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In this paper, we study dual quaternion, dual complex unit gain graphs, and their spectral properties in a unified frame of dual unit gain graphs. Unit dual quaternions represent rigid movements in the 3D space, and have wide applications in robotics and computer graphics. Dual complex numbers have found application in brain science recently. We establish the interlacing theorem for dual unit gain graphs, and show that the spectral radius of a dual unit gain graph is always not greater than the spectral radius of the underlying graph, and these two radii are equal if, and only if, the dual gain graph is balanced. By using dual cosine functions, we establish the closed form of the eigenvalues of adjacency and Laplacian matrices of dual complex and quaternion unit gain cycles. We then show the coefficient theorem holds for dual unit gain graphs. Similar results hold for the spectral radius of the Laplacian matrix of the dual unit gain graph too.

The gold deposit offshore of Northern Sanshandao is an ultra-large-scale gold deposit discovered in the Jiaodong ore area in recent years. This deposit is a fractured-zone altered-rock-type gold deposit; however, its ore genesis and precise mineralization processes are still highly controversial. Based on petrographical observation, the trace elements, sulfur isotopes, and rubidium–strontium isotopes of the gold-bearing pyrite were analyzed using LA-MC-ICP-MS to obtain the source of the ore-forming fluids and ore genesis. The results show that Au has a good positive correlation with Ag, As, and Cu. It is speculated that the As in the pyrite of the gold deposit offshore of Northern Sanshandao is in the form of As−, replacing S− and entering the pyrite, causing its lattice defects, and thus promoting the entry of Au+ into the gold-bearing pyrite. The Co/Ni ratios mainly range between 0.1 and 10, indicating that the mineralization process has experienced different forms of hydrothermal evolution and the mixing of different fluids. The results of the in-situ sulfur isotope analysis show that pyrite δ34S in the mineralization period is characterized by a high sulfur value. The authors of this study believe that the initial sulfur isotope composition has mantle-derived components. The large-scale, deep cutting, and high degree of fragmentation in the Sanshandao fault zone are conducive to the interaction between fluids and rocks, as well as the mixing and addition of seawater, resulting in the characteristic high δ34S value. The Sr isotopic compositions indicate a crust–mantle mixing attribute of the mineralized material source. The Rb–Sr isochron age of the pyrite is 118.5 ± 0.65 Ma, which represents the age of gold mineralization. According to the characteristics of the trace elements and sulfur isotopes, it is inferred that the gold deposit minerals offshore of Northern Sanshandao originated from deep magmatic-hydrothermal reservoirs, and the mixing of seawater and Au–As-rich hydrothermal fluids was the formation mechanism of huge amounts of gold precipitation.

Let ω(G) denote the number of components of a graph G. A connected graph G is said to be 1-tough if ω(G − X)≤|X| for all X ⊆ V(G) with ω(G − X)>1. It is well-known that every hamiltonian graph is 1-tough, but that the reverse statement is not true in general, and even not for triangle-free graphs. We present two classes of triangle-free graphs for which the reverse statement holds, i.e., for which hamiltonicity and 1-toughness are equivalent. Our two main results give partial answers to two conjectures due to Nikoghosyan.

The concept of energy of a signed digraph is extended to iota energy of a signed digraph‎. ‎The energy of a signed digraph $S$ is defined by $E(S)=\sum_{k=1}^n|{Re}(z_k)|$‎, ‎where ${Re}(z_k)$ is the real part of eigenvalue $z_k$ and $z_k$ is the eigenvalue of the adjacency matrix of $S$ with $n$ vertices‎, ‎$k=1, 2,\ldots,n$‎. ‎Then the iota energy of $S$ is defined by $E(S)=\sum_{k=1}^n|{Im}(z_k)|$‎, ‎where ${Im}(z_k)$ is the imaginary part of eigenvalue $z_k$‎. ‎In this paper‎, ‎we consider a special graph class for bicyclic signed digraphs $\mathcal{S}_n$ with $n$ vertices which have two vertex-disjoint signed directed even cycles‎. ‎We give two iota energy orderings of bicyclic signed digraphs‎, ‎one is including two positive or two negative directed even cycles‎, ‎the other is including one positive and one negative directed even cycles‎.

Abstract Background Clonal plants are important in maintaining wetland ecosystems. The main growth types of clonal plants are the guerrilla and phalanx types. However, little is known about the effects of these different clonal growth types on plant plasticity in response to heterogeneous resource distribution. We compared the growth performance of clonal wetland plants exhibiting the two growth forms (guerrilla growth form: Scirpus yagara, Typha orientalis, Phragmites australis and Sparganium stoloniferum; phalanx growth form: Acorus calamus, Schoenoplectus tabernaemontani and Butomus umbellatus) grown in soil substrates that were either homogeneous or heterogeneous but had the same total amount of nutrients. Results We found that the morphological traits (plant height, ramet number, spacer diameter and length) and biomass accumulation of the guerrilla clonal plants (T. orientalis) were significantly enhanced by heterogeneity, but those of the phalanx clonal plants (A. calamus, S. tabernaemontani and B. umbellatus) were not. The results showed that the benefits of environmental heterogeneity to clonal plants may be correlated with the type of clonal structure. Conclusions Guerrilla clonal plants, which have a dispersed, flexible linear structure, are better suited to habitats with heterogeneous resources. Phalanx clonal plants, which form compact structures, are better suited to habitats with homogeneous resources. Thus, wetland clonal species with the guerrilla clonal structure benefit more from soil nutrient heterogeneity.

