@phdthesis{7196,
abstract = {In this thesis we study certain mathematical aspects of evolution. The two primary forces that drive an evolutionary process are mutation and selection. Mutation generates new variants in a population. Selection chooses among the variants depending on the reproductive rates of individuals. Evolutionary processes are intrinsically random – a new mutation that is initially present in the population at low frequency can go extinct, even if it confers a reproductive advantage. The overall rate of evolution is largely determined by two quantities: the probability that an invading advantageous mutation spreads through the population (called fixation probability) and the time until it does so (called fixation time). Both those quantities crucially depend not only on the strength of the invading mutation but also on the population structure. In this thesis, we aim to understand how the underlying population structure affects the overall rate of evolution. Specifically, we study population structures that increase the fixation probability of advantageous mutants (called amplifiers of selection). Broadly speaking, our results are of three different types: We present various strong amplifiers, we identify regimes under which only limited amplification is feasible, and we propose population structures that provide different tradeoffs between high fixation probability and short fixation time.},
author = {Tkadlec, Josef},
issn = {2663-337X},
pages = {144},
publisher = {IST Austria},
title = {{A role of graphs in evolutionary processes}},
doi = {10.15479/AT:ISTA:7196},
year = {2020},
}
@phdthesis{7258,
abstract = {Many flows encountered in nature and applications are characterized by a chaotic motion known as turbulence. Turbulent flows generate intense friction with pipe walls and are responsible for considerable amounts of energy losses at world scale. The nature of turbulent friction and techniques aimed at reducing it have been subject of extensive research over the last century, but no definite answer has been found yet. In this thesis we show that in pipes at moderate turbulent Reynolds numbers friction is better described by the power law first introduced by Blasius and not by the Prandtl–von Kármán formula. At higher Reynolds numbers, large scale motions gradually become more important in the flow and can be related to the change in scaling of friction. Next, we present a series of new techniques that can relaminarize turbulence by suppressing a key mechanism that regenerates it at walls, the lift–up effect. In addition, we investigate the process of turbulence decay in several experiments and discuss the drag reduction potential. Finally, we examine the behavior of friction under pulsating conditions inspired by the human heart cycle and we show that under such circumstances turbulent friction can be reduced to produce energy savings.},
author = {Scarselli, Davide},
issn = {2663-337X},
pages = {174},
publisher = {IST Austria},
title = {{New approaches to reduce friction in turbulent pipe flow}},
doi = {10.15479/AT:ISTA:7258},
year = {2020},
}
@phdthesis{7460,
abstract = {Many methods for the reconstruction of shapes from sets of points produce ordered simplicial complexes, which are collections of vertices, edges, triangles, and their higher-dimensional analogues, called simplices, in which every simplex gets assigned a real value measuring its size. This thesis studies ordered simplicial complexes, with a focus on their topology, which reflects the connectedness of the represented shapes and the presence of holes. We are interested both in understanding better the structure of these complexes, as well as in developing algorithms for applications.
For the Delaunay triangulation, the most popular measure for a simplex is the radius of the smallest empty circumsphere. Based on it, we revisit Alpha and Wrap complexes and experimentally determine their probabilistic properties for random data. Also, we prove the existence of tri-partitions, propose algorithms to open and close holes, and extend the concepts from Euclidean to Bregman geometries.},
author = {Ölsböck, Katharina},
issn = {2663-337X},
keywords = {shape reconstruction, hole manipulation, ordered complexes, Alpha complex, Wrap complex, computational topology, Bregman geometry},
pages = {155},
publisher = {IST Austria},
title = {{The hole system of triangulated shapes}},
doi = {10.15479/AT:ISTA:7460},
year = {2020},
}
@phdthesis{7514,
abstract = {We study the interacting homogeneous Bose gas in two spatial dimensions in the thermodynamic limit at fixed density. We shall be concerned with some mathematical aspects of this complicated problem in many-body quantum mechanics. More specifically, we consider the dilute limit where the scattering length of the interaction potential, which is a measure for the effective range of the potential, is small compared to the average distance between the particles. We are interested in a setting with positive (i.e., non-zero) temperature. After giving a survey of the relevant literature in the field, we provide some facts and examples to set expectations for the two-dimensional system. The crucial difference to the three-dimensional system is that there is no Bose–Einstein condensate at positive temperature due to the Hohenberg–Mermin–Wagner theorem. However, it turns out that an asymptotic formula for the free energy holds similarly to the three-dimensional case.
