@phdthesis{10135, abstract = {Plants maintain the capacity to develop new organs e.g. lateral roots post-embryonically throughout their whole life and thereby flexibly adapt to ever-changing environmental conditions. Plant hormones auxin and cytokinin are the main regulators of the lateral root organogenesis. Additionally to their solo activities, the interaction between auxin and cytokinin plays crucial role in fine-tuning of lateral root development and growth. In particular, cytokinin modulates auxin distribution within the developing lateral root by affecting the endomembrane trafficking of auxin transporter PIN1 and promoting its vacuolar degradation (Marhavý et al., 2011, 2014). This effect is independent of transcription and translation. Therefore, it suggests novel, non-canonical cytokinin activity occuring possibly on the posttranslational level. Impact of cytokinin and other plant hormones on auxin transporters (including PIN1) on the posttranslational level is described in detail in the introduction part of this thesis in a form of a review (Semeradova et al., 2020). To gain insights into the molecular machinery underlying cytokinin effect on the endomembrane trafficking in the plant cell, in particular on the PIN1 degradation, we conducted two large proteomic screens: 1) Identification of cytokinin binding proteins using chemical proteomics. 2) Monitoring of proteomic and phosphoproteomic changes upon cytokinin treatment. In the first screen, we identified DYNAMIN RELATED PROTEIN 2A (DRP2A). We found that DRP2A plays a role in cytokinin regulated processes during the plant growth and that cytokinin treatment promotes destabilization of DRP2A protein. However, the role of DRP2A in the PIN1 degradation remains to be elucidated. In the second screen, we found VACUOLAR PROTEIN SORTING 9A (VPS9A). VPS9a plays crucial role in plant’s response to cytokin and in cytokinin mediated PIN1 degradation. Altogether, we identified proteins, which bind to cytokinin and proteins that in response to cytokinin exhibit significantly changed abundance or phosphorylation pattern. By combining information from these two screens, we can pave our way towards understanding of noncanonical cytokinin effects.}, author = {Semerádová, Hana}, isbn = {978-3-99078-014-5}, issn = {2663-337X}, publisher = {Institute of Science and Technology Austria}, title = {{Molecular mechanisms of the cytokinin-regulated endomembrane trafficking to coordinate plant organogenesis}}, doi = {10.15479/at:ista:10135}, 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}, } @phdthesis{10199, abstract = {The design and verification of concurrent systems remains an open challenge due to the non-determinism that arises from the inter-process communication. In particular, concurrent programs are notoriously difficult both to be written correctly and to be analyzed formally, as complex thread interaction has to be accounted for. The difficulties are further exacerbated when concurrent programs get executed on modern-day hardware, which contains various buffering and caching mechanisms for efficiency reasons. This causes further subtle non-determinism, which can often produce very unintuitive behavior of the concurrent programs. Model checking is at the forefront of tackling the verification problem, where the task is to decide, given as input a concurrent system and a desired property, whether the system satisfies the property. The inherent state-space explosion problem in model checking of concurrent systems causes naïve explicit methods not to scale, thus more inventive methods are required. One such method is stateless model checking (SMC), which explores in memory-efficient manner the program executions rather than the states of the program. State-of-the-art SMC is typically coupled with partial order reduction (POR) techniques, which argue that certain executions provably produce identical system behavior, thus limiting the amount of executions one needs to explore in order to cover all possible behaviors. Another method to tackle the state-space explosion is symbolic model checking, where the considered techniques operate on a succinct implicit representation of the input system rather than explicitly accessing the system. In this thesis we present new techniques for verification of concurrent systems. We present several novel POR methods for SMC of concurrent programs under various models of semantics, some of which account for write-buffering mechanisms. Additionally, we present novel algorithms for symbolic model checking of finite-state concurrent systems, where the desired property of the systems is to ensure a formally defined notion of fairness.