@article{9374, abstract = {If there are no constraints on the process of speciation, then the number of species might be expected to match the number of available niches and this number might be indefinitely large. One possible constraint is the opportunity for allopatric divergence. In 1981, Felsenstein used a simple and elegant model to ask if there might also be genetic constraints. He showed that progress towards speciation could be described by the build‐up of linkage disequilibrium among divergently selected loci and between these loci and those contributing to other forms of reproductive isolation. Therefore, speciation is opposed by recombination, because it tends to break down linkage disequilibria. Felsenstein then introduced a crucial distinction between “two‐allele” models, which are subject to this effect, and “one‐allele” models, which are free from the recombination constraint. These fundamentally important insights have been the foundation for both empirical and theoretical studies of speciation ever since.}, author = {Butlin, Roger K. and Servedio, Maria R. and Smadja, Carole M. and Bank, Claudia and Barton, Nicholas H and Flaxman, Samuel M. and Giraud, Tatiana and Hopkins, Robin and Larson, Erica L. and Maan, Martine E. and Meier, Joana and Merrill, Richard and Noor, Mohamed A. F. and Ortiz‐Barrientos, Daniel and Qvarnström, Anna}, issn = {1558-5646}, journal = {Evolution}, keywords = {Genetics, Ecology, Evolution, Behavior and Systematics, General Agricultural and Biological Sciences}, number = {5}, pages = {978--988}, publisher = {Wiley}, title = {{Homage to Felsenstein 1981, or why are there so few/many species?}}, doi = {10.1111/evo.14235}, volume = {75}, year = {2021}, } @misc{13062, abstract = {This paper analyzes the conditions for local adaptation in a metapopulation with infinitely many islands under a model of hard selection, where population size depends on local fitness. Each island belongs to one of two distinct ecological niches or habitats. Fitness is influenced by an additive trait which is under habitat-dependent directional selection. Our analysis is based on the diffusion approximation and accounts for both genetic drift and demographic stochasticity. By neglecting linkage disequilibria, it yields the joint distribution of allele frequencies and population size on each island. We find that under hard selection, the conditions for local adaptation in a rare habitat are more restrictive for more polygenic traits: even moderate migration load per locus at very many loci is sufficient for population sizes to decline. This further reduces the efficacy of selection at individual loci due to increased drift and because smaller populations are more prone to swamping due to migration, causing a positive feedback between increasing maladaptation and declining population sizes. Our analysis also highlights the importance of demographic stochasticity, which exacerbates the decline in numbers of maladapted populations, leading to population collapse in the rare habitat at significantly lower migration than predicted by deterministic arguments.}, author = {Szep, Eniko and Sachdeva, Himani and Barton, Nicholas H}, publisher = {Dryad}, title = {{Supplementary code for: Polygenic local adaptation in metapopulations: A stochastic eco-evolutionary model}}, doi = {10.5061/DRYAD.8GTHT76P1}, year = {2021}, } @article{10838, abstract = {Combining hybrid zone analysis with genomic data is a promising approach to understanding the genomic basis of adaptive divergence. It allows for the identification of genomic regions underlying barriers to gene flow. It also provides insights into spatial patterns of allele frequency change, informing about the interplay between environmental factors, dispersal and selection. However, when only a single hybrid zone is analysed, it is difficult to separate patterns generated by selection from those resulting from chance. Therefore, it is beneficial to look for repeatable patterns across replicate hybrid zones in the same system. We applied this approach to the marine snail Littorina saxatilis, which contains two ecotypes, adapted to wave-exposed rocks vs. high-predation boulder fields. The existence of numerous hybrid zones between ecotypes offered the opportunity to test for the repeatability of genomic architectures and spatial patterns of divergence. We sampled and phenotyped snails from seven replicate hybrid zones on the Swedish west coast and genotyped them for thousands of single nucleotide polymorphisms. Shell shape and size showed parallel clines across all zones. Many genomic regions showing steep clines and/or high differentiation were shared among hybrid zones, consistent with a common evolutionary history and extensive gene flow between zones, and supporting the importance of these regions for divergence. In particular, we found that several large putative inversions contribute to divergence in all locations. Additionally, we found evidence for consistent displacement of clines from the boulder–rock transition. Our results demonstrate patterns of spatial variation that would not be accessible without continuous spatial sampling, a large genomic data set and replicate hybrid zones.