@article{13129, abstract = {We study the representative volume element (RVE) method, which is a method to approximately infer the effective behavior ahom of a stationary random medium. The latter is described by a coefficient field a(x) generated from a given ensemble ⟨⋅⟩ and the corresponding linear elliptic operator −∇⋅a∇. In line with the theory of homogenization, the method proceeds by computing d=3 correctors (d denoting the space dimension). To be numerically tractable, this computation has to be done on a finite domain: the so-called representative volume element, i.e., a large box with, say, periodic boundary conditions. The main message of this article is: Periodize the ensemble instead of its realizations. By this, we mean that it is better to sample from a suitably periodized ensemble than to periodically extend the restriction of a realization a(x) from the whole-space ensemble ⟨⋅⟩. We make this point by investigating the bias (or systematic error), i.e., the difference between ahom and the expected value of the RVE method, in terms of its scaling w.r.t. the lateral size L of the box. In case of periodizing a(x), we heuristically argue that this error is generically O(L−1). In case of a suitable periodization of ⟨⋅⟩ , we rigorously show that it is O(L−d). In fact, we give a characterization of the leading-order error term for both strategies and argue that even in the isotropic case it is generically non-degenerate. We carry out the rigorous analysis in the convenient setting of ensembles ⟨⋅⟩ of Gaussian type, which allow for a straightforward periodization, passing via the (integrable) covariance function. This setting has also the advantage of making the Price theorem and the Malliavin calculus available for optimal stochastic estimates of correctors. We actually need control of second-order correctors to capture the leading-order error term. This is due to inversion symmetry when applying the two-scale expansion to the Green function. As a bonus, we present a stream-lined strategy to estimate the error in a higher-order two-scale expansion of the Green function.}, author = {Clozeau, Nicolas and Josien, Marc and Otto, Felix and Xu, Qiang}, issn = {1615-3383}, journal = {Foundations of Computational Mathematics}, publisher = {Springer Nature}, title = {{Bias in the representative volume element method: Periodize the ensemble instead of its realizations}}, doi = {10.1007/s10208-023-09613-y}, year = {2023}, } @article{13134, abstract = {We propose a characterization of discrete analytical spheres, planes and lines in the body-centered cubic (BCC) grid, both in the Cartesian and in the recently proposed alternative compact coordinate system, in which each integer triplet addresses some voxel in the grid. We define spheres and planes through double Diophantine inequalities and investigate their relevant topological features, such as functionality or the interrelation between the thickness of the objects and their connectivity and separation properties. We define lines as the intersection of planes. The number of the planes (up to six) is equal to the number of the pairs of faces of a BCC voxel that are parallel to the line.}, author = {Čomić, Lidija and Largeteau-Skapin, Gaëlle and Zrour, Rita and Biswas, Ranita and Andres, Eric}, issn = {0031-3203}, journal = {Pattern Recognition}, number = {10}, publisher = {Elsevier}, title = {{Discrete analytical objects in the body-centered cubic grid}}, doi = {10.1016/j.patcog.2023.109693}, volume = {142}, year = {2023}, } @article{13135, abstract = {In this paper we consider a class of stochastic reaction-diffusion equations. We provide local well-posedness, regularity, blow-up criteria and positivity of solutions. The key novelties of this work are related to the use transport noise, critical spaces and the proof of higher order regularity of solutions – even in case of non-smooth initial data. Crucial tools are Lp(Lp)-theory, maximal regularity estimates and sharp blow-up criteria. We view the results of this paper as a general toolbox for establishing global well-posedness for a large class of reaction-diffusion systems of practical interest, of which many are completely open. In our follow-up work [8], the results of this paper are applied in the specific cases of the Lotka-Volterra equations and the Brusselator model.