}, author = {Toman, Viktor}, issn = {2663-337X}, keywords = {concurrency, verification, model checking}, pages = {166}, publisher = {Institute of Science and Technology Austria}, title = {{Improved verification techniques for concurrent systems}}, doi = {10.15479/at:ista:10199}, year = {2021}, } @phdthesis{10293, abstract = {Indirect reciprocity in evolutionary game theory is a prominent mechanism for explaining the evolution of cooperation among unrelated individuals. In contrast to direct reciprocity, which is based on individuals meeting repeatedly, and conditionally cooperating by using their own experiences, indirect reciprocity is based on individuals’ reputations. If a player helps another, this increases the helper’s public standing, benefitting them in the future. This lets cooperation in the population emerge without individuals having to meet more than once. While the two modes of reciprocity are intertwined, they are difficult to compare. Thus, they are usually studied in isolation. Direct reciprocity can maintain cooperation with simple strategies, and is robust against noise even when players do not remember more than their partner’s last action. Meanwhile, indirect reciprocity requires its successful strategies, or social norms, to be more complex. Exhaustive search previously identified eight such norms, called the “leading eight”, which excel at maintaining cooperation. However, as the first result of this thesis, we show that the leading eight break down once we remove the fundamental assumption that information is synchronized and public, such that everyone agrees on reputations. Once we consider a more realistic scenario of imperfect information, where reputations are private, and individuals occasionally misinterpret or miss observations, the leading eight do not promote cooperation anymore. Instead, minor initial disagreements can proliferate, fragmenting populations into subgroups. In a next step, we consider ways to mitigate this issue. We first explore whether introducing “generosity” can stabilize cooperation when players use the leading eight strategies in noisy environments. This approach of modifying strategies to include probabilistic elements for coping with errors is known to work well in direct reciprocity. However, as we show here, it fails for the more complex norms of indirect reciprocity. Imperfect information still prevents cooperation from evolving. On the other hand, we succeeded to show in this thesis that modifying the leading eight to use “quantitative assessment”, i.e. tracking reputation scores on a scale beyond good and bad, and making overall judgments of others based on a threshold, is highly successful, even when noise increases in the environment. Cooperation can flourish when reputations are more nuanced, and players have a broader understanding what it means to be “good.” Finally, we present a single theoretical framework that unites the two modes of reciprocity despite their differences. Within this framework, we identify a novel simple and successful strategy for indirect reciprocity, which can cope with noisy environments and has an analogue in direct reciprocity. We can also analyze decision making when different sources of information are available. Our results help highlight that for sustaining cooperation, already the most simple rules of reciprocity can be sufficient.}, author = {Schmid, Laura}, issn = {2663-337X}, pages = {171}, publisher = {Institute of Science and Technology Austria}, title = {{Evolution of cooperation via (in)direct reciprocity under imperfect information}}, doi = {10.15479/at:ista:10293}, year = {2021}, } @phdthesis{10303, abstract = {Nitrogen is an essential macronutrient determining plant growth, development and affecting agricultural productivity. Root, as a hub that perceives and integrates local and systemic signals on the plant’s external and endogenous nitrogen resources, communicates with other plant organs to consolidate their physiology and development in accordance with actual nitrogen balance. Over the last years, numerous studies demonstrated that these comprehensive developmental adaptations rely on the interaction between pathways controlling nitrogen homeostasis and hormonal networks acting globally in the plant body. However, molecular insights into how the information about the nitrogen status is translated through hormonal pathways into specific developmental output are lacking. In my work, I addressed so far poorly understood mechanisms underlying root-to-shoot communication that lead to a rapid re-adjustment of shoot growth and development after nitrate provision. Applying a combination of molecular, cell, and developmental biology approaches, genetics and grafting experiments as well as hormonal analytics, I identified and characterized an unknown molecular framework orchestrating shoot development with a root nitrate sensory system. }, author = {Abualia, Rashed}, issn = {2663-337X}, pages = {139}, publisher = {Institute of Science and Technology Austria}, title = {{Role of hormones in nitrate regulated growth}}, doi = {10.15479/at:ista:10303}, year = {2021}, } @phdthesis{10307, abstract = {Bacteria-host interactions represent a continuous trade-off between benefit and risk. Thus, the host immune response is faced with a non-trivial problem – accommodate beneficial commensals and remove harmful pathogens. This is especially difficult as molecular patterns, such as lipopolysaccharide or specific surface organelles such as pili, are conserved in both, commensal and pathogenic bacteria. Type 1 pili, tightly regulated by phase variation, are considered an important virulence factor of pathogenic bacteria as they facilitate invasion into host cells. While invasion represents a de facto passive mechanism for pathogens to escape the host immune response, we demonstrate a fundamental role of type 1 pili as active modulators of the innate and adaptive immune response.