@inproceedings{791, abstract = {Consider the following random process: we are given n queues, into which elements of increasing labels are inserted uniformly at random. To remove an element, we pick two queues at random, and remove the element of lower label (higher priority) among the two. The cost of a removal is the rank of the label removed, among labels still present in any of the queues, that is, the distance from the optimal choice at each step. Variants of this strategy are prevalent in state-of-the-art concurrent priority queue implementations. Nonetheless, it is not known whether such implementations provide any rank guarantees, even in a sequential model. We answer this question, showing that this strategy provides surprisingly strong guarantees: Although the single-choice process, where we always insert and remove from a single randomly chosen queue, has degrading cost, going to infinity as we increase the number of steps, in the two choice process, the expected rank of a removed element is O(n) while the expected worst-case cost is O(n log n). These bounds are tight, and hold irrespective of the number of steps for which we run the process. The argument is based on a new technical connection between "heavily loaded" balls-into-bins processes and priority scheduling. Our analytic results inspire a new concurrent priority queue implementation, which improves upon the state of the art in terms of practical performance.}, author = {Alistarh, Dan-Adrian and Kopinsky, Justin and Li, Jerry and Nadiradze, Giorgi}, booktitle = {Proceedings of the ACM Symposium on Principles of Distributed Computing}, isbn = {978-145034992-5}, location = {Washington, WA, USA}, pages = {283 -- 292}, publisher = {ACM}, title = {{The power of choice in priority scheduling}}, doi = {10.1145/3087801.3087810}, volume = {Part F129314}, year = {2017}, } @article{792, abstract = {The chaotic dynamics of low-dimensional systems, such as Lorenz or Rössler flows, is guided by the infinity of periodic orbits embedded in their strange attractors. Whether this is also the case for the infinite-dimensional dynamics of Navier–Stokes equations has long been speculated, and is a topic of ongoing study. Periodic and relative periodic solutions have been shown to be involved in transitions to turbulence. Their relevance to turbulent dynamics – specifically, whether periodic orbits play the same role in high-dimensional nonlinear systems like the Navier–Stokes equations as they do in lower-dimensional systems – is the focus of the present investigation. We perform here a detailed study of pipe flow relative periodic orbits with energies and mean dissipations close to turbulent values. We outline several approaches to reduction of the translational symmetry of the system. We study pipe flow in a minimal computational cell at Re=2500, and report a library of invariant solutions found with the aid of the method of slices. Detailed study of the unstable manifolds of a sample of these solutions is consistent with the picture that relative periodic orbits are embedded in the chaotic saddle and that they guide the turbulent dynamics.}, author = {Budanur, Nazmi B and Short, Kimberly and Farazmand, Mohammad and Willis, Ashley and Cvitanović, Predrag}, issn = {0022-1120}, journal = {Journal of Fluid Mechanics}, pages = {274 -- 301}, publisher = {Cambridge University Press}, title = {{Relative periodic orbits form the backbone of turbulent pipe flow}}, doi = {10.1017/jfm.2017.699}, volume = {833}, year = {2017}, } @article{794, abstract = {We show that c-planarity is solvable in quadratic time for flat clustered graphs with three clusters if the combinatorial embedding of the underlying graph is fixed. In simpler graph-theoretical terms our result can be viewed as follows. Given a graph G with the vertex set partitioned into three parts embedded on a 2-sphere, our algorithm decides if we can augment G by adding edges without creating an edge-crossing so that in the resulting spherical graph the vertices of each part induce a connected sub-graph. We proceed by a reduction to the problem of testing the existence of a perfect matching in planar bipartite graphs. We formulate our result in a slightly more general setting of cyclic clustered graphs, i.e., the simple graph obtained by contracting each cluster, where we disregard loops and multi-edges, is a cycle.