@article{9627, abstract = {We compute the deficiency spaces of operators of the form đ»đŽâŠ—Ì‚ đŒ+đŒâŠ—Ì‚ đ»đ”, for symmetric đ»đŽ and self-adjoint đ»đ”. This enables us to construct self-adjoint extensions (if they exist) by means of von Neumann's theory. The structure of the deficiency spaces for this case was asserted already in Ibort et al. [Boundary dynamics driven entanglement, J. Phys. A: Math. Theor. 47(38) (2014) 385301], but only proven under the restriction of đ»đ” having discrete, non-degenerate spectrum.}, author = {Lenz, Daniel and Weinmann, Timon and Wirth, Melchior}, issn = {1464-3839}, journal = {Proceedings of the Edinburgh Mathematical Society}, number = {3}, pages = {443--447}, publisher = {Cambridge University Press}, title = {{Self-adjoint extensions of bipartite Hamiltonians}}, doi = {10.1017/S0013091521000080}, volume = {64}, year = {2021}, } @article{9629, abstract = {Intestinal organoids derived from single cells undergo complex crypt–villus patterning and morphogenesis. However, the nature and coordination of the underlying forces remains poorly characterized. Here, using light-sheet microscopy and large-scale imaging quantification, we demonstrate that crypt formation coincides with a stark reduction in lumen volume. We develop a 3D biophysical model to computationally screen different mechanical scenarios of crypt morphogenesis. Combining this with live-imaging data and multiple mechanical perturbations, we show that actomyosin-driven crypt apical contraction and villus basal tension work synergistically with lumen volume reduction to drive crypt morphogenesis, and demonstrate the existence of a critical point in differential tensions above which crypt morphology becomes robust to volume changes. Finally, we identified a sodium/glucose cotransporter that is specific to differentiated enterocytes that modulates lumen volume reduction through cell swelling in the villus region. Together, our study uncovers the cellular basis of how cell fate modulates osmotic and actomyosin forces to coordinate robust morphogenesis.}, author = {Yang, Qiutan and Xue, Shi-lei and Chan, Chii Jou and Rempfler, Markus and Vischi, Dario and Maurer-Gutierrez, Francisca and Hiiragi, Takashi and Hannezo, Edouard B and Liberali, Prisca}, issn = {1476-4679}, journal = {Nature Cell Biology}, pages = {733–744}, publisher = {Springer Nature}, title = {{Cell fate coordinates mechano-osmotic forces in intestinal crypt formation}}, doi = {10.1038/s41556-021-00700-2}, volume = {23}, year = {2021}, } @misc{9636, author = {Higginbotham, Andrew P}, publisher = {Institute of Science and Technology Austria}, title = {{Data for "Breakdown of induced p ± ip pairing in a superconductor-semiconductor hybrid"}}, 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{9641, abstract = {At the encounter with a novel environment, contextual memory formation is greatly enhanced, accompanied with increased arousal and active exploration. Although this phenomenon has been widely observed in animal and human daily life, how the novelty in the environment is detected and contributes to contextual memory formation has lately started to be unveiled. The hippocampus has been studied for many decades for its largely known roles in encoding spatial memory, and a growing body of evidence indicates a differential involvement of dorsal and ventral hippocampal divisions in novelty detection. In this brief review article, we discuss the recent findings of the role of mossy cells in the ventral hippocampal moiety in novelty detection and put them in perspective with other novelty-related pathways in the hippocampus. We propose a mechanism for novelty-driven memory acquisition in the dentate gyrus by the direct projection of ventral mossy cells to dorsal dentate granule cells. By this projection, the ventral hippocampus sends novelty signals to the dorsal hippocampus, opening a gate for memory encoding in dentate granule cells based on information coming from the entorhinal cortex. We conclude that, contrary to the presently accepted functional independence, the dorsal and ventral hippocampi cooperate to link the novelty and contextual information, and this dorso-ventral interaction is crucial for the novelty-dependent memory formation.