**Further Information**: If you have any questions regarding the seminars below, please direct them to Romina Gaburro (+353 61 2131930), email romina.gaburro@ul.ie or Clifford Nolan (+353 61 202766), __clifford.nolan@ul.ie__.

** 20 September, 2019**: Dr. Valentina Balbi (UL, Maths & Stats)

**Title**: The mechanics of a “twisted” brain.

**Abstract**: Biological soft tissues are particularly common in nature. For instance, many organs in the human body such as the skin, the brain, the gastro-intestinal system are made of soft tissues. The brain, among all is particularly soft and delicate. Following an impact to the skull, brain matter can experience large stretches, possibly resulting in Diffuse Axonal Injury (DAI), which is the second leading cause of death from traumatic brain injury. Previous studies have focused on linear (uni-axial) stretches of brain to investigate DAI, but in reality brain matter undergoes a mix of deformation modes during an accident. This talk will focus on the mechanical behavior of the brain under torsion (twisting). In collaboration with University College Dublin, we collected data from torsion tests on (pigs) brain samples and modelled the experiments to finally quantify the elastic properties of the brain tissue. I will show that torsional impacts, such as a hook punch in boxing and a side impact in a car accident can also lead to dangerous levels of stretch compatible with DAI.

** 27 September, 2019**: Prof. Nikolai Nefedov Moscow State University)

**Title:** Asymptotic Method of Differential Inequalities and Its Applications for Direct and Inverse Problems for

Burgers type Equation.

**Abstract**: Recent results for some classes of initial boundary value problem for some classes of Burgers type equations, for which we investigate moving fronts by using the developed comparison technique are presented. There are also presented our recent results on singularly perturbed reaction-advection-diffusion problems, which are based on a further development of the asymptotic comparison principle.

** 03 October, 2019**: Alessio Benavoli (CSIS)

**Title:** Rationality and computational rationality in the age of AI.

**Abstract**:

Artificial intelligence (AI) and Machine Learning research is revolutionising our lives and leading us to a world with self-driving cars, automated trading on stock exchanges etc.. Such applications require AI methods to be able to make rational choices and make robust decisions. Rationality means that an AI agent is assumed to take account of available information and uncertainty, potential costs and benefits, and to act consistently (logically) in choosing the best action. Robustness in decision making is required to both the known unknowns (the uncertainty in the world about which the agent can reason explicitly) and the unknown unknowns (unmodelled aspects).

However, the current methods are not sufficiently suited to address these issues. In this seminar, I will briefly discuss the pitfalls of "general-recipe" machine learning (from a statistics point of view) and then introduce probabilistic (Bayesian) machine learning from a Von Neumann–Morgenstern perspective: "a rational AI agent maximises their expected utility".

I will briefly discuss about a general framework to model rationality, that encompasses different definitions of rationality from decision/market/game theory like no-Dutch-book, no-arbitrage, Nash-equilibrium theorems. Finally I will discuss computational rationality, that is about identifying decisions with highest expected utility, while taking into consideration the costs of computation in complex real-world problems in which most relevant calculations can only be approximated. In other words, how can an AI agent make rational decisions when their computational power and computational time is limited? How can we formalize a theory of computational rationality? How does Nature solve this problem?

** 11 October, 2019**: Prof. Antony Unwin (Institut für Mathematik, Universität Augsburg, Germany)

**Title:** Understanding Potential Outliers using the O3 Plot.

**Abstract**: Outliers may be important, in error, or irrelevant, but they are tricky to identify and deal with. Whether a case is identified as an outlier depends on the other cases in the dataset, on the variables available, and on the criteria used. A case can stand out as unusual on one or two variables, while appearing middling on the others. If a case is identified as an outlier, it is useful to find out why. This talk discusses the O3 plot (Overview Of Outliers) for supporting outlier analyses. O3 plots show which cases are often identified as outliers, which are identified in single dimensions, and which are only identified in higher dimensions. They highlight which variables and combinations of variables may be affected by possible outliers. Applications include a demographic dataset for the Bundestag constituencies in Germany and a university ranking dataset.

** 18 October, 2019**: Prof. Martin Stynes (Beijing CSRS)

**Title**: Time-fractional differential equations and their numerical solution.

**Abstract**: First, an extended introduction to fractional derivatives and some of their properties is presented. The regularity of solutions to Caputo fractional initial-value problems in one dimension is then discussed; it is shown that typical solutions have a weak singularity at the initial time t=0. This singularity has to be taken into account when designing and analysing numerical methods for the solution of such problems. (But many published papers pretend the singularity is not present! Some sharp criticisms will be made.) To address this difficulty we use graded meshes, which cluster mesh points near t=0, and answer the question: how exactly should the mesh grading be chosen? Finally, initial-boundary value problems in one space dimension are considered, where the time derivative is a Caputo fractional derivative. (This is a fractional-derivative generalisation of the classical parabolic heat equation.) Once again a weak singularity appears at t=0, and the mesh in the time coordinate should be graded to compute satisfactory numerical solutions.

