Asymptotic Expansions for Sub-Critical Lagrangean Forms

Asymptotic expansions for the Taylor coefficients of the Lagrangean form phi(z)=zf(phi(z)) are examined with a focus on the calculations of the asymptotic coefficients. The expansions are simple and useful, and we discuss their use in some enumerating sequences in trees, lattice paths and planar maps

Secrecy Throughput Maximization for Full-Duplex Wireless Powered IoT Networks under Fairness Constraints

In this paper, we study the secrecy throughput of a full-duplex wireless powered communication network (WPCN) for internet of things (IoT). The WPCN consists of a full-duplex multi-antenna base station (BS) and a number of sensor nodes. The BS transmits energy all the time, and each node harvests energy prior to its transmission time slot. The nodes sequentially transmit their confidential information to the BS, and the other nodes are considered as potential eavesdroppers. We first formulate the sum secrecy throughput optimization problem of all the nodes. The optimization variables are the duration of the time slots and the BS beamforming vectors in different time slots. The problem is shown to be non-convex. To tackle the problem, we propose a suboptimal two stage approach, referred to as sum secrecy throughput maximization (SSTM). In the first stage, the BS focuses its beamforming to blind the potential eavesdroppers (other nodes) during information transmission time slots. Then, the optimal beamforming vector in the initial non-information transmission time slot and the optimal time slots are derived. We then consider fairness among the nodes and propose max-min fair (MMF) and proportional fair (PLF) algorithms. The MMF algorithm maximizes the minimum secrecy throughput of the nodes, while the PLF tries to achieve a good trade-off between the sum secrecy throughput and fairness among the nodes. Through numerical simulations, we first demonstrate the superior performance of the SSTM to uniform time slotting and beamforming in different settings. Then, we show the effectiveness of the proposed fair algorithms

Brain MRI-based 3D Convolutional Neural Networks for Classification of Schizophrenia and Controls

Convolutional Neural Network (CNN) has been successfully applied on classification of both natural images and medical images but not yet been applied to differentiating patients with schizophrenia from healthy controls. Given the subtle, mixed, and sparsely distributed brain atrophy patterns of schizophrenia, the capability of automatic feature learning makes CNN a powerful tool for classifying schizophrenia from controls as it removes the subjectivity in selecting relevant spatial features. To examine the feasibility of applying CNN to classification of schizophrenia and controls based on structural Magnetic Resonance Imaging (MRI), we built 3D CNN models with different architectures and compared their performance with a handcrafted feature-based machine learning approach. Support vector machine (SVM) was used as classifier and Voxel-based Morphometry (VBM) was used as feature for handcrafted feature-based machine learning. 3D CNN models with sequential architecture, inception module and residual module were trained from scratch. CNN models achieved higher cross-validation accuracy than handcrafted feature-based machine learning. Moreover, testing on an independent dataset, 3D CNN models greatly outperformed handcrafted feature-based machine learning. This study underscored the potential of CNN for identifying patients with schizophrenia using 3D brain MR images and paved the way for imaging-based individual-level diagnosis and prognosis in psychiatric disorders.Comment: 4 PAGE

Decomposing 3D Neuroimaging into 2+1D Processing for Schizophrenia Recognition

Deep learning has been successfully applied to recognizing both natural images and medical images. However, there remains a gap in recognizing 3D neuroimaging data, especially for psychiatric diseases such as schizophrenia and depression that have no visible alteration in specific slices. In this study, we propose to process the 3D data by a 2+1D framework so that we can exploit the powerful deep 2D Convolutional Neural Network (CNN) networks pre-trained on the huge ImageNet dataset for 3D neuroimaging recognition. Specifically, 3D volumes of Magnetic Resonance Imaging (MRI) metrics (grey matter, white matter, and cerebrospinal fluid) are decomposed to 2D slices according to neighboring voxel positions and inputted to 2D CNN models pre-trained on the ImageNet to extract feature maps from three views (axial, coronal, and sagittal). Global pooling is applied to remove redundant information as the activation patterns are sparsely distributed over feature maps. Channel-wise and slice-wise convolutions are proposed to aggregate the contextual information in the third view dimension unprocessed by the 2D CNN model. Multi-metric and multi-view information are fused for final prediction. Our approach outperforms handcrafted feature-based machine learning, deep feature approach with a support vector machine (SVM) classifier and 3D CNN models trained from scratch with better cross-validation results on publicly available Northwestern University Schizophrenia Dataset and the results are replicated on another independent dataset

