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Cryptography for Transparent SocietyMI 02.08.011 (Boltzmannstr. 3, 85748 Garching)

Digital society is built heavily on information and communication technology (ICT). However, programs running on computers are invisible, thus it is difficult to observe when these technologies are being misused, harming individuals and society.

Cryptography studies mechanisms to control information flow or restrict certain procedures within a network of systems. Moreover, it provides verification means to ensure that each entity is behaving according to a predetermined set of rules. Therefore, they are important tools for designing secure and fair systems and bring transparency in digital society. Mathematics is necessary to make sure that cryptographic protocols and primitives achieve the designed criteria.

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Supercritical percolation on finite transitive graphs(using zoom) (Parkring 11, 85748 Garching-Hochbrück)

In Bernoulli bond percolation, each edge of some graph are chosen to be either deleted or retained independently at random with retention probability p. For many large finite graphs, there is a phase transition such that if p is sufficiently large then there exists a giant cluster whose volume is proportional to that of the graph with high probability. We prove that in this phase the giant cluster must be unique with high probability: this was previously known only for tori and expander graphs via methods specific to those cases. Joint work with Philip Easo.

Introduction of an environmental stress level to model tumor cell growth and survivalvia ZOOM (Boltzmannstr. 3, 85748 Garching)

Survival of living cells underlies many influences such as nutrient saturation, oxygen level, drug concentrations or mechanical forces. Data-supported mathematical modeling can be a powerful tool to get a better understanding of cell behavior in different settings. However, under consideration of numerous environmental factors mathematical modeling can get challenging. We present an approach to model the separate influences of each environmental quantity on the cells in a collective manner by introducing the ”environmental stress level”. It is an artificial, immeasurable variable, which quantifies to what extent viable cells would get in a stressed state, if exposed to certain conditions. A high stress level can inhibit cell growth, promote cell death and influence cell movement. As a proof of concept, we compare two systems of ordinary differential equations, which model tumor cell dynamics under various nutrient saturations respectively with and without considering an environmental stress level. Particle-based Bayesian inversion methods are used to calibrate unknown model parameters with time resolved measurements of in vitro populations of liver cancer cells.

Link and Passcode: https://tum-conf.zoom.us/j/96536097137 Code 101816

Data collaboratives and big data for social goodvia ZOOM (Boltzmannstr. 3, 85748 Garching)

Please register at: https://forms.gle/YfPt578EpjAoA9x48

Abstract: New sources of human behavior data can empower humanitarian projects, but they need to be carefully handled, properly anonymized and aggregated. In this talk, I will discuss the potential benefits and risks of data collaboratives for social good. Data collaboratives are public-private partnerships for data sharing and both legal and ethical aspects are very important for these initiatives. I will give examples from the Data for Refugees (D4R) Challenge, which was a non-profit challenge initiated to improve the conditions of the Syrian refugees in Turkey by providing a special database to the scientific community for enabling research on urgent problems concerning refugees, including health, education, unemployment, safety, and social integration. Collected from 1 million telecommunications customers over a one-year period, the mobile CDR database shows the activity and movement of refugees and citizens over the entire country. I will also briefly describe the Hummingbird Horizon2020 project that started last year, which uses similar mobile data to investigate irregular migration.

Modularity maximisation for graphonsVirtuelle Veranstaltung (Boltzmannstr. 3, 85748 Garching)

Networks are a widely-used tool to investigate the large-scale connectivity structure in complex systems and graphons have been proposed as an infinite size limit of dense networks. The detection of communities or other meso-scale structures is a prominent topic in network science as it allows the identification of functional building blocks in complex systems. When such building blocks may be present in graphons is an open question. In this paper, we define a graphon-modularity and demonstrate that it can be maximised to detect communities in graphons. We then investigate specific synthetic graphons and show that they may show a wide range of different community structures. We also reformulate the graphon-modularity maximisation as a continuous optimisation problem and so prove the optimal community structure or lack thereof for some graphons, something that is usually not possible for networks. Furthermore, we demonstrate that estimating a graphon from network data as an intermediate step can improve the detection of communities, in comparison with exclusively maximising the modularity of the network. While the choice of graphon-estimator may strongly influence the accord between the community structure of a network and its estimated graphon, we find that there is a substantial overlap if an appropriate estimator is used. Our study demonstrates that community detection for graphons is possible and may serve as a privacy-preserving way to cluster network data.

