Efficient Reduction of Polynomial Zero-One Optimization to the Quadratic Case

2008 ◽  
Vol 18 (4) ◽  
pp. 1398-1413 ◽  
Author(s):  
Christoph Buchheim ◽  
Giovanni Rinaldi
Keyword(s):  
Efficient Reduction ◽  
Polynomial Zero ◽  
Quadratic Case

Cerium oxide nanomaterial with dual antioxidative scavenging potential: Synthesis and characterization

2021 ◽  
pp. 088532822110134
Author(s):  
Sushant Singh ◽  
Udit Kumar ◽  
David Gittess ◽  
Tamil S Sakthivel ◽  
Balaashwin Babu ◽  
...  
Keyword(s):  
Cerium Oxide ◽  
Biological Systems ◽  
Mixed Valence ◽  
Stable Solution ◽  
Ability To Act ◽  
Valence States ◽  
Transmission Electron ◽  
Efficient Reduction ◽  
Rich Media

Many studies have linked reactive oxygen species (ROS) to various diseases. Biomedical research has therefore sought a way to control and regulate ROS produced in biological systems. In recent years, cerium oxide nanoparticles (nanoceria, CNPs) have been pursued due to their ability to act as regenerative ROS scavengers. In particular, they are shown to have either superoxide dismutase (SOD) or catalase mimetic (CAT) potential depending on the ratio of Ce3+/Ce4+ valence states. Moreover, it has been demonstrated that SOD mimetic activity can be diminished by the presence of phosphate, which can be a problem given that many biological systems operate in a phosphate-rich environment. Herein, we report a CNP formulation with both SOD and catalase mimetic activity that is preserved in a phosphate-rich media. Characterization demonstrated a highly dispersed, stable solution of uniform-sized, spherical-elliptical shaped CNP of 12 ± 2 nm, as determined through dynamic light scattering, zeta potential, and transmission electron microscopy. Mixed valence states of Ce ions were observed via UV/Visible spectroscopy and XPS (Ce3+/Ce4+ > 1) (Ce3+∼ 62%). X-ray diffraction and XPS confirmed the presence of oxygen-deficient cerium oxide (CeO2-x) particles. Finally, the CNP demonstrated very good biocompatibility and efficient reduction of hydrogen peroxide under in-vitro conditions.

scholarly journals Can we Beat the Square Root Bound for ECDLP over 𝔽p2 via Representation?

2020 ◽  
Vol 14 (1) ◽  
pp. 293-306
Author(s):  
Claire Delaplace ◽  
Alexander May
Keyword(s):  
Elliptic Curve ◽  
Quadratic Field ◽  
Discrete Logarithm ◽  
Field Size ◽  
Square Root ◽  
Multivariate Polynomial ◽  
Bivariate Polynomial ◽  
Testing Problem ◽  
Polynomial Zero ◽  
Representation Technique

AbstractWe give a 4-list algorithm for solving the Elliptic Curve Discrete Logarithm (ECDLP) over some quadratic field 𝔽p2. Using the representation technique, we reduce ECDLP to a multivariate polynomial zero testing problem. Our solution of this problem using bivariate polynomial multi-evaluation yields a p1.314-algorithm for ECDLP. While this is inferior to Pollard’s Rho algorithm with square root (in the field size) complexity 𝓞(p), it still has the potential to open a path to an o(p)-algorithm for ECDLP, since all involved lists are of size as small as $\begin{array}{} p^{\frac 3 4}, \end{array}$ only their computation is yet too costly.

Systematic Approach to Measuring ILI Tool Performance

2014 ◽  
Author(s):  
Sean Keane ◽  
Karmun Cheng ◽  
Kaitlyn Korol
Keyword(s):  
Performance Measurement ◽  
Performance Measures ◽  
New Technologies ◽  
Efficient Reduction ◽  
Tool Performance ◽  
Typical Performance ◽  
Substantial Investment ◽  
Integrity Management ◽  
Insight Into

In-line inspection (ILI) tools play an important role within integrity management and substantial investment is made to continuously advance performance of the existing technologies and, where necessary, to develop new technologies. Performance measurement is typically focused for the purpose of understanding the measured performance in relation to the ILI vendor specification and for the determination of residual uncertainty regarding pipeline integrity. These performance measures may not provide the necessary insight into what type of investment into a technology is necessary to further reduce residual uncertainty regarding pipeline integrity, and beyond that, what investment, as an operator, results in an effective and efficient reduction in uncertainty. The paper proposes a reliability based approach for investigating uncertainty associated with ultrasonic crack ILI technology for the purpose of identifying efficient investment into the technology that results in an effective and measurable improvement. Typical performance measures and novel performance measurement methods are presented and reviewed with respect to what information they can provide to assist in investment decisions. Finally, general observations are made regarding Enbridge’s experience using ultrasonic crack ILI technology and areas currently being investigated.

Sign in / Sign up

Export Citation Format

Share Document