}, author = {Fredes, Felipe and Shigemoto, Ryuichi}, issn = {1095-9564}, journal = {Neurobiology of Learning and Memory}, publisher = {Elsevier}, title = {{The role of hippocampal mossy cells in novelty detection}}, doi = {10.1016/j.nlm.2021.107486}, volume = {183}, 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 JesĂșs-CortĂ©s, HĂ©ctor and Maes, Margaret E and Nagy, Balint and Reilly-AndĂșjar, 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}, } @inproceedings{9644, abstract = {We present a new approach to proving non-termination of non-deterministic integer programs. Our technique is rather simple but efficient. It relies on a purely syntactic reversal of the program's transition system followed by a constraint-based invariant synthesis with constraints coming from both the original and the reversed transition system. The latter task is performed by a simple call to an off-the-shelf SMT-solver, which allows us to leverage the latest advances in SMT-solving. Moreover, our method offers a combination of features not present (as a whole) in previous approaches: it handles programs with non-determinism, provides relative completeness guarantees and supports programs with polynomial arithmetic. The experiments performed with our prototype tool RevTerm show that our approach, despite its simplicity and stronger theoretical guarantees, is at least on par with the state-of-the-art tools, often achieving a non-trivial improvement under a proper configuration of its parameters.}, author = {Chatterjee, Krishnendu and Goharshady, Ehsan Kafshdar and NovotnĂœ, Petr and Zikelic, Dorde}, booktitle = {Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation}, isbn = {9781450383912}, location = {Online}, pages = {1033--1048}, publisher = {Association for Computing Machinery}, title = {{Proving non-termination by program reversal}}, doi = {10.1145/3453483.3454093}, year = {2021}, } @inproceedings{9645, abstract = {We consider the fundamental problem of reachability analysis over imperative programs with real variables. Previous works that tackle reachability are either unable to handle programs consisting of general loops (e.g. symbolic execution), or lack completeness guarantees (e.g. abstract interpretation), or are not automated (e.g. incorrectness logic). In contrast, we propose a novel approach for reachability analysis that can handle general and complex loops, is complete, and can be entirely automated for a wide family of programs. Through the notion of Inductive Reachability Witnesses (IRWs), our approach extends ideas from both invariant generation and termination to reachability analysis. We first show that our IRW-based approach is sound and complete for reachability analysis of imperative programs. Then, we focus on linear and polynomial programs and develop automated methods for synthesizing linear and polynomial IRWs. In the linear case, we follow the well-known approaches using Farkas' Lemma. Our main contribution is in the polynomial case, where we present a push-button semi-complete algorithm. We achieve this using a novel combination of classical theorems in real algebraic geometry, such as Putinar's Positivstellensatz and Hilbert's Strong Nullstellensatz. Finally, our experimental results show we can prove complex reachability objectives over various benchmarks that were beyond the reach of previous methods.}, author = {Asadi, Ali and Chatterjee, Krishnendu and Fu, Hongfei and Goharshady, Amir Kafshdar and Mahdavi, Mohammad}, booktitle = {Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation}, isbn = {9781450383912}, location = {Online}, pages = {772--787}, publisher = {Association for Computing Machinery}, title = {{Polynomial reachability witnesses via StellensĂ€tze}}, doi = {10.1145/3453483.3454076}, year = {2021}, } @inproceedings{9646, abstract = {We consider the fundamental problem of deriving quantitative bounds on the probability that a given assertion is violated in a probabilistic program. We provide automated algorithms that obtain both lower and upper bounds on the assertion violation probability. The main novelty of our approach is that we prove new and dedicated fixed-point theorems which serve as the theoretical basis of our algorithms and enable us to reason about assertion violation bounds in terms of pre and post fixed-point functions. To synthesize such fixed-points, we devise algorithms that utilize a wide range of mathematical tools, including repulsing ranking supermartingales, Hoeffding's lemma, Minkowski decompositions, Jensen's inequality, and convex optimization. On the theoretical side, we provide (i) the first automated algorithm for lower-bounds on assertion violation probabilities, (ii) the first complete algorithm for upper-bounds of exponential form in affine programs, and (iii) provably and significantly tighter upper-bounds than the previous approaches. On the practical side, we show our algorithms can handle a wide variety of programs from the literature and synthesize bounds that are remarkably tighter than previous results, in some cases by thousands of orders of magnitude.