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Let $G$ be a graph of size $m$ and $\rho(G)$ be the spectral radius of its adjacency matrix. A graph is said to be $F$-free if it does not contain a subgraph isomorphic to $F$. In this paper, we prove that if $G$ is a $K_{2,r+1}$-free non-star graph with $m\geq (4r+2)^2+1$, then $\rho(G)\leq \rho(S_m^1)$, with equality if and only if $G\cong S_m^1$. Recently, Li, Sun and Wei showed that for any $\theta_{1,2,3}$-free graph of size $m\geq 8$, $\rho(G)\leq \frac{1+\sqrt{4m-3}}{2}$, with equality if and only if $G\cong S_{\frac{m+3}{2},2}$. However, this bound is not attainable when $m$ is even. We proved that if $G$ is $\theta_{1,2,3}$-free and $G\ncong S_{\frac{m+3}{2},2}$ with $m\geq 22$, then $\rho(G)\leq \rho(F_{m,1})$ if $m$ is even, with equality if and only if $G\cong F_{m,1}$, and $\rho(G)\leq \rho(F_{m,2})$ if $m$ is odd, with equality if and only if $G\cong F_{m,2}$., Comment: 15 pages, 3 figures

Let $G =(V_{G}, E_{G})$ be a simple connected graph with its vertex set $V_{G}$ and edge set $E_{G}$. The Mostar index $Mo(G)$ was defined as $Mo(G)=\sum\limits_{e=uv\in E(G)}|n_{u}-n_{v}|$, where $n_{u}$ (resp., $n_{v}$) is the number of vertices whose distance to vertex $u$ (resp., $v$) is smaller than the distance to vertex $v$ (resp., $u$). In this study, we determine the first three minimum Mostar indices of tree-like phenylenes and characterize all the tree-like phenylenes attaining these values. At last, we give some numerical examples and discussion., Comment: 17 pages, 6 figures

This article is devoted to obtain a general method of calculating the expected values and variances for degree-based topological indices in random hexagonal, phenylene and polyphenyl chains. Based on the general method, some important degree-based topological indices are discussed and the explicit analytical expressions of their expected values and variances are presented, in which some known results are included. Besides, the expected values and variances for degree-based topological indices in these random chains are compared. In the end, the extremal values and the average values for degree-based topological indices in these random chains are determined.

In this paper, a general method of calculating the expected values and variances for degree-based topological indices in random spiro chains are obtained. Based on the general method, the explicit analytical expressions for the expected values and variances of some important degree-based topological indices in random spiro chains are presented, in which some known results are included. Besides, the expected values and variances for degree-based topological indices in random spiro chains are compared. In the end, the extremal values and the average values for degree-based topological indices of a spiro chain with n hexagons are determined.

With the increasing running speed, the aerodynamic issues of high-speed trains are being raised and impact the running stability and energy efficiency. The optimization design of the head shape is significantly important in improving the aerodynamic performance of high-speed trains. Existing aerodynamic optimization methods are limited by the parametric modeling methods of train heads which are unable to accurately and completely parameterize both global shapes and local details. Due to this reason, they cannot optimize both global and local shapes of train heads. In order to tackle this problem, we propose a novel multi-objective aerodynamic optimization method of high-speed train heads based on the partial differential equation (PDE) parametric modeling. With this method, the half of a train head is parameterized with 17 PDE surface patches which describe global shapes and local details and keep the surface smooth. We take the aerodynamic drag and lift as optimization objectives; divide the optimization design process into two stages: global optimization and local optimization; and develop global and local optimization methods, respectively. In the first stage, the non-dominated sorting genetic algorithm (NSGA-II) is adopted to obtain the framework of the train head with an optimized global shape. In the second stage, Latin hypercube sampling (LHS) is applied in the local shape optimization of the PDE surface patches determined by the optimized framework to improve local details. The effectiveness of our proposed method is demonstrated by better aerodynamic performance achieved from the optimization solutions in global and local optimization stages in comparison with the original high-speed train head.

Let $ G $ be a graph of order $ n $ and $ \mu $ be an adjacency eigenvalue of $ G $ with multiplicity $ k\geq 1 $. A star complement for $ \mu $ in $ G $ is an induced subgraph of $ G $ of order $ n-k $ with no eigenvalue $ \mu $. In this paper, we characterize the maximal graphs with the bipartite graph $ K_{2, s} $ as a star complement for eigenvalues $ \mu = -2, 1 $ and study the cases of other eigenvalues for further research.