}, author = {Fulek, Radoslav}, journal = {Computational Geometry: Theory and Applications}, pages = {1 -- 13}, publisher = {Elsevier}, title = {{C-planarity of embedded cyclic c-graphs}}, doi = {10.1016/j.comgeo.2017.06.016}, volume = {66}, year = {2017}, } @article{795, abstract = {We introduce a common generalization of the strong Hanani–Tutte theorem and the weak Hanani–Tutte theorem: if a graph G has a drawing D in the plane where every pair of independent edges crosses an even number of times, then G has a planar drawing preserving the rotation of each vertex whose incident edges cross each other evenly in D. The theorem is implicit in the proof of the strong Hanani–Tutte theorem by Pelsmajer, Schaefer and Štefankovič. We give a new, somewhat simpler proof.}, author = {Fulek, Radoslav and Kynčl, Jan and Pálvölgyi, Dömötör}, issn = {1077-8926}, journal = {Electronic Journal of Combinatorics}, number = {3}, publisher = {International Press}, title = {{Unified Hanani Tutte theorem}}, doi = {10.37236/6663}, volume = {24}, year = {2017}, } @article{796, abstract = {We present the fabrication and characterization of an aluminum transmon qubit on a silicon-on-insulator substrate. Key to the qubit fabrication is the use of an anhydrous hydrofluoric vapor process which selectively removes the lossy silicon oxide buried underneath the silicon device layer. For a 5.6 GHz qubit measured dispersively by a 7.1 GHz resonator, we find T1 = 3.5 μs and T∗2 = 2.2 μs. This process in principle permits the co-fabrication of silicon photonic and mechanical elements, providing a route towards chip-scale integration of electro-opto-mechanical transducers for quantum networking of superconducting microwave quantum circuits. The additional processing steps are compatible with established fabrication techniques for aluminum transmon qubits on silicon.}, author = {Keller, Andrew J and Dieterle, Paul and Fang, Michael and Berger, Brett and Fink, Johannes M and Painter, Oskar}, issn = {0003-6951}, journal = {Applied Physics Letters}, number = {4}, publisher = {American Institute of Physics}, title = {{Al transmon qubits on silicon on insulator for quantum device integration}}, doi = {10.1063/1.4994661}, volume = {111}, year = {2017}, } @article{797, abstract = {Phasenübergänge helfen beim Verständnis von Vielteilchensystemen in der Festkörperphysik und Fluiddynamik bis hin zur Teilchenphysik. Unserer internationalen Kollaboration ist es gelungen, einen neuartigen Phasenübergang in einem Quantensystem zu beobachten [1]. In einem Mikrowellenresonator konnte erstmals die spontane Zustandsänderung von undurchsichtig zu transparent nachgewiesen werden.}, author = {Fink, Johannes M}, journal = {Physik in unserer Zeit}, number = {3}, pages = {111 -- 113}, publisher = {Wiley}, title = {{Photonenblockade aufgelöst}}, doi = {10.1002/piuz.201770305}, volume = {48}, year = {2017}, } @article{798, abstract = {Nonreciprocal circuit elements form an integral part of modern measurement and communication systems. Mathematically they require breaking of time-reversal symmetry, typically achieved using magnetic materials and more recently using the quantum Hall effect, parametric permittivity modulation or Josephson nonlinearities. Here we demonstrate an on-chip magnetic-free circulator based on reservoir-engineered electromechanic interactions. Directional circulation is achieved with controlled phase-sensitive interference of six distinct electro-mechanical signal conversion paths. The presented circulator is compact, its silicon-on-insulator platform is compatible with both superconducting qubits and silicon photonics, and its noise performance is close to the quantum limit. With a high dynamic range, a tunable bandwidth of up to 30 MHz and an in situ reconfigurability as beam splitter or wavelength converter, it could pave the way for superconducting qubit processors with multiplexed on-chip signal processing and readout.