@article{10607, abstract = {The evidence linking innate immunity mechanisms and neurodegenerative diseases is growing, but the specific mechanisms are incompletely understood. Experimental data suggest that microglial TLR4 mediates the uptake and clearance of α-synuclein also termed synucleinophagy. The accumulation of misfolded α-synuclein throughout the brain is central to Parkinson's disease (PD). The distribution and progression of the pathology is often attributed to the propagation of α-synuclein. Here, we apply a classical α-synuclein propagation model of prodromal PD in wild type and TLR4 deficient mice to study the role of TLR4 in the progression of the disease. Our data suggest that TLR4 deficiency facilitates the α-synuclein seed spreading associated with reduced lysosomal activity of microglia. Three months after seed inoculation, more pronounced proteinase K-resistant α-synuclein inclusion pathology is observed in mice with TLR4 deficiency. The facilitated propagation of α-synuclein is associated with early loss of dopamine transporter (DAT) signal in the striatum and loss of dopaminergic neurons in substantia nigra pars compacta of TLR4 deficient mice. These new results support TLR4 signaling as a putative target for disease modification to slow the progression of PD and related disorders.}, author = {Venezia, Serena and Kaufmann, Walter and Wenning, Gregor K. and Stefanova, Nadia}, issn = {1873-5126}, journal = {Parkinsonism & Related Disorders}, pages = {59--65}, publisher = {Elsevier}, title = {{Toll-like receptor 4 deficiency facilitates α-synuclein propagation and neurodegeneration in a mouse model of prodromal Parkinson's disease}}, doi = {10.1016/j.parkreldis.2021.09.007}, volume = {91}, year = {2021}, } @article{10608, abstract = {We consider infinite-dimensional properties in coarse geometry for hyperspaces consisting of finite subsets of metric spaces with the Hausdorff metric. We see that several infinite-dimensional properties are preserved by taking the hyperspace of subsets with at most n points. On the other hand, we prove that, if a metric space contains a sequence of long intervals coarsely, then its hyperspace of finite subsets is not coarsely embeddable into any uniformly convex Banach space. As a corollary, the hyperspace of finite subsets of the real line is not coarsely embeddable into any uniformly convex Banach space. It is also shown that every (not necessarily bounded geometry) metric space with straight finite decomposition complexity has metric sparsification property.}, author = {Weighill, Thomas and Yamauchi, Takamitsu and Zava, Nicolò}, issn = {2199-6768}, journal = {European Journal of Mathematics}, publisher = {Springer Nature}, title = {{Coarse infinite-dimensionality of hyperspaces of finite subsets}}, doi = {10.1007/s40879-021-00515-3}, year = {2021}, } @inproceedings{10609, abstract = {We study Multi-party computation (MPC) in the setting of subversion, where the adversary tampers with the machines of honest parties. Our goal is to construct actively secure MPC protocols where parties are corrupted adaptively by an adversary (as in the standard adaptive security setting), and in addition, honest parties’ machines are compromised. The idea of reverse firewalls (RF) was introduced at EUROCRYPT’15 by Mironov and Stephens-Davidowitz as an approach to protecting protocols against corruption of honest parties’ devices. Intuitively, an RF for a party P is an external entity that sits between P and the outside world and whose scope is to sanitize P ’s incoming and outgoing messages in the face of subversion of their computer. Mironov and Stephens-Davidowitz constructed a protocol for passively-secure two-party computation. At CRYPTO’20, Chakraborty, Dziembowski and Nielsen constructed a protocol for secure computation with firewalls that improved on this result, both by extending it to multi-party computation protocol, and considering active security in the presence of static corruptions. In this paper, we initiate the study of RF for MPC in the adaptive setting. We put forward a definition for adaptively secure MPC in the reverse firewall setting, explore relationships among the security notions, and then construct reverse firewalls for MPC in this stronger setting of adaptive security. We also resolve the open question of Chakraborty, Dziembowski and Nielsen by removing the need for a trusted setup in constructing RF for MPC. Towards this end, we construct reverse firewalls for adaptively secure augmented coin tossing and adaptively secure zero-knowledge protocols and obtain a constant round adaptively secure MPC protocol in the reverse firewall setting without setup. Along the way, we propose a new multi-party adaptively secure coin tossing protocol in the plain model, that is of independent interest.