Approximability of Connected Factors

Finding a d-regular spanning subgraph (or d-factor) of a graph is easy by Tutte's reduction to the matching problem. By the same reduction, it is easy to find a minimal or maximal d-factor of a graph. However, if we require that the d-factor is connected, these problems become NP-hard - finding a minimal connected 2-factor is just the traveling salesman problem (TSP). Given a complete graph with edge weights that satisfy the triangle inequality, we consider the problem of finding a minimal connected $d$-factor. We give a 3-approximation for all $d$ and improve this to an (r+1)-approximation for even d, where r is the approximation ratio of the TSP. This yields a 2.5-approximation for even d. The same algorithm yields an (r+1)-approximation for the directed version of the problem, where r is the approximation ratio of the asymmetric TSP. We also show that none of these minimization problems can be approximated better than the corresponding TSP. Finally, for the decision problem of deciding whether a given graph contains a connected d-factor, we extend known hardness results.Comment: To appear in the proceedings of WAOA 201

Linking international clinical research with stateless populations to justice in global health

BACKGROUND: In response to calls to expand the scope of research ethics to address justice in global health, recent scholarship has sought to clarify how external research actors from high-income countries might discharge their obligation to reduce health disparities between and within countries. An ethical framework-'research for health justice'-was derived from a theory of justice (the health capability paradigm) and specifies how international clinical research might contribute to improved health and research capacity in host communities. This paper examines whether and how external funders, sponsors, and researchers can fulfill their obligations under the framework. METHODS: Case study research was undertaken on the Shoklo Malaria Research Unit's (SMRU) vivax malaria treatment trial, which was performed on the Thai-Myanmar border with Karen and Myanmar refugees and migrants. We conducted nineteen in-depth interviews with trial stakeholders, including investigators, trial participants, community advisory board members, and funder representatives; directly observed at trial sites over a five-week period; and collected trial-related documents for analysis. RESULTS: The vivax malaria treatment trial drew attention to contextual features that, when present, rendered the 'research for health justice' framework's guidance partially incomplete. These insights allowed us to extend the framework to consider external research actors' obligations to stateless populations. Data analysis then showed that framework requirements are largely fulfilled in relation to the vivax malaria treatment trial by Wellcome Trust (funder), Oxford University (sponsor), and investigators. At the same time, this study demonstrates that it may be difficult for long-term collaborations to shift the focus of their research agendas in accordance with the changing burden of illness in their host communities and to build the independent research capacity of host populations when working with refugees and migrants. Obstructive factors included the research funding environment and staff turnover due to resettlement or migration. CONCLUSIONS: Our findings show that obligations for selecting research targets, research capacity strengthening, and post-trial benefits that link clinical trials to justice in global health can be upheld by external research actors from high-income countries when working with stateless populations in LMICs. However, meeting certain framework requirements for long-term collaborations may not be entirely feasible

Applications of 18(F) FDG PET/CT in oncology

The escalating costs of conventional diagnostic technology in oncology have yet to obviate futile surgery intervention and the spiralling treatment cost. The evolution in engineering technology which looks at the correlation of the anatomy and the function of tumours i.e. Positron Emission Tomography-Computed Tomography (PET-CT) have impacted on the improved diagnostic accuracy and treatment in oncology. Clinical data have demonstrated that the information provided by PET/CT often changes patient management. This review addresses the value of PET-CT as a surrogate molecular marker in tumours and to discuss some issues in adopting PET/CT in routine daily practice as supported by the numbers of literature reviews of its application in oncology since it was first commercialized in 2001. The description of the technology used in multimodality imaging has gained encouraging interest among physicians, policy makers and insurance companies on the importance of the PET-CT, for which roles are not limited to the staging, disease prognostication and treatment monitoring with potential impact on treatment cost and justification of radiation safety for the patient. PET/CT is a useful tool in cancer investigation as evidenced by its role as a surrogate marker in underpinning the cellular reprogramming of different pathological entities

How to specify, estimate, and validate higher-order constructs in PLS-SEM

Higher-order constructs, which facilitate modeling a construct on a more abstract higher-level dimension and its more concrete lower-order subdimensions, have become an increasingly visible trend in applications of partial least squares structural equation modeling (PLS-SEM). Unfortunately, researchers frequently confuse the specification, estimation, and validation of higher-order constructs, for example, when it comes to assessing their reliability and validity. Addressing this concern, this paper explains how to evaluate the results of higher-order constructs in PLS-SEM using the repeated indicators and the two-stage approaches, which feature prominently in applied social sciences research. Focusing on the reflective-reflective and reflective-formative types of higher-order constructs, we use the well-known corporate reputation model example to illustrate their specification, estimation, and validation. Thereby, we provide the guidance that scholars, marketing researchers, and practitioners need when using higher-order constructs in their studies

Spin-degeneracy breaking and parity transitions in three-terminal Josephson junctions

Harnessing spin and parity degrees of freedom is of fundamental importance for the realization of emergent quantum devices. Nanostructures embedded in superconductor--semiconductor hybrid materials offer novel and yet unexplored routes for addressing and manipulating fermionic modes. Here we spectroscopically probe the two-dimensional band structure of Andreev bound states in a phase-controlled hybrid three-terminal Josephson junction. Andreev bands reveal spin-degeneracy breaking, with level splitting in excess of 9 GHz, and zero-energy crossings associated to ground state fermion parity transitions, in agreement with theoretical predictions. Both effects occur without the need of external magnetic fields or sizable charging energies and are tuned locally by controlling superconducting phase differences. Our results highlight the potential of multiterminal hybrid devices for engineering quantum states

Zeeman and Orbital Driven Phase Transitions in Planar Josephson Junctions

We perform supercurrent and tunneling spectroscopy measurements on gate-tunable InAs/Al Josephson junctions (JJs) in an in-plane magnetic field, and report on phase shifts in the current-phase relation measured with respect to an absolute phase reference. The impact of orbital effects is investigated by studying multiple devices with different superconducting lead sizes. At low fields, we observe gate-dependent phase shifts of up to ${\varphi_{0}=0.5\pi}$ which are consistent with a Zeeman field coupling to highly-transmissive Andreev bound states via Rashba spin-orbit interaction. A distinct phase shift emerges at larger fields, concomitant with a switching current minimum and the closing and reopening of the superconducting gap. These signatures of an induced phase transition, which might resemble a topological transition, scale with the superconducting lead size, demonstrating the crucial role of orbital effects. Our results elucidate the interplay of Zeeman, spin-orbit and orbital effects in InAs/Al JJs, giving new understanding to phase transitions in hybrid JJs and their applications in quantum computing and superconducting electronics