@article{9410, abstract = {Antibiotic concentrations vary dramatically in the body and the environment. Hence, understanding the dynamics of resistance evolution along antibiotic concentration gradients is critical for predicting and slowing the emergence and spread of resistance. While it has been shown that increasing the concentration of an antibiotic slows resistance evolution, how adaptation to one antibiotic concentration correlates with fitness at other points along the gradient has not received much attention. Here, we selected populations of Escherichia coli at several points along a concentration gradient for three different antibiotics, asking how rapidly resistance evolved and whether populations became specialized to the antibiotic concentration they were selected on. Populations selected at higher concentrations evolved resistance more slowly but exhibited equal or higher fitness across the whole gradient. Populations selected at lower concentrations evolved resistance rapidly, but overall fitness in the presence of antibiotics was lower. However, these populations readily adapted to higher concentrations upon subsequent selection. Our results indicate that resistance management strategies must account not only for the rates of resistance evolution but also for the fitness of evolved strains.}, author = {Lagator, Mato and Uecker, Hildegard and Neve, Paul}, issn = {1744-957X}, journal = {Biology letters}, number = {5}, publisher = {Royal Society of London}, title = {{Adaptation at different points along antibiotic concentration gradients}}, doi = {10.1098/rsbl.2020.0913}, volume = {17}, year = {2021}, } @article{8601, abstract = {We consider large non-Hermitian real or complex random matrices X with independent, identically distributed centred entries. We prove that their local eigenvalue statistics near the spectral edge, the unit circle, coincide with those of the Ginibre ensemble, i.e. when the matrix elements of X are Gaussian. This result is the non-Hermitian counterpart of the universality of the Tracy–Widom distribution at the spectral edges of the Wigner ensemble.}, author = {Cipolloni, Giorgio and Erdös, László and Schröder, Dominik J}, issn = {1432-2064}, journal = {Probability Theory and Related Fields}, publisher = {Springer Nature}, title = {{Edge universality for non-Hermitian random matrices}}, doi = {10.1007/s00440-020-01003-7}, year = {2021}, } @article{9318, abstract = {We consider a system of N bosons in the mean-field scaling regime for a class of interactions including the repulsive Coulomb potential. We derive an asymptotic expansion of the low-energy eigenstates and the corresponding energies, which provides corrections to Bogoliubov theory to any order in 1/N.}, author = {Bossmann, Lea and Petrat, Sören P and Seiringer, Robert}, issn = {2050-5094}, journal = {Forum of Mathematics, Sigma}, publisher = {Cambridge University Press}, title = {{Asymptotic expansion of low-energy excitations for weakly interacting bosons}}, doi = {10.1017/fms.2021.22}, volume = {9}, year = {2021}, } @article{8198, abstract = {We investigate how the critical driving amplitude at the Floquet many-body localized (MBL) to ergodic phase transition differs between smooth and nonsmooth drives. To this end, we numerically study a disordered spin-1/2 chain which is periodically driven by a sine or square-wave drive over a wide range of driving frequencies. In both cases the critical driving amplitude increases monotonically with the frequency, and at large frequencies it is identical for the two drives. However, at low and intermediate frequencies the critical amplitude of the square-wave drive depends strongly on the frequency, while that of the sinusoidal drive is almost constant over a wide frequency range. By analyzing the density of drive-induced resonances we conclude that this difference is due to resonances induced by the higher harmonics which are present (absent) in the Fourier spectrum of the square-wave (sine) drive. Furthermore, we suggest a numerically efficient method for estimating the frequency dependence of the critical driving amplitudes for different drives which is based on calculating the density of drive-induced resonances. We conclude that delocalization occurs once the density of drive-induced resonances reaches a critical value determined only by the static system.