@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},
}
@phdthesis{7629,
abstract = {This thesis is based on three main topics: In the first part, we study convergence of discrete gradient flow structures associated with regular finite-volume discretisations of Fokker-Planck equations. We show evolutionary I convergence of the discrete gradient flows to the L2-Wasserstein gradient flow corresponding to the solution of a Fokker-Planck
equation in arbitrary dimension d >= 1. Along the argument, we prove Mosco- and I-convergence results for discrete energy functionals, which are of independent interest for convergence of equivalent gradient flow structures in Hilbert spaces.
The second part investigates L2-Wasserstein flows on metric graph. The starting point is a Benamou-Brenier formula for the L2-Wasserstein distance, which is proved via a regularisation scheme for solutions of the continuity equation, adapted to the peculiar geometric structure of metric graphs. Based on those results, we show that the L2-Wasserstein space over a metric graph admits a gradient flow which may be identified as a solution of a Fokker-Planck equation.
In the third part, we focus again on the discrete gradient flows, already encountered in the first part. We propose a variational structure which extends the gradient flow structure to Markov chains violating the detailed-balance conditions. Using this structure, we characterise contraction estimates for the discrete heat flow in terms of convexity of
corresponding path-dependent energy functionals. In addition, we use this approach to derive several functional inequalities for said functionals.},
author = {Forkert, Dominik L},
issn = {2663-337X},
pages = {154},
publisher = {IST Austria},
title = {{Gradient flows in spaces of probability measures for finite-volume schemes, metric graphs and non-reversible Markov chains}},
doi = {10.15479/AT:ISTA:7629},
year = {2020},
}
@phdthesis{8156,
abstract = {We present solutions to several problems originating from geometry and discrete mathematics: existence of equipartitions, maps without Tverberg multiple points, and inscribing quadrilaterals. Equivariant obstruction theory is the natural topological approach to these type of questions. However, for the specific problems we consider it had yielded only partial or no results. We get our results by complementing equivariant obstruction theory with other techniques from topology and geometry.},
author = {Avvakumov, Sergey},
pages = {119},
publisher = {IST Austria},
title = {{Topological methods in geometry and discrete mathematics}},
doi = {10.15479/AT:ISTA:8156},
year = {2020},
}
@phdthesis{7680,
abstract = {Proteins and their complex dynamic interactions regulate cellular mechanisms from sensing and transducing extracellular signals, to mediating genetic responses, and sustaining or changing cell morphology. To manipulate these protein-protein interactions (PPIs) that govern the behavior and fate of cells, synthetically constructed, genetically encoded tools provide the means to precisely target proteins of interest (POIs), and control their subcellular localization and activity in vitro and in vivo. Ideal synthetic tools react to an orthogonal cue, i.e. a trigger that does not activate any other endogenous process, thereby allowing manipulation of the POI alone.
In optogenetics, naturally occurring photosensory domain from plants, algae and bacteria are re-purposed and genetically fused to POIs. Illumination with light of a specific wavelength triggers a conformational change that can mediate PPIs, such as dimerization or oligomerization. By using light as a trigger, these tools can be activated with high spatial and temporal precision, on subcellular and millisecond scales. Chemogenetic tools consist of protein domains that recognize and bind small molecules. By genetic fusion to POIs, these domains can mediate PPIs upon addition of their specific ligands, which are often synthetically designed to provide highly specific interactions and exhibit good bioavailability.
Most optogenetic tools to mediate PPIs are based on well-studied photoreceptors responding to red, blue or near-UV light, leaving a striking gap in the green band of the visible light spectrum. Among both optogenetic and chemogenetic tools, there is an abundance of methods to induce PPIs, but tools to disrupt them require UV illumination, rely on covalent linkage and subsequent enzymatic cleavage or initially result in protein clustering of unknown stoichiometry.
This work describes how the recently structurally and photochemically characterized green-light responsive cobalamin-binding domains (CBDs) from bacterial transcription factors were re-purposed to function as a green-light responsive optogenetic tool. In contrast to previously engineered optogenetic tools, CBDs do not induce PPI, but rather confer a PPI already upon expression, which can be rapidly disrupted by illumination. This was employed to mimic inhibition of constitutive activity of a growth factor receptor, and successfully implement for cell signalling in mammalian cells and in vivo to rescue development in zebrafish. This work further describes the development and application of a chemically induced de-dimerizer (CDD) based on a recently identified and structurally described bacterial oxyreductase. CDD forms a dimer upon expression in absence of its cofactor, the flavin derivative F420. Safety and of domain expression and ligand exposure are demonstrated in vitro and in vivo in zebrafish. The system is further applied to inhibit cell signalling output from a chimeric receptor upon F420 treatment.
CBDs and CDD expand the repertoire of synthetic tools by providing novel mechanisms of mediating PPIs, and by recognizing previously not utilized cues. In the future, they can readily be combined with existing synthetic tools to functionally manipulate PPIs in vitro and in vivo.},
author = {Kainrath, Stephanie},
issn = {2663-337X},
pages = {98},
publisher = {IST Austria},
title = {{Synthetic tools for optogenetic and chemogenetic inhibition of cellular signals}},
doi = {10.15479/AT:ISTA:7680},
year = {2020},
}
@phdthesis{7944,
abstract = {This thesis considers two examples of reconfiguration problems: flipping edges in edge-labelled triangulations of planar point sets and swapping labelled tokens placed on vertices of a graph. In both cases the studied structures – all the triangulations of a given point set or all token placements on a given graph – can be thought of as vertices of the so-called reconfiguration graph, in which two vertices are adjacent if the corresponding structures differ by a single elementary operation – by a flip of a diagonal in a triangulation or by a swap of tokens on adjacent vertices, respectively. We study the reconfiguration of one instance of a structure into another via (shortest) paths in the reconfiguration graph.