Creating high-quality polygonal meshes which represent the membrane surface of neurons for both visualization and numerical simulation purposes is an important yet nontrivial task, due to their irregular and complicated structures. In this paper, we develop a novel approach of constructing a watertight 3D mesh from the abstract point-and-diameter representation of the given neuronal morphology. The membrane shape of the neuron is reconstructed by progressively deforming an initial sphere with the guidance of the neuronal skeleton, which can be regarded as a digital sculpting process. To efficiently deform the surface, a local mapping is adopted to simulate the animation skinning. As a result, only the vertices within the region of influence (ROI) of the current skeletal position need to be updated. The ROI is determined based on the finite-support convolution kernel, which is convolved along the line skeleton of the neuron to generate a potential field that further smooths the overall surface at both unidirectional and bifurcating regions. Meanwhile, the mesh quality during the entire evolution is always guaranteed by a set of quasi-uniform rules, which split excessively long edges, collapse undersized ones, and adjust vertices within the tangent plane to produce regular triangles. Additionally, the local vertices density on the result mesh is decided by the radius and curvature of neurites to achieve adaptiveness.

Let α be a real number with 0 ≤ α 1 , G be a uniform hypergraph, and A α ( G ) = α D ( G ) + ( 1 − α ) A ( G ) , where D ( G ) and A ( G ) are the diagonal degree tensor and the adjacency tensor of G , respectively. The spectral radius of A α ( G ) is called the α -spectral radius of G . In this paper, some properties for the α -spectral radius of connected k -uniform hypergraphs are investigated, the unique k -uniform supertree with the largest α -spectral radius among all k -uniform supertrees with a given degree sequence is characterized, and the majorization theorem for k -uniform supertrees is obtained. By applying the majorization theorem, we determine the k -uniform supertrees obtaining the three largest α -spectral radius among all k -uniform supertrees with n vertices, give a new proof ordering the eight largest spectral radius among all k -uniform supertrees with n vertices, propose an open problem for further research, and characterize the unique k -uniform supertree with the largest α -spectral radius among all k -uniform supertrees with given different parameters, e.g., the maximum degree △ , or the number of pendent vertices.

In this paper, we define $k$-uniform tensors for $k\geq 2$, which are more closely related to the $k$-uniform hypergraphs than the general tensors, and introduce the parameter $r^{(q)}_{i}(\mathbb{A})$ for a tensor $\mathbb{A}$, which is the generalization of the $i$-th slice sum $r_ {i}(\mathbb{A})$ (also the $i$-th average 2-slice sum $m_{i}(\mathbb{A})$). By using $r^{(q)}_{i}(\mathbb{A})$ for $q\geq1$, we obtain a general result on the sharp upper bound for the spectral radius of a nonnegative $k$-uniform tensor. When $k = 2, q = 1, 2, 3$, this result deduces the main results for nonnegative matrices in [ 1 , 8 , 27 ]; when $k\geq 3, q = 1$, this result deduces the main results in [ 5 , 20 ]. We also find that the upper bounds obtained from different $q$ can not be compared. Furthermore, we can obtain some known or new upper bounds by applying the general result to $k$-uniform hypergraphs and $k$-uniform directed hypergraphs, respectively.

Reservoir operation strategies with low cost and high efficiency have been proposed to control algal blooms. However, the key hydrodynamic principle for performing reservoir operation strategies is still unknown, posing an obstacle to practical applications. To address this challenge, we proposed short-term emergency reservoir operation strategies (EROSs), established a three-dimensional (3D) eutrophication model of the Zipingpu Reservoir, and designed six 14-day reservoir operation cases to explore the mechanism of EROSs in controlling algal blooms. Large outflows with rapid water exchange should be adopted early in EROSs to control algal blooms in the reservoir. Small variations in the surface water temperature or the mixed layer depth/euphotic layer depth (Z

BackgroundThe incidence of thyroid cancer (THCA) continues to increase in recent decades. Accumulating evidence showed that the unbalanced alternative splicing (AS) promotes the occurrence of cancers and leads to poor prognosis of patients. However, the research on alternative splicing events in THCA is lacking, and its underlying mechanism is not fully understood. This study identifies a novel prognostic signature based on AS events to reveal the relationship of AS with tumor immune microenvironment.MethodsBased on the AS data, transcriptional data, and clinical information, the differentially expressed alternative splicings (DEASs) were screened out. Least absolute shrinkage and selection operator (LASSO) regression and multi-Cox regression analyses were employed to identify prognostic results related to AS events and establish a prognostic signature. The predictive ability of the signature was assessed by Kaplan-Meier (K-M) survival curve, risk plots, and receiver operating characteristic (ROC) curves. Furthermore, correlations between tumor-infiltrating immune cells, immune checkpoints, immune score and prognostic signature were analyzed.ResultsAccording to the LASSO regression analysis, a total of five AS events were selected to construct the signature. K-M survival curve showed that the higher the risk score, the worse the OS of the patients. Risk plots further confirmed this result. ROC curves indicated the high predictive efficiency of the prognostic signature. As for tumor immune microenvironment, patients in the high-risk group had a higher proportion of immune cells, including plasma cell, CD8+ T cell, macrophages (M0 and M2), and activated dendritic cell. Immune checkpoint proteins, such as PDCD1LG2, HAVCR2, CD274, etc., were significantly higher in the high-risk group. We also found that the ESTIMATE score, stromal score, and immune score were lower in the high-risk group, while the result of tumor purity was the opposite.ConclusionsCollectively, a prognostic signature consisting of five AS events in THCA was established. Furthermore, there was an inextricable correlation between immune cell infiltration, immune checkpoint proteins, and AS events. This study will provide a basis for THCA immunotherapy in the future.

