@article{18173, abstract = {Using a two-dimensional version of the delta method, we establish an asymptotic formula for the number of rational points of bounded height on non-singular complete intersections of cubic and quadric hypersurfaces of dimension at least 23 over Fq(t), provided char (Fq)>3. Under the same hypotheses, we also verify weak approximation.}, author = {Glas, Jakob}, issn = {1469-7750}, journal = {Journal of the London Mathematical Society}, number = {4}, publisher = {London Mathematical Society}, title = {{Rational points on complete intersections of cubic and quadric hypersurfaces over Fq(t)}}, doi = {10.1112/jlms.12991}, volume = {110}, year = {2024}, } @unpublished{18295, abstract = {By developing a suitable version of the circle method, we show that the space of degree e rational curves on a smooth hypersurface of degree d has only canonical singularities provided its dimension is sufficiently large with respect to e and d.}, author = {Glas, Jakob}, booktitle = {arXiv}, title = {{Canonical singularities on moduli spaces of rational curves via the circle method}}, doi = {10.48550/arXiv.2405.16648}, year = {2024}, } @phdthesis{18667, abstract = {Many chemical and physical properties of materials are determined by the material’s shape, for example the size of its pores and the width of its tunnels. This makes materials science a prime application area for geometrical and topological methods. Nevertheless many methods in topological data analysis have not been satisfyingly extended to the needs of materials science. This thesis provides new methods and new mathematical theorems targeted at those specific needs by answering four different research questions. While the motivation for each of the research questions arises from materials science, the methods are versatile and can be applied in different areas as well. The first research question is concerned with image data, for example a three-dimensional computed tomography (CT) scan of a material, like sand or stone. There are two commonly used topologies for digital images and depending on the application either of them might be required. However, software for computing the topological data analysis method persistence homology, usually supports only one of the two topologies. We answer the question how to compute persistent homology of an image with respect to one of the two topologies using software that is intended for the other topology. The second research question is concerned with image data as well, and asks how much of the topological information of an image is lost when the resolution is coarsened. As computer tomography scanners are more expensive the higher the resolution, it is an important question in materials science to know which resolution is enough to get satisfying persistent homology. We give theoretical bounds on the information loss based on different geometrical properties of the object to be scanned. In addition, we conduct experiments on sand and stone CT image data. The third research question is motivated by comparing crystalline materials efficiently. As the atoms within a crystal repeat periodically, crystalline materials are either modeled by unmanageable infinite periodic point sets, or by one of their fundamental domains, which is unstable under perturbation. Therefore a fingerprint of crystalline materials is needed, with appropriate properties such that comparing the crystals can be eased by comparing the fingerprints instead. We define the density fingerprint and prove the necessary properties. The fourth research question is motivated by studying the hole-structure or connectedness, i.e. persistent homology or merge trees, of crystalline materials. A common way to deal with periodicity is to take a fundamental domain and identify opposite boundaries to form a torus. However, computing persistent homology or merge trees on that torus loses some of the information materials scientists are interested in and is additionally not stable under certain noise. We therefore decorate the merge tree stemming from the torus with additional information describing the density and growth rate of the periodic copies of a component within a growing spherical window. We prove all desired properties, like stability and efficient computability.