Abarzua, N., Pomareda, R., & Vega, O. (2018). Feet in orthogonal-Buekenhout-Metz unitals. Adv. Geom., 18(2), 229–236.
Abstract: Given an orthogonal-Buekenhout-Metz unital U-alpha,U-beta, embedded in PG(2, q(2)), and a point P is not an element of U-alpha,U-beta, we study the set tau(p)(U-alpha,U-beta) of feet of P in U-alpha,U-beta. We characterize geometrically each of these sets as either q + 1 collinear points or as q + 1 points partitioned into two arcs. Other results about the geometry of these sets are also given.
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Agostini, C. A., Silva, C., & Nasirov, S. (2017). Failure of Energy Mega-Projects in Chile: A Critical Review from Sustainability Perspectives. Sustainability, 9(6), 17 pp.
Abstract: A number of successive energy crises over the last decade due to the lack of a balanced investment planning in the energy sector in Chile has led to a strong dependence on external sources and also doubled energy prices in the country, thus posing a significant challenge to the local economy. With the purpose of reaching long-term goals while simultaneously addressing short-term urgencies, Chile seeks to build a consistent and integrated energy policy in order to attract investment in the sector. Despite an overall attractive investment climate and encouraging market conditions in the country, the energy sector has been adversely affected, in particular, by the communities' opposition to mega-projects based on their expected environmental and social impacts. The study highlights recent experiences of energy generation mega-projects in terms of addressing aspects of sustainability. Based on these experiences, it discusses underdeveloped role of environmental evaluations and the main regulatory challenges ahead, recommending then public policies to effectively address these challenges.
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Akian, M., Gaubert, S., & Hochart, A. (2020). A Game Theory Approach To The Existence And Uniqueness Of Nonlinear Perron-Frobenius Eigenvectors. Discret. Contin. Dyn. Syst., 40(1), 207–231.
Abstract: We establish a generalized Perron-Frobenius theorem, based on a combinatorial criterion which entails the existence of an eigenvector for any nonlinear order-preserving and positively homogeneous map f acting on the open orthant R->0(n). This criterion involves dominions, i.e., sets of states that can be made invariant by one player in a two-person game that only depends on the behavior of f “at infinity”. In this way, we characterize the situation in which for all alpha, beta > 0, the “slice space” S-alpha(beta) :={x is an element of R->0(n) vertical bar alpha x <= f(x) <= beta x} is bounded in Hilbert's projective metric, or, equivalently, for all uniform perturbations g of f, all the orbits of g are bounded in Hilbert's projective metric. This solves a problem raised by Gaubert and Gunawardena (Trans. AMS, 2004). We also show that the uniqueness of an eigenvector is characterized by a dominion condition, involving a different game depending now on the local behavior of f near an eigenvector. We show that the dominion conditions can be verified by directed hypergraph methods. We finally illustrate these results by considering specific classes of nonlinear maps, including Shapley operators, generalized means and nonnegative tensors.
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Cominetti, R., Roshchina, V., & Williamson, A. (2019). A counterexample to De Pierro's conjecture on the convergence of under-relaxed cyclic projections. Optimization, 68(1), 3–12.
Abstract: The convex feasibility problem consists in finding a point in the intersection of a finite family of closed convex sets. When the intersection is empty, a best compromise is to search for a point that minimizes the sum of the squared distances to the sets. In 2001, de Pierro conjectured that the limit cycles generated by the -under-relaxed cyclic projection method converge when towards a least squares solution. While the conjecture has been confirmed under fairly general conditions, we show that it is false in general by constructing a system of three compact convex sets in for which the -under-relaxed cycles do not converge.
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Gatica, M., Navarro, C. F., Lavado, A., Reig, G., Pulgar, E., Llanos, P., et al. (2023). VolumePeeler: a novel FIJI plugin for geometric tissue peeling to improve visualization and quantification of 3D image stacks. BMC Bioinformatics, 24(1), 283.
Abstract: Motivation Quantitative descriptions of multi-cellular structures from optical microscopy imaging are prime to understand the variety of three-dimensional (3D) shapes in living organisms. Experimental models of vertebrates, invertebrates and plants, such as zebrafish, killifish, Drosophila or Marchantia, mainly comprise multilayer tissues, and even if microscopes can reach the needed depth, their geometry hinders the selection and subsequent analysis of the optical volumes of interest. Computational tools to “peel” tissues by removing specific layers and reducing 3D volume into planar images, can critically improve visualization and analysis.Results We developed VolumePeeler, a versatile FIJI plugin for virtual 3D “peeling” of image stacks. The plugin implements spherical and spline surface projections. We applied VolumePeeler to perform peeling in 3D images of spherical embryos, as well as non-spherical tissue layers. The produced images improve the 3D volume visualization and enable analysis and quantification of geometrically challenging microscopy datasets.