}, author = {Westram, Anja M and Faria, Rui and Johannesson, Kerstin and Butlin, Roger}, issn = {1365-294X}, journal = {Molecular Ecology}, keywords = {Genetics, Ecology, Evolution, Behavior and Systematics}, number = {15}, pages = {3797--3814}, publisher = {Wiley}, title = {{Using replicate hybrid zones to understand the genomic basis of adaptive divergence}}, doi = {10.1111/mec.15861}, volume = {30}, year = {2021}, } @article{9288, abstract = {• The phenylpropanoid pathway serves a central role in plant metabolism, providing numerous compounds involved in diverse physiological processes. Most carbon entering the pathway is incorporated into lignin. Although several phenylpropanoid pathway mutants show seedling growth arrest, the role for lignin in seedling growth and development is unexplored. • We use complementary pharmacological and genetic approaches to block CINNAMATE‐4‐HYDROXYLASE (C4H) functionality in Arabidopsis seedlings and a set of molecular and biochemical techniques to investigate the underlying phenotypes. • Blocking C4H resulted in reduced lateral rooting and increased adventitious rooting apically in the hypocotyl. These phenotypes coincided with an inhibition in auxin transport. The upstream accumulation in cis‐cinnamic acid was found to likely cause polar auxin transport inhibition. Conversely, a downstream depletion in lignin perturbed phloem‐mediated auxin transport. Restoring lignin deposition effectively reestablished phloem transport and, accordingly, auxin homeostasis. • Our results show that the accumulation of bioactive intermediates and depletion in lignin jointly cause the aberrant phenotypes upon blocking C4H, and demonstrate that proper deposition of lignin is essential for the establishment of auxin distribution in seedlings. Our data position the phenylpropanoid pathway and lignin in a new physiological framework, consolidating their importance in plant growth and development.}, author = {El Houari, I and Van Beirs, C and Arents, HE and Han, Huibin and Chanoca, A and Opdenacker, D and Pollier, J and Storme, V and Steenackers, W and Quareshy, M and Napier, R and Beeckman, T and Friml, Jiří and De Rybel, B and Boerjan, W and Vanholme, B}, issn = {1469-8137}, journal = {New Phytologist}, number = {6}, pages = {2275--2291}, publisher = {Wiley}, title = {{Seedling developmental defects upon blocking CINNAMATE-4-HYDROXYLASE are caused by perturbations in auxin transport}}, doi = {10.1111/nph.17349}, volume = {230}, year = {2021}, } @article{10836, author = {Pranger, Christina L. and Fazekas-Singer, Judit and Köhler, Verena K. and Pali‐Schöll, Isabella and Fiocchi, Alessandro and Karagiannis, Sophia N. and Zenarruzabeitia, Olatz and Borrego, Francisco and Jensen‐Jarolim, Erika}, issn = {1398-9995}, journal = {Allergy}, keywords = {Immunology, Immunology and Allergy}, number = {5}, pages = {1553--1556}, publisher = {Wiley}, title = {{PIPE‐cloned human IgE and IgG4 antibodies: New tools for investigating cow's milk allergy and tolerance}}, doi = {10.1111/all.14604}, volume = {76}, year = {2021}, } @article{8608, abstract = {To adapt to the diverse array of biotic and abiotic cues, plants have evolved sophisticated mechanisms to sense changes in environmental conditions and modulate their growth. Growth-promoting hormones and defence signalling fine tune plant development antagonistically. During host-pathogen interactions, this defence-growth trade-off is mediated by the counteractive effects of the defence hormone salicylic acid (SA) and the growth hormone auxin. Here we revealed an underlying mechanism of SA regulating auxin signalling by constraining the plasma membrane dynamics of PIN2 auxin efflux transporter in Arabidopsis thaliana roots. The lateral diffusion of PIN2 proteins is constrained by SA signalling, during which PIN2 proteins are condensed into hyperclusters depending on REM1.2-mediated nanodomain compartmentalisation. Furthermore, membrane nanodomain compartmentalisation by SA or Remorin (REM) assembly significantly suppressed clathrin-mediated endocytosis. Consequently, SA-induced heterogeneous surface condensation disrupted asymmetric auxin distribution and the resultant gravitropic response. Our results demonstrated a defence-growth trade-off mechanism by which SA signalling crosstalked with auxin transport by concentrating membrane-resident PIN2 into heterogeneous compartments.