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

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

Two factor saturated designs: cycles, Gini index and state polytopes

In this paper we analyze and characterize the saturated fractions of two-factor designs under the simple effect model. Using Li et al.ear algebra, we define a criterion to check whether a given fraction is saturated or not. We also compute the number of saturated fractions, providing an alternative proof of the Cayley's formula. Finally we show how, given a list of saturated fractions, Gini indexes of their margins and the associated state polytopes could be used to classify them

Elements of mathematics in problems. Through olympiads and circles to profession

This is a collection of teaching materials used in several Russian universities, schools, and mathematical circles. Most problems are chosen in such a way that in the course of the solution and discussion a reader learns important mathematical ideas and theories. The materials can be used by pupils and students for self-study, and by teachers. This is an abridged pre-copyedit version of the published book submitted with the permission of the publisher. Each included individual material is self-contained and ready-for-use. Solutions to problems are not included intentionally. This collection consolidates updates of several arXiv submissions, e.g., arXiv:1305.2598.Comment: Edited by A. Skopenkov, M. Skopenkov, A. Zaslavsky. In Russian. Optimized for printing on A5 paper. Moscow Center for Continuous Mathematical Education, 2018, 592pp (in Russian

Solar Neutrino Constraints on the BBN Production of Li

Using the recent WMAP determination of the baryon-to-photon ratio, 10^{10} \eta = 6.14 to within a few percent, big bang nucleosynthesis (BBN) calculations can make relatively accurate predictions of the abundances of the light element isotopes which can be tested against observational abundance determinations. At this value of \eta, the Li7 abundance is predicted to be significantly higher than that observed in low metallicity halo dwarf stars. Among the possible resolutions to this discrepancy are 1) Li7 depletion in the atmosphere of stars; 2) systematic errors originating from the choice of stellar parameters - most notably the surface temperature; and 3) systematic errors in the nuclear cross sections used in the nucleosynthesis calculations. Here, we explore the last possibility, and focus on possible systematic errors in the He3(\alpha,\gamma)Be7 reaction, which is the only important Li7 production channel in BBN. The absolute value of the cross section for this key reaction is known relatively poorly both experimentally and theoretically. The agreement between the standard solar model and solar neutrino data thus provides additional constraints on variations in the cross section (S_{34}). Using the standard solar model of Bahcall, and recent solar neutrino data, we can exclude systematic S_{34} variations of the magnitude needed to resolve the BBN Li7 problem at > 95% CL. Additional laboratory data on He3(\alpha,\gamma)Be7 will sharpen our understanding of both BBN and solar neutrinos, particularly if care is taken in determining the absolute cross section and its uncertainties. Nevertheless, it already seems that this ``nuclear fix'' to the Li7 BBN problem is unlikely; other possible solutions are briefly discussed.Comment: 21 pages, 3 ps figure

The effects of crop diversity and crop type on biological diversity in agricultural landscapes: a systematic review protocol.

Agricultural intensification is a well-known driver of biodiversity loss. Crop diversity and its changes over space and time drive land use intensity and impact biodiversity of agricultural landscapes, while meeting the growing demand for human food and nutrition resources. Loss of biodiversity in agricultural landscapes reduces primary productivity and soil health and erodes a range of other ecosystem services. At present, while having partial understanding of many processes, we lack a general synthesis of our knowledge of the links between crop diversity and biodiversity. We will therefore conduct a systematic review by searching multiple agriculture, ecology and environmental science databases (e.g. Web of Science, Geobase, Agris, AGRICOLA, GreenFILE) to identify studies reporting the impacts of crop diversity and crop type on the biological diversity of fauna and flora in agricultural landscapes. Response variables will include metrics of species richness, abundance, assemblage, community composition and species rarity. Screening, data coding and data extraction will be carried out by one researcher and a subset will be independently carried out by a second researcher for quality control. Study quality and risk of bias will be assessed. Evidence will first be mapped to species/taxa then assessed for further narrative or statistical synthesis based on comparability of results and likely robustness. Gaps in the evidence base will also be identified with a view toward future research and policy directions for nutrition, food systems and ecology

Multiple primary tumours in women following breast cancer, 1973–2000

We investigated the predictors of the risk of developing a second primary cancer after breast cancer, this occurring in about 12% of affected women. The analysis included 335 191 females, registered in the National Cancer Institute's Surveillance Epidemiology and End Results (SEER) database, who had been diagnosed with breast cancer. Observed numbers of subsequent cancers in the SEER database with a first breast cancer diagnosed from 1973 to 2000 were compared with the expected numbers based on age-adjusted incidence rates to calculate standardised incidence ratios. Kaplan–Meier curves were conducted to determine the median time until the second primary cancer diagnosis. Average number of years until diagnosis varied by site and by age as well as median years until second cancer diagnosis. Most cancer risks decreased with age, but there was an increase in aging-related cancers such as lung cancer. The median years of follow-up were well beyond the 5-year mark. Breast cancer survivors should be advised of their increased risk for developing certain cancers in their lifetime