Abstract The paper studies covert communication over a continuous-time Gaussian channel. The covertness condition requires that the channel output must statistically resemble pure noise. When the additive Gaussian noise is “white” over the bandwidth of interest, a formal coding theorem is proven, extending earlier results on covert Gaussian communication in discrete time. This coding theorem is applied to study scenarios where the input bandwidth can be infinite and where positive or even infinite per-second rates may be achievable.

Let $G=(V(G),E(G))$ be a digraph without loops and‎ ‎multiarcs‎, ‎where $V(G)=\{v_1,v_2,$ $\ldots,v_n\}$ and $E(G)$ are the‎ ‎vertex set and the arc set of $G$‎, ‎respectively‎. ‎Let $d_i^{+}$ be the‎ ‎outdegree of the vertex $v_i$‎. ‎Let $A(G)$ be the adjacency matrix of‎ ‎$G$ and $D(G)=\textrm{diag}(d_1^{+},d_2^{+},\ldots,d_n^{+})$ be the‎ ‎diagonal matrix with outdegrees of the vertices of $G$‎. ‎Then we call‎ ‎$Q(G)=D(G)+A(G)$ the signless Laplacian matrix of $G$‎. ‎The spectral‎ ‎radius of $Q(G)$ is called the signless Laplacian spectral radius of‎ ‎$G$‎, ‎denoted by $q(G)$‎. ‎In this paper‎, ‎some upper bounds for $q(G)$‎ ‎are obtained‎. ‎Furthermore‎, ‎some upper bounds on‎ ‎$q(G)$ involving outdegrees and the average 2-outdegrees of the‎ ‎vertices of $G$ are also derived‎.

In shallow lake ecosystems, flooding is a key disturbance factor of aquatic vegetation. Aquatic plants, especially submerged plants, play key roles in water ecosystems. Liangzi Lake experienced severe flooding in July 2010, and the elevated water levels lasted for 3 months. In this study, 10 transects with 120 monitoring points were set up for monthly monitoring during the 3-year period, encompassing the period before and after the flooding (2009–2011). The numbers, biomass, and diversity of the submerged plants, as well as the physical and chemical characteristics of the lake water, were surveyed. There were 12 species belonging to 7 families and 7 genera in Liangzi Lake. Eleven of the submerged plant species were found in 2009, but, after the flood, that number decreased to five in 2011. The total biomass differed significantly over the three years (P < 0.05), with the largest biomass in 2009 and smallest in 2011. In 2009 and 2010, Potamogeton maackianus was the dominant species, but its dominant position weakened in 2011. After the flood, water transparency decreased, and the water depth, turbidity, total nitrogen, and total phosphorus increased. A redundancy analysis between the submerged plants and environmental factors found that the water transparency, turbidity, and water depth were the key environmental factors affecting the plants. These results suggest that the long-lasting severe flooding of Liangzi Lake in 2010 led to the degradation of both the submerged plant community and water quality.

High-precision and -resolution atmospheric boundary layer height (BLH) has received increasing attention in air pollution research in recent years. The low time resolution of sounding data is the main challenge to validate BLH retrieval from lidar observations. To resolve this issue, we conducted simultaneous tethered balloon sounding and lidar observations at the Semi-Arid Climate and Environment Observatory of Lanzhou University (SACOL) during winter 2019–2020. The BLHs derived from the tethered balloon sounding data were 170, 210, 393, 676, 423, and 190 m at 02:00, 08:00, 11:00, 14:00, 17:00, and 20:00 (Beijing time), respectively. The diurnal evolution of BLH was reasonably captured by lidar observation-based wavelet covariance transform and ideal profile fitting methods, which exhibited correlation coefficients of 0.91 and 0.89, respectively, with the BLHs determined from tethered balloon sounding data. The lidar results slightly overestimated the BLHs, though all results were acceptable when considering both the absolute and relative errors with respect to BLHs from the tethered balloon data. Our results revealed high-precision and -resolution diurnal variations in BLH at SACOL in Northwest China and suggest the importance of validating lidar-based BLHs using simultaneous sounding data.