}, author = {Chakraborty, Suvradip and Ganesh, Chaya and Pancholi, Mahak and Sarkar, Pratik}, booktitle = {27th International Conference on the Theory and Application of Cryptology and Information Security}, isbn = {978-3-030-92074-6}, issn = {1611-3349}, location = {Virtual, Singapore}, pages = {335--364}, publisher = {Springer Nature}, title = {{Reverse firewalls for adaptively secure MPC without setup}}, doi = {10.1007/978-3-030-92075-3_12}, volume = {13091}, year = {2021}, } @article{10613, abstract = {Motivated by the recent preprint [\emph{arXiv:2004.08412}] by Ayala, Carinci, and Redig, we first provide a general framework for the study of scaling limits of higher-order fields. Then, by considering the same class of infinite interacting particle systems as in [\emph{arXiv:2004.08412}], namely symmetric simple exclusion and inclusion processes in the d-dimensional Euclidean lattice, we prove the hydrodynamic limit, and convergence for the equilibrium fluctuations, of higher-order fields. In particular, the limit fields exhibit a tensor structure. Our fluctuation result differs from that in [\emph{arXiv:2004.08412}], since we considered-dimensional Euclidean lattice, we prove the hydrodynamic limit, and convergence for the equilibrium fluctuations, of higher-order fields. In particular, the limit fields exhibit a tensor structure. Our fluctuation result differs from that in [\emph{arXiv:2004.08412}], since we consider a different notion of higher-order fluctuation fields.}, author = {Chen, Joe P. and Sau, Federico}, issn = {1024-2953}, journal = {Markov Processes And Related Fields}, keywords = {interacting particle systems, higher-order fields, hydrodynamic limit, equilibrium fluctuations, duality}, number = {3}, pages = {339--380}, publisher = {Polymat Publishing}, title = {{Higher-order hydrodynamics and equilibrium fluctuations of interacting particle systems}}, volume = {27}, year = {2021}, } @article{10616, abstract = {Electrons in moiré flat band systems can spontaneously break time-reversal symmetry, giving rise to a quantized anomalous Hall effect. In this study, we use a superconducting quantum interference device to image stray magnetic fields in twisted bilayer graphene aligned to hexagonal boron nitride. We find a magnetization of several Bohr magnetons per charge carrier, demonstrating that the magnetism is primarily orbital in nature. Our measurements reveal a large change in the magnetization as the chemical potential is swept across the quantum anomalous Hall gap, consistent with the expected contribution of chiral edge states to the magnetization of an orbital Chern insulator. Mapping the spatial evolution of field-driven magnetic reversal, we find a series of reproducible micrometer-scale domains pinned to structural disorder.}, author = {Tschirhart, C. L. and Serlin, M. and Polshyn, Hryhoriy and Shragai, A. and Xia, Z. and Zhu, J. and Zhang, Y. and Watanabe, K. and Taniguchi, T. and Huber, M. E. and Young, A. F.}, issn = {1095-9203}, journal = {Science}, keywords = {multidisciplinary}, number = {6548}, pages = {1323--1327}, publisher = {American Association for the Advancement of Science}, title = {{Imaging orbital ferromagnetism in a moiré Chern insulator}}, doi = {10.1126/science.abd3190}, volume = {372}, year = {2021}, } @article{10617, abstract = {When a flat band is partially filled with electrons, strong Coulomb interactions between them may lead to the emergence of topological gapped states with quantized Hall conductivity. Such emergent topological states have been found in partially filled Landau levels1 and Hofstadter bands2,3; however, in both cases, a large magnetic field is required to produce the underlying flat band. The recent observation of quantum anomalous Hall effects in narrow-band moiré materials4,5,6,7 has led to the theoretical prediction that such phases could be realized at zero magnetic field8,9,10,11,12. Here we report the observation of insulators with Chern number C = 1 in the zero-magnetic-field limit at half-integer filling of the moiré superlattice unit cell in twisted monolayer–bilayer graphene7,13,14,15. Chern insulators in a half-filled band suggest the spontaneous doubling of the superlattice unit cell2,3,16, and our calculations find a ground state of the topological charge density wave at half-filling of the underlying band. The discovery of these topological phases at fractional superlattice filling enables the further pursuit of zero-magnetic-field phases that have fractional statistics that exist either as elementary excitations or bound to lattice dislocations.