Let $n$ be a positive integer and $a$ an integer prime to $n$ . Multiplication by $a$ induces a permutation over $\mathbb{Z}/n\mathbb{Z}=\{\overline{0},\overline{1},\ldots ,\overline{n-1}\}$ . Lerch’s theorem gives the sign of this permutation. We explore some applications of Lerch’s result to permutation problems involving quadratic residues modulo $p$ and confirm some conjectures posed by Sun [‘Quadratic residues and related permutations and identities’, Preprint, 2018, arXiv:1809.07766]. We also study permutations involving arbitrary $k$ th power residues modulo $p$ and primitive roots modulo a power of  $p$ .

The production of abstract engravings is considered an indicator of modern human cognition and a means for the long-term recording and transmission of information. This article reports the discovery of two engraved bones from the Lingjing site in Henan Province, China, dated to 105–125 kya. The carefully engraved nature of the incisions, made on weathered rib fragments, precludes the possibility of unintentional or utilitarian origins. Residue analysis demonstrates the presence of ochre within the incised lines on one specimen. This research provides the first evidence for the deliberate use of ochred engravings for symbolic purposes by East Asian Late Pleistocene hominins.

Although topographic mapping missions and geological surveys carried out by Autonomous Underwater Vehicles (AUVs) are becoming increasingly prevalent, the lack of precise navigation in these scenarios still limits their application. This paper deals with the problems of long-term underwater navigation for AUVs and provides new mapping techniques by developing a Bathymetric Simultaneous Localisation And Mapping (BSLAM) method based on graph SLAM technology. To considerably reduce the calculation cost, the trajectory of the AUV is divided into various submaps based on Differences of Normals (DoN). Loop closures between submaps are obtained by terrain matching; meanwhile, maximum likelihood terrain estimation is also introduced to build weak data association within the submap. Assisted by one weight voting method for loop closures, the global and local trajectory corrections work together to provide an accurate navigation solution for AUVs with weak data association and inaccurate loop closures. The viability, accuracy and real-time performance of the proposed algorithm are verified with data collected onboard, including an 8 km planned track recorded at a speed of 4 knots in Qingdao, China.

The order Onchoproteocephalidea (Eucestoda) was recently erected to accommodate the hook-bearing tetraphyllideans and the proteocephalideans, which are characterized by internal proglottization and a tetra-acetabulate scolex. The recognized subfamilies in the Proteocephalidae appeared to be non-monophyletic based on 28S recombinant DNA (rDNA) sequence data. Other molecular markers with higher phylogenetic resolution, such as large mitochondrial DNA fragments and multiple genes, are obviously needed. Thus the mitochondrial genome of Gangesia oligonchis, belonging to the putative earliest diverging group of the Proteocephalidae, was sequenced. The circular mitogenome of G. oligonchis was 13,958 bp in size, and contained the standard 36 genes: 22 transfer RNA genes, two rRNA genes and 12 protein-coding genes, as well as two major non-coding regions. A short NCR and a large NCR (lNCR) region were 216 bp and 419 bp in size, respectively. Highly repetitive regions in the lNCR region were detected with that of 11 repeat units. The mitogenome of G. oligonchis shared 71.1% nucleotide identity with Testudotaenia sp. WL-2016. Phylogenetic analyses of the complete mitochondrial genomes with Bayesian inference and maximum likelihood methods indicated that G. oligonchis formed a sister clade with Testudotaenia sp. WL-2016 with maximum support. The ordinal topology is (Caryophyllidea, (Diphyllobothriidea, (Bothriocephalidea, (Onchoproteocephalidea, Cyclophyllidea)))). The mitogenomic gene arrangement of G. oligonchis was identical to that of Testudotaenia sp. WL-2016. Both mitogenomic and nuclear sequence data for many more taxa are required to effectively explore the inter-relationships among the Onchoproteocephalidea.

Maternal effects on offspring seeds are mainly caused by seed position on, and the abiotic environment of, the mother plant. Seed heteromorphism, a special form of position effect, is the production by an individual plant of morphologically distinct seed types, usually with different ecological behaviours. Seed heteromorphism is assumed to be a form of bet hedging and provides an ideal biological model to test theoretical predictions. Most studies of maternal effects on seeds have focused on abiotic environmental factors and changes in mean seed traits of offspring. Suaeda salsa is an annual halophyte that produces dimorphic seeds within the same inflorescence. We tested the hypothesis that plants grown from brown seeds of S. salsa have a higher offspring brown seed:black seed morph ratio and variance in seed size than plants from black seeds. Results from a pot experiment showed that plants grown from brown seeds had a higher brown seed:black seed ratio than plants grown from black seeds. This is the first layer of dynamic bet hedging. Brown seeds had higher size variation than black seeds, and seeds produced by plants from brown seeds also had higher seed size variation than plants grown from black seeds. This is the second layer of dynamic bet hedging. Thus, the maternal effect of seed heteromorphism is dual dynamic bet hedging. Furthermore, for seed traits we verified for the first time the theoretical prediction that an increase in offspring size variability induces an increase in the mean size of offspring.