}, author = {Ke, M and Ma, Z and Wang, D and Sun, Y and Wen, C and Huang, D and Chen, Z and Yang, L and Tan, Shutang and Li, R and Friml, Jiří and Miao, Y and Chen, X}, issn = {1469-8137}, journal = {New Phytologist}, number = {2}, pages = {963--978}, publisher = {Wiley}, title = {{Salicylic acid regulates PIN2 auxin transporter hyper-clustering and root gravitropic growth via Remorin-dependent lipid nanodomain organization in Arabidopsis thaliana}}, doi = {10.1111/nph.16915}, volume = {229}, year = {2021}, } @article{7900, abstract = {Hartree–Fock theory has been justified as a mean-field approximation for fermionic systems. However, it suffers from some defects in predicting physical properties, making necessary a theory of quantum correlations. Recently, bosonization of many-body correlations has been rigorously justified as an upper bound on the correlation energy at high density with weak interactions. We review the bosonic approximation, deriving an effective Hamiltonian. We then show that for systems with Coulomb interaction this effective theory predicts collective excitations (plasmons) in accordance with the random phase approximation of Bohm and Pines, and with experimental observation.}, author = {Benedikter, Niels P}, issn = {1793-6659}, journal = {Reviews in Mathematical Physics}, number = {1}, publisher = {World Scientific}, title = {{Bosonic collective excitations in Fermi gases}}, doi = {10.1142/s0129055x20600090}, volume = {33}, year = {2021}, } @article{10852, abstract = { We review old and new results on the Fröhlich polaron model. The discussion includes the validity of the (classical) Pekar approximation in the strong coupling limit, quantum corrections to this limit, as well as the divergence of the effective polaron mass.}, author = {Seiringer, Robert}, issn = {1793-6659}, journal = {Reviews in Mathematical Physics}, keywords = {Mathematical Physics, Statistical and Nonlinear Physics}, number = {01}, publisher = {World Scientific Publishing}, title = {{The polaron at strong coupling}}, doi = {10.1142/s0129055x20600120}, volume = {33}, year = {2021}, } @phdthesis{9056, abstract = {In this thesis we study persistence of multi-covers of Euclidean balls and the geometric structures underlying their computation, in particular Delaunay mosaics and Voronoi tessellations. The k-fold cover for some discrete input point set consists of the space where at least k balls of radius r around the input points overlap. Persistence is a notion that captures, in some sense, the topology of the shape underlying the input. While persistence is usually computed for the union of balls, the k-fold cover is of interest as it captures local density, and thus might approximate the shape of the input better if the input data is noisy. To compute persistence of these k-fold covers, we need a discretization that is provided by higher-order Delaunay mosaics. We present and implement a simple and efficient algorithm for the computation of higher-order Delaunay mosaics, and use it to give experimental results for their combinatorial properties. The algorithm makes use of a new geometric structure, the rhomboid tiling. It contains the higher-order Delaunay mosaics as slices, and by introducing a filtration function on the tiling, we also obtain higher-order α-shapes as slices. These allow us to compute persistence of the multi-covers for varying radius r; the computation for varying k is less straight-foward and involves the rhomboid tiling directly. We apply our algorithms to experimental sphere packings to shed light on their structural properties. Finally, inspired by periodic structures in packings and materials, we propose and implement an algorithm for periodic Delaunay triangulations to be integrated into the Computational Geometry Algorithms Library (CGAL), and discuss the implications on persistence for periodic data sets.}, author = {Osang, Georg F}, issn = {2663-337X}, pages = {134}, publisher = {Institute of Science and Technology Austria}, title = {{Multi-cover persistence and Delaunay mosaics}}, doi = {10.15479/AT:ISTA:9056}, year = {2021}, } @phdthesis{9022, abstract = {In the first part of the thesis we consider Hermitian random matrices. Firstly, we consider sample covariance matrices XX∗ with X having independent identically distributed (i.i.d.) centred entries. We prove a Central Limit Theorem for differences of linear statistics of XX∗ and its minor after removing the first column of X. Secondly, we consider Wigner-type matrices and prove that the eigenvalue statistics near cusp singularities of the limiting density of states are universal