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The purpose of this study was to profile the mechanisms of action of probiotic, Bacillus subtilis E20 in activating the immunity of white shrimp, Litopenaeus vannamei. Two groups of shrimp were studied. One group was fed a control diet without probiotic supplementation and the other was fed a probiotic-containing diet at a level of 109 cfu kg diet−1. After the 8-week feeding regimen, the metabolite composition in the hepatopancreas of shrimp were investigated using 1H nuclear magnetic resonance (1H NMR) based metabolomic analysis. Results from the 1H NMR analysis revealed that 16 hepatopancreatic metabolites were matched and identified among groups, of which 2 metabolites, creatinine and glutamine were significantly higher in probiotic group than in the control group. This result was confirmed by the reverse-phase high-performance liquid chromatography (RP-HPLC) and spectrophotometric analysis. Transcriptome analysis indicated the expressions of 10 genes associated with antioxidant enzymes, pattern recognition proteins and antimicrobial molecules, more active expression in the shrimp fed a diet supplemented with probiotic as compared to that of shrimp in control. In addition, the expressions of 4 genes involved with hexosamine biosynthesis pathway (HBP) and UDP-N-acetylglucosamine-peptide N-acetylglucosaminyltransferase for protein O-glycosylation were also higher in hepatopancreas of probiotic-treated shrimp than in shrimp fed a control diet. Western blot and enzyme-linked immunosorbent assay showed that heat shock factor 1, heat shock protein 70, and protein O-glycosylation in hepatopancreas were higher in probiotic group than the control group. These findings suggest that probiotic, B. subtilis E20 promotes the digestibility of glutamine in the diet, and that the increased glutamine in shrimp can be used as fuel for immune cells or may be used to regulate immune molecule expressions and protein O-glycosylation via the HBP to increase protein O-glycosylation, thereby improving the health of shrimp.

BACKGROUND AND OBJECTIVES Planning platelet collection and inventory must rely not only on adequate forecasts of transfusion demand but also sophisticated mathematical modeling techniques. This research aims to develop a better demand forecasting model of apheresis platelets and a mathematical programming model to determine the best target amounts of apheresis platelet collection. MATERIALS AND METHODS Time series data of apheresis platelets collected from donors and platelets supplied to hospitals daily in Taipei Blood Center from January 2014 to December 2015 was used to fit a forecasting model which combines a regression-type model for formulating the deterministic trends and seasonal variation and an autoregressive moving average model (ARMA) for explaining remaining serial correlations. A seasonal autoregressive integrated moving average (SARIMA) model was also used for benchmarking the prediction performance. A linear programming model was then formulated to solve for the optimal daily target collection volumes that maximize the total social benefits. RESULTS The time series model achieved good predictive power with a mean absolute percentage error less than 10%. The appropriateness of the proposed target collection volumes was also verified by using a simulation model, and the proportion of the total platelets requested by hospitals that can be filled by collected apheresis platelets can increase significantly by using the new policy. CONCLUSION The methods proposed in this study can be easily implemented to enhance the management efficiency of blood collecting and supplying of a blood center, and to decrease the costs of the blood outdates and shortages.

This study aimed to evaluate the effects of a synbiotic composite an extract from a by-product of king oyster mushroom, Pleurotus eryngii (KOME), and probiotic Lactobacillus plantarum 7–40 on the growth performance and health status of white shrimp, Litopenaeus vannamei. The KOME was able to stimulate the growth of probiotic, but not the growth of Vibrio-like pathogens, including V. alginolyticus, V. parahaemolyticus, and V. harveyi. Four diets were formulated, including a control diet supplemented without prebiotic and probiotic, a basal diet supplemented with KOME (5 g kg−1) (ME), a basal diet supplemented with probiotic (1×108 CFU kg−1) (LP), and a basal diet supplemented with KOME (5 g kg−1) and probiotic (1×108 CFU kg−1) (SYN). Shrimp fed the ME, LP, and SYN diets had significantly higher survival than that of shrimp fed with the control diet for 8 weeks. Shrimp in the SYN group also had a significantly higher weight gain and total final weight in comparison with the control and other treatments. In the intestinal tract, lactic acid bacteria count was significantly higher in the SYN group, whereas the Vibrio-like bacteria count was significantly higher in the ME group than in the control group. For the health status assessment, the disease resistance of shrimp against V. alginolyticus was improved in all treatments compared to the shrimp in control. Shrimps in the SYN group had significantly lower cumulative mortality due to the significant increase in immune responses, including phenoloxidase, respiratory burst, and lysozyme activity, and the gene expression of pexn and pen4 in the haemocytes, and lgbp, sp, propoii, pexn, pen3a, pen4, and gpx in the haepatopancreas of shrimp as compared to the control. Therefore, it is suggested that a combination of KOME and probiotics can be used as a synbiotic to improve the growth performance and reduce the risk of infectious diseases caused by Vibrio and at the same time significantly contribute to the circular economy.

