@inbook{17075,
  abstract     = {Disorders associated with the malfunction of amino acid transporters mainly affect the function of the intestine, kidney, brain, and liver. Mutations of brain amino acid transporters, for example, alter neuronal excitability (e.g., episodic ataxia due to SLC1A3 (EAAT1) defect and hyperekplexia due to SLC6A5 (GLYT2) deficiency) or brain development (SLC1A1 (EAAT3), SLC3A2/SLC7A5 (CD98hc/LAT1), and SLC1A4 (ASCT1) deficiencies). Mutations of renal and intestinal amino acid transporters SLC3A1/SLC7A9 (rBAT/b0,+AT) and SLC1A1 (EAAT3) cause renal problems (cystinuria and dicarboxylic aminoaciduria, respectively) and malabsorption that can affect whole-body homoeostasis (Hartnup disorder SLC6A19 (B0AT1), lysinuric protein intolerance SLC3A2/SLC7A7 (CD98hc/y+LAT1), and hyperdibasic aminoaciduria type 1). Mutations in the neuronal system A amino acid transporter SLC38A8 (SNAT8) cause eye developmental and visual defects. Inborn errors associated with mitochondrial SLC25 family members such as SLC25A12 (neuronal- and muscle-specific mitochondrial aspartate/glutamate transporter 1; AGC1) (global cerebral hypomyelination), SLC25A13 (aspartate/glutamate transporter 2) (citrin deficiency), SLC25A15 (ornithine-citrulline carrier 2) (homocitrullinuria, hyperornithinemia, and hyperammonemia syndrome), and SLC25A22 (mitochondrial glutamate/H+ symporter 1, GC1) (neonatal myoclonic epilepsy) will be dealt within Chap. 43 (defects of mitochondrial carriers).},
  author       = {Palacín, Manuel and Bröer, Stefan and Novarino, Gaia},
  booktitle    = {Physician's Guide to the Diagnosis, Treatment, and Follow-Up of Inherited Metabolic Diseases},
  editor       = {Blau, Nenad and Vici, Carlo Dionisi and Ferreira, Carlos R.  and Vianey-Saban, Christine and van Karnebeek, Clara D.M.},
  isbn         = {9783030677268},
  pages        = {291--312},
  publisher    = {Springer Nature},
  title        = {{Amino Acid Transport Defects}},
  doi          = {10.1007/978-3-030-67727-5_18},
  year         = {2022},
}

@article{17077,
  abstract     = {Resolving a conjecture of Füredi from 1988, we prove that with high probability, the random graph 𝔾(𝑛, 1/2) admits a friendly bisection of its vertex set, i.e., a
partition of its vertex set into two parts whose sizes differ by at most one in which
𝑛 − 𝑜(𝑛) vertices have more neighbours in their own part as across. Our proof is constructive, and in the process, we develop a new method to study stochastic processes
driven by degree information in random graphs; this involves combining enumeration
techniques with an abstract second moment argument.},
  author       = {Ferber, Asaf and Kwan, Matthew Alan and Narayanan, Bhargav and Sah, Ashwin and Sawhney, Mehtaab},
  issn         = {2692-3688},
  journal      = {Communications of the American Mathematical Society},
  number       = {10},
  pages        = {380--416},
  publisher    = {American Mathematical Society},
  title        = {{Friendly bisections of random graphs}},
  doi          = {10.1090/cams/13},
  volume       = {2},
  year         = {2022},
}

