Reconstructing the gravitational field of the local universe

Tests of gravity at the galaxy scale are in their infancy. As a first step to systematically uncovering the gravitational significance of galaxies, we map three fundamental gravitational variables -- the Newtonian potential, acceleration and curvature -- over the galaxy environments of the local universe to a distance of approximately 200 Mpc. Our method combines the contributions from galaxies in an all-sky redshift survey, halos from an N-body simulation hosting low-luminosity objects, and linear and quasi-linear modes of the density field. We use the ranges of these variables to determine the extent to which galaxies expand the scope of generic tests of gravity and are capable of constraining specific classes of model for which they have special significance. Finally, we investigate the improvements afforded by upcoming galaxy surveys.Comment: 12 pages, 4 figures; revised to match MNRAS accepted versio

Export Tourism: Rejoinder to Palmer. Quarterly Economic Commentary, November 1983

There appear to be three central points in Noel Palmer's comments. These pertain to: I: The treatment of the government sector - should it be regarded as exogenous ( as in Norton, 1982) or endogenous? II: An assumtion of the input-output model used by me, namely, its failure to distinguish oetween average and marginal values of parameters. III: The relative capital intensity of export tourism

Galaxy morphology rules out astrophysically relevant Hu-Sawicki f(R)f(R) gravity

$f(R)$ is a paradigmatic modified gravity theory that typifies extensions to General Relativity with new light degrees of freedom and hence screened fifth forces between masses. These forces produce observable signatures in galaxy morphology, caused by a violation of the weak equivalence principle due to a differential impact of screening among galaxies' mass components. We compile statistical datasets of two morphological indicators -- offsets between stars and gas in galaxies and warping of stellar disks -- and use them to constrain the strength and range of a thin-shell-screened fifth force. This is achieved by applying a comprehensive set of upgrades to past work (Desmond et al 2018a,b): we construct a robust galaxy-by-galaxy Bayesian forward model for the morphological signals, including full propagation of uncertainties in the input quantities and marginalisation over an empirical model describing astrophysical noise. Employing more stringent data quality cuts than previously we find no evidence for a screened fifth force of any strength $\Delta G/G_\text{N}$ in the Compton wavelength range $0.3-8$ Mpc, setting a $1\sigma$ bound of $\Delta G/G_\text{N}<0.8$ at $\lambda_C=0.3$ Mpc that strengthens to $\Delta G/G_\text{N}<3\times10^{-5}$ at $\lambda_C=8$ Mpc. These are the tightest bounds to date beyond the Solar System by over an order of magnitude. For the Hu-Sawicki model of $f(R)$ with $n=1$ we require a background scalar field value $f_{R0} < 1.4 \times 10^{-8}$, forcing practically all astrophysical objects to be screened. We conclude that this model can have no relevance to astrophysics or cosmology.Comment: 15 pages, 6 figures; minor revision, matches PRD accepted versio

CONTEST : a Controllable Test Matrix Toolbox for MATLAB

Large, sparse networks that describe complex interactions are a common feature across a number of disciplines, giving rise to many challenging matrix computational tasks. Several random graph models have been proposed that capture key properties of real-life networks. These models provide realistic, parametrized matrices for testing linear system and eigenvalue solvers. CONTEST (CONtrollable TEST matrices) is a random network toolbox for MATLAB that implements nine models. The models produce unweighted directed or undirected graphs; that is, symmetric or unsymmetric matrices with elements equal to zero or one. They have one or more parameters that affect features such as sparsity and characteristic pathlength and all can be of arbitrary dimension. Utility functions are supplied for rewiring, adding extra shortcuts and subsampling in order to create further classes of networks. Other utilities convert the adjacency matrices into real-valued coefficient matrices for naturally arising computational tasks that reduce to sparse linear system and eigenvalue problems

Ensemble approach combining multiple methods improves human transcription start site prediction

Dineen DG, Schroeder M, Higgins DG, Cunningham P. Ensemble approach combining multiple methods improves human transcription start site prediction. BMC Genomics. 2010;11(1): 677.Background: The computational prediction of transcription start sites is an important unsolved problem. Some recent progress has been made, but many promoters, particularly those not associated with CpG islands, are still difficult to locate using current methods. These methods use different features and training sets, along with a variety of machine learning techniques and result in different prediction sets. Results: We demonstrate the heterogeneity of current prediction sets, and take advantage of this heterogeneity to construct a two-level classifier ('Profisi Ensemble') using predictions from 7 programs, along with 2 other data sources. Support vector machines using 'full' and 'reduced' data sets are combined in an either/or approach. We achieve a 14% increase in performance over the current state-of-the-art, as benchmarked by a third-party tool. Conclusions: Supervised learning methods are a useful way to combine predictions from diverse sources

Perceptions of a Bible Belt State\u27s Proposed Casino Gaming Legislation by Religious Affiliation: The Case of Kentucky Residents