Polyphenylene as an Active Support for Ru-Catalyzed Hydrogenolysis of 5-Hydroxymethylfurfural

Selective transformation of biomass feedstocks to platform molecules is a key pursuit for sustainable chemical production. Compared to petrochemical processes, biomass transformation requires the defunctionalization of highly polar molecules at relatively low temperatures. As a result, catalysts based on functional organic polymers may play a prominent role. Targeting the hydrogenolysis of the platform chemical 5-hydroxymethylfurfural (5-HMF), here, we design a polyphenylene (PPhen) framework with purely sp2-hybridized carbons that can isolate 5-HMF via π–π stacking, preventing hemiacetal and humin formation. With good swellability, the PPhen framework here has successfully supported and dispersed seven types of metal particles via a newly developed swelling-impregnation method, including Ru, Pt, Au, Fe, Co, Ni, and Cu. Ru/PPhen is studied for 5-HMF hydrogenolysis, achieving a 92% yield of 2,5-dimethylfuran (DMF) under mild conditions, outperforming the state-of-the-art catalysts reported in the literature. In addition, PPhen helps perform a solventless reaction, achieving direct 5-HMF to DMF conversion in the absence of any liquid solvent or reagent. This approach in designing support–reactant/solvent/metal interactions will play an important role in surface catalysis

Methyl 2-(tert-but­oxy­carbonyl­amino)-1,3-thia­zole-5-carboxyl­ate

The title compound, C10H14N2O4S, was synthesized by the reaction of methyl 2-amino­thia­zole-5-carboxyl­ate and di-tert-butyl carbonate. In this structure, the thia­zole ring is planar (mean deviation = 0.0011 Å). Two weak intra­molecular C—H⋯O hydrogen bonds are formed between two of the methyl groups and one carbonyl O atom, resulting in the formation of two twisted six-membered rings. Inter­molecular N—H⋯N hydrogen bonds link the mol­ecules to form centrosymmetric dimeric units, and the hydrogen-bond scheme is completed by inter­molecular C—H⋯O contacts

Expression and clinical significance of <i>Pax6</i> gene in retinoblastoma

AIM: To discuss the expression and clinical significance of <i>Pax6 </i>gene in retinoblastoma(Rb). <p>METHODS: Totally 15 cases of fresh Rb organizations were selected as observation group and 15 normal retinal organizations as control group. Western-Blot and reverse transcriptase polymerase chain reaction(RT-PCR)methods were used to detect <i>Pax6</i> protein and <i>Pax6 </i>mRNA expressions of the normal retina organizations and Rb organizations. At the same time, Western Blot method was used to detect the <i>Pax6</i> gene downstream MATH5 and BRN3b differentiation gene protein level expression. After the comparison between two groups, the expression and clinical significance of <i>Pax6</i> gene in Rb were discussed. <p>RESULTS: In the observation group, average value of mRNA expression of <i>Pax6</i> gene was 0.99±0.03; average value of <i>Pax6</i> gene protein expression was 2.07±0.15; average value of BRN3b protein expression was 0.195±0.016; average value of MATH5 protein expression was 0.190±0.031. They were significantly higher than the control group, and the differences were statistically significant(<i>P</i><0.05). <p>CONCLUSION: Abnormal expression of <i>Pax6</i> gene is likely to accelerate the occurrence of Rb