}, author = {Heiss, Teresa}, isbn = {978-3-99078-052-7}, issn = {2663-337X}, keywords = {persistent homology, topological data analysis, periodic, crystalline materials, images, fingerprint}, pages = {111}, publisher = {Institute of Science and Technology Austria}, title = {{New methods for applying topological data analysis to materials science}}, doi = {10.15479/at:ista:18667}, year = {2024}, } @unpublished{18673, abstract = {Motivated by applications to crystalline materials, we generalize the merge tree and the related barcode of a filtered complex to the periodic setting in Euclidean space. They are invariant under isometries, changing bases, and indeed changing lattices. In addition, we prove stability under perturbations and provide an algorithm that under mild geometric conditions typically satisfied by crystalline materials takes O((n+m)logn) time, in which n and m are the numbers of vertices and edges in the quotient complex, respectively. }, author = {Edelsbrunner, Herbert and Heiss, Teresa}, booktitle = {arXiv}, title = {{Merge trees of periodic filtrations}}, doi = {10.48550/arXiv.2408.16575}, year = {2024}, } @phdthesis{14711, abstract = {In nature, different species find their niche in a range of environments, each with its unique characteristics. While some thrive in uniform (homogeneous) landscapes where environmental conditions stay relatively consistent across space, others traverse the complexities of spatially heterogeneous terrains. Comprehending how species are distributed and how they interact within these landscapes holds the key to gaining insights into their evolutionary dynamics while also informing conservation and management strategies. For species inhabiting heterogeneous landscapes, when the rate of dispersal is low compared to spatial fluctuations in selection pressure, localized adaptations may emerge. Such adaptation in response to varying selection strengths plays an important role in the persistence of populations in our rapidly changing world. Hence, species in nature are continuously in a struggle to adapt to local environmental conditions, to ensure their continued survival. Natural populations can often adapt in time scales short enough for evolutionary changes to influence ecological dynamics and vice versa, thereby creating a feedback between evolution and demography. The analysis of this feedback and the relative contributions of gene flow, demography, drift, and natural selection to genetic variation and differentiation has remained a recurring theme in evolutionary biology. Nevertheless, the effective role of these forces in maintaining variation and shaping patterns of diversity is not fully understood. Even in homogeneous environments devoid of local adaptations, such understanding remains elusive. Understanding this feedback is crucial, for example in determining the conditions under which extinction risk can be mitigated in peripheral populations subject to deleterious mutation accumulation at the edges of species’ ranges as well as in highly fragmented populations. In this thesis we explore both uniform and spatially heterogeneous metapopulations, investigating and providing theoretical insights into the dynamics of local adaptation in the latter and examining the dynamics of load and extinction as well as the impact of joint ecological and evolutionary (eco-evolutionary) dynamics in the former. The thesis is divided into 5 chapters. Chapter 1 provides a general introduction into the subject matter, clarifying concepts and ideas used throughout the thesis. In chapter 2, we explore how fast a species distributed across a heterogeneous landscape adapts to changing conditions marked by alterations in carrying capacity, selection pressure, and migration rate. In chapter 3, we investigate how migration selection and drift influences adaptation and the maintenance of variation in a metapopulation with three habitats, an extension of previous models of adaptation in two habitats. We further develop analytical approximations for the critical threshold required for polymorphism to persist. The focus of chapter 4 of the thesis is on understanding the interplay between ecology and evolution as coupled processes. We investigate how eco-evolutionary feedback between migration, selection, drift, and demography influences eco-evolutionary outcomes in marginal populations subject to deleterious mutation accumulation. Using simulations as well as theoretical approximations of the coupled dynamics of population size and allele frequency, we analyze how gene flow from a large mainland source influences genetic load and population size on an island (i.e., in a marginal population) under genetically realistic assumptions. Analyses of this sort are important because small isolated populations, are repeatedly affected by complex interactions between ecological and evolutionary processes, which can lead to their death. Understanding these interactions can therefore provide an insight into the conditions under which extinction risk can be mitigated in peripheral populations thus, contributing to conservation and restoration efforts. Chapter 5 extends the analysis in chapter 4 to consider the dynamics of load (due to deleterious mutation accumulation) and extinction risk in a metapopulation. We explore the role of gene flow, selection, and dominance on load and extinction risk and further pinpoint critical thresholds required for metapopulation persistence. Overall this research contributes to our understanding of ecological and evolutionary mechanisms that shape species’ persistence in fragmented landscapes, a crucial foundation for successful conservation efforts and biodiversity management.