Convex Quadratic Equations and Functions

Three interconnected main results (1)-(3) are presented in closed forms. (1) Regarding the convex quadratic equation (CQE), an analytical equivalent solvability condition and parameterization of all solutions are completely formulated, in a unified framework. The design concept is based on the matrix algebra, while facilitated by a novel equivalence/coordinate transformation. Notably, the parameter-solution bijection is also verified. Two applications are selected as the other two main results. (2) The focus is set on both the infinite and finite-time horizon nonlinear optimal control. By virtue of (1), the CQEs associated with the underlying Hamilton-Jacobi Equation, Hamilton-Jacobi Inequality, and Hamilton-Jacobi-Bellman Equation are algebraically solved, respectively. Each solution set captures the gradient of the associated value function. Moving forward, a preliminary to recover the optimality using the state-dependent (differential) Riccati equation is provided, which can also be used to more efficiently implement the last main result. (3) The nonlinear programming/convex optimization is analyzed via a novel method and perspective. The philosophy is based on the new analysis of CQE in (1), which helps explain the geometric structure of the convex quadratic function (CQF), and the CQE-CQF relation. An impact on the quadratic programming (QP), a basis in the literature, is demonstrated. Specifically, the QPs subject to equality, inequality, equality-and-inequality, and extended constraints are algebraically solved, resp., without knowing a feasible point.Comment: This manuscript is only preliminary and still growing. Therefore, with expectations, we deeply appreciate all kinds of input

Image Tamper Detection and Recovery by Intersecting Signatures

In this paper, we propose an exact image authentication scheme that can, in the best case, detect image tampering with the accuracy of one pixel. This method is based on constructing blocks in the image in such a manner that they intersect with one another in different directions. Such a technique is very useful to identify whether an individual image pixel has been tampered with. Moreover, the tampered region can be well recovered with the embedded recover data

Microwave-Assisted Thermal Remediation of Diesel Contaminated Soil

Leakage of petroleum products, gasoline and diesel, at gas station had become one of major soil contamination sources in Taiwan. Total number of 154 petroleum contaminated gas stations was successively ascertained since the implementation of Soil and Groundwater Remediation Act in 2002. One of the contaminated gas stations, mainly diesel polluted, was studied for the feasibility of microwave-assisted thermal remediation. The average of total petroleum hydrocarbons (TPHt) in hotspot of this site was 2,845 mg/kg exceeding regulatory limit (1,000 mg/kg). According to the groundwater condition in the site, soil samples treated by microwave radiation with and without water as saturation and vadose zones were respectively tested in laboratory. The results show that a 12-min microwave energy can heat soil with water to reach 235°C and degrade its TPHt to 934 mg/kg; additionally, a 5 min microwave energy can heat soil without water to reach 220°C and degrade its TPHt to 520 mg/kg. Both soil samples passed TPHt regulatory limit and microwave remediation with fast and effective advantages for petroleum products contaminated soil was also verified

JCMT POL-2 and ALMA polarimetric observations of 6000-100 au scales in the protostar B335: linking magnetic field and gas kinematics in observations and MHD simulations

We present our analysis of the magnetic field structures from 6000 au to 100 au scales in the Class 0 protostar B335 inferred from our JCMT POL-2 observations and the ALMA archival polarimetric data. To interpret the observational results, we perform a series of (non-)ideal MHD simulations of the collapse of a rotating non-turbulent dense core, whose initial conditions are adopted to be the same as observed in B335, and generate synthetic polarization maps. The comparison of our JCMT and simulation results suggests that the magnetic field on a 6000 au scale in B335 is pinched and well aligned with the bipolar outflow along the east-west direction. Among all our simulations, the ALMA polarimetric results are best explained with weak magnetic field models having an initial mass-to-flux ratio of 9.6. However, we find that with the weak magnetic field, the rotational velocity on a 100 au scale and the disk size in our simulations are larger than the observational estimates by a factor of several. An independent comparison of our simulations and the gas kinematics in B335 observed with the SMA and ALMA favors strong magnetic field models with an initial mass-to-flux ratio smaller than 4.8. We discuss two possibilities resulting in the different magnetic field strengths inferred from the polarimetric and molecular-line observations, (1) overestimated rotational-to-gravitational energy in B335 and (2) additional contributions in the polarized intensity due to scattering on a 100 au scale.Comment: Accepted by Ap

Antioxidant activity and growth inhibition of human colon cancer cells by crude and purified fucoidan preparations extracted from Sargassum cristaefolium

AbstractFucose-containing sulfated polysaccharides, also termed “fucoidans”, which are known to possess antioxidant, anticoagulant, anticancer, antiviral, and immunomodulating properties, are normally isolated from brown algae via various extraction techniques. In the present study, two methods (SC1 and SC2) for isolation of fucoidan from Sargassum cristaefolium were compared, with regard to the extraction yields, antioxidant activity, and inhibition of growth of human colon cancer cells exhibited by the respective extracts. SC1 and SC2 differ in the number of extraction steps and concentration of ethanol used, as well as the obtained sulfated polysaccharide extracts, namely, crude fucoidan preparation (CFP) and purified fucoidan preparation (PFP), respectively. Thin layer chromatography, Fourier transform infrared analysis, and measurements of fucose and sulfate contents revealed that the extracts were fucoidan. There was a higher extraction yield for CFP, which contained less fucose and sulfate but more uronic acid, and had weaker antioxidant activity and inhibition of growth in human colon cancer cells. In contrast, there was a lower extraction yield for PFP, which contained more fucose and sulfate but less uronic acid, and had stronger antioxidant activity and inhibition of growth in human colon cancer cells. Thus, since the difference in bioactive activities between CFP and PFP was not remarkable, the high extraction yield of SC1 might be favored as a method in industrial usage for extracting fucoidan