}, author = {Polshyn, Hryhoriy and Zhang, Y. and Kumar, M. A. and Soejima, T. and Ledwith, P. and Watanabe, K. and Taniguchi, T. and Vishwanath, A. and Zaletel, M. P. and Young, A. F.}, issn = {1745-2481}, journal = {Nature Physics}, keywords = {general physics, astronomy}, publisher = {Springer Nature}, title = {{Topological charge density waves at half-integer filling of a moiré superlattice}}, doi = {10.1038/s41567-021-01418-6}, year = {2021}, } @article{10628, abstract = {The surface states of 3D topological insulators in general have negligible quantum oscillations (QOs) when the chemical potential is tuned to the Dirac points. In contrast, we find that topological Kondo insulators (TKIs) can support surface states with an arbitrarily large Fermi surface (FS) when the chemical potential is pinned to the Dirac point. We illustrate that these FSs give rise to finite-frequency QOs, which can become comparable to the extremal area of the unhybridized bulk bands. We show that this occurs when the crystal symmetry is lowered from cubic to tetragonal in a minimal two-orbital model. We label such surface modes as 'shadow surface states'. Moreover, we show that the sufficient next-nearest neighbor out-of-plane hybridization leading to shadow surface states can be self-consistently stabilized for tetragonal TKIs. Consequently, shadow surface states provide an important example of high-frequency QOs beyond the context of cubic TKIs.}, author = {Ghazaryan, Areg and Nica, Emilian M. and Erten, Onur and Ghaemi, Pouyan}, issn = {1367-2630}, journal = {New Journal of Physics}, number = {12}, publisher = {IOP Publishing}, title = {{Shadow surface states in topological Kondo insulators}}, doi = {10.1088/1367-2630/ac4124}, volume = {23}, year = {2021}, } @inproceedings{10629, abstract = {Product graphs arise naturally in formal verification and program analysis. For example, the analysis of two concurrent threads requires the product of two component control-flow graphs, and for language inclusion of deterministic automata the product of two automata is constructed. In many cases, the component graphs have constant treewidth, e.g., when the input contains control-flow graphs of programs. We consider the algorithmic analysis of products of two constant-treewidth graphs with respect to three classic specification languages, namely, (a) algebraic properties, (b) mean-payoff properties, and (c) initial credit for energy properties. Our main contributions are as follows. Consider a graph G that is the product of two constant-treewidth graphs of size n each. First, given an idempotent semiring, we present an algorithm that computes the semiring transitive closure of G in time Õ(n⁴). Since the output has size Θ(n⁴), our algorithm is optimal (up to polylog factors). Second, given a mean-payoff objective, we present an O(n³)-time algorithm for deciding whether the value of a starting state is non-negative, improving the previously known O(n⁴) bound. Third, given an initial credit for energy objective, we present an O(n⁵)-time algorithm for computing the minimum initial credit for all nodes of G, improving the previously known O(n⁸) bound. At the heart of our approach lies an algorithm for the efficient construction of strongly-balanced tree decompositions of constant-treewidth graphs. Given a constant-treewidth graph G' of n nodes and a positive integer λ, our algorithm constructs a binary tree decomposition of G' of width O(λ) with the property that the size of each subtree decreases geometrically with rate (1/2 + 2^{-λ}).}, author = {Chatterjee, Krishnendu and Ibsen-Jensen, Rasmus and Pavlogiannis, Andreas}, booktitle = {41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science}, isbn = {978-3-9597-7215-0}, issn = {1868-8969}, location = {Virtual}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Quantitative verification on product graphs of small treewidth}}, doi = {10.4230/LIPIcs.FSTTCS.2021.42}, volume = {213}, year = {2021}, } @inproceedings{10630, abstract = {In the Intersection Non-emptiness problem, we are given a list of finite automata A_1, A_2,… , A_m over a common alphabet Σ as input, and the goal is to determine whether some string w ∈ Σ^* lies in the intersection of the languages accepted by the automata in the list. We analyze the complexity of the Intersection Non-emptiness problem under the promise that all input automata accept