Optimal Investment in the Development of Oil and Gas Field

Let an oil and gas field consists of clusters in each of which an investor can launch at most one project. During the implementation of a particular project, all characteristics are known, including annual production volumes, necessary investment volumes, and profit. The total amount of investments that the investor spends on developing the field during the entire planning period we know. It is required to determine which projects to implement in each cluster so that, within the total amount of investments, the profit for the entire planning period is maximum. The problem under consideration is NP-hard. However, it is solved by dynamic programming with pseudopolynomial time complexity. Nevertheless, in practice, there are additional constraints that do not allow solving the problem with acceptable accuracy at a reasonable time. Such restrictions, in particular, are annual production volumes. In this paper, we considered only the upper constraints that are dictated by the pipeline capacity. For the investment optimization problem with such additional restrictions, we obtain qualitative results, propose an approximate algorithm, and investigate its properties. Based on the results of a numerical experiment, we conclude that the developed algorithm builds a solution close (in terms of the objective function) to the optimal one

Parent formulation at the Lagrangian level

The recently proposed first-order parent formalism at the level of equations of motion is specialized to the case of Lagrangian systems. It is shown that for diffeomorphism-invariant theories the parent formulation takes the form of an AKSZ-type sigma model. The proposed formulation can be also seen as a Lagrangian version of the BV-BRST extension of the Vasiliev unfolded approach. We also discuss its possible interpretation as a multidimensional generalization of the Hamiltonian BFV--BRST formalism. The general construction is illustrated by examples of (parametrized) mechanics, relativistic particle, Yang--Mills theory, and gravity.Comment: 26 pages, discussion of the truncation extended, typos corrected, references adde

First order parent formulation for generic gauge field theories

We show how a generic gauge field theory described by a BRST differential can systematically be reformulated as a first order parent system whose spacetime part is determined by the de Rham differential. In the spirit of Vasiliev's unfolded approach, this is done by extending the original space of fields so as to include their derivatives as new independent fields together with associated form fields. Through the inclusion of the antifield dependent part of the BRST differential, the parent formulation can be used both for on and off-shell formulations. For diffeomorphism invariant models, the parent formulation can be reformulated as an AKSZ-type sigma model. Several examples, such as the relativistic particle, parametrized theories, Yang-Mills theory, general relativity and the two dimensional sigma model are worked out in details.Comment: 36 pages, additional sections and minor correction

Generalized quark-antiquark potential at weak and strong coupling

We study a two-parameter family of Wilson loop operators in N=4 supersymmetric Yang-Mills theory which interpolates smoothly between the 1/2 BPS line or circle and a pair of antiparallel lines. These observables capture a natural generalization of the quark-antiquark potential. We calculate these loops on the gauge theory side to second order in perturbation theory and in a semiclassical expansion in string theory to one-loop order. The resulting determinants are given in integral form and can be evaluated numerically for general values of the parameters or analytically in a systematic expansion around the 1/2 BPS configuration. We comment about the feasibility of deriving all-loop results for these Wilson loops.Comment: 43 pages: 15 comprising the main text and 25 for detailed appendice

Linear broadening of the confining string in Yang-Mills theory at low temperature

The logarithmic broadening predicted by the systematic low-energy effective field theory for the confining string has recently been verified in numerical simulations of (2+1)-d SU(2) lattice Yang-Mills theory at zero temperature. The same effective theory predicts linear broadening of the string at low non-zero temperature. In this paper, we verify this prediction by comparison with very precise Monte Carlo data. The comparison involves no additional adjustable parameters, because the low-energy constants of the effective theory have already been fixed at zero temperature. It yields very good agreement between the underlying Yang-Mills theory and the effective string theory.Comment: 10 pages, 3 figures. Version published in JHEP; improved figures 1 and

Inductively guided circuits for ultracold dressed atoms

Recent progress in optics, atomic physics and material science has paved the way to study quantum effects in ultracold atomic alkali gases confined to non-trivial geometries. Multiply connected traps for cold atoms can be prepared by combining inhomogeneous distributions of DC and radio-frequency electromagnetic fields with optical fields that require complex systems for frequency control and stabilization. Here we propose a flexible and robust scheme that creates closed quasi-one-dimensional guides for ultracold atoms through the ‘dressing’ of hyperfine sublevels of the atomic ground state, where the dressing field is spatially modulated by inductive effects over a micro-engineered conducting loop. Remarkably, for commonly used atomic species (for example, 7Li and 87Rb), the guide operation relies entirely on controlling static and low-frequency fields in the regimes of radio-frequency and microwave frequencies. This novel trapping scheme can be implemented with current technology for micro-fabrication and electronic control

Evidence for the role of EPHX2 gene variants in anorexia nervosa.

