Department Colloquia
18th October: Dr Colin Torney (University of Glasgow)Title: Cues and decision-making in collective systems
Date: 3.30pm Wednesday 18th October
Venue: Livingstone Tower, 9th floor, room LT908
Abstract:
Title: TBA
Date: 3.30pm Wednesday 1st November
Venue: Livingstone Tower, 9th floor, room LT908
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Title: To approximate or not to approximate, that is the question
Date: 3.30pm Wednesday 15th November
Venue: Livingstone Tower, 9th floor, room LT908
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Title: Diffraction of hydroelastic waves by a vertical cylinder
Date: 3.30pm Wednesday 29th November
Venue: Livingstone Tower, 9th floor, room LT908
Abstract: Linear problem of wave diffraction is studied for a circular vertical cylinder mounted at the sea bed and piercing the fluid surface covered by ice plate of infinite extent. The ice plate is modeled by a thin elastic plate of constant thickness clamped to the surface of the cylinder. One-dimensional incident hydroelastic wave of small amplitude propagates towards the cylinder and is diffracted on the cylinder. Deflection of the ice plate and the bending stresses in it are determined by two methods: (a) using the integral Weber transform in radial direction, (b) using the vertical modes for the fluid of constant depth with the rigid bottom and elastic upper boundary. The solution by the second method is straightforward but we cannot prove that the solution is complete because the properties of the vertical modes are not known yet. The solution by the Weber transform is more complicated but this solution is unique. In this talk we will show that these two solutions are identical. This result justifies the method of the vertical modes in the hydroelastic wave diffraction problems.
Applied Analysis
Continuum Mechanics and Industrial Mathematics
26th September: Dr Alex Wray (University of Strathclyde)Title: The evaporative behaviour of asymmetric drops
Date: 1.00pm Tuesday 26th September
Venue: Livingstone Tower, 9th floor, room LT907
Abstract:
The evaporation of liquid drops has received extensive attention over time due to its fundamental significance in a variety of industrial contexts, not to mention the widespread consideration given to the so-called `coffee-stain effect’. Of particular interest are drops that are in some way asymmetric: it is known that the flow inside such drops is itself asymmetric as a result of non-uniformities in the evaporative flux, but the exact mechanism was not previously understood. Unfortunately the system is not amenable to the standard method described in the seminal 1997 paper of Deegan et al., but I discuss how the system may nonetheless be modelled. The finer details, especially in situations where the drop is non-slender, prove to be rather challenging, and much remains as yet unknown. I discuss what progress has been made so far, and discuss promising avenues.
Title: Phase change at the nanoscale
Date: 4.00pm Thursday 28th September
Venue: Livingstone Tower, 9th floor, room LT907
Abstract:
Nanotechnology has been a very important research topic due to the wide range of applications it has to offer
in multiple fields such as industry or medicine. Many of these applications involve high temperatures which can
even lead to a phase change and therefore it is crucial to understand how these processes occur at small length
scales.
It is widely known that heat transport at the nanoscale cannot be described in the same manner as for
macroscopic objects. There exists a large number of experimental observations which show that many thermodynamic
properties, such as the melt temperature or the thermal conductivity, become highly size-dependent at
the nanoscale and thus developing mathematical models which are able to describe this dependence accurately
is very important. In addition, most of the mathematical models describing heat transfer processes are based
on Fourier’s law, which states that the heat flux is proportional to the temperature gradient. However, it has
been shown that the classical equations break down at the nanoscale and thus other approaches are necessary
to describe heat conduction at small length or short time scales correctly. The Guyer-Krumhansl equation is a
very popular extension to the classical Fourier law that incorporates memory and non-localities, which become
significant at the nanoscale.
In this talk we will discuss the mathematical modelling of phase change and how nanoscale effects have been
incorporated into the mathematical description. We will show that the widely accepted equations are incorrect
and we will provide a new system. A mathematical model for the size-dependent melt temperature will also be
presented and we will show that there is an excellent agreement with experimental observations. In the end we
will discuss how the Guyer-Krumhansl equation affects a solidification process in a simple geometry.
Title: Analysis of a Fractal Ultrasonic Transducer
Date: 1.00pm Tuesday 10th October
Venue: Livingstone Tower, 9th floor, room LT907
Abstract:
Ultrasonic transducers are an essential tool in medical imaging, in imaging cracks in nuclear plants, and in a wide range of inverse problems.This talk will provide some theorems which can be used to predict the dynamics of a fractal ultrasound transducer whose piezoelectric components span a range of length scales. As far as we know this is the first to study waves in the complement to the Sierpinski gasket. This is an important mathematical development as the complement is formed from a broad distribution of length scales whereas the Sierpinski gasket is formed from triangles of equal size. A finite element method is used to discretise the model and a renormalisation approach is then used to develop a recursion scheme that analytically describes the key components from the discrete matrices that arise. It transpires that the fractal device has a significantly higher reception sensitivity and a significantly wider bandwidth than an equivalent Euclidean (standard) device. So much so that our engineering colleagues have built the world’s first fractal ultrasonic transducer which I will try and bring along !