For triangulations of point sets in which each edge has a unique label and a flip transfers the label from the removed edge to the new edge, we prove a polynomial-time testable condition, called the Orbit Theorem, that characterizes when two triangulations of the same point set lie in the same connected component of the reconfiguration graph. The condition was first conjectured by Bose, Lubiw, Pathak and Verdonschot. We additionally provide a polynomial time algorithm that computes a reconfiguring flip sequence, if it exists. Our proof of the Orbit Theorem uses topological properties of a certain high-dimensional cell complex that has the usual reconfiguration graph as its 1-skeleton.
In the context of token swapping on a tree graph, we make partial progress on the problem of finding shortest reconfiguration sequences. We disprove the so-called Happy Leaf Conjecture and demonstrate the importance of swapping tokens that are already placed at the correct vertices. We also prove that a generalization of the problem to weighted coloured token swapping is NP-hard on trees but solvable in polynomial time on paths and stars.},
author = {Masárová, Zuzana},
isbn = {978-3-99078-005-3},
issn = {2663-337X},
keywords = {reconfiguration, reconfiguration graph, triangulations, flip, constrained triangulations, shellability, piecewise-linear balls, token swapping, trees, coloured weighted token swapping},
pages = {160},
publisher = {IST Austria},
title = {{Reconfiguration problems}},
doi = {10.15479/AT:ISTA:7944},
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{8032,
abstract = {Algorithms in computational 3-manifold topology typically take a triangulation as an input and return topological information about the underlying 3-manifold. However, extracting the desired information from a triangulation (e.g., evaluating an invariant) is often computationally very expensive. In recent years this complexity barrier has been successfully tackled in some cases by importing ideas from the theory of parameterized algorithms into the realm of 3-manifolds. Various computationally hard problems were shown to be efficiently solvable for input triangulations that are sufficiently “tree-like.”
In this thesis we focus on the key combinatorial parameter in the above context: we consider the treewidth of a compact, orientable 3-manifold, i.e., the smallest treewidth of the dual graph of any triangulation thereof. By building on the work of Scharlemann–Thompson and Scharlemann–Schultens–Saito on generalized Heegaard splittings, and on the work of Jaco–Rubinstein on layered triangulations, we establish quantitative relations between the treewidth and classical topological invariants of a 3-manifold. In particular, among other results, we show that the treewidth of a closed, orientable, irreducible, non-Haken 3-manifold is always within a constant factor of its Heegaard genus.},
author = {Huszár, Kristóf},
isbn = {978-3-99078-006-0},
issn = {2663-337X},
pages = {xviii+120},
publisher = {IST Austria},
title = {{Combinatorial width parameters for 3-dimensional manifolds}},
doi = {10.15479/AT:ISTA:8032},
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{7896,
abstract = {A search problem lies in the complexity class FNP if a solution to the given instance of the problem can be verified efficiently. The complexity class TFNP consists of all search problems in FNP that are total in the sense that a solution is guaranteed to exist. TFNP contains a host of interesting problems from fields such as algorithmic game theory, computational topology, number theory and combinatorics. Since TFNP is a semantic class, it is unlikely to have a complete problem. Instead, one studies its syntactic subclasses which are defined based on the combinatorial principle used to argue totality. Of particular interest is the subclass PPAD, which contains important problems
like computing Nash equilibrium for bimatrix games and computational counterparts of several fixed-point theorems as complete. In the thesis, we undertake the study of averagecase hardness of TFNP, and in particular its subclass PPAD.
Almost nothing was known about average-case hardness of PPAD before a series of recent results showed how to achieve it using a cryptographic primitive called program obfuscation.
However, it is currently not known how to construct program obfuscation from standard cryptographic assumptions. Therefore, it is desirable to relax the assumption under which average-case hardness of PPAD can be shown. In the thesis we take a step in this direction. First, we show that assuming the (average-case) hardness of a numbertheoretic
problem related to factoring of integers, which we call Iterated-Squaring, PPAD is hard-on-average in the random-oracle model. Then we strengthen this result to show that the average-case hardness of PPAD reduces to the (adaptive) soundness of the Fiat-Shamir Transform, a well-known technique used to compile a public-coin interactive protocol into a non-interactive one. As a corollary, we obtain average-case hardness for PPAD in the random-oracle model assuming the worst-case hardness of #SAT. Moreover, the above results can all be strengthened to obtain average-case hardness for the class CLS ⊆ PPAD.
Our main technical contribution is constructing incrementally-verifiable procedures for computing Iterated-Squaring and #SAT. By incrementally-verifiable, we mean that every intermediate state of the computation includes a proof of its correctness, and the proof can be updated and verified in polynomial time. Previous constructions of such procedures relied on strong, non-standard assumptions. Instead, we introduce a technique called recursive proof-merging to obtain the same from weaker assumptions. },
author = {Kamath Hosdurg, Chethan},
issn = {2663-337X},
pages = {126},
publisher = {IST Austria},
title = {{On the average-case hardness of total search problems}},
doi = {10.15479/AT:ISTA:7896},
year = {2020},
}
@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},
}