}, author = {Tomasek, Kathrin}, issn = {2663-337X}, pages = {73}, publisher = {Institute of Science and Technology Austria}, title = {{Pathogenic Escherichia coli hijack the host immune response}}, doi = {10.15479/at:ista:10307}, year = {2021}, } @phdthesis{10422, abstract = {Those who aim to devise new materials with desirable properties usually examine present methods first. However, they will find out that some approaches can exist only conceptually without high chances to become practically useful. It seems that a numerical technique called automatic differentiation together with increasing supply of computational accelerators will soon shift many methods of the material design from the category ”unimaginable” to the category ”expensive but possible”. Approach we suggest is not an exception. Our overall goal is to have an efficient and generalizable approach allowing to solve inverse design problems. In this thesis we scratch its surface. We consider jammed systems of identical particles. And ask ourselves how the shape of those particles (or the parameters codifying it) may affect mechanical properties of the system. An indispensable part of reaching the answer is an appropriate particle parametrization. We come up with a simple, yet generalizable and purposeful scheme for it. Using our generalizable shape parameterization, we simulate the formation of a solid composed of pentagonal-like particles and measure anisotropy in the resulting elastic response. Through automatic differentiation techniques, we directly connect the shape parameters with the elastic response. Interestingly, for our system we find that less isotropic particles lead to a more isotropic elastic response. Together with other results known about our method it seems that it can be successfully generalized for different inverse design problems.}, author = {Piankov, Anton}, issn = {2791-4585}, publisher = {Institute of Science and Technology Austria}, title = {{Towards designer materials using customizable particle shape}}, doi = {10.15479/at:ista:10422}, year = {2021}, } @phdthesis{10429, abstract = {The scalability of concurrent data structures and distributed algorithms strongly depends on reducing the contention for shared resources and the costs of synchronization and communication. We show how such cost reductions can be attained by relaxing the strict consistency conditions required by sequential implementations. In the first part of the thesis, we consider relaxation in the context of concurrent data structures. Specifically, in data structures such as priority queues, imposing strong semantics renders scalability impossible, since a correct implementation of the remove operation should return only the element with highest priority. Intuitively, attempting to invoke remove operations concurrently creates a race condition. This bottleneck can be circumvented by relaxing semantics of the affected data structure, thus allowing removal of the elements which are no longer required to have the highest priority. We prove that the randomized implementations of relaxed data structures provide provable guarantees on the priority of the removed elements even under concurrency. Additionally, we show that in some cases the relaxed data structures can be used to scale the classical algorithms which are usually implemented with the exact ones. In the second part, we study parallel variants of the stochastic gradient descent (SGD) algorithm, which distribute computation among the multiple processors, thus reducing the running time. Unfortunately, in order for standard parallel SGD to succeed, each processor has to maintain a local copy of the necessary model parameter, which is identical to the local copies of other processors; the overheads from this perfect consistency in terms of communication and synchronization can negate the speedup gained by distributing the computation. We show that the consistency conditions required by SGD can be relaxed, allowing the algorithm to be more flexible in terms of tolerating quantized communication, asynchrony, or even crash faults, while its convergence remains asymptotically the same.}, author = {Nadiradze, Giorgi}, issn = {2663-337X}, pages = {132}, publisher = {Institute of Science and Technology Austria}, title = {{On achieving scalability through relaxation}}, doi = {10.15479/at:ista:10429}, year = {2021}, } @article{10635, abstract = {The brain efficiently performs nonlinear computations through its intricate networks of spiking neurons, but how this is done remains elusive. While nonlinear computations can be implemented successfully in spiking neural networks, this requires supervised training and the resulting connectivity can be hard to interpret. In contrast, the required connectivity for any computation in the form of a linear dynamical system can be directly derived and understood with the spike coding network (SCN) framework. These networks also have biologically realistic activity patterns and are highly robust to cell death. Here we extend the SCN framework to directly implement any polynomial dynamical system, without the need for training. This results in networks requiring a mix of synapse types (fast, slow, and multiplicative), which we term multiplicative spike coding networks (mSCNs). Using mSCNs, we demonstrate how to directly derive the required connectivity for several nonlinear dynamical systems. We also show how to carry out higher-order polynomials with coupled networks that use only pair-wise multiplicative synapses, and provide expected numbers of connections for each synapse type. Overall, our work demonstrates a novel method for implementing nonlinear computations in spiking neural networks, while keeping the attractive features of standard SCNs (robustness, realistic activity patterns, and interpretable connectivity). Finally, we discuss the biological plausibility of our approach, and how the high accuracy and robustness of the approach may be of interest for neuromorphic computing.