and that they form a Pearcey process. Since the limiting eigenvalue distribution admits only square root (edge) and cubic root (cusp) singularities, this concludes the third and last remaining case of the Wigner-Dyson-Mehta universality conjecture. The main technical ingredients are an optimal local law at the cusp, and the proof of the fast relaxation to equilibrium of the Dyson Brownian motion in the cusp regime. In the second part we consider non-Hermitian matrices X with centred i.i.d. entries. We normalise the entries of X to have variance N −1. It is well known that the empirical eigenvalue density converges to the uniform distribution on the unit disk (circular law). In the first project, we prove universality of the local eigenvalue statistics close to the edge of the spectrum. This is the non-Hermitian analogue of the TracyWidom universality at the Hermitian edge. Technically we analyse the evolution of the spectral distribution of X along the Ornstein-Uhlenbeck flow for very long time (up to t = +∞). In the second project, we consider linear statistics of eigenvalues for macroscopic test functions f in the Sobolev space H2+ϵ and prove their convergence to the projection of the Gaussian Free Field on the unit disk. We prove this result for non-Hermitian matrices with real or complex entries. The main technical ingredients are: (i) local law for products of two resolvents at different spectral parameters, (ii) analysis of correlated Dyson Brownian motions. In the third and final part we discuss the mathematically rigorous application of supersymmetric techniques (SUSY ) to give a lower tail estimate of the lowest singular value of X − z, with z ∈ C. More precisely, we use superbosonisation formula to give an integral representation of the resolvent of (X − z)(X − z)∗ which reduces to two and three contour integrals in the complex and real case, respectively. The rigorous analysis of these integrals is quite challenging since simple saddle point analysis cannot be applied (the main contribution comes from a non-trivial manifold). Our result improves classical smoothing inequalities in the regime |z| ≈ 1; this result is essential to prove edge universality for i.i.d. non-Hermitian matrices.}, author = {Cipolloni, Giorgio}, issn = {2663-337X}, pages = {380}, publisher = {Institute of Science and Technology Austria}, title = {{Fluctuations in the spectrum of random matrices}}, doi = {10.15479/AT:ISTA:9022}, year = {2021}, } @inproceedings{9416, abstract = {We study the inductive bias of two-layer ReLU networks trained by gradient flow. We identify a class of easy-to-learn (`orthogonally separable') datasets, and characterise the solution that ReLU networks trained on such datasets converge to. Irrespective of network width, the solution turns out to be a combination of two max-margin classifiers: one corresponding to the positive data subset and one corresponding to the negative data subset. The proof is based on the recently introduced concept of extremal sectors, for which we prove a number of properties in the context of orthogonal separability. In particular, we prove stationarity of activation patterns from some time onwards, which enables a reduction of the ReLU network to an ensemble of linear subnetworks.}, author = {Bui Thi Mai, Phuong and Lampert, Christoph}, booktitle = {9th International Conference on Learning Representations}, location = {Virtual}, title = {{The inductive bias of ReLU networks on orthogonally separable data}}, year = {2021}, } @article{9225, abstract = {The Landau–Pekar equations describe the dynamics of a strongly coupled polaron. Here, we provide a class of initial data for which the associated effective Hamiltonian has a uniform spectral gap for all times. For such initial data, this allows us to extend the results on the adiabatic theorem for the Landau–Pekar equations and their derivation from the Fröhlich model obtained in previous works to larger times.}, author = {Feliciangeli, Dario and Rademacher, Simone Anna Elvira and Seiringer, Robert}, issn = {15730530}, journal = {Letters in Mathematical Physics}, publisher = {Springer Nature}, title = {{Persistence of the spectral gap for the Landau–Pekar equations}}, doi = {10.1007/s11005-020-01350-5}, volume = {111}, year = {2021}, } @unpublished{9787, abstract = {We investigate the Fröhlich polaron model on a three-dimensional torus, and give a proof of the second-order quantum corrections to its ground-state energy in the strong-coupling limit. Compared to previous work in the confined case, the translational symmetry (and its breaking in the Pekar approximation) makes the analysis substantially more challenging.