}, author = {Diringer, Asaf A. and Gulden, Tobias}, issn = {2469-9969}, journal = {Physical Review B}, number = {21}, publisher = {American Physical Society}, title = {{Impact of drive harmonics on the stability of Floquet many-body localization}}, doi = {10.1103/PhysRevB.103.214204}, volume = {103}, year = {2021}, } @article{9603, abstract = {Mosaic analysis with double markers (MADM) offers one approach to visualize and concomitantly manipulate genetically defined cells in mice with single-cell resolution. MADM applications include the analysis of lineage, single-cell morphology and physiology, genomic imprinting phenotypes, and dissection of cell-autonomous gene functions in vivo in health and disease. Yet, MADM can only be applied to <25% of all mouse genes on select chromosomes to date. To overcome this limitation, we generate transgenic mice with knocked-in MADM cassettes near the centromeres of all 19 autosomes and validate their use across organs. With this resource, >96% of the entire mouse genome can now be subjected to single-cell genetic mosaic analysis. Beyond a proof of principle, we apply our MADM library to systematically trace sister chromatid segregation in distinct mitotic cell lineages. We find striking chromosome-specific biases in segregation patterns, reflecting a putative mechanism for the asymmetric segregation of genetic determinants in somatic stem cell division.}, author = {Contreras, Ximena and Amberg, Nicole and Davaatseren, Amarbayasgalan and Hansen, Andi H and Sonntag, Johanna and Andersen, Lill and Bernthaler, Tina and Streicher, Carmen and Heger, Anna-Magdalena and Johnson, Randy L. and Schwarz, Lindsay A. and Luo, Liqun and Rülicke, Thomas and Hippenmeyer, Simon}, issn = {2211-1247}, journal = {Cell Reports}, number = {12}, publisher = {Cell Press}, title = {{A genome-wide library of MADM mice for single-cell genetic mosaic analysis}}, doi = {10.1016/j.celrep.2021.109274}, volume = {35}, year = {2021}, } @article{9363, abstract = {Optogenetics has been harnessed to shed new mechanistic light on current and future therapeutic strategies. This has been to date achieved by the regulation of ion flow and electrical signals in neuronal cells and neural circuits that are known to be affected by disease. In contrast, the optogenetic delivery of trophic biochemical signals, which support cell survival and are implicated in degenerative disorders, has never been demonstrated in an animal model of disease. Here, we reengineered the human and Drosophila melanogaster REarranged during Transfection (hRET and dRET) receptors to be activated by light, creating one-component optogenetic tools termed Opto-hRET and Opto-dRET. Upon blue light stimulation, these receptors robustly induced the MAPK/ERK proliferative signaling pathway in cultured cells. In PINK1B9 flies that exhibit loss of PTEN-induced putative kinase 1 (PINK1), a kinase associated with familial Parkinson’s disease (PD), light activation of Opto-dRET suppressed mitochondrial defects, tissue degeneration and behavioral deficits. In human cells with PINK1 loss-of-function, mitochondrial fragmentation was rescued using Opto-dRET via the PI3K/NF-кB pathway. Our results demonstrate that a light-activated receptor can ameliorate disease hallmarks in a genetic model of PD. The optogenetic delivery of trophic signals is cell type-specific and reversible and thus has the potential to inspire novel strategies towards a spatio-temporal regulation of tissue repair.}, author = {Inglés Prieto, Álvaro and Furthmann, Nikolas and Crossman, Samuel H. and Tichy, Alexandra Madelaine and Hoyer, Nina and Petersen, Meike and Zheden, Vanessa and Bicher, Julia and Gschaider-Reichhart, Eva and György, Attila and Siekhaus, Daria E and Soba, Peter and Winklhofer, Konstanze F. and Janovjak, Harald L}, issn = {1553-7404}, journal = {PLoS genetics}, number = {4}, pages = {e1009479}, publisher = {Public Library of Science}, title = {{Optogenetic delivery of trophic signals in a genetic model of Parkinson's disease}}, doi = {10.1371/journal.pgen.1009479}, volume = {17}, year = {2021}, } @article{9640, abstract = {Selection and random drift determine the probability that novel mutations fixate in a population. Population structure is known to affect the dynamics of the evolutionary process. Amplifiers of selection are population structures that increase the fixation probability of beneficial mutants compared to well-mixed populations. Over the past 15 years, extensive research has produced remarkable structures called strong amplifiers which guarantee that every beneficial mutation fixates with high probability. But strong amplification has come at the cost of considerably delaying the fixation event, which can slow down the overall rate of evolution. However, the precise relationship between fixation probability and time has remained elusive. Here we characterize the slowdown effect of strong amplification. First, we prove that all strong amplifiers must delay the fixation event at least to some extent. Second, we construct strong amplifiers that delay the fixation event only marginally as compared to the well-mixed populations. Our results thus establish a tight relationship between fixation probability and time: Strong amplification always comes at a cost of a slowdown, but more than a marginal slowdown is not needed.