Monomial Hopf Algebras

Let $K$ be a field of characteristic 0 containing all roots of unity. We classify all the Hopf structures on monomial $K$-coalgebras, or, in dual version, on monomial $K$-algebras.Comment: 24 page

Towards Query-Efficient Black-Box Adversary with Zeroth-Order Natural Gradient Descent

Despite the great achievements of the modern deep neural networks (DNNs), the vulnerability/robustness of state-of-the-art DNNs raises security concerns in many application domains requiring high reliability. Various adversarial attacks are proposed to sabotage the learning performance of DNN models. Among those, the black-box adversarial attack methods have received special attentions owing to their practicality and simplicity. Black-box attacks usually prefer less queries in order to maintain stealthy and low costs. However, most of the current black-box attack methods adopt the first-order gradient descent method, which may come with certain deficiencies such as relatively slow convergence and high sensitivity to hyper-parameter settings. In this paper, we propose a zeroth-order natural gradient descent (ZO-NGD) method to design the adversarial attacks, which incorporates the zeroth-order gradient estimation technique catering to the black-box attack scenario and the second-order natural gradient descent to achieve higher query efficiency. The empirical evaluations on image classification datasets demonstrate that ZO-NGD can obtain significantly lower model query complexities compared with state-of-the-art attack methods.Comment: accepted by AAAI 202

Influence of Molecular Organization on the Electrical Characteristics of {\pi}-conjugated Self-assembled Monolayers

Two new thiol compounds with {\sigma}-{\pi}-{\sigma} structure were synthesized and self-assembled on gold substrates. The morphology and the structural characterization of SAMs assessed by infrared spectroscopy, contact angle, XPS, electrochemistry and scanning tunneling microscopy (STM) show the formation of monolayers. SAMs with a terthiophene (3TSH) core as conjugated system are much better organized compared to those with a naphthalene carbodiimide (NaphSH) core as demonstrated by the cyclic voltammetry and STM studies. The surface concentration of 3TSH and NaphSH is respectively three and six times lower than ordered SAMs of pure alkyl chains. A large number of I/V characteristics have been studied either by STS measurements on gold substrates or by C-AFM on gold nanodots. Transition Voltage Spectroscopy (TVS) was used to clearly identify the transport in these partially organized monolayers. The chemical nature of the conjugated system, donor for 3TSH and acceptor for NaphSH, involves an opposite rectification associated to the asymmetrical coupling of the molecular orbitals and the electrodes. The conductance histograms show that the 3TSH junctions are less dispersed than those of NaphSH junctions. This is explained by a better control of the molecular organization in the molecular junctions.Comment: Full paper with supporting informatio