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• In the abstract, the correct definition of A ex (G) is added. • The definitions for the matrix A and for the matrix SDD are added. • The adjacency matrix A (G) was defined. • On page 2, after "For recent research along these lines, we added: see [5,20,33] and "Recall that the extended adjacency matrix is just one among a large number of degree-based graph matrices; for details see [A]." • On page 10, together with Refs. [17, 21, 19] we quoted also [B]:r • On page 10, together with Ref. [27] we quoted also Ref [A]. • Two following refs are added: [A] K. C. Das, I. Gutman, I. Milovanovi'c, E. Milovanovi'c, B. Furtula, Degree-based energies of graphs, Linear Algebra Appl. 554 (2018) 185–204. [B] I. Gutman, H. Ramane, Research on graph energies in 2019, MATCH Commun. Math. Comput. Chem. 84 (2020) 277–292. The extended adjacency matrix of graph G , A e x is a symmetric real matrix that if i ≠ j and u i u j ∈ E (G) , then the i j th entry is d u i 2 + d u j 2 / 2 d u i d u j , and zero otherwise, where d u indicates the degree of vertex u. In the present paper, several investigations of the extended adjacency matrix are undertaken and then some spectral properties of A e x are given. Moreover, we present some lower and upper bounds on extended adjacency spectral radii of graphs. Besides, we also study the behavior of the extended adjacency energy of a graph G. [ABSTRACT FROM AUTHOR]

Let G = { G 1 , ... , G 2 n } be a bipartite graph collection on the common vertex bipartition (X , Y) with | X | = | Y | = n. We say that G is bipancyclic if there exists a partial G -transversal isomorphic to an ℓ -cycle for each even integer ℓ ∈ [ 4 , 2 n ] , while G is vertex-bipancyclic if any vertex v ∈ X ∪ Y is contained in a partial G -transversal isomorphic to an ℓ -cycle for each even integer ℓ ∈ [ 4 , 2 n ]. Bradshaw in [Transversals and bipancyclicity in bipartite graph families, Electron. J. Comb., 2021] showed that for each i ∈ [ 2 n ] , if d G i (x) > n 2 for each x ∈ X and d G i (y) ≥ n 2 for each y ∈ Y , then G is bipancyclic, which generalizes a classical result of Schmeichel and Mitchem in [Bipartite graphs with cycles of all even lengths, J. Graph Theory, 1982] on the bipancyclicity of bipartite graphs to the setting of graph transversals. Motivated by their work, we study vertex-bipancyclicity in bipartite graph collections and prove that if δ (G i) ≥ n + 1 2 for any i ∈ [ 2 n ] , then G is vertex-bipancyclic unless n = 3 and G consists of 6 identical copies of a 6-cycle. Moreover, we also show the Hamiltonian connectivity of G. [ABSTRACT FROM AUTHOR]

The construction of active materials with controllable optical response facilitates the development of advanced photonic devices. However, the achievement of robust active materials with wide wavelength tunable and broadband emission remains a great challenge, mainly due to the fixed energy levels of conventional active dopants and limited inhomogeneous broadening in common hosts. Here, the study proposes that the cluster in the mesoscopic scale of ≈1 nm may break this bottleneck issue and demonstrate a strategy for the management of photon emission by engineering the cluster evolution. The amorphous glass as the host to tailor the characteristic configuration of Te clusters from 1 to 2 nm by control of the topological structures in glass is employed. Impressively, it presents a distinct optical response totally different from the conventional active centers and this enables to construct of active photonic glass with continuously tunable emission from 888 to 1064 nm. More importantly, Te cluster‐activated photonic glass fibers are fabricated and the broadband on‐off gain is successfully achieved. Furthermore, benefiting from the unique tunable emission, novel near‐infrared devices are constructed and their application in imaging is demonstrated. The approach of cluster engineering mediated tunable optical response is believed to bring new opportunities for developing advanced photonic devices. [ABSTRACT FROM AUTHOR]

Bismuth (Bi)‐doped glass and fiber materials exhibit excellent optical performance and have potential in fields such as fiber communication and tunable lasers. However, the preparation of Bi‐doped glass and fiber with high optical activity is still confronted with huge challenges. This study proposes a germanium oxide hybridization strategy to enhance near‐infrared emission in Bi‐doped glass. In addition, by the systematical optimization of the optical response and processability of the glass system, Bi‐doped glass fibers are successfully constructed. The constructed glass fibers have excellent optical performance, and the enhanced amplified spontaneous emission is realized. They show potentials for applications in broadband fiber amplifiers and tunable lasers. [ABSTRACT FROM AUTHOR]

Given the ever‐increasing demand for transmission capacity in optical fiber communication systems, there is a growing focus on developing active fibers and devices with an optical response across a wider spectrum. Bismuth (Bi)‐doped photonic glasses have attracted significant interest for their exceptional ultra‐broadband optical response, particularly within telecommunication bands. However, developing advanced Bi‐activated materials with robust optical response, high compatibility with commercial transmission systems, and low processing temperature remains a huge challenge. Herein, an anion hybridization strategy is proposed to overcome the aforementioned limitations. The anion hybridization significantly enhances the broadband optical response (≈10 times) of the Bi center following the introduction of fluorine ions, and reduces the transition temperature of the photonic glass (≈200 °C). Moreover, the near‐infrared optical response bandwidth experiences significant broadening, a result attributed to the larger inhomogeneous broadening. Furthermore, successful fabrication of the anion‐hybridized Bi‐activated glass fiber is achieved, demonstrating excellent compatibility with commercial transmission fibers. Additionally, the fabricated fiber exhibits an amplified spontaneous emission and on‐off gain across a broad waveband, further validating its efficacy. These results indicate that anion hybridization offers an effective strategy to optimize the optical and thermal properties of photonic materials to develop novel advanced photonic devices. [ABSTRACT FROM AUTHOR]