}, author = {Agresti, Antonio and Veraar, Mark}, issn = {1090-2732}, journal = {Journal of Differential Equations}, number = {9}, pages = {247--300}, publisher = {Elsevier}, title = {{Reaction-diffusion equations with transport noise and critical superlinear diffusion: Local well-posedness and positivity}}, doi = {10.1016/j.jde.2023.05.038}, volume = {368}, year = {2023}, } @article{13136, abstract = {Despite its fundamental importance for development, the question of how organs achieve their correct size and shape is poorly understood. This complex process requires coordination between the generation of cell mass and the morphogenetic mechanisms that sculpt tissues. These processes are regulated by morphogen signalling pathways and mechanical forces. Yet, in many systems, it is unclear how biochemical and mechanical signalling are quantitatively interpreted to determine the behaviours of individual cells and how they contribute to growth and morphogenesis at the tissue scale. In this review, we discuss the development of the vertebrate neural tube and somites as an example of the state of knowledge, as well as the challenges in understanding the mechanisms of tissue size control in vertebrate organogenesis. We highlight how the recent advances in stem cell differentiation and organoid approaches can be harnessed to provide new insights into this question.}, author = {Minchington, Thomas and Rus, Stefanie and Kicheva, Anna}, issn = {2452-3100}, journal = {Current Opinion in Systems Biology}, publisher = {Elsevier}, title = {{Control of tissue dimensions in the developing neural tube and somites}}, doi = {10.1016/j.coisb.2023.100459}, volume = {35}, year = {2023}, } @article{13138, abstract = {We consider the spin- 1 2 Heisenberg chain (XXX model) weakly perturbed away from integrability by an isotropic next-to-nearest neighbor exchange interaction. Recently, it was conjectured that this model possesses an infinite tower of quasiconserved integrals of motion (charges) [D. Kurlov et al., Phys. Rev. B 105, 104302 (2022)]. In this work we first test this conjecture by investigating how the norm of the adiabatic gauge potential (AGP) scales with the system size, which is known to be a remarkably accurate measure of chaos. We find that for the perturbed XXX chain the behavior of the AGP norm corresponds to neither an integrable nor a chaotic regime, which supports the conjectured quasi-integrability of the model. We then prove the conjecture and explicitly construct the infinite set of quasiconserved charges. Our proof relies on the fact that the XXX chain perturbed by next-to-nearest exchange interaction can be viewed as a truncation of an integrable long-range deformation of the Heisenberg spin chain.}, author = {Orlov, Pavel and Tiutiakina, Anastasiia and Sharipov, Rustem and Petrova, Elena and Gritsev, Vladimir and Kurlov, Denis V.}, issn = {2469-9969}, journal = {Physical Review B}, number = {18}, publisher = {American Physical Society}, title = {{Adiabatic eigenstate deformations and weak integrability breaking of Heisenberg chain}}, doi = {10.1103/PhysRevB.107.184312}, volume = {107}, year = {2023}, } @inproceedings{13139, abstract = {A classical problem for Markov chains is determining their stationary (or steady-state) distribution. This problem has an equally classical solution based on eigenvectors and linear equation systems. However, this approach does not scale to large instances, and iterative solutions are desirable. It turns out that a naive approach, as used by current model checkers, may yield completely wrong results. We present a new approach, which utilizes recent advances in partial exploration and mean payoff computation to obtain a correct, converging approximation.}, author = {Meggendorfer, Tobias}, booktitle = {TACAS 2023: Tools and Algorithms for the Construction and Analysis of Systems}, isbn = {9783031308222}, issn = {1611-3349}, location = {Paris, France}, pages = {489--507}, publisher = {Springer Nature}, title = {{Correct approximation of stationary distributions}}, doi = {10.1007/978-3-031-30823-9_25}, volume = {13993}, year = {2023}, } @inproceedings{13141, abstract = {We automatically compute a new class of environment assumptions in two-player turn-based finite graph games which characterize an “adequate cooperation” needed from the environment to allow the system player to win. Given an ω-regular winning condition Φ for the system player, we compute an ω-regular assumption Ψ for the environment player, such that (i) every environment strategy compliant with Ψ allows the system to fulfill Φ (sufficiency), (ii) Ψ can be fulfilled by the environment for every strategy of the system (implementability), and (iii) Ψ does not prevent any cooperative strategy choice (permissiveness). For parity games, which are canonical representations of ω-regular games, we present a polynomial-time algorithm for the symbolic computation of adequately permissive assumptions and show that our algorithm runs faster and produces better assumptions than existing approaches—both theoretically and empirically. To the best of our knowledge, for ω -regular games, we provide the first algorithm to compute sufficient and implementable environment assumptions that are also permissive.