Multi-dimensional Boltzmann Sampling of Languages

This paper addresses the uniform random generation of words from a context-free language (over an alphabet of size $k$), while constraining every letter to a targeted frequency of occurrence. Our approach consists in a multidimensional extension of Boltzmann samplers \cite{Duchon2004}. We show that, under mostly \emph{strong-connectivity} hypotheses, our samplers return a word of size in $[(1-\varepsilon)n, (1+\varepsilon)n]$ and exact frequency in $\mathcal{O}(n^{1+k/2})$ expected time. Moreover, if we accept tolerance intervals of width in $\Omega(\sqrt{n})$ for the number of occurrences of each letters, our samplers perform an approximate-size generation of words in expected $\mathcal{O}(n)$ time. We illustrate these techniques on the generation of Tetris tessellations with uniform statistics in the different types of tetraminoes.Comment: 12p

LS-CS-residual (LS-CS): Compressive Sensing on Least Squares Residual

We consider the problem of recursively and causally reconstructing time sequences of sparse signals (with unknown and time-varying sparsity patterns) from a limited number of noisy linear measurements. The sparsity pattern is assumed to change slowly with time. The idea of our proposed solution, LS-CS-residual (LS-CS), is to replace compressed sensing (CS) on the observation by CS on the least squares (LS) residual computed using the previous estimate of the support. We bound CS-residual error and show that when the number of available measurements is small, the bound is much smaller than that on CS error if the sparsity pattern changes slowly enough. We also obtain conditions for "stability" of LS-CS over time for a signal model that allows support additions and removals, and that allows coefficients to gradually increase (decrease) until they reach a constant value (become zero). By "stability", we mean that the number of misses and extras in the support estimate remain bounded by time-invariant values (in turn implying a time-invariant bound on LS-CS error). The concept is meaningful only if the bounds are small compared to the support size. Numerical experiments backing our claims are shown.Comment: Accepted (with mandatory minor revisions) to IEEE Trans. Signal Processing. 12 pages, 5 figure

Integrating fluctuations into distribution of resources in transportation networks

We propose a resource distribution strategy to reduce the average travel time in a transportation network given a fixed generation rate. Suppose that there are essential resources to avoid congestion in the network as well as some extra resources. The strategy distributes the essential resources by the average loads on the vertices and integrates the fluctuations of the instantaneous loads into the distribution of the extra resources. The fluctuations are calculated with the assumption of unlimited resources, where the calculation is incorporated into the calculation of the average loads without adding to the time complexity. Simulation results show that the fluctuation-integrated strategy provides shorter average travel time than a previous distribution strategy while keeping similar robustness. The strategy is especially beneficial when the extra resources are scarce and the network is heterogeneous and lowly loaded.Comment: 14 pages, 4 figure

Experimental and theoretical characterization of microbial bioanodes formed in pulp and paper mill effluent in electrochemically controlled conditions

Microbial bioanodes were formed in pulp and paper effluent on graphite plate electrodes under constant polarization at -0.3 V/SCE, without any addition of nutriment or substrate. The bioanodes were characterized in 3-electrode set-ups, in continuous mode, with hydraulic retention times from 6 to 48 h and inlet COD from 500 to 5200 mg/L. Current densities around 4 A/m2 were obtained and voltammetry curves indicated that 6 A/m2 could be reached at +0.1 V/SCE. A theoretical model was designed, which allowed the effects of HRT and COD to be distinguished in the complex experimental data obtained with concomitant variations of the two parameters. COD removal due to the electrochemical process was proportional to the hydraulic retention time and obeyed a Michaelis–Menten law with respect to the COD of the outlet flow, with a Michaelis constant KCOD of 400 mg/L. An inhibition effect occurred above inlet COD of around 3000 mg/L