Fungal delignification can be a feasible process to pretreat biomass for bioethanol production if its performance is improved in terms of efficiency through a few modifications. The aim of this study was to enhance the biodelignification pretreatment of rice straw using laccase in the presence of ionic liquid (1-Allyl-3-methylimidazolium chloride, [AMIM]Cl) or surfactant (TritonX-100). Addition of 750 mg/L [AMIM]Cl and 500 mg/L TritonX-100 increases the lignin removal to 18.49% and 31.79%, which is higher than that of laccase only (11.97%). The enzymatic saccharification process was carried out based on different strategies. The highest cellulose conversion, 40.96%, 38.24%, and 37.91%, was obtained after 72 h of enzymatic saccharification when the substrate was washed with distilled water after pretreatment of rice straw with laccase + TritonX-100, laccase + [AMIM]Cl, and laccase only, respectively. In addition, the morphology and structure changes of pretreated and untreated rice straw were studied. Both surface area and cellulose crystallinity are substantially altered after laccase + [AMIM]Cl and laccase + TritonX-100 pretreatment. Enhanced saccharification efficiency of rice straw was achieved by laccase pretreatment with ionic liquid or surfactant in a single system.

Daphnia similis chitin and its derivative chitosan were prepared as immunostimulants to boost the immune response and determine the ability to control infectious disease caused by Vibrio alginolyticus in white shrimp, Litopenaeus vannamei. Three experimental diets supplemented with 0% chitin or chitosan (control) and 0.4% chitin or 0.4% chitosan were fed to shrimp for 56 days. Dietary inclusion of 0.4% chitosan accelerated shrimp growth compared to chitin and control. The survival and disease resistance of shrimp increased significantly when fed chitin and chitosan diets, after pathogenic injection, as indicated by the up-regulated immune responses in respiratory burst (RB), superoxide dismutase (SOD), and phagocytic activity (PA). There were no significant differences in the total haemocyte count (THC), phenoloxidase (PO)activity, and lysozyme (LYZ) activity among the groups. No significant differences were observed for prophenoloxidase system-related gene expressions among groups. However, shrimp fed chitin, and chitosan expressed significantly higher levels of antimicrobial proteins (penaeidin 3a, crustin, and anti-lipopolysaccharide factor 2) in the haemocytes than in control. The gene expressions of catalase and heat shock protein 70 increased in the hepatopancreas of shrimp fed chitosan diet compared to the chitin and control diet. The O-linked N-acetylglucosamine transferase (ogt) was significantly higher in the haemocytes of shrimp fed chitosan and chitin than the control, but ogt was only significantly higher in the hepatopancreas of shrimp fed chitosan. Dietary chitin and chitosan also showed positive effects on the transcription of peritrophin-like protein. These findings suggest that both chitin and chitosan from D. similis are efficacious at boosting the immunity of shrimp by preventing and controlling infectious diseases caused by Vibrio and have great potential to be used as a feasible immunostimulant that significantly contributes to the circular economy.

Traditional means of achieving highly reliable wireless communications are to rely on a closed-loop communication methodology, which needs to implement complicated feedback communication mechanisms. Such closed-loop communication means inevitably incur feedback communication latency and thus lead to a fundamental tradeoff problem of simultaneously achieving high reliability and low latency. To avoid encountering this tradeoff problem, in this paper we adopt an open-loop communication methodology in a mobile network and propose a multi-cell association scheme to enhance the reliability of open-loop communication. The multi-cell association scheme helps users connect to multiple base stations (BSs), which form a virtual cell of the user. We first characterize the distribution of the number of the users associating with a BS for the multi-cell association scheme and then use it to establish the accurate models of signal-to-interference ratios (SIRs) in the downlink and uplink. The downlink and uplink communication reliabilities, which are defined based on the SIRs in the downlink and uplink, are accurately analyzed and their explicit upper bounds are found. Our analytical and simulated results show that jointly adopting open-loop communication and multi-cell association is able to significantly improve the communication reliability of users, thereby creating an ultra-reliable mobile network.

