Character sets of strings

Given a string S over a finite alphabet Σ, the character set (also called the fingerprint) of a substring S^′ of S is the subset CΣ of the symbols occurring in S^′. The study of the character sets of all the substrings of a given string (or a given collection of strings) appears in several domains such as rule induction for natural language processing or comparative genomics. Several computational problems concerning the character sets of a string arise from these applications, especially:

(1) Output all the maximal locations of substrings having a given character set.

(2) Output for each character set C occurring in a given string (or a given collection of strings) all the maximal locations of C.

Denoting by n the total length of the considered string or collection of strings, we solve the first problem in Θ(n) time using Θ(n) space. We present two algorithms solving the second problem. The first one runs in Θ(n²) time using Θ(n) space. The second algorithm has Θ(n|Σ|log|Σ|) time and Θ(n) space complexity and is an adaptation of an algorithm by Amir et al. [A. Amir, A. Apostolico, G.M. Landau, G. Satta, Efficient text fingerprinting via Parikh mapping, J. Discrete Algorithms 26 (2003) 1–13].     

Anisotropic Meshless Frames on ℝ n

We present a construction of anisotropic multiresolution and anisotropic wavelet frames based on multilevel ellipsoid covers (dilations) of ℝ ⁿ . The wavelets we construct are C ^∞ functions, can have any prescribed number of vanishing moments and fast decay with respect to the anisotropic quasi-distance induced by the cover. The dual wavelets are also C ^∞, with the same number of vanishing moments, but with only mild decay with respect to the quasi-distance. An alternative construction yields a meshless frame whose elements do not have vanishing moments, but do have fast anisotropic decay.     

Nanoparticle dispersion laser

Lasing action from a dispersion of nanoparticles is reported for the first time to our knowledge. The nanoparticles are Nd(2)O(3) modified with dimethyldichlorosilane (DMDCS) in dimethylsulfoxide. The laser was pumped with a pulsed laser at 802 nm and yielded 2.7 mJ with a slope efficiency of 50%. This was compared to a standard Nd-doped phosphate glass that yielded very similar results in the same setup.     

Migration and Precipitation of Platinum in Anion-Exchange Membrane Fuel Cells

Despite the recent progress in increasing the power generation of Anion-exchange membrane fuel cells (AEMFCs), their durability is still far lower than that of Proton exchange membrane fuel cells (PEMFCs). Using the complementary techniques of X-ray micro-computed tomography (CT), Scanning Electron Microscopy (SEM) and Energy Dispersive X-ray (EDX) spectroscopy, we have identified Pt ion migration as an important factor to explain the decay in performance of AEMFCs. In alkaline media Pt⁺² ions are easily formed which then either undergo dissolution into the carbon support or migrate to the membrane. In contrast to PEMFCs, where hydrogen cross over reduces the ions forming a vertical “Pt line” within the membrane, the ions in the AEM are trapped by charged groups within the membrane, leading to disintegration of the membrane and failure. Diffusion of the metal components is still observed when the Pt/C of the cathode is substituted with a FeCo−N−C catalyst, but in this case the Fe and Co ions are not trapped within the membrane, but rather migrate into the anode, thereby increasing the stability of the membrane.