}, author = {Barzanjeh, Shabir and Wulf, Matthias and Peruzzo, Matilda and Kalaee, Mahmoud and Dieterle, Paul and Painter, Oskar and Fink, Johannes M}, issn = {2041-1723}, journal = {Nature Communications}, number = {1}, publisher = {Nature Publishing Group}, title = {{Mechanical on chip microwave circulator}}, doi = {10.1038/s41467-017-01304-x}, volume = {8}, year = {2017}, } @article{799, abstract = {Membrane traffic at the trans-Golgi network (TGN) is crucial for correctly distributing various membrane proteins to their destination. Polarly localized auxin efflux proteins, including PIN-FORMED1 (PIN1), are dynamically transported between the endosomes and the plasma membrane (PM) in the plant cells. The intracellular trafficking of PIN1 protein is sensitive to a fungal toxin brefeldin A (BFA), which is known to inhibit guanine-nucleotide exchange factors for ADP ribosylation factors (ARF GEFs) such as GNOM. However, the molecular details of the BFA-sensitive trafficking pathway have not been revealed fully. In a previous study, we have identified an Arabidopsis mutant BFA-visualized endocytic trafficking defective 3 (ben3) which exhibited reduced sensitivity to BFA in terms of BFA-induced intracellular PIN1 agglomeration. Here, we show that BEN3 encodes a member of BIG family ARF GEFs, BIG2. Fluorescent proteins tagged BEN3/BIG2 co-localized with markers for TGN / early endosome (EE). Inspection of conditionally induced de novo synthesized PIN1 confirmed that its secretion to the PM is BFA-sensitive and established BEN3/BIG2 as a crucial component of this BFA action at the level of TGN/EE. Furthermore, ben3 mutation alleviated BFA-induced agglomeration of another TGN-localized ARF GEF BEN1/MIN7. Taken together our results suggest that BEN3/BIG2 is an ARF GEF component, which confers BFA sensitivity to the TGN/EE in Arabidopsis.}, author = {Kitakura, Saeko and Adamowski, Maciek and Matsuura, Yuki and Santuari, Luca and Kouno, Hirotaka and Arima, Kohei and Hardtke, Christian and Friml, Jirí and Kakimoto, Tatsuo and Tanaka, Hirokazu}, issn = {0032-0781}, journal = {Plant and Cell Physiology}, number = {10}, publisher = {Oxford University Press}, title = {{BEN3/BIG2 ARF GEF is involved in brefeldin a-sensitive trafficking at the trans-Golgi network/early endosome in Arabidopsis thaliana}}, doi = {10.1093/pcp/pcx118}, volume = {58}, year = {2017}, } @article{800, abstract = {Gamma oscillations (30–150 Hz) in neuronal networks are associated with the processing and recall of information. We measured local field potentials in the dentate gyrus of freely moving mice and found that gamma activity occurs in bursts, which are highly heterogeneous in their spatial extensions, ranging from focal to global coherent events. Synaptic communication among perisomatic-inhibitory interneurons (PIIs) is thought to play an important role in the generation of hippocampal gamma patterns. However, how neuronal circuits can generate synchronous oscillations at different spatial scales is unknown. We analyzed paired recordings in dentate gyrus slices and show that synaptic signaling at interneuron-interneuron synapses is distance dependent. Synaptic strength declines whereas the duration of inhibitory signals increases with axonal distance among interconnected PIIs. Using neuronal network modeling, we show that distance-dependent inhibition generates multiple highly synchronous focal gamma bursts allowing the network to process complex inputs in parallel in flexibly organized neuronal centers.}, author = {Strüber, Michael and Sauer, Jonas and Jonas, Peter M and Bartos, Marlene}, issn = {2041-1723}, journal = {Nature Communications}, number = {1}, publisher = {Nature Publishing Group}, title = {{Distance-dependent inhibition facilitates focality of gamma oscillations in the dentate gyrus}}, doi = {10.1038/s41467-017-00936-3}, volume = {8}, year = {2017}, } @article{803, abstract = {Eukaryotic cells store their chromosomes in a single nucleus. This is important to maintain genomic integrity, as chromosomes packaged into separate nuclei (micronuclei) are prone to massive DNA damage. During mitosis, higher eukaryotes disassemble their nucleus and release individualized chromosomes for segregation. How numerous chromosomes subsequently reform a single nucleus has remained unclear. Using image-based screening of human cells, we identified barrier-to-autointegration factor (BAF) as a key factor guiding membranes to form a single nucleus. Unexpectedly, nuclear assembly does not require BAF?s association with inner nuclear membrane proteins but instead relies on BAF?s ability to bridge distant DNA sites. Live-cell imaging and in vitro reconstitution showed that BAF enriches around the mitotic chromosome ensemble to induce a densely cross-bridged chromatin layer that is mechanically stiff and limits membranes to the surface. Our study reveals that BAF-mediated changes in chromosome mechanics underlie nuclear assembly with broad implications for proper genome function.