Title: On the dependence of solutions of pdes on the coefficients
Date: 1.00pm Tuesday 24th October
Venue: Livingstone Tower, 9th floor, room LT907
Abstract:
We provide a framework that allows for the study of continuous dependence of solution operators of pdes on their coefficients. The results have applications to homogenisation theory.
Numerical Analysis and Scientific Computing
10th October: Dr Prashanth Nadukandi (University of Manchester)Title: Stable computation of the trigonometric matrix functions: cos(sqrt(A)) and sinc(sqrt(A))
Date: 4.00pm Tuesday 10th October
Venue: Livingstone Tower, 9th floor, room LT907
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Date: 4.00pm Tuesday 14th November
Venue: Livingstone Tower, 9th floor, room LT907
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Title:
Date: 4.00pm Tuesday 21st November
Venue: Livingstone Tower, 9th floor, room LT907
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Population Modelling and Epidemiology
30th March: Dr Robert Wilson (Mathematics and Statistics, University of Strathclyde)Title: Zooplankton Diapause in a Warmer World: Modelling the Impact of 21st Century Climate Change on Calanus Finmarchicus
Date: 1pm Wednesday 30th March 2016
Venue: Livingstone Tower, 9th floor, room LT907
Abstract: To avoid starving in winter, many zooplankton species spend over six months dormant in deep waters. The time animals can remain dormant will likely be reduced by global warming. We therefore modelled changes in potential dormancy duration in the key species Calanus finmarchicus under 21st century climate change. Climate change impacts varied markedly. Western Atlantic populations see large reductions in potential dormancy duration, but the Norwegian Sea experiences only marginal change. The reductions in the Western Atlantic will likely cause important changes to the populations of C. finmarchicus and species that prey on it.
Title: TBA
Date: 1pm Wednesday 6th April 2016
Venue: Livingstone Tower, 9th floor, room LT907
Abstract: TBA
Title: A General Methodological Framework for Identifying Disease Risk Spatial Clusters Based Upon Mixtures of Temporal Trends
Date: 1pm Wednesday 26th October 2016
Venue: Livingstone Tower, 9th floor, room LT907
Abstract: We present a novel general Bayesian hierarchical mixture model for clustering areas based on their temporal trends. Our approach is general in that it allows the user to choose the shape of the temporal trends to include in the model, and examples include linear, general monotonic, and changepoint trends. Inference from the model is based on Metropolis coupled Markov chain Monte Carlo (MC)^3 techniques in order to prevent issues pertaining to multimodality often associated with mixture models. The effectiveness of (MC)^3 is demonstrated in a simulation study, before applying the model to hospital admission rates due to respiratory disease in the city of Glasgow between 2002 and 2011. Software for implementing this model will be made freely available as part of the R package CARBayesST.
Title: The Risk of Dengue for Non-Immune Foreign Visitors to the 2016 Summer Olympic Games in Rio de Janeiro, Brazil
Date: 1.00pm, Wednesday 25th May 2016
Venue: Livingstone Tower, 9th Floor, LT9.07
Abstract: Dengue is a viral infection caused by 4 dengue serotypes transmitted by mosquitoes that is an increasing problem in Brazil and other countries in the tropics and subtropics. As Brazil is the country with the highest number of dengue cases worldwide. Rio de Janeiro, the venue for the 2016 Olympic Games, has been of major importance for the epidemiology of dengue in Brazil. After the DENV 1–4 introductions in 1986, 1990, 2000 and 2011, respectively, the city has suffered explosive outbreaks. Properly quantifying the risk of dengue for foreign visitors to the Olympics is important. A mathematical model to calculate the risk of developing dengue for foreign tourists attending the Olympic Games in Rio de Janeiro in 2016 is proposed. A system of differential equation models the spread of dengue amongst the resident population and a stochastic approximation is used to assess the risk to tourists.
Title: Optimal Vaccination Age for Dengue in Brazil with a Tetravalent Dengue Vaccine
Date: 1pm Wednesday 2nd November 2016
Venue: Livingstone Tower, 9th floor, room LT907
Abstract: With the first vaccine against Dengue being licensed in several endemic countries an important aspect that needs to be considered is the age at which it should be administered. If vaccination is done too early it is ineffective as individuals are protected by maternal antibodies, but if it is done later the infection may spread in the younger age groups, also the risks of hospitalisation and mortality change with age of infection, which is influenced by vaccination. However, to find the optimal vaccination age the possible coexistence of up to four distinct Dengue serotypes and the cross-reactions between these serotypes and Dengue antibodies need to be taken into account. We adapt a method previously applied to other infectious diseases and define the lifetime expected risk due to Dengue with respect to two different risk measures (hospitalization and lethality) which we then seek to minimize for a given three-dose vaccination strategy. Our results show that the optimal vaccination age not only depends on the risk measure but also on the number and combination of serotypes in circulation, as well as on underlying assumptions about cross-immunity and antibody dependent enhancement (ADE).
