abstracts

Increasing life expectancy, falling birth rates, ultra-low or rapidly increasing interest rates and the guarantees associated with pension benefits are putting a lot of pressure on governments and pension industry. Possible and extremely unpopular solutions may be to reduce pensions or to increase the retirement age.

In this talk, we first discuss the mathematics behind the idea of reforming the pay-as-you-go (state) pension system, so that suitable investments could compensate future deficits, at least temporarily.

In the second part, for a unit-linked private pension scheme, we look at the expected costs of an insurance company that covers all pension cuts - and in this way offers a stable lower limit for the pensions.

What are the factors influencing young women’s sense of belonging to STEM? In her talk, Melissa Nielsen (LEA) presents key findings of the study “MINT the Gap! Educational and career choice processes of young women” (2023), commissioned by LEA and conducted by social research institute L&R Social Research. Her talk provides information on what motivates young women to choose a career in STEM, what hinders them from doing so and what obstacles they have to overcome if they want to stay in their field. The talk identifies key factors promoting women’s sense of belonging to STEM and points out what could be done to reduce the STEM gap in Austria and worldwide. 

Cross-diffusion systems are nonlinear parabolic systems that model the evolution of densities or concentrations of multicomponent populations in interaction. In this talk, we study the evolutionary dynamics of two species in competition, modeled by a triangular cross-diffusion system driven by dietary diversity. More precisely, we show the existence of weak solutions by rigorously proving the passage from an approximating Lotka-Volterra reaction-diffusion system with linear diffusion, towards a cross-diffusion system at the fast reaction limit. The resulting limit gives a cross-diffusion system of starvation-driven type. The main tools used to pass the limit rigorously consist of a priori estimates, given by the analysis of an entropy functional, and compactness arguments.

In this work, we focus on the numerical approximations of Piecewise Diffusion Markov Processes (PDifMPs), particularly when the explicit flow maps are unavailable. Our approach is based on the thinning method for modelling the jump mechanism and combines the Euler-Maruyama scheme to approximate the underlying flow dynamics. For the proposed approximation schemes we study both the strong and weak convergence. Weak convergence of the algorithms is established by a martingale problem formulation. Moreover, we employ these results to simulate the migration patterns exhibited by a moving glioma cells. Notably, we employ both the Thinned Euler-Maruyama and the Splitting schemes in our simulation example, allowing us to compare both methods.

Radiofrequency catheter ablation (RFCA) is an effective treatment for cardiac arrhythmia. During the RFCA procedure, the electrode on the catheter tip is used to deliver RF current, at 500 kHz to ablate arrhythmogenic tissues. RF current flows between the electrode tip and the dispersive patch (DP) placed on the patient's skin, usually on the back or thigh. In a clinical aspect, during RFCA, different electrode placements produces varying electric fields within the cardiac tissue. We developed a 3D computational model using thoracic CT scans obtained from patients. After segmentation, we generated a finite element mesh and embedded a spherical electrode with radius 1.165mm. In our mathematical model, we solved electrostatic partial differential equation (PDE) for electrical potential%, to simulate the electric fields. We investigate the impact of the position of the DP on the distribution of electrical current around the electrode at the catheter tip during RFCA.

We study a dynamic portfolio optimization problem in which stock returns tend to continue over short horizons, so-called momentum, and revert over longer horizons, so-called mean-reversion or reversal. We extend the continuous-time framework of Koijen et. al. (2009) into a partial information one, where the investor (trader) can not observe the proportion of the drift that is attributable to the mean-reversion. Due to the Gaussian nature of the problem, the Kalman filter is used to obtain estimates for unobservable mean-reversion level. Since essentially the filtering and stochastic optimal control problems are separable, we reduce the optimization problem under partial information to the one with full information. It turns out that the market becomes complete after reduction and that we obtain the optimal portfolio weights and optimal portfolio value. In a special one-factor case, the coefficients in the formula for the value function under partial information can be expressed using the coefficients of the full information case, thus illustrating the loss of utility that results from incomplete information The differences in the optimal trading strategies under full and partial information are computed in an extensive simulation study as well as using real data.

Lifetime modeling provides valuable insights into the behavior of systems, products, and processes over time in various industries and disciplines. This work investigates the fatigue lifetime model invented by Castillo and Fernandez-Canteli with the aim of stabilizing the estimation process and increasing its accuracy. This thesis focuses on two important points in the estimation procedure:

(i) finding initial values for the geometric parameters of the Castillo-Canteli model and

(ii) parameter inference for the three parameter Weibull distribution.

