**8** Publications

- Page
**1**of**1**

Phys Rev E 2022 Feb;105(2-1):024121

Department of Mathematics, Swansea University, Bay Campus, SA1 8EN, Swansea, Wales, United Kingdom.

We use persistent homology and persistence images as an observable of three variants of the two-dimensional XY model to identify and study their phase transitions. We examine models with the classical XY action, a topological lattice action, and an action with an additional nematic term. In particular, we introduce a way of computing the persistent homology of lattice spin model configurations and, by considering the fluctuations in the output of logistic regression and k-nearest neighbor models trained on persistence images, we develop a methodology to extract estimates of the critical temperature and the critical exponent of the correlation length. We put particular emphasis on finite-size scaling behavior and producing estimates with quantifiable error. For each model we successfully identify its phase transition(s) and are able to get an accurate determination of the critical temperatures and critical exponents of the correlation length.

## Download full-text PDF |
Source |
---|---|

http://dx.doi.org/10.1103/PhysRevE.105.024121 | DOI Listing |

February 2022

Phys Rev Lett 2022 Feb;128(8):081603

Department of Mathematics, Swansea University, Bay Campus, SA1 8EN, Swansea, Wales, United Kingdom.

We propose inverse renormalization group transformations within the context of quantum field theory that produce the appropriate critical fixed point structure, give rise to inverse flows in parameter space, and evade the critical slowing down effect in calculations pertinent to criticality. Given configurations of the two-dimensional ϕ^{4} scalar field theory on sizes as small as V=8^{2}, we apply the inverse transformations to produce rescaled systems of size up to V^{'}=512^{2} which we utilize to extract two critical exponents. We conclude by discussing how the approach is generally applicable to any method that successfully produces configurations from a statistical ensemble and how it can give novel insights into the structure of the renormalization group.

## Download full-text PDF |
Source |
---|---|

http://dx.doi.org/10.1103/PhysRevLett.128.081603 | DOI Listing |

February 2022

Phys Rev E 2020 Nov;102(5-1):053306

Department of Mathematics, Swansea University, Bay Campus, SA1 8EN, Swansea, Wales, United Kingdom.

We demonstrate, by means of a convolutional neural network, that the features learned in the two-dimensional Ising model are sufficiently universal to predict the structure of symmetry-breaking phase transitions in considered systems irrespective of the universality class, order, and the presence of discrete or continuous degrees of freedom. No prior knowledge about the existence of a phase transition is required in the target system and its entire parameter space can be scanned with multiple histogram reweighting to discover one. We establish our approach in q-state Potts models and perform a calculation for the critical coupling and the critical exponents of the ϕ^{4} scalar field theory using quantities derived from the neural network implementation. We view the machine learning algorithm as a mapping that associates each configuration across different systems to its corresponding phase and elaborate on implications for the discovery of unknown phase transitions.

## Download full-text PDF |
Source |
---|---|

http://dx.doi.org/10.1103/PhysRevE.102.053306 | DOI Listing |

November 2020

J R Soc Interface 2020 12 9;17(173):20200775. Epub 2020 Dec 9.

Swansea University Medical School, Swansea University, Swansea SA2 8PP, UK.

Controlling the regional re-emergence of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) after its initial spread in ever-changing personal contact networks and disease landscapes is a challenging task. In a landscape context, contact opportunities within and between populations are changing rapidly as lockdown measures are relaxed and a number of social activities re-activated. Using an individual-based metapopulation model, we explored the efficacy of different control strategies across an urban-rural gradient in Wales, UK. Our model shows that isolation of symptomatic cases or regional lockdowns in response to local outbreaks have limited efficacy unless the overall transmission rate is kept persistently low. Additional isolation of non-symptomatic infected individuals, who may be detected by effective test-and-trace strategies, is pivotal to reducing the overall epidemic size over a wider range of transmission scenarios. We define an 'urban-rural gradient in epidemic size' as a correlation between regional epidemic size and connectivity within the region, with more highly connected urban populations experiencing relatively larger outbreaks. For interventions focused on regional lockdowns, the strength of such gradients in epidemic size increased with higher travel frequencies, indicating a reduced efficacy of the control measure in the urban regions under these conditions. When both non-symptomatic and symptomatic individuals are isolated or regional lockdown strategies are enforced, we further found the strongest urban-rural epidemic gradients at high transmission rates. This effect was reversed for strategies targeted at symptomatic individuals only. Our results emphasize the importance of test-and-trace strategies and maintaining low transmission rates for efficiently controlling SARS-CoV-2 spread, both at landscape scale and in urban areas.

