2020.06.15.
PACH Janos (Rényi Intézet): Low-dimensional combinatorics?
We discuss some notoriously hard combinatorial problems for large classes of graphs and hypergraphs arising in geometric, algebraic, and practical applications. These structures escape the “curse of dimensionality”: they can be embedded in a bounded-dimensional space, or they have small VC-dimension or a short algebraic description.
What are the advantages of low dimensionality? (a) With the help of suitable topological and algebraic separator theorems, large families of geometric objects embedded in a fixed-dimensional space can be split into subfamilies of roughly the same size, and then the smaller families can be analyzed recursively. (b) Geometric objects in space can be compared by a number of naturally defined partial orders, so that one can utilize the theory of partially ordered sets. (c) Graphs and hypergraphs of bounded VC-dimension admit very small epsilon-nets and can be particularly well approximated by random sampling. (d) If the description complexity of a family of geometric objects is small, then the “combinatorial complexity” (number of various dimensional faces) of their arrangements is also small. This typically guarantees the existence of efficient algorithms to visualize, describe, control, and manipulate these arrangements.
2020.06.08
DÉNES Ádám (KOKI): Inflammation, infection and brain injury – past lessons to understand how COVID-19 impacts on the brain
2020.05.18.
Bakács Tibor, M.D., Ph.D., D.Sc. (Valoszinusegszamitas es statisztika osztaly, Renyi Intezet): Virus against virus – eradicating viral diseases with a harmless virus using the superinfection therapy
The transmission characteristic of COVID-19 is of similar magnitude to 1918 pandemic influenza. There is no current evidence from random clinical trials to recommend any specific anti-COVID-19 treatment for patients with suspected or confirmed COVID-19 infection. In order to mitigate the impact of the COVID-19 the outbreak, we proposed an innovative superinfection therapeutic (SIT) strategy, which could complement the development of prophylactic vaccines. SIT is based on clinical observations that unrelated viruses might interact in co-infected patients. During SIT, the patient benefit from superinfection with an apathogenic dsRNA virus such as the infectious bursal disease virus (IBDV), which is a powerful activator of the interferon-dependent antiviral gene program. An attenuated vaccine strain of IBDV was already successfully administered to resolve acute and persistent infections induced by two completely different viruses, the hepatitis B (DNA) and C (RNA) viruses (HBV/HCV)
2020.05.04.
Márton Karsai (CEU) : Data-driven modelling of spreading processes
Models of contagion processes conventionally rely on unstructured populations and the homogenous mixing assumption, while the importance of networks have been shown recently to be crucial to determine their critical behaviour and final outcome. Earlier studies built on synthetic networks provided the advantage to be analytically treatable but were hardly applicable for real world scenarios. However, in the last ten years the access to high resolution human behavioural datasets from mobile devices, communication, and pervasive technologies has propelled a wealth of developments in the analysis of social networks and human mobility. Such datasets can be integrated into models of spreading processes leading to hybrid data-driven models where data is engaged with synthetic spreading dynamics for more realistic models of contagion phenomena.
In this talk we will take an overview on the different ways of data-driven modelling of spreading processes, like information spreading, social or biological contagion. We will discuss how and what kind of data can be useful, how they can be engaged with modelled dynamical processes, and what knowledge we can gain with these techniques. We will pay special attention on data-driven modelling of large-scale epidemics and we will discuss the latest efforts taken to understand the COVID-19 pandemic using data-driven models of epidemic processes.
2020.04.27.
Endre Csóka : Algorithms for sample pooling and application
Sample pooling or group testing means a test that tells about a small group of people (or group of samples) whether at least
one of them is infected. It is particularly efficient when the infection rate is low, because one negative test result implies that
none of the people in the group are infected. Beyond the pure mathematical motivations and approaches, we also focus on real-life
applications, especially in the current epidemic.
Below you can download Endres Csoka's paper related to the talk followed by the recording of the talk: https://arxiv.org/pdf/2005.02388
2020.04.20.
Péter Simon (ELTE TTK): Epidemic propagation on networks
Epidemic spread on networks can be described by continuous time Markov chains. The size of its state space blows up exponentially as the number of vertices is increased, hence several averaging methods leading to low-dimensional non-linear differential equations were derived. The approximation of the system by differential equations, containing some characteristics of the underlying graph, is one of the most important tools of investigation. In this talk we give an introduction to this field with emphasis on the mathematical methods introduced so far. Besides considering spreading processes onstatic networks we will deal with adaptive networks, when the epidemic dynamics on the network is coupled with a network which evolves in time. Moreover, we show how this approach leads to the control of the network process, a mathematical problem attracting significant research interest nowdays.
Reference:
Kiss., I.Z, Miller, J.C., Simon, P.L., Mathematics of Epidemics on Networks; From Exact to Approximate Models, Springer (2017)