Let $\mathcal {R}f$ be the randomization of an analytic function over the unit disk in the complex plane

$$ \begin{align*}\mathcal{R} f(z) =\sum_{n=0}^\infty a_n X_n z^n \in H({\mathbb D}), \end{align*} $$

$f(z)=\sum _{n=0}^\infty a_n z^n \in H({\mathbb D})$

$(X_n)_{n \geq 0}$

$f \in H({\mathbb D})$

${\mathcal R} f$

Using Patterson–Sullivan measures, we investigate growth problems for groups acting on a metric space with a strongly contracting element.

We introduce a formula for translating any upper bound on the percolation threshold of a lattice $G$ into a lower bound on the exponential growth rate of lattice animals $a(G)$ and vice versa. We exploit this in both directions. We obtain the rigorous lower bound ${\dot{p}_c}({\mathbb{Z}}^3)\gt 0.2522$ for 3-dimensional site percolation. We also improve on the best known asymptotic bounds on $a({\mathbb{Z}}^d)$ as $d\to \infty$. Our formula remains valid if instead of lattice animals we enumerate certain subspecies called interfaces. Enumerating interfaces leads to functional duality formulas that are tightly connected to percolation and are not valid for lattice animals, as well as to strict inequalities for the percolation threshold.

Incidentally, we prove that the rate of the exponential decay of the cluster size distribution of Bernoulli percolation is a continuous function of $p\in (0,1)$.

Genetics is key to the improvement of welfare in broiler chickens at both juvenile and adult (breeder) stages but progress is hampered currently by the seemingly conflicting demands of welfare, commercial production, food security and calls for increasing intensification to curb climate change. Animal welfare is therefore most likely to be improved on a commercial scale by future breeding programmes that incorporate multiple goals of different stakeholders as far as possible and give higher priority to animal welfare. These include: i) broilers with high welfare traits; ii) broiler breeders that do not need feed restriction; iii) birds that can be grown in an economically profitable way; iv) birds with low disease levels without the need for routine medication; v) chicken meat that is healthy and good for humans to eat; and (vi) broilers and breeders that thrive in systems that are environmentally sustainable. Progress towards achieving these goals is hampered currently by the assumptions that high juvenile growth rate is incompatible with good welfare and that feed restriction in adults is inevitable with fast-growing juveniles. We challenge these assumptions at both genetic and whole-animal level and argue that the conflict between good welfare and productivity can be reduced by making use of all available genetic variation from existing breeds and other sources and selecting birds in the range of environments they will encounter in commercial production.

The cusped hyperbolic n-orbifolds of minimal volume are well known for $n\leq 9$ . Their fundamental groups are related to the Coxeter n-simplex groups $\Gamma _{n}$ . In this work, we prove that $\Gamma _{n}$ has minimal growth rate among all non-cocompact Coxeter groups of finite covolume in $\textrm{Isom}\mathbb H^{n}$ . In this way, we extend previous results of Floyd for $n=2$ and of Kellerhals for $n=3$ , respectively. Our proof is a generalization of the methods developed together with Kellerhals for the cocompact case.

We address the hypothesis that keeping kids and mothers together would have positive effects on the milk composition of the mother and the behaviour of the kids. Kids were either permanently separated (SEP), daily separated between 7.30 and 15 h (DAY-SEP) or kept with mothers 24 h/d (NON-SEP). The NON-SEP kids were only allowed to suckle one teat. All kids had similar growth rate throughout the study (lactation days 5–70). DAY-SEP kids spent 24% of their time with their mother at both ages. NON-SEP spent only 15% of the time with their mothers at 2 weeks of age and this increased to 28% at 2 months of age. NON-SEP kids showed more hiding behaviour at 2 weeks and SEP were more active alone, at both 2 weeks and 2 months, compared to the other treatments. The mean available milk yield and fat concentration were higher in DAY-SEP goats (2420 g ± 119 g and 4.9 ± 0.1%) compared with NON-SEP goats (2149 ± 79 g and 4.4 ± 0.1%). There were no differences between DAY-SEP and NON-SEP goats in total protein, lactose, or casein concentrations. Based on these data it was estimated that 7.1 kg milk was needed to produce 1 kg semi-hard cheese in DAY-SEP goats and 7.5 kg in NON-SEP goats, respectively. When comparing milk yield and composition between udder halves, the milk yield was, as expected, higher from the machine milked teat than from the suckled one in the NON-SEP goats but there was no difference between right and left udder halves in DAY-SEP goats. Milk fat concentration varied between teats at morning and afternoon milkings in NON-SEP goats, but there was no difference in milk fat between udder-halves in DAY-SEP goats. In conclusion, the kid growth rate was similar in all treatments, however, an altered behaviour was seen in permanently separated kids (SEP). The results show that it is possible to have a high milk yield and fat concentration with one kid together with the dam.

