Pell and Pell-Lucas numbers of the form −2a−3b+5c-2^a-3^b+5^c

summary:In this paper, we find all Pell and Pell-Lucas numbers written in the form $-2^a-3^b+5^c$, in nonnegative integers $a$, $b$, $c$, with $0\leq \max \{a,b\}\leq c$

Certificateless Proxy Signature from RSA

Although some good results were achieved in speeding up the computation of pairing function in recent years, it is still interesting to design efficient cryptosystems with less bilinear pairing operation. A proxy signature scheme allows a proxy signer to sign messages on behalf of an original signer within a given context. We propose a certificateless proxy signature (CLPS) scheme from RSA and prove its security under the strongest security model where the Type I/II adversary is a super Type I/II adversary

Security and privacy in smart cities: challenges and opportunities

Smart cities are expected to improve the quality of daily life, promote sustainable development, and improve the functionality of urban systems. Now that many smart systems have been implemented, security and privacy issues have become a major challenge that requires effective countermeasures. However, traditional cybersecurity protection strategies cannot be applied directly to these intelligent applications because of the heterogeneity, scalability, and dynamic characteristics of smart cities. Furthermore, it is necessary to be aware of security and privacy threats when designing and implementing new mechanisms or systems. Motivated by these factors, we survey the current situations of smart cities with respect to security and privacy to provide an overview of both the academic and industrial fields and to pave the way for further exploration. Specifically, this survey begins with an overview of smart cities to provide an integrated context for readers. Then, we discuss the privacy and security issues in current smart applications along with the corresponding requirements for building a stable and secure smart city. In the next step, we summarize the existing protection technologies. Finally, we present open research challenges and identify some future research directions

Amide proton transfer-weighted imaging of pediatric brainstem glioma and its predicted value for H3 K27 alteration

BACKGROUND: Non-invasive determination of H3 K27 alteration of pediatric brainstem glioma (pedBSG) remains a clinical challenge. PURPOSE: To predict H3 K27-altered pedBSG using amide proton transfer-weighted (APTw) imaging. MATERIAL AND METHODS: This retrospective study included patients with pedBSG who underwent APTw imaging and had the H3 K27 alteration status determined by immunohistochemical staining. The presence or absence of foci of markedly increased APTw signal in the lesion was visually assessed. Quantitative APTw histogram parameters within the entire solid portion of tumors were extracted and compared between H3 K27-altered and wild-type groups using Student's t-test. The ability of APTw for differential diagnosis was evaluated using logistic regression. RESULTS: Sixty pedBSG patients included 48 patients with H3 K27-altered tumor (aged 2-48 years) and 12 patients with wild-type tumor (aged 3-53 years). Visual assessment showed that the foci of markedly increased APTw signal intensity were more common in the H3 K27-altered group than in wild-type group (60% vs. 16%, P = 0.007). Histogram parameters of APTw signal intensity in the H3 K27-altered group were significantly higher than those in the wild-type group (median, 2.74% vs. 2.22%, P = 0.02). The maximum (area under the receiver operating characteristic curve [AUC] = 0.72, P = 0.01) showed the highest diagnostic performance among histogram analysis. A combination of age, median and maximum APTw signal intensity could predict H3 K27 alteration with a sensitivity of 81%, specificity of 75% and AUC of 0.80. CONCLUSION: APTw imaging may serve as an imaging biomarker for H3 K27 alteration of pedBSGs

KIF2A silencing inhibits the proliferation and migration of breast cancer cells and correlates with unfavorable prognosis in breast cancer

Background; Kinesin family member 2a (KIF2A), a type of motor protein found in eukaryotic cells, is associated with development and progression of various human cancers. The role of KIF2A during breast cancer tumorigenesis and progression was studied. Methods; Immunohistochemical staining, real time RT-PCR and western blot were used to examine the expression of KIF2A in cancer tissues and adjacent normal tissues from breast cancer patients. Patients’ survival in relation to KIF2A expression was estimated using the Kaplan–Meier survival and multivariate analysis. Breast cancer cell line, MDA-MB-231 was used to study the proliferation, migration and invasion of cells following KIF2A-siRNA transfection. Results; The expression of KIF2A in cancer tissues was higher than that in normal adjacent tissues from the same patient (P < 0.05). KIF2A expression in cancer tissue with lymph node metastasis and HER2 positive cancer were higher than that in cancer tissue without (P < 0.05). A negative correlation was found between KIF2A expression levels in breast cancer and the survival time of breast cancer patients (P < 0.05). In addition, multivariate analysis indicated that KIF2A was an independent prognostic for outcome in breast cancer (OR: 16.55, 95% CI: 2.216-123.631, P = 0.006). The proliferation, migration and invasion of cancer cells in vitro were suppressed by KIF2A gene silencing (P < 0.05). Conclusions; KIF2A may play an important role in breast cancer progression and is potentially a novel predictive and prognostic marker for breast cancer

Robust estimation of bacterial cell count from optical density

Optical density (OD) is widely used to estimate the density of cells in liquid culture, but cannot be compared between instruments without a standardized calibration protocol and is challenging to relate to actual cell count. We address this with an interlaboratory study comparing three simple, low-cost, and highly accessible OD calibration protocols across 244 laboratories, applied to eight strains of constitutive GFP-expressing E. coli. Based on our results, we recommend calibrating OD to estimated cell count using serial dilution of silica microspheres, which produces highly precise calibration (95.5% of residuals &lt;1.2-fold), is easily assessed for quality control, also assesses instrument effective linear range, and can be combined with fluorescence calibration to obtain units of Molecules of Equivalent Fluorescein (MEFL) per cell, allowing direct comparison and data fusion with flow cytometry measurements: in our study, fluorescence per cell measurements showed only a 1.07-fold mean difference between plate reader and flow cytometry data

Lucas Numbers Which Are Concatenations of Two Repdigits

In this paper, we find all Lucas numbers written in the form c⋯cd⋯d&macr;, where c⋯cd⋯d&macr; is the concatenation of two repdigits in base 10 with c,d&isin;{0,1,⋯,9}, c&ne;d and c&gt;0

Certificateless Proxy Signature from RSA

Although some good results were achieved in speeding up the computation of pairing function in recent years, it is still interesting to design efficient cryptosystems with less bilinear pairing operation. A proxy signature scheme allows a proxy signer to sign messages on behalf of an original signer within a given context. We propose a certificateless proxy signature (CLPS) scheme from RSA and prove its security under the strongest security model where the Type I/II adversary is a super Type I/II adversary

Fibonacci and Lucas Numbers of the Form 2a + 3b + 5c + 7d

In this paper, we find all Fibonacci and Lucas numbers written in the form 2 a + 3 b + 5 c + 7 d , in non-negative integers a , b , c , d , with 0 &le; max { a , b , c } &le; d