‘Lassoing’ a phylogenetic tree I: basic properties, shellings, and covers

A classical result, fundamental to evolutionary biology, states that an edge-weighted tree T with leaf set X, positive edge weights, and no vertices of degree 2 can be uniquely reconstructed from the leaf-to-leaf distances between any two elements of X. In biology, X corresponds to a set of taxa (e.g. extant species), the tree T describes their phylogenetic relationships, the edges correspond to earlier species evolving for a time until splitting in two or more species by some speciation/bifurcation event, and their length corresponds to the genetic change accumulating over that time in such a species. In this paper, we investigate which subsets of ${\binom{X}{2}}$ suffice to determine (??lasso??) the tree T from the leaf-to-leaf distances induced by that tree. The question is particularly topical since reliable estimates of genetic distance??even (if not in particular) by modern mass-sequencing methods??are, in general, available only for certain combinations of taxa.     

Coupling-induced population synchronization in an excitatory population of subthreshold Izhikevich neurons

We consider an excitatory population of subthreshold Izhikevich neurons which exhibit noise-induced firings. By varying the coupling strength J, we investigate population synchronization between the noise-induced firings which may be used for efficient cognitive processing such as sensory perception, multisensory binding, selective attention, and memory formation. As J is increased, rich types of population synchronization (e.g., spike, burst, and fast spike synchronization) are found to occur. Transitions between population synchronization and incoherence are well described in terms of an order parameter $\mathcal{O}$ . As a final step, the coupling induces oscillator death (quenching of noise-induced spikings) because each neuron is attracted to a noisy equilibrium state. The oscillator death leads to a transition from firing to non-firing states at the population level, which may be well described in terms of the time-averaged population spike rate $\overline{R}$ . In addition to the statistical-mechanical analysis using $\mathcal{O}$ and $\overline{R}$ , each population and individual state are also characterized by using the techniques of nonlinear dynamics such as the raster plot of neural spikes, the time series of the membrane potential, and the phase portrait. We note that population synchronization of noise-induced firings may lead to emergence of synchronous brain rhythms in a noisy environment, associated with diverse cognitive functions.     

Quantifying the risk of mis-estimating correlation significance of climate–tree growth relationships

In dendroecology, sampling effort has a strong influence of both regional chronology properties and climate–tree growth relationships assessment. Recent studies evidenced that decreasing sample size leads to a weakening of the bootstrapped correlation coefficients ( ${\text{BCC}}$ BCC ). The present analysis focused on the risk of mis-estimating the significance of population ${\text{BCC}}\,\left( {{\text{BCC}}_{\text{POP}} } \right)$ BCC ( BCC POP ) from a sample of N trees, and then proposed an approach to detect and correct mis-estimations using the properties of the sample. The sample size effect and the limits of the correction were illustrated from 840 individual growth chronologies of Corsican pine (Pinus nigra Arnold ssp. laricio Poiret var. Corsicana) sampled in Western France. The 840 trees were used to assess the population characteristics, and the effect of sampling effort was investigated through a simulation approach based on a resampling procedure of N trees amongst 840 (N ? [5; 50]). Our results evidenced that the risk strongly varied amongst the climatic regressors. The highest risks were evidenced for significant ${\text{BCC}}_{\text{POP}}$ BCC POP , with a percentage of mis-estimation ranging from 25 to 80. On the contrary, small samples allowed providing an reliable estimation of the significance of non-significant ${\text{BCC}}_{\text{POP}}$ BCC POP . To a lesser extent, the risk slightly decreased with increasing N, according to a negative exponential trend. The detection and correction method was found relevant to detect mis-estimation only for significant ${\text{BCC}}_{\text{POP}}$ BCC POP ; otherwise, the ${\text{BCC}}_{\text{POP}}$ BCC POP significance was generally overestimated.     

Do calcium buffers always slow down the propagation of calcium waves?

