Nonlinear Integer Programming

Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject to integrality requirements for the variables. This chapter is dedicated to this topic. The primary goal is a study of a simple version of general nonlinear integer problems, where all constraints are still linear. Our focus is on the computational complexity of the problem, which varies significantly with the type of nonlinear objective function in combination with the underlying combinatorial structure. Numerous boundary cases of complexity emerge, which sometimes surprisingly lead even to polynomial time algorithms. We also cover recent successful approaches for more general classes of problems. Though no positive theoretical efficiency results are available, nor are they likely to ever be available, these seem to be the currently most successful and interesting approaches for solving practical problems. It is our belief that the study of algorithms motivated by theoretical considerations and those motivated by our desire to solve practical instances should and do inform one another. So it is with this viewpoint that we present the subject, and it is in this direction that we hope to spark further research.Comment: 57 pages. To appear in: M. J\"unger, T. Liebling, D. Naddef, G. Nemhauser, W. Pulleyblank, G. Reinelt, G. Rinaldi, and L. Wolsey (eds.), 50 Years of Integer Programming 1958--2008: The Early Years and State-of-the-Art Surveys, Springer-Verlag, 2009, ISBN 354068274

Implementation of a quantum algorithm to solve Bernstein-Vazirani's parity problem without entanglement on an ensemble quantum computer

Bernstein and Varizani have given the first quantum algorithm to solve parity problem in which a strong violation of the classical imformation theoritic bound comes about. In this paper, we refine this algorithm with fewer resource and implement a two qubits algorithm in a single query on an ensemble quantum computer for the first time

Assessing the causal role of epigenetic clocks in the development of multiple cancers: a Mendelian randomization study

Background: Epigenetic clocks have been associated with cancer risk in several observational studies. Nevertheless, it is unclear whether they play a causal role in cancer risk or if they act as a non-causal biomarker. Methods: We conducted a two-sample Mendelian randomization (MR) study to examine the genetically predicted effects of epigenetic age acceleration as measured by HannumAge (nine single-nucleotide polymorphisms (SNPs)), Horvath Intrinsic Age (24 SNPs), PhenoAge (11 SNPs), and GrimAge (4 SNPs) on multiple cancers (i.e. breast, prostate, colorectal, ovarian and lung cancer). We obtained genome-wide association data for biological ageing from a meta-analysis (N = 34,710), and for cancer from the UK Biobank (N cases = 2671-13,879; N controls = 173,493-372,016), FinnGen (N cases = 719-8401; N controls = 74,685-174,006) and several international cancer genetic consortia (N cases = 11,348-122,977; N controls = 15,861-105,974). Main analyses were performed using multiplicative random effects inverse variance weighted (IVW) MR. Individual study estimates were pooled using fixed effect meta-analysis. Sensitivity analyses included MR-Egger, weighted median, weighted mode and Causal Analysis using Summary Effect Estimates (CAUSE) methods, which are robust to some of the assumptions of the IVW approach. Results: Meta-analysed IVW MR findings suggested that higher GrimAge acceleration increased the risk of colorectal cancer (OR = 1.12 per year increase in GrimAge acceleration, 95% CI 1.04-1.20, p = 0.002). The direction of the genetically predicted effects was consistent across main and sensitivity MR analyses. Among subtypes, the genetically predicted effect of GrimAge acceleration was greater for colon cancer (IVW OR = 1.15, 95% CI 1.09-1.21, p = 0.006), than rectal cancer (IVW OR = 1.05, 95% CI 0.97-1.13, p = 0.24). Results were less consistent for associations between other epigenetic clocks and cancers. Conclusions: GrimAge acceleration may increase the risk of colorectal cancer. Findings for other clocks and cancers were inconsistent. Further work is required to investigate the potential mechanisms underlying the results. Funding: FMB was supported by a Wellcome Trust PhD studentship in Molecular, Genetic and Lifecourse Epidemiology (224982/Z/22/Z which is part of grant 218495/Z/19/Z). KKT was supported by a Cancer Research UK (C18281/A29019) programme grant (the Integrative Cancer Epidemiology Programme) and by the Hellenic Republic's Operational Programme 'Competitiveness, Entrepreneurship & Innovation' (OΠΣ 5047228). PH was supported by Cancer Research UK (C18281/A29019). RMM was supported by the NIHR Biomedical Research Centre at University Hospitals Bristol and Weston NHS Foundation Trust and the University of Bristol and by a Cancer Research UK (C18281/A29019) programme grant (the Integrative Cancer Epidemiology Programme). RMM is a National Institute for Health Research Senior Investigator (NIHR202411). The views expressed are those of the author(s) and not necessarily those of the NIHR or the Department of Health and Social Care. GDS and CLR were supported by the Medical Research Council (MC_UU_00011/1 and MC_UU_00011/5, respectively) and by a Cancer Research UK (C18281/A29019) programme grant (the Integrative Cancer Epidemiology Programme). REM was supported by an Alzheimer's Society project grant (AS-PG-19b-010) and NIH grant (U01 AG-18-018, PI: Steve Horvath). RCR is a de Pass Vice Chancellor's Research Fellow at the University of Bristol