Abstract Let M be a mixed graph and H ( M ) $H(M)$ be its Hermitian-adjacency matrix. If we add a Randić weight to every edge and arc in M, then we can get a new weighted Hermitian-adjacency matrix. What are the properties of this new matrix? Motivated by this, we define the Hermitian-Randić matrix R H ( M ) = ( r h ) k l $R_{H}(M)=(r_{h})_{kl}$ of a mixed graph M, where ( r h ) k l = − ( r h ) l k = i d k d l $(r_{h})_{kl}=-(r_{h})_{lk}=\frac{\mathbf{i}}{\sqrt {d_{k}d_{l}}}$ ( i = − 1 $\mathbf{i}=\sqrt{-1}$ ) if ( v k , v l ) $(v_{k},v_{l})$ is an arc of M, ( r h ) k l = ( r h ) l k = 1 d k d l $(r_{h})_{kl}=(r_{h})_{lk}=\frac{1}{\sqrt{d_{k}d_{l}}}$ if v k v l $v_{k}v_{l}$ is an undirected edge of M, and ( r h ) k l = 0 $(r_{h})_{kl}=0$ otherwise. In this paper, firstly, we compute the characteristic polynomial of the Hermitian-Randić matrix of a mixed graph. Furthermore, we give bounds on the Hermitian-Randić energy of a general mixed graph. Finally, we give some results about the Hermitian-Randić energy of mixed trees.

This paper studies the discrete-time Poisson channel and the noiseless binary channel where, after recording a 1, the channel output is stuck at 0 for a certain period; this period is called the “dead time.” The communication capacities of these channels are analyzed, with main focus on the regime where the allowed average input power is close to zero, either because the bandwidth is large, or because the available continuous-time input power is low.

Following publication of the original article [1], the authors flagged that the article had published with an error in one of the equations (Eq. 46), in addition to a few minor formatting errors (concerning spacing and parentheses).

Understanding the biotic and abiotic factors that influence the susceptibility of a community to invasion is beneficial for the prediction and management of invasive species and the conservation of native biodiversity. However, the relationships between factors and invasibility of a community have not been fully confirmed, and the factors most associated with the susceptibility of a community to invasion have rarely been identified. In this study, we investigated the species richness patterns in aquatic exotic and native plants and the relationships of exotic species richness with habitat and water environment factors in 262 aquatic plant communities in China. A total of 11 exotic plant species were recorded in our field survey, and we found neither a negative nor a positive relationship between aquatic exotic and native plant species richness. The aquatic exotic plant species richness is negatively correlated with the relative coverage and biomass of native plants but positively correlated with the total nitrogen (TN), total phosphorus (TP), and chemical oxygen demand (COD) concentrations in the water. The native plant species richness, native species’ relative coverage, and native species’ biomass were positively related to each other, whereas the TP, TN, and COD were also positively related to each other. The native plant species richness, native species’ relative coverage, and native species biomass were each negatively correlated with the TP, TN, and COD. In addition, biotic rather than abiotic predictors accounted for most of the variation in exotic plant richness. Our results suggest that improving the vegetation coverage and the biodiversity of native plants is the most effective approach for preventing alien plant invasions and minimizing their impacts on freshwater ecosystems.

In recent years, investigating the trend of aquatic plant diversity in response to different disturbance events has received increasing interest. However, there is limited knowledge of the different stages of aquatic vegetation succession over a long period in eutrophic lakes. In this study, we analyzed aquatic plant species richness and its relation to the physical and chemical characteristics of water in Chenghai Lake for the period of 1980−2018. This study shows that the richness and distribution of aquatic vegetation in Chenghai Lake are related to chlorophyll-a concentration, dissolved nutrients, base cations, and micronutrients. The results show that the long-term succession of aquatic plants in this lake classified in different stages: (I) A peak in species richness occurred at an intermediate stage that lasted from 1980 to 1992, and this was caused by more aquatic species being able to coexist since the competition for resources was lower; (II) after 26 years of secondary succession (1992−2018), the diversity and distribution area of aquatic plants gradually declined because pioneer species or human activities may have altered habitat conditions to render habitats less beneficial to pioneer species and more suitable for new aquatic plant species. Thus, species diversity and growth performance of aquatic plants in their communities may be useful indicators of Chenghai Lake’s trophic status, especially during the transition period from a mesotrophic lake to a eutrophic one.

Conventional quantum key distribution (QKD) typically uses binary encoding based on photon polarization or time-bin degrees of freedom and achieves a key capacity of at most one bit per photon. Under photon-starved conditions the rate of detection events is much lower than the photon generation rate, because of losses in long distance propagation and the relatively long recovery times of available single-photon detectors. Multi-bit encoding in the photon arrival times can be beneficial in such photon-starved situations. Recent security proofs indicate high-dimensional encoding in the photon arrival times is robust and can be implemented to yield high secure throughput. In this work we demonstrate entanglement-based QKD with high-dimensional encoding whose security against collective Gaussian attacks is provided by a high-visibility Franson interferometer. We achieve unprecedented key capacity and throughput for an entanglement-based QKD system because of four principal factors: Franson interferometry that does not degrade with loss; error correction coding that can tolerate high error rates; optimized time–energy entanglement generation; and highly efficient WSi superconducting nanowire single-photon detectors. The secure key capacity yields as much as 8.7 bits per coincidence. When optimized for throughput we observe a secure key rate of 2.7 Mbit s ^−1 after 20 km fiber transmission with a key capacity of 6.9 bits per photon coincidence. Our results demonstrate a viable approach to high-rate QKD using practical photonic entanglement and single-photon detection technologies.