Numerical modeling of braided channels showed no significant differences in the number of cross-sectional branches between different water periods in the middle reaches of the Yarlung Tsangpo River. During most of the year (wet, normal and dry periods), flow velocities in the higher-branching (HB) channels were significantly lower than in the other two branching categories, while the overall distribution of depth in the higher-branching channels maintained a high degree of consistency with the moderate-branching channels (MB), which partly explains why the HB channels are important habitats for fish spawning, nursery and baiting (lower flow velocity distribution with a wider range of depth). Based on the examination of the water surface width, the water surface width may not be a limiting factor for fish habitat within braided rivers. Simulation of the hydrodynamic parameters of the fish-spawning grounds revealed that the average cross-sectional flow velocity and water depth fluctuated the least at different flows during the fish-spawning period for the HB channels. By counting the hydraulic parameters of the spawning grounds during the spawning period, it can be seen that the most preferred flow velocity for fish in the braided river in the study section was 0.1-0.4 m/s, and the water depth was 0-1.2 m. This article analyses the characteristics of the hydraulic parameters of the braided river and provides theoretical support for the restoration of fish habitats in braided rivers.

We obtain the sharp upper and lower bounds for the spectral radius of a nonnegative weakly irreducible tensor. By using the technique of the representation associate matrix of a tensor and the associate directed graph of the matrix, the equality cases of the bounds are completely characterized by graph theory methods. Applying these bounds to a nonnegative irreducible matrix or a connected graph (digraph), we can improve the results of L. H. You, Y. J. Shu, and P. Z. Yuan [Linear Multilinear Algebra, 2017, 65(1): 113–128], and obtain some new or known results. Applying these bounds to a uniform hypergraph, we obtain some new results and improve some known results of X. Y. Yuan, M. Zhang, and M. Lu [Linear Algebra Appl., 2015, 484: 540–549]. Finally, we give a characterization of a strongly connected k-uniform directed hypergraph, and obtain some new results by applying these bounds to a uniform directed hypergraph.

Let M be a partitioned matrix and B be its equitable quotient matrix. In this paper, we prove the inclusion of their spectra σ ( B ) ⊆ σ ( M ) , and the equality of their spectral radii ρ ( B ) = ρ ( M ) if M is nonnegative. Moreover, σ ( M ) is shown to be completely determined by σ ( B ) if M is from a class of special matrices. Then we apply these results to obtain the spectra of some well-known matrices associated with graphs or digraphs, and then determine the extremal values of different spectral radii associated with connected graphs or strongly connected digraphs with given vertex connectivity.

Combination of coagulation and ozonation was used to treat brine derived from a three-stage reverse osmosis (RO) process during coal gasification wastewater reclamation. Effects of operating parameters on the removals of total organic carbon (TOC), color and UV absorbance at 254 nm (A254) were investigated during coagulation and ozonation. All the removal efficiencies of TOC, A254 and color of FeCl3 coagulant are about twice those of AlCl3 coagulant at the same molar dose since almost all the molecular weight fractions of RO concentrate (ROC) could be removed effectively by FeCl3 coagulant while only the fractions of molecular weight > 3 k Da could be removed effectively by AlCl3 coagulant. The TOC removal increases with the increasing of ozone dose and reaction temperature during ozonation of ROC after coagulation pretreatment. TOC and color of ROC after pretreated by coagulation could be further removed effectively during ozonation since ozonation can significant reduce the fluorescence response of all the fractions of effluent organic matter in ROC. It is unexpectedly found that the increase of A254 is observed after ozonation, this is because the intensity of absorbance at 254 nm by the low molecular weight transformation products (

Since diverse and complex emotions need to be expressed by different facial deformation and appearances, facial animation has become a serious and on-going challenge for computer animation industry. Face reconstruction techniques based on 3D morphable face model and deep learning provide one effective solution to reuse existing databases and create believable animation of new characters from images or videos in seconds, which greatly reduce heavy manual operations and a lot of time. In this paper, we review the databases and state-of-the-art methods of 3D face reconstruction from a single RGB image. First, we classify 3D reconstruction methods into three categories and review each of them. These three categories are: Shape-from-Shading (SFS), 3D Morphable Face Model (3DMM), and Deep Learning (DL) based 3D face reconstruction. Next, we introduce existing 2D and 3D facial databases. After that, we review 10 methods of deep learning-based 3D face reconstruction and evaluate four representative ones among them. Finally, we draw conclusions of this paper and discuss future research directions.

