Oxford Centre for Industrial and Applied Mathematics

Chalfont Saint Giles, United Kingdom

Oxford Centre for Industrial and Applied Mathematics

Chalfont Saint Giles, United Kingdom
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Trinh P.H.,Oxford Centre for Industrial and Applied Mathematics
Journal of Fluid Mechanics | Year: 2017

In 1983, Tulin published a report proposing a framework for reducing the equations for gravity waves generated by moving bodies into a single nonlinear differential equation solvable in closed form (Proceedings of the 14th Symposium on Naval Hydrodynamics, 1983, pp. 19-51). Several new and puzzling issues were highlighted by Tulin, notably the existence of weak and strong wave-making regimes, and the paradoxical fact that the theory seemed to be applicable to flows at low speeds, 'but not too low speeds'. These important issues were left unanswered, and despite the novelty of the ideas, Tulin's report fell into relative obscurity. Now, 30 years later, we will revive Tulin's observations, and explain how an asymptotically consistent framework allows us to address these concerns. Most notably, we demonstrate, using the asymptotic method of steepest descents, how the production of free-surface waves can be related to the arrangement of integration contours connected to the shape of the moving body. This approach provides a new and powerful methodology for the study of geometrically nonlinear wave-body interactions. © 2017 Cambridge University Press.

De Domenico M.,Rovira i Virgili University | Granell C.,University of North Carolina at Chapel Hill | Porter M.A.,Oxford Centre for Industrial and Applied Mathematics | Porter M.A.,University of Oxford | And 2 more authors.
Nature Physics | Year: 2016

Despite the success of traditional network analysis, standard networks provide a limited representation of complex systems, which often include different types of relationships (or multiplexity') between their components. Such structural complexity has a significant effect on both dynamics and function. Throwing away or aggregating available structural information can generate misleading results and be a major obstacle towards attempts to understand complex systems. The recent multilayer approach for modelling networked systems explicitly allows the incorporation of multiplexity and other features of realistic systems. It allows one to couple different structural relationships by encoding them in a convenient mathematical object. It also allows one to couple different dynamical processes on top of such interconnected structures. The resulting framework plays a crucial role in helping to achieve a thorough, accurate understanding of complex systems. The study of multilayer networks has also revealed new physical phenomena that remain hidden when using ordinary graphs, the traditional network representation. Here we survey progress towards attaining a deeper understanding of spreading processes on multilayer networks, and we highlight some of the physical phenomena related to spreading processes that emerge from multilayer structure. © 2016 Macmillan Publishers Limited, part of Springer Natural. All rights reserved.

Vasistha N.A.,University of Oxford | Garcia-Moreno F.,University of Oxford | Arora S.,Oxford Centre for Industrial and Applied Mathematics | Cheung A.F.P.,University of Oxford | And 2 more authors.
Cerebral Cortex | Year: 2015

The individual contribution of different progenitor subtypes towards the mature rodent cerebral cortex is not fully understood. Intermediate progenitor cells (IPCs) are key to understanding the regulation of neuronal number during cortical development and evolution, yet their exact contribution is much debated. Intermediate progenitors in the cortical subventricular zone are defined by expression of T-box brain-2 (Tbr2). In this study we demonstrate by using the Tbr2Cre mouse line and stateof-the-art cell lineage labeling techniques, that IPC derived cells contribute substantial proportions 67.5% of glutamatergic but not GABAergic or astrocytic cells to all cortical layers including the earliest generated subplate zone. We also describe the laminar dispersion of clonally derived cells from IPCs using a recently described clonal analysis tool (CLoNe) and show that pair-generated cells in different layers cluster closer (142.1±76.8 ìm) than unrelated cells (294.9±105.4 ìm). The clonal dispersion from individual Tbr2 positive intermediate progenitors contributes to increasing the cortical surface. Our study also describes extracortical contributions from Tbr2+ progenitors to the lateral olfactory tract and ventromedial hypothalamic nucleus. © 2014 The Author.

