@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}, } @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{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{9733, abstract = {This thesis is the result of the research carried out by the author during his PhD at IST Austria between 2017 and 2021. It mainly focuses on the Fröhlich polaron model, specifically to its regime of strong coupling. This model, which is rigorously introduced and discussed in the introduction, has been of great interest in condensed matter physics and field theory for more than eighty years. It is used to describe an electron interacting with the atoms of a solid material (the strength of this interaction is modeled by the presence of a coupling constant α in the Hamiltonian of the system). The particular regime examined here, which is mathematically described by considering the limit α →∞, displays many interesting features related to the emergence of classical behavior, which allows for a simplified effective description of the system under analysis. The properties, the range of validity and a quantitative analysis of the precision of such classical approximations are the main object of the present work. We specify our investigation to the study of the ground state energy of the system, its dynamics and its effective mass. For each of these problems, we provide in the introduction an overview of the previously known results and a detailed account of the original contributions by the author.}, author = {Feliciangeli, Dario}, issn = {2663-337X}, pages = {180}, publisher = {Institute of Science and Technology Austria}, title = {{The polaron at strong coupling}}, doi = {10.15479/at:ista:9733}, 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}, } @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{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}, } @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}, } @phdthesis{9418, abstract = {Deep learning is best known for its empirical success across a wide range of applications spanning computer vision, natural language processing and speech. Of equal significance, though perhaps less known, are its ramifications for learning theory: deep networks have been observed to perform surprisingly well in the high-capacity regime, aka the overfitting or underspecified regime. Classically, this regime on the far right of the bias-variance curve is associated with poor generalisation; however, recent experiments with deep networks challenge this view. This thesis is devoted to investigating various aspects of underspecification in deep learning. First, we argue that deep learning models are underspecified on two levels: a) any given training dataset can be fit by many different functions, and b) any given function can be expressed by many different parameter configurations. We refer to the second kind of underspecification as parameterisation redundancy and we precisely characterise its extent. Second, we characterise the implicit criteria (the inductive bias) that guide learning in the underspecified regime. Specifically, we consider a nonlinear but tractable classification setting, and show that given the choice, neural networks learn classifiers with a large margin. Third, we consider learning scenarios where the inductive bias is not by itself sufficient to deal with underspecification. We then study different ways of ‘tightening the specification’: i) In the setting of representation learning with variational autoencoders, we propose a hand- crafted regulariser based on mutual information. ii) In the setting of binary classification, we consider soft-label (real-valued) supervision. We derive a generalisation bound for linear networks supervised in this way and verify that soft labels facilitate fast learning. Finally, we explore an application of soft-label supervision to the training of multi-exit models.}, author = {Bui Thi Mai, Phuong}, issn = {2663-337X}, pages = {125}, publisher = {Institute of Science and Technology Austria}, title = {{Underspecification in deep learning}}, doi = {10.15479/AT:ISTA:9418}, 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}, } @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}, } @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}, } @article{9818, abstract = {Triangle mesh-based simulations are able to produce satisfying animations of knitted and woven cloth; however, they lack the rich geometric detail of yarn-level simulations. Naive texturing approaches do not consider yarn-level physics, while full yarn-level simulations may become prohibitively expensive for large garments. We propose a method to animate yarn-level cloth geometry on top of an underlying deforming mesh in a mechanics-aware fashion. Using triangle strains to interpolate precomputed yarn geometry, we are able to reproduce effects such as knit loops tightening under stretching. In combination with precomputed mesh animation or real-time mesh simulation, our method is able to animate yarn-level cloth in real-time at large scales.