lower CVP was associated with increased CO, which may improve the 28-day prognosis in patients with circulatory shock. Notably, higher CO derived from lower CVP may also contribute to renal function improvement. Central venous pressure (CVP) is the pressure in the thoracic vena cava near the right atrium. CVP is an important factor in critical care medicine because it can be used to estimate a patient's fluid volume status, assess cardiac function, and gauge how well the right ventricle of the heart is functioning . Due to Based on the Frank-Starling mechanism and venous return (VR) theory proposed by Guyton, VR should match cardiac output (CO) as determined by the mean systemic filling pressure (MSFP) and the CVP gradient , 13. ChaThis study is retrospective, and all the patients authorized us to use their clinical data. The research protocol was reviewed and approved by the Ethics Committee of Peking Union Medical College Hospital (PUMCH-S616). When PICCO catherization was needed, the patients or their family members were fully informed of the details, and they signed informed consent forms.The Critical Care Monitor System and Administrative Database of Peking Union Medical College Hospital was built in 2013 . This da2 ≥ 70% (SvO2 ≥ 65%) based on early goal-directed therapy (EGDT)  ≥ 65 mmHg, CVP 8–12 mmHg and ScVOy (EGDT) .2 < 70% (SvO2 < 65%) and hematocrit <30%, blood transfusion was adopted; and (4) if ScvO2 < 70% (SvO2 < 65%) and hematocrit ≥30%, inotropic drugs were used to achieve ScvO2 ≥ 70% (SvO2 ≥ 65%). After the resuscitation was completed, a restrictive fluid management strategy was used; if satisfactory perfusion indicators were obtained , P(v−a)CO2 < 6, and decreased lactate levels), limited fluid therapy was used during treatment. The strategy to control fluid balance measures did not rule out the use of artificial means of dehydration, including diuretics, and renal replacement therapy.First, we worked hard to ensure that patients achieved EGDT targets within 6 h after PICCO initiation. The specific measures were as follows: (1) assessed volume responsiveness and continuous fluid resuscitation to achieve and maintain CVP 8–12 mmHg; (2) if the negative fluid challenge or the blood pressure did not increase after the volume responsiveness, vasoconstrictor drugs were used to achieve a MAP ≥65 mmHg; (3) if ScvOCVP measurement: Using an indwelling central venous catheter via the internal jugular or subclavian vein, a pressure sensor was connected to a monitor (Philips). While the patients were supine, the sensor was positioned in the axillary line at the fourth intercostal level. The pressure waveform and CVP values were read at the end expiratory time and recorded by ICU physicians.CO, cardiac output index (CI), cardiac function index (CFI), extravascular lung water index (EVLWI), and other hemodynamic data were measured by the thermodilution method. The femoral PICCO™ catheter was connected to a module PICCO plus® system  and recalibrated for the detection of hemodynamic data in accordance with the manufacturer's instructions. To ensure the accuracy of the measurements, transpulmonary thermodilution measurements were acquired in triplicate by 15 ml 0–4°C normal iced saline solution bolus injection through a central vein to obtain an average value, which was used for statistical analysis.2, ScvO2 and lactate: Arterial blood and superior vena cava blood were collected simultaneously. Arterial and venous blood samples were tested by a blood gas analyzer (GEM® PREMIER™ 3000). ScvO2 and lactate were read directly from the results. P(v−a)CO2 was calculated by PvCO2-PaCO2.P(v-a)COBasic clinical characteristics were collected, including underlying disease, source of infection, organ function, APACHE II and SOFA scores, mechanical ventilation application, vasoactive drug use, fluid balance, hemodynamic parameters, tissue perfusion index, pulmonary vascular permeability index, and 28-day mortality. All the data came from the Critical Care Monitor System and Administrative Database of Peking Union Medical College Hospital .t-test and analysis of variance (ANOVA) were used to compare means between two groups or three or more groups, respectively. The results for qualitative variables were expressed as percentages and compared between groups using a chi-square test. Survival curves up to day 28 were estimated using the Kaplan-Meier method, and the log-rank (Mantel-Cox) test was used to estimate differences between the groups. Repeated measures ANOVA was used to describe the dynamic changes in renal function among different groups at different time points after PICCO catheterization . Statistical