Search

This abstract seeks to introduce the ISSAC community to the DEWCAD project, which is based at Coventry University and the University of Bath, in the United Kingdom. The project seeks to push back the Doubly Exponential Wall of Cylindrical Algebraic Decomposition, through the integration of SAT/SMT technology, the extension of Lazard projection theory, and the development of new algorithms based on CAD technology but without producing CADs themselves. The project also seeks to develop applications of CAD and will focus on applications in the domains of economics and bio-network analysis., Comment: 5 pages. Accepted as short communication at ISSAC 2021

The field of exoplanetary science is making rapid progress both in statistical studies of exoplanet properties as well as in individual characterization. As space missions provide an emerging picture of formation and evolution of exoplanetary systems, the search for habitable worlds becomes one of the fundamental issues to address. To tackle such a complex challenge, we need to specify the conditions favorable for the origin, development and sustainment of life as we know it. This requires the understanding of global (astrospheric) and local (atmospheric, surface and internal) environments of exoplanets in the framework of the physical processes of the interaction between evolving planet-hosting stars along with exoplanetary evolution over geological timescales, and the resulting impact on climate and habitability of exoplanets. Feedbacks between astrophysical, physico-chemical atmospheric and geological processes can only be understood through interdisciplinary studies with the incorporation of progress in heliophysics, astrophysics, planetary, Earth sciences, astrobiology, and the origin of life communities. The assessment of the impacts of host stars on the climate and habitability of terrestrial (exo)planets and potential exomoons around them may significantly modify the extent and the location of the habitable zone and provide new directions for searching for signatures of life. Thus, characterization of stellar ionizing outputs becomes an important task for further understanding the extent of habitability in the universe. The goal of this white paper is to identify and describe promising key research goals to aid the theoretical characterization and observational detection of ionizing radiation from quiescent and flaring upper atmospheres of planet hosts as well as properties of stellar coronal mass ejections and stellar energetic particle events., Comment: White Paper submitted to the Astronomy and Astrophysics Decadal Survey (Astro2020), 8 pages, 1 figure

We consider a problem from biological network analysis of determining regions in a parameter space over which there are multiple steady states for positive real values of variables and parameters. We describe multiple approaches to address the problem using tools from Symbolic Computation. We describe how progress was made to achieve semi-algebraic descriptions of the multistationarity regions of parameter space, and compare symbolic results to numerical methods. The biological networks studied are models of the mitogen-activated protein kinases (MAPK) network which has already consumed considerable effort using special insights into its structure of corresponding models. Our main example is a model with 11 equations in 11 variables and 19 parameters, 3 of which are of interest for symbolic treatment. The model also imposes positivity conditions on all variables and parameters. We apply combinations of symbolic computation methods designed for mixed equality/inequality systems, specifically virtual substitution, lazy real triangularization and cylindrical algebraic decomposition, as well as a simplification technique adapted from Gaussian elimination and graph theory. We are able to determine multistationarity of our main example over a 2-dimensional parameter space. We also study a second MAPK model and a symbolic grid sampling technique which can locate such regions in 3-dimensional parameter space., Comment: 60 pages - author preprint. Accepted in the Journal of Symbolic Computation

We consider problems originating in economics that may be solved automatically using mathematical software. We present and make freely available a new benchmark set of such problems. The problems have been shown to fall within the framework of non-linear real arithmetic, and so are in theory soluble via Quantifier Elimination (QE) technology as usually implemented in computer algebra systems. Further, they all can be phrased in prenex normal form with only existential quantifiers and so are also admissible to those Satisfiability Module Theory (SMT) solvers that support the QF_NRA. There is a great body of work considering QE and SMT application in science and engineering, but we demonstrate here that there is potential for this technology also in the social sciences., Comment: To appear in Proc. SC-Square 2018. Dataset described is hosted by Zenodo at: https://doi.org/10.5281/zenodo.1226892 . arXiv admin note: substantial text overlap with arXiv:1804.10037

We consider the use of Quantifier Elimination (QE) technology for automated reasoning in economics. There is a great body of work considering QE applications in science and engineering but we demonstrate here that it also has use in the social sciences. We explain how many suggested theorems in economics could either be proven, or even have their hypotheses shown to be inconsistent, automatically via QE. However, economists who this technology could benefit are usually unfamiliar with QE, and the use of mathematical software generally. This motivated the development of a Mathematica Package TheoryGuru, whose purpose is to lower the costs of applying QE to economics. We describe the package's functionality and give examples of its use., Comment: To appear in Proc ICMS 2018

We show that a strong well-based cylindrical algebraic decomposition P of a bounded semi-algebraic set is a regular cell decomposition, in any dimension and independently of the method by which P is constructed. Being well-based is a global condition on P that holds for the output of many widely used algorithms. We also show the same for S of dimension at most 3 and P a strong cylindrical algebraic decomposition that is locally boundary simply connected: this is a purely local extra condition.

