Quantum Optimization Problems

Krentel [J. Comput. System. Sci., 36, pp.490--509] presented a framework for an NP optimization problem that searches an optimal value among exponentially-many outcomes of polynomial-time computations. This paper expands his framework to a quantum optimization problem using polynomial-time quantum computations and introduces the notion of an ``universal'' quantum optimization problem similar to a classical ``complete'' optimization problem. We exhibit a canonical quantum optimization problem that is universal for the class of polynomial-time quantum optimization problems. We show in a certain relativized world that all quantum optimization problems cannot be approximated closely by quantum polynomial-time computations. We also study the complexity of quantum optimization problems in connection to well-known complexity classes.Comment: date change

Worst case and probabilistic analysis of the 2-Opt algorithm for the TSP

2-Opt is probably the most basic local search heuristic for the TSP. This heuristic achieves amazingly good results on “real world” Euclidean instances both with respect to running time and approximation ratio. There are numerous experimental studies on the performance of 2-Opt. However, the theoretical knowledge about this heuristic is still very limited. Not even its worst case running time on 2-dimensional Euclidean instances was known so far. We clarify this issue by presenting, for every p∈N , a family of L p instances on which 2-Opt can take an exponential number of steps. Previous probabilistic analyses were restricted to instances in which n points are placed uniformly at random in the unit square [0,1]2, where it was shown that the expected number of steps is bounded by O~(n10) for Euclidean instances. We consider a more advanced model of probabilistic instances in which the points can be placed independently according to general distributions on [0,1] d , for an arbitrary d≥2. In particular, we allow different distributions for different points. We study the expected number of local improvements in terms of the number n of points and the maximal density ϕ of the probability distributions. We show an upper bound on the expected length of any 2-Opt improvement path of O~(n4+1/3⋅ϕ8/3) . When starting with an initial tour computed by an insertion heuristic, the upper bound on the expected number of steps improves even to O~(n4+1/3−1/d⋅ϕ8/3) . If the distances are measured according to the Manhattan metric, then the expected number of steps is bounded by O~(n4−1/d⋅ϕ) . In addition, we prove an upper bound of O(ϕ√d) on the expected approximation factor with respect to all L p metrics. Let us remark that our probabilistic analysis covers as special cases the uniform input model with ϕ=1 and a smoothed analysis with Gaussian perturbations of standard deviation σ with ϕ∼1/σ d

Innovate to eliminate: a prerequisite in NTD programmes

Innovation plays a critical role in progress towards achievement of the World Health Organization's road map for neglected tropical diseases 2021-2030. As disease prevalence decreases, the cost to identify and treat remaining cases goes up. Additionally, as programmes move to the surveillance phase, diagnostic tests need to be highly sensitive and affordable. Until the early end to the Ascend West and Central Africa programme, the Ascend Learning and Innovation Fund supported five projects from 2019 to 2021. Designed for innovation, the fund encompassed a range of activities, including operational research, product development and social behavioural change. This flexibility allowed innovation to bridge the gap between strategic policy and practical implementation, piloting and proving business models to respond to information found through Ascend

Ground state properties of a Tonks-Girardeau Gas in a periodic potential

In this paper, we investigate the ground-state properties of a bosonic Tonks-Girardeau gas confined in a one-dimensional periodic potential. The single-particle reduced density matrix is computed numerically for systems up to $N=265$ bosons. Scaling analysis of the occupation number of the lowest orbital shows that there are no Bose-Einstein Condensation(BEC) for the periodically trapped TG gas in both commensurate and incommensurate cases. We find that, in the commensurate case, the scaling exponents of the occupation number of the lowest orbital, the amplitude of the lowest orbital and the zero-momentum peak height with the particle numbers are 0, -0.5 and 1, respectively, while in the incommensurate case, they are 0.5, -0.5 and 1.5, respectively. These exponents are related to each other in a universal relation.Comment: 9 pages, 10 figure

Promoting gender, equity, human rights and ethnic equality in neglected tropical disease programmes.

