The definition of antipower introduced by Fici et al. (ICALP 2016) captures the notion of being the opposite of a power : a sequence of k pairwise distinct blocks of the same length. Recently, Alamro et al. (CPM 2019) defined a string to have an antiperiod if it is a prefix of an antipower, and gave complexity bounds for the offline computation of the minimum antiperiod and all the antiperiods of a word. In this paper, we address the same problems in the online setting. Our solutions rely on new arrays that compactly and incrementally store antiperiods and antipowers as the word grows, obtaining in the process this information for all the word's prefixes. We show how to compute those arrays online in O(n log n) space, O(n log n) time, and o(n) delay per character, for any constant > 0. Running times are worst-case and hold with high probability. We also discuss more space-efficient solutions returning the correct result with high probability, and small data structures to support random access to those arrays.

Kinetics of coordination of Pd(II) by the macrocyclic porphyrin 5,10,15,20-tetrakis(1-methyl-4-pyridyl)porphyrin (H2P4+) is investigated and confirms quantitative formation of a planar PdP4+complex at room temperature (formation rate 0.19 M-1 s-1 at 25 °C, 0.2 M NaCl, pH 3). Then, the binding ability to DNA of the pre-formed PdP4+complex is analysed. To achieve this aim, spectrophotometry, spectrofluorometry and viscometry are used. Thermodynamic parameters for binding, obtained by the temperature dependence of the equilibrium constants, are deltaH = -71 kJ mol-1 and deltaS = -134 J mol-1 K-1. These values, being both highly negative, agree with full PdP4+intercalation into DNA. Moreover, kinetics of the binding reaction is analysed by the T-jump technique (reaction times in the 1-5 ms range). Experiments on the porphyrin ligand retention on negative SDS and positive DTAC micellar surfaces are also done. Taken altogether, these data provide mechanistic details on complex formation and on DNA binding and relevant energies and driving forces. It is found that interaction between PdP4+and base pairs is very strong (KabsDNA = 8.0E5 M-1 at 25 °C, 1.0 M NaCl), not only owing to the high positive charge borne by the complex, but also to the contribution of high hydrophobicity of the porphyrin ring. In the dye/DNA complex, PdP4+is buried into the helix, as confirmed also by fluorescence quenching tests. Both presence and type of metal ion play a major role, as lower affinity and lower induced helix conformation changes are found in the case of the H2P4+/DNA and CuP4+/DNA systems