A Fully Automatic Theorem Prover with Human-Style Output.

This paper describes a program that solves elementary mathematical problems, mostly in metric space theory, and presents solutions that are hard to distinguish from solutions that might be written by human mathematicians.Research supported by a Royal Society 2010 Anniversary Research Professorship.This is the final version of the article. It first appeared from Springer via http://dx.doi.org/10.1007/s10817-016-9377-

Two-stage clustering in genotype-by-environment analyses with missing data

Cluster analysis has been commonly used in genotype-by-environment (G x E) analyses, but current methods are inadequate when the data matrix is incomplete. This paper proposes a new method, referred to as two-stage clustering, which relies on a partitioning of squared Euclidean distance into two independent components, the G x E interaction and the genotype main effect. These components are used in the first and second stages of clustering respectively. Two-stage clustering forms the basis for imputing missing values in the G x E matrix so that a more complete data array is available for other GxE analyses. Imputation for a given genotype uses information from genotypes with similar interaction profiles. This imputation method is shown to improve on an existing nearest cluster method that confounds the G x E interaction and the genotype main effect

Latent cluster analysis of ALS phenotypes identifies prognostically differing groups

BACKGROUND Amyotrophic lateral sclerosis (ALS) is a degenerative disease predominantly affecting motor neurons and manifesting as several different phenotypes. Whether these phenotypes correspond to different underlying disease processes is unknown. We used latent cluster analysis to identify groupings of clinical variables in an objective and unbiased way to improve phenotyping for clinical and research purposes. METHODS Latent class cluster analysis was applied to a large database consisting of 1467 records of people with ALS, using discrete variables which can be readily determined at the first clinic appointment. The model was tested for clinical relevance by survival analysis of the phenotypic groupings using the Kaplan-Meier method. RESULTS The best model generated five distinct phenotypic classes that strongly predicted survival (p<0.0001). Eight variables were used for the latent class analysis, but a good estimate of the classification could be obtained using just two variables: site of first symptoms (bulbar or limb) and time from symptom onset to diagnosis (p<0.00001). CONCLUSION The five phenotypic classes identified using latent cluster analysis can predict prognosis. They could be used to stratify patients recruited into clinical trials and generating more homogeneous disease groups for genetic, proteomic and risk factor research

RNAseq Analyses Identify Tumor Necrosis Factor-Mediated Inflammation as a Major Abnormality in ALS Spinal Cord

ALS is a rapidly progressive, devastating neurodegenerative illness of adults that produces disabling weakness and spasticity arising from death of lower and upper motor neurons. No meaningful therapies exist to slow ALS progression, and molecular insights into pathogenesis and progression are sorely needed. In that context, we used high-depth, next generation RNA sequencing (RNAseq, Illumina) to define gene network abnormalities in RNA samples depleted of rRNA and isolated from cervical spinal cord sections of 7 ALS and 8 CTL samples. We aligned \u3e50 million 2X150 bp paired-end sequences/sample to the hg19 human genome and applied three different algorithms (Cuffdiff2, DEseq2, EdgeR) for identification of differentially expressed genes (DEG’s). Ingenuity Pathways Analysis (IPA) and Weighted Gene Co-expression Network Analysis (WGCNA) identified inflammatory processes as significantly elevated in our ALS samples, with tumor necrosis factor (TNF) found to be a major pathway regulator (IPA) and TNFα-induced protein 2 (TNFAIP2) as a major network “hub” gene (WGCNA). Using the oPOSSUM algorithm, we analyzed transcription factors (TF) controlling expression of the nine DEG/hub genes in the ALS samples and identified TF’s involved in inflammation (NFkB, REL, NFkB1) and macrophage function (NR1H2::RXRA heterodimer). Transient expression in human iPSC-derived motor neurons of TNFAIP2 (also a DEG identified by all three algorithms) reduced cell viability and induced caspase 3/7 activation. Using high-density RNAseq, multiple algorithms for DEG identification, and an unsupervised gene co-expression network approach, we identified significant elevation of inflammatory processes in ALS spinal cord with TNF as a major regulatory molecule. Overexpression of the DEG TNFAIP2 in human motor neurons, the population most vulnerable to die in ALS, increased cell death and caspase 3/7 activation. We propose that therapies targeted to reduce inflammatory TNFα signaling may be helpful in ALS patients

A proposed staging system for amyotrophic lateral sclerosis

Amyotrophic lateral sclerosis is a neurodegenerative disorder characterized by progressive loss of upper and lower motor neurons, with a median survival of 2–3 years. Although various phenotypic and research diagnostic classification systems exist and several prognostic models have been generated, there is no staging system. Staging criteria for amyotrophic lateral sclerosis would help to provide a universal and objective measure of disease progression with benefits for patient care, resource allocation, research classifications and clinical trial design. We therefore sought to define easily identified clinical milestones that could be shown to occur at specific points in the disease course, reflect disease progression and impact prognosis and treatment. A tertiary referral centre clinical database was analysed, consisting of 1471 patients with amyotrophic lateral sclerosis seen between 1993 and 2007. Milestones were defined as symptom onset (functional involvement by weakness, wasting, spasticity, dysarthria or dysphagia of one central nervous system region defined as bulbar, upper limb, lower limb or diaphragmatic), diagnosis, functional involvement of a second region, functional involvement of a third region, needing gastrostomy and non-invasive ventilation. Milestone timings were standardized as proportions of time elapsed through the disease course using information from patients who had died by dividing time to a milestone by disease duration. Milestones occurred at predictable proportions of the disease course. Diagnosis occurred at 35% through the disease course, involvement of a second region at 38%, a third region at 61%, need for gastrostomy at 77% and need for non-invasive ventilation at 80%. We therefore propose a simple staging system for amyotrophic lateral sclerosis. Stage 1: symptom onset (involvement of first region); Stage 2A: diagnosis; Stage 2B: involvement of second region; Stage 3: involvement of third region; Stage 4A: need for gastrostomy; and Stage 4B: need for non-invasive ventilation. Validation of this staging system will require further studies in other populations, in population registers and in other clinic databases. The standardized times to milestones may well vary between different studies and populations, although the stages themselves and their meanings are likely to remain unchanged

Towards mathematical AI via a model of the content and process of mathematical question and answer dialogues

This paper outlines a strategy for building semantically meaningful representations and carrying out effective reasoning in technical knowledge domains such as mathematics. Our central assertion is that the semi-structured Q and A format, as used on the popular Stack Exchange network of websites, exposes domain knowledge in a form that is already reasonably close to the structured knowledge formats that computers can reason about. The knowledge in question is not only facts - but discursive, dialectical, argument for purposes of proof and pedagogy. We therefore assert that modelling the Q and A process computationally provides a route to domain understanding that is compatible with the day-to-day practices of mathematicians and students. This position is supported by a small case study that analyses one question from Mathoverflow in detail, using concepts from argumentation theory. A programme of future work, including a rigorous evaluation strategy, is then advanced