}, author = {Wang, Jinyi and Sun, Yican and Fu, Hongfei and Chatterjee, Krishnendu and Goharshady, Amir Kafshdar}, booktitle = {Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation}, isbn = {9781450383912}, location = {Online}, pages = {1171--1186}, publisher = {Association for Computing Machinery}, title = {{Quantitative analysis of assertion violations in probabilistic programs}}, doi = {10.1145/3453483.3454102}, year = {2021}, } @article{9647, abstract = {Gene expression is regulated by the set of transcription factors (TFs) that bind to the promoter. The ensuing regulating function is often represented as a combinational logic circuit, where output (gene expression) is determined by current input values (promoter bound TFs) only. However, the simultaneous arrival of TFs is a strong assumption, since transcription and translation of genes introduce intrinsic time delays and there is no global synchronisation among the arrival times of different molecular species at their targets. We present an experimentally implementable genetic circuit with two inputs and one output, which in the presence of small delays in input arrival, exhibits qualitatively distinct population-level phenotypes, over timescales that are longer than typical cell doubling times. From a dynamical systems point of view, these phenotypes represent long-lived transients: although they converge to the same value eventually, they do so after a very long time span. The key feature of this toy model genetic circuit is that, despite having only two inputs and one output, it is regulated by twenty-three distinct DNA-TF configurations, two of which are more stable than others (DNA looped states), one promoting and another blocking the expression of the output gene. Small delays in input arrival time result in a majority of cells in the population quickly reaching the stable state associated with the first input, while exiting of this stable state occurs at a slow timescale. In order to mechanistically model the behaviour of this genetic circuit, we used a rule-based modelling language, and implemented a grid-search to find parameter combinations giving rise to long-lived transients. Our analysis shows that in the absence of feedback, there exist path-dependent gene regulatory mechanisms based on the long timescale of transients. The behaviour of this toy model circuit suggests that gene regulatory networks can exploit event timing to create phenotypes, and it opens the possibility that they could use event timing to memorise events, without regulatory feedback. The model reveals the importance of (i) mechanistically modelling the transitions between the different DNA-TF states, and (ii) employing transient analysis thereof.}, author = {Petrov, Tatjana and Igler, Claudia and Sezgin, Ali and Henzinger, Thomas A and Guet, Calin C}, issn = {0304-3975}, journal = {Theoretical Computer Science}, pages = {1--16}, publisher = {Elsevier}, title = {{Long lived transients in gene regulation}}, doi = {10.1016/j.tcs.2021.05.023}, volume = {893}, year = {2021}, } @article{9656, abstract = {Tropisms, growth responses to environmental stimuli such as light or gravity, are spectacular examples of adaptive plant development. The plant hormone auxin serves as a major coordinative signal. The PIN auxin exporters, through their dynamic polar subcellular localizations, redirect auxin fluxes in response to environmental stimuli and the resulting auxin gradients across organs underly differential cell elongation and bending. In this review, we discuss recent advances concerning regulations of PIN polarity during tropisms, focusing on PIN phosphorylation and trafficking. We also cover how environmental cues regulate PIN actions during tropisms, and a crucial role of auxin feedback on PIN polarity during bending termination. Finally, the interactions between different tropisms are reviewed to understand plant adaptive growth in the natural environment.