}, author = {Anand, Ashwani and Mallik, Kaushik and Nayak, Satya Prakash and Schmuck, Anne Kathrin}, booktitle = {TACAS 2023: Tools and Algorithms for the Construction and Analysis of Systems}, isbn = {9783031308192}, issn = {1611-3349}, location = {Paris, France}, pages = {211--228}, publisher = {Springer Nature}, title = {{Computing adequately permissive assumptions for synthesis}}, doi = {10.1007/978-3-031-30820-8_15}, volume = {13994}, year = {2023}, } @inproceedings{13142, abstract = {Reinforcement learning has received much attention for learning controllers of deterministic systems. We consider a learner-verifier framework for stochastic control systems and survey recent methods that formally guarantee a conjunction of reachability and safety properties. Given a property and a lower bound on the probability of the property being satisfied, our framework jointly learns a control policy and a formal certificate to ensure the satisfaction of the property with a desired probability threshold. Both the control policy and the formal certificate are continuous functions from states to reals, which are learned as parameterized neural networks. While in the deterministic case, the certificates are invariant and barrier functions for safety, or Lyapunov and ranking functions for liveness, in the stochastic case the certificates are supermartingales. For certificate verification, we use interval arithmetic abstract interpretation to bound the expected values of neural network functions.}, author = {Chatterjee, Krishnendu and Henzinger, Thomas A and Lechner, Mathias and Zikelic, Dorde}, booktitle = {Tools and Algorithms for the Construction and Analysis of Systems }, isbn = {9783031308222}, issn = {1611-3349}, location = {Paris, France}, pages = {3--25}, publisher = {Springer Nature}, title = {{A learner-verifier framework for neural network controllers and certificates of stochastic systems}}, doi = {10.1007/978-3-031-30823-9_1}, volume = {13993}, year = {2023}, } @inproceedings{13143, abstract = {GIMPS and PrimeGrid are large-scale distributed projects dedicated to searching giant prime numbers, usually of special forms like Mersenne and Proth primes. The numbers in the current search-space are millions of digits large and the participating volunteers need to run resource-consuming primality tests. Once a candidate prime N has been found, the only way for another party to independently verify the primality of N used to be by repeating the expensive primality test. To avoid the need for second recomputation of each primality test, these projects have recently adopted certifying mechanisms that enable efficient verification of performed tests. However, the mechanisms presently in place only detect benign errors and there is no guarantee against adversarial behavior: a malicious volunteer can mislead the project to reject a giant prime as being non-prime. In this paper, we propose a practical, cryptographically-sound mechanism for certifying the non-primality of Proth numbers. That is, a volunteer can – parallel to running the primality test for N – generate an efficiently verifiable proof at a little extra cost certifying that N is not prime. The interactive protocol has statistical soundness and can be made non-interactive using the Fiat-Shamir heuristic. Our approach is based on a cryptographic primitive called Proof of Exponentiation (PoE) which, for a group G, certifies that a tuple (x,y,T)∈G2×N satisfies x2T=y (Pietrzak, ITCS 2019 and Wesolowski, J. Cryptol. 2020). In particular, we show how to adapt Pietrzak’s PoE at a moderate additional cost to make it a cryptographically-sound certificate of non-primality.}, author = {Hoffmann, Charlotte and Hubáček, Pavel and Kamath, Chethan and Pietrzak, Krzysztof Z}, booktitle = {Public-Key Cryptography - PKC 2023}, isbn = {9783031313677}, issn = {1611-3349}, location = {Atlanta, GA, United States}, pages = {530--553}, publisher = {Springer Nature}, title = {{Certifying giant nonprimes}}, doi = {10.1007/978-3-031-31368-4_19}, volume = {13940}, year = {2023}, } @article{13145, abstract = {We prove a characterization of the Dirichlet–Ferguson measure over an arbitrary finite diffuse measure space. We provide an interpretation of this characterization in analogy with the Mecke identity for Poisson point processes.