}, author = {Tkadlec, Josef and Pavlogiannis, Andreas and Chatterjee, Krishnendu and Nowak, Martin A.}, issn = {2041-1723}, journal = {Nature Communications}, number = {1}, publisher = {Springer Nature}, title = {{Fast and strong amplifiers of natural selection}}, doi = {10.1038/s41467-021-24271-w}, volume = {12}, year = {2021}, } @article{10401, abstract = {Theoretical and experimental studies of the interaction between spins and temperature are vital for the development of spin caloritronics, as they dictate the design of future devices. In this work, we propose a two-terminal cold-atom simulator to study that interaction. The proposed quantum simulator consists of strongly interacting atoms that occupy two temperature reservoirs connected by a one-dimensional link. First, we argue that the dynamics in the link can be described using an inhomogeneous Heisenberg spin chain whose couplings are defined by the local temperature. Second, we show the existence of a spin current in a system with a temperature difference by studying the dynamics that follows the spin-flip of an atom in the link. A temperature gradient accelerates the impurity in one direction more than in the other, leading to an overall spin current similar to the spin Seebeck effect.}, author = {Barfknecht, Rafael E. and Foerster, Angela and Zinner, Nikolaj T. and Volosniev, Artem}, issn = {2399-3650}, journal = {Communications Physics}, number = {1}, publisher = {Springer Nature}, title = {{Generation of spin currents by a temperature gradient in a two-terminal device}}, doi = {10.1038/s42005-021-00753-7}, volume = {4}, year = {2021}, } @article{9908, abstract = {About eight million animal species are estimated to live on Earth, and all except those belonging to one subphylum are invertebrates. Invertebrates are incredibly diverse in their morphologies, life histories, and in the range of the ecological niches that they occupy. A great variety of modes of reproduction and sex determination systems is also observed among them, and their mosaic-distribution across the phylogeny shows that transitions between them occur frequently and rapidly. Genetic conflict in its various forms is a long-standing theory to explain what drives those evolutionary transitions. Here, we review (1) the different modes of reproduction among invertebrate species, highlighting sexual reproduction as the probable ancestral state; (2) the paradoxical diversity of sex determination systems; (3) the different types of genetic conflicts that could drive the evolution of such different systems.}, author = {Picard, Marion A L and Vicoso, Beatriz and Bertrand, Stéphanie and Escriva, Hector}, issn = {2073-4425}, journal = {Genes}, number = {8}, publisher = {MDPI}, title = {{Diversity of modes of reproduction and sex determination systems in invertebrates, and the putative contribution of genetic conflict}}, doi = {10.3390/genes12081136}, volume = {12}, year = {2021}, } @article{9256, abstract = {We consider the ferromagnetic quantum Heisenberg model in one dimension, for any spin S≥1/2. We give upper and lower bounds on the free energy, proving that at low temperature it is asymptotically equal to the one of an ideal Bose gas of magnons, as predicted by the spin-wave approximation. The trial state used in the upper bound yields an analogous estimate also in the case of two spatial dimensions, which is believed to be sharp at low temperature.}, author = {Napiórkowski, Marcin M and Seiringer, Robert}, issn = {1573-0530}, journal = {Letters in Mathematical Physics}, number = {2}, publisher = {Springer Nature}, title = {{Free energy asymptotics of the quantum Heisenberg spin chain}}, doi = {10.1007/s11005-021-01375-4}, volume = {111}, year = {2021}, } @article{9097, abstract = {Psoriasis is a chronic inflammatory skin disease clinically characterized by the appearance of red colored, well-demarcated plaques with thickened skin and with silvery scales. Recent studies have established the involvement of a complex signalling network of interactions between cytokines, immune cells and skin cells called keratinocytes. Keratinocytes form the cells of the outermost layer of the skin (epidermis). Visible plaques in psoriasis are developed due to the fast proliferation and unusual differentiation of keratinocyte cells. Despite that, the exact mechanism of the appearance of these plaques in the cytokine-immune cell network is not clear. A mathematical model embodying interactions between key immune cells believed to be involved in psoriasis, keratinocytes and relevant cytokines has been developed. The complex network formed of these interactions poses several challenges. Here, we choose to study subnetworks of this complex network and initially focus on interactions involving TNFα, IL-23/IL-17, and IL-15. These