Lexicographic balanced optimization problems

We introduce the lexicographic balanced optimization problem (LBaOP) and show that it can be solved efficiently if an associated lexicographic bottleneck problem can be solved efficiently. For special cases of cuts in a graph and base system of a matroid, improved algorithms are proposed. A generalization of LBaOP is also discussed.     

Twistor spaces of hypercomplex manifolds are balanced

A hypercomplex structure on a differentiable manifold consists of three integrable almost complex structures that satisfy quaternionic relations. If, in addition, there exists a metric on the manifold which is Hermitian with respect to the three structures, and such that the corresponding Hermitian forms are closed, the manifold is said to be hyperkähler. In the paper “Non-Hermitian Yang–Mills connections” [13], Kaledin and Verbitsky proved that the twistor space of a hyperkähler manifold admits a balanced metric; these were first studied in the article “On the existence of special metrics in complex geometry” [17] by Michelsohn. In the present article, we review the proof of this result and then generalize it and show that twistor spaces of general compact hypercomplex manifolds are balanced.     

Bulk heterojunction perovskite solar cells incorporated with solution-processed TiOx nanoparticles as the electron acceptors

In the past ten years, perovskite solar cells were rapidly developed, but the intrinsic unbalanced charge carrier diffusion lengths within perovskite materials were not fully addressed by either a planar heterojunction or meso-superstructured perovskite solar cells. In this study, we report bulk heterojunction perovskite solar cells, where perovskite materials CH₃NH₃PbI₃ is blended with solution-processed n-type TiO_x nanoparticles as the photoactive layer. Studies indicate that one-step solution-processed CH₃NH₃PbI₃:TiO_x bulk-heterojunction thin film possesses enhanced and balanced charge carrier mobilities, superior film morphology with enlarged crystal sizes, and suppressed trap-induced charge recombination. Thus, bulk heterojunction perovskite solar cells by CH₃NH₃PbI₃ mixed with 5 wt% of TiO_x, which is processed by one-step method rather than typical two-step method, show a short-circuit current density of 20.93 mA/cm², an open-circuit voltage of 0.90 V, a fill factor of 80% and with a corresponding power conversion efficiency of 14.91%, which is more than 30% enhancement as compared with that of perovskite solar cells with a planar heterojunction device structure. Moreover, bulk heterojunction perovskite solar cells possess enhanced device stability. All these results demonstrate that perovskite solar cells with a bulk heterojunction device structure are one of apparent approaches to boost device performance.     

A natural selection from the core of a TU game: the core-center

We present a new allocation rule for the class of games with a nonempty core: the core-center. This allocation rule selects a centrally located point within the core of any such game. We provide a deep discussion of its main properties.     

Linearization formula for the product of associated q-ultraspherical polynomials

We obtain an explicit formula for the linearization coefficient of the product of two associated q-ultraspherical polynomials in terms of a multiple of a balanced, terminating very-well-poised ₁₀φ₉ series. We also discuss the nonnegativity properties of the coefficients as well as some special cases. 2000 Mathematics Subject Classification Primary—33D45; Secondary—33D8 This work was supported in part by an NSERC grant A6197.     

Facets of the balanced (acyclic) induced subgraph polytope

A signed graph is a graph whose edges are labelled positive or negative. A signed graph is said to be balanced if the set of negative edges form a cut. The balanced induced subgraph polytopeP(G) of a graphG is the convex hull of the incidence vectors of all node sets that induce balanced subgraphs ofG. In this paper we exhibit various (rank) facet defining inequalities. We describe several methods with which new facet defining inequalities ofP(G) can be constructed from known ones. Finding a maximum weighted balanced induced subgraph of a series parallel graph is a polynomial problem. We show that for this class of graphsP(G) may have complicated facet defining inequalities. We derive analogous results for the polytope of acyclic induced subgraphs.Research supported in part by the Natural Sciences and Engineering Research Council of Canada; the second author has also been supported by C.P. Rail.     

The balanced minimum evolution problem under uncertain data

We investigate the Robust Deviation Balanced Minimum Evolution Problem (RDBMEP), a combinatorial optimization problem that arises in computational biology when the evolutionary distances from taxa are uncertain and varying inside intervals. By exploiting some fundamental properties of the objective function, we present a mixed integer programming model to exactly solve instances of the RDBMEP and discuss the biological impact of uncertainty on the solutions to the problem. Our results give perspective on the mathematics of the RDBMEP and suggest new directions to tackle phylogeny estimation problems affected by uncertainty.     

Cardinality constrained connected balanced partitions of trees under different criteria

In this paper we study the problem of partitioning a tree with $n$ weighted vertices into $p$ connected components. For each component, we measure its gap, that is, the difference between the maximum and the minimum weight of its vertices, with the aim of minimizing the sum of such differences. We present an $O\left(n^3{p}^2\right)$ time and $O\left(n^{3}p\right)$ space algorithm for this problem. Then, we generalize it, requiring a minimum of $ϵ\ge 1$ nodes in each connected component, and provide an $O\left(n^3{p}^2{ϵ}^2\right)$ time and $O\left(n^{3}pϵ\right)$ space algorithm to solve this new problem version. We provide a refinement of our analysis involving the topology of the tree and an improvement of the algorithms for the special case in which the weights of the vertices have a heap structure. All presented algorithms can be straightforwardly extended to other similar objective functions. Actually, for the problem of minimizing the maximum gap with a minimum number of nodes in each component, we propose an algorithm which is independent of $ϵ$ and requires $O(n^{2}logn{p}^2)$ time and $O\left(n^{2}p\right)$ space.     

Mew mathematical properties of the semivalues of cooperative tu games *

The Semivalues were introduced by Dubey, Neiman and Weber (1981), as the values of TU games satisfying a set of axioms, precisely:linearity, symmetry, monotomcity and projection axioms. In this paper, a potential approach is used to prove a characterization of Semivalues as the unique values satisfying a new type of consistency relative to a new implicitly defined reduced game of Hart Mas Colell type and weighted standardness for all two person games. The definition of the reduced game requires some combinatorial results on the auxiliary game of the given game. As a byproduct, we derive from these results two other combinatorial properties of the Semivalues: (i) any Semivalue is the Shapley value of the auxiliary game of the given game, and (ii) any Semivalue satisfies the fairness principle introduced by Myerson (1977) as the principle of balanced contributions