Sustainable edge computing (SEC) is a promising technology that can reduce energy consumption and computing latency for the mobile Internet of things (IoT). By collecting solar or wind energy from the environment, an SEC cloudlet outside the electric grid can provide powerful computing capabilities for resource-constrained mobile IoT devices. Considering significant density variation of sustainable energy over time, the SEC cloudlet needs to dynamically adjust the clock frequency of the central processing unit (CPU) to balance energy consumption and computing power. In this paper, we consider the limited energy storage of the cloudlet and develop an offline optimal CPU frequency scaling policy to maximize the overall computing power of the cloudlet within a certain period of time. The tightest string policy that gives a graphical viewpoint of the optimal CPU frequency scaling is found.

Our work presents and investigates the effectiveness of a model-based proximity effect correction method for helium ion beam lithography (HIBL). This method iteratively modulates the shape of a pattern by a feedback compensation mechanism until the simulated patterning fidelity satisfies specific constraints. A point spread function (PSF) is utilized to account for all phenomena involved during the scattering events of incident ion beam particles in the resist. Patterning prediction for subsequent correction process is derived from the energy intensity distribution due to convolution between the PSF and the pattern, with an adequate cut-off threshold. The performance of this method for HIBL is examined through several designed layouts from 15- to 5-nm in half pitches, under specific process parameters, including acceleration voltage, resist thickness, and resist sensitivity. Preliminary results show its effectiveness in improving the patterning fidelity of HIBL.

To limit the shadowing effect, improve the process stability, and enhance the optical performance of extreme ultraviolet (EUV) masks, several absorbers have been proposed in previous studies. We investigated the effects of some of these absorbers on electron scattering events through Monte Carlo simulations in which the mask throughput was considered at 5 keV. A two-layer structure consisting of a resist and an absorber substrate, rather than a full-mask structure, was used to eliminate the influence of electron scattering on the resist. The effects of electron interaction volume, ray tracing, and scattering dependency on penetration depth, backscattering coefficient, lateral radius, and absorbed energy distribution were analyzed for absorber materials of conventional argon fluoride and advanced EUV masks. The results of the proposed method for electron scattering analysis and prediction exhibited greater agreement with the simulation results than those of relevant conventional methods.

This study aims to assess and determine the oral-administration of probiotic, Lactobacillus pentosus BD6 on growth performance, immunity and disease resistance of white shrimp, Litopenaeus vannamei. Lac. pentosus BD6 effectively inhibited the growth of aquatic pathogens, which was used in the test. Shrimp were fed with the control diet (without probiotic supplement) for 60 days and the probiotic-containing diets at 107, 108, 109, and 1010 cfu kg−1, respectively. Shrimp fed with the diet containing probiotic at the doses of 109−10 cfu kg−1 showed significant increase in growth performance as well as feed efficiency than that of the control. After a challenge test with Vibrio alginolyticus, shrimp fed with a probiotic diet at a dose of 1010 cfu kg−1 showed a significantly lower mortality as compared to the control and that of shrimp fed the diet containing probiotic at the levels up to 107−8 cfu kg−1. In addition, a therapeutic potential of Lac. pentosus BD6 was discovered because the cumulative mortalities of shrimp fed with probiotic and pathogen V. parahaemolyticus simultaneously were significantly lower when compared to control shrimp. Probiotic in diet at a dose of 109−10 cfu kg−1 significantly increased PO activity of shrimp, while shrimp receiving probiotic at the doses of 108−10 cfu kg−1 showed significant increase in lysozyme activity and phagocytic activity. Shrimp fed with the diet containing probiotic at the level of 1010 cfu kg−1 also indicated higher gene expression of prophenoloxidase (proPO) I, but not proPO II, lipopolysaccharide and β-1,3-glucan-binding protein and penaeidin 4. Analysis of the bacterial microbiota of the shrimp intestine revealed that oral administration of probiotic increased the relative abundance of beneficial bacteria and reduced the abundance of harmful pathogenic bacteria in the gut flora of shrimp. Despite no statistically significant difference, an analysis of microbial diversity recorded higher species richness, Shannon–Weaver diversity index and evenness in the probiotic group, compared to the control group. It was concluded that Lac. pentosus BD6 has great antibacterial ability against a wide range of pathogens and has therapeutic potential to reduce the mortality of shrimp infected with V. parahaemolyticus. Additionally, dietary Lac. pentosus BD6 at the level of 1010 cfu kg−1 was recommended to improve growth performance, immunity and disease resistance of shrimp against V. alginolyticus.