}, author = {Sperl, Georg and Narain, Rahul and Wojtan, Christopher J}, issn = {1557-7368}, journal = {ACM Transactions on Graphics}, number = {4}, publisher = {Association for Computing Machinery}, title = {{Mechanics-aware deformation of yarn pattern geometry}}, doi = {10.1145/3450626.3459816}, volume = {40}, year = {2021}, } @misc{9327, abstract = {This archive contains the missing sweater mesh animations and displacement models for the code of "Mechanics-Aware Deformation of Yarn Pattern Geometry" Code Repository: https://git.ist.ac.at/gsperl/MADYPG}, author = {Sperl, Georg and Narain, Rahul and Wojtan, Christopher J}, publisher = {IST Austria}, title = {{Mechanics-Aware Deformation of Yarn Pattern Geometry (Additional Animation/Model Data)}}, doi = {10.15479/AT:ISTA:9327}, year = {2021}, } @inproceedings{9826, abstract = {Automated contract tracing aims at supporting manual contact tracing during pandemics by alerting users of encounters with infected people. There are currently many proposals for protocols (like the “decentralized” DP-3T and PACT or the “centralized” ROBERT and DESIRE) to be run on mobile phones, where the basic idea is to regularly broadcast (using low energy Bluetooth) some values, and at the same time store (a function of) incoming messages broadcasted by users in their proximity. In the existing proposals one can trigger false positives on a massive scale by an “inverse-Sybil” attack, where a large number of devices (malicious users or hacked phones) pretend to be the same user, such that later, just a single person needs to be diagnosed (and allowed to upload) to trigger an alert for all users who were in proximity to any of this large group of devices. We propose the first protocols that do not succumb to such attacks assuming the devices involved in the attack do not constantly communicate, which we observe is a necessary assumption. The high level idea of the protocols is to derive the values to be broadcasted by a hash chain, so that two (or more) devices who want to launch an inverse-Sybil attack will not be able to connect their respective chains and thus only one of them will be able to upload. Our protocols also achieve security against replay, belated replay, and one of them even against relay attacks.}, author = {Auerbach, Benedikt and Chakraborty, Suvradip and Klein, Karen and Pascual Perez, Guillermo and Pietrzak, Krzysztof Z and Walter, Michael and Yeo, Michelle X}, booktitle = {Topics in Cryptology – CT-RSA 2021}, isbn = {9783030755386}, issn = {1611-3349}, location = {Virtual Event}, pages = {399--421}, publisher = {Springer Nature}, title = {{Inverse-Sybil attacks in automated contact tracing}}, doi = {10.1007/978-3-030-75539-3_17}, volume = {12704}, year = {2021}, } @phdthesis{10035, abstract = {Many security definitions come in two flavors: a stronger “adaptive” flavor, where the adversary can arbitrarily make various choices during the course of the attack, and a weaker “selective” flavor where the adversary must commit to some or all of their choices a-priori. For example, in the context of identity-based encryption, selective security requires the adversary to decide on the identity of the attacked party at the very beginning of the game whereas adaptive security allows the attacker to first see the master public key and some secret keys before making this choice. Often, it appears to be much easier to achieve selective security than it is to achieve adaptive security. A series of several recent works shows how to cleverly achieve adaptive security in several such scenarios including generalized selective decryption [Pan07][FJP15], constrained PRFs [FKPR14], and Yao’s garbled circuits [JW16]. Although the above works expressed vague intuition that they share a common technique, the connection was never made precise. In this work we present a new framework (published at Crypto ’17 [JKK+17a]) that connects all of these works and allows us to present them in a unified and simplified fashion. Having the framework in place, we show how to achieve adaptive security for proxy re-encryption schemes (published at PKC ’19 [FKKP19]) and provide the first adaptive security proofs for continuous group key agreement protocols (published at S&P ’21 [KPW+21]). Questioning optimality of our framework, we then show that currently used proof techniques cannot lead to significantly better security guarantees for "graph-building" games (published at TCC ’21 [KKPW21a]). These games cover generalized selective decryption, as well as the security of prominent constructions for constrained PRFs, continuous group key agreement, and proxy re-encryption. Finally, we revisit the adaptive security of Yao’s garbled circuits and extend the analysis of Jafargholi and Wichs in two directions: While they prove adaptive security only for a modified construction with increased online complexity, we provide the first positive results for the original construction by Yao (published at TCC ’21 [KKP21a]). On the negative side, we prove that the results of Jafargholi and Wichs are essentially optimal by showing that no black-box reduction can provide a significantly better security bound (published at Crypto ’21 [KKPW21c]).