The method to obtain initial values for the geometric parameters proposed by Castillo and Fernandez-Canteli can give invalid initial values. This work proposes a grid search algorithm as a working alternative. Four different methods for estimating the parameters of the three parameter Weibull distribution are examined: Maximum Likelihood Estimation (MLE), a graphical method, the method of Probability Weighted Moments (PWM), and a Bayesian estimation approach. Confidence intervals are obtained using asymptotic properties (for the MLE method), a bootstrap procedure (for MLE, PWM and graphical method), and quantiles of the posterior distribution (for the Bayesian approach). The estimation methods are compared in a simulation study with 7 200 simulated data sets. The simulation study suggests using a sample size >=100 to obtain reliable estimates and using the Bayes method with highest posterior density intervals for the most accurate confidence intervals. PWM + bootstrap underperformed compared to other methods, and in samples of size 1 000 and above, all methods performed equally well. The results justify using the seemingly simple but effective graphical method used especially by engineers for parameter estimation.

The paper illustrates the main results of a non-stationary spatio-temporal precipitation model interpolation process of three different precipitation scenarios distributed throughout Austria for the years 1973-1982 and 2013-2022. We model mean and maximum precipitation as well as dry spells with a Gamma, blended generalized extreme value and negative Binomial distribution. A generalized additive model accounts for influencing covariates as elevation and the coordinates of the monitoring stations which is then rewritten in a Bayesian hierarchical form. The spatial component of the model is represented through the stochastic partial differential equation (SPDE) approach and the temporal one through an AR(1) process. Inference is performed through integrated nested Laplace approximation (INLA) which comes along with a user friendly R-INLA package. The model outputs are visualised and give insights into changes in precipitation scenarios over two different time periods.

During this talk, I will go through the history of the continuum problem along the cardinal hierarchy. Specifically, I will talk about the question of whether there are cardinalities within \kappa and 2^\kappa for some arbitrary cardinal kappa (here 2^\kappa stands for the cardinality of the power set of \kappa). Afterward, I will focus on the singular cardinal case, and at the end, I will motivate some of my current research and results.

Non-unique factorization of elements into irreducibles has been observed in the ring of integer-valued polynomials and its generalizations. A particularity of non-UFDs is that there is is in general no saying how the powers of an irreducible element factor. From a factorization-theoretic point of view, one therefore wants to identify those elements among the irreducibles whose powers factor uniquely---a property in between irreducibility and primality. We call such elements absolutely irreducible. This talk provides an overview on factorization-theoretic aspects in rings of integer-valued polynomials with focus on absolutely irreducible elements, including recent results from joint work with Sophie Frisch, Moritz Hiebler, Sarah Nakato, and Daniel Windisch.

This talk aims at initializing a dynamical aspect of symbolic summation by studying stability problems in difference fields. We present some basic properties of stable sequences that enable us to characterize two special families of stable sequences including rational sequences and hypergeometric sequences. 

The classical Ore-Sato theorem reveals that any multivariate hypergeometric terms can be written as the product of a rational function and several factorial terms. We extend it to the the additive case that any hyperarithmetic term can be written as the sum of a rational function and several Psi functions and their derivatives.

We introduce five equivalent representations of a phylogenetic tree, as well as some conversions in between them.

The discrete alpha-neighbor p-center problem is an emerging variant of the classical p-center problem which recently got attention in literature. In this problem, we are given a discrete set of points and we need to locate p facilities on these points in such a way that the maximum distance between each point where no facility is located and its alpha-closest facility is minimized. The only existing algorithms in literature for solving the problem are approximation algorithms and two recently proposed heuristics. In this talk, we present two integer programming formulations for the discrete alpha-neighbor p-center problem, together with lifting of inequalities, valid inequalities, inequalities that do not change the optimal objective function value and variable fixing procedures. We describe theoretical results on the strength of the formulations and present convergence results for the lower bounds obtained after applying the lifting procedures or the variable fixing procedures in an iterative fashion. We also present branch-and-cut (B&C) algorithms based on our formulations and our theoretical results. These algorithms are further enhanced with a starting heuristic and a primal heuristic. We evaluate the effectiveness of our B&C algorithms using instances from literature. Our algorithms are able to solve 116 out of 194 instances from literature to proven optimality, with a runtime of under a minute for most of them. By doing so, we also provide improved solution values for 116 instances.

