@article{6339,
  abstract     = {We introduce a diagrammatic Monte Carlo approach to angular momentum properties of quantum many-particle systems possessing a macroscopic number of degrees of freedom. The treatment is based on a diagrammatic expansion that merges the usual Feynman diagrams with the angular momentum diagrams known from atomic and nuclear structure theory, thereby incorporating the non-Abelian algebra inherent to quantum rotations. Our approach is applicable at arbitrary coupling, is free of systematic errors and of finite-size effects, and naturally provides access to the impurity Green function. We exemplify the technique by obtaining an all-coupling solution of the angulon model; however, the method is quite general and can be applied to a broad variety of systems in which particles exchange quantum angular momentum with their many-body environment.},
  author       = {Bighin, Giacomo and Tscherbul, Timur and Lemeshko, Mikhail},
  journal      = {Physical Review Letters},
  number       = {16},
  publisher    = {American Physical Society},
  title        = {{Diagrammatic Monte Carlo approach to angular momentum in quantum many-particle systems}},
  doi          = {10.1103/physrevlett.121.165301},
  volume       = {121},
  year         = {2018},
}

@inproceedings{6340,
  abstract     = {We  present  a  secure  approach  for  maintaining  andreporting  credit  history  records  on  the  Blockchain.  Our  ap-proach  removes  third-parties  such  as  credit  reporting  agen-cies  from  the  lending  process  and  replaces  them  with  smartcontracts.  This  allows  customers  to  interact  directly  with  thelenders  or  banks  while  ensuring  the  integrity,  unmalleabilityand  privacy  of  their  credit  data.  Additionally,  each  customerhas  full  control  over  complete  or  selective  disclosure  of  hercredit records, eliminating the risk of privacy violations or databreaches. Moreover, our approach provides strong guaranteesfor the lenders as well. A lender can check both correctness andcompleteness of the credit data disclosed to her. This is the firstapproach  that  can  perform  all  credit  reporting  tasks  withouta  central  authority  or  changing  the  financial  mechanisms*.},
  author       = {Goharshady, Amir Kafshdar and Behrouz, Ali and Chatterjee, Krishnendu},
  booktitle    = {Proceedings of the IEEE International Conference on Blockchain},
  isbn         = {978-1-5386-7975-3 },
  location     = {Halifax, Canada},
  pages        = {1343--1348},
  publisher    = {IEEE},
  title        = {{Secure Credit Reporting on the Blockchain}},
  doi          = {10.1109/Cybermatics_2018.2018.00231},
  year         = {2018},
}

@article{6354,
  abstract     = {Blood platelets are critical for hemostasis and thrombosis, but also play diverse roles during immune responses. We have recently reported that platelets migrate at sites of infection in vitro and in vivo. Importantly, platelets use their ability to migrate to collect and bundle fibrin (ogen)-bound bacteria accomplishing efficient intravascular bacterial trapping. Here, we describe a method that allows analyzing platelet migration in vitro, focusing on their ability to collect bacteria and trap bacteria under flow.},
  author       = {Fan, Shuxia and Lorenz, Michael and Massberg, Steffen and Gärtner, Florian R},
  issn         = {2331-8325},
  journal      = {Bio-Protocol},
  keywords     = {Platelets, Cell migration, Bacteria, Shear flow, Fibrinogen, E. coli},
  number       = {18},
  publisher    = {Bio-Protocol},
  title        = {{Platelet migration and bacterial trapping assay under flow}},
  doi          = {10.21769/bioprotoc.3018},
  volume       = {8},
  year         = {2018},
}

@article{6355,
  abstract     = {We  prove  that  any  cyclic  quadrilateral  can  be  inscribed  in  any  closed  convex C1-curve.  The smoothness condition is not required if the quadrilateral is a rectangle.},
  author       = {Akopyan, Arseniy and Avvakumov, Sergey},
  issn         = {2050-5094},
  journal      = {Forum of Mathematics, Sigma},
  publisher    = {Cambridge University Press},
  title        = {{Any cyclic quadrilateral can be inscribed in any closed convex smooth curve}},
  doi          = {10.1017/fms.2018.7},
  volume       = {6},
  year         = {2018},
}