This study seeks to explore whether differences exist among Kentucky residents\u27 perception of casino gaming based on religious affiliation. A survey was conducted to sample 600 residents regarding currently a widely debated introduction of land-based casinos in the state, yielding a response rate of 38.4%. The results support earlier studies regarding the impact religion has on people\u27s attitudes toward gaming. The findings suggest that Catholics have a more positive attitude toward the legalization of gambling than persons of Protestant faiths

Exhaustive Symbolic Regression

Symbolic Regression (SR) algorithms learn analytic expressions which both accurately fit data and, unlike traditional machine-learning approaches, are highly interpretable. Conventional SR suffers from two fundamental issues which we address in this work. First, since the number of possible equations grows exponentially with complexity, typical SR methods search the space stochastically and hence do not necessarily find the best function. In many cases, the target problems of SR are sufficiently simple that a brute-force approach is not only feasible, but desirable. Second, the criteria used to select the equation which optimally balances accuracy with simplicity have been variable and poorly motivated. To address these issues we introduce a new method for SR -- Exhaustive Symbolic Regression (ESR) -- which systematically and efficiently considers all possible equations and is therefore guaranteed to find not only the true optimum but also a complete function ranking. Utilising the minimum description length principle, we introduce a principled method for combining these preferences into a single objective statistic. To illustrate the power of ESR we apply it to a catalogue of cosmic chronometers and the Pantheon+ sample of supernovae to learn the Hubble rate as a function of redshift, finding $\sim$40 functions (out of 5.2 million considered) that fit the data more economically than the Friedmann equation. These low-redshift data therefore do not necessarily prefer a $\Lambda$CDM expansion history, and traditional SR algorithms that return only the Pareto-front, even if they found this successfully, would not locate $\Lambda$CDM. We make our code and full equation sets publicly available.Comment: 14 pages, 6 figures, 2 tables. Submitted to IEEE Transactions on Pattern Analysis and Machine Intelligenc

Priors for symbolic regression

When choosing between competing symbolic models for a data set, a human will naturally prefer the "simpler" expression or the one which more closely resembles equations previously seen in a similar context. This suggests a non-uniform prior on functions, which is, however, rarely considered within a symbolic regression (SR) framework. In this paper we develop methods to incorporate detailed prior information on both functions and their parameters into SR. Our prior on the structure of a function is based on a $n$-gram language model, which is sensitive to the arrangement of operators relative to one another in addition to the frequency of occurrence of each operator. We also develop a formalism based on the Fractional Bayes Factor to treat numerical parameter priors in such a way that models may be fairly compared though the Bayesian evidence, and explicitly compare Bayesian, Minimum Description Length and heuristic methods for model selection. We demonstrate the performance of our priors relative to literature standards on benchmarks and a real-world dataset from the field of cosmology.Comment: 8+2 pages, 2 figures. Submitted to The Genetic and Evolutionary Computation Conference (GECCO) 2023 Workshop on Symbolic Regressio

Cross-platform comparison and visualisation of gene expression data using co-inertia analysis

BACKGROUND: Rapid development of DNA microarray technology has resulted in different laboratories adopting numerous different protocols and technological platforms, which has severely impacted on the comparability of array data. Current cross-platform comparison of microarray gene expression data are usually based on cross-referencing the annotation of each gene transcript represented on the arrays, extracting a list of genes common to all arrays and comparing expression data of this gene subset. Unfortunately, filtering of genes to a subset represented across all arrays often excludes many thousands of genes, because different subsets of genes from the genome are represented on different arrays. We wish to describe the application of a powerful yet simple method for cross-platform comparison of gene expression data. Co-inertia analysis (CIA) is a multivariate method that identifies trends or co-relationships in multiple datasets which contain the same samples. CIA simultaneously finds ordinations (dimension reduction diagrams) from the datasets that are most similar. It does this by finding successive axes from the two datasets with maximum covariance. CIA can be applied to datasets where the number of variables (genes) far exceeds the number of samples (arrays) such is the case with microarray analyses. RESULTS: We illustrate the power of CIA for cross-platform analysis of gene expression data by using it to identify the main common relationships in expression profiles on a panel of 60 tumour cell lines from the National Cancer Institute (NCI) which have been subjected to microarray studies using both Affymetrix and spotted cDNA array technology. The co-ordinates of the CIA projections of the cell lines from each dataset are graphed in a bi-plot and are connected by a line, the length of which indicates the divergence between the two datasets. Thus, CIA provides graphical representation of consensus and divergence between the gene expression profiles from different microarray platforms. Secondly, the genes that define the main trends in the analysis can be easily identified. CONCLUSIONS: CIA is a robust, efficient approach to coupling of gene expression datasets. CIA provides simple graphical representations of the results making it a particularly attractive method for the identification of relationships between large datasets