@inproceedings{17084,
  abstract     = {Given a graph where every vertex has exactly one labeled token, how can we most quickly execute a given permutation on the tokens? In (sequential) token swapping, the goal is to use the shortest possible sequence of swaps, each of which exchanges the tokens at the two endpoints of an edge of the graph. In parallel token swapping, the goal is to use the fewest rounds, each of which consists of one or more swaps on the edges of a matching. We prove that both of these problems remain NP-hard when the graph is restricted to be a tree. These token swapping problems have been studied by disparate groups of researchers in discrete mathematics, theoretical computer science, robot motion planning, game theory, and engineering. Previous work establishes NP-completeness on general graphs (for both problems), constant-factor approximation algorithms, and some poly-time exact algorithms for simple graph classes such as cliques, stars, paths, and cycles. Sequential and parallel token swapping on trees were first studied over thirty years ago (as "sorting with a transposition tree") and over twenty-five years ago (as "routing permutations via matchings"), yet their complexities were previously unknown. We also show limitations on approximation of sequential token swapping on trees: we identify a broad class of algorithms that encompass all three known polynomial-time algorithms that achieve the best known approximation factor (which is 2) and show that no such algorithm can achieve an approximation factor less than 2.},
  author       = {Aichholzer, Oswin and Demaine, Erik D. and Korman, Matias and Lubiw, Anna and Lynch, Jayson and Masárová, Zuzana and Rudoy, Mikhail and Vassilevska Williams, Virginia and Wein, Nicole},
  booktitle    = {30th Annual European Symposium on Algorithms},
  location     = {Berlin/Potsdam, Germany},
  publisher    = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
  title        = {{Hardness of token swapping on trees}},
  doi          = {10.4230/LIPIcs.ESA.2022.3},
  volume       = {244},
  year         = {2022},
}

@inbook{17085,
  abstract     = {Mosses are a cosmopolitan group of land plants, sister to vascular plants, with a high potential for molecular and cell biological research. The species Physcomitrium patens has helped gaining better understanding of the biological processes of the plant cell, and it has become a central system to understand water-to-land plant transition through 2D-to-3D growth transition, regulation of asymmetric cell division, shoot apical cell establishment and maintenance, phyllotaxis and regeneration. P. patens was the first fully sequenced moss in 2008, with the latest annotated release in 2018. It has been shown that many gene functions and networks are conserved in mosses when compared to angiosperms. Importantly, this model organism has a simplified and accessible body structure that facilitates close tracking in time and space with the support of live cell imaging set-ups and multiple reporter lines. This has become possible thanks to its fully established molecular toolkit, with highly efficient PEG-assisted, CRISPR/Cas9 and RNAi transformation and silencing protocols, among others. Here we provide examples on how mosses exhibit advantages over vascular plants to study several processes and their future potential to answer some other outstanding questions in plant cell biology.},
  author       = {Floriach-Clark, Jordi and Tang, Han and Willemsen, Viola},
  booktitle    = {Model Organisms in Plant Genetics},
  editor       = {Abdurakhmonov, Ibrokhim Y.},
  isbn         = {9781839697500},
  publisher    = {IntechOpen},
  title        = {{Mosses: Accessible Systems for Plant Development Studies}},
  doi          = {10.5772/intechopen.100535},
  year         = {2022},
}

@inproceedings{17086,
  abstract     = {We consider a high-dimensional mean estimation problem over a binary hidden Markov model, which illuminates the interplay between memory in data, sample size, dimension, and signal strength in statistical inference. In this model, an estimator observes n samples of a d-dimensional parameter vector θ∗∈Rd, multiplied by a random sign Si (1≤i≤n), and corrupted by isotropic standard Gaussian noise. The sequence of signs {Si}i∈[n]∈{−1,1}n is drawn from a stationary homogeneous Markov chain with flip probability δ∈[0,1/2]. As δ varies, this model smoothly interpolates two well-studied models: the Gaussian Location Model for which δ=0 and the Gaussian Mixture Model for which δ=1/2. Assuming that the estimator knows δ, we establish a nearly minimax optimal (up to logarithmic factors) estimation error rate, as a function of ∥θ∗∥,δ,d,n. We then provide an upper bound to the case of estimating δ, assuming a (possibly inaccurate) knowledge of θ∗. The bound is proved to be tight when θ∗ is an accurately known constant. These results are then combined to an algorithm which estimates θ∗ with δ unknown a priori, and theoretical guarantees on its error are stated.},
  author       = {Zhang, Yihan and Weinberger, Nir},
  booktitle    = {36th Conference on Neural Information Processing Systems},
  isbn         = {9781713871088},
  location     = {New Orleans, LA, United States},
  publisher    = {ML Research Press},
  title        = {{Mean estimation in high-dimensional binary Markov Gaussian mixture models}},
  volume       = {35},
  year         = {2022},
}