The fenofibrate functions in mammals could be affected by many factors such as dietary nutrient levels and physiological status. However, this phenomenon has not been well studied in fish. The goal of our study was to investigate the effect of dietary protein contents on metabolic regulation of fenofibrate in Nile tilapia. An 8-week experiment was conducted to feed fish with four diets at two protein levels (28% and 38%) with or without the supplementation of fenofibrate (200 mg/kg body weight/day). After the trial, the body morphometric parameters, plasma biochemical parameters and qPCR data were examined. These results showed that fenofibrate significantly reduced the feeding intake and weight gain rate, increased the oxidative stress (increased plasma methane dicarboxylic aldehyde, MDA) and liver/body ratio (increased hepatosomatic index, HSI) in the LP (low protein)-fed fish. In contrast, fenofibrate exhibited a lipid-lowering (reduced hepatic lipid) effect and up-regulated the expressions of the genes related to lipid catabolism, transport and anabolic metabolism in the HP (high protein) fed-fish. The present study suggested that lipid-lowering effect of fenofibrate would be strengthened in the fish fed with HP diet containing high energy, but in the fish fed with the LP diet containing low energy, the fenofibrate treatment would cause adverse effects for metabolism. Taking together, our study showed that the metabolic regulation of fenofibrate in Nile tilapia was not only dependent on feed energy content, but also dependent on dietary nutrient composition, such as dietary protein and/or lipid levels.

The continental shelf strata provide information regarding sea-level fluctuation and climate changes in the Quaternary period. A 5831.47-km-long high-resolution seismic profile and borehole core (YS01) were acquired to reconstruct the evolutionary history of the strata in South Yellow Sea (SYS) during the late Pleistocene. The strata recorded three transgression events (HI, HII, and HIII) and three stages of paleochannel development (LI, LII, and LIII). Based on the distribution, thickness, and volume of the strata formed in the three transgressions, we concluded that the scale of the three transgressions during the late Pleistocene was HIII, HI, and HII, in descending order. In addition, our data show that the Yellow River extended to the Yellow Sea Trough during the last glacial maximum. The influence of the tectonic framework on sedimentation in the SYS was completely concealed by sea-level changes and sediment supply in the late Pleistocene (~Marine Isotope Stage 5). Since then, the accommodation space, a crucial prerequisite for sedimentation, has been controlled solely by sea-level changes in the SYS. Furthermore, two “source to sink” models of the neritic shelf in the marine and terrestrial environments were established, including high sea-level and shelf-exposure models.

Repetitive motion planning and control (RMPC) is a significant issue in the research of redundant robot manipulators. Moreover, noise from rounding error, truncation error, and robot uncertainty is an important factor that greatly affects RMPC schemes. In this study, the RMPC of redundant robot manipulators in a noisy environment is investigated. By incorporating the proportional and integral information of the desired path, a new RMPC scheme with pseudoinverse-type (P-type) formulation is proposed. Such a P-type RMPC scheme possesses the suppression of constant and bounded time-varying noises. Comparative simulation results based on a five-link robot manipulator and a PUMA560 robot manipulator are presented to further validate the effectiveness and superiority of the proposed P-type RMPC scheme over the previous one.

We assessed inheritance of resistance to sugarcane brown rust (Puccinia melanocephala) in selfing F1 populations of wild sugarcane germplasm Erianthus rockii ‘Yundian 95-19’ and E. rockii ‘Yundian 95-20’. We tested parent and selfing F1 individuals for the brown rust resistance gene, Bru1, that has been shown to confer resistance to brown rust in sugarcane. The Bru1 gene was not detected in E. rockii ‘Yundian 95-19’, E. rockii ‘Yundian 95-20’ or their selfing F1 individuals, and we found there was segregation of resistance in the two selfing F1 populations (segregation ratio: 3:1). The results confirmed resistance in E. rockii ‘Yundian 95-19’ and E. rockii ‘Yundian 95-20’ to sugarcane brown rust is controlled by a novel, single dominant gene.

Cryoconite is a dark-coloured granular sediment that contains biological and mineralogical components, and it plays a pivotal role in geochemistry, carbon cycling and glacier mass balance. In this work, we collected cryoconite samples from Laohugou Glacier No. 12 (LHG) on the north-eastern Tibetan Plateau during the summer of 2015 and measured the spectral albedo. To explore the impacts of this sediment on surface ablation, the ice melting differences between the cryoconite-free (removed) ice and the intact layers were compared. The results showed that the mean concentrations of black carbon (BC), organic carbon (OC) and total iron (Fe) in the LHG cryoconite were 1.28, 11.18 and 39.94 mg g−1, respectively. BC was found to play a stronger role in solar light adsorption than OC and free Fe. In addition, ice covered by cryoconite exhibited the lowest mean reflectance (i.e., <0.1). Compared with the cryoconite-free ice surface, cryoconite effectively absorbed solar energy and enhanced glacial melting at a rate of 2.27–3.28 cm d−1, and free Fe, BC and OC were estimated to contribute 1.01, 0.99 and 0.76 cm d−1, respectively. This study provides important insights for understanding the role of cryoconite in the glacier mass balance of the northern Tibetan Plateau.