}, author = {Olusanya, Oluwafunmilola O}, issn = {2663-337X}, pages = {183}, publisher = {Institute of Science and Technology Austria}, title = {{Local adaptation, genetic load and extinction in metapopulations}}, doi = {10.15479/at:ista:14711}, year = {2024}, } @phdthesis{17156, abstract = {This dissertation is the summary of the author’s work, concerning the relations between cohomology rings of algebraic varieties and rings of functions on zero schemes and fixed point schemes. For most of the thesis, the focus is on smooth complex varieties with an action of a principally paired group, e.g. a parabolic subgroup of a reductive group. The fundamental theorem 5.2.11 from co-authored article [66] says that if the principal nilpotent has a unique zero, then the zero scheme over the Kostant section is isomorphic to the spectrum of the equivariant cohomology ring, remembering the grading in terms of a C^* action. A similar statement is proved also for the G-invariant functions on the total zero scheme over the whole Lie algebra. Additionally, we are able to prove an analogous result for the GKM spaces, which poses the question on a joint generalisation. We also tackle the situation of a singular variety. As long as it is embedded in a smooth variety with regular action, we are able to study its cohomology as well by means of the zero scheme. In case of e.g. Schubert varieties this determines the cohomology ring completely. In largest generality, this allows us to see a significant part of the cohomology ring. We also show (Theorem 6.2.1) that the cohomology ring of spherical varieties appears as the ring of functions on the zero scheme. The computational aspect is not easy, but one can hope that this can bring some concrete information about such cohomology rings. Lastly, the K-theory conjecture 6.3.1 is studied, with some results attained for GKM spaces. The thesis includes also an introduction to group actions on algebraic varieties. In particular, the vector fields associated to the actions are extensively studied. We also provide a version of the Kostant section for arbitrary principally paired group, which parametrises the regular orbits in the Lie algebra of an algebraic group. Before proving the main theorem, we also include a historical overview of the field. In particular we bring together the results of Akyildiz, Carrell and Lieberman on non-equivariant cohomology rings.}, author = {Rychlewicz, Kamil P}, issn = {2663-337X}, keywords = {equivariant cohomology, zero schemes, algebraic groups, Lie algebras}, pages = {117}, publisher = {Institute of Science and Technology Austria}, title = {{Equivariant cohomology and rings of functions}}, doi = {10.15479/at:ista:17156}, year = {2024}, } @phdthesis{18515, abstract = {Understanding the role of evolutionary processes in shaping genetic variation has been a primary goal in evolutionary genetics. In this regard, a key question is how genetically distinct populations evolve in the face of gene flow, thereby generating genetic and phenotypic divergence and reproductive isolation (RI). This requires quantifying the role and relative contributions of prezygotic and postzygotic isolating mechanisms on the reduction of gene exchange between populations, and identifying regions in the genome that mediate RI, which is often polygenic. Further, this needs distinguishing neutral and selected regions in the genome, and discerning how selection influences patterns of neutral divergence. Population structure, defined as any deviation from panmixia, such as geographic distribution, movement and mating patterns of individuals, influences how genetic variation is structured in space and shapes the neutral null model. Availability of large scale spatial genomic datasets now enables us to detect signatures of population structure in genetic data and infer population genetic parameters. Such inferences are crucial and have wide applications in biodiversity, conservation genetics, population management and medical genetics. However, inferences are based on assumptions that do not always match the complex reality, thus leading to erroneous conclusions. Moreover, the role and interaction of heterogeneous population density and dispersal, which are ubiquitous in nature, has been challenging to study owing to their mathematical complexity. In such scenarios, feedback between theory, data and simulations can prove to be useful. In this thesis, I examine the effect of population structure on neutral genetic variation and barriers to gene exchange in hybridising populations, thereby bridging together the fields of spatial population genetics and speciation. Despite being a key concept in speciation, reproductive isolation (RI) lacks a quantitative definition and has been used and measured differently across different fields. Chapter 2 gives a quantitative definition of RI, in terms of the effect of genetic differences on gene flow. We give analytical predictions for RI in a range of scenarios, in terms of effective migration rates for discrete populations