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Mulders, G. D., Pascucci, I., Ciesla, F. J., & Fernandes, R. B. (2021). The Mass Budgets and Spatial Scales of Exoplanet Systems and Protoplanetary Disks. Astrophys. J., 920(2), 66.
Abstract: Planets are born from disks of gas and dust, and observations of protoplanetary disks are used to constrain the initial conditions of planet formation. However, dust mass measurements of Class II disks with ALMA have called into question whether they contain enough solids to build the exoplanets that have been detected to date. In this paper, we calculate the mass and spatial scale of solid material around Sun-like stars probed by transit and radial velocity exoplanet surveys and compare those to the observed dust masses and sizes of Class II disks in the same stellar-mass regime. We show that the apparent mass discrepancy disappears when accounting for observational selection and detection biases. We find a discrepancy only when the planet formation efficiency is below 100%, or if there is a population of undetected exoplanets that significantly contributes to the mass in solids. We identify a positive correlation between the masses of planetary systems and their respective orbital periods, which is consistent with the trend between the masses and the outer radii of Class II dust disks. This implies that, despite a factor 100 difference in spatial scale, the properties of protoplanetary disks seem to be imprinted on the exoplanet population.
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Ogunmodede, O., Lamas, P., Brickey, A., Bogin, G., & Newman, A. (2022). Underground production scheduling with ventilation and refrigeration considerations. Optim. Eng., 23(3), 1677–1705.
Abstract: Underground mine production scheduling determines when, if ever, activities associated with the extraction of ore should be executed. The accumulation of heat in the mine where operators are working is a major concern. At the time of this writing, production scheduling and ventilation decisions are not made in concert. Correspondingly, heat limitations are largely ignored. Our mixed-integer program maximizes net present value subject to constraints on precedence, and mill and extraction capacities with the consideration of heat using thermodynamic principles, while affording the option of activating refrigeration to mitigate heat accumulation. In seconds to hours, depending on the problem size (up to thousands of activities and 900 daily time periods), a corresponding methodology that exploits the mathematical problem structure provides schedules that maintain a safe working environment for mine operators; optimality gaps are no more than 15% and average less than half that for otherwise-intractable instances.
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Yee, S. W., Winn, J. N., Hartman, J. D., Rodriguez, J. E., Zhou, G., Quinn, S. N., et al. (2022). The TESS Grand Unified Hot Jupiter Survey. I. Ten TESS Planets. Astron. J., 164(2), 70.
Abstract: Hot Jupiters-short-period giant planets-were the first extrasolar planets to be discovered, but many questions about their origin remain. NASA's Transiting Exoplanet Survey Satellite (TESS), an all-sky search for transiting planets, presents an opportunity to address these questions by constructing a uniform sample of hot Jupiters for demographic study through new detections and unifying the work of previous ground-based transit surveys. As the first results of an effort to build this large sample of planets, we report here the discovery of 10 new hot Jupiters (TOI-2193A b, TOI-2207b, TOI-2236b, TOI-2421b, TOI-2567b, TOI-2570b, TOI-3331b, TOI-3540A b, TOI-3693b, TOI-4137b). All of the planets were identified as planet candidates based on periodic flux dips observed by TESS, and were subsequently confirmed using ground-based time-series photometry, high-angular-resolution imaging, and high-resolution spectroscopy coordinated with the TESS Follow-up Observing Program. The 10 newly discovered planets orbit relatively bright F and G stars (G < 12.5, T (eff) between 4800 and 6200 K). The planets' orbital periods range from 2 to 10 days, and their masses range from 0.2 to 2.2 Jupiter masses. TOI-2421b is notable for being a Saturn-mass planet and TOI-2567b for being a “sub-Saturn,” with masses of 0.322 +/- 0.073 and 0.195 +/- 0.030 Jupiter masses, respectively. We also measured a detectably eccentric orbit (e = 0.17 +/- 0.05) for TOI-2207b, a planet on an 8 day orbit, while placing an upper limit of e < 0.052 for TOI-3693b, which has a 9 day orbital period. The 10 planets described here represent an important step toward using TESS to create a large and statistically useful sample of hot Jupiters.
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