In this talk, we review the history of one of the most important theorems in Number Theory "the Prime Number Theorem". Then, we provide one of the applications of this theorem in cryptography, particularly in the RSA cryptosystem, where numbers of the form $pq$, with $p$ and $q$, two distinct proportional primes, play an important role.

The task of identifying an algebraic surface from a single branching curve (apparent contour) can be simplified by deriving a homogeneous equation from its discriminant. Current efforts focus on successfully reconstructing various surfaces, including smooth surfaces, surfaces with ordinary singularities, ruled surfaces, and, notably, Darboux cyclides. Recognizing Darboux cyclides is facilitated by their singularity along the absolute conic, enabling identification through Euclidean similarity transforma- tions. This approach extends to reconstructing a planar map from a given branch- ing curve, using the ramification curve obtained through linear normalization of a branching curve of a parametric surface. Additionally, ongoing analysis involves the examination and categorization of Dupin cyclides, which arise through inversion applied to tori, cylinders, or double cones. The self-duality of Dupin cyclides establishes a correspondence between the apparent contour and the dual of the planar section, allowing for characterization based on specific planar sections. 

Planar rigid body motions can be interpolated by piecewise rotational and translational motions. In this talk we show some advantages of this simple interpolation: the distance between the original motion and its interpolation as between curves in a suitable kinematic image space converges quadratically to zero. This implies the same rate of convergence between point trajectories under the two motions. Furthermore, the trajectory of any point under the approximated motion is then an arc spline, i.e. a curve composed of circular arcs and line segments. For objects with arc spline boundaries, the boundary of the volume swept by the object and the motion is also an arc spline and can be computed effectively. 

The sampling problem involves finding conditions under which a signal can be reconstructed from its samples taken on a discrete subset of its domain. The most classical assumption about the sampled signal is that it belongs to a Paley-Wiener space (the space of signals whose Fourier transform is supported on a given compact set). In multidimensional settings, finding a stable sampling set for this type of signal remains a very challenging task. One important line of research considers the Paley-Wiener spaces whose spectrum has the property of multi-tiling the space along lattice translations. For these signals, it is known that there exists a stable sampling set in the form of a finite union of translations of a lattice (a non-uniform periodic set) that meets Landau's density benchmark. In practice, explicitly identifying such sets requires a substantial level of effort. In this presentation, we will discuss a probabilistic approach to this problem, extending it to a broader signal model of shift-invariant spaces. This model includes the case of Paley-Wiener spaces with a multi-tiling spectrum. In particular, we will show that by slightly exceeding Landau’s density benchmark, one can obtain non-uniform periodic sampling sets with overwhelming probability. This is a joint work with Jorge Antezana (Autonomous University of Madrid) and José Luis Romero (University of Vienna).

In this talk we will first briefly introduce frames and frame multipliers. The concept of a frame for a Hilbert space H extends the concept of an orthonormal basis for a Hilbert space H and still guarantees perfect reconstruction of all the elements of H, though not necessarily in a unique way anymore, which is however very useful in signal processing. Frame multipliers are operators whose action can be described in three steps: a signal is first analysed (via some frame) and some scalar sequence is obtained; in the second step, the scalar sequence is modified (via a multiplication with given numbers according to a desired change of the signal); finally, the new scalar sequence is transferred to the signal domain (via some frame) leading to a modified signal. After introducing the main concepts, we will discuss some applications in signal processing and invertibility possibilities of frame multipliers.

Diffraction tomography is an inverse scattering technique used to reconstruct the spatial distribution of the material properties of a weakly scattering object. The object is exposed to radiation, typically light or ultrasound, and the scattered waves induced from different incident field angles are recorded. In conventional diffraction tomography, the incident wave is assumed to be a monochromatic plane wave, an unrealistic simplification in practical imaging scenarios. In this article, we extend conventional diffraction tomography by introducing the concept of customized illumination scenarios, with a pronounced emphasis on imaging with focused beams. We present a new forward model that incorporates a generalized incident field and extends the classical Fourier diffraction theorem to the use of this incident field. This yields a new two-step reconstruction process which we comprehensively evaluate through numerical experiments. 

