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

Inhibition of plasmin-mediated TAFI activation may affect development but not progression of abdominal aortic aneurysms

Objective: Thrombin-activatable fibrinolysis inhibitor (TAFI) reduces the breakdown of fibrin clots through its action as an indirect inhibitor of plasmin. Studies in TAFI-deficient mice have implicated a potential role for TAFI in Abdominal Aortic Aneurysm (AAA) disease. The role of TAFI inhibition on AAA formation in adult ApoE-/- mice is unknown. The aim of this paper was to investigate the effects of TAFI inhibition on AAA development and progression. Methods: Using the Angiotensin II model of AAA, male ApoE-/- mice were infused with Angiotensin II 750ng/kg/min with or without a monoclonal antibody inhibitor of plasmin-mediated activation of TAFI, MA-TCK26D6, or a competitive small molecule inhibitor of TAFI, UK-396082. Results: Inhibition of TAFI in the Angiotensin II model resulted in a decrease in the mortality associated with AAA rupture (from 40.0% to 16.6% with MA-TCK26D6 (log-rank Mantel Cox test p = 0.16), and 8.3% with UK-396082 (log-rank Mantel Cox test p = 0.05)). Inhibition of plasmin-mediated TAFI activation reduced the incidence of AAA from 52.4% to 30.0%. However, late treatment with MA-TCK26D6 once AAA were already established had no effect on the progression of AAA in this model. Conclusions: The formation of intra-mural thrombus is responsible for the dissection and early rupture in the angiotensin II model of AAA, and this process can be prevented through inhibition of TAFI. Late treatment with a TAFI inhibitor does not prevent AAA progression. These data may indicate a role for inhibition of plasmin-mediated TAFI activation in the early stages of AAA development, but not in its progression

Improved cross-validation for classifiers that make algorithmic choices to minimise runtime without compromising output correctness

Our topic is the use of machine learning to improve software by making choices which do not compromise the correctness of the output, but do affect the time taken to produce such output. We are particularly concerned with computer algebra systems (CASs), and in particular, our experiments are for selecting the variable ordering to use when performing a cylindrical algebraic decomposition of $n$-dimensional real space with respect to the signs of a set of polynomials. In our prior work we explored the different ML models that could be used, and how to identify suitable features of the input polynomials. In the present paper we both repeat our prior experiments on problems which have more variables (and thus exponentially more possible orderings), and examine the metric which our ML classifiers targets. The natural metric is computational runtime, with classifiers trained to pick the ordering which minimises this. However, this leads to the situation were models do not distinguish between any of the non-optimal orderings, whose runtimes may still vary dramatically. In this paper we investigate a modification to the cross-validation algorithms of the classifiers so that they do distinguish these cases, leading to improved results.Comment: 16 pages. Accepted into the Proceedings of MACIS 2019. arXiv admin note: text overlap with arXiv:1906.0145

Causes of Abnormal Ca2+ Transients in Guinea Pig Pathophysiological Ventricular Muscle Revealed by Ca2+ and Action Potential Imaging at Cellular Level

BACKGROUND: Abnormal Ca(2+) transients are often observed in heart muscles under a variety of pathophysiological conditions including ventricular tachycardia. To clarify whether these abnormal Ca(2+) transients can be attributed to abnormal action potential generation or abnormal Ca(2+) handling/excitation-contraction (EC) coupling, we developed a procedure to determine Ca(2+) and action potential signals at the cellular level in isolated heart tissues. METHODOLOGY/PRINCIPAL FINDINGS: After loading ventricular papillary muscle with rhod-2 and di-4-ANEPPS, mono-wavelength fluorescence images from rhod-2 and ratiometric images of two wavelengths of emission from di-4-ANEPPS were sequentially obtained. To mimic the ventricular tachycardia, the ventricular muscles were field-stimulated in non-flowing Krebs solution which elicited abnormal Ca(2+) transients. For the failed and alternating Ca(2+) transient generation, there were two types of causes, i.e., failed or abnormal action potential generation and abnormal EC coupling. In cells showing delayed initiation of Ca(2+) transients with field stimulation, action potential onset was delayed and the rate of rise was slower than in healthy cells. Similar delayed onset was also observed in the presence of heptanol, an inhibitor of gap junction channels but having a non-specific channel blocking effect. A Na(+) channel blocker, on the other hand, reduced the rate of rise of the action potentials but did not result in desynchronization of the action potentials. The delayed onset of action potentials can be explained primarily by impaired gap junctions and partly by Na(+) channel inactivation. CONCLUSIONS/SIGNIFICANCE: Our results indicate that there are multiple patterns for the causes of abnormal Ca(2+) signals and that our methods are useful for investigating the physiology and pathophysiology of heart muscle

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

Dilated Cardiomyopathy with Increased SR Ca2+ Loading Preceded by a Hypercontractile State and Diastolic Failure in the α1CTG Mouse

