Subtropical Real Root Finding

We describe a new incomplete but terminating method for real root finding for large multivariate polynomials. We take an abstract view of the polynomial as the set of exponent vectors associated with sign information on the coefficients. Then we employ linear programming to heuristically find roots. There is a specialized variant for roots with exclusively positive coordinates, which is of considerable interest for applications in chemistry and systems biology. An implementation of our method combining the computer algebra system Reduce with the linear programming solver Gurobi has been successfully applied to input data originating from established mathematical models used in these areas. We have solved several hundred problems with up to more than 800000 monomials in up to 10 variables with degrees up to 12. Our method has failed due to its incompleteness in less than 8 percent of the cases

The timing of leaf flush in European beech (Fagus sylvatica L.) saplings

Spring phenology is considered one of the most important determinants of growth and survival in young stands. It is relatively easy to monitor and is expected to respond to climate changes that will affect the favourable period for growth in temperate regions. The response of trees to the environmental cues that govern spring phenology is largely under genetic control and inter-populational differences exist within species. This suggests that the trait undergoes site-specific selection. Data obtained through monitoring of bud burst at multiple beech provenance-trials were compared with specific site and weather data to reveal geographical clines in beech phenology. We fitted the Weibull function to harmonise phenology data collected using various flushing scales and at different intensities of monitoring. By comparing data from 20 annual census of phenology performed across 13 sites throughout Europe, we showed that accumulated temperature sum > 5°C modelled the timing and duration of flushing more consistently than other temperature sum models > 0°C or > 8°C, or simply Julian Day. Inconsistency in the number of degree hours required for flushing among sites, reinforced the need for testing of more complex mechanistic models that include photoperiod, chilling period, and summer drought in addition to temperature sum. South-North, East-West, and low-high elevational clines were confirmed from the analysis. These findings; reinforce the need for caution in planting provenances from the south-east of Europe, suited to warmer-drier summers, in more north-westerly sites; and highlight the location of some potentially valuable late-flushing populations that also tolerate warm dry temperatures.Peer reviewe

Antiferromagnetic spintronics

Antiferromagnetic materials are magnetic inside, however, the direction of their ordered microscopic moments alternates between individual atomic sites. The resulting zero net magnetic moment makes magnetism in antiferromagnets invisible on the outside. It also implies that if information was stored in antiferromagnetic moments it would be insensitive to disturbing external magnetic fields, and the antiferromagnetic element would not affect magnetically its neighbors no matter how densely the elements were arranged in a device. The intrinsic high frequencies of antiferromagnetic dynamics represent another property that makes antiferromagnets distinct from ferromagnets. The outstanding question is how to efficiently manipulate and detect the magnetic state of an antiferromagnet. In this article we give an overview of recent works addressing this question. We also review studies looking at merits of antiferromagnetic spintronics from a more general perspective of spin-ransport, magnetization dynamics, and materials research, and give a brief outlook of future research and applications of antiferromagnetic spintronics.Comment: 13 pages, 7 figure

On the relationship between standard intersection cuts, lift-and-project cuts, and generalized intersection cuts

We examine the connections between the classes of cuts in the title. We show that lift-and-project (L&P) cuts from a given disjunction are equivalent to generalized intersection cuts from the family of polyhedra obtained by taking positive combinations of the complements of the inequalities of each term of the disjunction. While L&P cuts from split disjunctions are known to be equivalent to standard intersection cuts (SICs) from the strip obtained by complementing the terms of the split, we show that L&P cuts from more general disjunctions may not be equivalent to any SIC. In particular, we give easily verifiable necessary and sufficient conditions for a L&P cut from a given disjunction D to be equivalent to a SIC from the polyhedral counterpart of D. Irregular L&P cuts, i.e. those that violate these conditions, have interesting properties. For instance, unlike the regular ones, they may cut off part of the corner polyhedron associated with the LP solution from which they are derived. Furthermore, they are not exceptional: their frequency exceeds that of regular cuts. A numerical example illustrates some of the above properties. © 2016 Springer-Verlag Berlin Heidelberg and Mathematical Optimization Societ

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

Sources of scientific creativity: participant observation of a public research institute in Korea

This study aims to find the factors of scientists' creative thoughts by observing directly their laboratories in Korea Research Institute of Chemical Technology (KRICT). The participant observation was performed for 5 months from December 2013 through April 2014, and the research object was the lab which had been selected both as Top KRICT laboratory and Top National R&D Project. For in-depth examination, the target lab was supposed to be observed for a long time, taking part in the lab meetings, interviewing the researchers. From the interview data, Protocol analysis or Verbal data analysis was employed to analyze the recorded data. The research results are as follows. First, as several studies had suggested, the frequent use of analogies was verified as an important source for scientists' creative thoughts, in that those analogies were used for 12 times in 2 lab meetings, which was 6 times per each. Secondly, the frequent appearance of unexpected findings was found, that is, 8 out of 15 experiment findings were unexpected. We found that the scientists pay close attention to the unexpected findings in that 67 out of 88 intra-group interactions were about the unexpected findings, and 21 out of 24 individual reasoningblocks were about the unexpected findings. Finally, we found that the seeds of new knowledge and ideas sprouted and spread through the distributed reasoning process, which is the major characteristic of modern science that is generally conducted by group of scientists. The findings have two theoretical implications. First, it may increase the availability of Ikujiro Nonaka's knowledge-creation model by adding another case study. It may also contribute to balance between supply-side and demand-side perspective of Innovation. System studies by supplementing supply-side perspective

Analysis of ecological thresholds in a temperate forest undergoing dieback.

Positive feedbacks in drivers of degradation can cause threshold responses in natural ecosystems. Though threshold responses have received much attention in studies of aquatic ecosystems, they have been neglected in terrestrial systems, such as forests, where the long time-scales required for monitoring have impeded research. In this study we explored the role of positive feedbacks in a temperate forest that has been monitored for 50 years and is undergoing dieback, largely as a result of death of the canopy dominant species (Fagus sylvatica, beech). Statistical analyses showed strong non-linear losses in basal area for some plots, while others showed relatively gradual change. Beech seedling density was positively related to canopy openness, but a similar relationship was not observed for saplings, suggesting a feedback whereby mortality in areas with high canopy openness was elevated. We combined this observation with empirical data on size- and growth-mediated mortality of trees to produce an individual-based model of forest dynamics. We used this model to simulate changes in the structure of the forest over 100 years under scenarios with different juvenile and mature mortality probabilities, as well as a positive feedback between seedling and mature tree mortality. This model produced declines in forest basal area when critical juvenile and mature mortality probabilities were exceeded. Feedbacks in juvenile mortality caused a greater reduction in basal area relative to scenarios with no feedback. Non-linear, concave declines of basal area occurred only when mature tree mortality was 3-5 times higher than rates observed in the field. Our results indicate that the longevity of trees may help to buffer forests against environmental change and that the maintenance of old, large trees may aid the resilience of forest stands. In addition, our work suggests that dieback of forests may be avoidable providing pressures on mature and juvenile trees do not pass critical thresholds