Antidepressant-Like Activity of the Ethanolic Extract from Uncaria lanosa Wallich var. appendiculata Ridsd in the Forced Swimming Test and in the Tail Suspension Test in Mice

This study investigated the antidepressant activity of ethanolic extract of U. lanosa Wallich var. appendiculata Ridsd (ULEtOH) for two-weeks administrations by using FST and TST on mice. In order to understand the probable mechanism of antidepressant-like activity of ULEtOH in FST and TST, the researchers measured the levels of monoamines and monoamine oxidase activities in mice brain, and combined the antidepressant drugs (fluoxetine, imipramine, maprotiline, clorgyline, bupropion and ketanserin). Lastly, the researchers analyzed the content of RHY in the ULEtOH. The results showed that ULEtOH exhibited antidepressant-like activity in FST and TST in mice. ULEtOH increased the levels of 5-HT and 5-HIAA in cortex, striatum, hippocampus, and hypothalamus, the levels of NE and MHPG in cortex and hippocampus, the level of NE in striatum, and the level of DOPAC in striatum. Two-week injection of IMI, CLO, FLU and KET enhanced the antidepressant-like activity of ULEtOH. ULEtOH inhibited the activity of MAO-A. The amount of RHY in ULEtOH was 17.12 mg/g extract. Our findings support the view that ULEtOH exerts antidepressant-like activity. The antidepressant-like mechanism of ULEtOH may be related to the increase in monoamines levels in the hippocampus, cortex, striatum, and hypothalamus of mice

A positive feedback loop of IL-17B-IL-17RB activates ERK/β-catenin to promote lung cancer metastasis

Inflammation contributes to the development and progression of cancer. Interleukin-17 (IL-17) is an inflammatory cytokine that functions in inflammation and cancer, as well as several other cellular processes. In this study, we investigated the roles and the prognostic value of IL-17 and the IL-17 receptor (IL-17R) in lung cancer. Gene expression microarray analysis followed by Kaplan-Meier survival curve showed that IL-17B was associated with poor patient survival, and IL-17B receptor (IL-17RB) was up-regulated in lung cancer tissue compared with normal tissue. Expression of IL-17RB was associated with lymph node metastasis and distant metastasis, as well as poor patient survival. IL-17RB overexpression significantly increased cancer cell invasion/migration and metastasis in vitro and in vivo. IL-17RB induced ERK phosphorylation, resulting in GSK3β inactivation and leading to β-catenin up-regulation. IL-17RB also participated in IL-17B synthesis via the ERK pathway. IL-17RB activation is required for IL-17B-mediated ERK phosphorylation. Taken together, IL-17B-IL-17RB signaling and ERK participate in a positive feedback loop that enhances invasion/migration ability in lung cancer cell lines. IL-17RB may therefore serve as an independent prognostic factor and a therapeutic target for lung cancer

Significance of Coronary Calcification for Prediction of Coronary Artery Disease and Cardiac Events Based on 64-Slice Coronary Computed Tomography Angiography

This work aims to validate the clinical significance of coronary artery calcium score (CACS) in predicting coronary artery disease(CAD) and cardiac events in 100 symptomatic patients (aged 37–87 years, mean 62.5, 81 males) that were followed up for a mean of 5 years. Our results showed that patients with CAD and cardiac events had significantly higher CACS than those without CAD and cardiac events, respectively. The corresponding data were 1450.42 ± 3471.24 versus 130 ± 188.29 (P 1000. Increased CACS (>100)was also associated with an increased frequency of multi-vessel disease. Nonetheless, 3 (20%) out of 15 patients with zero CACS had single-vessel disease. Significant correlation (P < 0.001) was observed between CACS and CAD on a vessel-based analysis for coronary arteries. It is concluded that CACS is significantly correlated with CAD and cardiac events

Gender Difference in Statin Intervention on Blood Lipid Control among Patients with Coronary Heart Disease

SummaryBackgroundThe aim of this study was to clarify the current status in the effective control of dyslipidemia in Taiwanese women and men with coronary heart disease (CHD).Materials and methodsA total 1584 patients with CHD (1188 men, aged 64.8 ± 11.6 years and 396 women, aged 69.0 ± 9.8 years) from 3486 patients who had atherosclerotic vascular disease and complete lipids measured values [total cholesterol (TC), high-density lipoprotein cholesterol (HDL-C), triglycerides (TG), and low-density lipoprotein cholesterol (LDL-C)] were used for analysis.ResultsThe waist, height, weight, and creatinine levels were higher in men than in women. The systolic blood pressure, TC, HDL-C, LDL-C, fasting blood glucose, and platelet were lower in men than in women. Men were more likely to achieve the target goal than women in TC < 160 mg/dL, LDL-C < 100 mg/dL, and TG < 150 mg/dL as well as to achieve HDL-C goal.ConclusionA significant gap was found between the guidelines and clinical practice in statin intervention among these CHD patients, particularly for women. The strategy in control of dyslipidemia should consider gender difference