}, author = {Han, Huibin and Adamowski, Maciek and Qi, Linlin and Alotaibi, SS and Friml, Jiƙí}, issn = {1469-8137}, journal = {New Phytologist}, number = {2}, pages = {510--522}, publisher = {Wiley}, title = {{PIN-mediated polar auxin transport regulations in plant tropic responses}}, doi = {10.1111/nph.17617}, volume = {232}, year = {2021}, } @article{9657, abstract = {To overcome nitrogen deficiency, legume roots establish symbiotic interactions with nitrogen-fixing rhizobia that is fostered in specialized organs (nodules). Similar to other organs, nodule formation is determined by a local maximum of the phytohormone auxin at the primordium site. However, how auxin regulates nodule development remains poorly understood. Here, we found that in soybean, (Glycine max), dynamic auxin transport driven by PIN-FORMED (PIN) transporter GmPIN1 is involved in nodule primordium formation. GmPIN1 was specifically expressed in nodule primordium cells and GmPIN1 was polarly localized in these cells. Two nodulation regulators, (iso)flavonoids trigger expanded distribution of GmPIN1b to root cortical cells, and cytokinin rearranges GmPIN1b polarity. Gmpin1abc triple mutants generated with CRISPR-Cas9 showed impaired establishment of auxin maxima in nodule meristems and aberrant divisions in the nodule primordium cells. Moreover, overexpression of GmPIN1 suppressed nodule primordium initiation. GmPIN9d, an ortholog of Arabidopsis thaliana PIN2, acts together with GmPIN1 later in nodule development to acropetally transport auxin in vascular bundles, fine-tuning the auxin supply for nodule enlargement. Our findings reveal how PIN-dependent auxin transport modulates different aspects of soybean nodule development and suggest that establishment of auxin gradient is a prerequisite for the proper interaction between legumes and rhizobia.}, author = {Gao, Z and Chen, Z and Cui, Y and Ke, M and Xu, H and Xu, Q and Chen, J and Li, Y and Huang, L and Zhao, H and Huang, D and Mai, S and Xu, T and Liu, X and Li, S and Guan, Y and Yang, W and Friml, Jiƙí and PetrĂĄĆĄek, J and Zhang, J and Chen, X}, issn = {1532-298x}, journal = {Plant Cell}, number = {9}, pages = {2981–3003}, publisher = {American Society of Plant Biologists}, title = {{GmPIN-dependent polar auxin transport is involved in soybean nodule development}}, doi = {10.1093/plcell/koab183}, volume = {33}, year = {2021}, } @article{9669, abstract = {The set of known stable phases of water may not be complete, and some of the phase boundaries between them are fuzzy. Starting from liquid water and a comprehensive set of 50 ice structures, we compute the phase diagram at three hybrid density-functional-theory levels of approximation, accounting for thermal and nuclear fluctuations as well as proton disorder. Such calculations are only made tractable because we combine machine-learning methods and advanced free-energy techniques. The computed phase diagram is in qualitative agreement with experiment, particularly at pressures â‰Č 8000 bar, and the discrepancy in chemical potential is comparable with the subtle uncertainties introduced by proton disorder and the spread between the three hybrid functionals. None of the hypothetical ice phases considered is thermodynamically stable in our calculations, suggesting the completeness of the experimental water phase diagram in the region considered. Our work demonstrates the feasibility of predicting the phase diagram of a polymorphic system from first principles and provides a thermodynamic way of testing the limits of quantum-mechanical calculations.}, author = {Reinhardt, Aleks and Cheng, Bingqing}, issn = {2041-1723}, journal = {Nature Communications}, number = {1}, publisher = {Springer Nature}, title = {{Quantum-mechanical exploration of the phase diagram of water}}, doi = {10.1038/s41467-020-20821-w}, volume = {12}, year = {2021}, } @article{9679, abstract = {The relative motion of three impenetrable particles on a ring, in our case two identical fermions and one impurity, is isomorphic to a triangular quantum billiard. Depending on the ratio Îș of the impurity and fermion masses, the billiards can be integrable or non-integrable (also referred to in the main text as chaotic). To set the stage, we first investigate the energy level distributions of the billiards as a function of 1/Îș ∈ [0, 1] and find no evidence of integrable cases beyond the limiting values 1/Îș = 1 and 1/Îș = 0. Then, we use machine learning tools to analyze properties of probability distributions of individual quantum states. We find that convolutional neural networks can correctly classify integrable and non-integrable states. The decisive features of the wave functions are the normalization and a large number of zero elements, corresponding to the existence of a nodal line. The network achieves typical accuracies of 97%, suggesting that machine learning tools can be used to analyze and classify the morphology of probability densities obtained in theory or experiment.