and barrier strength for continuous populations. In addition to this, we discuss current measures of RI and their limitations, and propose the need for new measures that combine organismal and genetic perspectives of RI. In chapter 3, I examine the combined effect of assortative mating, sexual selection and viability selection on RI. For this, we consider a polygenic ‘magic’ trait under a mainland-island model. We obtain novel theoretical predictions for molecular divergence in terms of effective migration rates, which bears a simple relationship to measurable fitness components of migrants and various early generation hybrids. We explore the conditions under which local adaptation can be maintained despite maladaptive gene flow and quantify the relative contributions of viability and sexual selection to genome-wide barriers to gene flow. The next two chapters of the thesis focus on a hybrid zone of Antirrhinum majus that consist of two subspecies- the magenta flowered A. m. pseudomajus and the yellow flowered A.m. striatum. Previous studies have suggested that flower colour is target of pollinator mediated selection and is influenced only by few genes. While these regions show high genetic differentiation between the subspecies, the rest of the genome is seen to be well mixed. Chapter 4 examines the effects of heterogeneous population density and leptokurtic dispersal on isolation by distance and the distribution of heterozygosity by focusing on non-flower colour markers. Chapter 5 analyses cline shapes and associations among 6 focal flower colour markers to understand how selection and dispersal maintain this hybrid zone. We see sharp coincident stepped clines at all loci and positive associations throughout the hybrid zone, contrary to the expected patterns from diffusive gene flow. With a novel scheme of inferring dispersal combined with multilocus simulations, we show that stepped clines do not reflect genetic barriers to gene flow, but are rather a result of long-distance migration. This framework allows us to get realistic estimates gene flow and selection and shows how traditional cline analysis may lead to inaccurate conclusions when assumptions of the theory are not met. Overall, this thesis investigates how different features of population structure leave detectable signatures in genetic variation, namely in patterns of isolation by distance, linkage disequilibrium and genetic divergence. It also highlights how effective migration rates provide useful way of analysing polygenic architectures and shed new light into hybrid zones. In doing so, I identify scenarios when simple models become insufficient and suggest possibe directions by combining genetic data with simulations.}, author = {Surendranadh, Parvathy}, issn = {2663-337X}, pages = {219}, publisher = {Institute of Science and Technology Austria}, title = {{Effect of population structure on neutral genetic variation and barriers to gene exchange}}, doi = {10.15479/at:ista:18515}, year = {2024}, } @unpublished{18689, abstract = {Multiplexed fluorescence microscopy imaging is widely used in biomedical applications. However, simultaneous imaging of multiple fluorophores can result in spectral leaks and overlapping, which greatly degrades image quality and subsequent analysis. Existing popular spectral unmixing methods are mainly based on computational intensive linear models and the performance is heavily dependent on the reference spectra, which may greatly preclude its further applications. In this paper, we propose a deep learning-based blindly spectral unmixing method, termed AutoUnmix, to imitate the physical spectral mixing process. A tranfer learning framework is further devised to allow our AutoUnmix adapting to a variety of imaging systems without retraining the network. Our proposed method has demonstrated real-time unmixing capabilities, surpassing existing methods by up to 100-fold in terms of unmixing speed. We further validate the reconstruction performance on both synthetic datasets and biological samples. The unmixing results of AutoUnmix achieve a highest SSIM of 0.99 in both three- and four-color imaging, with nearly up to 20% higher than other popular unmixing methods. Due to the desirable property of data independency and superior blind unmixing performance, we believe AutoUnmix is a powerful tool to study the interaction process of different organelles labeled by multiple fluorophores.