@article{6368,
  abstract     = {An optical network of superconducting quantum bits (qubits) is an appealing platform for quantum communication and distributed quantum computing, but developing a quantum-compatible link between the microwave and optical domains remains an outstanding challenge. Operating at T < 100 mK temperatures, as required for quantum electrical circuits, we demonstrate a mechanically mediated microwave–optical converter with 47% conversion efficiency, and use a classical feed-forward protocol to reduce added noise to 38 photons. The feed-forward protocol harnesses our discovery that noise emitted from the two converter output ports is strongly correlated because both outputs record thermal motion of the same mechanical mode. We also discuss a quantum feed-forward protocol that, given high system efficiencies, would allow quantum information to be transferred even when thermal phonons enter the mechanical element faster than the electro-optic conversion rate.},
  author       = {Higginbotham, Andrew P and Burns, P. S. and Urmey, M. D. and Peterson, R. W. and Kampel, N. S. and Brubaker, B. M. and Smith, G. and Lehnert, K. W. and Regal, C. A.},
  issn         = {1745-2473},
  journal      = {Nature Physics},
  number       = {10},
  pages        = {1038--1042},
  publisher    = {Springer Nature},
  title        = {{Harnessing electro-optic correlations in an efficient mechanical converter}},
  doi          = {10.1038/s41567-018-0210-0},
  volume       = {14},
  year         = {2018},
}

@article{6369,
  abstract     = {We construct a metamaterial from radio-frequency harmonic oscillators, and find two topologically distinct phases resulting from dissipation engineered into the system. These phases are distinguished by a quantized value of bulk energy transport. The impulse response of our circuit is measured and used to reconstruct the band structure and winding number of circuit eigenfunctions around a dark mode. Our results demonstrate that dissipative topological transport can occur in a wider class of physical systems than considered before.},
  author       = {Rosenthal, Eric I. and Ehrlich, Nicole K. and Rudner, Mark S. and Higginbotham, Andrew P and Lehnert, K. W.},
  issn         = {2469-9950},
  journal      = {Physical Review B},
  number       = {22},
  publisher    = {American Physical Society (APS)},
  title        = {{Topological phase transition measured in a dissipative metamaterial}},
  doi          = {10.1103/physrevb.97.220301},
  volume       = {97},
  year         = {2018},
}

@article{64,
  abstract     = {Tropical geometry, an established field in pure mathematics, is a place where string theory, mirror symmetry, computational algebra, auction theory, and so forth meet and influence one another. In this paper, we report on our discovery of a tropical model with self-organized criticality (SOC) behavior. Our model is continuous, in contrast to all known models of SOC, and is a certain scaling limit of the sandpile model, the first and archetypical model of SOC. We describe how our model is related to pattern formation and proportional growth phenomena and discuss the dichotomy between continuous and discrete models in several contexts. Our aim in this context is to present an idealized tropical toy model (cf. Turing reaction-diffusion model), requiring further investigation.},
  author       = {Kalinin, Nikita and Guzmán Sáenz, Aldo and Prieto, Y and Shkolnikov, Mikhail and Kalinina, V and Lupercio, Ernesto},
  issn         = {00278424},
  journal      = {PNAS: Proceedings of the National Academy of Sciences of the United States of America},
  number       = {35},
  pages        = {E8135 -- E8142},
  publisher    = {National Academy of Sciences},
  title        = {{Self-organized criticality and pattern emergence through the lens of tropical geometry}},
  doi          = {10.1073/pnas.1805847115},
  volume       = {115},
  year         = {2018},
}