Glycan-binding protein C-type lectin (CTL), one of the pattern recognition receptors (PRRs), binds to carbohydrates on the surface of pathogens and elicits antimicrobial responses in shrimp innate immunity. The objective was to identify and characterize a novel C-type lectin LvCTL 4.2 in Litopenaeus vannamei. The LvCTL 4.2 protein consisted of a signal peptide at the N terminal and a carbohydrate-recognition domain (CRD) with a mutated mannose-binding (Glu-Pro-Ala; EPA) motif at the C terminal, and thereby has a putative secreted mannose-binding C-type lectin architecture. LvCTL 4.2 was highly expressed in nervous tissue and stomach. Infection with white spot syndrome virus (WSSV) induced expression of LvCTL 4.2 in shrimp stomach at 12 h post infection. Conversely, there was no obvious upregulation in expression of LvCTL 4.2 in stomach or hepatopancreas of shrimp with AHPND (acute hepatopancreas necrosis disease). Pathogen binding assays confirmed recombinant LvCTL 4.2 protein (rLvCTL 4.2) had significant binding ability with the WSSV virion, Gram-negative, and Gram-positive bacteria. Moreover, rLvCTL 4.2 had strong growth inhibition of Vibrio parahaemolyticus. Silencing LvCTL 4.2 suppressed WSSV replication, whereas pretreatment of WSSV with rLvCTL 4.2 facilitated viral replication in vivo. In conclusion, LvCTL 4.2 acted as a PRR that inhibited AHPND-causing bacteria, but facilitated WSSV pathogenesis.

This paper aims to propose a three-dimensional (3D) point process that can be employed to generally deploy unmanned aerial vehicles (UAVs) in a large-scale cellular network and tractably analyze the fundamental network-wide performances of the network. This 3D point process is devised based on a 2D marked Poisson point process in which each point and its random mark uniquely correspond to the projection and the altitude of each point in the 3D point process, respectively. We elaborate on some important statistical properties of the proposed 3D point process and use them to tractably analyze the coverage performances of a UAV-enabled cellular network wherein all the UAVs equipped with multiple antennas are served as aerial base stations. The downlink coverage of the UAV-enabled cellular network is found and its closed-form results for some special cases are explicitly derived as well. Furthermore, the fundamental limits achieved by cell-free massive antenna array are characterized when coordinating all the UAVs to jointly perform non-coherent downlink transmission. These findings are validated by numerical simulation., 6 pages, 4 figures, conference paper. arXiv admin note: substantial text overlap with arXiv:2007.09866

Loss in activity remains key challenges for the potential use of laccase in industrial and environmental biotechnology. Enzyme immobilization is an exciting alternative for improving the stability and reusability of enzymatic processes. In this study, the laccase enzyme was successfully immobilized onto SiO2 supports through covalent binding. The stability and durability during the reuse of immobilized laccase were superior to free laccase. After 30 reaction cycles of continuous use, the relative activity was above 80%. In addition, immobilized laccase was able to degrade Bisphenol A (BPA) more effectively than free laccase, especially in the presence of TX-100. The BPA was completely degraded within an incubation time of 5 h. The results suggest that immobilization is feasible for improving the stability and reusability of laccase for many applications.