@inproceedings{17088,
  abstract     = {In this paper, we consider the problem of sparsifying BERT models, which are a key building block for natural language processing, in order to reduce their storage and computational cost. We introduce the Optimal BERT Surgeon (oBERT), an efficient and accurate pruning method based on approximate second-order information, which we show to yield state-of-the-art results in both stages of language tasks: pre-training and fine-tuning. Specifically, oBERT extends existing work on second-order pruning by allowing for pruning weight blocks, and is the first such method that is applicable at BERT scale. Second, we investigate compounding compression approaches to obtain highly compressed but accurate models for deployment on edge devices. These models significantly push boundaries of the current state-of-the-art sparse BERT models with respect to all metrics: model size, inference speed and task accuracy. For example, relative to the dense BERT-base, we obtain 10x model size compression with < 1% accuracy drop, 10x CPU-inference speedup with < 2% accuracy drop, and 29x CPU-inference speedup with < 7.5% accuracy drop. Our code, fully integrated with Transformers and SparseML, is available at https://github.com/neuralmagic/sparseml/tree/main/research/optimal_BERT_surgeon_oBERT.},
  author       = {Kurtic, Eldar and Campos, Daniel and Nguyen, Tuan and Frantar, Elias and Kurtz, Mark and Fineran, Benjamin and Goin, Michael and Alistarh, Dan-Adrian},
  booktitle    = {Proceedings of the 2022 Conference on Empirical Methods in Natural Language Processing},
  location     = {Abu Dhabi, United Arab Emirates},
  pages        = {4163--4181},
  publisher    = {Association for Computational Linguistics},
  title        = {{The optimal BERT surgeon: Scalable and accurate second-order pruning for large language models}},
  doi          = {10.18653/v1/2022.emnlp-main.279},
  year         = {2022},
}

@unpublished{17115,
  abstract     = {Cascades are RNA-guided multi-subunit CRISPR-Cas surveillances complexes that target foreign nucleic acids for destruction. Here, we present a 2.9-Å resolution cryo-electron (cryo-EM) structure of the <jats:italic>D. vulgaris</jats:italic> type I-C Cascade bound to a double-stranded (ds)DNA target. Our data shows how the 5’-TTC-3’ protospacer adjacent motif (PAM) sequence is recognized, and provides a unique mechanism through which the displaced, single-stranded non-target strand (NTS) is stabilized via stacking interactions with protein subunits in order to favor R-loop formation and prevent dsDNA re-annealing. Additionally, we provide structural insights into how diverse anti-CRISPR (Acr) proteins utilize distinct strategies to achieve a shared mechanism of type I-C Cascade inhibition by blocking initial DNA binding. These observations provide a structural basis for directional R-loop formation and reveal how divergent Acr proteins have converged upon common molecular mechanisms to efficiently shut down CRISPR immunity.},
  author       = {O’Brien, Roisin E. and Bravo, Jack Peter Kelly and Ramos, Delisa and Hibshman, Grace N. and Wright, Jacquelyn T. and Taylor, David W.},
  booktitle    = {bioRxiv},
  publisher    = {Cold Spring Harbor Laboratory},
  title        = {{Modes of inhibition used by phage anti-CRISPRs to evade type I-C Cascade}},
  doi          = {10.1101/2022.06.15.496202},
  year         = {2022},
}