Calcium buffers are large proteins that act as binding sites for free cytosolic calcium. Since a large fraction of cytosolic calcium is bound to calcium buffers, calcium waves are widely observed under the condition that free cytosolic calcium is heavily buffered. In addition, all physiological buffered excitable systems contain multiple buffers with different affinities. It is thus important to understand the properties of waves in excitable systems with the inclusion of buffers. There is an ongoing controversy about whether or not the addition of calcium buffers into the system always slows down the propagation of calcium waves. To solve this controversy, we incorporate the buffering effect into the generic excitable system, the FitzHugh–Nagumo model, to get the buffered FitzHugh–Nagumo model, and then to study the effect of the added buffer with large diffusivity on traveling waves of such a model in one spatial dimension. We can find a critical dissociation constant ( $K=K(a)$ ) characterized by system excitability parameter $a$ such that calcium buffers can be classified into two types: weak buffers ( $K\in (K(a),\infty )$ ) and strong buffers ( $K\in (0,K(a))$ ). We analytically show that the addition of weak buffers or strong buffers but with its total concentration $b_0^1$ below some critical total concentration $b_{0,c}^1$ into the system can generate a traveling wave of the resulting system which propagates faster than that of the origin system, provided that the diffusivity $D_1$ of the added buffers is sufficiently large. Further, the magnitude of the wave speed of traveling waves of the resulting system is proportional to $\sqrt{D_1}$ as $D_1\rightarrow \infty $ . In contrast, the addition of strong buffers with the total concentration $b_0^1>b_{0,c}^1$ into the system may not be able to support the formation of a biologically acceptable wave provided that the diffusivity $D_1$ of the added buffers is sufficiently large.     

Analysis of {}^{13}{\text{C}}^{{{\upalpha}}} and {}^{13}{\text{C}}^{{{\upbeta}}} chemical shifts of cysteine and cystine residues in proteins: a quantum chemical approach

Cysteines possess a unique property among the 20 naturally occurring amino acids: it can be present in proteins in either the reduced or oxidized form, and can regulate the activity of some proteins. Consequently, to augment our previous treatment of the other types of residues, the $ {}^{13}{\text{C}}^{{{\upalpha}}} $ and $ {}^{13}{\text{C}}^{{{\upbeta}}} $ chemical shifts of 837 cysteines in disulfide-bonded cystine from a set of seven non-redundant proteins, determined by X-ray crystallography and NMR spectroscopy, were computed at the DFT level of theory. Our results indicate that the errors between observed and computed $ {}^{13}{\text{C}}^{{{\upalpha}}} $ chemical shifts of such oxidized cysteines can be attributed to several effects such as: (a) the quality of the NMR-determined models, as evaluated by the conformational-average (ca) rmsd value; (b) the existence of high B-factor or crystal-packing effects for the X-ray-determined structures; (c) the dynamics of the disulfide bonds in solution; and (d) the differences in the experimental conditions under which the observed $ {}^{13}{\text{C}}^{{{\upalpha}}} $ chemical shifts and the protein models were determined by either X-ray crystallography or NMR-spectroscopy. These quantum-chemical-based calculations indicate the existence of two, almost non-overlapped, basins for the oxidized and reduced ?SH $ {}^{13}{\text{C}}^{{{\upbeta}}} $ , but not for the $ {}^{13}{\text{C}}^{{{\upalpha}}} $ , chemical shifts, in good agreement with the observation of 375 $ {}^{13}{\text{C}}^{{{\upalpha}}} $ and 337 $ {}^{13}{\text{C}}^{{{\upbeta}}} $ resonances from 132 proteins by Sharma and Rajarathnam (2000). Overall, our results indicate that explicit consideration of the disulfide bonds is a necessary condition for an accurate prediction of $ {}^{13}{\text{C}}^{{{\upalpha}}} $ and $ {}^{13}{\text{C}}^{{{\upbeta}}} $ chemical shifts of cysteines in cystines.     

Cherry Picking: A Characterization of the Temporal Hybridization Number for a Set of Phylogenies

Recently, we have shown that calculating the minimum–temporal-hybridization number for a set ${\mathcal{P}}$ of rooted binary phylogenetic trees is NP-hard and have characterized this minimum number when ${\mathcal{P}}$ consists of exactly two trees. In this paper, we give the first characterization of the problem for ${\mathcal{P}}$ being arbitrarily large. The characterization is in terms of cherries and the existence of a particular type of sequence. Furthermore, in an online appendix to the paper, we show that this new characterization can be used to show that computing the minimum–temporal hybridization number for two trees is fixed-parameter tractable.     