Distance Estimates in the Random Connection Model(using zoom) (Parkring 11, 85748 Garching-Hochbrück)

We introduce the weight-dependent random connection model, which is a general class of geometric random graphs. The vertices are given by a marked Poisson process on Euclidean space, and the probability of an edge between two marked Poisson points is given through a connectivity function. We consider a specific choice of connectivity function and derive a random graph model that corresponds to a continuum version of the scale-free percolation model introduced by Deijfen, van der Hofstad, and Hooghiemstra (2013). We sketch how one can transfer results about the degree distribution and about the graph distances from the scale-free percolation model to the random connection model.

Numerical solution of the Vlasov equation: structure and efficiencyMI 02.08.011 (Boltzmannstr. 3, 85748 Garching)

A kinetic description of a plasma in external and self-consistent fields is given by the Vlasov equation for the particle distribution functions coupled to Maxwell's equation. The model is computational challenging due to its multiscale structure and the its relatively high dimensionality. This talk will give an overview of numerical solution methods and discuss structure-preserving particle methods as well as low-rank tensor discretizations in particular. A framework of structure-preserving particle in cell methods will be presented that allows for a long-time stable solution of the system. On the other hand, low-rank tensor methods are an efficient tool to compress multidimensional functions. We will demonstrate for benchmark problems that the essential features of the solution can be captured with a relatively low-rank.

Link and Passcode: https://tum-conf.zoom.us/j/96536097137 Code 101816

A Magnus-type integrator for semilinear parabolic non-autonomous SPDEsVirtuelle Veranstaltung (Boltzmannstr. 3, 85748 Garching)

Stochastic partial differential equations (SPDEs) are widely used to model many real world phenomena such as stock market prices and fluid flows. Since explicit solutions of many SPDEs are unknown, developing numerical schemes is a good alternative to provide their approximations, and is therefore a hot topic. Numerical methods for autonomous SPDEs are thoroughly investigated in the literature, while to the best of our knowledge the non-autonomous cases are not yet well understood. In this talk, we propose a Magnus-type integrator for time-dependent stochastic advection-reaction-diffusion equation, which is based on an approximation of the Magnus series. We use finite element method for the approximation in space and provide the strong convergence error of the fully discrete scheme toward the mild solution. Joint work with Antoine Tambue Western Norway University of Applied Sciences (HVL)

TBA(using zoom) (Parkring 11, 85748 Garching-Hochbrück)

TBA

Thermodynamics of structure-forming systems (J. Korbel, S. Lindner, R. Hanel, S. Thurner)Virtuelle Veranstaltung (Boltzmannstr. 3, 85748 Garching)

Structure-forming systems are ubiquitous in nature, ranging from atoms building molecules to self-assembly of colloidal amphibolic particles. The understanding of the underlying thermodynamics of such systems remains an important problem. In this talk, I derive the entropy for structure-forming systems that differs from Boltzmann-Gibbs entropy by a term that explicitly captures clustered states. For large systems and low concentrations, the approach is equivalent to the grand-canonical ensemble; for small systems, we find significant deviations. We derive the detailed fluctuation theorem and Crooks’ work fluctuation theorem for structure-forming systems. The connection to the theory of particle self-assembly is discussed. We apply the results to several physical systems. We present the phase diagram for patchy particles described by the Kern-Frenkel potential. We show that the Curie-Weiss model with molecule structures exhibits a first-order phase transition.

Orthogonal polynomials of Lévy white noise and umbral calculus(using zoom) (Parkring 11, 85748 Garching-Hochbrück)

Classical umbral calculus is the theory of Sheffer polynomial sequences, which are characterised by the exponential form of their generating function. Meixner in 1934 found all Sheffer sequences that are orthogonal with respect to a probability measure on the real line. The class of such probability measures consists of Gaussian, Poisson, gamma, negative binomial and Meixner distributions. Note that all these measures are infinitely divisible, hence they give rise to a corresponding Lévy process. Let $\mathcal D$ denote the space of all smooth functions on the real line with compact support, and let $\mathcal D'$ be its dual space, i.e., the space of all generalized functions on the real line. We will introduce the notion of a polynomial sequence on $\mathcal D'$ and a Sheffer sequence on $\mathcal D'$. A Lévy white noise measure is a probability measure on $\mathcal D?$ which is the law of a generalised stochastic process obtained as the (generalised) derivative of a Lévy process. We will find the class of all Lévy white noises for which there exists an orthogonal polynomial sequence on $\mathcal D'$. This class will be in one-to-one correspondence with the Meixner class of probability measures on the real line, and the corresponding orthogonal polynomial sequences on $\mathcal D'$ are all Sheffer sequences. Extending Grabiner's result related to the one-dimensional umbral calculus, we will construct a class of spaces of entire functions on the complexification of $\mathcal D'$ that is spanned by Sheffer polynomial sequences. This will, in particular, extend the well-known characterisation of the Hida test space of Gaussian white noise as a space of entire functions.