Although the speaker’s main interest is the numerical solution of these problems, at most one-third of this talk is devoted to numerical analysis, and it won’t get very heavy. No knowledge of fractional derivatives is assumed. But some basic familiarity with differential equations is helpful.

** 25 October, 2019**: Dr. Khalad Khatab (TBC)

**Title**: Child Health and Epidemiology using Bayesian Geo-Additive Latent Variable Models

**Abstract**: This presents both theoretical contributions and empirical applications of advanced statistical techniques including geo-additive models that link individual measures with area variables to account for spatial correlation; multilevel models that address the issue of clustering within family and household; and flexible parametric alternatives to existing intensity model

Previous studies which have focused on childhood disease in developing counties have typically neglected aspects of the associations between diseases. The notable exception to this are studies conducted before focused more on separate geoadditive probit models for childhood diseases. However, the diseases often coexist in the same eco-epidemiological settings and may share common risk factors, and morbidity and mortality may be a result of cumulative effects of different diseases. Khatab (2007), Khatab and Fharmeir (2009), and Khatab (2010), Khatab and Kandala (2011), and Khatab.et al (2017) considered the different types of diseases as a health status indicator, and different types of undernutrition (stunting, wasting, and underweight) as nutritional status for the latent variable model. These analytical techniques are illustrated mainly through modelling maternal and child health in the African context, using data from demographic and health surveys.

** 01 November, 2019**: Dr. Yuri Dumaresq Sobral (Departamento de Matemática, Universidade de Brasília, Brazil

Department of Applied Mathematics and Theoretical Physics, University of Cambridge)

**Title**: Numerical simulations of immersed granular collapses with dense and loose initial packings

**Abstract**: The collapse of granular columns in a viscous fluid is a common model case for submarine geophysical flows. In immersed granular collapses, dense packings result in slow dynamics and short runout distances, while loose packings are associated with fast dynamics and long runout distances. However, the underlying mechanisms of the triggering and runout, particularly regarding the complex fluid-particle interactions at the pore-scale, are yet to be fully understood. In this study, a three-dimensional approach coupling the Lattice Boltzmann Method and the Discrete Element Method is adopted to investigate the influence of packing density on the collapsing dynamics. The direct numerical simulation of fluid-particle interactions provides evidence of the pore pressure feedback mechanism. In dense cases, a strong arborescent contact force network can form to prevent particles from sliding, resulting in a creeping failure behavior. In contrast, the granular phase is liquefied substantially in loose cases, leading to a rapid and catastrophic failure. Furthermore, hydroplaning can take place in loose cases due to the fast-moving surge front, which reduces the frictional resistance dramatically and thereby results in a longer runout distance. More quantitatively, we are able to linearly correlate the normalized runout distance and the densimetric Froude number across a wide range of length scales, including small-scale numerical/experimental data and large-scale field data.

** 08 November, 2019**: Prof. Bob Barmish, Boston University

**Title: **On human versus mathematical expectation when conservatism is paramount.

**Abstract: **

Our motivation for the research to be described is derived from the following fact: The expected value of a random variable X, denoted E(X), is often inconsistent with what human beings may actually expect. This is particularly important when predictions involving life-threatening situations arise. To bring this issue into sharp focus, this seminar begins with a set of questions related to the recent rampage of Hurricane Irma from the Gulf of Mexico into in the State of Florida. If the use of empirical data leads to an expected value forecast of storm surge wave height which is unduly pessimistic, will the "boy who cried wolf" effect be in play the next time a hurricane approaches the mainland? On the other hand, if the formally calculated expected wave height is too optimistic, might it be the case that many will take inadequate protective measures? Based on such considerations, we define a new alternative to E(X) which we believe is quite useful for "mission critical" situations with downside risk being of paramount concern. We call this new metric the *Conservative Expected Value* and denote it by CEV(X). In this talk, we provide the technical definition of the CEV, compare it with the classical expected value and describe some aspects of the rich mathematical theory which accompanies it. We also include a description of some of the studies we have conducted using the CEV with historical data.

** 22 November, 2019**: Harold Benjamin (IRC postdoctoral researcher, School of Mathematics Statistics and Applied Mathematics, NUIG)

**Title**: Modelling wave propagation in solid materials with memory

**Time/Room**: A2-002, 3.00 p.m.

**Abstract**:

Dissipation is an important aspect of the mechanical behaviour of solid materials. In particular, an accurate mathematical description of dissipation is crucial in computational acoustics, non-destructive testing, and seismology. Most of the nonlinear viscoelasticity theories are either based on convolution products or on memory variables. In this framework, strain- or stress-like variables of state are introduced to account for memory effects. However, such models of viscoelastic behaviour are not sufficient to describe the response of various geomaterials (rocks, concrete), for which long-time relaxation effects called *slow dynamics* are observed. Including several numerical examples, the presentation covers classical nonlinear viscoelasticity theories, as well as modifications to account for slow dynamics.

** 29 November, 2019**: TBA

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**Abstract**: TBC

** 06 December, 2019**: TBC

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** 13 December, 2019**: TBC

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