Glyphodes pyloalis Walker (Lepidoptera: Pyralididae) is a common pest in sericulture and has developed resistance to different insecticides. However, the mechanisms involved in insecticide resistance of G. pyloalis are poorly understood. Here, we present the first whole-transcriptome analysis of differential expression genes in insecticide-resistant and susceptible G. pyloalis. Clustering and enrichment analysis of DEGs revealed several biological pathways and enriched Gene Ontology terms were related to detoxification or insecticide resistance. Genes involved in insecticide metabolic processes, including cytochrome P450, glutathione S-transferases and carboxylesterase, were identified in the larval midgut of G. pyloalis. Among them, CYP324A19, CYP304F17, CYP6AW1, CYP6AB10, GSTs5, and AChE-like were significantly increased after propoxur treatment, while CYP324A19, CCE001c, and AChE-like were significantly induced by phoxim, suggesting that these genes were involved in insecticide metabolism. Furthermore, the sequence variation analysis identified 21 single nucleotide polymorphisms within CYP9A20, CYP6AB47, and CYP6AW1. Our findings reveal many candidate genes related to insecticide resistance of G. pyloalis. These results provide novel insights into insecticide resistance and facilitate the development of insecticides with greater specificity to G. pyloalis.

This paper presents a neural network-based four-direction search scheme of path planning for mobile agents, given a known environmental map with stationary obstacles. Firstly, the map collision energy is modeled for all the obstacles based on neural network. Secondly, for the shorted path-search purpose, the path energy is considered. Thirdly, to decrease the path-search time, a variable step-length is designed with respect to collision energy of the previous iteration path. Simulation results demonstrate that the variable step-length is effective and can decrease the iteration time substantially. Lastly, experimental results show that the mobile agent tracks the generated path well. Both the simulation and experiment results substantiate the feasibility and realizability of the presented scheme.

Global inequity in access to and availability of essential mental health services is well recognized. The mental health treatment gap is approximately 50% in all countries, with up to 90% of people in the lowest-income countries lacking access to required mental health services. Increased investment in global mental health (GMH) has increased innovation in mental health service delivery in LMICs. Situational analyses in areas where mental health services and systems are poorly developed and resourced are essential when planning for research and implementation, however, little guidance is available to inform methodological approaches to conducting these types of studies. This scoping review provides an analysis of methodological approaches to situational analysis in GMH, including an assessment of the extent to which situational analyses include equity in study designs. It is intended as a resource that identifies current gaps and areas for future development in GMH. Formative research, including situational analysis, is an essential first step in conducting robust implementation research, an essential area of study in GMH that will help to promote improved availability of, access to and reach of mental health services for people living with mental illness in low- and middle-income countries (LMICs). While strong leadership in this field exists, there remain significant opportunities for enhanced research representing different LMICs and regions.

Geochronological, major and trace element, and Sr–Nd–Hf isotopic data are reported for the monzonitic rocks of the Fushan pluton in the Taihang Mountains, central North China Craton, in order to investigate their sources, petrogenesis and tectonic implications. Zircon U–Pb dating results reveal that the Fushan pluton was emplaced during the Early Cretaceous (∼126–124 Ma). The monzonites and quartz monzonites are mainly characterized by calc-alkaline and magnesian features and display light rare earth element (LREE) enrichment and flat heavy REE (HREE) patterns with slightly positive Eu anomalies. They have similar whole-rock initial 87Sr/86Sr ratios (0.70653–0.70819), εNd(t) values (−13.6 to −18.6) and zircon εHf(t) values (−21.8 to −17.3). The primary magma of the Fushan pluton was derived from the partial melting of a spinel-facies amphibole-bearing ancient enriched lithospheric mantle. The monzonitic rocks also have high Ba–Sr and low Y and Yb contents, with high Sr/Y and La/Yb ratios. These geochemical features of monzonitic rocks are not only inherited from the magma source but also significantly enhanced by crystal fractionation during magmatic evolution; e.g. hornblende fractionation increased the Ba–Sr concentrations and Sr/Y ratios. During the Early Cretaceous, the slab sinking and roll-back of the Palaeo-Pacific Plate could have created an ancient big mantle wedge beneath East Asia and induced a lithospheric extensional process in the central North China Craton within an intracontinental setting.