Title: Dancing in the Moonlight: Vertical Migration of Arctic Zooplankton during the Polar Night
Date: 1pm Wednesday 16th November 2016
Venue: Livingstone Tower, 9th floor, room LT907
Abstract: This talk will focus on the results from my PhD, which I completed this year at the Scottish Association for Marine Science before starting here at Strathclyde. In recent years, evidence has been found of Diel Vertical Migration (DVM) in zooplankton during the Polar Night in the Arctic Ocean. However, the drivers of this light mediated behaviour during an apparent lack of illumination and food are poorly understood. A novel dataset comprising 58 deployments of moored Acoustic Doppler Current Profilers is used in this study to observe the vertical migratory behaviour of zooplankton on a pan-Arctic scale. Methods of circadian rhythm analysis are applied to detect synchronous activity. During the Polar Night, the moon is seen to control the vertical positioning of zooplankton, and a new type of migratory behaviour is described: Lunar Vertical Migration (LVM). This exists as LVM-day (24.8 hour periodicity) and LVM-month (29.5 day periodicity), and is observed throughout the Arctic Ocean. The results presented here show continuous activity throughout winter, and challenge assumptions of a quiescent Polar Night.
Title: Disease Mapping and Visualization using Data from Spatio-Temporally Referenced Prevalence Surveys
Date: 1pm Wednesday 3rd May 2017
Venue: Livingstone Tower, 9th floor, room LT907
Abstract: We set out general principles and develop statistical tools for the analysis of data from spatio-temporally referenced prevalence surveys. Our objective is to provide a tutorial guide that can be used in order to identify parsimonious geostatistical models for prevalence mapping. A general variogram-based Monte Carlo procedure is proposed to check the validity of the modelling assumptions. We describe and contrast likelihood-based and Bayesian methods of inference, showing how to account for parameter uncertainty under each of the two paradigms. We also describe extensions of the standard model for disease prevalence that can be used when stationarity of the spatio-temporal covariance function is not supported by the data. We discuss how to define predictive targets and argue that exceedance probabilities provide one of the most effective ways to convey uncertainty in prevalence estimates. We describe statistical software for the visualization of spatio-temporal predictive summaries of prevalence through interactive animations. Finally, we illustrate an application to historical malaria prevalence data from 1334 surveys conducted in Senegal between 1905 and 2014.
Title: Including biology in spatial statistical models. Examples from vector-borne disease studies.
Date: 12.30pm, Thursday 1st June 2017
Venue: Livingstone Tower, 9th floor, room LT907
Abstract:
Vector borne diseases (e.g. Malaria, Dengue, Leishmaniasis) account for 20% of all infectious diseases, causing several million of infections and more than 1 million deaths annually. The majority of the vectors are insects (e.g. mosquitoes, midges and flies) and ticks, which biology and epidemiology are not often fully understood.
Biological and statistical models are used for mapping and modelling vector-borne diseases, however, rarely these methods are combined to produce maps and tools for disease surveillance and control (e.g. vector hot spots). In this talk I will present some techniques that can make data biologically meaningful; and the use of geo-bio-statistical models for tsetse flies (sleeping sickness) surveillance and control in Zambia. We show how mapping tsetse flies immigration, emigration, mortality and fertility can be the key element for successful disease eradication.
Title: Non-local Schrodinger Operators and Related Jump Processes
Date: 3pm Wednesday 15th March 2017
Abstract: Classical Schrödinger operators have been the object of much research involving functional analysis, probability and mathematical physics in the past decades. The recent interest in non-local Schrödinger operators consisting of the sum of a pseudo-differential operator and a multiplication operator greatly extended the range of applications, and inspired much new research in pure mathematics too. I will discuss how Feynman-Kac-type representations can be derived for the non-local cases and which random processes they give rise to. Then I will consider various sample path properties of these jump processes in terms of spectral properties of the generating non-local operators, and will contrast them with diffusions and classical Schrödinger operators.
