The relationship of a problem-based calculus course and students' views of mathematical thinking

It has been held that heuristic training alone is not enough for developing one's mathematical thinking. One missing component is a mathematical point of view. Many educational researchers have proposed problem-based curricula to improve students' views of mathematical thinking. The present study reports findings regarding effects of a problem-based calculus course, using historical problems, to foster Taiwanese college students' views of mathematical thinking. The present study consisted of three stages. During the initial phase, 44 engineering majors' views on mathematical thinking were tabulated by a six-item, open-ended questionnaire and nine randomly selected students were invited to participate in follow-up interviews. Students then received an 18-week problem-based calculus course in which mathematical concepts were problematized in order to challenge their personally expressed empirical beliefs in doing mathematics. Several tasks and instructional approaches served to reach the goal. Near the end of the semester, all participants answered the same questionnaire and the same students were interviewed to pinpoint their shift in views on mathematical thinking. It was found that participants were more likely to value logical sense, creativity, and imagination in doing mathematics. Further, students leaned toward a conservative attitude in the certainty of mathematical knowledge. Participants focus seemingly shifted from mathematics as a product to mathematics as a process

Federated Deep Reinforcement Learning for THz-Beam Search with Limited CSI

Terahertz (THz) communication with ultra-wide available spectrum is a promising technique that can achieve the stringent requirement of high data rate in the next-generation wireless networks, yet its severe propagation attenuation significantly hinders its implementation in practice. Finding beam directions for a large-scale antenna array to effectively overcome severe propagation attenuation of THz signals is a pressing need. This paper proposes a novel approach of federated deep reinforcement learning (FDRL) to swiftly perform THz-beam search for multiple base stations (BSs) coordinated by an edge server in a cellular network. All the BSs conduct deep deterministic policy gradient (DDPG)-based DRL to obtain THz beamforming policy with limited channel state information (CSI). They update their DDPG models with hidden information in order to mitigate inter-cell interference. We demonstrate that the cell network can achieve higher throughput as more THz CSI and hidden neurons of DDPG are adopted. We also show that FDRL with partial model update is able to nearly achieve the same performance of FDRL with full model update, which indicates an effective means to reduce communication load between the edge server and the BSs by partial model uploading. Moreover, the proposed FDRL outperforms conventional non-learning-based and existing non-FDRL benchmark optimization methods

Design and synthesis of active heparan sulfate-based probes

A chemoenzymatic approach for synthesizing heparan sulfate oligosaccharides with a reactive diazoacetyl saccharide residue is reported. The resultant oligosaccharides were demonstrated to serve as specific inhibitors for heparan sulfate sulfotransferases, offering a new set of tools to probe the structural selectivity for heparan sulfate-binding proteins

Uncovering the Relationship between Sulphation Patterns and Conformation of Iduronic Acid in Heparan Sulphate

The L-iduronic acid (IdoA) residue is a critically important structural component in heparan sulphate polysaccharide for the biological functions. The pyranose ring of IdoA is present in 1C4-chair, 2SO-skew boat, and less frequently, in 4C1-chair conformations. Here, we analyzed the conformation of IdoA residue in eight hexasaccharides by NMR. The data demonstrate a correlation between the conformation of IdoA and sulphations in the surrounding saccharide residues. For the 2-O-sulpho IdoA residue, a high degree of sulphation on neighboring residues drives ring dynamics towards the 2SO-skew boat conformer. In contrast, the nonsulphated IdoA residue is pushed towards the 1C4-chair conformer when the neighboring residues are highly sulphated. Our data suggest that the conformation of IdoA is regulated by the sulphation pattern of nearby saccharides that is genetically controlled by the heparan sulphate biosynthetic pathway

Outcomes and prognostic factors of simple partial cystectomy for localized bladder urothelial cell carcinoma

AbstractRadical cystectomy has remained the gold standard for recurrent superficial or muscle invasive bladder tumor. However, partial cystectomy still has a role in those who reject or have contraindications for radical cystectomy. In this study, we sought to identify predictors of bladder recurrence and overall survival after simple partial cystectomy. We included 27 patients with bladder tumor who received simple partial cystectomy without pelvic lymph node dissection between March 2000 and September 2013. Adjuvant chemotherapy or radiation therapy was prescribed according to the pathological results. Parameters were compared on the basis of bladder recurrence and overall survival. During a mean follow-up time of 39 months, five patients (18.5%) experienced bladder recurrence. An older age, a higher pathological stage, positive surgical margins, and distant metastases were significant predictors of overall survival (p = 0.031, p = 0.001, p = 0.001, and p = 0.011, respectively). Meanwhile, previous bladder instillation and positive surgical margins were significant predictors of bladder recurrence (p = 0.026 and p = 0.027, respectively). The rate of consecutive distant metastases (33.3%) was almost twice the rate of bladder recurrence (18.5%), and six patients developed consecutive distant metastases without first experiencing bladder recurrence. In patients who received a simple partial cystectomy as an alternative treatment, previous bladder instillation and positive surgical margins were significant predictors of bladder recurrence. Patients with an older age, positive surgical margins, and consecutive distant metastases had worse overall survival. Partial cystectomy with routine lymph node dissection may be a better option for achieving favorable long-term outcomes