}, author = {Gallei, Michelle C and Truckenbrodt, Sven M and Kreuzinger, Caroline and Inumella, Syamala and Vistunou, Vitali and Sommer, Christoph M and Tavakoli, Mojtaba and Agudelo Duenas, Nathalie and Vorlaufer, Jakob and Jahr, Wiebke and Randuch, Marek and Johnson, Alexander J and Benková, Eva and Friml, Jiří and Danzl, Johann G}, booktitle = {bioRxiv}, title = {{Super-resolution expansion microscopy in plant roots}}, doi = {10.1101/2024.02.21.581330}, year = {2024}, } @phdthesis{18681, author = {Tavakoli, Mojtaba}, isbn = {978-3-99078-048-0}, issn = {2663-337X}, pages = {230}, publisher = {Institute of Science and Technology Austria}, title = {{Developing molecular and structural tools for studying brain architecture with super resolution expansion microscopy. LICONN: Molecularly-informed connectomics reconstruction with light microscopy}}, doi = {10.15479/at:ista:18681}, year = {2024}, } @phdthesis{15094, abstract = {Point sets, geometric networks, and arrangements of hyperplanes are fundamental objects in discrete geometry that have captivated mathematicians for centuries, if not millennia. This thesis seeks to cast new light on these structures by illustrating specific instances where a topological perspective, specifically through discrete Morse theory and persistent homology, provides valuable insights. At first glance, the topology of these geometric objects might seem uneventful: point sets essentially lack of topology, arrangements of hyperplanes are a decomposition of Rd, which is a contractible space, and the topology of a network primarily involves the enumeration of connected components and cycles within the network. However, beneath this apparent simplicity, there lies an array of intriguing structures, a small subset of which will be uncovered in this thesis. Focused on three case studies, each addressing one of the mentioned objects, this work will showcase connections that intertwine topology with diverse fields such as combinatorial geometry, algorithms and data structures, and emerging applications like spatial biology. }, author = {Cultrera di Montesano, Sebastiano}, issn = {2663-337X}, pages = {108}, publisher = {Institute of Science and Technology Austria}, title = {{Persistence and Morse theory for discrete geometric structures}}, doi = {10.15479/at:ista:15094}, year = {2024}, } @article{13182, abstract = {We characterize critical points of 1-dimensional maps paired in persistent homology geometrically and this way get elementary proofs of theorems about the symmetry of persistence diagrams and the variation of such maps. In particular, we identify branching points and endpoints of networks as the sole source of asymmetry and relate the cycle basis in persistent homology with a version of the stable marriage problem. Our analysis provides the foundations of fast algorithms for maintaining a collection of sorted lists together with its persistence diagram.}, author = {Biswas, Ranita and Cultrera Di Montesano, Sebastiano and Edelsbrunner, Herbert and Saghafian, Morteza}, issn = {2367-1734}, journal = {Journal of Applied and Computational Topology}, pages = {1101--1119}, publisher = {Springer Nature}, title = {{Geometric characterization of the persistence of 1D maps}}, doi = {10.1007/s41468-023-00126-9}, volume = {8}, year = {2024}, } @inproceedings{15093, abstract = {We present a dynamic data structure for maintaining the persistent homology of a time series of real numbers. The data structure supports local operations, including the insertion and deletion of an item and the cutting and concatenating of lists, each in time O(log n + k), in which n counts the critical items and k the changes in the augmented persistence diagram. To achieve this, we design a tailor-made tree structure with an unconventional representation, referred to as banana tree, which may be useful in its own right.}, author = {Cultrera di Montesano, Sebastiano and Edelsbrunner, Herbert and Henzinger, Monika H and Ost, Lara}, booktitle = {Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)}, editor = {Woodruff, David P.}, location = {Alexandria, VA, USA}, pages = {243 -- 295}, publisher = {Society for Industrial and Applied Mathematics}, title = {{Dynamically maintaining the persistent homology of time series}}, doi = {10.1137/1.9781611977912.11}, year = {2024}, } @unpublished{15091, abstract = {Motivated by applications in the medical sciences, we study finite chromatic sets in Euclidean space from a topological perspective. Based on the persistent homology for images, kernels and cokernels, we design provably stable homological quantifiers that describe the geometric micro- and macro-structure of how the color classes mingle. These can be efficiently computed using chromatic variants of Delaunay and alpha complexes, and code that does these computations is provided.}, author = {Cultrera di Montesano, Sebastiano and Draganov, Ondrej and Edelsbrunner, Herbert and Saghafian, Morteza}, booktitle = {arXiv}, title = {{Chromatic alpha complexes}}, doi = {10.48550/arXiv.2212.03128}, year = {2024}, } @phdthesis{18766, abstract = {Poxviruses are large pleomorphic double-stranded DNA viruses that include well known members such as variola virus, the causative agent of smallpox, Mpox virus, as well as Vaccinia virus (VACV), which serves as a vaccination strain for formerly mentioned viruses. VACV is a valuable model for studying large pleomorphic DNA viruses in general and poxviruses specifically, as many features, such as core morphology and structural proteins, are well conserved within this family. Despite decades of