analyses were performed with SPSS version 13.0 .The data distribution test and the homogeneity of variance test were performed on the data . The resn = 75) that required resuscitation treatment and a non-resuscitation group (n = 91) that did not need resuscitation treatment based on the EGDT criterion. A total of 43 patients in the resuscitation group achieved MAP ≥ 65 mmHg, CVP ≥ 8 mmHg, and ScVO2 ≥ 70% within the initial 6 h resuscitation treatment based on the 6 h “sepsis bundle.” The remaining 32 patients did not meet the resuscitation standard and were excluded. Therefore, 91 patients from the non-resuscitation group and 43 patients who met the resuscitation standards within the initial 6 h period were included in the subsequent analysis. Based on the changes and the relationship between CO and CVP at the start of PICCO and 24 h after PICCO, these 134 patients were further divided into four groups according to the differences in CVP and CO between PICCO initiation and 24 h after PICCO: a CVP↑+ CO↑ group, a CVP↑+ CO↓ group, a CVP↓+ CO↑ group, and a CVP↓+ CO↓ group (P < 0.05). The CVP↓+CO↑ group had the lowest 28-day mortality rate (P < 0.05). In addition, there were no significant differences in terms of age, sex, sources of infection (excluding pulmonary), pathogens detected, frequency of continuous renal replacement therapy (CRRT) and mechanical ventilation (MV), and respiratory function indices, including PEEP, FiO2%, and PO2/FiO2%, among the five groups.In this study, we included 231 patients with circulatory shock who underwent PICCO during the observation period. Of these patients, 65 were excluded due to any missing data at 24 h after PICCO. Complete data were available for 166 patients. On the basis of the hemodynamic characteristics from PICCO, circulatory shock was classified in 166 patients as follows: hypovolemia , cardiogenic factors , obstruction , or distributive factors . These patients were divided into a resuscitation group (O↓ group . The demn = 166) were divided into eight stratifications by every 10% increase and decrease in CVP. The 28-day mortality rates for these eight stratifications are shown in Post-hoc tests showed that there were statistically significant differences in 28-day survival rates among the CVP↑+ CO↑, CVP↑+ CO↓, CVP↓+ CO↑, and CVP↓+ CO↓ groups  . Simultaneously, the excluded group had higher P(v−a)CO2, systemic vascular resistance index (SVRI), and EVLWI and lower CO, CI, stroke volume index (SVI), global ejection fraction (GEF), and CFI. Therefore, the excluded groups were excluded from the following study because they needed more time to reach a satisfactory perfusion index. According to P < 0.05). The CVP↓+ CO↑ (13.0 ± 3.1 mmHg) and CVP↓+ CO↓ (13.9 ± 4.1 mmHg) groups had higher CVP than the CVP↑+ CO↑ (10.8 ± 2.2 mmHg) and CVP↑+ CO↓ (10.4 ± 2.9 mmHg) groups (P < 0.05) at PICCO initiation. Twenty-four hours after PICCO, the CVP of the CVP↓+ CO↑ (8.7 ± 2.3 mmHg) and CVP↓+ CO↓ (8.9 ± 2.4 mmHg) groups decreased significantly (P < 0.05). Accordingly, the CO of the CVP↓+ CO↑ group increased from 4.9 ± 1.6 L/min to 5.7 ± 1.3 L/min (P < 0.05), while the CO of the CVP↓+ CO↓ group decreased from 6.2 ± 1.6 L/min to 4.9 ± 1.6 L/min (P < 0.05). The CI showed the same trend as the CO. The relationship between CVP and CO changes was accompanied by changes in CFI, EVLWI, and lactate (P < 0.05). The CFIs of the CVP↑+ CO↑, CVP↑+ CO↓, CVP↓+ CO↑, and CVP↓+ CO↓ groups were 5.2 ± 1.9/min, 4.7 ± 1.2/min, 4.5 ± 1.3/min, and 4.4 ± 1.5/min 24 h after PICCO, respectively. The CFI increase in the CVP↓+ CO↑ group at initiation and 24 h after PICCO showed a trend that was not significant (P = 0.07). In addition, the CVP↓+ CO↑ and CVP↓+ CO↓ groups had higher EVLWI than the other groups (P < 0.05). However, only the CVP↓+ CO↑ group had lower EVLWI at 24 h after PICCO compared with its EVLWI values when resuscitation standards were met or resuscitation was completed . The CVP↓+ CO↑ and CVP↓+ CO↓ groups had lower lactate levels than the other two groups (P < 0.05). With the exception of the CVP↓+ CO↓ group, the other three groups showed a decreasing trend in lactate levels. The decreases in lactate levels in the CVP↓+ CO↑ [1.8 (1.1–2.8) mmol/L] and CVP↑+ CO↓ [2.4 (1.2–7.2) mmol/L] groups 24 h after PICCO were statistically significant (P < 0.05). Regarding the pulmonary vascular permeability index (PVPI), the data from the four groups were not significantly different.The hemodynamic characteristics of all included patients when they met the resuscitation standards or completed resuscitation are shown in  lactate . The CVPP < 0.05). The CVP↑+ CO↑ group consumed more fluid during