A nested Krylov subspace method to compute the sign function of large complex matrices

We present an acceleration of the well-established Krylov-Ritz methods to compute the sign function of large complex matrices, as needed in lattice QCD simulations involving the overlap Dirac operator at both zero and nonzero baryon density. Krylov-Ritz methods approximate the sign function using a projection on a Krylov subspace. To achieve a high accuracy this subspace must be taken quite large, which makes the method too costly. The new idea is to make a further projection on an even smaller, nested Krylov subspace. If additionally an intermediate preconditioning step is applied, this projection can be performed without affecting the accuracy of the approximation, and a substantial gain in efficiency is achieved for both Hermitian and non-Hermitian matrices. The numerical efficiency of the method is demonstrated on lattice configurations of sizes ranging from 4^4 to 10^4, and the new results are compared with those obtained with rational approximation methods.Comment: 17 pages, 12 figures, minor corrections, extended analysis of the preconditioning ste

Ground-state properties of fermionic mixtures with mass imbalance in optical lattices

Ground-state properties of fermionic mixtures confined in a one-dimensional optical lattice are studied numerically within the spinless Falicov-Kimball model with a harmonic trap. A number of remarkable results are found. (i) At low particle filling the system exhibits the phase separation with heavy atoms in the center of the trap and light atoms in the surrounding regions. (ii) Mott-insulating phases always coexist with metallic phases. (iii) Atomic-density waves are observed in the insulating regions for all particle fillings near half-filled lattice case. (iv) The variance of the local density exhibits the universal behavior (independent of the particle filling, the Coulomb interaction and the strength of a confining potential) over the whole region of the local density values.Comment: 10 pages, 5 figure

Dissynergies of mergers among local banks

In this paper, we investigate how bank mergers affect bank revenues and present empirical evidence that mergers among banks have a substantial and persistent negative impact on merging banks’ revenues. We refer to merger related negative effects on banks’ revenues as dissynergies and suggest that they are a result of organizational diseconomies, the loss of customers and the temporary distraction of management from day-to-day operations by effecting the merger. For our analyses we draw on a proprietary data set with detailed financials of all 457 regional savings banks in Germany, which have been involved in 212 mergers between 1994 and 2006. We find that the negative impact of a merger on net operating revenues amounts to 3% of pro-forma consolidated banks’ operating profits and persists not only for the year of the merger but for up to four years post-merger. Only thereafter mergers exhibit a significantly superior performance compared to their respective pre-merger performance or the performance of their non-merging peers. The magnitude and persistence of merger related revenue dissynergies highlight their economic relevance. Previous research on post-merger performance mainly focuses on the effects from mergers on banks’ (cost) efficiency and profitability but fails to provide clear and consistent results. We are the first, to our knowledge, to examine the post-merger performance of banks’ net operating revenues and to empirically verify significant negative implications of mergers for banks’ net operating revenues. We propose that our finding of negative merger related effects on banks’ operating revenues is the reason why previous research fails to show merger related gains

Where did anthropology go?: or the need for 'human nature'

I was recently asked the question: “Where did anthropology go? ” by a psycholinguist from a famous American university. She was commenting on the fact that she had tried to establish contact with the anthropology department of her institution, hoping that she would find somebody who would contribute to a discussion of her main research interest: the relation of words to concepts. She had assumed that the socio- cultural anthropologists would have general theories or, at least, ask general questions, about the way children’s upbringing in different cultures and environments would constrain, or not constrain, how children represented the material and the social world. She was hoping for information about exotic societies in order to gain a broader cross-cultural perspective. She was hoping that her enquiry about a topic that is inevitable in any discussion about culture would be equally central to the three disciplines of psychology, linguistics and anthropology, and would therefore be an ideal ground for constructive co-operation, that is, one where the different parties could articulate and challenge the theories on which their different disciplines are built. In fact she found that nobody was interested in working with her, but what surprised her most was the hostility she perceived, caused, not only by the suggestion that cultural social anthropologists were interested in simple exotic societies, but even more by the idea that they might be interested in formulating and answering general questions about the nature of the human species and that, therefore, their work could be compatible with disciplines such as hers. The lack of any generalising theoretical framework within which her research interest might find a place is not surprising when we look at what kind of thing is done in many university departments under the label social or cultural anthropology. Take for example the interests listed on the web site of th