A distributed procedure for computing stochastic expansions with Mathematica

The solution of a (stochastic) differential equation can be locally approximated by a (stochastic) expansion. If the vector field of the differential equation is a polynomial, the corresponding expansion is a linear combination of iterated integrals of the drivers and can be calculated using Picard Iterations. However, such expansions grow exponentially fast in their number of terms, due to their specific algebra, rendering their practical use limited. We present a Mathematica procedure that addresses this issue by reparametrizing the polynomials and distributing the load in as small as possible parts that can be processed and manipulated independently, thus alleviating large memory requirements and being perfectly suited for parallelized computation. We also present an iterative implementation of the shuffle product (as opposed to a recursive one, more usually implemented) as well as a fast way for calculating the expectation of iterated Stratonovich integrals for Brownian motion

A Distributed Procedure for Computing Stochastic Expansions with Mathematica

The solution of a (stochastic) differential equation can be locally approximated by a (stochastic) expansion. If the vector field of the differential equation is a polynomial, the corresponding expansion is a linear combination of iterated integrals of the drivers and can be calculated using Picard Iterations. However, such expansions grow exponentially fast in their number of terms, due to their specific algebra, rendering their practical use limited. We present a Mathematica procedure that addresses this issue by re-parametrising the polynomials and distributing the load in as small as possible parts that can be processed and manipulated independently, thus alleviating large memory requirements and being perfectly suited for parallelized computation. We also present an iterative implementation of the shuffle product (as opposed to a recursive one, more usually implemented) as well as a fast way for calculating the expectation of iterated Stratonovich integrals for Brownian Motion.Comment: 15 pages, 2 figures. Submitte

Identifying interactions in the time and frequency domains in local and global networks : a Granger causality approach

Background Reverse-engineering approaches such as Bayesian network inference, ordinary differential equations (ODEs) and information theory are widely applied to deriving causal relationships among different elements such as genes, proteins, metabolites, neurons, brain areas and so on, based upon multi-dimensional spatial and temporal data. There are several well-established reverse-engineering approaches to explore causal relationships in a dynamic network, such as ordinary differential equations (ODE), Bayesian networks, information theory and Granger Causality. Results Here we focused on Granger causality both in the time and frequency domain and in local and global networks, and applied our approach to experimental data (genes and proteins). For a small gene network, Granger causality outperformed all the other three approaches mentioned above. A global protein network of 812 proteins was reconstructed, using a novel approach. The obtained results fitted well with known experimental findings and predicted many experimentally testable results. In addition to interactions in the time domain, interactions in the frequency domain were also recovered. Conclusions The results on the proteomic data and gene data confirm that Granger causality is a simple and accurate approach to recover the network structure. Our approach is general and can be easily applied to other types of temporal data

Investigating the predictive validity of TOEFL iBT® scores and their use in informing policy in a UK university setting

The project examined the predictive validity of TOEFL®iBT with a focus on the relationship between TOEFL®iBT scores and students’ subsequent academic success in postgraduate studies in one leading university in the UK, paying specific attention to the role of linguistic preparedness as perceived by students and tutors. We employed a mixed-methods approach in order to enrich traditionally quantitatively oriented studies with a qualitative perspective. For the sample of 504 students who entered the university for postgraduate studies in the years 2011-2013 on the basis of a TOEFL®iBT score, we analyzed the relation between TOEFL®iBT scores and final academic award by correlation and regression analyses, taking into consideration discipline, nationality, and additional language support. For the qualitative strand, students entering the university in 2013 on the basis of a TOEFL®iBT score were invited to questionnaires and interviews, as were their EAP and academic tutors. A total 48 students and 58 tutors participated, with 25 students and 36 tutors being interviewed at three points over the course of the year.Our findings show that students entering the university on the basis of TOEFL®iBT scores feel well prepared, and generally regard the test as an effective means of preparation for their academic studies in a UK setting. They cope well with the linguistic demands and a vast majority graduate successfully. Our findings support the appropriateness of the university’s entrance policy with regard to setting minimum test score requirements, thus underpinning the predictive validity of TOEFL®iBT in a UK setting

Beyond element-wise interactions: identifying complex interactions in biological processes

Background: Biological processes typically involve the interactions of a number of elements (genes, cells) acting on each others. Such processes are often modelled as networks whose nodes are the elements in question and edges pairwise relations between them (transcription, inhibition). But more often than not, elements actually work cooperatively or competitively to achieve a task. Or an element can act on the interaction between two others, as in the case of an enzyme controlling a reaction rate. We call “complex” these types of interaction and propose ways to identify them from time-series observations. Methodology: We use Granger Causality, a measure of the interaction between two signals, to characterize the influence of an enzyme on a reaction rate. We extend its traditional formulation to the case of multi-dimensional signals in order to capture group interactions, and not only element interactions. Our method is extensively tested on simulated data and applied to three biological datasets: microarray data of the Saccharomyces cerevisiae yeast, local field potential recordings of two brain areas and a metabolic reaction. Conclusions: Our results demonstrate that complex Granger causality can reveal new types of relation between signals and is particularly suited to biological data. Our approach raises some fundamental issues of the systems biology approach since finding all complex causalities (interactions) is an NP hard problem