}, author = {Nardin, Michele and Phillips, James W. and Podlaski, William F. and Keemink, Sander W.}, issn = {2804-3871}, journal = {Peer Community Journal}, publisher = {Peer Community In}, title = {{Nonlinear computations in spiking neural networks through multiplicative synapses}}, doi = {10.24072/pcjournal.69}, volume = {1}, year = {2021}, } @inproceedings{10665, abstract = {Formal verification of neural networks is an active topic of research, and recent advances have significantly increased the size of the networks that verification tools can handle. However, most methods are designed for verification of an idealized model of the actual network which works over real arithmetic and ignores rounding imprecisions. This idealization is in stark contrast to network quantization, which is a technique that trades numerical precision for computational efficiency and is, therefore, often applied in practice. Neglecting rounding errors of such low-bit quantized neural networks has been shown to lead to wrong conclusions about the network’s correctness. Thus, the desired approach for verifying quantized neural networks would be one that takes these rounding errors into account. In this paper, we show that verifying the bitexact implementation of quantized neural networks with bitvector specifications is PSPACE-hard, even though verifying idealized real-valued networks and satisfiability of bit-vector specifications alone are each in NP. Furthermore, we explore several practical heuristics toward closing the complexity gap between idealized and bit-exact verification. In particular, we propose three techniques for making SMT-based verification of quantized neural networks more scalable. Our experiments demonstrate that our proposed methods allow a speedup of up to three orders of magnitude over existing approaches.}, author = {Henzinger, Thomas A and Lechner, Mathias and Zikelic, Dorde}, booktitle = {Proceedings of the AAAI Conference on Artificial Intelligence}, isbn = {978-1-57735-866-4}, issn = {2374-3468}, location = {Virtual}, number = {5A}, pages = {3787--3795}, publisher = {AAAI Press}, title = {{Scalable verification of quantized neural networks}}, volume = {35}, year = {2021}, } @inproceedings{10666, abstract = {Adversarial training is an effective method to train deep learning models that are resilient to norm-bounded perturbations, with the cost of nominal performance drop. While adversarial training appears to enhance the robustness and safety of a deep model deployed in open-world decision-critical applications, counterintuitively, it induces undesired behaviors in robot learning settings. In this paper, we show theoretically and experimentally that neural controllers obtained via adversarial training are subjected to three types of defects, namely transient, systematic, and conditional errors. We first generalize adversarial training to a safety-domain optimization scheme allowing for more generic specifications. We then prove that such a learning process tends to cause certain error profiles. We support our theoretical results by a thorough experimental safety analysis in a robot-learning task. Our results suggest that adversarial training is not yet ready for robot learning.}, author = {Lechner, Mathias and Hasani, Ramin and Grosu, Radu and Rus, Daniela and Henzinger, Thomas A}, booktitle = {2021 IEEE International Conference on Robotics and Automation}, isbn = {978-1-7281-9078-5}, issn = {2577-087X}, location = {Xi'an, China}, pages = {4140--4147}, title = {{Adversarial training is not ready for robot learning}}, doi = {10.1109/ICRA48506.2021.9561036}, year = {2021}, } @inproceedings{10667, abstract = {Bayesian neural networks (BNNs) place distributions over the weights of a neural network to model uncertainty in the data and the network's prediction. We consider the problem of verifying safety when running a Bayesian neural network policy in a feedback loop with infinite time horizon systems. Compared to the existing sampling-based approaches, which are inapplicable to the infinite time horizon setting, we train a separate deterministic neural network that serves as an infinite time horizon safety certificate. In particular, we show that the certificate network guarantees the safety of the system over a subset of the BNN weight posterior's support. Our method first computes a safe weight set and then alters the BNN's weight posterior to reject samples outside this set. Moreover, we show how to extend our approach to a safe-exploration reinforcement learning setting, in order to avoid unsafe trajectories during the training of the policy. We evaluate our approach on a series of reinforcement learning benchmarks, including non-Lyapunovian safety specifications.