}, author = {Dello Schiavo, Lorenzo and Lytvynov, Eugene}, issn = {1083-589X}, journal = {Electronic Communications in Probability}, pages = {1--12}, publisher = {Institute of Mathematical Statistics}, title = {{A Mecke-type characterization of the Dirichlet–Ferguson measure}}, doi = {10.1214/23-ECP528}, volume = {28}, year = {2023}, } @inproceedings{13161, author = {Schlögl, Alois and Elefante, Stefano and Hodirnau, Victor-Valentin}, booktitle = {ASHPC23 - Austrian-Slovenian HPC Meeting 2023}, location = {Maribor, Slovenia}, pages = {59--59}, publisher = {EuroCC}, title = {{Running Windows-applications on a Linux HPC cluster using WINE}}, year = {2023}, } @inproceedings{13162, author = {Elefante, Stefano and Stadlbauer, Stephan and Alexander, Michael F and Schlögl, Alois}, booktitle = {ASHPC23 - Austrian-Slovenian HPC Meeting 2023}, location = {Maribor, Slovenia}, pages = {42--42}, publisher = {EuroCC}, title = {{Cryo-EM software packages: A sys-admins point of view}}, year = {2023}, } @article{13164, abstract = {Molecular compatibility between gametes is a prerequisite for successful fertilization. As long as a sperm and egg can recognize and bind each other via their surface proteins, gamete fusion may occur even between members of separate species, resulting in hybrids that can impact speciation. The egg membrane protein Bouncer confers species specificity to gamete interactions between medaka and zebrafish, preventing their cross-fertilization. Here, we leverage this specificity to uncover distinct amino acid residues and N-glycosylation patterns that differentially influence the function of medaka and zebrafish Bouncer and contribute to cross-species incompatibility. Curiously, in contrast to the specificity observed for medaka and zebrafish Bouncer, seahorse and fugu Bouncer are compatible with both zebrafish and medaka sperm, in line with the pervasive purifying selection that dominates Bouncer’s evolution. The Bouncer-sperm interaction is therefore the product of seemingly opposing evolutionary forces that, for some species, restrict fertilization to closely related fish, and for others, allow broad gamete compatibility that enables hybridization.}, author = {Gert, Krista R.B. and Panser, Karin and Surm, Joachim and Steinmetz, Benjamin S. and Schleiffer, Alexander and Jovine, Luca and Moran, Yehu and Kondrashov, Fyodor and Pauli, Andrea}, issn = {2041-1723}, journal = {Nature Communications}, publisher = {Springer Nature}, title = {{Divergent molecular signatures in fish Bouncer proteins define cross-fertilization boundaries}}, doi = {10.1038/s41467-023-39317-4}, volume = {14}, year = {2023}, } @article{13165, abstract = {A graph G=(V, E) is called fully regular if for every independent set I c V, the number of vertices in V\I that are not connected to any element of I depends only on the size of I. A linear ordering of the vertices of G is called successive if for every i, the first i vertices induce a connected subgraph of G. We give an explicit formula for the number of successive vertex orderings of a fully regular graph. As an application of our results, we give alternative proofs of two theorems of Stanley and Gao & Peng, determining the number of linear edge orderings of complete graphs and complete bipartite graphs, respectively, with the property that the first i edges induce a connected subgraph. As another application, we give a simple product formula for the number of linear orderings of the hyperedges of a complete 3-partite 3-uniform hypergraph such that, for every i, the first i hyperedges induce a connected subgraph. We found similar formulas for complete (non-partite) 3-uniform hypergraphs and in another closely related case, but we managed to verify them only when the number of vertices is small.