Modeling analysis of the lipid bilayer–cytoskeleton coupling in erythrocyte membrane

Studies of thermal fluctuations in discocytes, echinocytes, and spherocytes suggest that the coupling between lipid bilayer and cytoskeleton can affect viscoelastic behavior of single erythrocyte membranes. To test this hypothesis, we developed a 3D constitutive model describing viscoelastic behavior of erythrocyte membranes, at long relaxation times \(t \in [0.20\,\mathrm {s}, 1.05\,\mathrm {s}]\) and short relaxation times \(t \in [0.03\,\mathrm {s}, 0.20\,\mathrm {s}]\) . The model was constructed using combination of spring and spring pot rheological elements arranged in parallel. The rearrangement of cytoskeleton induced by changing the bending state of lipid bilayer was described by a modified Eyring model. The model predictions point to an anomalous nature of energy dissipation and an ordered harmonic nature of the coupling mechanism described by a series of fractional derivatives of the order n \(\alpha \) (where \( n \in [- 1, 2]\) ). As a result, the stress generated within the lipid bilayer is related to the rate of change of the irreversible stress within the cytoskeleton.     

A locally convergent rotationally invariant particle swarm optimization algorithm

Several well-studied issues in the particle swarm optimization algorithm are outlined and some earlier methods that address these issues are investigated from the theoretical and experimental points of view. These issues are the: stagnation of particles in some points in the search space, inability to change the value of one or more decision variables, poor performance when the swarm size is small, lack of guarantee to converge even to a local optimum (local optimizer), poor performance when the number of dimensions grows, and sensitivity of the algorithm to the rotation of the search space. The significance of each of these issues is discussed and it is argued that none of the particle swarm optimizers we are aware of can address all of these issues at the same time. To address all of these issues at the same time, a new general form of velocity update rule for the particle swarm optimization algorithm that contains a user-definable function \(f\) is proposed. It is proven that the proposed velocity update rule guarantees to address all of these issues if the function \(f\) satisfies the following two conditions: (i) the function \(f\) is designed in such a way that for any input vector \(\vec {y}\) in the search space, there exists a region \(A\) which contains \(\vec {y}\) and \( f\!\left( {\vec {y}} \right) \) can be located anywhere in \(A\) , and (ii) \(f\) is invariant under any affine transformation. An example of function \(f\) is provided that satisfies these conditions and its performance is examined through some experiments. The experiments confirm that the proposed algorithm (with an appropriate function \(f)\) can effectively address all of these issues at the same time. Also, comparisons with earlier methods show that the overall ability of the proposed method for solving benchmark functions is significantly better.     

When does pathogen evolution maximize the basic reproductive number in well-mixed host–pathogen systems?

Pathogen evolution towards the largest basic reproductive number, $\mathcal R _0$ , has been observed in many theoretical models, but this conclusion does not hold universally. Previous studies of host–pathogen systems have defined general conditions under which $\mathcal R _0$ maximization occurs in terms of $\mathcal R _0$ itself. However, it is unclear what constraints these conditions impose on the functional forms of pathogen related processes (e.g. transmission, recover, or mortality) and how those constraints relate to the characteristics of natural systems. Here we focus on well-mixed SIR-type host–pathogen systems and, via a synthesis of results from the literature, we present a set of sufficient mathematical conditions under which evolution maximizes $\mathcal R _0$ . Our conditions are in terms of the functional responses of the system and yield three general biological constraints on when $\mathcal R _0$ maximization will occur. First, there are no genotype-by-environment interactions. Second, the pathogen utilizes a single transmission pathway (i.e. either horizontal, vertical, or vector transmission). Third, when mortality is density dependent: (i) there is a single infectious class that individuals cannot recover from, (ii) mortality in the infectious class is entirely density dependent, and (iii) the rates of recovery, infection progression, and mortality in the exposed classes are independent of the pathogen trait. We discuss how this approach identifies the biological mechanisms that increase the dimension of the environmental feedback and prevent $\mathcal R _0$ maximization.     

