Abstract There is a longstanding debate whether the Kolmogorov–Arnold representation theorem can explain use of more than one hidden layer in neural networks. The decomposes multivariate function into an interior and outer therefore has indeed similar structure as network with two layers. But there are distinctive differences. One main obstacles that depends on represented be wildly varying eve...

Watermarking is one of the best solutions for copyright protection and authentication of multimedia contents. In this paper a hybrid scheme is proposed using wavelet and shearlet transforms with singular value decomposition. For better security, Arnold map is used for encryption. Examining the results and comparing with other methods show that this hybrid proposed scheme with simultaneous utili...

The theory of sexual selection was formulated by Darwin (1871) to explain the origin of sexually dimorphic traits that are detrimental to survival. Darwin believed that sexual selection arises from either mate choice or intrasexual competition for mates, reasoning that such traits could evolve if they conferred a fitness advantage on their bearer. In part because of the obvious difficulties in ...

M Arnold--Chamney, S Bateman, K Owen, Jesudason, McDonald, O Pearson, N Sinclair, I Williamson, O, Donnell K, J Kelly

The Arnold conjecture yields a lower bound to the number of periodic classical trajectories in a Hamiltonian system. Here we count these trajectories with the help of a path integral, which we inspect using properties of the spectral flow of a Dirac operator in the background of a Sp(2N) valued gauge field. We compute the spectral flow from the Atiyah-Patodi-Singer index theorem, and apply the ...