}, author = {Lechner, Mathias and Žikelić, Ðorđe and Chatterjee, Krishnendu and Henzinger, Thomas A}, booktitle = {35th Conference on Neural Information Processing Systems}, location = {Virtual}, title = {{Infinite time horizon safety of Bayesian neural networks}}, doi = {10.48550/arXiv.2111.03165}, year = {2021}, } @inproceedings{10668, abstract = {Robustness to variations in lighting conditions is a key objective for any deep vision system. To this end, our paper extends the receptive field of convolutional neural networks with two residual components, ubiquitous in the visual processing system of vertebrates: On-center and off-center pathways, with an excitatory center and inhibitory surround; OOCS for short. The On-center pathway is excited by the presence of a light stimulus in its center, but not in its surround, whereas the Off-center pathway is excited by the absence of a light stimulus in its center, but not in its surround. We design OOCS pathways via a difference of Gaussians, with their variance computed analytically from the size of the receptive fields. OOCS pathways complement each other in their response to light stimuli, ensuring this way a strong edge-detection capability, and as a result an accurate and robust inference under challenging lighting conditions. We provide extensive empirical evidence showing that networks supplied with OOCS pathways gain accuracy and illumination-robustness from the novel edge representation, compared to other baselines.}, author = {Babaiee, Zahra and Hasani, Ramin and Lechner, Mathias and Rus, Daniela and Grosu, Radu}, booktitle = {Proceedings of the 38th International Conference on Machine Learning}, issn = {2640-3498}, location = {Virtual}, pages = {478--489}, publisher = {ML Research Press}, title = {{On-off center-surround receptive fields for accurate and robust image classification}}, volume = {139}, year = {2021}, } @inproceedings{10669, abstract = {We show that Neural ODEs, an emerging class of timecontinuous neural networks, can be verified by solving a set of global-optimization problems. For this purpose, we introduce Stochastic Lagrangian Reachability (SLR), an abstraction-based technique for constructing a tight Reachtube (an over-approximation of the set of reachable states over a given time-horizon), and provide stochastic guarantees in the form of confidence intervals for the Reachtube bounds. SLR inherently avoids the infamous wrapping effect (accumulation of over-approximation errors) by performing local optimization steps to expand safe regions instead of repeatedly forward-propagating them as is done by deterministic reachability methods. To enable fast local optimizations, we introduce a novel forward-mode adjoint sensitivity method to compute gradients without the need for backpropagation. Finally, we establish asymptotic and non-asymptotic convergence rates for SLR.}, author = {Grunbacher, Sophie and Hasani, Ramin and Lechner, Mathias and Cyranka, Jacek and Smolka, Scott A and Grosu, Radu}, booktitle = {Proceedings of the AAAI Conference on Artificial Intelligence}, isbn = {978-1-57735-866-4}, issn = {2374-3468}, location = {Virtual}, number = {13}, pages = {11525--11535}, publisher = {AAAI Press}, title = {{On the verification of neural ODEs with stochastic guarantees}}, volume = {35}, year = {2021}, } @inproceedings{10670, abstract = {Imitation learning enables high-fidelity, vision-based learning of policies within rich, photorealistic environments. However, such techniques often rely on traditional discrete-time neural models and face difficulties in generalizing to domain shifts by failing to account for the causal relationships between the agent and the environment. In this paper, we propose a theoretical and experimental framework for learning causal representations using continuous-time neural networks, specifically over their discrete-time counterparts. We evaluate our method in the context of visual-control learning of drones over a series of complex tasks, ranging from short- and long-term navigation, to chasing static and dynamic objects through photorealistic environments. Our results demonstrate that causal continuous-time deep models can perform robust navigation tasks, where advanced recurrent models fail. These models learn complex causal control representations directly from raw visual inputs and scale to solve a variety of tasks using imitation learning.}, author = {Vorbach, Charles J and Hasani, Ramin and Amini, Alexander and Lechner, Mathias and Rus, Daniela}, booktitle = {35th Conference on Neural Information Processing Systems}, location = {Virtual}, title = {{Causal navigation by continuous-time neural networks}}, year = {2021}, } @inproceedings{10671, abstract = {We introduce a new class of time-continuous recurrent neural network models. Instead of declaring a learning system’s dynamics by implicit nonlinearities, we construct networks of linear first-order dynamical systems modulated via nonlinear interlinked gates. The resulting models represent dynamical systems with varying (i.e., liquid) time-constants coupled to their hidden state, with outputs being computed by numerical differential equation solvers. These neural networks exhibit stable and bounded behavior, yield superior expressivity within the family of neural ordinary differential equations, and give rise to improved performance on time-series prediction tasks. To demonstrate these properties, we first take a theoretical approach to find bounds over their dynamics, and compute their expressive power by the trajectory length measure in a latent trajectory space. We then conduct a series of time-series prediction experiments to manifest the approximation capability of Liquid Time-Constant Networks (LTCs) compared to classical and modern RNNs.