Efficiently solvable special cases of bottleneck travelling salesman problems

AbstractThe paper investigates bottleneck travelling salesman problems (BTSP) which can be solved in polynomial time. At first a BTSP whose cost matrix is a circulant is treated. It is shown that in the symmetric case such a BTSP can be solved in O(n log n) time. Secondly conditions are derived which guarantee that an optimal solution is a pyramidal tour. Thus this problem can be solved in O(n2) time. Finally it is shown that a BTSP with cost matrix C = (cij, where cij = aibj with a1 ≤ … ≤ an and b1 ≥ … ≥ bn can be solved in O(n2) time

Controlling the Floquet state population and observing micromotion in a periodically driven two-body quantum system

Near-resonant periodic driving of quantum systems promises the implementation of a large variety of novel effective Hamiltonians. The challenge of Floquet engineering lies in the preparation and measurement of the desired quantum state. We address these aspects in a model system consisting of interacting fermions in a periodically driven array of double wells created by an optical lattice. The singlet and triplet fractions and the double occupancy of the Floquet states are measured, and their behavior as a function of the interaction strength is analyzed in the high- and low-frequency regimes. We demonstrate full control of the Floquet state population and find suitable ramping protocols and time-scales which adiabatically connect the initial ground state to different targeted Floquet states. The micromotion which exactly describes the time evolution of the system within one driving cycle is observed. Additionally, we provide an analytic description of the model and compare it to numerical simulations

Enhancement and sign change of magnetic correlations in a driven quantum many-body system

Periodic driving can be used to coherently control the properties of a many-body state and to realize new phases which are not accessible in static systems. For example, exposing materials to intense laser pulses enables to provoke metal-insulator transitions, control the magnetic order and induce transient superconducting behaviour well above the static transition temperature. However, pinning down the responsible mechanisms is often difficult, since the response to irradiation is governed by complex many-body dynamics. In contrast to static systems, where extensive calculations have been performed to explain phenomena such as high-temperature superconductivity, theoretical analyses of driven many-body Hamiltonians are more demanding and new theoretical approaches have been inspired by the recent observations. Here, we perform an experimental quantum simulation in a periodically modulated hexagonal lattice and show that anti-ferromagnetic correlations in a fermionic many-body system can be reduced or enhanced or even switched to ferromagnetic correlations. We first demonstrate that in the high frequency regime, the description of the many-body system by an effective Floquet-Hamiltonian with a renormalized tunnelling energy remains valid, by comparing the results to measurements in an equivalent static lattice. For near-resonant driving, the enhancement and sign reversal of correlations is explained by a microscopic model, in which the particle tunnelling and magnetic exchange energies can be controlled independently. In combination with the observed sufficiently long lifetime of correlations, Floquet engineering thus constitutes an alternative route to experimentally investigate unconventional pairing in strongly correlated systems.Comment: 6+7 pages, 4+4 figure

Early community-based family practice elective positively influences medical students’ career considerations – a Pre-post-comparison

BACKGROUND: Demographic change and recruitment problems in family practice are increasingly threatening an adequate primary care workforce in many countries. Thus, it is important to attract young physicians to the field. The purpose of the present study was to examine the effect of an early community-based 28-h family practice elective with one-to-one mentoring on medical students’ consideration of family practice as a career option, their interest in working office-based, and several perceptions with regard to specific aspects of a family physician’s work. METHODS: First- and second-year medical students completed questionnaires before and after a short community-based family practice elective, consisting of a preparatory course and a community-based practical experience with one-to-one mentoring by trained family physicians. RESULTS: We found a significantly higher rate of students favoring family practice as a career option after the elective (32.7% vs. 26.0%, p = 0.039). Furthermore, the ranking of family practice among other considered career options improved (p = 0.002). Considerations to work office-based in the future did not change significantly. Perceptions regarding a family physician’s job changed positively with regard to the possibility of long-term doctor-patient relationships and treatment of complex disease patterns. The majority of the students described identification with the respective family physician tutor as a professional role model and an increased interest in the specialty. CONCLUSIONS: Our results indicate that a short community-based family practice elective early in medical education may positively influence medical students’ considerations of a career in family practice. Furthermore, perceptions regarding the specialty with significant impact on its attractiveness may be positively adjusted. Further research is needed to evaluate the influence of different components of a family practice curriculum on the de facto career decisions of young physicians after graduation