Background: Peroral endoscopic myotomy (POEM) has emerged as a widely accepted treatment for achalasia, with limited studies for over 2 years. Additionally, traditional measurements of achalasia after POEM have deficiencies. The study aimed to analyze the long-term outcomes of POEM under different criteria. Methods: Patients with achalasia who received POEM between November 2012 and March 2021 were recruited. Patients and characteristics were shown, and risk factors related to two novel definitions of recurrence, symptomatic reflux, and reflux esophagitis were analyzed. Results: Three hundred and twenty-one patients were included. At a median follow-up of 52 months, twenty-three failures happened (7.17%) under the modified criterion, and forty-seven failures occurred (14.64%) under the normal standard. Hospitalization (P = 0.027) and esophageal myotomy length (P = 0.039) were significantly associated with long-term efficacy under the modified and normal criteria, respectively. Fifty-two patients (16.20%) reported reflux symptoms and endoscopy performed in 88 patients revealed reflux esophagitis in 22 cases (25.00%). There were no predictors in the analysis of symptomatic reflux and gender (P = 0.010), LESP (P = 0.013), IRP (P = 0.015), and the esophageal myotomy length (P = 0.032) were statistically related to reflux esophagitis. Conclusion: POEM is an extremely safe and effective treatment for achalasia with long-term follow-up. Shorter hospitalization and shorter esophageal myotomy length may decrease the incidence of recurrence under the modified and normal criteria, respectively. Long-term outcomes of POEM are unpredictable. No risk factors were related to symptomatic reflux, and male patients with low preoperative LESP and IRP needed relatively shorter esophageal myotomy to prevent reflux esophagitis. [ABSTRACT FROM AUTHOR]

• The hydrodynamics characteristics of spinner flasks cannot be reproduced at scale. • Stirred tank reactors are unsuitable for microcarrier based cultured meat at scale. • Sparging causes more hydrodynamic stress than agitation in stirred tank reactors. • Stirring at >120 rpm in a 250 mL spinner flask is needed to mimic scaling-up effects. Cultured meat has emerged as a potential alternative source of animal proteins and fat. Commercially viable cultured meat production likely requires proliferation bioreactors much larger than those used in the pharmaceutical industry today. However, most lab-scale process developments are carried out in spinner flasks that cannot be readily scaled-up using conventional, semi-empirical methods. We systematically investigated the hydrodynamics and mass transfer characteristics of a 250 mL spinner flask under 30−120 rpm stirring speeds and 50 or 100 mL filling volumes, as well as 0−30 g/L microcarriers, to facilitate scale-down experiment design hence the transfer of lab-generated knowledge to large scale bioreactors. It was found that meat cells are typically cultured under operating conditions that give a combination of <10 s mixing time and about 1 mW/kg energy dissipation rate, but with high dissolved oxygen concentrations. Computational fluid dynamics moelling was performed for both the spinner flask and a generic cell culture reactor of 20 m³ working volume. Simulations suggested that it might not be possible to reproduce the most favourable conditions in large scale reactors. In particular, even when operated at a stirring speed close to the N js , the shear exerted by the impellers alone could cause cell detachment from microcarriers, while even more hydrodynamic stress is introduced via sparging. [ABSTRACT FROM AUTHOR]

In the present study, a series of biobased anionic-nonionic surfactants were used to evaluate their physicochemical properties for predicting the effectiveness in chemical enhanced oil recovery (EOR) applications. And the amphoterics surfactants are lignin polyether sulfonates with different polymerization degrees. The results indicated that the hydrophobic carbon chain length and oxyethyl groups in surfactant molecular structure effected on the surface tension, salt tolerance, adsorption amount on the quartz sand and interfacial tension of the lignin polyether sulfonates. The salt tolerance experiments demonstrated that the lignin polyether sulfonates exhibited good tolerance to salt addition, even in the salinity solutions containing divalent metal ions. The adsorption amount of lignin polyether sulfonates on the quartz sand was higher by increasing the ratio of liquid to solid or increasing surfactant concentration until the saturated adsorption was achieved. Interfacial tension (IFT) studies indicated the effects of the concentration of NaOH and inorganic salts on the IFT between lignin polyether sulfonates and Daqing crude oil, and ultra-low IFT would be obtained. • The physicochemical properties of lignin polyether sulfonates are investigated. • The molecular structure of surfactant has a great influence on cmc values and γ cmc values. • The lignin polyether sulfonates exhibit high tolerance to Na+ and Ca2+. [ABSTRACT FROM AUTHOR]

Based on the all-atomic molecular dynamics simulation method, the tensile creep behavior of epoxy-based polymer was discussed. The physical and mechanical properties of the model were characterized, such as glass transition temperature and yield strength. The simulation results are very close to the previous simulation and experimental results, and the correctness of the model is verified. On this basis, the tensile creep behavior and free volume evolution of polymer epoxy resin at different temperatures and stress levels were studied. The model fully predicted the three classical stages of epoxy resin creep (the primary, secondary and tertiary) and the dependent behavior of epoxy resin creep on temperature and stress level at the molecular level, and the creep rate increases with the increase of temperature and stress level. It was found that with the progress of the creep process, the proportion of free volume increases gradually under high stress levels, indicating that the effect of creep behavior on the structure of epoxy resin is that the interaction between atoms becomes weaker and weaker by increasing the distance between atoms, which finally induces creep failure in the material. [ABSTRACT FROM AUTHOR]

An edge-coloring of a connected graph is called a monochromatic connection coloring (MC-coloring, for short) if there is a monochromatic path joining each two vertices of the graph. For a connected graph G , the monochromatic connection number of G , denoted by m c (G) , is defined to be the maximum number of colors allowed in an MC-coloring of G. This concept was introduced by Caro and Yuster (2011). They proved that | E (G) | − | V (G) | + 2 ≤ m c (G) ≤ | E (G) | − | V (G) | + χ (G) for any connected graph G. Some graphs achieving the lower bound have been determined. In this paper, we first give a new upper bound for m c (G) , which is characterized by the structures of extremal colorings. Using this new bound, we then characterize all connected graphs G achieving the upper bound m c (G) = | E (G) | − | V (G) | + χ (G). [ABSTRACT FROM AUTHOR]

Abstract: For a simple graph , the energy is defined as the sum of the absolute values of all the eigenvalues of its adjacency matrix . Let , respectively, be the number of vertices and edges of . One well-known inequality is that , where is the spectral radius. If is -regular, we have . Denote . Balakrishnan [R. Balakrishnan, The energy of a graph, Linear Algebra Appl. 387 (2004) 287–295] proved that for each , there exist infinitely many for each of which there exists a -regular graph of order with and , and proposed an open problem that, given a positive integer , and , does there exist a -regular graph of order such that . In this paper, we show that for each , there exist infinitely many such that . Moreover, we construct another class of simpler graphs which also supports the first assertion that . [Copyright &y& Elsevier]

Abstract: The Randić index of a graph is defined by , where is the degree of a vertex in and the summation extends over all edges of . A conjecture about the Randić index says that for any triangle-free graph of order with minimum degree , one has , where the equality holds if and only if . In this short note we give a confirmative proof for the conjecture. [Copyright &y& Elsevier]