Interaction of ascorbate with photosystem I

Ascorbate is one of the key participants of the antioxidant defense in plants. In this work, we have investigated the interaction of ascorbate with the chloroplast electron transport chain and isolated photosystem I (PSI), using the EPR method for monitoring the oxidized centers \( {\text{P}}_{700}^{ + } \) and ascorbate free radicals. Inhibitor analysis of the light-induced redox transients of P₇₀₀ in spinach thylakoids has demonstrated that ascorbate efficiently donates electrons to \( {\text{P}}_{ 7 0 0}^{ + } \) via plastocyanin. Inhibitors (DCMU and stigmatellin), which block electron transport between photosystem II and Pc, did not disturb the ascorbate capacity for electron donation to \( {\text{P}}_{700}^{ + } \) . Otherwise, inactivation of Pc with CN^? ions inhibited electron flow from ascorbate to \( {\text{P}}_{700}^{ + } \) . This proves that the main route of electron flow from ascorbate to \( {\text{P}}_{700}^{ + } \) runs through Pc, bypassing the plastoquinone (PQ) pool and the cytochrome b ₆ f complex. In contrast to Pc-mediated pathway, direct donation of electrons from ascorbate to \( {\text{P}}_{700}^{ + } \) is a rather slow process. Oxidized ascorbate species act as alternative oxidants for PSI, which intercept electrons directly from the terminal electron acceptors of PSI, thereby stimulating photooxidation of P₇₀₀. We investigated the interaction of ascorbate with PSI complexes isolated from the wild type cells and the MenB deletion strain of cyanobacterium Synechocystis sp. PCC 6803. In the MenB mutant, PSI contains PQ in the quinone-binding A₁-site, which can be substituted by high-potential electron carrier 2,3-dichloro-1,4-naphthoquinone (Cl₂NQ). In PSI from the MenB mutant with Cl₂NQ in the A₁-site, the outflow of electrons from PSI is impeded due to the uphill electron transfer from A₁ to the iron-sulfur cluster F_X and further to the terminal clusters F_A/F_B, which manifests itself as a decrease in a steady-state level of \( {\text{P}}_{700}^{ + } \) . The addition of ascorbate promoted photooxidation of P₇₀₀ due to stimulation of electron outflow from PSI to oxidized ascorbate species. Thus, accepting electrons from PSI and donating them to \( {\text{P}}_{700}^{ + } \) , ascorbate can mediate cyclic electron transport around PSI. The physiological significance of ascorbate-mediated electron transport is discussed.     

Deriving fluorometer-specific values of relative PSI fluorescence intensity from quenching of F 0 fluorescence in leaves of Arabidopsis thaliana and Zea mays

The effect of stepwise increments of red light intensities on pulse-amplitude modulated (PAM) chlorophyll (Chl) fluorescence from leaves of A. thaliana and Z. mays was investigated. Minimum and maximum fluorescence were measured before illumination (F ₀ and F _M, respectively) and at the end of each light step ( $ F^{\prime}_{0} $ and $ F^{\prime}_{\text{M}} $ , respectively). Calculated $ F^{\prime}_{0} $ values derived from F ₀, F _M and $ F^{\prime}_{\text{M}} $ fluorescence according to Oxborough and Baker (1997) were lower than the corresponding measured $ F^{\prime}_{0} $ values. Based on the concept that calculated $ F^{\prime}_{0} $ values are under-estimated because the underlying theory ignores PSI fluorescence, a method was devised to gain relative PSI fluorescence intensities from differences between calculated and measured $ F^{\prime}_{0} $ . This method yields fluorometer-specific PSI data as its input data (F ₀, F _M, $ F^{\prime}_{0} $ and $ F^{\prime}_{\text{M}} $ ) depend solely on the spectral properties of the fluorometer used. Under the present conditions, the PSI contribution to F ₀ fluorescence was 0.24 in A. thaliana and it was independent on the light acclimation status; the corresponding value was 0.50 in Z. mays. Correction for PSI fluorescence affected Z. mays most: the linear relationship between PSI and PSII photochemical yields was clearly shifted toward the one-to-one proportionality line and maximum electron transport was increased by 50 %. Further, correction for PSI fluorescence increased the PSII reaction center-specific parameter, 1/F ₀ ? 1/F _M, up to 50 % in A. thaliana and up to 400 % in Z. mays.     