are chosen based on known evidence of their therapeutic efficacy. In addition, we explore the role of IL-15 in the pathogenesis of psoriasis and its potential as a future drug target for a novel treatment option. We perform steady state analyses for these subnetworks and demonstrate that the interactions between cells, driven by cytokines could cause the emergence of a psoriasis state (hyper-proliferation of keratinocytes) when levels of TNFα, IL-23/IL-17 or IL-15 are increased. The model results explain and support the clinical potentiality of anti-cytokine treatments. Interestingly, our results suggest different dynamic scenarios underpin the pathogenesis of psoriasis, depending upon the dominant cytokines of subnetworks. We observed that the increase in the level of IL-23/IL-17 and IL-15 could lead to psoriasis via a bistable route, whereas an increase in the level of TNFα would lead to a monotonic and gradual disease progression. Further, we demonstrate how this insight, bistability, could be exploited to improve the current therapies and develop novel treatment strategies for psoriasis.}, author = {Pandey, Rakesh and Al-Nuaimi, Yusur and Mishra, Rajiv Kumar and Spurgeon, Sarah K. and Goodfellow, Marc}, issn = {2045-2322}, journal = {Scientific Reports}, publisher = {Springer Nature}, title = {{Role of subnetworks mediated by TNF α, IL-23/IL-17 and IL-15 in a network involved in the pathogenesis of psoriasis}}, doi = {10.1038/s41598-020-80507-7}, volume = {11}, year = {2021}, } @article{8430, abstract = {While recent advancements in computation and modelling have improved the analysis of complex traits, our understanding of the genetic basis of the time at symptom onset remains limited. Here, we develop a Bayesian approach (BayesW) that provides probabilistic inference of the genetic architecture of age-at-onset phenotypes in a sampling scheme that facilitates biobank-scale time-to-event analyses. We show in extensive simulation work the benefits BayesW provides in terms of number of discoveries, model performance and genomic prediction. In the UK Biobank, we find many thousands of common genomic regions underlying the age-at-onset of high blood pressure (HBP), cardiac disease (CAD), and type-2 diabetes (T2D), and for the genetic basis of onset reflecting the underlying genetic liability to disease. Age-at-menopause and age-at-menarche are also highly polygenic, but with higher variance contributed by low frequency variants. Genomic prediction into the Estonian Biobank data shows that BayesW gives higher prediction accuracy than other approaches.}, author = {Ojavee, Sven E and Kousathanas, Athanasios and Trejo Banos, Daniel and Orliac, Etienne J and Patxot, Marion and Lall, Kristi and Magi, Reedik and Fischer, Krista and Kutalik, Zoltan and Robinson, Matthew Richard}, issn = {2041-1723}, journal = {Nature Communications}, number = {1}, publisher = {Nature Research}, title = {{Genomic architecture and prediction of censored time-to-event phenotypes with a Bayesian genome-wide analysis}}, doi = {10.1038/s41467-021-22538-w}, volume = {12}, year = {2021}, } @article{9407, abstract = {High impact epidemics constitute one of the largest threats humanity is facing in the 21st century. In the absence of pharmaceutical interventions, physical distancing together with testing, contact tracing and quarantining are crucial in slowing down epidemic dynamics. Yet, here we show that if testing capacities are limited, containment may fail dramatically because such combined countermeasures drastically change the rules of the epidemic transition: Instead of continuous, the response to countermeasures becomes discontinuous. Rather than following the conventional exponential growth, the outbreak that is initially strongly suppressed eventually accelerates and scales faster than exponential during an explosive growth period. As a consequence, containment measures either suffice to stop the outbreak at low total case numbers or fail catastrophically if marginally too weak, thus implying large uncertainties in reliably estimating overall epidemic dynamics, both during initial phases and during second wave scenarios.