}, author = {Feliciangeli, Dario and Seiringer, Robert}, booktitle = {arXiv}, title = {{The strongly coupled polaron on the torus: Quantum corrections to the Pekar asymptotics}}, year = {2021}, } @inproceedings{9987, abstract = {Stateless model checking (SMC) is one of the standard approaches to the verification of concurrent programs. As scheduling non-determinism creates exponentially large spaces of thread interleavings, SMC attempts to partition this space into equivalence classes and explore only a few representatives from each class. The efficiency of this approach depends on two factors: (a) the coarseness of the partitioning, and (b) the time to generate representatives in each class. For this reason, the search for coarse partitionings that are efficiently explorable is an active research challenge. In this work we present RVF-SMC , a new SMC algorithm that uses a novel reads-value-from (RVF) partitioning. Intuitively, two interleavings are deemed equivalent if they agree on the value obtained in each read event, and read events induce consistent causal orderings between them. The RVF partitioning is provably coarser than recent approaches based on Mazurkiewicz and “reads-from” partitionings. Our experimental evaluation reveals that RVF is quite often a very effective equivalence, as the underlying partitioning is exponentially coarser than other approaches. Moreover, RVF-SMC generates representatives very efficiently, as the reduction in the partitioning is often met with significant speed-ups in the model checking task.}, author = {Agarwal, Pratyush and Chatterjee, Krishnendu and Pathak, Shreya and Pavlogiannis, Andreas and Toman, Viktor}, booktitle = {33rd International Conference on Computer-Aided Verification }, isbn = {978-3-030-81684-1}, issn = {1611-3349}, location = {Virtual}, pages = {341--366}, publisher = {Springer Nature}, title = {{Stateless model checking under a reads-value-from equivalence}}, doi = {10.1007/978-3-030-81685-8_16}, volume = {12759 }, year = {2021}, } @phdthesis{10007, abstract = {The present thesis is concerned with the derivation of weak-strong uniqueness principles for curvature driven interface evolution problems not satisfying a comparison principle. The specific examples being treated are two-phase Navier-Stokes flow with surface tension, modeling the evolution of two incompressible, viscous and immiscible fluids separated by a sharp interface, and multiphase mean curvature flow, which serves as an idealized model for the motion of grain boundaries in an annealing polycrystalline material. Our main results - obtained in joint works with Julian Fischer, Tim Laux and Theresa M. Simon - state that prior to the formation of geometric singularities due to topology changes, the weak solution concept of Abels (Interfaces Free Bound. 9, 2007) to two-phase Navier-Stokes flow with surface tension and the weak solution concept of Laux and Otto (Calc. Var. Partial Differential Equations 55, 2016) to multiphase mean curvature flow (for networks in R^2 or double bubbles in R^3) represents the unique solution to these interface evolution problems within the class of classical solutions, respectively. To the best of the author's knowledge, for interface evolution problems not admitting a geometric comparison principle the derivation of a weak-strong uniqueness principle represented an open problem, so that the works contained in the present thesis constitute the first positive results in this direction. The key ingredient of our approach consists of the introduction of a novel concept of relative entropies for a class of curvature driven interface evolution problems, for which the associated energy contains an interfacial contribution being proportional to the surface area of the evolving (network of) interface(s). The interfacial part of the relative entropy gives sufficient control on the interface error between a weak and a classical solution, and its time evolution can be computed, at least in principle, for any energy dissipating weak solution concept. A resulting stability estimate for the relative entropy essentially entails the above mentioned weak-strong uniqueness principles. The present thesis contains a detailed introduction to our relative entropy approach, which in particular highlights potential applications to other problems in curvature driven interface evolution not treated in this thesis.