@unpublished{17116,
  abstract     = {CRISPR (Clustered regularly interspaced short palindromic repeats)-Cas (CRISPR-associated) systems are a type of adaptive immune response in bacteria and archaea that utilize crRNA (CRISPR RNA)-guided effector complexes to target complementary RNA or DNA for destruction. The prototypical type III-A and III-B CRISPR-Cas systems utilize multi-subunit effector complexes composed of individual proteins to cleave ssRNA targets at 6-nt intervals, as well as non-specifically degrading ssDNA and activating cyclic oligoadenylate (cOA) synthesis. Recent studies have shown that type III systems can contain subunit fusions yet maintain canonical type III RNA-targeting capabilities. To understand how a multi-subunit fusion effector functions, we determine structures of a variant type III-D effector and biochemically characterize how it cleaves RNA targets. These findings provide insights into how multi-subunit fusion proteins are tethered together and assemble into an active and programmable RNA endonuclease, how the effector utilizes a novel mechanism for target RNA seeding, and the structural basis for the evolution of type III effector complexes. Furthermore, our results provide a blueprint for fusing subunits in class 1 effectors for design of user-defined effector complexes with disparate activities.</jats:p><jats:sec><jats:title>Important note</jats:title><jats:p>While this manuscript was in preparation, a manuscript describing the structure of the type III-E effector was published<jats:sup>1</jats:sup>. We reference these important findings; however, a careful comparison of the structures will follow once the coordinates have been released by the PDB.},
  author       = {Schwartz, Evan A. and Bravo, Jack Peter Kelly and Macias, Luis A. and McCafferty, Caitlyn L. and Dangerfield, Tyler L. and Walker, Jada N. and Brodbelt, Jennifer S. and Fineran, Peter C. and Fagerlund, Robert D. and Taylor, David W.},
  booktitle    = {bioRxiv},
  publisher    = {Cold Spring Harbor Laboratory},
  title        = {{Assembly of multi-subunit fusion proteins into the RNA-targeting type III-D CRISPR-Cas effector complex}},
  doi          = {10.1101/2022.06.13.496011},
  year         = {2022},
}

@unpublished{17117,
  abstract     = {Cas12a2 is a CRISPR-associated nuclease that performs RNA-guided degradation of non-specific single-stranded (ss)RNA, ssDNA and double-stranded (ds)DNA upon recognition of a complementary RNA target, culminating in abortive infection (Dmytrenko 2022). Here, we report structures of Cas12a2 in binary, ternary, and quaternary complexes to reveal a complete activation pathway. Our structures reveal that Cas12a2 is autoinhibited until binding a cognate RNA target, which exposes the RuvC active site within a large, positively charged cleft. Double-stranded DNA substrates are captured through duplex distortion and local melting, stabilized by pairs of ‘aromatic clamp’ residues that are crucial for dsDNA degradation and in <jats:italic>vivo</jats:italic> immune system function. Our work provides a structural basis for this unprecedented mechanism of abortive infection to achieve population-level immunity, which can be leveraged to create rational mutants that degrade a spectrum of collateral substrates.},
  author       = {Bravo, Jack Peter Kelly and Hallmark, Thom and Naegle, Bronson and Beisel, Chase L. and Jackson, Ryan N. and Taylor, David W.},
  booktitle    = {bioRxiv},
  publisher    = {Cold Spring Harbor Laboratory},
  title        = {{Large-scale structural rearrangements unleash indiscriminate nuclease activity of CRISPR-Cas12a2}},
  doi          = {10.1101/2022.06.13.495754},
  year         = {2022},
}