Vibrio parahaemolyticus is a Gram-negative bacterium causing acute hepatopancreatic necrosis disease (AHPND) in white shrimp, Litopenaeus vannamei. LpxD gene, a principal component of lipid A, which plays a vital role in the biosynthesis of lipopolysaccharides (LPSs) responsible for the pathogenesis of Gram-negative bacteria However, the function of lpxD in V. parahaemolyticus’ virulence has not been studied. In this study, lpxD gene knockout and its role in V. parahaemolyticus’ virulence in white shrimp were determined. The lpxD gene was knocked out by homologous recombination. Virulence and immunogenicity of the lpxD gene was disrupted and the pirA, the major virulence factor of AHPND, and AP1 gene were intact in white shrimp. White shrimp fed with normal diet with VP△lpxD displayed protection (reduced mortality rate from 66 to 27%) after challenge with V. parahaemolyticus. Our results indicated that knockout of the lpxD gene can cause attenuation of V. parahaemolyticus in white shrimp, and VP△lpxD could be used as a live attenuated oral vaccine against V. parahaemolyticus in white shrimp.

The aims of this study were to evaluate the probiotic efficiency of Bacillus subtilis E20 (10⁹ colony‐forming units kg⁻¹) on the growth and apparent digestibility coefficients (ADCs) of dry matter (DM), crude protein (CP), amino acids (AAs), and crude lipids (CLs) of the white shrimp, Litopenaeus vannamei. A control diet without probiotic supplementation was used. Shrimp exhibited significant increases in growth performance and feed utilization after being fed the test diet for 56 days. Shrimp were then used to evaluate the apparent nutrient digestibility using 0.1% Cr₂O₃ in the diet as an indicator. During the trial, faeces was collected from triplicate groups of shrimp twice daily. ADCs of CP and DM in the test diet significantly increased compared to those of the control diet. Although the ADCs of CLs did not significantly differ between the control and probiotic group, the ADC of CLs was higher in the probiotic group than in the control group. In addition, ADCs of most AAs in the test diet were significantly higher compared to those of the control diet. These results suggest that shrimp in the test group had significantly better growth performance, which was due to increases in nutrient digestibility and absorption.

Full-duplex (FD) transmission in a point-to-point (P2P) link, wherein bidirectional traffic flows simultaneously share the same spectrum, has the capability of doubling the link rate by completely removing self-interferences. However, the rate gain of FD transmission in an interference-limited network is not as clear as a P2P link due to the interferences induced by complex FD and half-duplex (HD) transmission behaviors in the network. To thoroughly investigate the achievable link rates of users and base stations (BSs) in a heterogeneous network (HetNet) with decoupled user association, a general approach is proposed to model a HetNet in which all BSs and users can perform HD or FD transmission depending on their traffic patterns. We first characterize the decoupled rate-optimal user association scheme and use it to define the downlink and uplink rates in the HetNet. The tight lower bounds on the link rates of the FD users and BSs are found in a neat form that characterizes general channel fading, user and BS intensities and imperfect self-interference cancellation. These bounds outline the rate regions of the FD users that inspire proposing the opportunistic FD scheduling algorithms maximizing the sum rate of each bidirectional traffic and stabilize each of the queues in the HetNet., 32 pages, 5 figures, journal

In a heterogeneous cellular network (HetNet) consisting of multiple different types (tiers) of base stations (BSs), the void cell event in which a BS does not have any users has been shown to exist due to user-centric BS association, and its probability is dominated by the cell load of each tier. Such a void cell phenomenon has not been well characterized in the modeling and analytical framework of simultaneous wireless information and power transmission (SWIPT) in a HetNet. This paper aims to accurately exploit the fundamental performance limits of the SWIPT between the BS and its user by modeling the cell-load impact on the downlink and uplink transmissions of each BS. We first characterize the power-splitting receiver architecture at a user and analyze the statistical properties and limits of its harvested power and energy, which reveals how much of the average energy can be harvested by users and how likely the self-powered sustainability of users can be achieved. We then derive the downlink and uplink rates that characterize the cell-load and user association effects and use them to define the energy efficiency of a user. The optimality of the energy efficiency is investigated, which maximizes the SWIPT performance of the receiver architecture for different user association and network deployment scenarios.

Innate immunity and resistance against Vibrio alginolyticus in white shrimp, Litopenaeus vannamei, that received α-phellandrene were examined. The results indicated that the percent survival of shrimp receiving 4, 8, and 12 μg g−1 α-phellandrene was significantly higher than that of control shrimp after 72 h (p 4 μg g−1 α-phellandrene. These results indicated that α-phellandrene plays an important role in the innate immunity of white shrimp.