}, author = {Klein, Karen}, issn = {2663-337X}, pages = {276}, publisher = {Institute of Science and Technology Austria}, title = {{On the adaptive security of graph-based games}}, doi = {10.15479/at:ista:10035}, year = {2021}, } @article{9760, abstract = {The quantum approximate optimization algorithm (QAOA) is a prospective near-term quantum algorithm due to its modest circuit depth and promising benchmarks. However, an external parameter optimization required in the QAOA could become a performance bottleneck. This motivates studies of the optimization landscape and search for heuristic ways of parameter initialization. In this work we visualize the optimization landscape of the QAOA applied to the MaxCut problem on random graphs, demonstrating that random initialization of the QAOA is prone to converging to local minima with suboptimal performance. We introduce the initialization of QAOA parameters based on the Trotterized quantum annealing (TQA) protocol, parameterized by the Trotter time step. We find that the TQA initialization allows to circumvent the issue of false minima for a broad range of time steps, yielding the same performance as the best result out of an exponentially scaling number of random initializations. Moreover, we demonstrate that the optimal value of the time step coincides with the point of proliferation of Trotter errors in quantum annealing. Our results suggest practical ways of initializing QAOA protocols on near-term quantum devices and reveal new connections between QAOA and quantum annealing.}, author = {Sack, Stefan and Serbyn, Maksym}, issn = {2521-327X}, journal = {Quantum}, publisher = {Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften}, title = {{Quantum annealing initialization of the quantum approximate optimization algorithm}}, doi = {10.22331/Q-2021-07-01-491}, volume = {5}, year = {2021}, } @unpublished{10077, abstract = {Although much is known about how single neurons in the hippocampus represent an animal’s position, how cell-cell interactions contribute to spatial coding remains poorly understood. Using a novel statistical estimator and theoretical modeling, both developed in the framework of maximum entropy models, we reveal highly structured cell-to-cell interactions whose statistics depend on familiar vs. novel environment. In both conditions the circuit interactions optimize the encoding of spatial information, but for regimes that differ in the signal-to-noise ratio of their spatial inputs. Moreover, the topology of the interactions facilitates linear decodability, making the information easy to read out by downstream circuits. These findings suggest that the efficient coding hypothesis is not applicable only to individual neuron properties in the sensory periphery, but also to neural interactions in the central brain.}, author = {Nardin, Michele and Csicsvari, Jozsef L and Tkačik, Gašper and Savin, Cristina}, booktitle = {bioRxiv}, publisher = {Cold Spring Harbor Laboratory}, title = {{The structure of hippocampal CA1 interactions optimizes spatial coding across experience}}, doi = {10.1101/2021.09.28.460602}, 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{9992, abstract = {Blood – this is what animals use to heal wounds fast and efficient. Plants do not have blood circulation and their cells cannot move. However, plants have evolved remarkable capacities to regenerate tissues and organs preventing further damage. In my PhD research, I studied the wound healing in the Arabidopsis root. I used a UV laser to ablate single cells in the root tip and observed the consequent wound healing. Interestingly, the inner adjacent cells induced a division plane switch and subsequently adopted the cell type of the killed cell to replace it. We termed this form of wound healing “restorative divisions”. This initial observation triggered the questions of my PhD studies: How and why do cells orient their division planes, how do they feel the wound and why does this happen only in inner adjacent cells. For answering these questions, I used a quite simple experimental setup: 5 day - old seedlings were stained with propidium iodide to visualize cell walls and dead cells; ablation was carried out using a special laser cutter and a confocal microscope. Adaptation of the novel vertical microscope system made it possible to observe wounds in real time. This revealed that restorative divisions occur at increased frequency compared to normal divisions. Additionally, the major plant hormone auxin accumulates in wound adjacent cells and drives the expression of the wound-stress responsive transcription factor ERF115. Using this as a marker gene for wound responses, we found that an important part of wound signalling is the sensing of the collapse of the ablated cell. The collapse causes a radical pressure drop, which results in strong tissue deformations. These deformations manifest in an invasion of the now free spot specifically by the inner adjacent cells within seconds, probably because of higher pressure of the inner tissues. Long-term imaging revealed that those deformed cells continuously expand towards the wound hole and that this is crucial for the restorative division. These wound-expanding cells exhibit an abnormal, biphasic polarity of microtubule arrays before the division. Experiments inhibiting cell expansion suggest that it is the biphasic stretching that induces those MT arrays. Adapting the micromanipulator aspiration system from animal scientists at our institute confirmed the hypothesis that stretching influences microtubule stability. In conclusion, this shows that microtubules react to tissue deformation and this facilitates the observed division plane switch. This puts mechanical cues and tensions at the most prominent position for explaining the growth and wound healing properties of plants. Hence, it shines light onto the importance of understanding mechanical signal transduction. }, author = {Hörmayer, Lukas}, issn = {2663-337X}, pages = {168}, publisher = {Institute of Science and Technology Austria}, title = {{Wound healing in the Arabidopsis root meristem}}, doi = {10.15479/at:ista:9992}, year = {2021}, }