research, our understanding of the structural components and proteins that comprise the poxvirus core in mature virions remains limited. Although major core proteins were identified via indirect experimental evidence, the core's complexity, with its large size, structure and number of involved proteins, has hindered efforts to achieve high-resolution insights and to define the roles of the individual proteins. The specific protein composition of the core's individual layers, including the palisade layer and the inner core wall, has remained unclear. In this study, we have merged multiple approaches, including single particle cryo electron microscopy of purified virus cores, cryo-electron tomography and subtomogram averaging of mature virions and molecular modeling to elucidate the structural determinants of the VACV core. Due to the lack of experimentally derived structures, either in situ or reconstituted in vitro, we used Alphafold to predict models of the putative major core protein candidates, A10, 23k, A3, A4, and L4. Our results show that the VACV core is composed of several layers with varying local symmetries, forming more intricate interactions than observed previously. This allowed us to identify several molecular building blocks forming the viral core lattice. In particular, we identified trimers of protein A10 as a major core structure that forms the palisade layer of the viral core. Additionally, we revealed that six petals of a flower shaped core pore within the core wall are composed of A10 trimers. Furthermore, we obtained a cryo-EM density for the inner core wall that could potentially accommodate an A3 dimer. Integrating descriptions of protein interactions from previous studies enabled us to provide a detailed structural model of the poxvirus core wall, and our findings indicate that the interactions within A10 trimers are likely consistent across orthopox- and parapoxviruses. This combined application of cryo-SPA and cryo-ET can help overcome obstacles in studying complex virus structures in the future, including their key assembly proteins, interactions, and the formation into a core lattice. Our work provides important fundamental new insights into poxvirus core architecture, also considering the recent re-emergence of poxviruses.}, author = {Datler, Julia}, isbn = {978-3-99078-049-7}, issn = {2663-337X}, keywords = {cryo-EM, cryo-ET, cryo-SPA, Structural Virology, Poxvirus, Vaccinia Virus, Structural Biology}, pages = {106}, publisher = {Institute of Science and Technology Austria}, title = {{Elucidating the structural determinants of the poxvirus core using multi-modal cryo-EM}}, doi = {10.15479/at:ista:18766}, year = {2024}, } @article{14979, abstract = {Poxviruses are among the largest double-stranded DNA viruses, with members such as variola virus, monkeypox virus and the vaccination strain vaccinia virus (VACV). Knowledge about the structural proteins that form the viral core has remained sparse. While major core proteins have been annotated via indirect experimental evidence, their structures have remained elusive and they could not be assigned to individual core features. Hence, which proteins constitute which layers of the core, such as the palisade layer and the inner core wall, has remained enigmatic. Here we show, using a multi-modal cryo-electron microscopy (cryo-EM) approach in combination with AlphaFold molecular modeling, that trimers formed by the cleavage product of VACV protein A10 are the key component of the palisade layer. This allows us to place previously obtained descriptions of protein interactions within the core wall into perspective and to provide a detailed model of poxvirus core architecture. Importantly, we show that interactions within A10 trimers are likely generalizable over members of orthopox- and parapoxviruses.}, author = {Datler, Julia and Hansen, Jesse and Thader, Andreas and Schlögl, Alois and Bauer, Lukas W and Hodirnau, Victor-Valentin and Schur, Florian KM}, issn = {1545-9985}, journal = {Nature Structural & Molecular Biology}, keywords = {Molecular Biology, Structural Biology}, pages = {1114--1123}, publisher = {Springer Nature}, title = {{Multi-modal cryo-EM reveals trimers of protein A10 to form the palisade layer in poxvirus cores}}, doi = {10.1038/s41594-023-01201-6}, volume = {31}, year = {2024}, } @phdthesis{15020, abstract = {This thesis consists of four distinct pieces of work within theoretical biology, with two themes in common: the concept of optimization in biological systems, and the use of information-theoretic tools to quantify biological stochasticity and statistical uncertainty. Chapter 2 develops a statistical framework for studying biological systems which we believe to be optimized for a particular utility function, such as retinal neurons conveying information about visual stimuli. We formalize such beliefs as maximum-entropy Bayesian priors, constrained by the expected utility. We explore how such priors aid inference of system parameters with limited data