}, author = {Huber, David and Marchukov, Oleksandr V. and Hammer, Hans Werner and Volosniev, Artem}, issn = {1367-2630}, journal = {New Journal of Physics}, number = {6}, publisher = {IOP Publishing}, title = {{Morphology of three-body quantum states from machine learning}}, doi = {10.1088/1367-2630/ac0576}, volume = {23}, year = {2021}, } @unpublished{9696, abstract = {Most water in the universe may be superionic, and its thermodynamic and transport properties are crucial for planetary science but difficult to probe experimentally or theoretically. We use machine learning and free energy methods to overcome the limitations of quantum mechanical simulations, and characterize hydrogen diffusion, superionic transitions, and phase behaviors of water at extreme conditions. We predict that a close-packed superionic phase with mixed stacking is stable over a wide temperature and pressure range, while a body-centered cubic phase is only thermodynamically stable in a small window but is kinetically favored. Our phase boundaries, which are consistent with the existing-albeit scarce-experimental observations, help resolve the fractions of insulating ice, different superionic phases, and liquid water inside of ice giants.}, author = {Cheng, Bingqing and Bethkenhagen, Mandy and Pickard, Chris J. and Hamel, Sebastien}, booktitle = {arXiv}, title = {{Predicting the phase behaviors of superionic water at planetary conditions}}, doi = {10.48550/arXiv.2103.09035}, year = {2021}, } @article{9698, abstract = {Machine learning models are poised to make a transformative impact on chemical sciences by dramatically accelerating computational algorithms and amplifying insights available from computational chemistry methods. However, achieving this requires a confluence and coaction of expertise in computer science and physical sciences. This review is written for new and experienced researchers working at the intersection of both fields. We first provide concise tutorials of computational chemistry and machine learning methods, showing how insights involving both can be achieved. We then follow with a critical review of noteworthy applications that demonstrate how computational chemistry and machine learning can be used together to provide insightful (and useful) predictions in molecular and materials modeling, retrosyntheses, catalysis, and drug design.}, author = {Keith, John A. and Valentin Vassilev-Galindo, Valentin and Cheng, Bingqing and Chmiela, Stefan and Gastegger, Michael and MĂŒller, Klaus-Robert and Tkatchenko, Alexandre}, issn = {1520-6890}, journal = {Chemical Reviews}, number = {16}, pages = {9816--9872}, publisher = {American Chemical Society}, title = {{Combining machine learning and computational chemistry for predictive insights into chemical systems}}, doi = {10.1021/acs.chemrev.1c00107}, volume = {121}, year = {2021}, } @article{9746, abstract = {Evolutionary adaptation is a major source of antibiotic resistance in bacterial pathogens. Evolution-informed therapy aims to constrain resistance by accounting for bacterial evolvability. Sequential treatments with antibiotics that target different bacterial processes were previously shown to limit adaptation through genetic resistance trade-offs and negative hysteresis. Treatment with homogeneous sets of antibiotics is generally viewed to be disadvantageous, as it should rapidly lead to cross-resistance. We here challenged this assumption by determining the evolutionary response of Pseudomonas aeruginosa to experimental sequential treatments involving both heterogenous and homogeneous antibiotic sets. To our surprise, we found that fast switching between only ÎČ-lactam antibiotics resulted in increased extinction of bacterial populations. We demonstrate that extinction is favored by low rates of spontaneous resistance emergence and low levels of spontaneous cross-resistance among the antibiotics in sequence. The uncovered principles may help to guide the optimized use of available antibiotics in highly potent, evolution-informed treatment designs.