Level Densities and Radiative Strength Functions in 170,171Yb

Level densities and radiative strength functions in {sup 171}Yb and{sup 170}Yb nuclei have been measured with the {sup 171}Yb({sup 3}He, {sup 3}He{prime}{gamma}){sup 171}Yb and {sup 171}Yb({sup 3}He,{alpha}{gamma}){sup 170}Yb reactions. A simultaneous determination of the nuclear level density and the radiative strength function was made. The present data adds to and is consistent with previous results for several other rare earth nuclei. The method will be briefly reviewed and the result from the analysis will be presented. The radiative strength function for {sup 171}Yb is compared to previously published work

Effects of social approval bias on self-reported fruit and vegetable consumption: a randomized controlled trial

<p>Abstract</p> <p>Background</p> <p>Self-reports of dietary intake in the context of nutrition intervention research can be biased by the tendency of respondents to answer consistent with expected norms (social approval bias). The objective of this study was to assess the potential influence of social approval bias on self-reports of fruit and vegetable intake obtained using both food frequency questionnaire (FFQ) and 24-hour recall methods.</p> <p>Methods</p> <p>A randomized blinded trial compared reported fruit and vegetable intake among subjects exposed to a potentially biasing prompt to that from control subjects. Subjects included 163 women residing in Colorado between 35 and 65 years of age who were randomly selected and recruited by telephone to complete what they were told would be a future telephone survey about health. Randomly half of the subjects then received a letter prior to the interview describing this as a study of fruit and vegetable intake. The letter included a brief statement of the benefits of fruits and vegetables, a 5-A-Day sticker, and a 5-a-Day refrigerator magnet. The remainder received the same letter, but describing the study purpose only as a more general nutrition survey, with neither the fruit and vegetable message nor the 5-A-Day materials. Subjects were then interviewed on the telephone within 10 days following the letters using an eight-item FFQ and a limited 24-hour recall to estimate fruit and vegetable intake. All interviewers were blinded to the treatment condition.</p> <p>Results</p> <p>By the FFQ method, subjects who viewed the potentially biasing prompts reported consuming more fruits and vegetables than did control subjects (5.2 vs. 3.7 servings per day, p < 0.001). By the 24-hour recall method, 61% of the intervention group but only 32% of the control reported eating fruits and vegetables on 3 or more occasions the prior day (p = 0.002). These associations were independent of age, race/ethnicity, education level, self-perceived health status, and time since last medical check-up.</p> <p>Conclusion</p> <p>Self-reports of fruit and vegetable intake using either a food frequency questionnaire or a limited 24-hour recall are both susceptible to substantial social approval bias. Valid assessments of intervention effects in nutritional intervention trials may require objective measures of dietary change.</p