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Aims: The purpose of this paper is to prospectively evaluate the performance of an artificial intelligence (AI) system in diagnosing thyroid nodules and to assess its potential value in comparison with the performance of radiologists with different levels of experience, as well as the factors affecting its diagnostic accuracy. Background: In recent years, medical imaging diagnosis using AI has become a popular topic in clinical application research. Objective: This study aimed to evaluate the performance of an AI system in diagnosing thyroid nodules and compare it with the performance levels of different radiologists. Method: This study involved 426 patients screened for thyroid nodules at the First Affiliated Hospital of Guangzhou Medical University between July 2017 and March 2019. All of the nodules were evaluated by radiologists with various levels of experience and an AI system. The diagnostic performances of two junior and two senior radiologists, an AI system, and an AI-assisted junior radiologist were compared, as were their diagnostic results with respect to nodules of different sizes. Result: The senior radiologists, the AI system, and the AI-assisted junior radiologist performed better than the junior radiologist (p < 0.05). The area under the curves of the AI system and the AI-assisted junior radiologist were similar to the curve of the senior radiologists (p > 0.05). The diagnostic results concerning the two nodule sizes showed that the diagnostic error rates of the AI system, junior radiologists, and senior radiologists for nodules with a maximum diameter of ≤1 cm (Dmax ≤ 1 cm) were higher than those for nodules with a maximum diameter of ＞1 cm (Dmax > 1 cm) (23.4% vs. 12.1%, p = 0.002; 26.6% vs. 7.3%, p < 0.001; and 38.3% vs. 14.6%, p < 0.001). Conclusion: The AI system is a decision-making tool that could potentially improve the diagnostic efficiency of junior radiologists. Micronodules with Dmax ≤ 1cm were significantly correlated with diagnostic accuracy; accordingly, more micronodules of this size, in particular, should be added to the AI system as training samples. Other: The system could be a potential decision-making tool for effectively improving the diagnostic efficiency of junior radiologists in the community.

The pandemic of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has been engendering enormous hazards to the world. We obtained the complete genome sequences of SARS-CoV-2 from imported cases admitted to the Guangzhou Eighth People's Hospital, which was appointed by the Guangdong provincial government to treat coronavirus disease 2019 (COVID-19). The SARS-CoV-2 diversity was analyzed, and the mutation characteristics, time, and regional trend of variant emergence were evaluated.In total, 177 throat swab samples were obtained from COVID-19 patients (from October 2020 to May 2021). High-throughput sequencing technology was used to detect the viral sequences of patients infected with SARS-CoV-2. Phylogenetic and molecular evolutionary analyses were used to evaluate the mutation characteristics and the time and regional trends of variants.We observed that the imported cases mainly occurred after January 2021, peaking in May 2021, with the highest proportion observed from cases originating from the United States. The main lineages were found in Europe, Africa, and North America, and B.1.1.7 and B.1.351 were the two major sublineages. Sublineage B.1.618 was the Asian lineage (Indian) found in this study, and B.1.1.228 was not included in the lineage list of the Pangolin web. A reasonably high homology was observed among all samples. The total frequency of mutations showed that the open reading frame 1a (ORF1a) protein had the highest mutation density at the nucleotide level, and the D614G mutation in the spike protein was the commonest at the amino acid level. Most importantly, we identified some amino acid mutations in positions S, ORF7b, and ORF9b, and they have neither been reported on the Global Initiative of Sharing All Influenza Data nor published in PubMed among all missense mutations.These results suggested the diversity of lineages and sublineages and the high homology at the amino acid level among imported cases infected with SARS-CoV-2 in Guangdong Province, China.

Background: The phenomenon of COVID-19 patients tested positive for SARS-CoV-2 after discharge (redetectable as positive, RP) emerged globally. The data of incidence rate and risk factors for RP event and the clinical features of RP patients may provide recommendations for virus containment and discharge assessment for COVID-19. Methods: The baseline included 285 adult inpatients (≥18 years old) with laboratory-confirmed COVID-19 from Guangzhou Eighth People's Hospital. We started the Observation on Jan 20, 2020, and acquired all their definite clinical outcome (becoming RP or keeping normal during post-discharge surveillance) by Mar 10, 2020. The dynamic clinical data of patients during observation were prospectively collected and analyzed. Univariate and multivariate-adjusted logistic regression were used to explore the risk factors related to RP events in COVID-19 patients. Results: By March 10, 27 (9.5%) discharged patients had tested positive for SARS-CoV-2 in their nasopharyngeal swab after a median duration of 7·0 days (IQR 5·0-8·0). Age, sex, epidemiological history, clinical symptoms and underlying diseases were similar between RP and non-RP patients (p>0.05). Compared to first admission, RP patients generally had milder clinical symptoms, lower viral load, shorter length of stay and improved pulmonary conditions at readmission (p10 days) during the first hospitalization [adjusted odds ratio [aOR]: 5.82, 95% confidence interval [CI]: 2.50-13.57 for N gene; aOR: 9.64, 95% CI: 3.91-23.73 for ORF gene] and higher Ct value (ORF) in the third week of the first hospitalization (aOR: 0.69; 95% CI: 0.50-0.95) were associated with RP events. Conclusions: RP events occurred in nearly 10% of COVID-19 patients which deserves globally attention. During hospitalization, patients’ low efficiency of viral clearance was a risk factor for RP event. Elderly RP patients were more likely to develop clinical symptoms. To reduce the possibility of reinfection and readmission during the management of COVID-19, more rigorously monitoring on patients’ viral load should be carried out especially in elder patients and later stage of hospitalization.