@unpublished{17157,
  abstract     = {An action of a complex reductive group G on a smooth projective variety X is regular when all regular unipotent elements in G act with finitely many fixed points. Then the complex G-equivariant cohomology ring of X is isomorphic to the coordinate ring of a certain regular fixed point scheme. Examples include partial flag varieties, smooth Schubert varieties and Bott-Samelson varieties. We also show that a more general version of the fixed point scheme allows a generalisation to GKM spaces, such as toric varieties.},
  author       = {Hausel, Tamás and Rychlewicz, Kamil P},
  booktitle    = {arXiv},
  title        = {{Spectrum of equivariant cohomology as a fixed point scheme}},
  doi          = {10.48550/arXiv.2212.11836},
  year         = {2022},
}

@article{18606,
  abstract     = {Shear thickening is an intriguing rheological behaviour which consists in a brutal increase in the viscosity above a critical shear rate. It is famously encountered in suspensions of corn starch in water. Despite having been discovered in the early 1930's, its underlying mechanisms remained a mystery for a long time. In 2013–14, numerical and theoretical works [[1], [2], [3]] put forward a frictional transition scenario to explain this phenomenon.
In this talk, I will present experimental work investigating this frictional transition scenario. In order to test the ideas of this model, one has to go further than standard rheological techniques, since they do not provide access to the frictional state of the measured suspension. I will thus focus on the techniques that we developed in order to evidence the frictional transition and link it to the presence of a shear-thickening behaviour.},
  author       = {Clavaud, Cécile},
  issn         = {2772-5693},
  journal      = {Science Talks},
  publisher    = {Elsevier},
  title        = {{Shear thickening in dense suspensions: an experimental study}},
  doi          = {10.1016/j.sctalk.2022.100038},
  volume       = {3},
  year         = {2022},
}

@inproceedings{18876,
  abstract     = {Convolutional neural networks were the standard for solving many computer vision tasks until recently, when Transformers of MLP-based architectures have started to show competitive performance. These architectures typically have a vast number of weights and need to be trained on massive datasets; hence, they are not suitable for their use in low-data regimes. In this work, we propose a simple yet effective framework to improve generalization from small amounts of data. We augment modern CNNs with fully-connected (FC) layers and show the massive impact this architectural change has in low-data regimes. We further present an online joint knowledge-distillation method to utilize the extra FC layers at train time but avoid them during test time. This allows us to improve the generalization of a CNN-based model without any increase in the number of weights at test time. We perform classification experiments for a large range of network backbones and several standard datasets on supervised learning and active learning. Our experiments significantly outperform the networks without fully-connected layers, reaching a relative improvement of up to 16% validation accuracy in the supervised setting without adding any extra parameters during inference.},
  author       = {Kocsis, Peter and Súkeník, Peter and Brasó, Guillem and Niessner, Matthias and Leal-Taixé, Laura and Elezi, Ismail},
  booktitle    = {36th Conference on Neural Information Processing Systems},
  issn         = {1049-5258},
  location     = {New Orleans, LA, United States},
  pages        = {1896--1908},
  publisher    = {Neural Information Processing Systems Foundation},
  title        = {{The unreasonable effectiveness of fully-connected layers for low-data regimes}},
  volume       = {35},
  year         = {2022},
}

@article{19490,
  abstract     = {Abstract. We study integral points on the quadratic twists ED : y2 = x3 −
D2x of the congruent number curve. We give upper bounds on the number of
integral points in each coset of 2ED(Q) in ED(Q) and show that their total is
 (3.8)rank ED(Q). We further show that the average number of non-torsion
integral points in this family is bounded above by 2. As an application we also
deduce from our upper bounds that the system of simultaneous Pell equations
aX2 − bY 2 = d, bY 2 − cZ2 = d for pairwise coprime positive integers a, b, c, d,
has at most  (3.6)ω(abcd) integer solutions.},
  author       = {Chan, Yik Tung},
  issn         = {1088-6850},
  journal      = {Transactions of the American Mathematical Society},
  number       = {9},
  pages        = {6675--6700},
  publisher    = {American Mathematical Society},
  title        = {{Integral points on the congruent number curve}},
  doi          = {10.1090/tran/8732},
  volume       = {375},
  year         = {2022},
}