}, author = {Hensel, Sebastian}, issn = {2663-337X}, pages = {300}, publisher = {Institute of Science and Technology Austria}, title = {{Curvature driven interface evolution: Uniqueness properties of weak solution concepts}}, doi = {10.15479/at:ista:10007}, year = {2021}, } @article{10191, abstract = {In this work we solve the algorithmic problem of consistency verification for the TSO and PSO memory models given a reads-from map, denoted VTSO-rf and VPSO-rf, respectively. For an execution of n events over k threads and d variables, we establish novel bounds that scale as nk+1 for TSO and as nk+1· min(nk2, 2k· d) for PSO. Moreover, based on our solution to these problems, we develop an SMC algorithm under TSO and PSO that uses the RF equivalence. The algorithm is exploration-optimal, in the sense that it is guaranteed to explore each class of the RF partitioning exactly once, and spends polynomial time per class when k is bounded. Finally, we implement all our algorithms in the SMC tool Nidhugg, and perform a large number of experiments over benchmarks from existing literature. Our experimental results show that our algorithms for VTSO-rf and VPSO-rf provide significant scalability improvements over standard alternatives. Moreover, when used for SMC, the RF partitioning is often much coarser than the standard Shasha-Snir partitioning for TSO/PSO, which yields a significant speedup in the model checking task. }, author = {Bui, Truc Lam and Chatterjee, Krishnendu and Gautam, Tushar and Pavlogiannis, Andreas and Toman, Viktor}, issn = {2475-1421}, journal = {Proceedings of the ACM on Programming Languages}, keywords = {safety, risk, reliability and quality, software}, number = {OOPSLA}, publisher = {Association for Computing Machinery}, title = {{The reads-from equivalence for the TSO and PSO memory models}}, doi = {10.1145/3485541}, volume = {5}, year = {2021}, } @unpublished{10013, abstract = {We derive a weak-strong uniqueness principle for BV solutions to multiphase mean curvature flow of triple line clusters in three dimensions. Our proof is based on the explicit construction of a gradient-flow calibration in the sense of the recent work of Fischer et al. [arXiv:2003.05478] for any such cluster. This extends the two-dimensional construction to the three-dimensional case of surfaces meeting along triple junctions.}, author = {Hensel, Sebastian and Laux, Tim}, booktitle = {arXiv}, title = {{Weak-strong uniqueness for the mean curvature flow of double bubbles}}, doi = {10.48550/arXiv.2108.01733}, year = {2021}, } @article{9928, abstract = {There are two elementary superconducting qubit types that derive directly from the quantum harmonic oscillator. In one, the inductor is replaced by a nonlinear Josephson junction to realize the widely used charge qubits with a compact phase variable and a discrete charge wave function. In the other, the junction is added in parallel, which gives rise to an extended phase variable, continuous wave functions, and a rich energy-level structure due to the loop topology. While the corresponding rf superconducting quantum interference device Hamiltonian was introduced as a quadratic quasi-one-dimensional potential approximation to describe the fluxonium qubit implemented with long Josephson-junction arrays, in this work we implement it directly using a linear superinductor formed by a single uninterrupted aluminum wire. We present a large variety of qubits, all stemming from the same circuit but with drastically different characteristic energy scales. This includes flux and fluxonium qubits but also the recently introduced quasicharge qubit with strongly enhanced zero-point phase fluctuations and a heavily suppressed flux dispersion. The use of a geometric inductor results in high reproducibility of the inductive energy as guaranteed by top-down lithography—a key ingredient for intrinsically protected superconducting qubits.}, author = {Peruzzo, Matilda and Hassani, Farid and Szep, Gregory and Trioni, Andrea and Redchenko, Elena and Zemlicka, Martin and Fink, Johannes M}, issn = {2691-3399}, journal = {PRX Quantum}, keywords = {quantum physics, mesoscale and nanoscale physics}, number = {4}, pages = {040341}, publisher = {American Physical Society}, title = {{Geometric superinductance qubits: Controlling phase delocalization across a single Josephson junction}}, doi = {10.1103/PRXQuantum.2.040341}, volume = {2}, year = {2021}, } @phdthesis{10030, abstract = {This PhD thesis is primarily focused on the study of discrete transport problems, introduced for the first time in the seminal works of Maas [Maa11] and Mielke [Mie11] on finite state Markov chains and reaction-diffusion equations, respectively. More in detail, my research focuses on the study of transport costs on graphs, in particular the convergence and the stability of such problems in the discrete-to-continuum limit. This thesis also includes some results concerning non-commutative optimal transport. The first chapter of this thesis consists of a general introduction to the optimal transport problems, both in the discrete, the continuous, and the non-commutative setting. Chapters 2 and 