Partial differential equation (PDE) based geometric modelling has a number of advantages such as fewer design variables, avoidance of stitching adjacent patches together to achieve required continuities, and physics-based nature. Although a lot of papers have investigated PDE-based shape creation, shape manipulation, surface blending and volume blending as well as surface reconstruction using implicit PDE surfaces, there is little work of investigating PDE-based shape reconstruction using explicit PDE surfaces, specially satisfying the constraints on four boundaries of a PDE surface patch. In this paper, we propose a new method of using an accurate closed form solution to a fourth-order partial differential equation to reconstruct 3D surfaces from point clouds. It includes selecting a fourth-order partial differential equation, obtaining the closed form solutions of the equation, investigating the errors of using one of the obtained closed form solutions to reconstruct PDE surfaces from differential number of 3D points.

As the number of satellites available for global satellite navigation systems continues to increase, the possibility of simultaneous failures of multiple observations also increases. When the observation contains abnormal errors, the least square method is very sensitive to abnormal values, there will be unreliable errors in positioning. In order to reduce this integrity risk and improve the availability, it is necessary to use the Receiver Autonomous Integrity Monitoring (RAIM) and Fault Detection and Exclusion (FDE) algorithm to detect and exclude faults to ensure accurate positioning under multiple outliers. At present, there are still some problems in the existing algorithms under multiple faults, such as a huge computation burden, failed to completely eliminate the faults, missed detection and a prior assumption on the number of faults. So this paper proposes an adaptive RAIM-FDE method under multiple faults based on the non-Gaussian distribution. Firstly, the assumption of non-Gaussian distribution is adaptive for observations with faults or non-faults. It can iteratively calculate the different posterior probability of each satellite failure based on the observation, while the corresponding weights are adjusted adaptively to achieve a lower robust positioning error. Secondly, this method has a small amount of calculation which do not increase with the number of faults. Finally, we derived the formulation of protection level and verified its effectiveness. Experiments under multiple failure modes show that our method can effectively detect multiple failures, ensure a low integrity risk and a high level of availability, and also a lower positioning error, especially when the faults happened on half of all the observations.

Efficient creation of 3D organic models is an important topic. In this paper, we propose a new approach to create rough 3D organic base models easily and quickly. The proposed approach first generates 2D sketches by manually drawing outlines of 3D organic objects or extracting outlines from 2D images. Then the generated outlines are decomposed into parts. For each of the decomposed parts, a central line is calculated from the two corresponding sketch segments. A straight cylinder is bent so that its central line coincides with the central line of the two corresponding sketch segments. The radius of the cylinder is determined by minimizing the sum of the squared errors between the projected silhouette curves of the placed cylinder and the two corresponding sketch segments. Finally, an ordinary differential equation (ODE)-based and sketch-guided deformation algorithm is proposed to deform the cylinder so that the projected silhouette curves of the deformed cylinder exactly fit the two corresponding sketch segments. The experiment carried out in this paper demonstrates that the approach proposed in this paper can create 3D organic base models from 2D sketches easily and quickly.

Hexagonal chains are a special class of catacondensed benzenoid system and phenylene chains are a class of polycyclic aromatic compounds. Recently, A family of Sombor indices was introduced by Gutman in the chemical graph theory. It had been examined that these indices may be successfully applied on modeling thermodynamic properties of compounds. In this paper, we study the expected values of the Sombor indices in random hexagonal chains, phenylene chains, and consider the Sombor indices of some chemical graphs such as graphene, coronoid systems and carbon nanocones., Comment: 19 pages, 13 figures

Cross-section curves play an important role in many fields. Analytically representing cross-section curves can greatly reduce design variables and related storage costs and facilitate other applications. In this paper, we propose composite generalized elliptic curves to approximate open and closed cross-section curves, present their mathematical expressions, and derive the mathematical equations of surface reconstruction from composite generalized elliptic curves. The examples given in this paper demonstrate the effectiveness and high accuracy of the proposed method. Due to the analytical nature of composite generalized elliptic curves and the surfaces reconstructed from them, the proposed method can reduce design variables and storage requirements and facilitate other applications such as level of detail.

