Karlstad Applied Analysis Seminar (KAAS)

Subscribe to the KAAS calendar and stay updated automatically. Copy the link and add it to your online calendar.

Future seminars:

Talk-146

When: 22 January 2025
What: Fractional Boundary Value Problems: Analysis, Approximations and Applications
Who: Kateryna Marynets, Delft Institute of Applied Mathematics, TU Delft, The Netherlands
Where: online:https://kau-se.zoom.us/j/61616693592
Abstract:

Fractional calculus is a powerful tool in mathematical modeling, that gets more attention of
applied mathematicians and natural scientists since the past decades. Dynamical systems involving
fractional order derivatives are able to incorporate the so-called ‘memory effects’, and due to the non-
local nature of fractional differential operators they are usually used in modeling of the flows through
porous media (e.g., the groundwater flows), sub- and super-diffusion processes etc. Additionally, a large
choice of fractional derivatives and variations in their order gives more flexibility in comparison to the
classical integer-order models.
Since most physical processes are nonlinear and the exact solution of such models is, in general,
impossible to find, we are interested in construction of reliable iterative methods that enable us to deal
with this task.
In my talk I will present one of such approaches, that is based on analysis of a system of fractional
differential equations, subject to periodic boundary conditions. A proper perturbation of the studied
system allows us to reduce analysis of the boundary value problem to an equivalent initial value problem,
whose solutions are approximated using the numerical-analytic scheme. I will also demonstrate the
applicability and effectiveness of this method on a real-world problem.

Talk-147

When: T.B.D
What: Practical Synthetic Data Generation for Statistical Inference
Who: Lotte Pater, Dienst Uitvoering Onderwijs, Ministry of Education, Culture and Science, and University of Groningen, NL 
Where: online:https://kau-se.zoom.us/j/61616693592
Abstract:

In the present information age governments, universities, hospitals and many others collect large amounts of personal data. These data can be very useful for research and decision making, but often is not shared due to legal and ethical privacy implications. Synthetic data is a technique used to combine data usage with data privacy. A synthetic version of a dataset is created, ideally with the same statistical distributions as the real dataset (so that it is still useful) but without any personal information (so that there are no privacy risks). I work with an interdisciplinary team in the Dutch government to implement synthetic data operations. In this talk I will tackle two questions:

1. How can you generate potentially useful synthetic data? We use Classification and Regression Trees (CART) as implemented in the R package synthpop. This technique consistently comes out as generating the most useful synthetic data  (i.e. similar to the real data) in the comparative literature. I’ll explain what makes this technique tick and contrast it with the more popular General Adversional Networks (GAN) class of models. I will also compare it with the conceptually similar technique by Nicklas Jävergård et al. (2024).
2. How can you make potentially useful synthetic data actually useful? Generating synthetic data might seem like mainly a statistical problem. But in actually applying it, we also encountered legal, ethical, software development, governance, political and communication challenges. In many cases, combining mathematics with other skills was necessary to solve a problem. I will highlight some general experiences and talk about how we set down a privacy approach for synthetic data – a problem that combines mathematics, law, ethics and communication. 

Talk-148

When: T.B.D
What: Nonsmooth mechanics of fiber network microstructures
Who: Mykola Tkachuk, Karlstad University, Karlstad, Sweden.
Where: T.B.D and online:https://kau-se.zoom.us/j/61616693592
Abstract:

We wish to present the case that many problems in mechanics can be posed as mathematical programming.

Equilibrium of various structures can be determined via minimization of the potential energy or other suitable mechanical functional. We have developed a new discrete network model [2] for nonwoven materials.

The rate-independent sliding and the quasi-static equilibrium loading of such network structure are constituted within the theory of standard dissipative systems. A minimum principle for incremental potential is formulated with respect to the displacement-based variables: nodal coordinates, segment end-to-end vectors, segment lengths and incremental fiber slidings. It takes the form of second-order cone programming (SOCP) similarly to the case of elastic cable networks. A pure complementary energy principle is derived as the dual formulation in terms of stress-like variables: nodal reactions, fiber force vectors, axial forces and friction forces.

The model capture large irreversible deformations of nonwoven materials. The damage mechanism is implemented in the form of fiber pull-out. The network becomes disjoint as more and more sections of free tails are pulled through the end knots.