Mice over-expressing the α1−subunit (pore) of the L-type Ca2+ channel (α1CTG) by 4months (mo) of age exhibit an enlarged heart, hypertrophied myocytes, increased Ca2+ current and Ca2+ transient amplitude, but a normal SR Ca2+ load. With advancing age (8–11 mo), some mice demonstrate advanced hypertrophy but are not in congestive heart failure (NFTG), while others evolve to frank dilated congestive heart failure (FTG). We demonstrate that older NFTG myocytes exhibit a hypercontractile state over a wide range of stimulation frequencies, but maintain a normal SR Ca2+ load compared to age matched non-transgenic (NTG) myocytes. However, at high stimulation rates (2–4 Hz) signs of diastolic contractile failure appear in NFTG cells. The evolution of frank congestive failure in FTG is accompanied by a further increase in heart mass and myocyte size, and phospholamban and ryanodine receptor protein levels and phosphorylation become reduced. In FTG, the SR Ca2+ load increases and Ca2+ release following excitation, increases further. An enhanced NCX function in FTG, as reflected by an accelerated relaxation of the caffeine-induced Ca2+ transient, is insufficient to maintain a normal diastolic Ca2+ during high rates of stimulation. Although a high SR Ca2+ release following excitation is maintained, the hypercontractile state is not maintained at high rates of stimulation, and signs of both systolic and diastolic contractile failure appear. Thus, the dilated cardiomyopathy that evolves in this mouse model exhibits signs of both systolic and diastolic failure, but not a deficient SR Ca2+ loading or release, as occurs in some other cardiomyopathic models

Characterization of a fluvial aquifer at a range of depths and scales: the Triassic St Bees Sandstone Formation, Cumbria, UK

Fluvial sedimentary successions represent porous media that host groundwater and geothermal resources. Additionally, they overlie crystalline rocks hosting nuclear waste repositories in rift settings. The permeability characteristics of an arenaceous fluvial succession, the Triassic St Bees Sandstone Formation in England (UK), are described, from core-plug to well-test scale up to ~1 km depth. Within such lithified successions, dissolution associated with the circulation of meteoric water results in increased permeability (K~10−1–100 m/day) to depths of at least 150 m below ground level (BGL) in aquifer systems that are subject to rapid groundwater circulation. Thus, contaminant transport is likely to occur at relatively high rates. In a deeper investigation (> 150 m depth), where the aquifer has not been subjected to rapid groundwater circulation, well-test-scale hydraulic conductivity is lower, decreasing from K~10−2 m/day at 150–400 m BGL to 10−3 m/day down-dip at ~1 km BGL, where the pore fluid is hypersaline. Here, pore-scale permeability becomes progressively dominant with increasing lithostatic load. Notably, this work investigates a sandstone aquifer of fluvial origin at investigation depths consistent with highly enthalpy geothermal reservoirs (~0.7–1.1 km). At such depths, intergranular flow dominates in unfaulted areas with only minor contribution by bedding plane fractures. However, extensional faults represent preferential flow pathways, due to presence of high connective open fractures. Therefore, such faults may (1) drive nuclear waste contaminants towards the highly permeable shallow (< 150 m BGL) zone of the aquifer, and (2) influence fluid recovery in geothermal fields

The Chemokine Receptor CXCR4 Strongly Promotes Neuroblastoma Primary Tumour and Metastatic Growth, but not Invasion

Neuroblastoma (NB) is a heterogeneous, and particularly malignant childhood neoplasm in its higher stages, with a propensity to form metastasis in selected organs, in particular liver and bone marrow, and for which there is still no efficient treatment available beyond surgery. Recent evidence indicates that the CXCR4/CXCL12 chemokine/receptor axis may be involved in promoting NB invasion and metastasis. In this study, we explored the potential role of CXCR4 in the malignant behaviour of NB, using a combination of in vitro functional analyses and in vivo growth and metastasis assessment in an orthotopic NB mouse model. We show here that CXCR4 overexpression in non-metastatic CXCR4-negative NB cells IGR-NB8 and in moderately metastatic, CXCR4 expressing NB cells IGR-N91, strongly increased tumour growth of primary tumours and liver metastases, without altering the frequency or the pattern of metastasis. Moreover shRNA-mediated knock-down experiments confirmed our observations by showing that silencing CXCR4 in NB cells impairs in vitro and almost abrogates in vivo growth. High levels of CXCL12 were detected in the mouse adrenal gland (the primary tumour site), and in the liver suggesting a paracrine effect of host-derived CXCL12 on NB growth. In conclusion, this study reveals a yet unreported NB-specific predominant growth and survival-promoting role of CXCR4, which warrants a critical reconsideration of the role of CXCR4 in the malignant behaviour of NB and other cancers

Endothelial IGF‐1 receptor mediates crosstalk with the gut wall to regulate microbiota in obesity

Changes in composition of the intestinal microbiota are linked to the development of obesity and can lead to endothelial cell (EC) dysfunction. It is unknown whether EC can directly influence the microbiota. Insulin-like growth factor-1 (IGF-1) and its receptor (IGF-1R) are critical for coupling nutritional status and cellular growth; IGF-1R is expressed in multiple cell types including EC. The role of ECIGF-1R in the response to nutritional obesity is unexplored. To examine this, we use gene-modified mice with EC-specific overexpression of human IGF-1R (hIGFREO) and their wild-type littermates. After high-fat feeding, hIGFREO weigh less, have reduced adiposity and have improved glucose tolerance. hIGFREO show an altered gene expression and altered microbial diversity in the gut, including a relative increase in the beneficial genus Akkermansia. The depletion of gut microbiota with broad-spectrum antibiotics induces a loss of the favourable metabolic differences seen in hIGFREO mice. We show that IGF-1R facilitates crosstalk between the EC and the gut wall; this crosstalk protects against diet-induced obesity, as a result of an altered gut microbiota