Solving 0-1 Minimax Problems

It has been shown that it is possible to solve a minimax 0-1 programming problem by transforming the objective function coefficients and solving a minisum problem. This result is very useful for solving a ‘hard’ minimax problem when there exists a ‘relatively easy’ algorithm to solve the minisum problem. We discuss such problems and present a new transformation.     

Novel mixed-valent Co(II)₂Co(III)₄Ln(III)₄ aggregates with ligands derived from tris-(hydroxymethyl)aminomethane (Tris)

Isostructural Co(II)?Co(III)?Ln(III)? (Ln = Y (1), Gd (2) and Dy (3)) coordination clusters formed using the ligand Tris are the first examples of 3d-4f complexes involving this ligand and show weak ferromagnetic coupling between the Co(II) ions and slow relaxation (SMM) behaviour for 3.     

The equivalence of bar recursion and open recursion

Several extensions of Gödel's system T$\mathsf{T}$ with new forms of recursion have been designed for the purpose of giving a computational interpretation to classical analysis. One can organise many of these extensions into two groups: those based on bar recursion, which include Spector's original bar recursion, modified bar recursion and the more recent products of selections functions, or those based on open recursion   which in particular include the symmetric Berardi–Bezem–Coquand (BBC) functional. We relate these two groups by showing that both open recursion and the BBC functional are primitive recursively equivalent to a variant of modified bar recursion. Our results, in combination with existing research, essentially complete the classification up to primitive recursive equivalence of those extensions of system T$\mathsf{T}$ used to give a direct computational interpretation to choice principles.     

Optimal learning for sequential sampling with non-parametric beliefs

We propose a sequential learning policy for ranking and selection problems, where we use a non-parametric procedure for estimating the value of a policy. Our estimation approach aggregates over a set of kernel functions in order to achieve a more consistent estimator. Each element in the kernel estimation set uses a different bandwidth to achieve better aggregation. The final estimate uses a weighting scheme with the inverse mean square errors of the kernel estimators as weights. This weighting scheme is shown to be optimal under independent kernel estimators. For choosing the measurement, we employ the knowledge gradient policy that relies on predictive distributions to calculate the optimal sampling point. Our method allows a setting where the beliefs are expected to be correlated but the correlation structure is unknown beforehand. Moreover, the proposed policy is shown to be asymptotically optimal.     

Powergraph — a network-based approach to modelling and managing corporate strategic conflict and co-operation

Strategic relationships between companies are characterised by a combination of conflict and co-operation. Often the behaviour of partner/rival companies will appear arbitrary, almost irrational because of the necessary limitations on communication between the parties. Understanding, predicting and managing situations such as major project teamings or acquisition struggles is essential for the satisfactory governance of companies but existing conflict modelling has proven less than attractive to practitioners and their advisors. A network-based approach known as Powergraph is described in this study. It represents the corporate situation as a directed graph in which the nodes are the possible states of play. Connections between nodes are represented by logical expressions deriving from the capacities of the players individually or in coalition to bring about the transitions. By consideration of the ordinal preferences of the participants, trajectories of the situation can be described and these trajectories form the basis for management action and intelligence gathering. The method is illustrated by means of a real case study of three defence companies competing for two major contracts.     

Enhanced alternating energy minimization methods for stochastic galerkin matrix equations

BIT Numerical Mathematics - In uncertainty quantification, it is commonly required to solve a forward model consisting of a partial differential equation (PDE) with a spatially varying uncertain...     

Fiber-optic infrared reflectance spectroelectrochemical studies of osmium and ruthenium nitrosyl porphyrins containing alkoxide and thiolate ligands

We have examined the redox behavior of the osmium and ruthenium compounds (OEP)M(NO)(OEt) and (OEP)M(NO)(SEt) (OEP = octaethylporphyrinato dianion; M = Os, Ru) by cyclic voltammetry and infrared spectroelectrochemistry. The compound (OEP)Os(NO)(OEt) undergoes a single reversible oxidation process in dichloromethane. In contrast, the thiolate compound (OEP)Os(NO)(SEt) undergoes a net irreversible oxidation resulting in formal loss of the SEt ligand. Extended Hückel calculations on crystal structures of these two compounds provide insight into the nature of their HOMOs. In the case of the alkoxide compound, the HOMO is largely metal centered, with 70% of the charge located in the metal's orbital and approximately 25% on the porphyrin ring. However, the HOMO of the thiolate compound consists of a pi bonding interaction between the metal dxz orbital and the px orbital on the sulfur, and a pi antibonding interaction between the metal d orbital and a pi* orbital on NO. The redox behavior of the Ru analogues have been determined, and are compared with those of the Os compounds.     

Nickel-catalyzed cross-couplings of organosilicon reagents with unactivated secondary alkyl bromides

A metal-catalyzed cross-coupling of organosilicon compounds with alkyl halides has been developed. Noteworthy attributes of the method are its scope (secondary electrophiles), its high functional-group compatibility, and the air stability of the catalyst components.