@misc{6459,
  author       = {Petritsch, Barbara},
  keywords     = {Open Access, Publication Analysis},
  location     = {Graz, Austria},
  publisher    = {IST Austria},
  title        = {{Open Access at IST Austria 2009-2017}},
  doi          = {10.5281/zenodo.1410279},
  year         = {2018},
}

@article{6497,
  abstract     = {T cells are actively scanning pMHC-presenting cells in lymphoid organs and nonlymphoid tissues (NLTs) with divergent topologies and confinement. How the T cell actomyosin cytoskeleton facilitates this task in distinct environments is incompletely understood. Here, we show that lack of Myosin IXb (Myo9b), a negative regulator of the small GTPase Rho, led to increased Rho-GTP levels and cell surface stiffness in primary T cells. Nonetheless, intravital imaging revealed robust motility of Myo9b−/− CD8+ T cells in lymphoid tissue and similar expansion and differentiation during immune responses. In contrast, accumulation of Myo9b−/− CD8+ T cells in NLTs was strongly impaired. Specifically, Myo9b was required for T cell crossing of basement membranes, such as those which are present between dermis and epidermis. As consequence, Myo9b−/− CD8+ T cells showed impaired control of skin infections. In sum, we show that Myo9b is critical for the CD8+ T cell adaptation from lymphoid to NLT surveillance and the establishment of protective tissue–resident T cell populations.},
  author       = {Moalli, Federica and Ficht, Xenia and Germann, Philipp and Vladymyrov, Mykhailo and Stolp, Bettina and de Vries, Ingrid and Lyck, Ruth and Balmer, Jasmin and Fiocchi, Amleto and Kreutzfeldt, Mario and Merkler, Doron and Iannacone, Matteo and Ariga, Akitaka and Stoffel, Michael H. and Sharpe, James and Bähler, Martin and Sixt, Michael K and Diz-Muñoz, Alba and Stein, Jens V.},
  issn         = {1540-9538},
  journal      = {The Journal of Experimental Medicine},
  number       = {7},
  pages        = {1869–1890},
  publisher    = {Rockefeller University Press},
  title        = {{The Rho regulator Myosin IXb enables nonlymphoid tissue seeding of protective CD8+T cells}},
  doi          = {10.1084/jem.20170896},
  volume       = {2015},
  year         = {2018},
}

@article{6499,
  abstract     = {Expansion microscopy is a recently introduced imaging technique that achieves super‐resolution through physically expanding the specimen by ~4×, after embedding into a swellable gel. The resolution attained is, correspondingly, approximately fourfold better than the diffraction limit, or ~70 nm. This is a major improvement over conventional microscopy, but still lags behind modern STED or STORM setups, whose resolution can reach 20–30 nm. We addressed this issue here by introducing an improved gel recipe that enables an expansion factor of ~10× in each dimension, which corresponds to an expansion of the sample volume by more than 1,000‐fold. Our protocol, which we termed X10 microscopy, achieves a resolution of 25–30 nm on conventional epifluorescence microscopes. X10 provides multi‐color images similar or even superior to those produced with more challenging methods, such as STED, STORM, and iterative expansion microscopy (iExM). X10 is therefore the cheapest and easiest option for high‐quality super‐resolution imaging currently available. X10 should be usable in any laboratory, irrespective of the machinery owned or of the technical knowledge.},
  author       = {Truckenbrodt, Sven M and Maidorn, Manuel and Crzan, Dagmar and Wildhagen, Hanna and Kabatas, Selda and Rizzoli, Silvio O},
  issn         = {1469-3178},
  journal      = {EMBO reports},
  number       = {9},
  publisher    = {EMBO},
  title        = {{X10 expansion microscopy enables 25‐nm resolution on conventional microscopes}},
  doi          = {10.15252/embr.201845836},
  volume       = {19},
  year         = {2018},
}