We prove that for a simple graph G with | V (G) | ≥ 32 , if min { δ (G) , δ (G c) } ≥ 4 , then either G or its complementary graph G c has flow index strictly less than 3. This is proved by a newly developed closure operation, which may be useful in studying further flow index problems. In particular, our result supports a recent conjecture of Li et al. (2018), and improves a result of Hou et al. (2012) on nowhere-zero 3-flows. [ABSTRACT FROM AUTHOR]

A path in an edge-colored graph G is called monochromatic if any two edges on the path have the same color. For k ≥ 2 , an edge-colored graph G is said to be monochromatic k -edge-connected if every two distinct vertices of G are connected by at least k edge-disjoint monochromatic paths, and G is said to be uniformly monochromatic k -edge-connected if every two distinct vertices are connected by at least k edge-disjoint monochromatic paths such that all edges of these k paths are colored with a same color. We use m c k (G) and u m c k (G) to denote the maximum number of colors that ensures G to be monochromatic k -edge-connected and, respectively, G to be uniformly monochromatic k -edge-connected. In this paper, we first conjecture that for any k -edge-connected graph G , m c k (G) = e (G) − e (H) + ⌊ k 2 ⌋ , where H is a minimum k -edge-connected spanning subgraph of G. We verify the conjecture for k = 2. We also prove the conjecture for G = K k + 1 and G = K k , n with n ≥ k ≥ 3. When G is a minimal k -edge-connected graph, we give an upper bound of m c k (G) , i.e., m c k (G) ≤ k − 1. For the uniformly monochromatic k -edge-connectivity, we prove that for all k , u m c k (G) = e (G) − e (H) + 1 , where H is a minimum k -edge-connected spanning subgraph of G. [ABSTRACT FROM AUTHOR]

• A rational reactor scaling-up approach for cultured meat production is proposed. • CFD modeling provides an a priori estimation of reactor performance. • Reactor internals are necessary to improve flow homogeneity at scale. • A single reactor can potentially produce enough meat for 75,000 people. Cell-based meat, or cultured meat is at the early commercialization stage, but thorough considerations of the scaling-up challenges are scarce and the physiological data of animal muscle cells required by reliable process design are severely lacking. To make cultured meat an economically viable source of animal proteins, we propose a rational approach towards the design of a large scale air-lift reactor for cultured meat manufacturing. Computational fluid dynamics (CFD) modeling is used as a primary tool to provide an a priori estimation of the mass transfer and mixing performance of the reactor and the effects of reactor internals are investigated. The mass transfer coefficient of 36 1/h, energy dissipation rate of 46 W/m3 and a mixing time of 103 s are all within acceptable ranges typical to animal cells. It is estimated that a single reactor of 300 m3 can supply the meat demand of a population of 75,000. [ABSTRACT FROM AUTHOR]

A path P in an edge-colored graph is called a conflict-free path if there exists a color used on only one of the edges of P. An edge-colored graph G is called conflict-free connected if for each pair of distinct vertices of G there is a conflict-free path in G connecting them. The graph G is called strongly conflict-free connected if for every pair of vertices u and v of G there exists a conflict-free path of length d G (u, v) in G connecting them. For a connected graph G , the strong conflict-free connection number of G , denoted by scfc (G), is defined as the smallest number of colors that are required in order to make G strongly conflict-free connected. In this paper, we first show that if G t is a connected graph with m (≥ 2) edges and t edge-disjoint triangles, then scfc (G t) ≤ m − 2 t , and the equality holds if and only if G t ≅ S m − t , t . Then we characterize the graphs G with s c f c (G) = k for k ∈ { 1 , m − 3 , m − 2 , m − 1 , m }. In the end, we present a complete characterization for the cubic graphs G with s c f c (G) = 2. [ABSTRACT FROM AUTHOR]

Abstract: Orchid-like Cr-doped MnO2 nanostructures have been synthesized via a hydrothermal method, using KClO3 as the oxidant. The as-obtained samples were characterized by X-ray diffraction (XRD), X-ray photoelectron spectra (XPS), transmission electron microscopy (TEM) and field emission scanning electron microscopy (FE-SEM). Results show that the morphologies of orchid-like MnO2 are made up of nanorods. The influences of chromium in the solution on the morphology of the products are discussed. The electrochemical characterization was carried out by cyclic voltammetry, which indicated that the products were excellent electrode material for super-capacitor. [Copyright &y& Elsevier]

A novel organic composite coating was successfully fabricated through in situ mineralizing in artificial seawater for a lasting anti-corrosive coating. The mineralized composite films make full use of the advantages including rich hydroxyl group and special ring structure of β-cyclodextrin as well as superior adhesion and high flexibility of waterborne polyurethane coating. The results show the β-CD remarkably promotes the mineralization of CaCO 3 on WPU substances through the effective adsorption and complexation of hydrophobic cavity to calcium ions. The dense organic-inorganic composite film exhibits outstanding anti-corrosive performance with corrosion rate of 1.39 × 10−3 mm/year for 3CD-WPU sample, being much less than 7.36 × 10−2 mm/year for WPU coating under same conditions. The excellent anti-corrosion performance is mainly attributed to the uniform nucleation site provided by CD-WPU and further formation of dense CaCO 3 film. Furthermore, the radial distribution function and adsorb energy theoretic analysis by molecular dynamic simulation definitely reveal and support the mechanism of β-CD promoting the CaCO 3 mineralization. Unlabelled Image • A novel polyurethane-CaCO 3 film is developed via in situ mineralizing in seawater. • The compact self-healing film effectively improves anti-corrosion performance. • β-Cyclodextrin with rich hydroxyl and hydrophobic cavity promotes mineralization. • The mechanism via adsorption is firmly supported by molecular dynamic simulation. [ABSTRACT FROM AUTHOR]

With the rapid development of 5G networks, the Internet of Things, and new‐generation of AI, there are considerable demands on expanding the capacity of contemporary optical fiber communication systems. One of the most effective avenues involves the extension of the bandwidth of Er‐doped fiber amplifiers, but with limited success. Herein, an Er‐activated hybridized glass fiber are reported, which can help realize broadband telecommunication. The effect of element hybridization on the bandwidth of Er‐activated fiber is clarified and the structure‐optical response relationship is established. A two‐step deposition approach is proposed to overcome the immiscibility barrier of different hybridized elements, and Er‐activated fiber with uniform doping is constructed. The activated fiber presents excellent compatibility with commercial telecommunication systems, providing a small signal gain of >13 dB in the whole L‐band range and a maximum gain of 28 dB. Furthermore, the Er‐activated fiber amplifier device is successfully developed. It exhibits outstanding optical amplification performance with gain >24 dB in the range of 1580–1624 nm, gain fluctuation less than ±0.9 dB, and noise figure <6.5 dB. The results not only provide a new strategy for developing novel active broadband optical fibers, but a valuable solution for new‐generation large‐capacity optical fiber communication systems. [ABSTRACT FROM AUTHOR]