After many years of research and interventions around mathematics and gender, mathematics as an academic domain is still facing a participation gap. While recent scholars underlined the importance of action against this, practical implications and recommendations about teaching mathematics in a gender-equality promoting way, are rare. This paper aims to provide such practical implications based on a review on current literature and the theoretical approach of (un)doing gender that is further discussed. 

Alcoholism is the act of consuming alcoholic drinks with high intensity and continuously. Mathematical models can be used as an approach in predicting the spread of alcoholism in the future. Fractional order /alpha/ is a generalization of discrete order. This model is divided into five

compartments: the vulnerable population, the light addict population, the heavy addict population, the treatment population, and the recovered population. Based on the model analysis, two equilibrium points were obtained whose local stability was analyzed: the alcoholism-free equilibrium point E_0 and the alcoholism equilibrium point E_1. Basic Reproduction Number R_0 is used to represent the transmission potential of alcoholism. The R_0 calculation was obtained using the Next Generation Matrix (NGM) approach method. In this study, sensitivity analysis was used to determine the most influential parameters in this model. Numerical simulation of the alcoholism model is applied using the Predictor-Corrector method with /alpha/ variations, so that population dynamics in the spread of alcoholism can be interpreted. The results of this research show the importance of controlling the problem of alcoholism by caring for and treating alcoholics.

Keywords: Alcoholism, Stability, Fractional Order, and Equilibrium Point

Cluster algebras are a class of commutative rings introduced by Fomin and Zelevinsky (2002) endowed with a family of distinguished generators, which are constructed recursively using mutations. Cluster algebras have been the focus of intense research since, thanks to the many links that have been discovered with a wide range of subjects, although their ring-theoretic properties are not so well-explored. The main focus of the talk is on factorization-theoretical properties of upper cluster algebras, an upper bound for cluster algebras given by the Laurent phenomenon. We give a full description of the class group of full rank upper cluster algebras in term of the exchange polynomials. Understanding class groups allows us to study unique factorization properties of Krull domains. This extends results of Garcia-Elsener--Lampe--Smertnig (2019) on acyclic cluster algebras and of Cao--Keller--Qin (2022).

In certain imaging methods the orientation of the object of interest is unknown and has to be recovered in order to reconstruct the object itself. This is the case in optical microscopy of optically or acoustically trapped particles, that undergo a continuous motion during the imaging process. Opposed to standard microscopic imaging, where the probe is fixated, this technique allows imaging in a more natural environment. We consider two different models for recovering the rigid motion of a single particle: parallel beam tomography and diffraction tomography. Based on the Fourier slice and the Fourier diffraction theorem, we develop infinitesimal methods of the well-known common-line and common-circle method, respectively. Those methods assume a smooth motion over time and allow us to calculate the angular velocity of the rotational motion.

Statistical modeling serves as a cornerstone in the realm of sports data, playing a vital role in predicting player performance, decoding game dynamics, and refining the precision of odds and betting strategies. Our advanced analytics transform raw data- whether historical or live- into a strategic advantage for informed decision-making in the world of sports betting. Going beyond mere numerical manipulation, our approaches synthesize data into a comprehensive playbook, providing guidance to our customers through the complexities of crafting effective betting strategies. Whether the focus lies in score predictions or optimizing odds, our services platform yields nuanced insights that surpass conventional analyses.

We want to introduce d-fine Austria GmbH, where people with mathematical, physical and technological skills successfully support clients in industry and finance. In our projects we are focusing on quantitative real-world challenges using their analytical, quantitative and technical mindset. We will present to you our female leadership program that consists of networking, mentoring and promotion network. Besides we will give you an insight into projects from our every day’s work life, including topics like sustainability, data science and challenging optimization problems in the energy sector. This will be a joint presentation by Michaela Bundschuh, Esther Daus and Carina Hörandtner.

Mathematicians at KPMG are specialist professionals working in advisory and audit, particularly within the insurance and banking industries. Their expertise in areas such as risk management, data analytics, financial modeling, and optimization enables them to provide valuable insights and solutions to complex challenges faced by these sectors.

Elastography, as an imaging modality in general, aims at mapping the mechanical properties of a given sample. This modality is of use in Medicine, in particular for the non-invasive identification of malignant formations inside the human skin or tissue biopsies during surgeries. In term of diagnostics accuracy, one is interested in quantitative values of strain and stiffness mapped on top of the visualization of a sample, rather than only in qualitative images. For estimating the values quantitatively, we look at Elastography from the perspective of Inverse Problems.