The present work evaluated animal models comprising direct and maternal effects to estimate (co)variance components and genetic parameters of growth rates and Kleiber ratio in Harnali sheep. The information on pedigree and targeted traits of 1862 lambs born to 144 sires and 591 dams was collected for the period from 1998 to 2018. The traits studied were average daily gain from birth to 3 months of age (ADG1), 3 months to 6 months of age (ADG2), and 6 months to 12 months of age (ADG3) and their corresponding Kleiber ratios as KR1, KR2 and KR3, respectively. The statistical methods included the general linear model for analyzing the effects of fixed factors and animal models for deriving variance components for targeted traits. According to best model evaluated on the basis of likelihood ratio test, the estimated direct heritability was low in magnitude and ranged from 0.04 to 0.14. Direct heritability estimates for ADG1, ADG2, ADG3, KR1, KR2 and KR3 were 0.06, 0.14, 0.05, 0.04, 0.11 and 0.05, respectively. The maternal genetic effects contributed (4–7%) significantly for ADG1, KR1 and KR2 traits. The genetic correlations ranged from −0.35 ± 0.11 (ADG1-KR2) to 0.98 ± 0.01 (ADG2-KR2 and ADG3-KR3) and phenotypic correlations ranged from −0.36 ± 0.02 to 0.98 ± 0.01 for ADG1-KR2 and ADG2-KR2, respectively. The significant maternal effects along with low levels of direct effects for average daily gain and Kleiber ratio at different age group should be considered while setting selection and managerial strategies to achieve anticipated growth rates in Harnali sheep.

A southern population (S) from Xiushui County (29°1′N, 114°4′E) and a northern population (N) from Shenyang city (41°48′N, 123°23′E) of the cabbage beetle, Colaphellus bowringi vary greatly in their life-history traits, and may serve as an excellent model with which to study the inheritance of life-history traits. In the present study, we performed intraspecific hybridization using the two populations, comparing the key life-history traits (fecundity, development time, body weight, growth rate, and sexual size dimorphism (SDD)) between the two populations (S♀ × S♂ and N♀ × N♂) and their two hybrid populations (S♀ × N♂ and N♀ × S♂ populations) at 19, 22, 25, and 28°C. Our results showed that there were significant differences in life-history traits between the two parental populations, with the S population having a significantly higher fecundity, shorter larval development time, larger body weight, higher growth rate, and greater weight loss during metamorphosis than the N population at almost all temperatures. However, these life-history traits in the two hybrid populations were intermediate between those of their parents. The life-history traits in the S × N and N × S populations more closely resembled those of the maternal S population and N population, respectively, showing maternal effects. Weight loss for both sexes was highest in the S population, followed by the S × N, N × S, and N populations at all temperatures, suggesting that larger pupae lost more weight during metamorphosis. The changes in SSD with temperature were similar between the S and the S × N populations and between the N and the N × S populations, also suggesting a maternal effect. Overall, our results showed no drastic effect of hybridization on C. bowringi, being neither negative (hybrid inferiority) nor positive (heterosis). Rather, the phenotypes of hybrids were intermediate between the phenotypes of their parents.

Epidemic forecasting provides an opportunity to predict geographic disease spread and counts when an outbreak occurs and plays a key role in preventing or controlling their adverse impact. However, conventional prediction models based on complex mathematical modelling rely on the estimation of model parameters, which yields unreliable and unsustainable results. Herein, we proposed a simple model for predicting the epidemic transmission dynamics based on nonlinear regression of the epidemic growth rate and iterative methods, which is applicable to the progression of the COVID-19 outbreak under the strict control measures of the Chinese government. Our model yields reliable and accurate results as confirmed by the available data: we predicted that the total number of infections in mainland China would be 91 253, and the maximum number of beds required for hospitalised patients would be 62 794. We inferred that the inflection point (when the growth rate turns from positive to negative) of the epidemic across China would be mid-February, and the end of the epidemic would be in late March. This model is expected to contribute to resource allocation and planning in the health sector while providing a theoretical basis for governments to respond to future global health crises or epidemics.