Approximation of sojourn-times via maximal couplings: motif frequency distributions

Sojourn-times provide a versatile framework to assess the statistical significance of motifs in genome-wide searches even under non-Markovian background models. However, the large state spaces encountered in genomic sequence analyses make the exact calculation of sojourn-time distributions computationally intractable in long sequences. Here, we use coupling and analytic combinatoric techniques to approximate these distributions in the general setting of Polish state spaces, which encompass discrete state spaces. Our approximations are accompanied with explicit, easy to compute, error bounds for total variation distance. Broadly speaking, if \({\mathsf{T}}_n\) is the random number of times a Markov chain visits a certain subset \({\mathsf{T}}\) of states in its first \(n\) transitions, then we can usually approximate the distribution of \({\mathsf{T}}_n\) for \(n\) of order \((1-\alpha )^{-m}\) , where \(m\) is the largest integer for which the exact distribution of \({\mathsf{T}}_m\) is accessible and \(0\le \alpha \le 1\) is an ergodicity coefficient associated with the probability transition kernel of the chain. This gives access to approximations of sojourn-times in the intermediate regime where \(n\) is perhaps too large for exact calculations, but too small to rely on Normal approximations or stationarity assumptions underlying Poisson and compound Poisson approximations. As proof of concept, we approximate the distribution of the number of matches with a motif in promoter regions of C. elegans. Mathematical properties of the proposed ergodicity coefficients and connections with additive functionals of homogeneous Markov chains as well as ergodicity of non-homogeneous Markov chains are also explored.     

Towards a conceptualization of ETL and physical storage of semantic data warehouses as a service

The data warehouse technology has become the incontestable tool for businesses and organizations to make strategic decisions to ensure their competitively. The construction of a data warehouse ( $\mathcal{D}\mathcal{W}$ ) passes by selecting relevant information sources, extracting relevant data and loading them into the $\mathcal{D}\mathcal{W}$ . These processes require a precise expertise from designers related to logical and physical implementations of information sources, which is not usually an easy task. The diversity and heterogeneity of information sources makes the construction process of the $\mathcal{D}\mathcal{W}$ complex and time consuming. Domain ontologies have been proposed to reduce heterogeneity between sources, platforms, services, etc. They resolve syntax and semantic conflicts. The phenomenon of adopting domain ontologies by organizations creates a new type of databases, called semantic databases ( $\mathcal{S}\mathcal{D}\mathcal{B}$ ). As a consequence, they become a candidate for building the semantic $\mathcal{D}\mathcal{W}$ ( $\mathcal{S}\mathcal{D}\mathcal{W}$ ). To handle the diversity of information sources and hide the implementations aspects of sources, proposing a generic framework for constructing $\mathcal{D}\mathcal{W}$ becomes a necessity. In this paper, we first proposed an ontology-based approach for designing $\mathcal{S}\mathcal {D}\mathcal{B}$ . Secondly, ETL phases are defined at ontological level to hide the implementation details. Thirdly, a storage service for ontologies and its associated data is given. Finally, our proposal is validated through a case study and a tool.     

Estimation of viscosity from passage time of liquids flowing through a microchannel array

Recently, a microchannel flow analyzer (MC-FAN) has been used to study the flow properties of blood. However, the correlation between blood passage time measured by use of the MC-FAN and hemorheology has not been clarified. In this study, a simple model is proposed for estimation of liquid viscosity from the passage time t _p of liquids. The t _p data for physiological saline were well represented by the model. According to the model, the viscosity of Newtonian fluids was estimated reasonably well from the t _p data. For blood samples, although the viscosity $ \eta_{\text{mc}} $ estimated from t _p was shown to be smaller than the viscosity $ \eta_{{450{\text{s}}^{ - 1} }} $ measured by use of a rotatory viscometer at a shear rate of 450 s^?1, $ \eta_{\text{mc}} $ was correlated with $ \eta_{{450{\text{s}}^{ - 1} }} $ . An empirical equation for estimation of $ \eta_{{450{\text{s}}^{ - 1} }} $ from $ \eta_{\text{mc}} $ of blood samples is proposed.     