@article{19491,
  abstract     = {Using a recent breakthrough of Smith [18], we improve the results of Fouvry and Klüners [4, 5] on the solubility of the negative Pell equation. Let D denote the set of positive squarefree integers having no prime factors congruent to 3 modulo 4 . Stevenhagen [19] conjectured that the density of d in D such that the negative Pell equation x2−dy2=−1 is solvable with x,y∈Z is 58.1% , to the nearest tenth of a percent. By studying the distribution of the 8 -rank of narrow class groups Cl+(d) of Q(√d) , we prove that the infimum of this density is at least 53.8% .},
  author       = {Chan, Yik Tung and Koymans, Peter and Milovic, Djordjo and Pagano, Carlo},
  issn         = {2050-5094},
  journal      = {Forum of Mathematics, Sigma},
  publisher    = {Cambridge University Press},
  title        = {{The 8-rank of the narrow class group and the negative Pell equation}},
  doi          = {10.1017/fms.2022.40},
  volume       = {10},
  year         = {2022},
}

@article{19822,
  abstract     = {>Controlling spin wave excitations in magnetic materials underpins the burgeoning field of magnonics. Yet, little is known about how magnons interact with the conduction electrons of itinerant magnets, or how this interplay can be controlled. Via a surface-sensitive spectroscopic approach, we demonstrate a strong electron–magnon coupling at the Pd-terminated surface of the delafossite oxide PdCoO2, where a polar surface charge mediates a Stoner transition to itinerant surface ferromagnetism. We show how the coupling is enhanced sevenfold with increasing surface disorder, and concomitant charge carrier doping, becoming sufficiently strong to drive the system into a polaronic regime, accompanied by a significant quasiparticle mass enhancement. Our study thus sheds light on electron–magnon interactions in solid-state materials, and the ways in which these can be controlled.},
  author       = {Mazzola, F. and Yim, C. -M. and Sunko, Veronika and Khim, S. and Kushwaha, P. and Clark, O. J. and Bawden, L. and Marković, I. and Chakraborti, D. and Kim, T. K. and Hoesch, M. and Mackenzie, A. P. and Wahl, P. and King, P. D. C.},
  issn         = {2397-4648},
  journal      = {npj Quantum Materials},
  publisher    = {Springer Nature},
  title        = {{Tuneable electron–magnon coupling of ferromagnetic surface states in PdCoO2}},
  doi          = {10.1038/s41535-022-00428-8},
  volume       = {7},
  year         = {2022},
}

@inbook{19984,
  abstract     = {The first part of this paper is a survey of mathematical results on mirror symmetry phenomena between Hitchin systems for Langlands dual groups. The second part introduces
and discusses multiplicity algebras of the Hitchin system on Lagrangians, and considers
corresponding conjectural structures on their mirror.},
  author       = {Hausel, Tamás},
  booktitle    = {International Congress of Mathematicians},
  isbn         = {9783985470587},
  location     = {virtuel},
  pages        = {2228--2249},
  publisher    = {EMS Press},
  title        = {{Enhanced mirror symmetry for Langlands dual Hitchin systems}},
  doi          = {10.4171/icm2022/164},
  year         = {2022},
}

@inbook{20062,
  abstract     = {This article presents two fine-grained complexity lower bounds with relevance to algorithmic problems in computer aided verification. We have chosen these lower bounds as the proofs are relatively simple, but the techniques can be extended to give lower bounds for many more algorithmic problems. The goal is to present the bounds with minimal notation, making the results accessible to a broad community and stimulating further research in the area.