}, author = {Fang, Lixing and Huang, Hao and Pach, János and Tardos, Gábor and Zuo, Junchi}, issn = {1096-0899}, journal = {Journal of Combinatorial Theory. Series A}, number = {10}, publisher = {Elsevier}, title = {{Successive vertex orderings of fully regular graphs}}, doi = {10.1016/j.jcta.2023.105776}, volume = {199}, year = {2023}, } @article{13166, abstract = {Brachyury, a member of T-box gene family, is widely known for its major role in mesoderm specification in bilaterians. It is also present in non-bilaterian metazoans, such as cnidarians, where it acts as a component of an axial patterning system. In this study, we present a phylogenetic analysis of Brachyury genes within phylum Cnidaria, investigate differential expression and address a functional framework of Brachyury paralogs in hydrozoan Dynamena pumila. Our analysis indicates two duplication events of Brachyury within the cnidarian lineage. The first duplication likely appeared in the medusozoan ancestor, resulting in two copies in medusozoans, while the second duplication arose in the hydrozoan ancestor, resulting in three copies in hydrozoans. Brachyury1 and 2 display a conservative expression pattern marking the oral pole of the body axis in D. pumila. On the contrary, Brachyury3 expression was detected in scattered presumably nerve cells of the D. pumila larva. Pharmacological modulations indicated that Brachyury3 is not under regulation of cWnt signaling in contrast to the other two Brachyury genes. Divergence in expression patterns and regulation suggest neofunctionalization of Brachyury3 in hydrozoans.}, author = {Vetrova, Alexandra A. and Kupaeva, Daria M. and Kizenko, Alena and Lebedeva, Tatiana S. and Walentek, Peter and Tsikolia, Nikoloz and Kremnyov, Stanislav V.}, issn = {2045-2322}, journal = {Scientific Reports}, publisher = {Springer Nature}, title = {{The evolutionary history of Brachyury genes in Hydrozoa involves duplications, divergence, and neofunctionalization}}, doi = {10.1038/s41598-023-35979-8}, volume = {13}, year = {2023}, } @article{13168, abstract = {Urban-living individuals are exposed to many environmental factors that may combine and interact to influence mental health. While individual factors of an urban environment have been investigated in isolation, no attempt has been made to model how complex, real-life exposure to living in the city relates to brain and mental health, and how this is moderated by genetic factors. Using the data of 156,075 participants from the UK Biobank, we carried out sparse canonical correlation analyses to investigate the relationships between urban environments and psychiatric symptoms. We found an environmental profile of social deprivation, air pollution, street network and urban land-use density that was positively correlated with an affective symptom group (r = 0.22, Pperm < 0.001), mediated by brain volume differences consistent with reward processing, and moderated by genes enriched for stress response, including CRHR1, explaining 2.01% of the variance in brain volume differences. Protective factors such as greenness and generous destination accessibility were negatively correlated with an anxiety symptom group (r = 0.10, Pperm < 0.001), mediated by brain regions necessary for emotion regulation and moderated by EXD3, explaining 1.65% of the variance. The third urban environmental profile was correlated with an emotional instability symptom group (r = 0.03, Pperm < 0.001). Our findings suggest that different environmental profiles of urban living may influence specific psychiatric symptom groups through distinct neurobiological pathways.}, author = {Xu, Jiayuan and Liu, Nana and Polemiti, Elli and Garcia-Mondragon, Liliana and Tang, Jie and Liu, Xiaoxuan and Lett, Tristram and Yu, Le and Nöthen, Markus M. and Feng, Jianfeng and Yu, Chunshui and Marquand, Andre and Schumann, Gunter and Walter, Henrik and Heinz, Andreas and Ralser, Markus and Twardziok, Sven and Vaidya, Nilakshi and Serin, Emin and Jentsch, Marcel and Hitchen, Esther and Eils, Roland and Taron, Ulrike Helene and Schütz, Tatjana and Schepanski, Kerstin and Banks, Jamie and Banaschewski, Tobias and Jansone, Karina and Christmann, Nina and Meyer-Lindenberg, Andreas and Tost, Heike and Holz, Nathalie and Schwarz, Emanuel and Stringaris, Argyris and Neidhart, Maja and Nees, Frauke and Siehl, Sebastian and A. Andreassen, Ole and T. Westlye, Lars and Van Der Meer, Dennis and Fernandez, Sara and Kjelkenes, Rikka and Ask, Helga and Rapp, Michael and Tschorn, Mira and Böttger, Sarah Jane and Novarino, Gaia and Marr, Lena and Slater, Mel and Viapiana, Guillem Feixas and Orosa, Francisco Eiroa and Gallego, Jaime and Pastor, Alvaro and Forstner, Andreas and Hoffmann, Per and M. Nöthen, Markus and J. Forstner, Andreas and Claus, Isabelle and Miller, Abbi and Heilmann-Heimbach, Stefanie and Sommer, Peter and Boye, Mona and Wilbertz, Johannes and Schmitt, Karen and Jirsa, Viktor and Petkoski, Spase and Pitel, Séverine and Otten, Lisa and Athanasiadis, Anastasios Polykarpos and Pearmund, Charlie and Spanlang, Bernhard and Alvarez, Elena and Sanchez, Mavi and Giner, Arantxa and Hese, Sören and Renner, Paul and Jia, Tianye and Gong, Yanting and Xia, Yunman and Chang, Xiao and