6 research outputs found
TheoryGuru: A Mathematica Package to Apply Quantifier Elimination Technology to Economics
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 201
Comparing machine learning models to choose the variable ordering for cylindrical algebraic decomposition
There has been recent interest in the use of machine learning (ML) approaches
within mathematical software to make choices that impact on the computing
performance without affecting the mathematical correctness of the result. We
address the problem of selecting the variable ordering for cylindrical
algebraic decomposition (CAD), an important algorithm in Symbolic Computation.
Prior work to apply ML on this problem implemented a Support Vector Machine
(SVM) to select between three existing human-made heuristics, which did better
than anyone heuristic alone. The present work extends to have ML select the
variable ordering directly, and to try a wider variety of ML techniques.
We experimented with the NLSAT dataset and the Regular Chains Library CAD
function for Maple 2018. For each problem, the variable ordering leading to the
shortest computing time was selected as the target class for ML. Features were
generated from the polynomial input and used to train the following ML models:
k-nearest neighbours (KNN) classifier, multi-layer perceptron (MLP), decision
tree (DT) and SVM, as implemented in the Python scikit-learn package. We also
compared these with the two leading human constructed heuristics for the
problem: Brown's heuristic and sotd. On this dataset all of the ML approaches
outperformed the human made heuristics, some by a large margin.Comment: Accepted into CICM 201
Endocytosis and signalling: A meeting with mathematics
Although endocytosis has traditionally been understood as a signal attenuation mechanism, an emerging view considers endocytosis as an integral part of signal propagation and processing. On the short time scale, trafficking of endocytic vesicles contributes to signal propagation from the surface to distant targets, with bi-directional communication between signalling and trafficking. Mathematical modelling helps combine the mechanistic, molecular knowledge with rigorous analysis of the complex output dynamics of endocytosis in time and space. Simulations reveal novel roles for endocytosis, including the control of cell polarity, enhancing the spatial signal propagation, and controlling the signal magnitudes, kinetics, and synchronization with stimulus dynamics.SFI & NIH grants GM059570 & R33HL088283Deposited by bulk impor