}, author = {Scarselli, Davide and Budanur, Nazmi B and Timme, Marc and Hof, Björn}, issn = {2041-1723}, journal = {Nature Communications}, number = {1}, publisher = {Springer Nature}, title = {{Discontinuous epidemic transition due to limited testing}}, doi = {10.1038/s41467-021-22725-9}, volume = {12}, year = {2021}, } @article{9642, abstract = {Perineuronal nets (PNNs), components of the extracellular matrix, preferentially coat parvalbumin-positive interneurons and constrain critical-period plasticity in the adult cerebral cortex. Current strategies to remove PNN are long-lasting, invasive, and trigger neuropsychiatric symptoms. Here, we apply repeated anesthetic ketamine as a method with minimal behavioral effect. We find that this paradigm strongly reduces PNN coating in the healthy adult brain and promotes juvenile-like plasticity. Microglia are critically involved in PNN loss because they engage with parvalbumin-positive neurons in their defined cortical layer. We identify external 60-Hz light-flickering entrainment to recapitulate microglia-mediated PNN removal. Importantly, 40-Hz frequency, which is known to remove amyloid plaques, does not induce PNN loss, suggesting microglia might functionally tune to distinct brain frequencies. Thus, our 60-Hz light-entrainment strategy provides an alternative form of PNN intervention in the healthy adult brain.}, author = {Venturino, Alessandro and Schulz, Rouven and De Jesús-Cortés, Héctor and Maes, Margaret E and Nagy, Balint and Reilly-Andújar, Francis and Colombo, Gloria and Cubero, Ryan J and Schoot Uiterkamp, Florianne E and Bear, Mark F. and Siegert, Sandra}, issn = {2211-1247}, journal = {Cell Reports}, number = {1}, publisher = {Elsevier}, title = {{Microglia enable mature perineuronal nets disassembly upon anesthetic ketamine exposure or 60-Hz light entrainment in the healthy brain}}, doi = {10.1016/j.celrep.2021.109313}, volume = {36}, year = {2021}, } @article{9550, abstract = {We prove that the energy of any eigenvector of a sum of several independent large Wigner matrices is equally distributed among these matrices with very high precision. This shows a particularly strong microcanonical form of the equipartition principle for quantum systems whose components are modelled by Wigner matrices. }, author = {Bao, Zhigang and Erdös, László and Schnelli, Kevin}, issn = {2050-5094}, journal = {Forum of Mathematics, Sigma}, publisher = {Cambridge University Press}, title = {{Equipartition principle for Wigner matrices}}, doi = {10.1017/fms.2021.38}, volume = {9}, year = {2021}, } @article{9558, abstract = {We show that turbulent dynamics that arise in simulations of the three-dimensional Navier--Stokes equations in a triply-periodic domain under sinusoidal forcing can be described as transient visits to the neighborhoods of unstable time-periodic solutions. Based on this description, we reduce the original system with more than 10^5 degrees of freedom to a 17-node Markov chain where each node corresponds to the neighborhood of a periodic orbit. The model accurately reproduces long-term averages of the system's observables as weighted sums over the periodic orbits. }, author = {Yalniz, Gökhan and Hof, Björn and Budanur, Nazmi B}, issn = {1079-7114}, journal = {Physical Review Letters}, number = {24}, publisher = {American Physical Society}, title = {{Coarse graining the state space of a turbulent flow using periodic orbits}}, doi = {10.1103/PhysRevLett.126.244502}, volume = {126}, year = {2021}, } @article{9903, abstract = {Eigenstate thermalization in quantum many-body systems implies that eigenstates at high energy are similar to random vectors. Identifying systems where at least some eigenstates are nonthermal is an outstanding question. In this Letter we show that interacting quantum models that have a nullspace—a degenerate subspace of eigenstates at zero energy (zero modes), which corresponds to infinite temperature, provide a route to nonthermal eigenstates. We analytically show the existence of a zero mode which can be represented as a matrix product state for a certain class of local Hamiltonians. In the more general case we use a subspace disentangling algorithm to generate an orthogonal basis of zero modes characterized by increasing entanglement entropy. We show evidence for an area-law entanglement scaling of the least-entangled zero mode in the broad parameter regime, leading to a conjecture that all local Hamiltonians with the nullspace feature zero modes with area-law entanglement scaling and, as such, break the strong thermalization hypothesis. Finally, we find zero modes in constrained models and propose a setup for observing their experimental signatures.}, author = {Karle, Volker and Serbyn, Maksym and Michailidis, Alexios}, issn = {1079-7114}, journal = {Physical Review Letters}, number = {6}, publisher = {American Physical Society}, title = {{Area-law entangled eigenstates from nullspaces of local Hamiltonians}}, doi = {10.1103/physrevlett.127.060602}, volume = {127}, year = {2021}, } @inproceedings{9356, abstract = {In runtime verification, a monitor watches a trace of a system and, if possible, decides after observing each finite prefix whether or not the unknown infinite trace satisfies a given specification. We generalize the theory of runtime verification to monitors that attempt to estimate numerical values of quantitative trace properties (instead of attempting to conclude boolean values of trace specifications), such as maximal or average response