Since the development of the touch screen technology makes sketches simple to draw and obtain, sketch-based 3D shape retrieval has received increasing attention in the community of computer vision and graphics in recent years. The main challenge is the big domain discrepancy between 2D sketches and 3D shapes. Most existing works tried to simultaneously map sketches and 3D shapes into a joint feature embedding space, which has a low efficiency and high computational cost. In this paper, we propose a novel semantic similarity metric learning method based on a teacher-student strategy for sketch-based 3D shape retrieval. We first extract the pre-learned semantic features of 3D shapes from the teacher network and then use them to guide the feature learning of 2D sketches in the student network. The experiment results show that our method has a better retrieval performance.

By extending the work published at ICCS 2020 [ 1 ], in this paper we propose a method to achieve cost-effective 3D printing of stiffened thin-shell objects. Our proposed method consists of three parts. The first part integrates finite element analysis, Voronoi diagram, and conformal mapping to obtain stiffener distribution. The second part combines finite element analysis with optimization calculations to determine the optimal sizes of stiffeners. And the third part introduces Monte-Carlo simulation to find a global optimum. The experiments made in this paper indicate that our proposed method is effective in minimizing 3D printing material consumption of stiffened thin-shell objects.

Background: Benthic algae are at the bottom of the nutrient chain in the river ecosystem and are the basic guarantee to maintain the health of the river ecosystem. Human activities lead to changes in the hydrology and hydrodynamics of many rivers, which affect the growth of benthic diatoms. However, there is a lack of relevant studies on the effects of hydrodynamic conditions and exposure time on the growth of benthic diatoms, so the protection of benthic diatoms and other bait resources is difficult to be realized. Methods: Based on this, a continuous field observation was carried out to study the growth situation of benthic diatom on pebbles under different flow patterns. The three-dimensional hydrodynamic numerical simulation was used to further analyze the flow field surrounding the pebble. And then, the effects of hydrodynamic conditions and exposure time on the biomass of benthic diatoms were studied. Result: The research results show that (1) the species composition and dominant species of benthic diatoms are different at different growth stages; (2) there is an appropriate velocity range for the growth of benthic diatoms, and too low and too high flow rates are not conducive to the growth of benthic diatoms; (3) the growth suitability at different parts on the pebble for benthic diatoms from high to low is the rear part of the pebble (without direct erosion), the side parts of the pebble, the upper part of the pebble and the front part of the pebble (direct erosion); (4) most benthic diatoms die if exposed to air for more than four hours. Conclusion: The effects of hydrodynamic conditions on the biomass of benthic diatoms are obvious on the microscopic scale. The research results in this paper are helpful to further understand the growth status of benthic diatoms in microscopic environment and provide reference and information for the restoration of the hydraulic habitat of benthic diatoms in the reach affected by human activities.

Sketch-based image retrieval is a fundamental computer vision problem. Instead of using hand-designed features to represent sketches and images, recent researches apply deep learning approaches combined with fine-grained matching to retrieve images with fine-grained details. Although these researches allow user to use hand-free sketches drawn for retrieving similar objects, the color matching is ignored which induces a low retrieval precision. To address this problem, we propose a single color sketch-based image retrieval (SCSBIR) approach using HSV color feature considering both shape matching and color matching in this paper. The SCSBIR problem is investigated using deep learning networks, in which deep features are used to represent color sketches and images. A novel ranking method considering both shape matching and color matching is also proposed. In addition, we build a SCSBIR dataset with color sketches and images, and train and test our method by using this dataset. The test results show that our method has a better retrieval performance. The research in this paper can not only promote its application in the commercial field, but also provide reference for the future research in this field.

Facial Animation is a serious and ongoing challenge for the Computer Graphic industry.\ud Because diverse and complex emotions need to be expressed by different facial deformation and\ud animation, copying facial deformations from existing character to another is widely needed in both\ud industry and academia, to reduce time-consuming and repetitive manual work of modeling to create\ud the 3D shape sequences for every new character. But transfer of realistic facial animations between\ud two 3D models is limited and inconvenient for general use. Modern deformation transfer methods\ud require correspondences mapping, in most cases, which are tedious to get. In this paper, we present a\ud fast and automatic approach to transfer the deformations of the facial mesh models by obtaining the\ud 3D point-wise correspondences in the automatic manner. The key idea is that we could estimate the\ud correspondences with different facial meshes using the robust facial landmark detection method by\ud projecting the 3D model to the 2D image. Experiments show that without any manual labelling efforts,\ud our method detects reliable correspondences faster and simpler compared with the state-of-the-art\ud automatic deformation transfer method on the facial models.

