|Identifying groundwater recharge pathways in the Moscow sub-basin
Candel, J.H.J. ; Brooks, E.S. ; Verhoeff, Eric ; Dobre, Mariana ; Sanchez-Murillo, Ricardo ; Grader, Jr., George W. ; Dijksma, R. - \ 2016
Continual groundwater decline over the last 80 years in the Moscow-Pullman basin is motivating communities to explore a wide range of strategies ranging from reservoir development to direct injection to aquifers to ensure a sustainable regional water supply. Historic pumping records indicate the shallow Wanapum aquifer in the Moscow region does receive recharge however it is less certain that the deeper Grand Ronde aquifer is receiving any significant recharge. Moreover there is not a clear consensus in the region of the location of the major aquifer recharge flow paths. In this study we used both distributed hydrologic modeling based on detailed soil mapping and stable isotope tracers to explore and evaluate potential groundwater recharge pathways in the Moscow sub-basin. Modelling results indicate that subsurface water flow off the forested granitics in eastern margin of the sub-basin is likely a significant source of recharge. Biweekly water samples taken from 22 wells and 2 springs and high frequency streamflow and precipitation samples collected over a two year period throughout the Moscow sub-basin were analyzed for stable isotopes of hydrogen and oxygen. Frequency analysis of these stable isotope data suggest the some wells are receiving recharge. Furthermore many of these wells exist on the eastern margin of the sub-basin lending further support to the hypothesis that this region should be considered to be a critical ground recharge zone.
A copositive formulation for the stability number of infinite graphs
Dobre, Cristian ; Dür, Mirjam ; Frerick, Leonhard ; Vallentin, Frank - \ 2016
Mathematical Programming 160 (2016)1. - ISSN 0025-5610 - p. 65 - 83.
Completely positive cone of measures - Copositive cone of continuous Hilbert-Schmidt kernels - Extreme rays - Stability number
In the last decade, copositive formulations have been proposed for a variety of combinatorial optimization problems, for example the stability number (independence number). In this paper, we generalize this approach to infinite graphs and show that the stability number of an infinite graph is the optimal solution of some infinite-dimensional copositive program. For this we develop a duality theory between the primal convex cone of copositive kernels and the dual convex cone of completely positive measures. We determine the extreme rays of the latter cone, and we illustrate this theory with the help of the kissing number problem.
Exploiting symmetry in copositive programs via semidefinite hierarchies
Dobre, C. ; Vera, J. - \ 2015
Mathematical Programming 151 (2015)2. - ISSN 0025-5610 - p. 659 - 680.
Copositive programming is a relative young field which has evolved into a highly active research area in mathematical optimization. An important line of research is to use semidefinite programming to approximate conic programming over the copositive cone. Two major drawbacks of this approach are the rapid growth in size of the resulting semidefinite programs, and the lack of information about the quality of the semidefinite programming approximations. These drawbacks are an inevitable consequence of the intractability of the generic problems that such approaches attempt to solve. To address such drawbacks, we develop customized solution approaches for highly symmetric copositive programs, which arise naturally in several contexts. For instance, symmetry properties of combinatorial problems are typically inherited when they are addressed via copositive programming. As a result we are able to compute new bounds for crossing number instances in complete bipartite graphs.
Mathematical properties of the regular *-representation of matrix *-algebras with applications to semidefinite programming
Dobre, C. - \ 2013
Numerical Algebra, Control and Optimization 3 (2013)2. - ISSN 2155-3289 - p. 367 - 378.
In this paper we give a proof for the special structure of the Wedderburn decomposition of the regular *-representation of a given matrix *-algebra. This result was stated without proof in: de Klerk, E., Dobre, C. and Pasechnik, D.V.: Numerical block diagonalization of matrix *-algebras with application to semidefinite programming, Mathematical Programming-B, 129 (2011), 91--111; and is used in applications of semidefinite programming (SDP) for structured combinatorial optimization problems. In order to provide the proof for this special structure we derive several other mathematical properties of the regular *-representation.
|EU Environmental Policy
Bruyninckx, H.E.A. - \ 2005
In: Handbook on EU Affairs / Dobre, A.M., Martins-Gistelinck, M., Polacek, R., Hunink, R., Leuven : Institute for International and European Policy - p. 213 - 225.