and enable optimality hypothesis testing: is the utility higher than by chance? Chapter 3 examines the ultimate biological optimization process: evolution by natural selection. As some individuals survive and reproduce more successfully than others, populations evolve towards fitter genotypes and phenotypes. We formalize this as accumulation of genetic information, and use population genetics theory to study how much such information can be accumulated per generation and maintained in the face of random mutation and genetic drift. We identify the population size and fitness variance as the key quantities that control information accumulation and maintenance. Chapter 4 reuses the concept of genetic information from Chapter 3, but from a different perspective: we ask how much genetic information organisms actually need, in particular in the context of gene regulation. For example, how much information is needed to bind transcription factors at correct locations within the genome? Population genetics provides us with a refined answer: with an increasing population size, populations achieve higher fitness by maintaining more genetic information. Moreover, regulatory parameters experience selection pressure to optimize the fitness-information trade-off, i.e. minimize the information needed for a given fitness. This provides an evolutionary derivation of the optimization priors introduced in Chapter 2. Chapter 5 proves an upper bound on mutual information between a signal and a communication channel output (such as neural activity). Mutual information is an important utility measure for biological systems, but its practical use can be difficult due to the large dimensionality of many biological channels. Sometimes, a lower bound on mutual information is computed by replacing the high-dimensional channel outputs with decodes (signal estimates). Our result provides a corresponding upper bound, provided that the decodes are the maximum posterior estimates of the signal.}, author = {Hledik, Michal}, issn = {2663-337X}, keywords = {Theoretical biology, Optimality, Evolution, Information}, pages = {158}, publisher = {Institute of Science and Technology Austria}, title = {{Genetic information and biological optimization}}, doi = {10.15479/at:ista:15020}, year = {2024}, } @phdthesis{18568, abstract = {Locomotion is ubiquitous in the animal kingdom because an animal's survival depends on its ability to navigate its environment to find food, avoid predators and locate potential mates. These behaviours require control mechanisms that can extract information from the environment, particularly visual cues. Selective evolutionary pressures have thus refined such visuomotor transformations in a species-specific manner to meet the specific ecological and ethological challenges of each organism. However, a common challenge across organisms as visual information processing becomes increasingly detailed is the mechanisms required to synthesise disparate pieces of information into a coherent percept or unified picture of the world. In this thesis, I investigate how disparate visual information is combined in the brain of Drosophila melanogaster to effectively guide locomotion. For this, I first designed and built a behavioural setup to record locomotion and present visual stimuli to freely-walking fruit flies in a closed-loop manner. This setup allowed the investigation of innate visually-guided behaviours, including the optomotor reflex and courtship. Second, taking advantage of my system I investigated the optomotor response, a reflexive visual stabilisation behaviour in which flies turn in the direction of global motion to minimise retinal slip. This behaviour is thought to be mediated by Lobula plate tangential cells (LPTCs); a complex network of optic-flow-sensitive neurons essential for self-motion estimation. Using a novel genetic mutant, I demonstrate that electrical coupling between two LPTC subtypes, contralateral HS and H2 neurons, regulates the balance between smooth optomotor turning and saccadic anti-optomotor responses. These findings underscore the critical role of binocular motion cue integration in guiding course control. Finally, I developed a novel behavioural paradigm in which a sexually aroused male fruit fly is presented with an optomotor distractor. This setup creates competition between two visual behaviours, courtship tracking and the optomotor response, enabling me to explore how the visual system resolves this conflict. In this setting, males engaged in courtship selectively suppress their optomotor response based on the female's location. Furthermore, when this experiment is replicated with an “artificial female”, optogenetically aroused males alternate between tracking and optomotor responses. The probability and dynamics of this switching are determined by the relative strengths of the two competing stimuli. In summary, the results presented in this thesis explore two mechanisms – integration and competition - through which visual information is combined in the brain of the fruit fly to drive locomotion.