Wymbs N.F.,University of California at Santa Barbara | Bassett D.S.,University of California at Santa Barbara | Mucha P.J.,University of North Carolina at Chapel Hill | Porter M.A.,Oxford Centre for Industrial and Applied Mathematics | And 2 more authors.
Neuron | Year: 2012

Motor chunking facilitates movement production by combining motor elements into integrated units of behavior. Previous research suggests that chunking involves two processes: concatenation, aimed at the formation of motor-motor associations between elements or sets of elements, and segmentation, aimed at the parsing of multiple contiguous elements into shorter action sets. We used fMRI to measure the trial-wise recruitment of brain regions associated with these chunking processes as healthy subjects performed a cued-sequence production task. A dynamic network analysis identified chunking structure for a set of motor sequences acquired during fMRI and collected over 3 days of training. Activity in the bilateral sensorimotor putamen positively correlated with chunk concatenation, whereas a left-hemisphere frontoparietal network was correlated with chunk segmentation. Across subjects, there was an aggregate increase in chunk strength (concatenation) with training, suggesting that subcortical circuits play a direct role in the creation of fluid transitions across chunks.

De Domenico M.,Rovira i Virgili University | Sole-Ribalta A.,Rovira i Virgili University | Cozzo E.,University of Zaragoza | Kivela M.,Oxford Centre for Industrial and Applied Mathematics | And 5 more authors.
Physical Review X | Year: 2014

A network representation is useful for describing the structure of a large variety of complex systems. However, most real and engineered systems have multiple subsystems and layers of connectivity, and the data produced by such systems are very rich. Achieving a deep understanding of such systems necessitates generalizing "traditional"network theory, and the newfound deluge of data now makes it possible to test increasingly general frameworks for the study of networks. In particular, although adjacency matrices are useful to describe traditional single-layer networks, such a representation is insufficient for the analysis and description of multiplex and time-dependent networks. One must therefore develop a more general mathematical framework to cope with the challenges posed by multilayer complex systems. In this paper, we introduce a tensorial framework to study multilayer networks, and we discuss the generalization of several important network descriptors and dynamical processes-including degree centrality, clustering coefficients, eigenvector centrality, modularity, von Neumann entropy, and diffusion-for this framework. We examine the impact of different choices in constructing these generalizations, and we illustrate how to obtain known results for the special cases of single-layer and multiplex networks. Our tensorial approach will be helpful for tackling pressing problems in multilayer complex systems, such as inferring who is influencing whom (and by which media) in multichannel social networks and developing routing techniques for multimodal transportation systems.

Tsanas A.,Oxford Centre for Industrial and Applied Mathematics | Xifara A.,University of Cardiff
Energy and Buildings | Year: 2012

We develop a statistical machine learning framework to study the effect of eight input variables (relative compactness, surface area, wall area, roof area, overall height, orientation, glazing area, glazing area distribution) on two output variables, namely heating load (HL) and cooling load (CL), of residential buildings. We systematically investigate the association strength of each input variable with each of the output variables using a variety of classical and non-parametric statistical analysis tools, in order to identify the most strongly related input variables. Then, we compare a classical linear regression approach against a powerful state of the art nonlinear non-parametric method, random forests, to estimate HL and CL. Extensive simulations on 768 diverse residential buildings show that we can predict HL and CL with low mean absolute error deviations from the ground truth which is established using Ecotect (0.51 and 1.42, respectively). The results of this study support the feasibility of using machine learning tools to estimate building parameters as a convenient and accurate approach, as long as the requested query bears resemblance to the data actually used to train the mathematical model in the first place. © 2012 Elsevier B.V. All rights reserved.