Feeding monogastric livestock in organic agriculture is challenging due to several tradeoffs between animal welfare aspects, resource efficiency, as well as ecological and social sustainability. Organic standards may even increase such conflicts, as is currently the case with upcoming new regulations regarding restrictions of feed sources for organic pigs in Europe. In order to contribute data for balancing reasons to minimize tradeoffs, we compared four different piglet diets, each targeted to reach a high protein quality by either a high proportion of soybean cake (SOY), inclusion of milk powder (MILK), fermentatively produced lysine (LYS) or conventional potato protein (POT). All diets were designed to meet the nutritional requirements of piglets in the best possible way, however they all represented different conflicts with either organic regulations or sustainability goals. In each of five consecutive runs, respectively three litters were assigned to every dietary treatment, resulting in 15 litters per treatment in total. In each litter, seven focus animals were defined. The piglets were studied from birth until 58 days of age. They were weaned at day 46 and sold from the farm at day 58. Piglets were individually weighed at an average age of 3, 21, 43, 50 and 58 days with simultaneous assessment of body condition score (BCS) and prevalence of diarrhea. Feed intake (FI) was recorded litter wise weekly, starting from week three. Feed conversion ratio (FCR) was calculated for the period after weaning. Statistical analysis was executed using linear mixed effect models. Regarding FI, FCR and daily weight gains, no treatment effect was found. Only at day 21, BCS was lower for piglets receiving POT. Prevalence of diarrhea increased after weaning for all treatments. All four tested diets led to similar weight gains and feed conversion in the piglets. Animals fed diet POT recovered better from diarrhea compared to the other treatments. A high soybean cake content or lysine supplementation in the diet was disadvantageous with regard to the occurrence of diarrhea. LYS diet led to signs of threonine deficit, indicating that lysine addition alone may not solve the issue. The addition of milk powder provided no extra benefit. In recognition of the health benefits, the use of 5% potato protein, even if it is sourced from conventional production, must still be considered as a sustainable option for feeding organic piglets. The sustainability implications are discussed in the paper.

Dietary chitosan (CS) supplementation could improve the growth rate, small intestinal morphology, nutrients apparent digestibility and digestive enzyme activities in pigs, broiler chickens, rats and fish, whereas no data has been reported about the effect of CS on the growing Huoyan geese. Therefore, this study was designed to investigate the effects of CS on growth rate, small intestinal morphology, nutrients apparent utilization and digestive enzyme activities of growing Huoyan geese. Three hundred and twenty (28 days of age, gender balance) Huoyan geese were randomly divided into control, CS100, CS200 and CS400 groups (based on BW) with 20 geese per pen and 4 replicates pen per group, and the feeding experiment lasted for 4 weeks. The 4 diets contained 0, 100, 200 and 400 mg CS per kg feed, respectively. The results showed that CS200 groups had higher average daily gain, final BW, apparent utilization of DM and CP, and lower feed/gain ratio compared with the control group (P < 0.05). Meanwhile, CS100 and CS200 groups had higher villus height, villus height/crypt depth ratio and lower crypt depth in duodenum and jejunum than those in the control group (P < 0.05). The geese in CS100 and CS200 groups had higher villus height, villus height/crypt depth ratio and lower crypt depth of ileum compared with those in control and CS400 groups (P < 0.05). In addition, compared with the control group, CS200 group has higher trypsin activities and lower lipase activities in duodenal, jejunal and ileal contents (P < 0.05). The results suggested that addition of 200 mg/kg CS had positive effects on growth rate, small intestinal morphology, nutrients apparent utilization and digestive enzyme activities of growing Huoyan geese.

Incidences of myopathies such as white striping (WS), woody breast (WB) and spaghetti meat (SP) in breast meat from young broilers have been observed globally over the past decade. Some industry reports suggest up to 20% WB occurrence in fast growing heavy broilers (~4.0 kg) with an estimated cost of more than US$500 million/year to the US industry alone, but may actually be far higher. The proportions and severity of the anomaly appear to be flock-dependent and are related to factors such as genetics, nutrition (e.g. protein level during the fast-growing phase), growth rate, activity of the birds at young age, sudden bursts of activity, number of embryonic stem cells and litter management. These three myopathies can appear together or individually, but it appears that they are all related. When meat is processed, these myopathies represent quality issues (firmer meat and/or lower water binding, aesthetics) but do not present a food safety issue. The poultry industry is now focusing on ways to reduce or eliminate the occurrence of these myopathies. Recently some improvements have been made as more is learned about the interactions between environmental and management (e.g., nutrition) factors, and some producers are already implementing new procedures. Breeding programmes are starting to show some promise and are expected to help reduce WB (estimated at 10% of birds per year) and deliver more solutions in the future.