}, author = {Satapathy, Roshan K}, isbn = {978-3-99078-047-3}, issn = {2663-337X}, pages = {114}, publisher = {Institute of Science and Technology Austria}, title = {{Mechanisms of visual integration and competition in innate behaviours in Drosophila melanogaster}}, doi = {10.15479/at:ista:18568}, year = {2024}, } @article{18444, abstract = {Animals rely on compensatory actions to maintain stability and navigate their environment efficiently. These actions depend on global visual motion cues known as optic-flow. While the optomotor response has been the traditional focus for studying optic-flow compensation in insects, its simplicity has been insufficient to determine the role of the intricate optic-flow processing network involved in visual course control. Here, we reveal a series of course control behaviours in Drosophila and link them to specific neural circuits. We show that bilateral electrical coupling of optic-flow-sensitive neurons in the fly’s lobula plate are required for a proper course control. This electrical interaction works alongside chemical synapses within the HS-H2 network to control the dynamics and direction of turning behaviours. Our findings reveal how insects use bilateral motion cues for navigation, assigning a new functional significance to the HS-H2 network and suggesting a previously unknown role for gap junctions in non-linear operations.}, author = {Pokusaeva, Victoria and Satapathy, Roshan K and Symonova, Olga and Jösch, Maximilian A}, issn = {2041-1723}, journal = {Nature Communications}, publisher = {Springer Nature}, title = {{Bilateral interactions of optic-flow sensitive neurons coordinate course control in flies}}, doi = {10.1038/s41467-024-53173-w}, volume = {15}, year = {2024}, } @phdthesis{17336, abstract = {This thesis deals with the study of stochastic processes and their ergodicity properties. The variety of problems encountered calls for a set of different approaches, ranging from classical to modern ones: a special place is held by probabilistic methods based on couplings, by functional inequalities, and by the theory of gradient flows in the space of measures. The material is organized as follows. Chapter 1 contains the introduction to this thesis, starting with a general presentation of some of the relevant topics. Section 1.1 is dedicated to the theory of gradient flows in metric spaces, and introduces the first contribution of this thesis [DSMP24], which is presented in detail in Chapter 2. Section 1.2 moves to the topic of curvature of Markov chains, concluding with a brief description of our second contribution [Ped23], which is included in Chapter 3. Section 1.3 discusses applications of stochastic processes to the theory of sampling, in particular the recent framework of score-based diffusion models, and our contribution [PMM24], which is contained in Chapter 4. Section 1.4 discusses some related problems, concerning the regularization properties of the heat flow. It serves as a motivation for the work [BP24], which we report in Chapter 5. Finally, Section 1.5 discusses the last contribution of this thesis, which can be found in Chapter 6. It deals with the convergence to equilibrium of a particular stochastic model from quantitative genetics: this is established via some functional inequalities, which we prove with probabilistic arguments based on couplings. }, author = {Pedrotti, Francesco}, issn = {2663-337X}, pages = {183}, publisher = {Institute of Science and Technology Austria}, title = {{Functional inequalities and convergence of stochastic processes}}, doi = {10.15479/at:ista:17336}, year = {2024}, } @article{17143, abstract = {This paper deals with local criteria for the convergence to a global minimiser for gradient flow trajectories and their discretisations. To obtain quantitative estimates on the speed of convergence, we consider variations on the classical Kurdyka–Łojasiewicz inequality for a large class of parameter functions. Our assumptions are given in terms of the initial data, without any reference to an equilibrium point. The main results are convergence statements for gradient flow curves and proximal point sequences to a global minimiser, together with sharp quantitative estimates on the speed of convergence. These convergence results apply in the general setting of lower semicontinuous functionals on complete metric spaces, generalising recent results for smooth functionals on Rn. While the non-smooth setting covers very general spaces, it is also useful for (non)-smooth functionals on Rn. .}, author = {Dello Schiavo, Lorenzo and Maas, Jan and Pedrotti, Francesco}, issn = {1088-6850}, journal = {Transactions of the American Mathematical Society}, number = {6}, pages = {3779--3804}, publisher = {American Mathematical Society}, title = {{Local conditions for global convergence of gradient flows and proximal point sequences in metric spaces}}, doi = {10.1090/tran/9156}, volume = {377}, year = {2024}, }