Title: Stochastic Lotka-Volterra Food Chains
Date: 3.30pm Wednesday 19th April 2017
Abstract: We study the persistence and extinction of species in a simple food chain that is modelled by a Lotka-Volterra system with environmental stochasticity. There exist sharp results for deterministic Lotka-Volterra systems in the literature but few for their stochastic counterparts. The food chain we analyze consists of one prey and $n-1$ predators for $n\in\{2,3,4,\dots\}$. The $j$th predator eats the $j-1$th species and is eaten by the $j+1$th predator; this way each species only interacts with at most two other species - the ones that are immediately above or below it in the trophic chain. We show that one can classify, based on an explicit quantity depending on the interaction coefficients of the system, which species go extinct and which converge to their unique invariant probability measure. Our work can be seen as a natural extension of the deterministic results of Gard and Hallam '79 to a stochastic setting. A novelty of our analysis is the fact that we can describe the behavior the system when the noise is degenerate. This is relevant because of the possibility of strong correlations between the effects of the environment on the different species. This is joint work with Dang H. Nguyen.
Title: Time-Varying Feedback and its Control Ability
Date: 3.00pm Friday 19th May 2017
Abstract: Comparison to pure feedback control, time-varying feedback control has distinct advantages, e.g., in handling system nonlinearities, counteracting system uncertainties and achieving prescribed performance. But due to the time-variations, time-varying feedback always keeps most people away, and its potential has been investigated far from enough. Here I shall illustrate some good and ability of time-varying feedback, and introduce some applications in SDEs, as well as several problems to be further investigated.
Title: Last Passage Percolation Models in a Bernoulli Environment
Date: 3.00pm Wednesday 14th June 2017
Venue: Livingstone Tower, LT9.07
Abstract: We will discuss two different last passage percolation models in an i.i.d. Bernoulli random environment. In particular, I will show explicit laws of large numbers and order of fluctuations for the last passage time - the maximum number of Bernoulli points one can collect by following a sequence of admissible steps that ends in a predetermined lattice site. I will show how the behaviour of these models change depending on the set of admissible steps (e.g. the LLN changes, directions that belong in a "percolation cluster” change) and also show how the order of fluctuations change if the direction of the path endpoint changes. This is joint work with Janosch Ortmann and Federico Ciech (Univ. of Sussex).
Title: Quantized Feedback Control for Control Systems with Saturation Nonlinearity
Date: 3.30pm Friday 16th June 2017
Venue: Livingstone Tower, LT9.07
Abstract: In control systems, every physical actuator or sensor is subject to saturation owing to its maximum and minimum limits. Common examples of such limits are the deflection limits in aircraft actuators, the voltage limits in electrical actuators. Saturation nonlinearities are also purposely introduced into engineering systems such as control systems and neural network systems. In addition, one of the most important research areas in control theory is quantized control. Quantized feedback is found in many engineering systems including mechanical systems and networked systems. Since communication that need to transmit the feedback information from
the sensor to the controller may become less reliable as the bandwidth is limited. Here, I shall investigate quantized feedback control problems for systems subject to saturation nonlinearity.
Title: Stability of Two Kinds of Stochastic Runge-Kutta Methods for Stochastic Differential Equations
Date: 3.30pm Wednesday 5th July 2017
Venue: Livingstone Tower, LT9.07
Abstract: We present two kinds of explicit Runge–Kutta methods for solving stochastic differential equations by using the three–term recurrence relations of Chebyshev and Legendre polynomials. The almost sure stability and mean-square stability of the numerical solutions generated by the two kinds of methods are investigated respectively. Numerical examples are provided to confirm theoretical results.
Title: Bayes' Rule and the Law
Date: 3.00pm Thursday 24th August 2017
Venue: Livingstone Tower, LT9.07
Abstract: Bayesian inference is an approach in mathematical statistics where the probability of a hypothesis is updated as more evidence and data become available. It has wide applications in many areas such as machine learning, evolutionary biology, medicine and even in the judicial system. This talk will explore how Bayesian inference can be used in a specific court case to assist jurors in the process of legal decision making, demonstrating the power of mathematics in the court room.
Title: MLMC for Value-At-Risk
Date: 4.00pm Tuesday 19th September 2017
Venue: Livingstone Tower, LT9.07
Abstract: In this talk, I explore Monte Carlo methods to estimate the Value-At-Risk (VaR) of a portfolio, which is a measure of the risk of the portfolio in some short time horizon. It turns out that estimating VaR involves approximating a nested expectation where the outer expectation is taken with respect to stock values at the risk horizon and the inner expectation is taken with respect to the option index and stock values at some final time. Following (Giles, 2015), our approach is to use MLMC to approximate the outer expectation where deeper levels use more samples in the Monte Carlo estimate of the inner expectation. We look at various control variates to reduce the variance of such an estimate. We also explore using an adaptive strategy (Broadie et al, 2011) to determine the number of samples used in estimating the inner expectation. Finally, we discuss using unbiased MLMC (Rhee et al., 2015) when simulating stocks requires time discretization. Our results show that using MLMC to approximate a probability of large-loss with an error tolerance of order $\epsilon$, we are able to get an optimal complexity of order $\epsilon^{-2}(\log(\epsilon^{-1})^2$ that is independent of the number of options, for a large enough number of options.