In this study, a novel photoinitiated seeded reversible addition–fragmentation chain transfer (RAFT) dispersion polymerization is developed for the preparation of epoxy‐functionalized triblock copolymer nano‐objects at room temperature. Epoxy‐functionalized worms and vesicles prepared by photoinitiated RAFT dispersion polymerization of glycidyl methacrylate are used as seeds for chain extension by photoinitiated seeded RAFT dispersion polymerization of methacrylic and acrylic monomers. Good control is maintained during the polymerization with a high polymerization rate. Pure triblock copolymer worms can be prepared by the photoinitiated seeded RAFT dispersion polymerization with a broad degree of polymerization range of the third block. The room temperature feature of photoinitiated seeded RAFT dispersion polymerization is critical to ensure the survival of epoxy moiety after the polymerization. The obtained triblock copolymer nano‐objects can be cross‐linked by reacting with a diamine. Finally, cross‐linked worms are used as the stationary phase of chromatography for selective separation of organic dyes from water. Epoxy‐functionalized triblock copolymer nano‐objects are prepared by photoinitiated seeded reversible addition–fragmentation chain transfer dispersion polymerization at room temperature. The obtained triblock copolymer nano‐objects can be further cross‐linked by treating with a diamine reagent and used as a stationary phase of chromatography for selective separation of organic dyes from water. [ABSTRACT FROM AUTHOR]

Let S,T be two distinct finite Abelian groups with |S|=|T|. A fundamental theorem of Tutte shows that a graph admits a nowhere‐zero S‐flow if and only if it admits a nowhere‐zero T‐flow. Jaeger et al in 1992 introduced group connectivity as an extension of flow theory, and they asked whether such a relation holds for group connectivity analogy. It was negatively answered by Hušek et al in 2017 for graphs with edge‐connectivity 2 for the groups S=Z4 and T=Z22. In this paper, we extend their results to 3‐edge‐connected graphs (including both cubic and general graphs), which answers open problems proposed by Hušek et al and Lai et al. Combining some previous results, this characterizes all the equivalence of group connectivity under 3‐edge‐connectivity, showing that every 3‐edge‐connected S‐connected graph is T‐connected if and only if {S,T}≠{Z4,Z22}. [ABSTRACT FROM AUTHOR]

Broadband near‐infrared (NIR) photonic materials have wide applications. Although extensive studies on rare‐earth, transition‐metal, and even semiconductor‐activated materials have enabled the development of a rich NIR material pool, developing broadband and efficient photonic candidates covering the NIR I and II regions from 750 to 1500 nm has been met with limited success. Here, it is reported that a subnano Te cluster with a characteristic configuration different from that of the ion state may fill the aforementioned gap. Further, a strategy is proposed for the in situ generation and stabilization of Te clusters by tuning the cluster evolution in glass. A novel active photonic glass embedded with a Te cluster is fabricated; it exhibits intense and broadband short‐wave NIR luminescence with a central wavelength at 1030 nm and a bandwidth exceeding 330 nm. Interestingly, the glass exhibited a full visible‐spectrum conversion ability from 300 to 800 nm. The application of this unique broadband excitation feature for night vision and tissue penetration is demonstrated using a smartphone as the excitation source. These findings demonstrate a fundamental principle of cluster design in glass for creating new properties and provide a new direction for developing novel cluster‐derived functional composite materials. [ABSTRACT FROM AUTHOR]

The article discusses various papers published in this issue including one on graphs of ideals of commutative ring, one on Cayley graphs and one on Laplacian spectra of graphs.

Cultured meat has emerged as a breakthrough technology for the global food industry, which was considered as a potential solution to mitigate serious environmental, sustainability, global public health, and animal welfare concerns in the near future. Although there is promise that cultured meat can supplement or even replace conventional meat, many challenges still need to be resolved in the early stages. In this review, we focused on the characteristics of cultured meat and summarized the current technological challenges and their possible solutions based on tissue and bioreactor engineering, food science, and material science for preparing stem cells, optimizing culture conditions, and developing cost-effective culture media, bioreactor designs, and food processing systems. With rapid progress in tissue and bioreactor engineering, new technologies for culturing meat have been developed and significant progress has been made in recent years. However, as research on cultured meat is intrinsically complex, it is necessary to encourage the integration of multidisciplinary research in this field in the future. We propose some innovative approaches, such as the applications of synthetic biology and bioreactor engineering. These strategies will be helpful to scale-up cultured meat in future applications. • Cultured meat is produced by in vitro cultivation of animal cells, instead of animal farming and slaughtering. • Cultured meat has emerged as a research focus in cellular agriculture owning to its many potential benefits. • The latest developments in cultured meat are summarized and possible strategies to tackle current challenges are discussed. • The application of bioreactor engineering and synthetic biology techniques in cultured meat commercialization is proposed. [ABSTRACT FROM AUTHOR]

Abstract An edge-colored graph G is conflict-free connected if, between each pair of distinct vertices of G , there exists a path in G containing a color used on exactly one of its edges. The conflict-free connection number of a connected graph G , denoted by c f c (G) , is defined as the minimum number of colors that are required in order to make G conflict-free connected. In this paper, we firstly determine all trees T of order n for which c f c (T) = n − t , where t ≥ 1 and n ≥ 2 t + 2. Secondly, we prove that let G be a graph of order n , then 1 ≤ c f c (G) ≤ n − 1 , and characterize the graphs G with c f c (G) = 1 , n − 4 , n − 3 , n − 2 , n − 1 , respectively. Finally, we get the Nordhaus–Gaddum-type result for the conflict-free connection number of graphs, and prove that if G and G ¯ are connected graphs of order n (n ≥ 4), then 4 ≤ c f c (G) + c f c (G ¯) ≤ n and 4 ≤ c f c (G) ⋅ c f c (G ¯) ≤ 2 (n − 2) , moreover, c f c (G) + c f c (G ¯) = n or c f c (G) ⋅ c f c (G ¯) = 2 (n − 2) if and only if one of G and G ¯ is a tree with maximum degree n − 2 or a path of order 5, and the lower bounds are sharp. [ABSTRACT FROM AUTHOR]

