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22 maart 2023 14:00 t/m 15:00
[DMO] Barbara Terhal & Maarten Stroeks: Fermionic OptimizationA basic problem in physics is to determine the lowest eigenvalue, or `ground state energy', of a many-body Hamiltonian. For fermionic Hamiltonians, modeling electrons in solids or chemistry, this problem is the minimization of a low-degree polynomial in non-commutative Majorana variables (forming a Clifford algebra). Since determining the lowest eigenvalue is a (QMA)-hard problem, it has been of interest to upper and lower bound the eigenvalue by optimizing over simple classes of states resp. relaxing the problem to a SDP.
We prove that for sparse fermionic Hamiltonians the upperbound over so-called Gaussian fermionic states, a well-known efficiently described class of quantum states, achieves a constant approximation ratio, meaning that the scaling with the number of variables is the same as for the true lowest eigenvalue. This is in contrast to recent work showing that for a class of random dense fermionic Hamiltonians, with high probability, there is no constant approximation ratio. We discuss some further results and open questions in this area.
References: 1. Herasymenko, Stroeks, Helsen, Terhal, https://arxiv.org/abs/2211.16518 ; 2. Hastings, O'Donnell, https://dl.acm.org/doi/10.1145/3519935.3519960
30 maart 2023 16:00 t/m 17:00
[PDE & Applications seminar] Marco Bravin: A connection between homogenisation of compressible Navier-Stokes and fluid-structure problems.In this talk I will present some recent improvements in the study of homogenisation of compressible viscous fluid in the case of tiny holes and the connection with fluid structure problems. In particular I highlight a situation where the fluid + rigid body problem has more flexibility respect to case of the fluid alone. This flexibility helps us to deduce new ideas to study the homogenisation of compressible fluid in dimension two.
06 april 2023 16:00 t/m 17:00
[PDE & Applications seminar] Johan Dubbeldam: Using mathematical modeling and game theory to optimize therapy in cancer patientsIn this talk I will present a game-theoretic model of a cancer cell population where the treatment-induced resistance is a quantitative evolving trait and the sensitive and resistant cancer cells compete with each other. We first investigate whether a constant treatment dose can stabilize the tumor burden at an acceptable level. When stabilization is possible, we expand the model into a Stackelberg evolutionary game (SEG), with the physician as the leader and the cancer cells as followers. Here the physician chooses a treatment dose to maximize the patient's quality of life, while the cancer cells evolve resistance to the treatment in order to better proliferate and survive. We find the Nash and Stackelberg equilibria of the SEG game, corresponding to the ecological (or ecologically enlightened) therapy and evolutionary (or evolutionarily enlightened) therapy, respectively, and compare them to the outcomes of applying the maximum tolerable dose (MTD). Finally, some recent work about applying control theory to these models will be discussed. This work was done in collaboration with Hasti Garjani, Frederik Thomsen and Katerina Stankova, Monica Salvioli
17 april 2023 15:45 t/m 17:45
[STAT/AP] Paulo Serra: Uncertainty quantification in sparse quantile regression
20 april 2023 16:00 t/m 17:00
[PDE & Applications seminar] Zivorad Tomovski: Fractional Poisson process and ApplicationsThe name fractional Poisson process is due to Laskin 2003 who
one point counting distribution. The renewal process of Mittag Leffler
type was discussed by Gorenflo, Mainardi and Scalas in two papers
published in 2004 one of them specifically devoted to the process and
on the Vietnam Journal of Mathematics. Hilfer and Anton 1995 were the first
to recognize the relation between the Mittag Leffler function and the time
fractional diffusion equation. The use of the Mittag Leffler function in
framework can be traced back to works of Gnedenko and Kovalenko 1968 on
thinning and Balakrishnan 1985 on anomalous diffusion. We will discuss
Poisson process by considering Hilfer-Prabhakar derivative in
difference-differential equations governing the dynamics of generalized
renewal stochastic processes.
08 mei 2023 15:45 t/m 17:45
[STAT/AP] Christian Maes: Nonequilibrium calorimetryThis is a joint project started some time ago already with Karel Netocny (Academy of Sciences, Prague). Recently we got more examples and more results, especially concerning the low temperature behavior of driven systems. Such systems create an Escherian world where heat is no longer able to order the states.
We prove a Third Law for a class of Markov jump processes and we make some progress in associating heat capacities to graphs and networks.,
Faezeh Khodabandehlou, Christian Maes, Irene Maes and Karel Netočný, The vanishing of excess heat for nonequilibrium processes reaching zero ambient temperature, arXiv:2210.09858v1 [cond-mat.stat-mech].
10 mei 2023 12:45 t/m 13:30