@inproceedings{6558,
  abstract     = {This paper studies the problem of distributed stochastic optimization in an adversarial setting where, out of m machines which allegedly compute stochastic gradients every iteration, an α-fraction are Byzantine, and may behave adversarially. Our main result is a variant of stochastic gradient descent (SGD) which finds ε-approximate minimizers of convex functions in T=O~(1/ε²m+α²/ε²) iterations. In contrast, traditional mini-batch SGD needs T=O(1/ε²m) iterations, but cannot tolerate Byzantine failures. Further, we provide a lower bound showing that, up to logarithmic factors, our algorithm is information-theoretically optimal both in terms of sample complexity and time complexity.},
  author       = {Alistarh, Dan-Adrian and Allen-Zhu, Zeyuan and Li, Jerry},
  booktitle    = {Advances in Neural Information Processing Systems},
  location     = {Montreal, Canada},
  pages        = {4613--4623},
  publisher    = {Neural Information Processing Systems Foundation},
  title        = {{Byzantine stochastic gradient descent}},
  volume       = {2018},
  year         = {2018},
}

@inproceedings{6589,
  abstract     = {Distributed training of massive machine learning models, in particular deep neural networks, via Stochastic Gradient Descent (SGD) is becoming commonplace. Several families of communication-reduction methods, such as quantization, large-batch methods, and gradient sparsification, have been proposed. To date, gradient sparsification methods--where each node sorts gradients by magnitude, and only communicates a subset of the components, accumulating the rest locally--are known to yield some of the largest practical gains. Such methods can reduce the amount of communication per step by up to \emph{three orders of magnitude}, while preserving model accuracy. Yet, this family of methods currently has no theoretical justification. This is the question we address in this paper. We prove that, under analytic assumptions, sparsifying gradients by magnitude with local error correction provides convergence guarantees, for both convex and non-convex smooth objectives, for data-parallel SGD. The main insight is that sparsification methods implicitly maintain bounds on the maximum impact of stale updates, thanks to selection by magnitude. Our analysis and empirical validation also reveal that these methods do require analytical conditions to converge well, justifying existing heuristics.},
  author       = {Alistarh, Dan-Adrian and Hoefler, Torsten and Johansson, Mikael and Konstantinov, Nikola H and Khirirat, Sarit and Renggli, Cedric},
  booktitle    = {Advances in Neural Information Processing Systems 31},
  location     = {Montreal, Canada},
  pages        = {5973--5983},
  publisher    = {Neural Information Processing Systems Foundation},
  title        = {{The convergence of sparsified gradient methods}},
  volume       = {Volume 2018},
  year         = {2018},
}

@inproceedings{66,
  abstract     = {Crypto-currencies are digital assets designed to work as a medium of exchange, e.g., Bitcoin, but they are susceptible to attacks (dishonest behavior of participants). A framework for the analysis of attacks in crypto-currencies requires (a) modeling of game-theoretic aspects to analyze incentives for deviation from honest behavior; (b) concurrent interactions between participants; and (c) analysis of long-term monetary gains. Traditional game-theoretic approaches for the analysis of security protocols consider either qualitative temporal properties such as safety and termination, or the very special class of one-shot (stateless) games. However, to analyze general attacks on protocols for crypto-currencies, both stateful analysis and quantitative objectives are necessary. In this work our main contributions are as follows: (a) we show how a class of concurrent mean-payo games, namely ergodic games, can model various attacks that arise naturally in crypto-currencies; (b) we present the first practical implementation of algorithms for ergodic games that scales to model realistic problems for crypto-currencies; and (c) we present experimental results showing that our framework can handle games with thousands of states and millions of transitions.},
  author       = {Chatterjee, Krishnendu and Goharshady, Amir and Ibsen-Jensen, Rasmus and Velner, Yaron},
  isbn         = {978-3-95977-087-3},
  location     = {Beijing, China},
  publisher    = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
  title        = {{Ergodic mean-payoff games for the analysis of attacks in crypto-currencies}},
  doi          = {10.4230/LIPIcs.CONCUR.2018.11},
  volume       = {118},
  year         = {2018},
}