Dense wavelength division multiplexing (DWDM) is recognized as one of the leading technologies for resolving the internet data traffic capacity issue. Although the successful development of rare-earth doped fiber amplifiers enables to achieve optical signal amplification in various telecommunication wavebands, their bandwidth is limited by the inherent sharp 4f electronic transition. Here, we propose the clustering engineering strategy in tellurium (Te)-doped glass fiber for broadband optical amplification. The correlation among the glass system, chemical state of Te and the optical response are systematically studied. The active Te-doped phosphate glass with intense and broadband luminescence is successfully achieved by control of the cluster state of the Te atoms. Subsequently, Te-activated phosphate fiber is successfully drawn and the optical response is transferred smoothly. Importantly, the amplified spontaneous emission and broadband optical amplification are achieved for the first time in Te-doped glass fiber. A small signal on-off gain covering an ultra-wide range of O + E + S + C + L bands is observed under excitation at 808 nm. Our results establish a critical step toward advancing Te-based photonic materials for novel broadband fiber amplifiers serviced in telecommunication system. [ABSTRACT FROM AUTHOR]

Bismuth(Bi)‐doped photonic materials with broadband near‐infrared luminescence can be used in applications such as high‐capacity fiber communication, fiber laser, and biological imaging. The scalable fabrication of Bi‐doped fibers with high dopant solubility, high optical activity, and broadband optical response still remains a significant challenge. In this study, the comprehensive studies on the physical, chemical, mechanical, and optical responses of a Bi‐doped glass system are performed and a Bi‐doped germanate multicomponent glass system is proposed to be the promising candidate. The deactivation mechanism of Bi in a glass matrix is investigated and prevented by controlling the fiber drawing. In addition, a Bi‐doped multicomponent germanate glass fiber with a high level of Bi doping is successfully constructed. Finally, a principle compact fiber amplifier device is fabricated for broadband optical amplification. This device can be potentially used for increasing the capacity of telecommunication systems. [ABSTRACT FROM AUTHOR]

As ionizing radiation can cause harmful effects to human and electronic devices, accurate dose monitoring plays an important role in fields such as radiotherapy, nuclear industry, and aerospace. Currently, it is still a challenge to fabricate a miniaturized dosimeter that can achieve real‐time monitoring. Here, a gallosilicate glass with potential application in visualization detection of ultraviolet and ionizing radiation, as well as cumulative dose measurement, is presented. Color centers are induced in the glass upon exposure to ultraviolet or ionizing radiation, resulting in a darkening effect. The color change of glass is related to the energy and intensity of incident photons and can be erased by subsequent heat treatment. Electron paramagnetic resonance measurement indicates that the formation of color centers is associated with non‐bridging oxygen hole centers related to gallium. The glass can be fabricated into fiber with perfect core‐cladding structure, which provides an alternative for preparing a new type of high‐sensitivity radiation dosimeter. [ABSTRACT FROM AUTHOR]

Fault recognition is an important section in seismic interpretation and there are many methods for this technology, but no one can recognize fault exactly enough. For this problem, we proposed a new fault recognition method based on ant colony optimization which can locate fault precisely and extract fault from the seismic section. Firstly, seismic horizons are extracted by the connected component labeling algorithm; secondly, the fault location are decided according to the horizontal endpoints of each horizon; thirdly, the whole seismic section is divided into several rectangular blocks and the top and bottom endpoints of each rectangular block are considered as the nest and food respectively for the ant colony optimization algorithm. Besides that, the positive section is taken as an actual three dimensional terrain by using the seismic amplitude as a height. After that, the optimal route from nest to food calculated by the ant colony in each block is judged as a fault. Finally, extensive comparative tests were performed on the real seismic data. Availability and advancement of the proposed method were validated by the experimental results. [ABSTRACT FROM AUTHOR]

Abstract: Enzyme catalysis is a mild, efficient, and selective technique that has many applications in organic synthesis as well as polymer synthesis. Here, a novel enzyme‐catalysis‐induced reversible addition‐fragmentation chain transfer (RAFT)‐mediated dispersion polymerization for preparing AB diblock copolymer nano‐objects with complex morphologies at room temperature is described. Taking advantage of the room‐temperature feature, it is shown that pure, worm‐like polymer nano‐objects can be readily prepared by just monitoring the viscosity. Moreover, it is demonstrated that inorganic nanoparticles and proteins can be loaded in situ into vesicles by this method. Finally, a novel oxygen‐tolerant RAFT‐mediated dispersion polymerization initiated by enzyme cascade reaction that can be carried out in open vessels is developed. The enzyme‐initiated RAFT dispersion polymerization provides a facile platform for the synthesis of various functional polymer nano‐objects under mild conditions. [ABSTRACT FROM AUTHOR]

The ventilation system in the indoor environments plays a significant role in controlling the cross-infection of viruses and the risk of infection. This work investigated the effects of prevailing high-speed train ventilation modes on the spatial distribution features of droplets through computational fluid dynamics (CFD) simulation. The results revealed that under the current ventilation modes, the airflow barrier was formed in the middle of the aisle, and more than 77.36% of the released droplets were limited to accumulate in the releasing side. Moreover, we found that the strong recirculation flows appeared in the circumstance of top air supply mode suppressed the longitudinal transport of droplets. Also, compared to the standard ventilation case of mixed air supply mode, the suspending droplet fraction in the breathing zone decreased by 37.9% for 10 μm after 60 s under top air supply mode, while those decreased by 33.7% for 50 μm. Therefore, the potential infection risk in the high-speed train was less when the air-condition unit implemented top air supply mode. The research outcomes can be useful to optimize air-conditioning flow and reduce the contagion risk in high-speed trains and other public transport environments with similar air supply strategies. • The flow field in high-speed trains under prevailing compartment ventilation modes is computed and analyzed. • Influence of the ventilation modes on the spreading pattern of droplets with different initial sizes is investigated. • The top air supply mode is proved to be effective for the reduction of the transmission risk of respiratory diseases. • Sitting posture tends to attain less exposure risk than standing posture. [ABSTRACT FROM AUTHOR]

Let G be a graph with vertex set V (G) = { v 1 , ... , v n } and E P (G) be an n × n matrix whose (i , j) -entry is the maximum number of internally edge-disjoint paths between v i and v j , if i ≠ j , and zero otherwise. Also, define E P ¯ (G) = E P (G) + D , where D is a diagonal matrix whose i-th diagonal element is the number of edge-disjoint cycles containing v i , whose E P (G) is a multiple of J−I. Among other results, we determine the spectrum and the energy of the matrix E P ¯ (G) for an arbitrary bicyclic graph G. [ABSTRACT FROM AUTHOR]