}, author = {Batra, Aditi and Römhild, Roderich and Rousseau, Emilie and Franzenburg, Sören and Niemann, Stefan and Schulenburg, Hinrich}, issn = {2050-084X}, journal = {eLife}, publisher = {eLife Sciences Publications}, title = {{High potency of sequential therapy with only beta-lactam antibiotics}}, doi = {10.7554/elife.68876}, volume = {10}, year = {2021}, } @article{9759, author = {Bartlett, Michael John and Arslan, Feyza N and Bankston, Adriana and Sarabipour, Sarvenaz}, issn = {1553-7358}, journal = {PLoS Computational Biology}, number = {7}, publisher = {Public Library of Science}, title = {{Ten simple rules to improve academic work- life balance}}, doi = {10.1371/journal.pcbi.1009124}, volume = {17}, year = {2021}, } @article{9761, abstract = {The important roles of mitochondrial function and dysfunction in the process of neurodegeneration are widely acknowledged. Retinal ganglion cells (RGCs) appear to be a highly vulnerable neuronal cell type in the central nervous system with respect to mitochondrial dysfunction but the actual reasons for this are still incompletely understood. These cells have a unique circumstance where unmyelinated axons must bend nearly 90° to exit the eye and then cross a translaminar pressure gradient before becoming myelinated in the optic nerve. This region, the optic nerve head, contains some of the highest density of mitochondria present in these cells. Glaucoma represents a perfect storm of events occurring at this location, with a combination of changes in the translaminar pressure gradient and reassignment of the metabolic support functions of supporting glia, which appears to apply increased metabolic stress to the RGC axons leading to a failure of axonal transport mechanisms. However, RGCs themselves are also extremely sensitive to genetic mutations, particularly in genes affecting mitochondrial dynamics and mitochondrial clearance. These mutations, which systemically affect the mitochondria in every cell, often lead to an optic neuropathy as the sole pathologic defect in affected patients. This review summarizes knowledge of mitochondrial structure and function, the known energy demands of neurons in general, and places these in the context of normal and pathological characteristics of mitochondria attributed to RGCs. }, author = {Muench, Nicole A. and Patel, Sonia and Maes, Margaret E and Donahue, Ryan J. and Ikeda, Akihiro and Nickells, Robert W.}, issn = {2073-4409}, journal = {Cells}, number = {7}, publisher = {MDPI}, title = {{The influence of mitochondrial dynamics and function on retinal ganglion cell susceptibility in optic nerve disease}}, doi = {10.3390/cells10071593}, volume = {10}, year = {2021}, } @article{9769, abstract = {A few years ago, flow equations were introduced as a technique for calculating the ground-state energies of cold Bose gases with and without impurities. In this paper, we extend this approach to compute observables other than the energy. As an example, we calculate the densities, and phase fluctuations of one-dimensional Bose gases with one and two impurities. For a single mobile impurity, we use flow equations to validate the mean-field results obtained upon the Lee-Low-Pines transformation. We show that the mean-field approximation is accurate for all values of the boson-impurity interaction strength as long as the phase coherence length is much larger than the healing length of the condensate. For two static impurities, we calculate impurity-impurity interactions induced by the Bose gas. We find that leading order perturbation theory fails when boson-impurity interactions are stronger than boson-boson interactions. The mean-field approximation reproduces the flow equation results for all values of the boson-impurity interaction strength as long as boson-boson interactions are weak.}, author = {Brauneis, Fabian and Hammer, Hans-Werner and Lemeshko, Mikhail and Volosniev, Artem}, issn = {2542-4653}, journal = {SciPost Physics}, number = {1}, publisher = {SciPost Foundation}, title = {{Impurities in a one-dimensional Bose gas: The flow equation approach}}, doi = {10.21468/scipostphys.11.1.008}, volume = {11}, year = {2021}, }