Anorexia nervosa (AN) and related eating disorders are complex, multifactorial neuropsychiatric conditions with likely rare and common genetic and environmental determinants. To identify genetic variants associated with AN, we pursued a series of sequencing and genotyping studies focusing on the coding regions and upstream sequence of 152 candidate genes in a total of 1205 AN cases and 1948 controls. We identified individual variant associations in the Estrogen Receptor-ß (ESR2) gene, as well as a set of rare and common variants in the Epoxide Hydrolase 2 (EPHX2) gene, in an initial sequencing study of 261 early-onset severe AN cases and 73 controls (P=0.0004). The association of EPHX2 variants was further delineated in: (1) a pooling-based replication study involving an additional 500 AN patients and 500 controls (replication set P=0.00000016); (2) single-locus studies in a cohort of 386 previously genotyped broadly defined AN cases and 295 female population controls from the Bogalusa Heart Study (BHS) and a cohort of 58 individuals with self-reported eating disturbances and 851 controls (combined smallest single locus P<0.01). As EPHX2 is known to influence cholesterol metabolism, and AN is often associated with elevated cholesterol levels, we also investigated the association of EPHX2 variants and longitudinal body mass index (BMI) and cholesterol in BHS female and male subjects (N=229) and found evidence for a modifying effect of a subset of variants on the relationship between cholesterol and BMI (P<0.01). These findings suggest a novel association of gene variants within EPHX2 to susceptibility to AN and provide a foundation for future study of this important yet poorly understood condition

Regulation of Axonal HCN1 Trafficking in Perforant Path Involves Expression of Specific TRIP8b Isoforms

The functions of HCN channels in neurons depend critically on their subcellular localization, requiring fine-tuned machinery that regulates subcellular channel trafficking. Here we provide evidence that regulatory mechanisms governing axonal HCN channel trafficking involve association of the channels with specific isoforms of the auxiliary subunit TRIP8b. In the medial perforant path, which normally contains HCN1 channels in axon terminals in immature but not in adult rodents, we found axonal HCN1 significantly increased in adult mice lacking TRIP8b (TRIP8b−/−). Interestingly, adult mice harboring a mutation that results in expression of only the two most abundant TRIP8b isoforms (TRIP8b[1b/2]−/−) exhibited an HCN1 expression pattern similar to wildtype mice, suggesting that presence of one or both of these isoforms (TRIP8b(1a), TRIP8b(1a-4)) prevents HCN1 from being transported to medial perforant path axons in adult mice. Concordantly, expression analyses demonstrated a strong increase of expression of both TRIP8b isoforms in rat entorhinal cortex with age. However, when overexpressed in cultured entorhinal neurons of rats, TRIP8b(1a), but not TRIP8b(1a-4), altered substantially the subcellular distribution of HCN1 by promoting somatodendritic and reducing axonal expression of the channels. Taken together, we conclude that TRIP8b isoforms are important regulators of HCN1 trafficking in entorhinal neurons and that the alternatively-spliced isoform TRIP8b(1a) could be responsible for the age-dependent redistribution of HCN channels out of perforant path axon terminals

Acceptor binding energies in GaN and AlN

We employ effective mass theory for degenerate hole-bands to calculate the acceptor binding energies for Be, Mg, Zn, Ca, C and Si substitutional acceptors in GaN and AlN. The calculations are performed through the 6$\times$6 Rashba-Sheka-Pikus and the Luttinger-Kohn matrix Hamiltonians for wurtzite (WZ) and zincblende (ZB) crystal phases, respectively. An analytic representation for the acceptor pseudopotential is used to introduce the specific nature of the impurity atoms. The energy shift due to polaron effects is also considered in this approach. The ionization energy estimates are in very good agreement with those reported experimentally in WZ-GaN. The binding energies for ZB-GaN acceptors are all predicted to be shallower than the corresponding impurities in the WZ phase. The binding energy dependence upon the crystal field splitting in WZ-GaN is analyzed. Ionization levels in AlN are found to have similar `shallow' values to those in GaN, but with some important differences, which depend on the band structure parameterizations, especially the value of crystal field splitting used.Comment: REVTEX file - 1 figur