OpenMath and SMT-LIB

OpenMath and SMT-LIB are languages with very different origins, but both "represent mathematics". We describe SMT-LIB for the OpenMath community and consider adaptations for both languages to support the growing SC-Square initiative.Comment: Presented in the OpenMath 2017 Workshop, at CICM 2017, Edinburgh, U

Adapting Real Quantifier Elimination Methods for Conflict Set Computation

The satisfiability problem in real closed fields is decidable. In the context of satisfiability modulo theories, the problem restricted to conjunctive sets of literals, that is, sets of polynomial constraints, is of particular importance. One of the central problems is the computation of good explanations of the unsatisfiability of such sets, i.e.\ obtaining a small subset of the input constraints whose conjunction is already unsatisfiable. We adapt two commonly used real quantifier elimination methods, cylindrical algebraic decomposition and virtual substitution, to provide such conflict sets and demonstrate the performance of our method in practice

Altered Brain Structure in Infants with Turner Syndrome

Turner syndrome (TS) is a genetic disorder affecting approximately 1:2000 live-born females. It results from partial or complete X monosomy and is associated with a range of clinical issues including a unique cognitive profile and increased risk for certain behavioral problems. Structural neuroimaging studies in adolescents, adults, and older children with TS have revealed altered neuroanatomy but are unable to identify when in development differences arise. In addition, older children and adults have often been exposed to years of growth hormone and/or exogenous estrogen therapy with potential implications for neurodevelopment. The study presented here is the first to test whether brain structure is altered in infants with TS. Twenty-six infants with TS received high-resolution structural MRI scans of the brain at 1 year of age and were compared to 47 typically developing female and 39 typically developing male infants. Results indicate that the typical neuroanatomical profile seen in older individuals with TS, characterized by decreased gray matter volumes in premotor, somatosensory, and parietal-occipital cortex, is already present at 1 year of age, suggesting a stable phenotype with origins in the prenatal or early postnatal period

Real Algebraic Strategies for MetiTarski Proofs

Abstract. MetiTarski [1] is an automatic theorem prover that can prove inequalities involving sin, cos, exp, ln, etc. During its proof search, it generates a series of subproblems in nonlinear polynomial real arithmetic which are reduced to true or false using a decision procedure for the theory of real closed fields (RCF). These calls are often a bottleneck: RCF is fundamentally infeasible. However, by studying these subproblems, we can design specialised variants of RCF decision procedures that run faster and improve MetiTarski’s performance.

Combined Decision Techniques for the Existential Theory of the Reals

Methods for deciding quantifier-free non-linear arithmetical conjectures over *** are crucial in the formal verification of many real-world systems and in formalised mathematics. While non-linear (rational function) arithmetic over *** is decidable, it is fundamentally infeasible: any general decision method for this problem is worst-case exponential in the dimension (number of variables) of the formula being analysed. This is unfortunate, as many practical applications of real algebraic decision methods require reasoning about high-dimensional conjectures. Despite their inherent infeasibility, a number of different decision methods have been developed, most of which have "sweet spots" --- e.g., types of problems for which they perform much better than they do in general. Such "sweet spots" can in many cases be heuristically combined to solve problems that are out of reach of the individual decision methods when used in isolation. RAHD ("Real Algebra in High Dimensions") is a theorem prover that works to combine a collection of real algebraic decision methods in ways that exploit their respective "sweet-spots." We discuss high-level mathematical and design aspects of RAHD and illustrate its use on a number of examples

Search for composite and exotic fermions at LEP 2

A search for unstable heavy fermions with the DELPHI detector at LEP is reported. Sequential and non-canonical leptons, as well as excited leptons and quarks, are considered. The data analysed correspond to an integrated luminosity of about 48 pb^{-1} at an e^+e^- centre-of-mass energy of 183 GeV and about 20 pb^{-1} equally shared between the centre-of-mass energies of 172 GeV and 161 GeV. The search for pair-produced new leptons establishes 95% confidence level mass limits in the region between 70 GeV/c^2 and 90 GeV/c^2, depending on the channel. The search for singly produced excited leptons and quarks establishes upper limits on the ratio of the coupling of the excited fermio

Search for lightest neutralino and stau pair production in light gravitino scenarios with stau NLSP

Promptly decaying lightest neutralinos and long-lived staus are searched for in the context of light gravitino scenarios. It is assumed that the stau is the next to lightest supersymmetric particle (NLSP) and that the lightest neutralino is the next to NLSP (NNLSP). Data collected with the Delphi detector at centre-of-mass energies from 161 to 183 \GeV are analysed. No evidence of the production of these particles is found. Hence, lower mass limits for both kinds of particles are set at 95% C.L.. The mass of gaugino-like neutralinos is found to be greater than 71.5 GeV/c^2. In the search for long-lived stau, masses less than 70.0 to 77.5 \GeVcc are excluded for gravitino masses from 10 to 150 \eVcc . Combining this search with the searches for stable heavy leptons and Minimal Supersymmetric Standard Model staus a lower limit of 68.5 \GeVcc may be set for the stau mas