resuscitation, while more fluid was removed from the CVP↓+ CO↓ group (P < 0.05). Although the CVP↓+ CO↑ group also had a positive fluid balance, CO showed an increasing trend. The CVP↓+ CO↑ group showed an increase in CO as a result of CVP reduction because of dehydration.After the initial resuscitation was completed, the main interventions for all included patients were target blood pressure improvement, cardiac function enhancement, and fluid therapy. Vasoactive drug usage, cardiotonic drug usage, and total fluid volume within 24 h of PICCO were retrospectively collected. Comparisons were made among the CVP↑+ CO↑, CVP↑+ CO↓, CVP↓+ CO↑, and CVP↓+ CO↓ groups during the therapy process. F = 1.184, P = 0.322; F = 0.629, P = 0.599, respectively). There were significant differences in the SCr levels of the CVP↓+ CO↑ group and the BUN levels of the CVP↓+ CO↑ and CVP↑+CO↓ groups at various time points . SCr and BUN levels significantly improved in the CVP↓+ CO↑ group only. In addition, there was no interaction effect between the dynamics of the SCr and BUN levels in the four groups .A polynomial test was used to analyze the trend curves of the dynamic changes in renal function at PICCO initiation and at 24, 48, and 72 h after PICCO catheterization . The curThis single-center retrospective cohort study explored the relationship between CVP and prognosis. Furthermore, we explored the mechanisms of CVP changes in hemodynamics. Our results confirmed that lower CVP can result in increased CO, which may improve 28-day mortality in specific patients with circulatory shock. Higher CO caused by a reduction in CVP may also contribute to renal function improvement. We found that, in some patients, higher CO derived from the reduction in CVP can benefit from EVLWI decreases and renal function improvement through inotrope and dehydration treatment. Choosing fluid therapy for these patients requires careful choice.It has been acknowledged that CVP should not be used as the hemodynamic response to a fluid challenge , 19. HowBased on the abovementioned factors, lower CVP is better. However, in the pathophysiological state, we must obtain a suitable CO matched with the lower CVP. Therefore, a heart function curve must be used to illustrate the hemodynamic characteristics of higher CO induced by CVP reduction. In this study, we found that the CVP↓+ CO↑ group had lower CFI and higher EVLWI at PICCO initiation. Twenty-four hours after PICCO, the CFI significantly increased, and EVLWI decreased. Inotrope use and dehydration perhaps produced hemodynamic effects based on the Starling-Guyton theory , 28. As Recently, accumulating evidence has suggested that persistent positive fluid balance is associated with higher mortality in sepsis , 30. HowThis study has some limitations. First, it was a single-center, retrospective cohort study including only patients under PICCO monitoring and treatment. In addition, the sample size is limited. More importantly, we cannot exclude the differences in the indications of different patients when PICCO is placed. The selection bias of why, when, and how to use PICCO catheterization for severely ill patients may affect the final conclusion . Second,In general, this study challenges high-volume resuscitation, which is frequently used in everyday practice. We found that lower CVP is associated with a good prognosis, especially in patients with higher CO derived from CVP reduction, because these patients can exhibit EVLWI-level reduction, cardiac dysfunction amelioration, and renal function improvement through inotrope and dehydration treatment. The findings of this study can broaden the knowledge of such patients in clinical practice, allowing us to reduce CVP and acquire benefits.The data used to support the findings of this study were provided by DLiu and are under license; thus, they cannot be made freely available. Access to these data will be considered by the author upon request, with permission from the Department of Critical Care Medicine, Peking Union Medical College Hospital.The studies involving human participants were reviewed and approved by Ethics Committee of Peking Union Medical College Hospital. The patients/participants provided their written informed consent to participate in this study. Written informed consent was obtained from the individual(s) for the publication of any potentially identifiable images or data included in this article.DLiu and LS: conception and design. DLi and QZ: data extraction. PP and XZ: statistical analysis. LS and PP: interpretation of data and writing. DLiu, XW, and YL: review and revision of the manuscript.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.