Learning and generation of long-range correlated sequences

We study the capability to learn and to generate long-range, power-law correlated sequences by a fully connected asymmetric network. The focus is set on the ability of neural networks to extract statistical features from a sequence. We demonstrate that the average power-law behavior is learnable, namely, the sequence generated by the trained network obeys the same statistical behavior. The interplay between a correlated weight matrix and the sequence generated by such a network is explored. A weight matrix with a power-law correlation function along the vertical direction, gives rise to a sequence with a similar statistical behavior.Comment: 5 pages, 3 figures, accepted for publication in Physical Review

Monitoring of Traffic Manoeuvres with Imprecise Information

In monitoring, we algorithmically check if a single behavior satisfies a property. Here, we consider monitoring for Multi-Lane Spatial Logic (MLSL). The behavior is given as a finite transition sequence of MLSL and the property is that a spatial MLSL formula should hold at every point in time within the sequence. In our procedure we transform the transition sequence and the formula to the first-order theory of real-closed fields, which is decidable, such that the resulting formula is valid iff the MLSL formula holds throughout the transition sequence. We then assume that temporal data may have an error of up to $\varepsilon$, and that spatial data may have an error of up to $\delta$. We extend our procedure to check if the MLSL formula $\varepsilon$-$\delta$-robustly holds throughout the transition sequence.Comment: In Proceedings FVAV 2017, arXiv:1709.0212

Molecular recognition by van der Waals interaction between polymers with sequence-specific polarizabilities

We analyze van der Waals interactions between two rigid polymers with sequence-specific, anisotropic polarizabilities along the polymer backbones, so that the dipole moments fluctuate parallel to the polymer backbones. Assuming that each polymer has a quenched-in polarizability sequence which reflects, for example, the polynucleotide sequence of a double-stranded DNA molecule, we study the van der Waals interaction energy between a pair of such polymers with rod-like structure for the cases where their respective polarizability sequences are (i) distinct and (ii) identical, with both zero and non-zero correlation length of the polarizability correlator along the polymer backbones in the latter case. For identical polymers, we find a novel $r^{-5}$ scaling behavior of the van der Waals interaction energy for small inter-polymer separation $r$, in contradistinction to the $r^{-4}$ scaling behavior of distinct polymers, with furthermore a pronounced angular dependence favoring attraction between sufficiently aligned identical polymers. Such behavior can assist the molecular recognition between polymers.Comment: 16 pages, 5 figure