@inproceedings{6664,
  abstract     = {Reed-Muller (RM) and polar codes are a class of capacity-achieving channel coding schemes with the same factor graph representation. Low-complexity decoding algorithms fall short in providing a good error-correction performance for RM and polar codes. Using the symmetric group of RM and polar codes, the specific decoding algorithm can be carried out on multiple permutations of the factor graph to boost the error-correction performance. However, this approach results in high decoding complexity. In this paper, we first derive the total number of factor graph permutations on which the decoding can be performed. We further propose a successive permutation (SP) scheme which finds the permutations on the fly, thus the decoding always progresses on a single factor graph permutation. We show that SP can be used to improve the error-correction performance of RM and polar codes under successive-cancellation (SC) and SC list (SCL) decoding, while keeping the memory requirements of the decoders unaltered. Our results for RM and polar codes of length 128 and rate 0.5 show that when SP is used and at a target frame error rate of 10 -4 , up to 0.5 dB and 0.1 dB improvement can be achieved for RM and polar codes respectively.},
  author       = {Hashemi, Seyyed Ali and Doan, Nghia and Mondelli, Marco and Gross, Warren },
  booktitle    = {2018 IEEE 10th International Symposium on Turbo Codes & Iterative Information Processing},
  location     = {Hong Kong, China},
  pages        = {1--5},
  publisher    = {IEEE},
  title        = {{Decoding Reed-Muller and polar codes by successive factor graph permutations}},
  doi          = {10.1109/istc.2018.8625281},
  year         = {2018},
}

@inproceedings{6665,
  abstract     = {We prove that, at least for the binary erasure channel, the polar-coding paradigm gives rise to codes that not only approach the Shannon limit but, in fact, do so under the best possible scaling of their block length as a function of the gap to capacity. This result exhibits the first known family of binary codes that attain both optimal scaling and quasi-linear complexity of encoding and decoding. Specifically, for any fixed δ > 0, we exhibit binary linear codes that ensure reliable communication at rates within ε > 0 of capacity with block length n = O(1/ε 2+δ ), construction complexity Θ(n), and encoding/decoding complexity Θ(n log n).},
  author       = {Fazeli, Arman and Hassani, Hamed and Mondelli, Marco and Vardy, Alexander},
  booktitle    = {2018 IEEE Information Theory Workshop},
  location     = {Guangzhou, China},
  pages        = {1--5},
  publisher    = {IEEE},
  title        = {{Binary linear codes with optimal scaling: Polar codes with large kernels}},
  doi          = {10.1109/itw.2018.8613428},
  year         = {2018},
}

@inproceedings{6675,
  abstract     = {We present a coding paradigm that provides a new achievable rate for the primitive relay channel by combining compress-and-forward and decode-and-forward with a chaining construction. In the primitive relay channel model, the source broadcasts a message to the relay and to the destination; and the relay facilitates this communication by sending an additional message to the destination through a separate channel. Two well-known coding approaches for this setting are decode-and-forward and compress-and-forward: in the former, the relay decodes the message and sends some of the information to the destination; in the latter, the relay does not attempt to decode, but it sends a compressed description of the received sequence to the destination via Wyner-Ziv coding. In our scheme, we transmit over pairs of blocks and we use compress-and-forward for the first block and decode-and-forward for the second. In particular, in the first block, the relay does not attempt to decode and it sends only a part of the compressed description of the received sequence; in the second block, the relay decodes the message and sends this information plus the remaining part of the compressed sequence relative to the first block. As a result, we strictly outperform both compress-and- forward and decode-and-forward. Furthermore, this paradigm can be implemented with a low-complexity polar coding scheme that has the typical attractive features of polar codes, i.e., quasi-linear encoding/decoding complexity and super-polynomial decay of the error probability. Throughout the paper we consider as a running example the special case of the erasure relay channel and we compare the rates achievable by our proposed scheme with the existing upper and lower bounds.},
  author       = {Mondelli, Marco and Hassani, Hamed and Urbanke, Rudiger},
  booktitle    = {2018 IEEE International Symposium on Information Theory},
  issn         = {2157-8117},
  location     = {Vail, CO, United States},
  pages        = {351--355},
  publisher    = {IEEE},
  title        = {{A new coding paradigm for the primitive relay channel}},
  doi          = {10.1109/isit.2018.8437479},
  year         = {2018},
}