}, author = {Hasani, Ramin and Lechner, Mathias and Amini, Alexander and Rus, Daniela and Grosu, Radu}, booktitle = {Proceedings of the AAAI Conference on Artificial Intelligence}, isbn = {978-1-57735-866-4}, issn = {2374-3468}, location = {Virtual}, number = {9}, pages = {7657--7666}, publisher = {AAAI Press}, title = {{Liquid time-constant networks}}, volume = {35}, year = {2021}, } @inproceedings{10694, abstract = {In a two-player zero-sum graph game the players move a token throughout a graph to produce an infinite path, which determines the winner or payoff of the game. Traditionally, the players alternate turns in moving the token. In bidding games, however, the players have budgets, and in each turn, we hold an “auction” (bidding) to determine which player moves the token: both players simultaneously submit bids and the higher bidder moves the token. The bidding mechanisms differ in their payment schemes. Bidding games were largely studied with variants of first-price bidding in which only the higher bidder pays his bid. We focus on all-pay bidding, where both players pay their bids. Finite-duration all-pay bidding games were studied and shown to be technically more challenging than their first-price counterparts. We study for the first time, infinite-duration all-pay bidding games. Our most interesting results are for mean-payoff objectives: we portray a complete picture for games played on strongly-connected graphs. We study both pure (deterministic) and mixed (probabilistic) strategies and completely characterize the optimal and almost-sure (with probability 1) payoffs the players can respectively guarantee. We show that mean-payoff games under all-pay bidding exhibit the intriguing mathematical properties of their first-price counterparts; namely, an equivalence with random-turn games in which in each turn, the player who moves is selected according to a (biased) coin toss. The equivalences for all-pay bidding are more intricate and unexpected than for first-price bidding.}, author = {Avni, Guy and Jecker, Ismael R and Zikelic, Dorde}, booktitle = {Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms}, editor = {Marx, Dániel}, isbn = {978-1-61197-646-5}, location = {Virtual}, pages = {617--636}, publisher = {Society for Industrial and Applied Mathematics}, title = {{Infinite-duration all-pay bidding games}}, doi = {10.1137/1.9781611976465.38}, year = {2021}, } @article{8909, abstract = {Spin qubits are considered to be among the most promising candidates for building a quantum processor. Group IV hole spin qubits have moved into the focus of interest due to the ease of operation and compatibility with Si technology. In addition, Ge offers the option for monolithic superconductor-semiconductor integration. Here we demonstrate a hole spin qubit operating at fields below 10 mT, the critical field of Al, by exploiting the large out-of-plane hole g-factors in planar Ge and by encoding the qubit into the singlet-triplet states of a double quantum dot. We observe electrically controlled X and Z-rotations with tunable frequencies exceeding 100 MHz and dephasing times of 1μs which we extend beyond 15μs with echo techniques. These results show that Ge hole singlet triplet qubits outperform their electronic Si and GaAs based counterparts in speed and coherence, respectively. In addition, they are on par with Ge single spin qubits, but can be operated at much lower fields underlining their potential for on chip integration with superconducting technologies.}, author = {Jirovec, Daniel and Hofmann, Andrea C and Ballabio, Andrea and Mutter, Philipp M. and Tavani, Giulio and Botifoll, Marc and Crippa, Alessandro and Kukucka, Josip and Sagi, Oliver and Martins, Frederico and Saez Mollejo, Jaime and Prieto Gonzalez, Ivan and Borovkov, Maksim and Arbiol, Jordi and Chrastina, Daniel and Isella, Giovanni and Katsaros, Georgios}, issn = {1476-4660}, journal = {Nature Materials}, number = {8}, pages = {1106–1112}, publisher = {Springer Nature}, title = {{A singlet triplet hole spin qubit in planar Ge}}, doi = {10.1038/s41563-021-01022-2}, volume = {20}, year = {2021}, } @phdthesis{8934, abstract = {In this thesis, we consider several of the most classical and fundamental problems in static analysis and formal verification, including invariant generation, reachability analysis, termination analysis of probabilistic programs, data-flow analysis, quantitative analysis of Markov chains and Markov decision processes, and the problem of data packing in cache management. We use techniques from parameterized complexity theory, polyhedral geometry, and real algebraic geometry to significantly improve the state-of-the-art, in terms of both scalability and completeness guarantees, for the mentioned problems. In some cases, our results are the first theoretical improvements for the respective problems in two or three decades.}, author = {Goharshady, Amir Kafshdar}, issn = {2663-337X}, pages = {278}, publisher = {Institute of Science and Technology Austria}, title = {{Parameterized and algebro-geometric advances in static program analysis}}, doi = {10.15479/AT:ISTA:8934}, 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}, }