The MVGC multivariate Granger causality toolbox: a new approach to Granger-causal inference

Background: Wiener-Granger causality (“G-causality”) is a statistical notion of causality applicable to time series data, whereby cause precedes, and helps predict, effect. It is defined in both time and frequency domains, and allows for the conditioning out of common causal influences. Originally developed in the context of econometric theory, it has since achieved broad application in the neurosciences and beyond. Prediction in the G-causality formalism is based on VAR (Vector AutoRegressive) modelling. New Method: The MVGC Matlab c Toolbox approach to G-causal inference is based on multiple equivalent representations of a VAR model by (i) regression parameters, (ii) the autocovariance sequence and (iii) the cross-power spectral density of the underlying process. It features a variety of algorithms for moving between these representations, enabling selection of the most suitable algorithms with regard to computational efficiency and numerical accuracy. Results: In this paper we explain the theoretical basis, computational strategy and application to empirical G-causal inference of the MVGC Toolbox. We also show via numerical simulations the advantages of our Toolbox over previous methods in terms of computational accuracy and statistical inference. Comparison with Existing Method(s): The standard method of computing G-causality involves estimation of parameters for both a full and a nested (reduced) VAR model. The MVGC approach, by contrast, avoids explicit estimation of the reduced model, thus eliminating a source of estimation error and improving statistical power, and in addition facilitates fast and accurate estimation of the computationally awkward case of conditional G-causality in the frequency domain. Conclusions: The MVGC Toolbox implements a flexible, powerful and efficient approach to G-causal inference. Keywords: Granger causality, vector autoregressive modelling, time series analysi

Toward full-stack in silico synthetic biology: integrating model specification, simulation, verification, and biological compilation

YesWe present the Infobiotics Workbench (IBW), a user-friendly, scalable, and integrated computational environment for the computer-aided design of synthetic biological systems. It supports an iterative workflow that begins with specification of the desired synthetic system, followed by simulation and verification of the system in high- performance environments and ending with the eventual compilation of the system specification into suitable genetic constructs. IBW integrates modelling, simulation, verification and bicompilation features into a single software suite. This integration is achieved through a new domain-specific biological programming language, the Infobiotics Language (IBL), which tightly combines these different aspects of in silico synthetic biology into a full-stack integrated development environment. Unlike existing synthetic biology modelling or specification languages, IBL uniquely blends modelling, verification and biocompilation statements into a single file. This allows biologists to incorporate design constraints within the specification file rather than using decoupled and independent formalisms for different in silico analyses. This novel approach offers seamless interoperability across different tools as well as compatibility with SBOL and SBML frameworks and removes the burden of doing manual translations for standalone applications. We demonstrate the features, usability, and effectiveness of IBW and IBL using well-established synthetic biological circuits.The work of S.K. is supported by EPSRC (EP/R043787/1). N.K., A.W., and B.B. acknowledge a Royal Academy of Engineering Chair in Emerging Technologies award and an EPSRC programme grant (EP/N031962/1)

Muscle metabolism and activation heterogeneity by combined 31P chemical shift and T2 imaging, and pulmonary O2 uptake during incremental knee-extensor exercise.

The integration of skeletal muscle substrate depletion, metabolite accumulation, and fatigue during large muscle-mass exercise is not well understood. Measurement of intramuscular energy store degradation and metabolite accumulation is confounded by muscle heterogeneity. Therefore, to characterize regional metabolic distribution in the locomotor muscles, we combined 31P magnetic resonance spectroscopy, chemical shift imaging, and T2-weighted imaging with pulmonary oxygen uptake during bilateral knee-extension exercise to intolerance. Six men completed incremental tests for the following: (1) unlocalized 31P magnetic resonance spectroscopy; and (2) spatial determination of 31P metabolism and activation. The relationship of pulmonary oxygen uptake to whole quadriceps phosphocreatine concentration ([PCr]) was inversely linear, and three of four knee-extensor muscles showed activation as assessed by change in T2. The largest changes in [PCr], [inorganic phosphate] ([Pi]) and pH occurred in rectus femoris, but no voxel (72 cm3) showed complete PCr depletion at exercise cessation. The most metabolically active voxel reached 11 ± 9 mM [PCr] (resting, 29 ± 1 mM), 23 ± 11 mM [Pi] (resting, 7 ± 1 mM), and a pH of 6.64 ± 0.29 (resting, 7.08 ± 0.03). However, the distribution of 31P metabolites and pH varied widely between voxels, and the intervoxel coefficient of variation increased between rest (∼10%) and exercise intolerance (∼30-60%). Therefore, the limit of tolerance was attained with wide heterogeneity in substrate depletion and fatigue-related metabolite accumulation, with extreme metabolic perturbation isolated to only a small volume of active muscle (<5%). Regional intramuscular disturbances are thus likely an important requisite for exercise intolerance. How these signals integrate to limit muscle power production, while regional "recruitable muscle" energy stores are presumably still available, remains uncertain