@article{6678,
  abstract     = {We survey coding techniques that enable reliable transmission at rates that approach the capacity of an arbitrary discrete memoryless channel. In particular, we take the point of view of modern coding theory and discuss how recent advances in coding for symmetric channels help provide more efficient solutions for the asymmetric case. We consider, in more detail, three basic coding paradigms. The first one is Gallager's scheme that consists of concatenating a linear code with a non-linear mapping so that the input distribution can be appropriately shaped. We explicitly show that both polar codes and spatially coupled codes can be employed in this scenario. Furthermore, we derive a scaling law between the gap to capacity, the cardinality of the input and output alphabets, and the required size of the mapper. The second one is an integrated scheme in which the code is used both for source coding, in order to create codewords distributed according to the capacity-achieving input distribution, and for channel coding, in order to provide error protection. Such a technique has been recently introduced by Honda and Yamamoto in the context of polar codes, and we show how to apply it also to the design of sparse graph codes. The third paradigm is based on an idea of Böcherer and Mathar, and separates the two tasks of source coding and channel coding by a chaining construction that binds together several codewords. We present conditions for the source code and the channel code, and we describe how to combine any source code with any channel code that fulfill those conditions, in order to provide capacity-achieving schemes for asymmetric channels. In particular, we show that polar codes, spatially coupled codes, and homophonic codes are suitable as basic building blocks of the proposed coding strategy. Rather than focusing on the exact details of the schemes, the purpose of this tutorial is to present different coding techniques that can then be implemented with many variants. There is no absolute winner and, in order to understand the most suitable technique for a specific application scenario, we provide a detailed comparison that takes into account several performance metrics.},
  author       = {Mondelli, Marco and Hassani, Hamed and Urbanke, Rudiger },
  issn         = {0018-9448},
  journal      = {IEEE Transactions on Information Theory},
  number       = {5},
  pages        = {3371--3393},
  publisher    = {IEEE},
  title        = {{How to achieve the capacity of asymmetric channels}},
  doi          = {10.1109/tit.2018.2789885},
  volume       = {64},
  year         = {2018},
}

@article{67,
  abstract     = {Gene regulatory networks evolve through rewiring of individual components—that is, through changes in regulatory connections. However, the mechanistic basis of regulatory rewiring is poorly understood. Using a canonical gene regulatory system, we quantify the properties of transcription factors that determine the evolutionary potential for rewiring of regulatory connections: robustness, tunability and evolvability. In vivo repression measurements of two repressors at mutated operator sites reveal their contrasting evolutionary potential: while robustness and evolvability were positively correlated, both were in trade-off with tunability. Epistatic interactions between adjacent operators alleviated this trade-off. A thermodynamic model explains how the differences in robustness, tunability and evolvability arise from biophysical characteristics of repressor–DNA binding. The model also uncovers that the energy matrix, which describes how mutations affect repressor–DNA binding, encodes crucial information about the evolutionary potential of a repressor. The biophysical determinants of evolutionary potential for regulatory rewiring constitute a mechanistic framework for understanding network evolution.},
  author       = {Igler, Claudia and Lagator, Mato and Tkacik, Gasper and Bollback, Jonathan P and Guet, Calin C},
  journal      = {Nature Ecology and Evolution},
  number       = {10},
  pages        = {1633 -- 1643},
  publisher    = {Nature Publishing Group},
  title        = {{Evolutionary potential of transcription factors for gene regulatory rewiring}},
  doi          = {10.1038/s41559-018-0651-y},
  volume       = {2},
  year         = {2018},
}