Objective: Endoscopic resection (ER) is an effective treatment method for gastric submucosal tumors (G-SMTs), but endoscopic resection failure requires emergency surgery. The purpose of this study was to assess potential risk factors for endoscopic resection failure. Methods: A total of 1041 patients with G-SMT undergoing endoscopic resection were enrolled. Twenty-five patients in whom endoscopic resection failed, requiring a transition to surgery midway through the operation, were included in the failed group, and 1016 patients who received successful endoscopic resection were included in the successful endoscopic resection group. Baseline and lesion characteristics were recorded, and the differences in tumor characteristics and risk factors for resection failure of G-SMT were analyzed. Sensitivity analysis was performed to detect the stability of the indicator. Results: Of the 1041cases included, there were 25 cases (2.4%) of failed endoscopic resection. Binary logistic analysis showed that the independent risk factors included tumors originating from deep muscularis propria(OR = 14.42, 95% CI 4.47–46.52), size > 3 cm (OR = 7.75, 95% CI 2.64–22.70), exophytic growth pattern (OR = 4.98, 95% CI 1.62–15.29), endoscopist with less experience (OR = 5.99, 95% CI 1.07–12.19), and irregular borders (OR = 4.13, 95% CI 1.40–12.19). The stable risk factors were tumors size, tumor origin and growth pattern according to sensitivity analysis. Conclusions: Tumors originating from the deep muscularis propria, tumor size > 3 cm, endoscopists with less experience, an exophytic growth pattern, and irregular boundaries were found to be independent risk factors for endoscopic resection failure. To reduce the risk of endoscopic resection failure, physicians should carefully evaluate G-SMT characteristics preoperative. [ABSTRACT FROM AUTHOR]

A donor–acceptor (D–A) fluorescent molecule, Nph-An composed of anthracene and 1,8-Naphthalimide units, was designed and synthesized. It presented typical intramolecular charge transfer (ICT) emission from 1,8-Nphthalimide units to anthracene units, and this emission was enhanced obviously in aqueous solution, which was attributed to aggregation-induced enhanced emission (AIEE). Further, Nph-An was used as a fluorescent probe to detect 2,4,6-trinitrophenol (TNP) in aqueous solution. The proton transfer from TNP to Nph-An could efficiently block the ICT emission of Nph-An, and cause the fluorescence remarkably to be quenched. The calculated limit detection is 4.7 × 10 −7 M. [ABSTRACT FROM AUTHOR]

[Display omitted] • Light addressable potentiometric sensor modified by colloidal spherical lens array was proposed. • Polystyrene colloidal spherical lens array was monolayer, well-ordered and low-cost. • This LAPS device shows acceptable pH sensing. • This LAPS device widens the modulation frequency of the maximum photoresponse to 40 kHz. • This LAPS device shows high-spatiotemporal pH imaging capability. Visualizing the distribution of pH in a solution is an important basis for monitoring reaction processes and metabolic changes in micro-biochemical species. Light addressable potentiometric sensor (LAPS), as a simple structure, flexible imaging, low-cost and label-free electrochemical sensor, has been widely used to pH imaging. However, its spatiotemporal resolution is greatly affected by the frequency of modulation light, thus limiting its imaging performance. In this study, LAPS device modified by well-ordered and low-cost polystyrene (PS) colloidal monolayer as spherical lens array is proposed to obtain higher available modulation frequency of the maximum photoresponse. The morphology, optical properties and the electric field distribution of PS colloidal spherical lens array were tested and analyzed. pH sensing, imaging of uniform pH solution, the spatiotemporal pH imaging and dynamic imaging of enzymatic reactions of LAPS modified by PS colloidal spherical lens array were tested and evaluated. The experimental results show that LAPS modified by PS colloidal spherical lens array not only has acceptable pH sensing, but also widens the modulation frequency of the maximum photoresponse to 40 kHz. LAPS modified by colloidal spherical lens array modulated at the frequency of 40 kHz shows acceptable sensitivity and linearity, good reproducibility and stability, high SNR and high-spatiotemporal pH imaging capability. This work can be suitable for high-spatiotemporal monitoring of the changes in electrolyte environmental pH caused by the reaction and metabolism of the biochemical species. [ABSTRACT FROM AUTHOR]

The preparation of malonic acid-catalyzed carbon xerogels modified with nitric acid and their high performance for adsorption of Cu2+ were investigated. The treated and untreated carbon xerogels (nitrogen-doped carbon xerogel and carbon xerogel) are mainly microporous with high surface areas (1150.18 and 1201.46 m2 g−1) based on the analysis of N2 adsorption isotherm. Fourier transform infrared spectroscopy study demonstrates that modification process generates a number of functional groups such as carboxyl, carbonyl, and nitrate groups. X-ray photoelectron spectra analysis shows an increase in the content of O and N after oxidation. The adsorption performance for Cu2+ using different process parameters like initial concentration, contact time, and temperature was investigated. The result indicates that the pseudo-second order correlates with the experimental data, and the activation energy of Cu2+ adsorption onto nitrogen-doped carbon xerogel and carbon xerogel is calculated as 15.62 kJ mol−1 and 2.79 kJ mol−1, respectively, indicating the coexistence of chemisorption and ion-exchange. Langmuir and Freundlich isotherms were used to describe the adsorption behavior of Cu2+. The adsorption of Cu2+ by carbon xerogels modified with nitric acid was fast and had noticeable adsorption capacity, with a higher adsorption capacity than the original carbon xerogels (299.41 vs 260.42 mg g−1). Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In high-speed train operations, especially during the passage of two trains or when passing through tunnels, the surface of the train experiences intense transient alternating pressure. The resulting alternating aerodynamic loads can lead to fatigue damage in the train's structure. To address this issue, an experimental device is developed in this study to accurately replicate the alternating aerodynamic loads experienced by trains. In this research, a novel method for simulating variable loads using triangular pressure wave patterns is proposed. Validation tests are conducted to assess the effectiveness of the device in replicating the desired load profiles. Furthermore, a noise suppression mechanism is incorporated into the device design. By incorporating noise source analysis and optimization techniques, the device design effectively controls the noise level within 85 dBA during the loading process. The experimental results demonstrate that the proposed device can achieve a triangular wave loading frequency of 2.5 cycles per minute, with a pressure range of ±3000 Pa for a 250 m3 high-speed train cabin. The pressure load output stability has high consistency in the pressure‒time curves at various measurement points inside the tested object, with a maximum difference of 0.99%. The experimental device designed in this study meets the requirements for simulating the aerodynamic loads on the surface of high-speed trains travelling at speeds of up to 350 km/h. • Novel device accurately simulates aerodynamic alternating loads on high-speed trains. • Integrated mechanism maintains noise levels below 85 dBA during loading. • Achieves stable triangular wave loading, crucial for replicating aerodynamic stresses on train cabin.. [ABSTRACT FROM AUTHOR]

