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Let Pr denote an almost-prime with at most r prime factors, counted according to multiplicity. In this paper, it is proved that for every sufficiently large even integer N, the following equation N = p²1 + p²2 + x³ + p³3 + p³4 + p³5 is solvable with x being an almost-prime P7 and the other variables primes. This result constitutes a deepening upon that of previous results. [ABSTRACT FROM AUTHOR]

Background: Patients with cancer experience multiple symptoms related to cancer, cancer treatment, and the procedures involved in cancer care; however, many patients with pain, depression, and fatigue, especially those outside the hospital, receive inadequate treatment for their symptoms. Using an electronic patient-reported outcome (ePRO) platform to conduct symptom management follow-up in outpatients with advanced cancer could be a novel and potentially effective approach. However, empirical evidence describing in detail the preparation and implementation courses in a real setting is needed. Objective: The purpose of this paper was to describe the implementation process and evaluation of an ePRO platform that facilitates symptom management for patients with cancer, share our experiences and the problems we encountered during the process of implementation, and share the solutions we identified for those problems. Moreover, we tested the feasibility, safety, and efficacy of the ePRO platform. Methods: This was a real-world, ongoing, longitudinal, single-center, prospective study with a total of 7 follow-ups conducted within 4 weeks after the first visit to the symptom management clinic (on days 1, 3, 7, 10, 14, 21, and 28). Participants were encouraged to complete scales for physical symptoms (pain, fatigue, and shortness of breath), cognitive symptoms (memory problems and impaired concentration), and affective symptoms (especially depression and anxiety) during follow-up. The design and function of the ePRO-doctor client and ePRO-patient client, the patient-reported outcome (PRO) scales used in the study, and the strategies to promote symptom tracking have been described. Moreover, the training and evaluation for research assistants have been presented. The efficacy of the ePRO platform was assessed with a comparison of the baseline and 4-week outcomes on the MD Anderson Symptom Inventory. Results: Using the ePRO platform for symptom management follow-ups in advanced cancer patients was associated with a high completion rate (72.7%-86.4%) and a low drop-off rate (23.6%). The ePRO platform sent 293 alert notifications to both patients and doctors, which promoted patient security. The short and sharp PRO tool selection, user-friendly interface, automatic reminder notifications and alerts, and multiple dimensional training were essential components for the preparation and implementation of the ePRO system. The results showed significant improvements in the mean scores of pain, fatigue, and numbness from baseline to day 28 (P=.02, P=.02, and P<.001, respectively). Conclusions: The use of an ePRO platform for symptom management follow-ups in advanced cancer patients is time-saving, energy-saving, and effective. PRO tool selection, platform design, and training of research assistants are important aspects for implementation. Future research should validate the ePRO platform in a larger randomized controlled study. [ABSTRACT FROM AUTHOR]

The paper was to evaluate the resistance of indica rice varieties with bacterial blight resistance genes Xa21 and Xa23 under different genetic backgrounds. [Methods] The rice materials with bacterial blight resistance genes Xa21 or Xa23 were used as the donors, and those without the genes were used as the receptors. By back crossing, composite crossing and other methods, combined with molecular marker-assisted selection （MAS）, the materials with Xa21 or Xa23 gene, and their sister lines with/without Xa21 or Xa23 gene were inoculated with 7 widely used physiological races of Xanthomonas oryzae, and the resistance of the materials to bacterial blight was analyzed. [Results] The proportions of cumulative resistance （HR, R, MR） of rice materials with resistance gene Xa21 were HNA1-4/PXO86（84.62%）>YN24（82.14%）>GD1358（73.08%）>PXO99（67.86%）>GDA2（63.33%） > FuJ（6.67%）, indicating that the materials with Xa21 gene had no resistance to bacterial blight induced by strain FuJ, but for other strains, there were still 36.67%-15.38% of the materials susceptible to the disease. The cumulative resistance （HR, R, MR） of the materials with Xa23 gene was over 76%, but there were still 23.02%-15.52% of the materials that had no resistance to the 7 strains. The analysis of variation coefficient of lesion length showed that the resistance of materials with Xa21 or Xa23 genes varied among strains, or the resistance to the same strain varied among materials. Correlation analysis demonstrated that there was significant or extremely significant positive correlation between strain GDA2 or HNA1-4 and other 6 corresponding strains in the materials with Xa21 gene, and there was extremely significant positive correlation between strain YN24, GD1358 or PXO86 and other 6 corresponding strains in the materials with Xa23 gene. Selection of these strains for resistance identification could improve the efficiency of breeding. Analysis of sister lines showed that bacterial blight resistance of Xa21 or Xa23 genes was related to the donor of the materials. Correlation analysis showed that the resistance of the materials with Xa21 gene had extremely significant positive correlation with parents(R=0.572 5**), and the resistance of the materials with Xa23 gene had significant positive correlation with parents （R=0.221 2*）. [Conclusions] The study provides the reference for molecular resistance breeding of bacterial blight. [ABSTRACT FROM AUTHOR]