@inproceedings{6728,
  abstract     = {Polar codes are a channel coding scheme for the next generation of wireless communications standard (5G). The belief propagation (BP) decoder allows for parallel decoding of polar codes, making it suitable for high throughput applications. However, the error-correction performance of polar codes under BP decoding is far from the requirements of 5G. It has been shown that the error-correction performance of BP can be improved if the decoding is performed on multiple permuted factor graphs of polar codes. However, a different BP decoding scheduling is required for each factor graph permutation which results in the design of a different decoder for each permutation. Moreover, the selection of the different factor graph permutations is at random, which prevents the decoder to achieve a desirable error correction performance with a small number of permutations. In this paper, we first show that the permutations on the factor graph can be mapped into suitable permutations on the codeword positions. As a result, we can make use of a single decoder for all the permutations. In addition, we introduce a method to construct a set of predetermined permutations which can provide the correct codeword if the decoding fails on the original permutation. We show that for the 5G polar code of length 1024, the error-correction performance of the proposed decoder is more than 0.25 dB better than that of the BP decoder with the same number of random permutations at the frame error rate of 10 -4 .},
  author       = {Doan, Nghia and Hashemi, Seyyed Ali and Mondelli, Marco and Gross, Warren J.},
  booktitle    = {2018 IEEE Global Communications Conference },
  isbn         = {9781538647271},
  location     = {Abu Dhabi, United Arab Emirates},
  publisher    = {IEEE},
  title        = {{On the decoding of polar codes on permuted factor graphs}},
  doi          = {10.1109/glocom.2018.8647308},
  year         = {2018},
}

@article{6774,
  abstract     = {A central problem of algebraic topology is to understand the homotopy groups  𝜋𝑑(𝑋)  of a topological space X. For the computational version of the problem, it is well known that there is no algorithm to decide whether the fundamental group  𝜋1(𝑋)  of a given finite simplicial complex X is trivial. On the other hand, there are several algorithms that, given a finite simplicial complex X that is simply connected (i.e., with   𝜋1(𝑋)  trivial), compute the higher homotopy group   𝜋𝑑(𝑋)  for any given   𝑑≥2 . However, these algorithms come with a caveat: They compute the isomorphism type of   𝜋𝑑(𝑋) ,   𝑑≥2  as an abstract finitely generated abelian group given by generators and relations, but they work with very implicit representations of the elements of   𝜋𝑑(𝑋) . Converting elements of this abstract group into explicit geometric maps from the d-dimensional sphere   𝑆𝑑  to X has been one of the main unsolved problems in the emerging field of computational homotopy theory. Here we present an algorithm that, given a simply connected space X, computes   𝜋𝑑(𝑋)  and represents its elements as simplicial maps from a suitable triangulation of the d-sphere   𝑆𝑑  to X. For fixed d, the algorithm runs in time exponential in   size(𝑋) , the number of simplices of X. Moreover, we prove that this is optimal: For every fixed   𝑑≥2 , we construct a family of simply connected spaces X such that for any simplicial map representing a generator of   𝜋𝑑(𝑋) , the size of the triangulation of   𝑆𝑑  on which the map is defined, is exponential in size(𝑋) .},
  author       = {Filakovský, Marek and Franek, Peter and Wagner, Uli and Zhechev, Stephan Y},
  issn         = {2367-1734},
  journal      = {Journal of Applied and Computational Topology},
  number       = {3-4},
  pages        = {177--231},
  publisher    = {Springer},
  title        = {{Computing simplicial representatives of homotopy group elements}},
  doi          = {10.1007/s41468-018-0021-5},
  volume       = {2},
  year         = {2018},
}

