Analysis of Extended Algebraic Immunity of Boolean Functions

AbstractAlgebraic immunity (AI) is a new cryptographic criterion proposed against algebraic attacks. Extended algebraic immunity (EAI) extends the concept of algebraic immunity, whose point is that a Boolean function f may be replaced by another Boolean function fc called the algebraic complement of f In this paper, we investigate EAI of Boolean functions. Firstly, we present a sufficient and necessary condition to judge AI of a Boolean function equals to its EAI. Secondly, we prove that two classes of Boolean functions with maximum AI also have optimal EAI. Finally, we analyze that the structure of the annihilators of Boolean functions with the algebraic complement

Tribological performances of fabric self-lubricating liner with different weft densities under severe working conditions

Several woven fabric self-lubricating liners with weft densities of 200-450 root/10cm in a spacing of 50 root/10cm have been prepared to investigate the tribological performances of the liner under severe working conditions, such as low velocity and heavy load (110, 179 and 248 MPa) and high velocity and light load (9, 18 and 27 m/min) by utilizing the self-lubricating liner performance assessment tester, and MMU-5G friction and wear tester respectively. The worn surface is characterized using confocal laser scanning microscopy. The tribological results show that the fabric self-lubricating liners with different weft densities share almost the same tribological property variation tendency. Fabric tightness affects the wear rate and the stability of wear resistance of liners under severe working conditions. The overall level of friction coefficient and the wear rate of liners with different weft densities are influenced by the cold flow degree of the polymer. In addition, proper weft density improves the tribological properties of liner and a preferred weft density for the liner under severe working conditions is found to be 300-350 root/10cm

Network Algebraization and Port Relationship for Power-Electronic-Dominated Power Systems

Different from the quasi-static network in the traditional power system, the dynamic network in the power-electronic-dominated power system should be considered due to rapid response of converters' controls. In this paper, a nonlinear differential-algebraic model framework is established with algebraic equations for dynamic electrical networks and differential equations for the (source) nodes, by generalizing the Kron reduction. The internal and terminal voltages of source nodes including converters are chosen as ports of nodes and networks. Correspondingly, the impact of dynamic network becomes clear, namely, it serves as a voltage divider and generates the terminal voltage based on the internal voltage of the sources instantaneously, even when the dynamics of inductance are included. With this simplest model, the roles of both nodes and the network become apparent.Simulations verify the proposed model framework in the modified 9-bus system.Comment: 4 pages, 6 figure

Laplacian-regularized graph bandits: Algorithms and theoretical analysis

We consider a stochastic linear bandit problem with multiple users, where the relationship between users is captured by an underlying graph and user preferences are represented as smooth signals on the graph. We introduce a novel bandit algorithm where the smoothness prior is imposed via the random-walk graph Laplacian, which leads to a single-user cumulative regret scaling as $\tilde{\mathcal{O}}(\Psi d \sqrt{T})$ with time horizon $T$, feature dimensionality $d$, and the scalar parameter $\Psi \in (0,1)$ that depends on the graph connectivity. This is an improvement over $\tilde{\mathcal{O}}(d \sqrt{T})$ in \algo{LinUCB}~\Ccite{li2010contextual}, where user relationship is not taken into account. In terms of network regret (sum of cumulative regret over $n$ users), the proposed algorithm leads to a scaling as $\tilde{\mathcal{O}}(\Psi d\sqrt{nT})$, which is a significant improvement over $\tilde{\mathcal{O}}(nd\sqrt{T})$ in the state-of-the-art algorithm \algo{Gob.Lin} \Ccite{cesa2013gang}. To improve scalability, we further propose a simplified algorithm with a linear computational complexity with respect to the number of users, while maintaining the same regret. Finally, we present a finite-time analysis on the proposed algorithms, and demonstrate their advantage in comparison with state-of-the-art graph-based bandit algorithms on both synthetic and real-world data