The Potential and Challenges of CAD with Equational Constraints for SC-Square

Cylindrical algebraic decomposition (CAD) is a core algorithm within Symbolic Computation, particularly for quantifier elimination over the reals and polynomial systems solving more generally. It is now finding increased application as a decision procedure for Satisfiability Modulo Theories (SMT) solvers when working with non-linear real arithmetic. We discuss the potentials from increased focus on the logical structure of the input brought by the SMT applications and SC-Square project, particularly the presence of equational constraints. We also highlight the challenges for exploiting these: primitivity restrictions, well-orientedness questions, and the prospect of incrementality.Comment: Accepted into proceedings of MACIS 201

Advances in therapeutic peptides targeting G protein-coupled receptors.

Dysregulation of peptide-activated pathways causes a range of diseases, fostering the discovery and clinical development of peptide drugs. Many endogenous peptides activate G protein-coupled receptors (GPCRs) - nearly 50 GPCR peptide drugs have been approved to date, most of them for metabolic disease or oncology, and more than 10 potentially first-in-class peptide therapeutics are in the pipeline. The majority of existing peptide therapeutics are agonists, which reflects the currently dominant strategy of modifying the endogenous peptide sequence of ligands for peptide-binding GPCRs. Increasingly, novel strategies are being employed to develop both agonists and antagonists, to both introduce chemical novelty and improve drug-like properties. Pharmacodynamic improvements are evolving to allow biasing ligands to activate specific downstream signalling pathways, in order to optimize efficacy and reduce side effects. In pharmacokinetics, modifications that increase plasma half-life have been revolutionary. Here, we discuss the current status of the peptide drugs targeting GPCRs, with a focus on evolving strategies to improve pharmacokinetic and pharmacodynamic properties.Wellcome Trust [WT107715/Z/15/Z], Cambridge Biomedical Research Centre Biomedical Resources Gran

Nonexistence Certificates for Ovals in a Projective Plane of Order Ten

In 1983, a computer search was performed for ovals in a projective plane of order ten. The search was exhaustive and negative, implying that such ovals do not exist. However, no nonexistence certificates were produced by this search, and to the best of our knowledge the search has never been independently verified. In this paper, we rerun the search for ovals in a projective plane of order ten and produce a collection of nonexistence certificates that, when taken together, imply that such ovals do not exist. Our search program uses the cube-and-conquer paradigm from the field of satisfiability (SAT) checking, coupled with a programmatic SAT solver and the nauty symbolic computation library for removing symmetries from the search.Comment: Appears in the Proceedings of the 31st International Workshop on Combinatorial Algorithms (IWOCA 2020

Need Polynomial Systems Be Doubly-Exponential?

Polynomial Systems, or at least their algorithms, have the reputation of being doubly-exponential in the number of variables [Mayr and Mayer, 1982], [Davenport and Heintz, 1988]. Nevertheless, the Bezout bound tells us that that number of zeros of a zero-dimensional system is singly-exponential in the number of variables. How should this contradiction be reconciled? We first note that [Mayr and Ritscher, 2013] shows that the doubly exponential nature of Gr\"{o}bner bases is with respect to the dimension of the ideal, not the number of variables. This inspires us to consider what can be done for Cylindrical Algebraic Decomposition which produces a doubly-exponential number of polynomials of doubly-exponential degree. We review work from ISSAC 2015 which showed the number of polynomials could be restricted to doubly-exponential in the (complex) dimension using McCallum's theory of reduced projection in the presence of equational constraints. We then discuss preliminary results showing the same for the degree of those polynomials. The results are under primitivity assumptions whose importance we illustrate.Comment: Extended Abstract for ICMS 2016 Presentation. arXiv admin note: text overlap with arXiv:1605.0249

Worm Grunting, Fiddling, and Charming—Humans Unknowingly Mimic a Predator to Harvest Bait

Background: For generations many families in and around Florida’s Apalachicola National Forest have supported themselves by collecting the large endemic earthworms (Diplocardia mississippiensis). This is accomplished by vibrating a wooden stake driven into the soil, a practice called ‘‘worm grunting’’. In response to the vibrations, worms emerge to the surface where thousands can be gathered in a few hours. Why do these earthworms suddenly exit their burrows in response to vibrations, exposing themselves to predation? Principal Findings: Here it is shown that a population of eastern American moles (Scalopus aquaticus) inhabits the area where worms are collected and that earthworms have a pronounced escape response from moles consisting of rapidly exiting their burrows to flee across the soil surface. Recordings of vibrations generated by bait collectors and moles suggest that ‘‘worm grunters’ ’ unknowingly mimic digging moles. An alternative possibility, that worms interpret vibrations as rain and surface to avoid drowning is not supported. Conclusions: Previous investigations have revealed that both wood turtles and herring gulls vibrate the ground to elicit earthworm escapes, indicating that a range of predators may exploit the predator-prey relationship between earthworms and moles. In addition to revealing a novel escape response that may be widespread among soil fauna, the results sho

Machine Learning for Mathematical Software

While there has been some discussion on how Symbolic Computation could be used for AI there is little literature on applications in the other direction. However, recent results for quantifier elimination suggest that, given enough example problems, there is scope for machine learning tools like Support Vector Machines to improve the performance of Computer Algebra Systems. We survey the authors own work and similar applications for other mathematical software. It may seem that the inherently probabilistic nature of machine learning tools would invalidate the exact results prized by mathematical software. However, algorithms and implementations often come with a range of choices which have no effect on the mathematical correctness of the end result but a great effect on the resources required to find it, and thus here, machine learning can have a significant impact.Comment: To appear in Proc. ICMS 201

Integration of decision support systems to improve decision support performance

Decision support system (DSS) is a well-established research and development area. Traditional isolated, stand-alone DSS has been recently facing new challenges. In order to improve the performance of DSS to meet the challenges, research has been actively carried out to develop integrated decision support systems (IDSS). This paper reviews the current research efforts with regard to the development of IDSS. The focus of the paper is on the integration aspect for IDSS through multiple perspectives, and the technologies that support this integration. More than 100 papers and software systems are discussed. Current research efforts and the development status of IDSS are explained, compared and classified. In addition, future trends and challenges in integration are outlined. The paper concludes that by addressing integration, better support will be provided to decision makers, with the expectation of both better decisions and improved decision making processes

Recent advances in real geometric reasoning

In the 1930s Tarski showed that real quantifier elimination was possible, and in 1975 Collins gave a remotely practicable method, albeit with doubly-exponential complexity, which was later shown to be inherent. We discuss some of the recent major advances in Collins method: such as an alternative approach based on passing via the complexes, and advances which come closer to "solving the question asked" rather than "solving all problems to do with these polynomials"