Rank 2 quasiparabolic vector bundles on P1 and the variety of linear subspaces contained in two odd-dimensional quadrics

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A special point problem of Andr\'e-Pink-Zannier in the universal family of abelian varieties

The Andr\'e-Pink-Zannier conjecture concerns the intersection of subvarieties and the generalized Hecke orbit of a given point in mixed Shimura varieties. It is part of the Zilber-Pink conjecture. In this paper we focus on the universal family of principally polarized abelian varieties. We explain the moduli interpretation of the conjecture in this case and prove several different cases for this conjecture: its overlap with the Andr\'e-Oort conjecture; when the subvariety is contained in an abelian scheme over a curve and the point is a torsion point on its fiber; when the subvariety is a curve.Comment: Removed the algebraic point assumption. Comments are welcome

A Novel Hybrid Framework for Co-Optimization of Power and Natural Gas Networks Integrated With Emerging Technologies

In a power system with high penetration of renewable power sources, gas-fired units can be considered as a back-up option to improve the balance between generation and consumption in short-term scheduling. Therefore, closer coordination between power and natural gas systems is anticipated. This article presents a novel hybrid information gap decision theory (IGDT)-stochastic cooptimization problem for integrating electricity and natural gas networks to minimize total operation cost with the penetration of wind energy. The proposed model considers not only the uncertainties regarding electrical load demand and wind power output, but also the uncertainties of gas load demands for the residential consumers. The uncertainties of electric load and wind power are handled through a scenario-based approach, and residential gas load uncertainty is handled via IGDT approach with no need for the probability density function. The introduced hybrid model enables the system operator to consider the advantages of both approaches simultaneously. The impact of gas load uncertainty associated with the residential consumers is more significant on the power dispatch of gas-fired plants and power system operation cost since residential gas load demands are prior than gas load demands of gas-fired units. The proposed framework is a bilevel problem that can be reduced to a one-level problem. Also, it can be solved by the implementation of a simple concept without the need for Karush–Kuhn–Tucker conditions. Moreover, emerging flexible energy sources such as the power to gas technology and demand response program are considered in the proposed model for increasing the wind power dispatch, decreasing the total operation cost of the integrated network as well as reducing the effect of system uncertainties on the total operating cost. Numerical results indicate the applicability and effectiveness of the proposed model under different working conditions