Limited attention to tackling neglected tropical diseases (NTDs) through the lenses of gender, equity, ethnicity and human rights inadvertently undermines progress due to the exclusion of subgroups in populations living in conditions of vulnerability. Supporting national NTD programmes to make equity analysis part of their routine activities and revitalising intersectoral collaboration will be essential to achieve effective, sustainable service delivery with a person-centred approach. Gender, equity, human rights and ethnic equality for NTD programmes should therefore be incorporated in multisectoral engagements

Increasing Compliance with Mass Drug Administration Programs for Lymphatic Filariasis in India through Education and Lymphedema Management Programs

Global elimination of lymphatic filariasis requires giving drugs at least annually to populations who live at risk of becoming infected with the parasite. At least 80% of people at risk need to take the drugs annually for 5 or more years to stop transmission of the infection. People suffering from the long-term effects of infection, such as swollen legs, benefit from programs that teach self-care of their affected limbs. In this study, we assessed the impact of an educational campaign that, after addressing previously identified predictors of compliance, significantly improved drug compliance. The specific factors improving compliance included knowing about the drug distribution in advance, knowing that everyone is at risk for acquiring the infection, knowing that the drug distribution was for lymphatic filariasis prevention, and knowing at least one component of leg care. We also found that areas with programs to assist people with swollen legs had greater increases in compliance. This research provides evidence that program evaluation can be used to improve drug compliance. In addition, our work shows for the first time that programs to benefit people with swollen legs caused by lymphatic filariasis also increase the participation of people without disease in drug treatment programs

Assessing factors influencing communities' acceptability of mass drug administration for the elimination of lymphatic filariasis in Guyana.

BACKGROUND: Guyana is one of four countries in the Latin American Region where lymphatic filariasis (LF) remains endemic. In preparation for the introduction of a new triple drug therapy regimen (ivermectin, diethylcarbamazine, and albendazole (IDA)) in 2019, an acceptability study was embedded within sentinel site mapping in four regions to assess mass drug administration (MDA) coverage and compliance, acceptability, and perceptions about treatment and disease. The results from this survey would inform the rollout of IDA in Guyana in 2019. METHODS: Data collection for the study occurred in August 2019, using a validated questionnaire administered by trained enumerators. Across all regions, a total of 1,248 participants were sampled by the Filarial Mapping team. Four-hundred and fifty-one participants aged over 18 years were randomly selected for participation in an expanded acceptability questionnaire. All data were captured in Secure Data Kit (SDK). RESULTS: Acceptability was measured using a mean acceptability score. Unadjusted mean scores ranged from 24.6 to 29.3, with 22.5 as the threshold of acceptability. Regional variation occurred across many indicators of interest: self-rated understanding about LF, mechanisms of LF transmission, LF drug safety and history of treatment during MDA. Region IV (Georgetown) recorded higher knowledge about LF, but lower compliance and acceptability. Number of pills was not perceived as a concern. CONCLUSION: Acceptability of MDA was good across all four regions under study. Results from this study set a baseline level for key indicators and acceptability, from which the acceptability of IDA can be measured. Regional variations across indicators suggest that localized approaches should be considered for social mobilization and MDA delivery to capture these contextual differences

A scoping review establishes need for consensus guidance on reporting health equity in observational studies.

To evaluate the support from the available guidance on reporting of health equity in research for our candidate items and to identify additional items for the Strengthening Reporting of Observational studies in Epidemiology-Equity extension. We conducted a scoping review by searching Embase, MEDLINE, CINAHL, Cochrane Methodology Register, LILACS, and Caribbean Center on Health Sciences Information up to January 2022. We also searched reference lists and gray literature for additional resources. We included guidance and assessments (hereafter termed "resources") related to conduct and/or reporting for any type of health research with or about people experiencing health inequity. We included 34 resources, which supported one or more candidate items or contributed to new items about health equity reporting in observational research. Each candidate item was supported by a median of six (range: 1-15) resources. In addition, 12 resources suggested 13 new items, such as "report the background of investigators". Existing resources for reporting health equity in observational studies aligned with our interim checklist of candidate items. We also identified additional items that will be considered in the development of a consensus-based and evidence-based guideline for reporting health equity in observational studies