On the central levels problem

The central levels problem asserts that the subgraph of the (2m+1)-dimensional hypercube induced by all bitstrings with at least m+1-l many 1s and at most m+l many 1s, i.e., the vertices in the middle 2l levels, has a Hamilton cycle for any m>=1 and 1==1 and 1==2, that contains the symmetric chain decomposition constructed by Greene and Kleitman in the 1970s, and we provide a loopless algorithm for computing the corresponding Gray code

On the central levels problem

The \emph{central levels problem} asserts that the subgraph of the $(2m+1)$-dimensional hypercube induced by all bitstrings with at least $m+1-\ell$ many 1s and at most $m+\ell$ many 1s, i.e., the vertices in the middle $2\ell$ levels, has a Hamilton cycle for any $m\geq 1$ and $1\le \ell\le m+1$. This problem was raised independently by Buck and Wiedemann, Savage, Gregor and {\v{S}}krekovski, and by Shen and Williams, and it is a common generalization of the well-known \emph{middle levels problem}, namely the case $\ell=1$, and classical binary Gray codes, namely the case $\ell=m+1$. In this paper we present a general constructive solution of the central levels problem. Our results also imply the existence of optimal cycles through any sequence of $\ell$ consecutive levels in the $n$-dimensional hypercube for any $n\ge 1$ and $1\le \ell \le n+1$. Moreover, extending an earlier construction by Streib and Trotter, we construct a Hamilton cycle through the $n$-dimensional hypercube, $n\geq 2$, that contains the symmetric chain decomposition constructed by Greene and Kleitman in the 1970s, and we provide a loopless algorithm for computing the corresponding Gray code

Two-body quantum mechanical problem on spheres

The quantum mechanical two-body problem with a central interaction on the sphere ${\bf S}^{n}$ is considered. Using recent results in representation theory an ordinary differential equation for some energy levels is found. For several interactive potentials these energy levels are calculated in explicit form.Comment: 41 pages, no figures, typos corrected; appendix D was adde

The Dilemma of Delegating Search: Budgeting in Public Employment Services

The poor performance often attributed to many public employment services may be explained in part by a delegation problem between the central office and local job centers. In markets characterized by frictions, job centers function as match-makers, linking job seekers with relevant vacancies. Because their search intensity in contacting employers and collecting data is not verifiable by the central authority, a typical moral hazard problem can arise. To overcome the delegation problem and provide high-powered incentives for high levels of search effort on the part of job centers, we propose output-related schemes that assign greater staff capacity to agencies achieving high strike rates.matching unemployment, public employment service, delegation problem, moral hazard, search theory

The Dilemma of Delegating Search: Budgeting in Public Employment Service

The Recent German research has suggested that extending the number of caseworkers may have a very positive effect on PES performance. The present paper accepts this key insight but argues that there are other factors that may independently drive outcomes and in particular local agents’ discretion. That is, it focuses on the delegation problem between the central office and the local job center ‘matchmakers.’ Because their (search) effort in contacting employers and collecting data is not verifiable by the central authority, a typical moral hazard problem can arise. To overcome the delegation problem and provide high‐powered incentives for increased levels of search effort on the part of job centers, we propose output‐related schemes that assign greater staff capacity to agencies achieving high strike rates.matching unemployment, public employment service, active labor market policy, moral hazard, search theory

Altruism can proliferate through group/kin selection despite high random gene flow

The ways in which natural selection can allow the proliferation of cooperative behavior have long been seen as a central problem in evolutionary biology. Most of the literature has focused on interactions between pairs of individuals and on linear public goods games. This emphasis led to the conclusion that even modest levels of migration would pose a serious problem to the spread of altruism in group structured populations. Here we challenge this conclusion, by analyzing evolution in a framework which allows for complex group interactions and random migration among groups. We conclude that contingent forms of strong altruism can spread when rare under realistic group sizes and levels of migration. Our analysis combines group-centric and gene-centric perspectives, allows for arbitrary strength of selection, and leads to extensions of Hamilton's rule for the spread of altruistic alleles, applicable under broad conditions.Comment: 5 pages, 2 figures. Supplementary material with 50 pages and 26 figure

Modularity and Innovation in Complex Systems

The problem of designing, coordinating, and managing complex systems has been central to the management and organizations literature. Recent writings have tended to offer modularity as, at least, a partial solution to this design problem. However, little attention has been paid to the problem of identifying what constitutes an appropriate modularization of a complex system. We develop a formal simulation model that allows us to carefully examine the dynamics of innovation and performance in complex systems. The model points to the trade-off between the destabilizing effects of overly refined modularization and the modest levels of search and a premature fixation on inferior designs that can result from excessive levels of integration. The analysis highlights an asymmetry in this trade-off, with excessively refined modules leading to cycling behavior and a lack of performance improvement. We discuss the implications of these arguments for product and organization design.

Theoretical surgery: a new specialty in operative medicine

Theoretical surgery is defined as a nonoperative decision analysis and clinical and basic research supporting system for surgery. It developed to meet the needs of academic surgeons to coordinate communication with basic science disciplines. This article summarizes the development of this idea at the University of Marburg where theoretical surgery has reached departmental and institutional proportions. Its objectives and methods are described. Central to its operation are permanent working teams of 2 clinical surgeons, 1 basic scientist (theoretical surgeon), 1-2 technicians, and 1-2 students focusing on one problem in a joint interdisciplinary manner. Decision analysis with classification methods and the creation of decision trees and algorithms are central to the operation of this experiment. Lessons learned from this academic experiment and the accomplishments during the past 20 years are summarized on 3 levels of efficacy: performance, changing strategies, and outcome