For any integer n ≥ 2, let P(n) be the largest prime factor of n. In this paper, we prove that the number of primes p ≤ x with P(p−1) ≥ p c is more than (1−c+o(1))π(x) for 0 < c < 1/2. This extends a recent result of Luca, Menares and Madariaga for 1/4 ≤ c ≤ 1/2. We also pose two conjectures for further research.

A triple (a,b,c) ( a , b , c ) of positive integers is called a Markoff triple if it satisfies the Diophantine equation a 2 +b 2 +c 2 =3abc a 2 + b 2 + c 2 = 3 a b c . A famous old conjecture says that any Markoff triple (a,b,c) ( a , b , c ) with a⩽b⩽c a ⩽ b ⩽ c is determined uniquely by its largest member c . Let (a,b,c) ( a , b , c ) be a Markoff triple with a⩽b⩽c a ⩽ b ⩽ c . In 2001, Button proved that if c is of the form kp l k p l , where k is an integer with 1⩽k⩽10 35 1 ⩽ k ⩽ 10 35 and p l p l is a prime power, then c uniquely determines a and b . In this paper, as a complement to the result of Button, we prove that if either 3c−2 3 c − 2 or 3c+2 3 c + 2 is of the form kp l k p l , where k is an integer with 1⩽k⩽10 10 1 ⩽ k ⩽ 10 10 and p l p l is a prime power, then c uniquely determines a and b .

In this paper, we determine all sets A of integers such that, for any integral-valued polynomial f ( x ) which has no fixed divisor, for all integers l ⩾ 1 and n, there are infinitely many integers m > l and a choice of e i ∈ A such that n = e l f ( l ) + e l + 1 f ( l + 1 ) + ⋯ + e m f ( m ) . The earlier result shows that A = { − 1 , 1 } is such a set.

We give a sufficient and necessary condition on the sequence { a n } \{a_n\} of integers that for any integer l ≥ 1 l\ge 1 , every integer can be represented in the form ε l a l + ε l + 1 a l + 1 + ⋯ + ε k a k \varepsilon _l a_l+\varepsilon _{l+1} a_{l+1}+\cdots + \varepsilon _ka_k , where ε i ∈ { − 1 , 1 } ( i = l , l + 1 , … , k ) \varepsilon _i\in \{-1, 1\}\ (i=l,l+1,\ldots , k) . This generalizes the known result on integral-valued polynomial values. Moreover, we show that such sequences exist with any growth rate. This answers two problems posed by Bleicher. We also pose several problems for further research.

Let q be an odd prime. In this paper, we prove that if N is an odd perfect number with qα∥N then σ(N/qα)/qα≠p,p2,p3,p4,p1p2,p21p2, where p,p1, p2 are primes and p1≠p2. This improves a result of Dris and Luca [‘A note on odd perfect numbers’, arXiv:1103.1437v3 [math.NT]]: σ(N/qα)/qα≠1,2,3,4,5. Furthermore, we prove that for K≥1 , if N is an odd perfect number with qα ∥N and σ(N/qα)/qα ≤K, then N≤4K8.

Let N denote the set of all nonnegative integers. Let W be a nonempty subset of N . Denote by F ? ( W ) the set of all finite, nonempty subsets of W . Let A ( W ) be the set of all numbers of the form ? f ? F 2 f , where F ? F ? ( W ) . Let N = W 1 ? W 2 be a partition with 0 ? W 1 such that W 1 and W 2 are infinite. In this paper, we prove that A = A ( W 1 ) ? A ( W 2 ) is a minimal asymptotic basis of order 2 if and only if either W 1 contains no consecutive integers or W 2 contains consecutive integers or both. We resolve three problems on asymptotic bases of order 2 which had been posed by Nathanson.

Let A be a set of nonnegative integers. For h≥2, denote by hA the set of all the integers representable by a sum of h elements from A. In this paper, we prove that, if k≥3, and A={a0,a1,…,ak−1} is a finite set of integers such that 0=a0

Let m0, m1, m2, ... be positive integers with mi ≥ 2 for all i. It is well known that each nonnegative integer n can be uniquely represented as $$ n = a_0 + a_1 m_0 + a_2 m_0 m_1 + \cdots + a_t m_0 m_1 m_2 \cdots m_{t - 1} $$ where 0 ≤ ai ≤ mi − 1 for all i and at ≠ 0. Let each fi be a function defined on “0, 1, 2, ..., mi −1” with fi(0) = 0. Write $$ S\left( n \right) = \sum\limits_{i = 0}^t {f_i \left( {a_i } \right)} $$ .