We motivate this formula by considering a toy model with δ interaction potential. By restricting this model Hamiltonian to certain trial states with a quasi-condensate we obtain an upper bound for the free energy that still has the quasi-condensate fraction as a free parameter. When minimizing over the quasi-condensate fraction, we obtain the Berezinskii–Kosterlitz–Thouless critical temperature for superfluidity, which plays an important role in our rigorous contribution. The mathematically rigorous result that we prove concerns the specific free energy in the dilute limit. We give upper and lower bounds on the free energy in terms of the free energy of the non-interacting system and a correction term coming from the interaction. Both bounds match and thus we obtain the leading term of an asymptotic approximation in the dilute limit, provided the thermal wavelength of the particles is of the same order (or larger) than the average distance between the particles. The remarkable feature of this result is its generality: the correction term depends on the interaction potential only through its scattering length and it holds for all nonnegative interaction potentials with finite scattering length that are measurable. In particular, this allows to model an interaction of hard disks.},
author = {Mayer, Simon},
issn = {2663-337X},
pages = {148},
publisher = {IST Austria},
title = {{The free energy of a dilute two-dimensional Bose gas}},
doi = {10.15479/AT:ISTA:7514},
year = {2020},
}
@phdthesis{7525,
abstract = {The medial habenula (MHb) is an evolutionary conserved epithalamic structure important for the modulation of emotional memory. It is involved in regulation of anxiety, compulsive behavior, addiction (nicotinic and opioid), sexual and feeding behavior. MHb receives inputs from septal regions and projects exclusively to the interpeduncular nucleus (IPN). Distinct sub-regions of the septum project to different subnuclei of MHb: the bed nucleus of anterior commissure projects to dorsal MHb and the triangular septum projects to ventral MHb. Furthermore, the dorsal and ventral MHb project to the lateral and rostral/central IPN, respectively. Importantly, these projections have unique features of prominent co-release of different neurotransmitters and requirement of a peculiar type of calcium channel for release. In general, synaptic neurotransmission requires an activity-dependent influx of Ca2+ into the presynaptic terminal through voltage-gated calcium channels. The calcium channel family most commonly involved in neurotransmitter release comprises three members, P/Q-, N- and R-type with Cav2.1, Cav2.2 and Cav2.3 subunits, respectively. In contrast to most CNS synapses that mainly express Cav2.1 and/or Cav2.2, MHb terminals in the IPN exclusively express Cav2.3. In other parts of the brain, such as the hippocampus, Cav2.3 is mostly located to postsynaptic elements. This unusual presynaptic location of Cav2.3 in the MHb-IPN pathway implies unique mechanisms of glutamate release in this pathway. One potential example of such uniqueness is the facilitation of release by GABAB receptor (GBR) activation. Presynaptic GBRs usually inhibit the release of neurotransmitters by inhibiting presynaptic calcium channels. MHb shows the highest expression levels of GBR in the brain. GBRs comprise two subunits, GABAB1 (GB1) and GABAB2 (GB2), and are associated with auxiliary subunits, called potassium channel tetramerization domain containing proteins (KCTD) 8, 12, 12b and 16. Among these four subunits, KCTD12b is exclusively expressed in ventral MHb, and KCTD8 shows the strongest expression in the whole MHb among other brain regions, indicating that KCTD8 and KCTD12b may be involved in the unique mechanisms of neurotransmitter release mediated by Cav2.3 and regulated by GBRs in this pathway.
In the present study, we first verified that neurotransmission in both dorsal and ventral MHb-IPN pathways is mainly mediated by Cav2.3 using a selective blocker of R-type channels, SNX-482. We next found that baclofen, a GBR agonist, has facilitatory effects on release from ventral MHb terminal in rostral IPN, whereas it has inhibitory effects on release from dorsal MHb terminals in lateral IPN, indicating that KCTD12b expressed exclusively in ventral MHb may have a role in the facilitatory effects of GBR activation. In a heterologous expression system using HEK cells, we found that KCTD8 and KCTD12b but not KCTD12 directly bind with Cav2.3. Pre-embedding immunogold electron microscopy data show that Cav2.3 and KCTD12b are distributed most densely in presynaptic active zone in IPN with KCTD12b being present only in rostral/central but not lateral IPN, whereas GABAB, KCTD8 and KCTD12 are distributed most densely in perisynaptic sites with KCTD12 present more frequently in postsynaptic elements and only in rostral/central IPN. In freeze-fracture replica labelling, Cav2.3, KCTD8 and KCTD12b are co-localized with each other in the same active zone indicating that they may form complexes regulating vesicle release in rostral IPN.
On electrophysiological studies of wild type (WT) mice, we found that paired-pulse ratio in rostral IPN of KCTD12b knock-out (KO) mice is lower than those of WT and KCTD8 KO mice. Consistent with this finding, in mean variance analysis, release probability in rostral IPN of KCTD12b KO mice is higher than that of WT and KCTD8 KO mice. Although paired-pulse ratios are not different between WT and KCTD8 KO mice, the mean variance analysis revealed significantly lower release probability in rostral IPN of KCTD8 KO than WT mice. These results demonstrate bidirectional regulation of Cav2.3-mediated release by KCTD8 and KCTD12b without GBR activation in rostral IPN. Finally, we examined the baclofen effects in rostral IPN of KCTD8 and KCTD12b KO mice, and found the facilitation of release remained in both KO mice, indicating that the peculiar effects of the GBR activation in this pathway do not depend on the selective expression of these KCTD subunits in ventral MHb. However, we found that presynaptic potentiation of evoked EPSC amplitude by baclofen falls to baseline after washout faster in KCTD12b KO mice than WT, KCTD8 KO and KCTD8/12b double KO mice. This result indicates that KCTD12b is involved in sustained potentiation of vesicle release by GBR activation, whereas KCTD8 is involved in its termination in the absence of KCTD12b. Consistent with these functional findings, replica labelling revealed an increase in density of KCTD8, but not Cav2.3 or GBR at active zone in rostral IPN of KCTD12b KO mice compared with that of WT mice, suggesting that increased association of KCTD8 with Cav2.3 facilitates the release probability and termination of the GBR effect in the absence of KCTD12b.
In summary, our study provided new insights into the physiological roles of presynaptic Cav2.3, GBRs and their auxiliary subunits KCTDs at an evolutionary conserved neuronal circuit. Future studies will be required to identify the exact molecular mechanism underlying the GBR-mediated presynaptic potentiation on ventral MHb terminals. It remains to be determined whether the prominent presence of presynaptic KCTDs at active zone could exert similar neuromodulatory functions in different pathways of the brain.
},
author = {Bhandari, Pradeep},
issn = {2663-337X},
keywords = {Cav2.3, medial habenula (MHb), interpeduncular nucleus (IPN)},
pages = {79},
publisher = {IST Austria},
title = {{Localization and functional role of Cav2.3 in the medial habenula to interpeduncular nucleus pathway}},
doi = {10.15479/AT:ISTA:7525},
year = {2020},
}