3 present the content of two works, obtained in collaboration with Peter Gladbach, Eva Kopfer, and Jan Maas, where we have been able to show the convergence of discrete transport costs on periodic graphs to suitable continuous ones, which can be described by means of a homogenisation result. We first focus on the particular case of quadratic costs on the real line and then extending the result to more general costs in arbitrary dimension. Our results are the first complete characterisation of limits of transport costs on periodic graphs in arbitrary dimension which do not rely on any additional symmetry. In Chapter 4 we turn our attention to one of the intriguing connection between evolution equations and optimal transport, represented by the theory of gradient flows. We show that discrete gradient flow structures associated to a finite volume approximation of a certain class of diffusive equations (Fokker–Planck) is stable in the limit of vanishing meshes, reproving the convergence of the scheme via the method of evolutionary Γ-convergence and exploiting a more variational point of view on the problem. This is based on a collaboration with Dominik Forkert and Jan Maas. Chapter 5 represents a change of perspective, moving away from the discrete world and reaching the non-commutative one. As in the discrete case, we discuss how classical tools coming from the commutative optimal transport can be translated into the setting of density matrices. In particular, in this final chapter we present a non-commutative version of the Schrödinger problem (or entropic regularised optimal transport problem) and discuss existence and characterisation of minimisers, a duality result, and present a non-commutative version of the well-known Sinkhorn algorithm to compute the above mentioned optimisers. This is based on a joint work with Dario Feliciangeli and Augusto Gerolin. Finally, Appendix A and B contain some additional material and discussions, with particular attention to Harnack inequalities and the regularity of flows on discrete spaces.}, author = {Portinale, Lorenzo}, issn = {2663-337X}, publisher = {Institute of Science and Technology Austria}, title = {{Discrete-to-continuum limits of transport problems and gradient flows in the space of measures}}, doi = {10.15479/at:ista:10030}, year = {2021}, } @phdthesis{9920, abstract = {This work is concerned with two fascinating circuit quantum electrodynamics components, the Josephson junction and the geometric superinductor, and the interesting experiments that can be done by combining the two. The Josephson junction has revolutionized the field of superconducting circuits as a non-linear dissipation-less circuit element and is used in almost all superconducting qubit implementations since the 90s. On the other hand, the superinductor is a relatively new circuit element introduced as a key component of the fluxonium qubit in 2009. This is an inductor with characteristic impedance larger than the resistance quantum and self-resonance frequency in the GHz regime. The combination of these two elements can occur in two fundamental ways: in parallel and in series. When connected in parallel the two create the fluxonium qubit, a loop with large inductance and a rich energy spectrum reliant on quantum tunneling. On the other hand placing the two elements in series aids with the measurement of the IV curve of a single Josephson junction in a high impedance environment. In this limit theory predicts that the junction will behave as its dual element: the phase-slip junction. While the Josephson junction acts as a non-linear inductor the phase-slip junction has the behavior of a non-linear capacitance and can be used to measure new Josephson junction phenomena, namely Coulomb blockade of Cooper pairs and phase-locked Bloch oscillations. The latter experiment allows for a direct link between frequency and current which is an elusive connection in quantum metrology. This work introduces the geometric superinductor, a superconducting circuit element where the high inductance is due to the geometry rather than the material properties of the superconductor, realized from a highly miniaturized superconducting planar coil. These structures will be described and characterized as resonators and qubit inductors and progress towards the measurement of phase-locked Bloch oscillations will be presented.}, author = {Peruzzo, Matilda}, isbn = {978-3-99078-013-8}, issn = {2663-337X}, keywords = {quantum computing, superinductor, quantum metrology}, pages = {149}, publisher = {Institute of Science and Technology Austria}, title = {{Geometric superinductors and their applications in circuit quantum electrodynamics}}, doi = {10.15479/at:ista:9920}, year = {2021}, }