## Download full-text PDF |
Source |
---|---|

http://dx.doi.org/10.1098/rsif.2020.0775 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7811581 | PMC |

December 2020

BMJ Open 2020 10 21;10(10):e043010. Epub 2020 Oct 21.

School of Social Sciences, Cardiff University, Cardiff, South Glamorgan, UK.

## Download full-text PDF |
Source |
---|---|

http://dx.doi.org/10.1136/bmjopen-2020-043010 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7580065 | PMC |

October 2020

Phys Rev E 2020 Sep;102(3-1):033303

Department of Mathematics, Swansea University, Bay Campus, SA1 8EN, Swansea, Wales, United Kingdom.

We propose the use of Monte Carlo histogram reweighting to extrapolate predictions of machine learning methods. In our approach, we treat the output from a convolutional neural network as an observable in a statistical system, enabling its extrapolation over continuous ranges in parameter space. We demonstrate our proposal using the phase transition in the two-dimensional Ising model. By interpreting the output of the neural network as an order parameter, we explore connections with known observables in the system and investigate its scaling behavior. A finite-size scaling analysis is conducted based on quantities derived from the neural network that yields accurate estimates for the critical exponents and the critical temperature. The method improves the prospects of acquiring precision measurements from machine learning in physical systems without an order parameter and those where direct sampling in regions of parameter space might not be possible.

## Download full-text PDF |
Source |
---|---|

http://dx.doi.org/10.1103/PhysRevE.102.033303 | DOI Listing |

September 2020

Phys Rev Lett 2012 Sep 11;109(11):111601. Epub 2012 Sep 11.

School of Computing and Mathematics, Plymouth, PL4 8AA, United Kingdom.

The density of states is calculated for the SU(2), SU(3), and a compact U(1) lattice gauge theories using a modified version of the Wang-Landau algorithm. We find that the density of states of the SU(2) gauge theory can be reliably calculated over a range of 120,000 orders of magnitude for lattice sizes as big as 20(4). We demonstrate the potential of the algorithm by reproducing the SU(2) average action, its specific heat, and the critical couplings of the weak first order transition in U(1).

## Download full-text PDF |
Source |
---|---|

http://dx.doi.org/10.1103/PhysRevLett.109.111601 | DOI Listing |

September 2012

Philos Trans A Math Phys Eng Sci 2010 Aug;368(1924):3657-70

School of Physical Sciences, Swansea University, Singleton Park, Swansea SA2 8PP, UK.

Strong theoretical arguments suggest that the Higgs sector of the standard model of electroweak interactions is an effective low-energy theory, with a more fundamental theory expected to emerge at an energy scale of the order of a teraelectronvolt. One possibility is that the more fundamental theory is strongly interacting and the Higgs sector is given by the low-energy dynamics of the underlying theory. I review recent works aimed at determining observable quantities by numerical simulations of strongly interacting theories proposed in the literature to explain the electroweak symmetry-breaking mechanism. These investigations are based on Monte Carlo simulations of the theory formulated on a space-time lattice. I focus on the so-called minimal walking technicolour scenario, an SU(2) gauge theory with two flavours of fermions in the adjoint representation. The emerging picture is that this theory has an infrared fixed point that dominates the large-distance physics. I shall discuss the first numerical determinations of quantities of phenomenological interest for this theory and analyse future directions of quantitative studies of strongly interacting theories beyond the standard model with lattice techniques. In particular, I report on a finite size scaling determination of the chiral condensate anomalous dimension gamma, for which 0.05 < or = gamma < or = 0.25.

## Download full-text PDF |
Source |
---|---|

http://dx.doi.org/10.1098/rsta.2010.0030 | DOI Listing |

August 2010

-->