a language in some level of the dot-depth hierarchy, or some level of the Straubing-Thérien hierarchy. Automata accepting languages from the lowest levels of these hierarchies arise naturally in the context of model checking. We identify a dichotomy in the dot-depth hierarchy by showing that the problem is already NP-complete when all input automata accept languages of the levels B_0 or B_{1/2} and already PSPACE-hard when all automata accept a language from the level B_1. Conversely, we identify a tetrachotomy in the Straubing-Thérien hierarchy. More precisely, we show that the problem is in AC^0 when restricted to level L_0; complete for L or NL, depending on the input representation, when restricted to languages in the level L_{1/2}; NP-complete when the input is given as DFAs accepting a language in L_1 or L_{3/2}; and finally, PSPACE-complete when the input automata accept languages in level L_2 or higher. Moreover, we show that the proof technique used to show containment in NP for DFAs accepting languages in L_1 or L_{3/2} does not generalize to the context of NFAs. To prove this, we identify a family of languages that provide an exponential separation between the state complexity of general NFAs and that of partially ordered NFAs. To the best of our knowledge, this is the first superpolynomial separation between these two models of computation.}, author = {Arrighi, Emmanuel and Fernau, Henning and Hoffmann, Stefan and Holzer, Markus and Jecker, Ismael R and De Oliveira Oliveira, Mateus and Wolf, Petra}, booktitle = {41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science}, isbn = {978-3-9597-7215-0}, issn = {1868-8969}, location = {Virtual}, publisher = {Schloss Dagstuhl - Leibniz Zentrum für Informatik}, title = {{On the complexity of intersection non-emptiness for star-free language classes}}, doi = {10.4230/LIPIcs.FSTTCS.2021.34}, volume = {213}, year = {2021}, } @article{10631, abstract = {We combine experimental and theoretical approaches to explore excited rotational states of molecules embedded in helium nanodroplets using CS2 and I2 as examples. Laser-induced nonadiabatic molecular alignment is employed to measure spectral lines for rotational states extending beyond those initially populated at the 0.37 K droplet temperature. We construct a simple quantum-mechanical model, based on a linear rotor coupled to a single-mode bosonic bath, to determine the rotational energy structure in its entirety. The calculated and measured spectral lines are in good agreement. We show that the effect of the surrounding superfluid on molecular rotation can be rationalized by a single quantity, the angular momentum, transferred from the molecule to the droplet.}, author = {Cherepanov, Igor and Bighin, Giacomo and Schouder, Constant A. and Chatterley, Adam S. and Albrechtsen, Simon H. and Muñoz, Alberto Viñas and Christiansen, Lars and Stapelfeldt, Henrik and Lemeshko, Mikhail}, issn = {2469-9934}, journal = {Physical Review A}, number = {6}, publisher = {American Physical Society}, title = {{Excited rotational states of molecules in a superfluid}}, doi = {10.1103/PhysRevA.104.L061303}, volume = {104}, 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 = {Centre Mersenne ; Peer Community In}, title = {{Nonlinear computations in spiking neural networks through multiplicative synapses}}, doi = {10.24072/pcjournal.69}, volume = {1}, year = {2021}, } @misc{10644, abstract = {The purpose of this application note is to demonstrate a working example of a superconducting qubit measurement in a Bluefors cryostat using the Keysight quantum control hardware. Our motivation is twofold. First, we provide pre-qualification data that the Bluefors cryostat, including filtering and wiring, can support long-lived qubits. Second, we demonstrate that the Keysight system (controlled using Labber) provides a straightforward solution to perform these characterization measurements. This document is intended as a brief guide for starting an experimental platform for testing superconducting qubits. The setup described here is an immediate jumping off point for a suite of applications including testing quantum logical gates, quantum optics with microwaves, or even using the qubit itself as a sensitive probe of local electromagnetic fields. Qubit measurements rely on high performance of both the physical sample environment and the measurement electronics. An overview of the cryogenic system is shown in Figure 1, and an overview of the integration between the electronics and cryostat (including wiring details) is shown in Figure 2.