3D printing has been widely used in daily life, industry, architecture, aerospace, crafts, art, etc. Minimizing 3D printing material consumption can greatly reduce the costs. Therefore, how to design 3D printed objects with less materials while maintain structural soundness is an important problem. The current treatment is to use thin shells. However, thin shells have low strength. In this paper, we use stiffeners to stiffen 3D thin-shell objects for increasing the strength of the objects and propose a stress guided optimization framework to achieve minimum material consumption. First, we carry out finite element calculations to determine stress distribution in 3D objects and use the stress distribution to guide random generation of some points called seeds. Then we map the 3D objects and seeds to a 2D space and create a Voronoi Diagram from the seeds. The stiffeners are taken to be the edges of the Voronoi Diagram whose intersections with the edges of each of the triangles used to represent the polygon models of the 3D objects are used to define stiffeners. The obtained intersections are mapped back to 3D polygon models and the cross-section size of stiffeners is minimized under the constraint of the required strength. Monte-Carlo simulation is finally introduced to repeat the process from random seed generation to cross-section size optimization of stiffeners. Many experiments are presented to demonstrate the proposed framework and its advantages.

ABSTARCT: Partial differential equation (PDE) based surfaces own a lot of advantages, compared to other types of 3D representation. For instance, fewer variables are required to represent the same 3D shape; the position, tangent, and even curvature continuity between PDE surface patches can be naturally maintained when certain conditions are satisfied, and the physics-based nature is also kept. Although some works applied implicit PDEs to 3D surface reconstruction from images, there is little work on exploiting the explicit solutions of PDE to this topic, which is more efficient and accurate. In this paper, we propose a new method to apply the explicit solutions of a fourth-order partial differential equation to surface reconstruction from multi-view images. The method includes two stages: point clouds data are extracted from multi-view images in the first stage, which is followed by PDE-based surface reconstruction from the obtained point clouds data. Our computational experiments show that the reconstructed PDE surfaces exhibit good quality and can recover the ground truth with high accuracy. A comparison between various solutions with different complexity to the fourth-order PDE is also made to demonstrate the power and flexibility of our proposed explicit PDE for surface reconstruction from images. This research is supported by the PDE-GIR project, which has received funding from the European Union Horizon 2020 research and innovation programme under the Marie SkodowskaCurie grant agreement No 778035. Andres Iglesias also the project TIN2017-89275-R funded by MCIN/AEI/10.13039/501100011033/FEDER “Una manera de hacer Europa”.

Two graphs are said to be L -cospectral (respectively, Q -cospectral) if they have the same (respectively, signless) Laplacian spectra, and a graph G is said to be L − D S (respectively, Q − D S ) if there does not exist other non-isomorphic graph H such that H and G are L -cospectral (respectively, Q -cospectral). Let d 1 ( G ) ≥ d 2 ( G ) ≥ ⋯ ≥ d n ( G ) be the degree sequence of a graph G with n vertices. In this paper, we prove that except for two exceptions (respectively, the graphs with d 1 ( G ) ∈ { 4 , 5 } ), if H is L -cospectral (respectively, Q -cospectral) with a connected graph G and d 2 ( G ) = 2 , then H has the same degree sequence as G . A spider graph is a unicyclic graph obtained by attaching some paths to a common vertex of the cycle. As an application of our result, we show that every spider graph and its complement graph are both L − D S , which extends the corresponding results of Haemers et al. (2008), Liu et al. (2011), Zhang et al. (2009) and Yu et al. (2014).

This article is devoted to establish the distributions for Sombor indices in a general random chain, in which their explicit analytical expressions of the expected values and variances are obtained. As applications, these results for random hexagonal, random phenylene, random polyphenyl and random spiro chains are given. Finally, the distributions for the Sombor indices in these four random chains are asymptotic to normal distributions is shown.

Concern over declining populations of fish with drifting eggs due to the barrier effect caused by dam construction has led to intense interest in their conservation and management. As a major regulatory method, the studies on replenishing ecological flow through dam operation have mainly focused on the spawning period of fish with demersal or sticky eggs, and the potential impacts of this phenomenon on the reproduction of species with drifting eggs are not fully understood. With the establishment of an ecological model and status indicators, we quantified the barrier effect on spawning and hatching of the drifting-egg species, Coreius guichenoti, a dramatically declining endemic species in the Yalong River, China, and proposed that ecological base flow (EBF) closely links spawning and hatching opportunities to fish habitat demands. The results implied that the impacts differed across periods, with negative effects on fish spawning, while the most evident impacts occurred during hatching. The unsatisfactory hydraulic conditions during the hatching period were the drivers that limited local recruitment. Analysis of conservation strategies indicated that compared with regulating mainstream dams alone, the coordinated conservation of mainstream tributary dams caused a high positive change in fish resource supplementation. Reducing the water level of the downstream dam and cooperatively increasing the discharge of the tributary cascade when the upstream dam released EBF during the spawning (231.66 m3/s) and hatching periods (315.00 m3/s) were offered as management recommendations to reduce the barrier effect and preserve fish resources. Collectively, dammed mountain rivers offer a cautionary tale for developing nations with hydropower development intents, suggesting that while spawning habitat protection should remain an important component in fisheries management strategies, it will be crucial to link conservation with management strategies that encompass other early life stages.