Parameter non-identifiability of the Gyllenberg–Webb ODE model

An ODE model introduced by Gyllenberg and Webb (Growth Develop Aging 53:25–33, 1989) describes tumour growth in terms of the dynamics between proliferating and quiescent cell states. The passage from one state to another and vice versa is modelled by two functions $r_o$ and $r_i$ depending on the total tumour size. As these functions do not represent any observable quantities, they have to be identified from the observations. In this paper we show that there is an infinite number of pairs ( $r_o, r_i$ ) corresponding to the same solution of the ODE system and the functions ( $r_o, r_i$ ) will be classified in terms of this equivalence. Surprisingly, the technique used for this classification permits a uniqueness proof of the solution of the ODE model in a non-Lipschitz case. The reasoning can be widened to a more general setting including an extension of the Gyllenberg–Webb model with a nonlinear birth rate. The relevance of this result is discussed in a preclinical application scenario.     

An approach to sequential NMR assignments of proteins: application to chemical shift restraint-based structure prediction

A procedure for the simultaneous acquisition of {HNCOCANH & HCCCONH} chemical shift correlation spectra employing sequential \(^{1}\hbox {H}\) data acquisition for moderately sized proteins is presented. The suitability of the approach for obtaining sequential resonance assignments, including complete \(^{15}\hbox {N}{},\, ^{1}\hbox {H}{}^{N},\, ^{13}\hbox {CO}{},\, ^{13}\hbox {C}^{\alpha }{},\, ^{13}\hbox {C}^{\beta }\) and \(^{1}\hbox {H}^{\alpha }\) chemical shift information, is demonstrated experimentally for a \(^{13}\hbox {C}\) and \(^{15}\hbox {N}\) labelled sample of the C-terminal winged helix (WH) domain of the minichromosome maintenance (MCM) complex of Sulfolobus solfataricus. The chemical shift information obtained was used to calculate the global fold of this winged helix domain via CS-Rosetta. This demonstrates that our procedure provides a reliable and straight-forward protocol for a quick global fold determination of moderately-sized proteins.     

Capnographic parameters of the breathing pattern in healthy adults and patients with psychogenic dyspnea

Parameters of 5-min capnogram in 106 healthy humans (H group) were compared with those in 30 patients with psychogenic dyspnea (P group). Averaged values of end-tidal fractional concentration of carbon dioxide (FetCO₂) and respiration rate (f) were determined. The structure of the respiratory cycle was estimated by the ratio of the expiratory time to the total respiratory cycle time $\left( {R_{CO_2 } } \right)$ . The degree of breath arrhythmia was estimated using the coefficient of variation (CV) of $R_{CO_2 }$ , recorded during the 5-min capnography $\left( {R_{CO_2 } } \right)$ . The difference in the capnograms of H group and P group was reliable for all parameters, except for $R_{CO_2 }$ (structure of the respiratory cycle). For H group, FetCO₂ was 5.24 ± 0.36 vol %, and for P group, it was 4.07 ± 0.47 vol %. For H group, f was 14.3 ± 3.74 br./min; and for P group, it was 17.9 ± 4.50 br./min. For H group, $CVR_{CO_2 }$ was 8.91 ± 2.16%; and for P group, it was 12.7 ± 3.14%. The comprehensive parameter, which includes all three characteristics of the breathing pattern, such as a decrease in FetCO₂, an increase in f, and disorders of the breathing rhythm, appeared to be the most informative indicator of psychogenic dyspnea. It was shown that capnography with automatic processing of the breathing pattern is an objective method for studying the mechanisms of psychogenic dyspnea.     