Abstract: The energy of a simple graph , denoted by , is defined as the sum of the absolute values of all eigenvalues of its adjacency matrix. Let denote the cycle of order and the graph obtained from joining two cycles by a path with its two leaves. Let denote the class of all bipartite bicyclic graphs but not the graph , which is obtained from joining two cycles and ( and ) by an edge. In [I. Gutman, D. Vidović, Quest for molecular graphs with maximal energy: a computer experiment, J. Chem. Inf. Sci. 41(2001) 1002–1005], Gutman and Vidović conjectured that the bicyclic graph with maximal energy is , for and . In [X. Li, J. Zhang, On bicyclic graphs with maximal energy, Linear Algebra Appl. 427(2007) 87–98], Li and Zhang showed that the conjecture is true for graphs in the class . However, they could not determine which of the two graphs and has the maximal value of energy. In [B. Furtula, S. Radenković, I. Gutman, Bicyclic molecular graphs with the greatest energy, J. Serb. Chem. Soc. 73(4)(2008) 431–433], numerical computations up to were reported, supporting the conjecture. So, it is still necessary to have a mathematical proof to this conjecture. This paper is to show that the energy of is larger than that of , which proves the conjecture for bipartite bicyclic graphs. For non-bipartite bicyclic graphs, the conjecture is still open. [Copyright &y& Elsevier]

Abstract: For a simple graph , the energy is defined as the sum of the absolute values of all eigenvalues of its adjacency matrix. Let denote the set of unicyclic graphs with vertices and pendent vertices. In [H. Hua, M. Wang, Unicyclic graphs with given number of pendent vertices and minimal energy, Linear Algebra Appl. 426 (2007) 478–489], Hua and Wang discussed the graphs that have minimal energy in , and determined the minimal-energy graphs among almost all different cases of and . In their work, certain case of the values was left as an open problem in which the minimal-energy species have to be chosen in two candidate graphs, but cannot be determined by comparing of the corresponding coefficients of their characteristic polynomials. This paper aims at solving the problem completely, by using the well-known Coulson integral formula. [ABSTRACT FROM AUTHOR]

Abstract: An -edge-coloring of a graph is a surjective assignment of colors to the edges of . A heterochromatic tree is an edge-colored tree in which any two edges have different colors. The heterochromatic tree partition number of an -edge-colored graph , denoted by , is the minimum positive integer p such that whenever the edges of the graph are colored with colors, the vertices of can be covered by at most p vertex-disjoint heterochromatic trees. In this paper we give an explicit formula for the heterochromatic tree partition number of an -edge-colored complete bipartite graph . [Copyright &y& Elsevier]

We introduce a new graph parameter, the rupture degree. The rupture degree for a complete graph Kn is defined as 1 - n , and the rupture degree for an incomplete connected graph G is defined by r (G) =max {ω(G - X)- |X| - m(G - X) : X ⊂ V (G), ω(G - X) > 1}, where ω(G - X) is the number of components of G - X and m(G - X) is the order of a largest component of G - X. It is shown that this parameter can be used to measure the vulnerability of networks. Rupture degrees of several specific classes of graphs are determined. Formulas for the rupture degree of join graphs and some bounds of the rupture degree are given. We also obtain some Nordhaus–Gaddum type results for the rupture degree. [ABSTRACT FROM AUTHOR]

Let G be an undirected and loopless finite graph that is not a path. The smallest integer m such that the iterated line graph Lm(G) is hamiltonian is called the hamiltonian index of G, denoted by h(G). A reduction method to determine the hamiltonian index of a graph G with h(G)⩾2 is given here. We use it to establish a sharp lower bound and a sharp upper bound on h(G), respectively, thereby improving some known results of Catlin et al. [J. Graph Theory 14 (1990) 347] and Hong-Jian Lai [Discrete Math. 69 (1988) 43]. Examples show that h(G) may reach all integers between the lower bound and the upper bound. We also propose some questions on the topic. [Copyright &y& Elsevier]

For an edge-colored graph G, a set F of edges of G is called a proper edge-cut if F is an edge-cut of G and any pair of adjacent edges in F are assigned different colors. An edge-colored graph is proper disconnected if for each pair of distinct vertices of G there exists a proper edge-cut separating them. For a connected graph G, the proper disconnection number of G, denoted by pd(G), is the minimum number of colors that are needed in order to make G proper disconnected. In this paper, we first give the exact values of the proper disconnection numbers for some special families of graphs. Next, we obtain a sharp upper bound of pd(G) for a connected graph G of order n, i.e, p d (G) ≤ min { χ ′ (G) - 1 , n 2 } . Finally, we show that for given integers k and n, the minimum size of a connected graph G of order n with p d (G) = k is n - 1 for k = 1 and n + 2 k - 4 for 2 ≤ k ≤ ⌈ n 2 ⌉ . [ABSTRACT FROM AUTHOR]

Esophageal cancer is one of the most common cancer types in humans worldwide. Photodynamic therapy (PDT) is a promising therapeutic strategy for the treatment of cancer. However, its underlying mechanism needs to be studied thoroughly. The present study focused on the antitumor effect and underlying mechanism of the use of hematoporphyrin derivative (HpD)-PDT against human esophageal squamous cell carcinoma cells via regulation of the PI3K/AKT/mTOR signaling pathway. A Cell Counting Kit-8 assay was used to measure cell viability. Migration was evaluated using a wound healing assay. An annexin V-FITC/PI kit was used to determine cell apoptosis rates. Protein expression levels were analyzed via western blotting. Reverse transcription-quantitative PCR was used to detect gene expression levels. A 2′,7′-dichlorodihydrofluorescein diacetate kit was chosen to evaluate intracellular reactive oxygen species levels via flow cytometry. Cell viability and migration were decreased in KYSE-150 cells after HpD-PDT treatment. Cellular apoptosis was induced after HpD-PDT treatment, and the same trend was observed for autophagy. Furthermore, the PI3K/AKT/mTOR signaling pathway was inhibited. The viability and migration of KYSE-150 cells were significantly inhibited, and apoptosis was induced more effectively following treatment with a combination of HpD-PDT and the PI3K inhibitor, a final concentration of 20 µM LY294002. In conclusion, HpD-PDT could suppress esophageal cancer cell viability, induce apoptosis and inhibit migration by downregulating the PI3K/AKT/mTOR signaling pathway. Combination of HpD-PDT with PI3K inhibitor (LY294002) could enhance the therapeutic efficacy compared with that demonstrated by HpD-PDT alone. Further studies on combination therapy are required to achieve improved clinical outcomes. [ABSTRACT FROM AUTHOR]