Symbolic Computation and Satisfiability Checking are two research areas, both having their individual scientific focus but sharing also common interests in the development, implementation and application of decision procedures for arithmetic theories. Despite their commonalities, the two communities are rather weakly connected. The aim of our newly accepted SC-square project (H2020-FETOPEN-CSA) is to strengthen the connection between these communities by creating common platforms, initiating interaction and exchange, identifying common challenges, and developing a common roadmap from theory along the way to tools and (industrial) applications. In this paper we report on the aims and on the first activities of this project, and formalise some relevant challenges for the unified SC-square community.

Symbolic Computation and Satisfiability Checking are viewed as individual research areas, but they share common interests in the development, implementation and application of decision procedures for arithmetic theories. Despite these commonalities, the two communities are currently only weakly connected. We introduce a new project SC-square to build a joint community in this area, supported by a newly accepted EU (H2020-FETOPEN-CSA) project of the same name. We aim to strengthen the connection between these communities by creating common platforms, initiating interaction and exchange, identifying common challenges, and developing a common roadmap. This abstract and accompanying poster describes the motivation and aims for the project, and reports on the first activities., Comment: 3 page Extended Abstract to accompany an ISSAC 2016 poster. Poster available at http://www.sc-square.org/SC2-AnnouncementPoster.pdf

The SDSS III APOGEE survey recently identified two new $\sigma$ Ori E type candidates, HD 345439 and HD 23478, which are a rare subset of rapidly rotating massive stars whose large (kGauss) magnetic fields confine circumstellar material around these systems. Our analysis of multi-epoch photometric observations of HD 345439 from the KELT, SuperWASP, and ASAS surveys reveals the presence of a $\sim$0.7701 day period in each dataset, suggesting the system is amongst the faster known $\sigma$ Ori E analogs. We also see clear evidence that the strength of H-alpha, H I Brackett series lines, and He I lines also vary on a $\sim$0.7701 day period from our analysis of multi-epoch, multi-wavelength spectroscopic monitoring of the system from the APO 3.5m telescope. We trace the evolution of select emission line profiles in the system, and observe coherent line profile variability in both optical and infrared H I lines, as expected for rigidly rotating magnetosphere stars. We also analyze the evolution of the H I Br-11 line strength and line profile in multi-epoch observations of HD 23478 from the SDSS-III APOGEE instrument. The observed periodic behavior is consistent with that recently reported by Sikora and collaborators in optical spectra., Comment: Accepted in ApJL

We present the results of a blind exercise to test the recoverability of stellar rotation and differential rotation in Kepler light curves. The simulated light curves lasted 1000 days and included activity cycles, Sun-like butterfly patterns, differential rotation and spot evolution. The range of rotation periods, activity levels and spot lifetime were chosen to be representative of the Kepler data of solar like stars. Of the 1000 simulated light curves, 770 were injected into actual quiescent Kepler light curves to simulate Kepler noise. The test also included five 1000-day segments of the Sun's total irradiance variations at different points in the Sun's activity cycle. Five teams took part in the blind exercise, plus two teams who participated after the content of the light curves had been released. The methods used included Lomb-Scargle periodograms and variants thereof, auto-correlation function, and wavelet-based analyses, plus spot modelling to search for differential rotation. The results show that the `overall' period is well recovered for stars exhibiting low and moderate activity levels. Most teams reported values within 10% of the true value in 70% of the cases. There was, however, little correlation between the reported and simulated values of the differential rotation shear, suggesting that differential rotation studies based on full-disk light curves alone need to be treated with caution, at least for solar-type stars. The simulated light curves and associated parameters are available online for the community to test their own methods., Comment: Accepted for publication in MNRAS. Accepted, 13 April 2015. Received, 26 March 2015; in original form, 9 November 2014