time along a trace. Quantitative monitors are approximate: with every finite prefix, they can improve their estimate of the infinite trace's unknown property value. Consequently, quantitative monitors can be compared with regard to a precision-cost trade-off: better approximations of the property value require more monitor resources, such as states (in the case of finite-state monitors) or registers, and additional resources yield better approximations. We introduce a formal framework for quantitative and approximate monitoring, show how it conservatively generalizes the classical boolean setting for monitoring, and give several precision-cost trade-offs for monitors. For example, we prove that there are quantitative properties for which every additional register improves monitoring precision.}, author = {Henzinger, Thomas A and Sarac, Naci E}, booktitle = {Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science}, location = {Online}, publisher = {Institute of Electrical and Electronics Engineers}, title = {{Quantitative and approximate monitoring}}, doi = {10.1109/LICS52264.2021.9470547}, year = {2021}, } @article{9905, abstract = {Vaccines are thought to be the best available solution for controlling the ongoing SARS-CoV-2 pandemic. However, the emergence of vaccine-resistant strains may come too rapidly for current vaccine developments to alleviate the health, economic and social consequences of the pandemic. To quantify and characterize the risk of such a scenario, we created a SIR-derived model with initial stochastic dynamics of the vaccine-resistant strain to study the probability of its emergence and establishment. Using parameters realistically resembling SARS-CoV-2 transmission, we model a wave-like pattern of the pandemic and consider the impact of the rate of vaccination and the strength of non-pharmaceutical intervention measures on the probability of emergence of a resistant strain. As expected, we found that a fast rate of vaccination decreases the probability of emergence of a resistant strain. Counterintuitively, when a relaxation of non-pharmaceutical interventions happened at a time when most individuals of the population have already been vaccinated the probability of emergence of a resistant strain was greatly increased. Consequently, we show that a period of transmission reduction close to the end of the vaccination campaign can substantially reduce the probability of resistant strain establishment. Our results suggest that policymakers and individuals should consider maintaining non-pharmaceutical interventions and transmission-reducing behaviours throughout the entire vaccination period.}, author = {Rella, Simon and Kulikova, Yuliya A. and Dermitzakis, Emmanouil T. and Kondrashov, Fyodor}, issn = {2045-2322}, journal = {Scientific Reports}, number = {1}, publisher = {Springer Nature}, title = {{Rates of SARS-CoV-2 transmission and vaccination impact the fate of vaccine-resistant strains}}, doi = {10.1038/s41598-021-95025-3}, volume = {11}, year = {2021}, } @article{10067, abstract = {The search for novel entangled phases of matter has lead to the recent discovery of a new class of “entanglement transitions,” exemplified by random tensor networks and monitored quantum circuits. Most known examples can be understood as some classical ordering transitions in an underlying statistical mechanics model, where entanglement maps onto the free-energy cost of inserting a domain wall. In this paper we study the possibility of entanglement transitions driven by physics beyond such statistical mechanics mappings. Motivated by recent applications of neural-network-inspired variational Ansätze, we investigate under what conditions on the variational parameters these Ansätze can capture an entanglement transition. We study the entanglement scaling of short-range restricted Boltzmann machine (RBM) quantum states with random phases. For uncorrelated random phases, we analytically demonstrate the absence of an entanglement transition and reveal subtle finite-size effects in finite-size numerical simulations. Introducing phases with correlations decaying as 1/r^α in real space, we observe three regions with a different scaling of entanglement entropy depending on the exponent α. We study the nature of the transition between these regions, finding numerical evidence for critical behavior. Our work establishes the presence of long-range correlated phases in RBM-based wave functions as a required ingredient for entanglement transitions.}, author = {Medina Ramos, Raimel A and Vasseur, Romain and Serbyn, Maksym}, issn = {2469-9969}, journal = {Physical Review B}, number = {10}, publisher = {American Physical Society}, title = {{Entanglement transitions from restricted Boltzmann machines}}, doi = {10.1103/physrevb.104.104205}, volume = {104}, year = {2021}, }