2-Hydroxybenzylidene-2-phenylquinoline-4-carbonylhydrazone (H2L) and five Ln(III) complexes, [Ln(H2L)(NO3)2]NO3 [Ln = La (1), Pr (2), Sm (3), Eu (4), and Tb (5)], have been synthesized and characterized by 1H NMR, elemental analysis, conductivity measurements, mass spectra, IR spectra, and UV spectra. The interaction of these complexes with calf thymus DNA was investigated by UV absorption spectroscopy, fluorescence spectroscopy, circular dichroism spectroscopy and viscosity measurements. Results suggest that these complexes bind to DNA via groove binding.

To study PD-1 and PD-L1 expressions during 24 weeks telbivudine antiviral treatment in patients with chronic hepatitis B (CHB) and to explore the relationship between PD-1 expression and HBeAg/HBeAb seroconversion.Ten CHB cases with HLA-A2 and HBeAg positive were treated with telbivudine 600 mg/d orally for 24 weeks. Fresh blood samples were collected at week 0, 12 and 24 after treatment. HBV-specific CD8+ T cells were expanded in vitro. Cell culture medium were collected for interferon gamma (IFNgamma) detection. Flow cytometry was used to detect the HLA-A type, PD-1, PD-L1 and HBV specific CD8+ T cells. The expressions of PD-1 and PD-L1, the counts of HBV-specific CD8+ T cells in circulating CD8+ lymphocytes, and IFNgamma concentration in culture medium were evaluated during antiviral treatment.At week 0, 12 and 24 after telbivudine treatment, 7 of 10 patients were HBV DNA undetectable, 2 were HBeAg seroconversion and 2 were HBeAg lose but anti-HBe negative. The frequency of PD-1-positive PBMCs were 52.1%+/-17.0%, 39.1%+/-18.2% and 23.4%+/-16.3% (week 24 vs week 0, P0.01) respectively; PD-L1 positive PBMCs were 45.6%+/-15.4%, 34.6%+/-16.2% and 20.9%+/-9.5% respectively(week 24 vs week 0, P0.01; week 24 vs week 12, P0.05). The frequency of PD-1-positive CD8+ T cells were 76.2%+/-10.4%, 66.5%+/-15.4% and 49.5%+/-25.3% respectively (week 24 vs week 0, P0.01; week 12 vs week 0, P0.05; week 24 vs week 12, P0.05); HBV-specific CD8 cells were 1.3%+/-0.5%, 1.5%+/-1.0% and 2.2%+/-1.5%; IFNgamma levels in cell culture medium were (91.7+/-82.1) pg/ml, (99.4+/-93.5) pg/ml and (109.5+/-86.6) pg/ml. A remarkable decrease of PD-1 and PD-L1 expressions and increase of HBV-specific CD8+ T cells were observed in patients who had HBeAg/HBeAb seroconversion at week 24.Direct suppression of HBV replication by telbivudine in CHB patients can decrease PD-1 and PD-L1 expressions and restore HBV-specific CD8+T cells. The relationship between the changes of PD-1 expression and HBeAg/HBeAb seroconversion during antiviral therapy in HBeAg-positive patients need to confirm by future study.

A novel copper(II) thiocyanate complex with 4-(dimethylamino)pyridine (DMAP) and N,N-dimethylformamide (DMF), [Cu(DMAP)2(SCN)2(DMF)2], was synthesized. The title complex was crystallized in the triclinic system, space group P1 with a = 8.476(1)A, b = 9.404(1)A, c = 9.924(1)A, α = 91.186(2)°, β = 113.989(3)°, γ = 103.543(2)°, V = 696.6(2)A3 and Z = 1. In the title complex, the Cu(II) atom is placed in a centrosymmetric octahedral environment. The molecules are linked by two kinds of weak hydrogen-bonds, C-H…O and C-H…S, generating an extended two-dimensional supramolecular network structure in the ab plane.

The title POM-based organic-inorganic hybrid compound consists of one Anderson-type polyoxoanion, two [Cu(2,2′-bipy)Cl]+ cations, five Na+ cations and fourteen coordination H2O molecules and two solvent H2O molecules; the polyoxoanion was linked by Na+ to form a 2D layer. A 2D organic layer is also formed through a π-π stacking interaction. Through weak interactions between the adjacent layers, a 3D supramolecular compound is formed.

The title compound, C22H19N3O3, was synthesized and the structure was investigated by X-ray crystallography. It crystallizes in the monoclinic system, space group P21/c with a = 14.8281(15)A, b = 11.8051(14)A, c = 11.2260(11)A, β = 106.744(2)°, V = 1881.8(3)A3, Z = 4, R = 0.0489. The N-H…O hydrogen bonds between the compound and the solvent molecule stabilize the crystal structure by causing the formation of a one-dimensional chain structure.