Concepts of new fluttering wind and water mills led to general solution of flutter by a foil section free to pitch about an axis ahead of ${1}/{4}$ chord. The pitch damping of the vorticity being shed by lift change is negative singular via the imaginary part of the Theodorsen function. So a 2D airfoil can slowly flutter in pure pitch at a very high inertia with radian frequency and growth rate, reduced by windspeed/chord, resp. less than .087 and .01. At the frequency of nil net pitch damping, the binary inertia/damping cross determinant vanishes on a line in the imbalance vs inertia plane. The perturbed frequency contours just a bit above and below this ‘beab’ line spectacularly split to asymptote to the pure pitch inertia vertical of implied infinite heave stiffness. Higher frequency contours turn back towards the positive imbalance axis and then the origin, changing from hyperbolic to elliptical at exactly the same .087 and asymptoting to a line between the nexus and four times the nexus and a mode of effective pitch about ${3}/{4}$ chord. At .6 the pure pitch frequency the imaginary part dominates in the quadratic inertia and imbalance coefficients to bend the neutral contours down and across the quasi-steady line to even turn back to very large negative imbalance at small inertia, where kinematics then imply high mass. Diagonally mirror hyperbolae exist for greater than the pure pitch inertia with a different dynamic implication of very high foil mass.

Rabbit commercial maternal lines are usually selected for litter size (LS) and paternal lines for growth rate (GR). Line OR_LS was selected by ovulation rate (OR) and LS to improve LS more efficiently. In this study, growth traits of line OR_LS were evaluated by estimating the correlated response on weaning weight (WW), slaughter weight (SW) and GR during fattening period as well as their variability (DWW, DSW and DGR, respectively). Data were analyzed using Bayesian inference methods. Heritability estimates were low for growth traits (0.09, 0.13 and 0.14 for WW, SW and GR, respectively) and negligible for growth traits variability (0.01, 0.004 and 0.01 for DWW, DSW and DGR, respectively). Moderate common litter effect ratio (c2; 0.35, 0.28 and 0.27) and low maternal effect ratio (m2; 0.11, 0.05 and 0.01) were obtained for WW, SW and GR, respectively. Both c2 and m2 were lower at slaughter than at weaning. In addition, low common litter effect and negligible maternal effect were observed for growth traits variability. Genetic correlations between LS and both growth traits and their variability were close to zero. Positive genetic correlations were observed between OR and growth traits (0.19, 0.38 and 0.36 for WW, SW and GR, respectively) as well as between OR and growth traits variability (0.35, 0.62 and 0.20 for DWW, DSW and DGR, respectively). Positive correlated responses in both periods were obtained for growth traits, WW, SW and GR (0.037, 0.156 and 0.110 kg, respectively). The correlated response found in growth traits might be due to the positive genetic correlations between OR and these traits. However, selection for OR and LS using independent culling levels did not modify the growth traits variability. Therefore, no negative consequences on growth traits can be expected in current commercial maternal lines.

In this paper, we study the excitation of Gould–Trivelpiece (TG) waves by streaming ions in dusty plasma and derive the dispersion relation of the excited waves using first-order perturbation theory. The motion of charged particles is controlled by electromagnetic fields in plasma. The energy transfer processes which occur in this collisionless plasma are believed to be based on wave–particle interactions. We have found that the TG waves may be generated in a streaming ion plasma via Cerenkov interaction, and the ions may be accelerated by TG waves via cyclotron interaction, which enable energy and momentum transfer. The variation in the growth rate of TG wave with dust grain size and relative density of negatively charged dust grains is also studied. The dust can cause an unstable TG mode to be stable in Doppler resonance, and can induce an instability in Cerenkov interaction.

Life-history theory predicts a trade-off between the juvenile growth rate and adult traits related to survival. However, this hypothesized negative correlation is difficult to test robustly because many trade-offs are mild, and environmental variables, such as changes in nutrient availability, can ameliorate the trade-off or make it more pronounced. Thus, it is reasonable to expect that the expression of the trade-off can be condition-dependent. In the present study, we first examined the pre-adult life-history traits of the cotton bollworm, Helicoverpa armigera, collected from northern, central, and southern China at different temperatures. We found that the northern China population has a significantly shorter pre-adult developmental time and higher growth rate than the southern China population as a result of adaptation to the decreased seasonal length. Then, we tested for a trade-off between the juvenile growth rate and adult lifespan in different temperature and nutrient conditions. We found a negative relationship between juvenile growth rate and adult lifespan under starvation or desiccation conditions; however, a continuous supply of sugar can diminish or obviate the apparent negative relationship, in which the adult lifespan did not show a significant difference in most of the comparisons. These results suggested a resource-mediated trade-off may exist between juvenile growth rate and adult lifespan. However, the adult size may have some positive effect on the lifespan under starvation and desiccation conditions, which may affect the expression of trade-off.

We solve a problem posed by Blasco, Bonilla and Grosse-Erdmann in 2010 by constructing a harmonic function on ℝN, that is frequently hypercyclic with respect to the partial differentiation operator ∂/∂xk and which has a minimal growth rate in terms of the average L2-norm on spheres of radius r > 0 as r → ∞.