Calhoun, Vince and Liu, Jingyu and Thompson, Paul and Clinton, Nicholas and Desrivieres, Sylvane and H. Young, Allan and Stahl, Bernd and Ogoh, George}, issn = {1546-170X}, journal = {Nature Medicine}, pages = {1456--1467}, publisher = {Springer Nature}, title = {{Effects of urban living environments on mental health in adults}}, doi = {10.1038/s41591-023-02365-w}, volume = {29}, year = {2023}, } @misc{13173, abstract = {GABAB receptor (GBR) activation inhibits neurotransmitter release in axon terminals in the brain, except in medial habenula (MHb) terminals, which show robust potentiation. However, mechanisms underlying this enigmatic potentiation remain elusive. Here, we report that GBR activation on MHb terminals induces an activity-dependent transition from a facilitating, tonic to a depressing, phasic neurotransmitter release mode. This transition is accompanied by a 4.1-fold increase in readily releasable vesicle pool (RRP) size and a 3.5-fold increase of docked synaptic vesicles at the presynaptic active zone (AZ). Strikingly, tonic and phasic release exhibit distinct coupling distances and are selectively affected by deletion of synaptoporin (SPO) and Ca2+-dependent activator protein for secretion 2 (CAPS2), respectively. SPO modulates augmentation, the short-term plasticity associated with tonic release, and CAPS2 retains the increased RRP for initial responses in phasic response trains. Double pre-embedding immunolabeling confirmed the co-localization of CAPS2 and SPO inside the same terminal. The cytosolic protein CAPS2 showed a synaptic vesicle (SV)-associated distribution similar to the vesicular transmembrane protein SPO. A newly developed “Flash and Freeze-fracture” method revealed the release of SPO-associated vesicles in both tonic and phasic modes and activity-dependent recruitment of CAPS2 to the AZ during phasic release, which lasted several minutes. Overall, these results indicate that GBR activation translocates CAPS2 to the AZ along with the fusion of CAPS2-associated SVs, contributing to a persistent RRP increase. Thus, we discovered structural and molecular mechanisms underlying tonic and phasic neurotransmitter release and their transition by GBR activation in MHb terminals.}, author = {Shigemoto, Ryuichi}, keywords = {medial habenula, GABAB receptor, vesicle release, Flash and Freeze, Flash and Freeze-fracture}, publisher = {Institute of Science and Technology Austria}, title = {{Transition from tonic to phasic neurotransmitter release by presynaptic GABAB receptor activation in medial habenula terminals}}, doi = {10.15479/AT:ISTA:13173}, year = {2023}, } @phdthesis{13175, abstract = {About a 100 years ago, we discovered that our universe is inherently noisy, that is, measuring any physical quantity with a precision beyond a certain point is not possible because of an omnipresent inherent noise. We call this - the quantum noise. Certain physical processes allow this quantum noise to get correlated in conjugate physical variables. These quantum correlations can be used to go beyond the potential of our inherently noisy universe and obtain a quantum advantage over the classical applications. Quantum noise being inherent also means that, at the fundamental level, the physical quantities are not well defined and therefore, objects can stay in multiple states at the same time. For example, the position of a particle not being well defined means that the particle is in multiple positions at the same time. About 4 decades ago, we started exploring the possibility of using objects which can be in multiple states at the same time to increase the dimensionality in computation. Thus, the field of quantum computing was born. We discovered that using quantum entanglement, a property closely related to quantum correlations, can be used to speed up computation of certain problems, such as factorisation of large numbers, faster than any known classical algorithm. Thus began the pursuit to make quantum computers a reality. Till date, we have explored quantum control over many physical systems including photons, spins, atoms, ions and even simple circuits made up of superconducting material. However, there persists one ubiquitous theme. The more readily a system interacts with an external field or matter, the more easily we can control it. But this also means that such a system can easily interact with a noisy environment and quickly lose its coherence. Consequently, such systems like electron spins need to be protected from the environment to ensure the longevity of their coherence. Other systems like