Shell structures are extensively used in engineering due to their efficient load-carrying capacity relative to material volume. However, large-span shells require additional supporting structures to strengthen fragile regions. The problem of designing optimal stiffeners is therefore becoming a major challenge for shell applications. To address it, we propose a computational framework to design and optimize rib layout on arbitrary shell to improve the overall structural stiffness and mechanical performance. The essential of our method is to place ribs along the principal stress lines which reflect paths of material continuity and indicates trajectories of internal forces. Given a surface and user-specified external loads, we perform a Finite Element Analysis. Using the resulting principal stress field, we generate a quad-mesh whose edges align with this cross field. Then we extract an initial rib network from the quad-mesh. After simplifying rib network by removing ribs with little contribution, we perform a rib flow optimization which allows ribs to swing on surface to further adjust rib distribution. Finally, we optimize rib cross-section to maximally reduce material usage while achieving certain structural stiffness requirements. We demonstrate that our rib-reinforced shell structures achieve good static performances. And experimental results by 3D printed objects show the effectiveness of our method.

For a connected graph G on n vertices, recall that the distance signless Laplacian matrix of G is defined to be Q ( G ) = T r ( G ) + D ( G ) , where D ( G ) is the distance matrix, T r ( G ) = d i a g ( D 1 , D 2 , … , D n ) and D i is the row sum of D ( G ) corresponding to vertex v i . Denote by ρ D ( G ) , ρ m i n D ( G ) the largest eigenvalue and the least eigenvalue of D ( G ) , respectively. And denote by q D ( G ) , q m i n D ( G ) the largest eigenvalue and the least eigenvalue of Q ( G ) , respectively. The distance spread of a graph G is defined as S D ( G ) = ρ D ( G ) − ρ m i n D ( G ) , and the distance signless Laplacian spread of a graph G is defined as S Q ( G ) = q D ( G ) − q m i n D ( G ) . In this paper, we point out an error in the result of Theorem 2.4 in Yu et al. (2012) and modify it. As well, we obtain some lower bounds on distance signless Laplacian spread of a graph.

We define and study three different types of upper (and lower) triangular blocked tensors, which are all generalizations of the triangular blocked matrices, and are also generalizations of reducible or weakly reducible tensors. We study some common properties, as well as different properties of these three types of triangular blocked tensors. We obtain the formulas for the determinants, characteristic polynomials and spectra of the first and second type triangular blocked tensors, and give an example to show that these formulas no longer hold for the third type triangular blocked tensors. We prove that the product of any two ( n 1 , ⋯ , n r ) -upper (or lower) triangular blocked tensors of the first or second or third type is still an ( n 1 , ⋯ , n r ) -upper (or lower) triangular blocked tensor of the same type. We also prove that, if an ( n 1 , ⋯ , n r ) -upper triangular blocked tensor of the first or second or third type has a left k-inverse, then its unique left k-inverse is still an ( n 1 , ⋯ , n r ) -upper triangular blocked tensor of all the three types. Also if it has a right k-inverse, then all of its right k-inverses are still ( n 1 , ⋯ , n r ) -upper triangular blocked tensors of all the three types. By showing that the left k-inverse (if any) of a weakly irreducible nonsingular M-tensor is a positive tensor, we show that the left k-inverse (if any) of a first or second or third type normal ( n 1 , ⋯ , n r ) -upper triangular blocked nonsingular M-tensor is an ( n 1 , ⋯ , n r ) -upper triangular blocked tensor of all the three types all of whose diagonal blocks are positive tensors. We also show that every order m dimension n tensor is permutation similar to some third type normal upper triangular blocked tensor (all of whose diagonal blocks are irreducible). We give an example to show that this is not true for the first type normal upper triangular blocked tensor.

© 2019 John Wiley & Sons, Ltd. Although different approaches of segmenting and assembling geometric models for 3D printing have been proposed, it is difficult to find any research studies, which investigate model segmentation and assembly in head-mounted display (HMD) virtual reality (VR) environments for 3D printing. In this work, we propose a novel and interactive segmentation method for screwing assembly in the environments to tackle this problem. Our approach divides a large model into semantic parts with a screwing interface for repeated tight assembly. Specifically, after a user places the cutting interface, our algorithm computes the bounding box of the current part automatically for subsequent multicomponent semantic Boolean segmentations. Afterwards, the bolt is positioned with an improved K3M image thinning algorithm and is used for merging paired components with union and subtraction Boolean operations respectively. Moreover, we introduce a swept Boolean-based rotation collision detection and location method to guarantee a collision-free screwing assembly. Experiments show that our approach provides a new interactive multicomponent semantic segmentation tool that supports not only repeated installation and disassembly but also tight and aligned assembly.