It was recently proved that every planar graph is a subgraph of the strongproduct of a path and a graph with bounded treewidth. This paper surveys generalisationsof this result for graphs on surfaces, minor-closed classes, various nonminor-closed classes, and graph classes with polynomial growth. We then explorehow graph product structure might be applicable to more broadly defined graphclasses. In particular, we characterise when a graph class defined by a cartesian orstrong product has bounded or polynomial expansion. We then explore graph productstructure theorems for various geometrically defined graph classes, and presentseveral open problems.Zden

In this section, we first brief ML techniques useful in wireless communications and networking, and more details can be found in Generally speaking, it is well known that ML techniques can be viewed as the following three categories: supervised learning where a "teacher" is available (i.e. typically through training data set), unsupervised learning, and reinforcement learning (RL). However, to apply ML to wireless communications and networking, another concept to categorize ML techniques is more important, model-based or model-free.

Sparse subspace clustering (SSC) using greedy- based neighbor selection, such as matching pursuit (MP) and orthogonal matching pursuit (OMP), has been known as a popular computationally-efficient alternative to the conventional l 1 -minimization based solutions. Under deterministic bounded noise corruption, in this paper we derive coherence-based sufficient conditions guaranteeing correct neighbor identification using MP/OMP. Our analyses exploit the maximum/minimum inner product between two noisy data points subject to a known upper bound on the noise level. The obtained sufficient condition clearly reveals the impact of noise on greedy-based neighbor recovery. Specifically, it asserts that, as long as noise is sufficiently small and the resultant perturbed residual vectors stay close to the desired subspace, both MP and OMP succeed in returning a correct neighbor subset. Extensive numerical experiments are used to corroborate our theoretical study. A striking finding is that, as long as the ground truth subspaces are well-separated from each other, MP-based iterations, while enjoying lower algorithmic complexity, yields smaller perturbed residuals, thereby better able to identify correct neighbors and, in turn, achieving higher global data clustering accuracy.

Data dimensionality reduction via linear embedding is a typical approach to economizing the computational cost of machine learning systems. In the context of sparse subspace clustering (SSC), this paper proposes a two-step neighbor identification scheme using linear neighborhoodpreserving embedding. In the first step, a quadratically- constrained l 1 -minimization algorithm is solved for acquiring the side subspace neighborhood information, whereby a linear neighborhood-preserving embedding is designed accordingly. In the second step, a LASSO sparse regression algorithm is conducted for neighbor identification using the dimensionality- reduced data. The proposed embedding design explicitly takes into account the subspace neighborhood structure of the given data set. Computer simulations using real human face data show that the proposed embedding not only outperforms other existing dimensionality-reduction schemes but also improves the global data clustering accuracy when compared to the baseline solution without data compression.

Since the mechanisms by which cellular factors modulate replication of the shrimp viral pathogen white spot syndrome virus (WSSV) are still largely unknown, here we consider the sirtuins, a family of NAD+-dependent protein deacetylases that are known to function as regulatory factors that activate or suppress viral transcription and replication in mammals. In particular, we focus on SIRT1 by isolating and characterizing LvSIRT1 from white shrimp (Litopenaeus vannamei) and investigating its involvement in WSSV infection. DsRNA-mediated gene silencing led to the expression of WSSV genes and the replication of genomic DNAs being significantly decreased in LvSIRT1-silenced shrimp. The deacetylase activity of LvSIRT1 was significantly induced at the early stage (2 hpi) and the genome replication stage (12 hpi) of WSSV replication, but decreased at the late stage of WSSV replication (24 hpi). Treatment with the SIRT1 activator resveratrol further suggested that LvSIRT1 activation increased the expression of several WSSV genes (IE1, VP28 and ICP11). Lastly, we used transfection and dual luciferase assays in Sf9 insect cells to show that while the overexpression of LvSIRT1 facilitates the promoter activity of WSSV IE1, this enhancement of WSSV IE1 expression is achieved by a transactivation pathway that is NF-κB-independent.