}, author = {Lake, Russell and Simbierowicz, Slawomir and Krantz, Philip and Hassani, Farid and Fink, Johannes M}, keywords = {Application note}, pages = {9}, publisher = {Bluefors Oy}, title = {{The Bluefors dilution refrigerator as an integrated quantum measurement system}}, year = {2021}, } @misc{10645, abstract = {Superconducting qubits have emerged as a highly versatile and useful platform for quantum technological applications [1]. Bluefors and Zurich Instruments have supported the growth of this field from the 2010s onwards by providing well-engineered and reliable measurement infrastructure [2]– [6]. Having a long and stable qubit lifetime is a critical system property. Therefore, considerable effort has already gone into measuring qubit energy-relaxation timescales and their fluctuations, see Refs. [7]–[10] among others. Accurately extracting the statistics of a quantum device requires users to perform time consuming measurements. One measurement challenge is that the detection of the state-dependent response of a superconducting resonator due to a dispersively-coupled qubit requires an inherently low signal level. Consequently, measurements must be performed using a microwave probe that contains only a few microwave photons. Improving the signal-to-noise ratio (SNR) by using near-quantum limited parametric amplifiers as well as the use of optimized signal processing enabled by efficient room temperature instrumentation help to reduce measurement time. An empirical observation for fixed frequency transmons from recent literature is that as the energy-relaxation time 𝑇𝑇1 increases, so do its natural temporal fluctuations [7], [10]. This necessitates many repeated measurements to understand the statistics (see for example, Ref. [10]). In addition, as state-of-the-art qubits increase in lifetime, longer measurement times are expected to obtain accurate statistics. As described below, the scaling of the widths of the qubit energy-relaxation distributions also reveal clues about the origin of the energy-relaxation.}, author = {Simbierowicz, Slawomir and Shi, Chunyan and Collodo, Michele and Kirste, Moritz and Hassani, Farid and Fink, Johannes M and Bylander, Jonas and Perez Lozano, Daniel and Lake, Russell}, keywords = {Application note}, pages = {8}, publisher = {Bluefors Oy}, title = {{Qubit energy-relaxation statistics in the Bluefors quantum measurement system}}, year = {2021}, } @article{10649, abstract = {Harnessing the properties of vortices in superconductors is crucial for fundamental science and technological applications; thus, it has been an ongoing goal to locally probe and control vortices. Here, we use a scanning probe technique that enables studies of vortex dynamics in superconducting systems by leveraging the resonant behavior of a raster-scanned, magnetic-tipped cantilever. This experimental setup allows us to image and control vortices, as well as extract key energy scales of the vortex interactions. Applying this technique to lattices of superconductor island arrays on a metal, we obtain a variety of striking spatial patterns that encode information about the energy landscape for vortices in the system. We interpret these patterns in terms of local vortex dynamics and extract the relative strengths of the characteristic energy scales in the system, such as the vortex-magnetic field and vortex-vortex interaction strengths, as well as the vortex chemical potential. We also demonstrate that the relative strengths of the interactions can be tuned and show how these interactions shift with an applied bias. The high degree of tunability and local nature of such vortex imaging and control not only enable new understanding of vortex interactions, but also have potential applications in more complex systems such as those relevant to quantum computing.}, author = {Naibert, Tyler R. and Polshyn, Hryhoriy and Garrido-Menacho, Rita and Durkin, Malcolm and Wolin, Brian and Chua, Victor and Mondragon-Shem, Ian and Hughes, Taylor and Mason, Nadya and Budakian, Raffi}, issn = {2469-9969}, journal = {Physical Review B}, number = {22}, publisher = {American Physical Society}, title = {{Imaging and controlling vortex dynamics in mesoscopic superconductor-normal-metal-superconductor arrays}}, doi = {10.1103/physrevb.103.224526}, volume = {103}, year = {2021}, } @inproceedings{10651, abstract = {Electrons in the moiré flat bands of magic angle twisted bilayer graphene aligned to hexagonal boron nitride can break time reversal symmetry and open an interaction-driven, topological gap. The resulting magnetic order and associated quantized anomalous Hall effect