Correlations and comparisons of quantitative trait loci with family per se and testcross performance for grain yield and related traits in maize

Simultaneous improvement in grain yield and related traits in maize hybrids and their parents (inbred lines) requires a better knowledge of genotypic correlations between family per se performance (FP) and testcross performance (TP). Thus, to understand the genetic basis of yield-related traits in both inbred lines and their testcrosses, two F _2:3 populations (including 230 and 235 families, respectively) were evaluated for both FP and TP of eight yield-related traits in three diverse environments. Genotypic correlations between FP and TP, $ \hat{r}_{\text{g}} $ (FP, TP), were low (0–0.16) for grain yield per plant (GYPP) and kernel number per plant (KNPP) in the two populations, but relatively higher (0.32–0.69) for the other six traits with additive effects as the primary gene action. Similar results were demonstrated by the genotypic correlations between observed and predicted TP values based on quantitative trait loci positions and effects for FP, $ \hat{r}_{\text{g}} $ (M _FP, Y _TP). A total of 88 and 35 QTL were detected with FP and TP, respectively, across all eight traits in the two populations. However, the genotypic variances explained by the QTL detected in the cross-validation analysis were much lower than those in the whole data set for all traits. Several common QTL between FP and TP that accounted for large phenotypic variances were clustered in four genomic regions (bin 1.10, 4.05–4.06, 9.02, and 10.04), which are promising candidate loci for further map-based cloning and improvement in grain yield in maize. Compared with publicly available QTL data, these QTL were also detected in a wide range of genetic backgrounds and environments in maize. These results imply that effective selection based on FP to improve TP could be achieved for traits with prevailing additive effects.     

Comparative analysis of intermuscular bones in fish of different ploidies

We documented the number, morphology, and distribution of intermuscular bones in five fishes of different ploidy: Carassius auratus (Abbr.WCC, 2n=100), Carassius auratus variety PengZe (Abbr.PZCC, 3n=150), improved triploid crucian carp (Abbr.ITCC, 3n=150), improved red crucian carp (Carassius auratus red var., Abbr.IRCC, ♀, 2n=100), and improved allotetraploids (Abbr.G×AT, ♂, 4n=200). The number of intermuscular bones in WCC, PZCC, and G×AT ranged from 78 to 83 ( $\bar x$ =81), 80 to 86 ( $\bar x$ =84), and 77 to 84 ( $\bar x$ =82), respectively. The numbers in ITCC and IRCC were significantly lower, ranging from 77 to 82 ( $\bar x$ =79) and 58 to 77 ( $\bar x$ =71), respectively. The average number of intermuscular bones in each sarcomere, ranked in order from highest to lowest, was 0.721 (WCC), 0.673 (PZCC), 0.653 (G×AT), 0.633 (ITCC), and 0.608 (IRCC). There was no difference between ITCC and G×AT or between G×AT and PZCC. However, the average number of intermuscular bones in the sarcomeres of ITCC, WCC, and PZCC differed significantly, as did that of IRCC and the four other kinds of fish. The intermuscular bone of these five fishes was divided into seven shape categories, non-forked (卜), one-end-unequal-bi-fork (卜), one-end-equal-bi-fork (Y), one-end-multi-fork, two-end-bi-fork, two-end-multi-fork, and tree-branch types. Generally, the morphological complexity was higher in the anterior intermuscular bones than in the posterior body. The number of intermuscular bones was similar but not equal between the left and right sides of the body. ITCC had significantly fewer intermuscular bones than either WCC or PZCC, making it of greater commercial value. Additionally, IRCC and ITCC had fewer intermuscular bones than WCC. Our observations are significant in both fish bone developmental biology and genetic breeding.     

Counting glycans revisited

We present an algorithm for counting glycan topologies of order \(n\) that improves on previously described algorithms by a factor \(n\) in both time and space. More generally, we provide such an algorithm for counting rooted or unrooted \(d\) -ary trees with labels or masses assigned to the vertices, and we give a “recipe” to estimate the asymptotic growth of the resulting sequences. We provide constants for the asymptotic growth of \(d\) -ary trees and labeled quaternary trees (glycan topologies). Finally, we show how a classical result from enumeration theory can be used to count glycan structures where edges are labeled by bond types. Our method also improves time bounds for counting alkanes.