Review on the green synthesis of bisphenyl sulphonate Gemini surfactant and its physicochemical properties. [Display omitted] • Synthesis and characterization of bisphenyl sulphonate Gemini surfactant. • The physicochemical properties of synthesized surfactant are investigated. • The synthesized surfactant exhibits superior interfacial activities. In this study, we successfully synthesized a new bisphenyl sulphonate Gemini surfactant (BPSG) from lignin using a simple method. And a comprehensive evaluation of the physicochemical properties of this BPSG surfactant was conducted, including surface activity, emulsification stability, salinity tolerance, static adsorption, and oil/water interfacial activity. Comparing the BPSG surfactant with commonly used single-chain surfactants like dodecylbenzene sulfonate (SDBS) and lignin sulphobetaine zwitterionic surfactant (LSBA), our results demonstrated that the BPSG surfactant exhibited higher surface activity and superior emulsification stability. Even at a NaCl concentration of 5.0 wt%, the oil-water emulsion prepared by BPSG surfactant remained stable. Furthermore, the BPSG surfactant displayed remarkable interfacial activities and resistance to salt. It effectively reduced the interfacial tension (IFT) between Huabei crude oil and brine to an ultra-low level of 10−3 mN/m without any additional additives. And the BPSG surfactant showed enhanced alkali synergy compared to common surfactants and maintained the ultra-low oil/water IFT across a wide range of salinity levels. The static adsorption experiments revealed that BPSG had significantly lower adsorption amount on the quartz sand compared to ordinary surfactants, allowing for the sustained achievement of ultra-low IFT during the adsorption process for up to four consecutive days. [ABSTRACT FROM AUTHOR]

This prospective study was aimed to evaluate the clinical value of narrow-band imaging (NBI), magnification endoscopy with narrow-band imaging (NBIME) and magnification endoscopy with acetic acid enhancement and narrow-band imaging (AA-NBIME) in the diagnosis of small colorectal polyps. We studied 261 small colorectal polyps from 122 patients with the use of above three techniques. Lesions were resected for histopathological analysis. The endoscopic images were independently reviewed by three experts and three non-experts and the diagnostic accuracy and image definition were compared among the modalities. The "experts-agreed" diagnostic accuracy was 87.7% for NBI versus 91.6% for NBIME versus 94.6% for AA-NBIME. The "non-experts-agreed" diagnostic accuracy was 80.1% for NBI versus 84.3% for NBIME versus 89.3% for AA-NBIME. All experts and non-experts diagnosed the small colorectal polyps statistically more accurately with AA-NBIME than NBI (P < 0.05). In all three modalities, the expert group's diagnostic accuracies were statistically significantly higher compared with the non-expert group. For experts, the Kappa values for AA-NBIME, NBIME and NBI diagnosis were 0.962 (0.892–1.032), 0.577 (0.507–0.647) and 0.567 (0.497–0.637), respectively; while for nonexperts, 0.818 (0.748–0.888), 0.532 (0.462–0.602) and 0.530 (0.460–0.600). This demonstrated a good reproducibility of AA-NBIME diagnosis. The average scores (experts and non-experts) of images acquired using AA-NBIME were significantly higher than those acquired using NBIME and ME (P < 0.05). AA-NBIME is a promising tool to clearly visualize the mucosal pit pattern (PP) of colorectal polyps for better differentiating neoplastic polyps from non-neoplastic ones. [ABSTRACT FROM AUTHOR]

Background: Sertoli cells (SCs) create a specialized environment to support and dictate spermatogenesis. MicroRNAs (miRNAs), a kind of ~ 22 nt small noncoding RNAs, have been reported to be highly abundant in mouse SCs and play critical roles in spermatogenesis. However, the miRNAs of porcine SCs remain largely unknown. Methods: We isolated porcine SCs and conducted small RNA sequencing. By comparing miRNAs in germ cells, we systematically analyzed the miRNA expression pattern of porcine SCs. We screened the highly enriched SC miRNAs and predicted their functions by Gene Ontology analysis. The dual luciferase assay was used to elucidate the regulation of tumor necrosis factor receptor (TNFR)-associated factor 3 (TRAF3) by ssc-miR-149. Results: The analysis showed that 18 miRNAs were highly expressed in SCs and 15 miRNAs were highly expressed in germ cells. These miRNAs were predicted to mediate SC and germ cell functions. In addition, ssc-miR-149 played critical roles in SCs by targeting TRAF3. Conclusion: Our findings provide novel insights into the miRNA expression pattern and their regulatory roles of porcine SCs. [ABSTRACT FROM AUTHOR]

A spanning circuit in a graph is defined as a closed trail visiting each vertex of the graph. A compatible spanning circuit in an edge-colored graph refers to a spanning circuit in which each pair of edges traversed consecutively along the spanning circuit has distinct colors. As two extreme cases, sufficient conditions for the existence of compatible Hamilton cycles and compatible Euler tours have been obtained in previous literature. In this paper, we first establish sufficient conditions for the existence of compatible spanning circuits visiting each vertex exactly k times, for every feasible integer k , in edge-colored complete graphs and complete equipartition r -partite graphs. We also provide sufficient conditions for the existence of compatible spanning circuits visiting each vertex v at least ⌊ (d (v) − 1) ∕ 2 ⌋ times in edge-colored graphs satisfying Ore-type degree conditions. [ABSTRACT FROM AUTHOR]

Prediction of a battery's health in data centers plays a significant role in Battery Management Systems (BMS). Data centers use thousands of batteries, and their lifespan ultimately decreases over time. Predicting battery's degradation status is very critical, even before the first failure is encountered during its discharge cycle, which also turns out to be a very difficult task in real life. Therefore, a framework to improve Auto-Regressive Integrated Moving Average (ARIMA) accuracy for forecasting battery's health with clustered predictors is proposed. Clustering approaches, such as Dynamic Time Warping (DTW) or k-shape-based, are beneficial to find patterns in data sets with multiple time series. The aspect of large number of batteries in a data center is used to cluster the voltage patterns, which are further utilized to improve the accuracy of the ARIMA model. Our proposed work shows that the forecasting accuracy of the ARIMA model is significantly improved by applying the results of the clustered predictor for batteries in a real data center. This paper presents the actual historical data of 40 batteries of the large-scale data center for one whole year to validate the effectiveness of the proposed methodology. [ABSTRACT FROM AUTHOR]