The Birkhoff theorem for unitary matrices of arbitrary dimensions

It was shown recently that Birkhoff's theorem for doubly stochastic matrices can be extended to unitary matrices with equal line sums whenever the dimension of the matrices is prime. We prove a generalization of the Birkhoff theorem for unitary matrices with equal line sums for arbitrary dimension.Comment: This manuscript presents a proof for the general unitary birkhoff theorem, conjectured in arXiv:1509.0862

A Finite Exact Representation of Register Automata Configurations

A register automaton is a finite automaton with finitely many registers ranging from an infinite alphabet. Since the valuations of registers are infinite, there are infinitely many configurations. We describe a technique to classify infinite register automata configurations into finitely many exact representative configurations. Using the finitary representation, we give an algorithm solving the reachability problem for register automata. We moreover define a computation tree logic for register automata and solve its model checking problem.Comment: In Proceedings INFINITY 2013, arXiv:1402.661

Unfolding the impacts of transaction-specific investments: Moderation by out-of-thechannel-loop perceptions and achievement orientations

When distribution channel partners make specific investments, tailored to a particular supplier, it could prompt either opportunism or beneficial (e.g., extra-role) behaviors. The impact of the investment in turn may depend on whether the channel partner perceives that it is being left out of the channel loop by the supplier, as well as that partner’s achievement orientation. This study considers a sample of 155 IT professional service firms and finds that their knowledge-intensive, transaction-specific investments (TSIs) encourage distinct behavioral intentions. If they perceive that the supplier is leaving them out of the channel loop, the effects of the TSIs get amplified in relation to opportunistic and extra-role behavioral intentions. Furthermore, the firms’ achievement orientation moderates these influences. Suppliers thus should attend closely to achievement-oriented partners to ensure they do not perceive that they have been left out of the channel loop

Scale-Adaptive Group Optimization for Social Activity Planning

Studies have shown that each person is more inclined to enjoy a group activity when 1) she is interested in the activity, and 2) many friends with the same interest join it as well. Nevertheless, even with the interest and social tightness information available in online social networks, nowadays many social group activities still need to be coordinated manually. In this paper, therefore, we first formulate a new problem, named Participant Selection for Group Activity (PSGA), to decide the group size and select proper participants so that the sum of personal interests and social tightness of the participants in the group is maximized, while the activity cost is also carefully examined. To solve the problem, we design a new randomized algorithm, named Budget-Aware Randomized Group Selection (BARGS), to optimally allocate the computation budgets for effective selection of the group size and participants, and we prove that BARGS can acquire the solution with a guaranteed performance bound. The proposed algorithm was implemented in Facebook, and experimental results demonstrate that social groups generated by the proposed algorithm significantly outperform the baseline solutions.Comment: 20 pages. arXiv admin note: substantial text overlap with arXiv:1305.150

Assessment of density functional methods with correct asymptotic behavior

Long-range corrected (LC) hybrid functionals and asymptotically corrected (AC) model potentials are two distinct density functional methods with correct asymptotic behavior. They are known to be accurate for properties that are sensitive to the asymptote of the exchange-correlation potential, such as the highest occupied molecular orbital energies and Rydberg excitation energies of molecules. To provide a comprehensive comparison, we investigate the performance of the two schemes and others on a very wide range of applications, including the asymptote problems, self-interaction-error problems, energy-gap problems, charge-transfer problems, and many others. The LC hybrid scheme is shown to consistently outperform the AC model potential scheme. In addition, to be consistent with the molecules collected in the IP131 database [Y.-S. Lin, C.-W. Tsai, G.-D. Li, and J.-D. Chai, J. Chem. Phys., 2012, 136, 154109], we expand the EA115 and FG115 databases to include, respectively, the vertical electron affinities and fundamental gaps of the additional 16 molecules, and develop a new database AE113 (113 atomization energies), consisting of accurate reference values for the atomization energies of the 113 molecules in IP131. These databases will be useful for assessing the accuracy of density functional methods.Comment: accepted for publication in Phys. Chem. Chem. Phys., 46 pages, 4 figures, supplementary material include