In this article, we aim to improve the performance of visual tracking by combing different features of multiple modalities. The core idea is to use covariance matrices as feature descriptors and then use sparse coding to encode different features. The notion of sparsity has been successfully used in visual tracking. In this context, sparsity is used along appearance models often obtained from intensity/color information. In this work, we step outside this trend and propose to model the target appearance by local covariance descriptors (CovDs) in a pyramid structure. The proposed pyramid structure not only enables us to encode local and spatial information of the target appearance but also inherits useful properties of CovDs such as invariance to affine transforms. Since CovDs lie on a Riemannian manifold, we further propose to perform tracking through sparse coding by embedding the Riemannian manifold into an infinite-dimensional Hilbert space. Embedding the manifold into a Hilbert space allows us to perform sparse coding efficiently using the kernel trick. Our empirical study shows that the proposed tracking framework outperforms the existing state-ofthe- art methods in challenging scenarios. [ABSTRACT FROM AUTHOR]

Background: To evaluate the relationship between quality of life (QOL) and physical as well as psychological variables in Chinese breast cancer patients. Methods: This multicenter cross-sectional study enrolled 254 Chinese breast cancer patients in different stages and treatment phases. They answered standard instruments assessing QOL (EORTC), somatic symptom severity (PHQ-15), depression (PHQ-9), anxiety (GAD-7), health-related anxiety (WI-7), illness perception (BIPQ), and sense of coherence (SOC-9). Canonical correlation was applied to identify the strongest correlates between the physical, emotional and social QOL scales and the physical and psychological variables. Results: In our sample, a low global QOL was significantly associated with the following physical and psychological variables: symptom-related disability (Karnofsky Index) (r = .211, p < .01), somatic symptom severity (r = -.391, p < .001), depression (r = -.488, p < .001), anxiety (r = -.439, p < .001), health-related anxiety (r = -.398, p < .001), dysfunctional illness perception (r = -.411, p < .001), and sense of coherence (r = .371, p < .001). In the canonical correlation analysis, high somatic symptom severity, depression, anxiety, dysfunctional illness perception, and low sense of coherence showed the strongest correlations with low physical, emotional and social functioning. The first three significant canonical correlations between these two sets of variables were .78, .56, and .45. Conclusions: QOL in Chinese breast cancer patients is strongly associated with psychological factors. Our results suggest that Chinese physicians and nurses should incorporate these factors into their care for women with breast cancer to improve patients' QOL. [ABSTRACT FROM AUTHOR]

In the real world, the object does not exist in isolation, and it always appears in a certain scene. Usually the object is fixed in a particular scene and even in special spatial location. In this paper, we propose a method for judging scene consistency effectively. Scene semantics and geometry relation play a key role. In this paper, we use PatchNet to deal with these high-level scene structures. We construct a consistent scene database, using semantic information of PatchNet to determine whether the scene is consistent. The effectiveness of the proposed algorithm is verified by a lot of experiments. [ABSTRACT FROM AUTHOR]

The article discusses a study which evaluates corticospinal spinal tract and complication of surgery for insular lobe lesions among Chinese patients. The study has utilized intraoperative diffusion tensor imaging to observe motor dysfunction recovery after surgery. Results reveal that intraoperative fractional anisotropy is useful as prognostic indicator for motor function.

The article presents a study that evaluates the changes in the ventral language pathways among patients with low-grade glioma located in regions that can affect the dorsal language pathways. The study is undertaken through the use of fractional anisotropy and laterization index values in the left inferior longitudinal fascicculus. The results of the study indicate that the ventral language pathways may perform more functions in patients as compared in healthy subjects.

The article focuses on a study which examined the effect of acute or chronic extracerebral occupying lesions on white-matter fiber bundles in patients with meningioma. All participating patients underwent magnetic resonance-diffusion tensor imaging (MR-DTI) examination. In one case, the study found compression on the right lateral ventricle occipital horn and thinner optic radiation on the affected side. Information on the DTI fractional anisotropy value of meningioma patients is given.