have properties that diverge substantially from quantized anomalous Hall effects observed in other systems. I will present transport data and scanning probe magnetometry data acquired using a nanoSQUID-on-tip microscope. A quantitative analysis of the magnitude of the magnetization of the Chern magnet shows that the magnetic moment per moiré unit cell substantially exceeds 1 μB and grows rapidly in the topological gap, consistent with an orbital origin for the magnetic order. We find that the Barkhausen jumps observed in transport measurements can be mapped directly to microscopic motion of ferromagnetic domain walls. These domain walls are strongly pinned to disorder in the device and are reproducible across thermal cycles, suggesting coupling between the magnetic degrees of freedom and structural inhomogeneity.}, author = {Tschirhart, Charles and Serlin, Marec and Polshyn, Hryhoriy and Shragai, Avi G. and Xia, Zhengchao and Zhu, Jiacheng and Zhang, Yuxuan and Watanabe, Kenji and Taniguchi, Takashi and Huber, Martin E. and Young, Andrea}, booktitle = {APS March Meeting 2021}, issn = {0003-0503}, location = {Virtual, United States}, number = {1}, publisher = {American Physical Society}, title = {{Probing orbital Chern ferromagnet phase in twisted bilayer graphene}}, volume = {66}, year = {2021}, } @article{10655, abstract = {Adeno-associated viruses (AAVs) are widely used to deliver genetic material in vivo to distinct cell types such as neurons or glial cells, allowing for targeted manipulation. Transduction of microglia is mostly excluded from this strategy, likely due to the cells’ heterogeneous state upon environmental changes, which makes AAV design challenging. Here, we established the retina as a model system for microglial AAV validation and optimization. First, we show that AAV2/6 transduced microglia in both synaptic layers, where layer preference corresponds to the intravitreal or subretinal delivery method. Surprisingly, we observed significantly enhanced microglial transduction during photoreceptor degeneration. Thus, we modified the AAV6 capsid to reduce heparin binding by introducing four point mutations (K531E, R576Q, K493S, and K459S), resulting in increased microglial transduction in the outer plexiform layer. Finally, to improve microglial-specific transduction, we validated a Cre-dependent transgene delivery cassette for use in combination with the Cx3cr1CreERT2 mouse line. Together, our results provide a foundation for future studies optimizing AAV-mediated microglia transduction and highlight that environmental conditions influence microglial transduction efficiency. }, author = {Maes, Margaret E and Wögenstein, Gabriele M. and Colombo, Gloria and Casado Polanco, Raquel and Siegert, Sandra}, issn = {2329-0501}, journal = {Molecular Therapy - Methods and Clinical Development}, pages = {210--224}, publisher = {Elsevier}, title = {{Optimizing AAV2/6 microglial targeting identified enhanced efficiency in the photoreceptor degenerative environment}}, doi = {10.1016/j.omtm.2021.09.006}, volume = {23}, year = {2021}, } @inproceedings{11814, abstract = {Differentially private algorithms protect individuals in data analysis scenarios by ensuring that there is only a weak correlation between the existence of the user in the data and the result of the analysis. Dynamic graph algorithms maintain the solution to a problem (e.g., a matching) on an evolving input, i.e., a graph where nodes or edges are inserted or deleted over time. They output the value of the solution after each update operation, i.e., continuously. We study (event-level and user-level) differentially private algorithms for graph problems under continual observation, i.e., differentially private dynamic graph algorithms. We present event-level private algorithms for partially dynamic counting-based problems such as triangle count that improve the additive error by a polynomial factor (in the length T of the update sequence) on the state of the art, resulting in the first algorithms with additive error polylogarithmic in T. We also give ε-differentially private and partially dynamic algorithms for minimum spanning tree, minimum cut, densest subgraph, and maximum matching. The additive error of our improved MST algorithm is O(W log^{3/2}T / ε), where W is the maximum weight of any edge, which, as we show, is tight up to a (√{log T} / ε)-factor. For the other problems, we present a partially-dynamic algorithm with multiplicative error (1+β) for any constant β > 0 and additive error O(W log(nW) log(T) / (ε β)). Finally, we show that the additive error for a broad class of dynamic graph algorithms with user-level privacy must be linear in the value of the output solution’s range.