nuclear spins are naturally protected as they do not interact easily with the environment. But, due to the same reason, it is harder to interact with such systems. After decades of experimentation with various systems, we are convinced that no one type of quantum system would be the best for all the quantum applications. We would need hybrid systems which are all interconnected - much like the current internet where all sorts of devices can all talk to each other - but now for quantum devices. A quantum internet. Optical photons are the best contenders to carry information for the quantum internet. They can carry quantum information cheaply and without much loss - the same reasons which has made them the backbone of our current internet. Following this direction, many systems, like trapped ions, have already demonstrated successful quantum links over a large distances using optical photons. However, some of the most promising contenders for quantum computing which are based on microwave frequencies have been left behind. This is because high energy optical photons can adversely affect fragile low-energy microwave systems. In this thesis, we present substantial progress on this missing quantum link between microwave and optics using electrooptical nonlinearities in lithium niobate. The nonlinearities are enhanced by using resonant cavities for all the involved modes leading to observation of strong direct coupling between optical and microwave frequencies. With this strong coupling we are not only able to achieve almost 100\% internal conversion efficiency with low added noise, thus presenting a quantum-enabled transducer, but also we are able to observe novel effects such as cooling of a microwave mode using optics. The strong coupling regime also leads to direct observation of dynamical backaction effect between microwave and optical frequencies which are studied in detail here. Finally, we also report first observation of microwave-optics entanglement in form of two-mode squeezed vacuum squeezed 0.7dB below vacuum level. With this new bridge between microwave and optics, the microwave-based quantum technologies can finally be a part of a quantum network which is based on optical photons - putting us one step closer to a future with quantum internet. }, author = {Sahu, Rishabh}, isbn = {978-3-99078-030-5}, issn = {2663 - 337X}, keywords = {quantum optics, electrooptics, quantum networks, quantum communication, transduction}, pages = {202}, publisher = {Institute of Science and Technology Austria}, title = {{Cavity quantum electrooptics}}, doi = {10.15479/at:ista:13175}, year = {2023}, } @article{13177, abstract = {In this note we study the eigenvalue growth of infinite graphs with discrete spectrum. We assume that the corresponding Dirichlet forms satisfy certain Sobolev-type inequalities and that the total measure is finite. In this sense, the associated operators on these graphs display similarities to elliptic operators on bounded domains in the continuum. Specifically, we prove lower bounds on the eigenvalue growth and show by examples that corresponding upper bounds cannot be established.}, author = {Hua, Bobo and Keller, Matthias and Schwarz, Michael and Wirth, Melchior}, issn = {1088-6826}, journal = {Proceedings of the American Mathematical Society}, number = {8}, pages = {3401--3414}, publisher = {American Mathematical Society}, title = {{Sobolev-type inequalities and eigenvalue growth on graphs with finite measure}}, doi = {10.1090/proc/14361}, volume = {151}, year = {2023}, } @article{13178, abstract = {We consider the large polaron described by the Fröhlich Hamiltonian and study its energy-momentum relation defined as the lowest possible energy as a function of the total momentum. Using a suitable family of trial states, we derive an optimal parabolic upper bound for the energy-momentum relation in the limit of strong coupling. The upper bound consists of a momentum independent term that agrees with the predicted two-term expansion for the ground state energy of the strongly coupled polaron at rest and a term that is quadratic in the momentum with coefficient given by the inverse of twice the classical effective mass introduced by Landau and Pekar.}, author = {Mitrouskas, David Johannes and Mysliwy, Krzysztof and Seiringer, Robert}, issn = {2050-5094}, journal = {Forum of Mathematics}, pages = {1--52}, publisher = {Cambridge University Press}, title = {{Optimal parabolic upper bound for the energy-momentum relation of a strongly coupled polaron}}, doi = {10.1017/fms.2023.45}, volume = {11}, year = {2023}, }