Quadratically-Regularized Optimal Transport on Graphs

Optimal transportation provides a means of lifting distances between points on a geometric domain to distances between signals over the domain, expressed as probability distributions. On a graph, transportation problems can be used to express challenging tasks involving matching supply to demand with minimal shipment expense; in discrete language, these become minimum-cost network flow problems. Regularization typically is needed to ensure uniqueness for the linear ground distance case and to improve optimization convergence; state-of-the-art techniques employ entropic regularization on the transportation matrix. In this paper, we explore a quadratic alternative to entropic regularization for transport over a graph. We theoretically analyze the behavior of quadratically-regularized graph transport, characterizing how regularization affects the structure of flows in the regime of small but nonzero regularization. We further exploit elegant second-order structure in the dual of this problem to derive an easily-implemented Newton-type optimization algorithm.Comment: 27 page

New potential hydrocarbon source-rocks in the Lower Eocene Metlaoui Formation (Central-Northern Tunisia, Northern Africa)

New potential hydrocarbon source-rocks in the Lower EoceneMetlaoui Formation (Central-Northern Tunisia, Northern Africa)Significant quantities of organic matter accumulated and were preserved in central-northern Tunisia during theYpresian (Early Eocene). The organic geochemical characterization of the organic-rich facies of the YpresianMetlaoui Formation (Ousselat and Es-Sfeïa sections) shows their significant potential as source rocks andincreases interest in the Central-Northern Tunisia oil play. The TOC content in these rocks ranges from 0.09 to3.71% suggesting their petroleum potential, whereas their T maxfluctuates from 429 to 439°C. These values andthe predominance of the hetero compounds (NSO; 2-95%) point to low organic matter maturation. The diversematurity levels reported for these organic-rich rocks never reached the conventional oil window peak stage andresulted from their different locationswithin the basin. The HI values and the high saturate concentrations(1-91%) compared to aromatics (1-33%), as well as the predominance of short-chain n-alkanes centered at n-C18 and n-C20 are indicative of unequivocal type-II kerogen. The fluctuation of the pristane/phytane ratio(0.97-2.53) records changes of the basin redox conditions, which mainly evolved around the sub-oxic rang

Organic Geochemistry of the Cenomanian-Turonian Bahloul Formation Petroleum Source Rock, Central and Northern Tunisia

International audienceTotal organic carbon (TOC) determination, Rock-Eval pyrolysis, extractable organic matter content (EOM) fractionation, gas chromatography (GC) and gas chromatography-mass spectrometry (GC-MS) analyses, were carried out on 79 samples from eleven outcrop cross sections of the Bahloul Formation in central and northern Tunisia. The TOC content varied between 0.23 to 35.6%, the highest average values (18.73%, 8.46% and 4.02%) being at the east of the study area (at Ain Zakkar, Oued Bahloul and Dyr Ouled Yahia localities, respectively). The Rock-Eval maximum pyrolysis temperature (Tmax) values in the 424-453°C range delineated a general east-west trend increase in the organic matter (OM) maturity. The disparity in hydrogen index (HI) values, in the range 114-824 mg hydrocarbons (HC) g−1 TOC, is relevant for the discrepancy in the level of OM preservation and maturity among localities and samples. The n-alkane distributions, maximizing in the C17 to C20 range, are typical for a marine planktonic origin, whereas pristine/phytane (Pr/Ph) average values in the 1-2 range indicate an oxic to suboxic depositional environment. Pr/n-C17 and Ph/n-C18 ratios in the 0.38-6.2 and 0.68-3.25 range, respectively, are consistent with other maturity indicators and the contribution of specific bacteria to phytol as a precursor of isoprenoids. The thermal maturity varies between late diagenesis to main-stage of petroleum generation based on the optic and the cis-trans isomerisation of the C29 sterane [20S/(20S+20R) and 14β(H),17β(H)/(14β(H),17β(H)+14α(H),17α(H)), respectively] and the terpane [18α(H)22,29,30-Trisnorneohopane/(18α(H)22,29,30-Trisnorneohopane+17α(H)22,29,30-Trisnorhopane): Ts/(Ts+Tm)] ratios. The Bahloul OM is represented by an open marine to estuarine algal facies with a specific bacterial contribution as revealed by the relative abundance of the ααα-20R C27 (33-44%), C28 (22-28%) and C29 (34-41%) steranes and by the total terpanes/total steranes ratio (1.2-5.33). These results attested that the Bahloul OM richness was controlled both by an oxygen minimum zone induced by high productivity and restricted circulation in narrow half graben structures and around diapirs of the Triassic salt

Optimisation du nombre de spires et des angles de commandes d'un moteur à réluctance à double saillance pour application de traction électrique

National audienceDans le but d'optimiser les performances de l'ensemble machine à réluctance variable et son convertisseur nous traitons simultanément dans cet article, l'aspect dimensionnement de la machine en étudiant l'influence du nombre de spires et l'aspect commande du convertisseur statique en proposant une optimisation des angles de commande. Nous mettrons en évidence ces deux aspects en exposant les résultats de simulations