Virtual characters are 3D geometric models of characters. They have a lot of applications in multimedia. In this paper, we propose a new physics-based deformation method and efficient character modelling framework for creation of detailed 3D virtual character models. Our proposed physics-based deformation method uses PDE surfaces. Here PDE is the abbreviation of Partial Differential Equation, and PDE surfaces are defined as sculpting force-driven shape representations of interpolation surfaces. Interpolation surfaces are obtained by interpolating key cross-section profile curves and the sculpting force-driven shape representation uses an analytical solution to a vector-valued partial differential equation involving sculpting forces to quickly obtain deformed shapes. Our proposed character modelling framework consists of global modeling and local modeling. The global modeling is also called model building, which is a process of creating a whole character model quickly with sketch-guided and template-based modeling techniques. The local modeling produces local details efficiently to improve the realism of the created character model with four shape manipulation techniques. The sketch-guided global modeling generates a character model from three different levels of sketched profile curves called primary, secondary and key cross-section curves in three orthographic views. The template-based global modeling obtains a new character model by deforming a template model to match the three different levels of profile curves. Four shape manipulation techniques for local modeling are investigated and integrated into the new modelling framework. They include: partial differential equation-based shape manipulation, generalized elliptic curve-driven shape manipulation, sketch assisted shape manipulation, and template-based shape manipulation. These new local modeling techniques have both global and local shape control functions and are efficient in local shape manipulation. The final character models are represented with a collection of surfaces, which are modeled with two types of geometric entities: generalized elliptic curves (GECs) and partial differential equation-based surfaces. Our experiments indicate that the proposed modeling approach can build detailed and realistic character models easily and quickly.

We present Wowtao, an easy-to-use pottery manufacture system to take digital creativity into the real world. Our approach is able to create customized pottery virtually on mobile phones or tablet computers interactively and quickly. Our work takes integration of the customer in product personalization into consideration to support personal design in pottery manufacture field. Different from other virtual pottery design systems, our approach simulates the entire physical pottery design process, such as modeling, painting, seals, firing and customization, and provides the ability to have the designed results fabricated by real artists or a 3D printer. To make the designed results manufacturable by artists, our approach imposes some industrial constraints (both geometry and decorations) when the user designs his/her personalized potteries. Our method only requires simple and intuitive interactions, so even novices can follow the workflow to create pretty potteries easily. We optimize the design process to perform real-time operations. Our informal user study shows that a first-time user typically masters the operations within 10 minutes, and can construct interesting and satisfactory 3D pottery models within minutes.

The malting barley cultivar greatly affects the quality traits of malt, and thus that of final beer product. A fast, sensitive and quantitative method of barley variety discrimination is needed for maltsters. In the present study, six commonly used varieties in Chinese brewing industry, including the Australia malting barley varieties (Gairdner, Baudin, Hindmarsh and Vlamingh) and Chinese ones (Supi6 and Kenpi7) were selected for new method development. A two-dimensional electrophoresis profile of seed hordeins was obtained to explore the representative markers of each variety. By comparing the hordein profiles, 43 common spots and 14 specific spots that presented in only one barley cultivar gel were investigated and identified by matrix-assisted laser desorption/ionization time-of-flight. The blended Gairdner barley samples with a series of purity degrees were obtained by artificial mixing Gairdner seeds with those of Supi6 and Kenpi7 in the laboratory. Standard curves regarding the transcriptional level of hordein marker BMAI-1 to the variety purity of Gairdner were set using quantitative real-time PCR (qRT-PCR). Finally, the developed method based on qRT-PCR was shown to be accurate and time-saving compared with the conventional SDS–PAGE method by a double blind experiment. Copyright © 2016 The Institute of Brewing & Distilling

In this paper, we obtain the sharp upper and lower bounds for the spectral radius of a nonnegative irreducible matrix. We also apply these bounds to various matrices associated with a graph or a digraph, obtain some new results or known results about various spectral radii, including the adjacency spectral radius, the signless Laplacian spectral radius, the distance spectral radius, the distance signless Laplacian spectral radius of a graph or a digraph.

In [1], Abdo and Dimitov defined the total irregularity of a graph G=(V,E) as irrt(G)=1/2 ?u,v?V|dG(u)-dG(v)|, where dG(u) denotes the vertex degree of a vertex u ? V. In this paper, we investigate the minimal total irregularity of the connected graphs, determine the minimal, the second minimal, the third minimal total irregularity of trees, unicyclic graphs, bicyclic graphs on n vertices, and propose an open problem for further research.