Specifically, we first describe a lower bound on the symbolic complexity of computing strongly connected components, which can be extended to show lower bounds for fundamental model-checking questions in graphs, published in [CDHL16b]. Second we present a conditional lower bound for disjunctive safety problems on graphs from [CDHL18] in the RAM model of computation. This bound can be modified to give conditional lower bounds for disjunctive objectives for reachability, Büchi, coBüchi and Rabin objectives in MDPs. We also present various open questions.},
  author       = {Henzinger, Monika H},
  booktitle    = {Principles of Systems Design},
  editor       = {Raskin, Jean-François and Chatterjee, Krishnendu and Doyen, Laurent and Majumdar, Rupak},
  isbn         = {9783031223365},
  issn         = {1611-3349},
  pages        = {292--305},
  publisher    = {Springer Nature Switzerland},
  title        = {{Fine-Grained Complexity Lower Bounds for Problems in Computer Aided Verification}},
  doi          = {10.1007/978-3-031-22337-2_14},
  volume       = {13660},
  year         = {2022},
}

@article{20616,
  abstract     = {We establish two WDVV-style relations for the disk invariants of real symplectic fourfolds by implementing Georgieva’s suggestion to lift homology relations from the Deligne–Mumford moduli spaces of stable real curves. This is accomplished by lifting judiciously chosen cobordisms realizing these relations. The resulting lifted relations lead to the recursions for Welschinger invariants announced by Solomon in 2007 and have the same structure as his WDVV-style relations, but differ by signs from the latter. Our topological approach provides a general framework for lifting relations via morphisms between not necessarily orientable spaces.},
  author       = {Chen, Xujia},
  issn         = {1420-8970},
  journal      = {Geometric and Functional Analysis},
  number       = {3},
  pages        = {490--567},
  publisher    = {Springer Nature},
  title        = {{Steenrod pseudocycles, lifted cobordisms, and Solomon’s relations for Welschinger invariants}},
  doi          = {10.1007/s00039-022-00596-6},
  volume       = {32},
  year         = {2022},
}

@article{20617,
  abstract     = {Our previous paper describes a geometric translation of the construction of open Gromov–Witten invariants by Solomon and Tukachinsky from a perspective of $A_{\infty }$-algebras of differential forms. We now use this geometric perspective to show that these invariants reduce to Welschinger’s open Gromov–Witten invariants in dimension 6, inline with their and Tian’s expectations. As an immediate corollary, we obtain a translation of Solomon–Tukachinsky’s open WDVV equations into relations for Welschinger’s invariants.},
  author       = {Chen, Xujia},
  issn         = {1687-0247},
  journal      = {International Mathematics Research Notices},
  number       = {9},
  pages        = {7021--7055},
  publisher    = {Oxford University Press},
  title        = {{Solomon-Tukachinsky’s versus Welschinger’s open Gromov-Witten invariants of symplectic six-folds}},
  doi          = {10.1093/imrn/rnaa318},
  volume       = {2022},
  year         = {2022},
}

@article{20620,
  abstract     = {The 2016 papers of J. Solomon and S. Tukachinsky use bounding chains in Fukaya's $A_{\infty}$-algebras to define numerical disk counts relative to a Lagrangian under certain regularity assumptions on the moduli spaces of disks. We present a (self-contained) direct geometric analogue of their construction under weaker topological assumptions, extend it over arbitrary rings in the process, and sketch an extension without any assumptions over rings containing the rationals. This implements the intuitive suggestion represented by their drawing and P. Georgieva's perspective. We also note a curious relation for the standard Gromov-Witten invariants readily deducible from their work. In a sequel, we use the geometric perspective of this paper to relate Solomon-Tukachinsky's invariants to Welschinger's open invariants of symplectic sixfolds, confirming their belief and G. Tian's related expectation concerning K. Fukaya's earlier construction.},
  author       = {Chen, Xujia},
  journal      = {Peking Mathematical Journal },
  pages        = {279--348},
  publisher    = {Springer Nature},
  title        = {{A geometric depiction of Solomon-Tukachinsky's construction of open GW-invariants}},
  doi          = {10.1007/s42543-021-00044-8},
  volume       = {5},
  year         = {2022},
}