}, author = {Fichtenberger, Hendrik and Henzinger, Monika H and Ost, Wolfgang}, booktitle = {29th Annual European Symposium on Algorithms}, isbn = {9783959772044}, issn = {1868-8969}, location = {Lisbon, Portual}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Differentially private algorithms for graphs under continual observation}}, doi = {10.4230/LIPIcs.ESA.2021.42}, volume = {204}, year = {2021}, } @article{11886, abstract = {We present a deterministic (1+𝑜(1))-approximation (𝑛1/2+𝑜(1)+𝐷1+𝑜(1))-time algorithm for solving the single-source shortest paths problem on distributed weighted networks (the \sf CONGEST model); here 𝑛 is the number of nodes in the network, 𝐷 is its (hop) diameter, and edge weights are positive integers from 1 to poly(𝑛). This is the first nontrivial deterministic algorithm for this problem. It also improves (i) the running time of the randomized (1+𝑜(1))-approximation 𝑂̃ (𝑛√𝐷1/4+𝐷)-time algorithm of Nanongkai [in Proceedings of STOC, 2014, pp. 565--573] by a factor of as large as 𝑛1/8, and (ii) the 𝑂(𝜖−1log𝜖−1)-approximation factor of Lenzen and Patt-Shamir's 𝑂̃ (𝑛1/2+𝜖+𝐷)-time algorithm [in Proceedings of STOC, 2013, pp. 381--390] within the same running time. (Throughout, we use 𝑂̃ (⋅) to hide polylogarithmic factors in 𝑛.) Our running time matches the known time lower bound of Ω(𝑛/log𝑛‾‾‾‾‾‾‾√+𝐷) [M. Elkin, SIAM J. Comput., 36 (2006), pp. 433--456], thus essentially settling the status of this problem which was raised at least a decade ago [M. Elkin, SIGACT News, 35 (2004), pp. 40--57]. It also implies a (2+𝑜(1))-approximation (𝑛1/2+𝑜(1)+𝐷1+𝑜(1))-time algorithm for approximating a network's weighted diameter which almost matches the lower bound by Holzer and Pinsker [in Proceedings of OPODIS, 2015, Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern, Germany, 2016, 6]. In achieving this result, we develop two techniques which might be of independent interest and useful in other settings: (i) a deterministic process that replaces the “hitting set argument” commonly used for shortest paths computation in various settings, and (ii) a simple, deterministic construction of an (𝑛𝑜(1),𝑜(1))-hop set of size 𝑛1+𝑜(1). We combine these techniques with many distributed algorithmic techniques, some of which are from problems that are not directly related to shortest paths, e.g., ruling sets [A. V. Goldberg, S. A. Plotkin, and G. E. Shannon, SIAM J. Discrete Math., 1 (1988), pp. 434--446], source detection [C. Lenzen and D. Peleg, in Proceedings of PODC, 2013, pp. 375--382], and partial distance estimation [C. Lenzen and B. Patt-Shamir, in Proceedings of PODC, 2015, pp. 153--162]. Our hop set construction also leads to single-source shortest paths algorithms in two other settings: (i) a (1+𝑜(1))-approximation 𝑛𝑜(1)-time algorithm on congested cliques, and (ii) a (1+𝑜(1))-approximation 𝑛𝑜(1)-pass 𝑛1+𝑜(1)-space streaming algorithm. The first result answers an open problem in [D. Nanongkai, in Proceedings of STOC, 2014, pp. 565--573]. The second result partially answers an open problem raised by McGregor in 2006 [List of Open Problems in Sublinear Algorithms: Problem 14].}, author = {Henzinger, Monika H and Krinninger, Sebastian and Nanongkai, Danupon}, issn = {1095-7111}, journal = {SIAM Journal on Computing}, number = {3}, pages = {STOC16--98--STOC16--137}, publisher = {Society for Industrial & Applied Mathematics}, title = {{A deterministic almost-tight distributed algorithm for approximating single-source shortest paths}}, doi = {10.1137/16m1097808}, volume = {50}, year = {2021}, } @inproceedings{11919, abstract = {Maintaining and updating shortest paths information in a graph is a fundamental problem with many applications. As computations on dense graphs can be prohibitively expensive, and it is preferable to perform the computations on a sparse skeleton of the given graph that roughly preserves the shortest paths information. Spanners and emulators serve this purpose. Unfortunately, very little is known about dynamically maintaining sparse spanners and emulators as the graph is modified by a sequence of edge insertions and deletions. This paper develops fast dynamic algorithms for spanner and emulator maintenance and provides evidence from fine-grained complexity that these algorithms are tight. For unweighted undirected m-edge n-node graphs we obtain the following results. Under the popular OMv conjecture, there can be no decremental or incremental algorithm that maintains an n1+o(1) edge (purely additive) +nδ-emulator for any δ < 1/2 with arbitrary polynomial preprocessing time and total update time m1+o(1). Also, under the Combinatorial k-Clique hypothesis, any fully dynamic combinatorial algorithm that maintains an n1+o(1) edge (1 + ∊, no(1))-spanner or emulator for small ∊ must either have preprocessing time mn1–o(1) or amortized update time m1–o(1). Both of our conditional lower bounds are tight. As the above fully dynamic lower bound only applies to combinatorial algorithms, we also develop an algebraic spanner algorithm that improves over the m1–o(1) update time for dense graphs. For any constant ∊ ∊ (0, 1], there is a fully dynamic algorithm with worst-case update time O(n1.529) that whp maintains an n1+o(1) edge (1 + ∊, no(1))-spanner. Our new algebraic techniques allow us to also obtain a new fully dynamic algorithm for All-Pairs Shortest Paths (APSP) that can perform both edge updates and can report shortest paths in worst-case time O(n1.9), which are correct whp. This is the first path-reporting fully dynamic APSP algorithm with a truly subquadratic query time that beats O(n2.5) update time. It works against an oblivious adversary. Finally, we give two applications of our new dynamic spanner algorithms: (1) a fully dynamic (1 + ∊)-approximate APSP algorithm with update time O(n1.529) that can report approximate shortest paths in n1+o(1) time per query; previous subquadratic update/query algorithms could only report the distance, but not obtain the paths; (2) a fully dynamic algorithm for near-2-approximate Steiner tree maintenance with both terminal and edge updates.}, author = {Bergamaschi, Thiago and Henzinger, Monika H and Gutenberg, Maximilian Probst and Williams, Virginia Vassilevska and Wein, Nicole}, booktitle = {32nd Annual ACM-SIAM Symposium on Discrete Algorithms}, location = {Alexandria, VA, United States}, pages = {1836--1855}, publisher = {Society for Industrial and Applied Mathematics}, title = {{New techniques and fine-grained hardness for dynamic near-additive spanners}}, doi = {10.1137/1.9781611976465.110}, year = {2021}, } @inproceedings{11920, abstract = {In the dynamic minimum set cover problem, a challenge is to minimize the update time while guaranteeing close to the optimal min(O(log n), f) approximation factor. (Throughout, m, n, f, and C are parameters denoting the maximum number of sets, number of elements, frequency, and the cost range.) In the high-frequency range, when f = Ω(log n), this was achieved by a deterministic O(log n)-approximation algorithm with O(f log n) amortized update time [Gupta et al. STOC'17]. In the low-frequency range, the line of work by Gupta et al. [STOC'17], Abboud et al. [STOC'19], and Bhattacharya et al. [ICALP'15, IPCO'17, FOCS'19] led to a deterministic (1 + ∊) f-approximation algorithm with O(f log(Cn)/∊2) amortized update time. In this paper we improve the latter update time and provide the first bounds that subsume (and sometimes improve) the state-of-the-art dynamic vertex cover algorithms. We obtain: (1) (1 + ∊) f-approximation ratio in O(f log2(Cn)/∊3) worst-case update time: No non-trivial worst-case update time was previously known for dynamic set cover. Our bound subsumes and improves by a logarithmic factor the O(log3 n/poly(∊)) worst-case update time for unweighted dynamic vertex cover (i.e., when f = 2 and C = 1) by Bhattacharya et al. [SODA'17]. (2) (1 + ∊) f-approximation ratio in O ((f2/∊3) + (f/∊2) log C) amortized update time: This result improves the previous O(f log (Cn)/∊2) update time bound for most values of f in the low-frequency range, i.e. whenever f = o(log n). It is the first that is independent of m and n. It subsumes the constant amortized update time of Bhattacharya and Kulkarni [SODA'19] for unweighted dynamic vertex cover (i.e., when f = 2 and C = 1). These results are achieved by leveraging the approximate complementary slackness and background schedulers techniques. These techniques were used in the local update scheme for dynamic vertex cover. Our main technical contribution is to adapt these techniques within the global update scheme of Bhattacharya et al. [FOCS'19] for the dynamic set cover problem.}, author = {Bhattacharya, Sayan and Henzinger, Monika H and Nanongkai, Danupon and Wu, Xiaowei}, booktitle = {32nd Annual ACM-SIAM Symposium on Discrete Algorithms}, location = {Alexandria, VA, United States}, pages = {2537--2549}, publisher = {Society for Industrial and Applied Mathematics}, title = {{Dynamic set cover: Improved amortized and worst-case update time}}, doi = {10.1137/1.9781611976465.150}, year = {2021}, }