Mucha P.J.,University of North Carolina at Chapel Hill | Richardson T.,University of North Carolina at Chapel Hill | Richardson T.,North Carolina State University | Macon K.,University of North Carolina at Chapel Hill | And 3 more authors.
Science | Year: 2010

Network science is an interdisciplinary endeavor, with methods and applications drawn from across the natural, social, and information sciences. A prominent problem in network science is the algorithmic detection of tightly connected groups of nodes known as communities. We developed a generalized framework of network quality functions that allowed us to study the community structure of arbitrary multislice networks, which are combinations of individual networks coupled through links that connect each node in one network slice to itself in other slices. This framework allows studies of community structure in a general setting encompassing networks that evolve over time, have multiple types of links (multiplexity), and have multiple scales.

Van Gorder R.A.,Oxford Centre for Industrial and Applied Mathematics
Physics of Fluids | Year: 2015

While the Hasimoto planar vortex filament is one of the few exact solutions to the local induction approximation (LIA) approximating the self-induced motion of a vortex filament, it is natural to wonder whether such a vortex filament solution would exist for the non-local Biot-Savart dynamics exactly governing the filament motion, and if so, whether the non-local effects would drastically modify the solution properties. Both helical vortex filaments and vortex rings are known to exist under both the LIA and non-local Biot-Savart dynamics; however, the planar filament is a bit more complicated. In the present paper, we demonstrate that a planar vortex filament solution does exist for the non-local Biot-Savart formulation, provided that a specific non-linear integral equation (governing the spatial structure of such a filament) has a non-trivial solution. By using the Poincaré-Lindstedt method, we are able to obtain an accurate analytical approximation to the solution of this integral equation under physically reasonable assumptions. To obtain these solutions, we approximate local effects near the singularity of the integral equation using the LIA and non-local effects using the Biot-Savart formulation. Mathematically, the results constitute an analytical solution to an interesting nonlinear singular integrodifferential equation in space and time variables. Physically, these results show that planar vortex filaments exist and maintain their forms under the non-local Biot-Savart formulation, as one would hope. Due to the regularization approach utilized, we are able to compare the structure of the planar filaments obtained under both LIA and Biot-Savart formulations in a rather straightforward manner, in order to determine the role of the non-locality on the structure of the planar filament. © 2015 AIP Publishing LLC.

Moore P.J.,Oxford Centre for Industrial and Applied Mathematics
Proceedings. Biological sciences / The Royal Society | Year: 2014

We analyse time series from 100 patients with bipolar disorder for correlates of depression symptoms. As the sampling interval is non-uniform, we quantify the extent of missing and irregular data using new measures of compliance and continuity. We find that uniformity of response is negatively correlated with the standard deviation of sleep ratings (ρ = -0.26, p = 0.01). To investigate the correlation structure of the time series themselves, we apply the Edelson-Krolik method for correlation estimation. We examine the correlation between depression symptoms for a subset of patients and find that self-reported measures of sleep and appetite/weight show a lower average correlation than other symptoms. Using surrogate time series as a reference dataset, we find no evidence that depression is correlated between patients, though we note a possible loss of information from sparse sampling.

Trinh P.H.,Oxford Centre for Industrial and Applied Mathematics
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences | Year: 2016

The standard analytical approach for studying steady gravity free-surface waves generated by a moving body often relies upon a linearization of the physical geometry, where the body is considered asymptotically small in one or several of its dimensions. In this paper, a methodology that avoids any such geometrical simplification is presented for the case of steady-state flows at low speeds. The approach is made possible through a reduction of the water-wave equations to a complex-valued integral equation that can be studied using the method of steepest descents. The main result is a theory that establishes a correspondence between different bluff-bodied free-surface flow configurations, with the topology of the Riemann surface formed by the steepest descent paths. Then, when a geometrical feature of the body is modified, a corresponding change to the Riemann surface is observed, and the resultant effects to the water waves can be derived. This visual procedure is demonstrated for the case of two-dimensional free-surface flow past a surface-piercing ship and over an angled step in a channel. © 2016 The Author(s) Published by the Royal Society.

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