Hadwiger and Haj\'{o}s conjectured that for every positive integer $t$, $K_{t+1}$-minor free graphs and $K_{t+1}$-topological minor free graphs are properly $t$-colorable, respectively. Clustered coloring version of these two conjectures which only require monochromatic components to have bounded size has been extensively studied. In this paper we consider the clustered coloring version of the immersion-variant of Hadwiger's and Haj\'{o}s' conjecture proposed by Lescure and Meyniel and independently by Abu-Khzam and Langston. We determine the minimum number of required colors for $H$-immersion free graphs, for any fixed graph $H$, up to a small additive absolute constant. Our result is tight for infinitely many graphs $H$. A key machinery developed in this paper is a lemma that reduces a clustering coloring problem on graphs to the one on the torsos of their tree-cut decomposition or tree-decomposition. A byproduct of this machinery is a unified proof of a result of Alon, Ding, Oporowski and Vertigan and a result of the author and Oum about clustered coloring graphs of bounded maximum degree in minor-closed families.

Nash-Williams' Strong Immersion Conjecture states that graphs are well-quasi-ordered by the strong immersion relation. That is, given infinitely many graphs, one graph contains another graph as a strong immersion. In this paper we study the analogous problem for directed graphs. It is known that digraphs are not well-quasi-ordered by the strong immersion relation, but for all known such infinite antichains, paths that change direction arbitrarily many times can be found. This paper proves that the converse statement is true: for every positive integer $k$, the digraphs that do not contain a path that changes direction $k$ times are well-quasi-ordered by the strong immersion relation, even when vertices are labelled by a well-quasi-order. This result is optimal for classes of digraphs closed under taking subgraphs since paths that change direction arbitrarily many times with vertex-labels form an infinite antichain with respect to the strong immersion relation.

This paper aims to propose a three-dimensional (3D) point process model that can be employed to generally deploy unmanned aerial vehicles (UAVs) in a large-scale cellular network and tractably analyze the fundamental network-wide performances of the network. The proposed 3D point process is devised based on a 2D homogeneous marked Poisson point process (PPP) in which each point and its random mark uniquely correspond to the projection and the altitude of each point in the 3D point process, respectively. We study some of the important statistical properties of the proposed 3D point process and shed light on some crucial insights into these properties that facilitate the analyses of a UAV-enabled cellular network wherein all the UAVs equipped with multiple antennas are deployed by the proposed 3D point process to serve as aerial base stations. The salient features of the proposed 3D point process lie in its suitability in practical 3D channel modeling and tractability in analysis. The downlink coverage performances of the UAV-enabled cellular network are analyzed and found in neat expressions and their closed-form results for some special cases are also derived. Most importantly, their fundamental limits achieved by cell-free massive antenna array are characterized when coordinating all the UAVs to jointly perform non-coherent downlink transmission. Finally, numerical results are provided to validate some of the key findings in this paper., Comment: 17 pages, 6 figures, 1 table

In this work, an analytical framework for deriving the exact moments of multiple-input- multiple-output (MIMO) mutual information in the high-signal-to-noise ratio (SNR) regime is proposed. The idea is to make efficient use of the matrix-variate densities of channel matrices instead of the eigenvalue densities as in the literature. The framework is applied to the study of the emerging models of MIMO Rayleigh product channels and Jacobi MIMO channels, which include several well-known channels models as special cases. The corresponding exact moments of any order for the high-SNR mutual information are derived. The explicit moment expressions are utilized to construct simple yet accurate approximations to the outage probability. Despite the high-SNR nature, simulation shows usefulness of the approximations with finite SNR values in the scenario of low outage probability relevant to MIMO communications.

For nonnegative integers $k, d_1, \ldots, d_k$, a graph is $(d_1, \ldots, d_k)$-colorable if its vertex set can be partitioned into $k$ parts so that the $i$th part induces a graph with maximum degree at most $d_i$ for all $i\in\{1, \ldots, k\}$. A class $\mathcal C$ of graphs is balanced $k$-partitionable and unbalanced $k$-partitionable if there exists a nonnegative integer $D$ such that all graphs in $\mathcal C$ are $(D, \ldots, D)$-colorable and $(0, \ldots, 0, D)$-colorable, respectively, where the tuple has length $k$. A set $X$ of cycles is a cycle obstruction set of a class $\mathcal C$ of planar graphs if every planar graph containing none of the cycles in $X$ as a subgraph belongs to $\mathcal C$. This paper characterizes all cycle obstruction sets of planar graphs to be balanced $k$-partitionable and unbalanced $k$-partitionable for all $k$; namely, we identify all inclusionwise minimal cycle obstruction sets for all $k$.