One Dimensional Continuum Falicov-Kimball Model in the Strongly Correlated Limit

In this paper we study the thermodynamics of the one dimensional continuum analogue of the Falicov-Kimball model in the strongly correlated limit using a method developed by Salsburg, Zwanzig and Kirkwood for the Takahashi gas. In the ground state it is found that the $f$ electrons form a cluster. The effect of including a Takahashi repulsion between $f$ particles is also studied where it is found that as the repulsion is increased the ground state $f$ electron configuration changes discontinuously from the clustered configuration to a homogeneous or equal spaced configuration analogous to the checkerboard configuration which arises in the lattice Falicov-Kimball model.Comment: 17 pages, Standard Latex File (UUencoded Postscript file of figures available upon request. To appear in physica A) MELB-MATHS-PP-1096783, email: [email protected]

A Poly-algorithmic Approach to Quantifier Elimination

Cylindrical Algebraic Decomposition (CAD) was the first practical means for doing real quantifier elimination (QE), and is still a major method, with many improvements since Collins' original method. Nevertheless, its complexity is inherently doubly exponential in the number of variables. Where applicable, virtual term substitution (VTS) is more effective, turning a QE problem in $n$ variables to one in $n-1$ variables in one application, and so on. Hence there is scope for hybrid methods: doing VTS where possible then using CAD. This paper describes such a poly-algorithmic implementation, based on the second author's Ph.D. thesis. The version of CAD used is based on a new implementation of Lazard's recently-justified method, with some improvements to handle equational constraints

Non-linear Real Arithmetic Benchmarks derived from Automated Reasoning in Economics

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:1804.1003

Communication skills in children aged 6-8 years, without cerebral palsy cooled for neonatal hypoxic-ischemic encephalopathy

We assessed communication skills of 48 children without cerebral palsy (CP) treated with therapeutic hypothermia (TH) for neonatal hypoxic-ischemic encephalopathy (HIE) (cases) compared to 42 controls at early school-age and examined their association with white matter diffusion properties in both groups and 18-month Bayley-III developmental assessments in cases. Parents completed a Children’s Communication Checklist (CCC-2) yielding a General Communication Composite (GCC), structural and pragmatic language scores and autistic-type behavior score. GCC ≤ 54 and thresholds of structural and pragmatic language score differences defined language impairment. Using tract-based spatial statistics (TBSS), fractional anisotropy (FA) was compared between 31 cases and 35 controls. Compared to controls, cases had lower GCC (p = 0.02), structural (p = 0.03) and pragmatic language score (p = 0.04) and higher language impairments (p = 0.03). GCC correlated with FA in the mid-body of the corpus callosum, the cingulum and the superior longitudinal fasciculus (p < 0.05) in cases. Bayley-III Language Composite correlated with GCC (r = 0.34, p = 0.017), structural (r = 0.34, p = 0.02) and pragmatic (r = 0.32, p = 0.03) language scores and autistic-type behaviors (r = 0.36, p = 0.01)