}, author = {Samwer, Matthias and Schneider, Maximilian and Hoefler, Rudolf and Schmalhorst, Philipp S and Jude, Julian and Zuber, Johannes and Gerlic, Daniel}, issn = {0092-8674}, journal = {Cell}, number = {5}, pages = {956 -- 972}, publisher = {Cell Press}, title = {{DNA cross-bridging shapes a single nucleus from a set of mitotic chromosomes}}, doi = {10.1016/j.cell.2017.07.038}, volume = {170}, year = {2017}, } @article{804, abstract = {Polysaccharides (carbohydrates) are key regulators of a large number of cell biological processes. However, precise biochemical or genetic manipulation of these often complex structures is laborious and hampers experimental structure–function studies. Molecular Dynamics (MD) simulations provide a valuable alternative tool to generate and test hypotheses on saccharide function. Yet, currently used MD force fields often overestimate the aggregation propensity of polysaccharides, affecting the usability of those simulations. Here we tested MARTINI, a popular coarse-grained (CG) force field for biological macromolecules, for its ability to accurately represent molecular forces between saccharides. To this end, we calculated a thermodynamic solution property, the second virial coefficient of the osmotic pressure (B22). Comparison with light scattering experiments revealed a nonphysical aggregation of a prototypical polysaccharide in MARTINI, pointing at an imbalance of the nonbonded solute–solute, solute–water, and water–water interactions. This finding also applies to smaller oligosaccharides which were all found to aggregate in simulations even at moderate concentrations, well below their solubility limit. Finally, we explored the influence of the Lennard-Jones (LJ) interaction between saccharide molecules and propose a simple scaling of the LJ interaction strength that makes MARTINI more reliable for the simulation of saccharides.}, author = {Schmalhorst, Philipp S and Deluweit, Felix and Scherrers, Roger and Heisenberg, Carl-Philipp J and Sikora, Mateusz K}, issn = {1549-9618}, journal = {Journal of Chemical Theory and Computation}, number = {10}, pages = {5039 -- 5053}, publisher = {American Chemical Society}, title = {{Overcoming the limitations of the MARTINI force field in simulations of polysaccharides}}, doi = {10.1021/acs.jctc.7b00374}, volume = {13}, year = {2017}, } @article{805, abstract = {During corticogenesis, distinct classes of neurons are born from progenitor cells located in the ventricular and subventricular zones, from where they migrate towards the pial surface to assemble into highly organized layer-specific circuits. However, the precise and coordinated transcriptional network activity defining neuronal identity is still not understood. Here, we show that genetic depletion of the basic helix-loop-helix (bHLH) transcription factor E2A splice variant E47 increased the number of Tbr1-positive deep layer and Satb2-positive upper layer neurons at E14.5, while depletion of the alternatively spliced E12 variant did not affect layer-specific neurogenesis. While ChIP-Seq identified a big overlap for E12- and E47-specific binding sites in embryonic NSCs, including sites at the cyclin-dependent kinase inhibitor (CDKI) Cdkn1c gene locus, RNA-Seq revealed a unique transcriptional regulation by each splice variant. E47 activated the expression of the CDKI Cdkn1c through binding to a distal enhancer. Finally, overexpression of E47 in embryonic NSCs in vitro impaired neurite outgrowth and E47 overexpression in vivo by in utero electroporation disturbed proper layer-specific neurogenesis and upregulated p57(KIP2) expression. Overall, this study identified E2A target genes in embryonic NSCs and demonstrates that E47 regulates neuronal differentiation via p57(KIP2).}, author = {Pfurr, Sabrina and Chu, Yu and Bohrer, Christian and Greulich, Franziska and Beattie, Robert J and Mammadzada, Könül and Hils, Miriam and Arnold, Sebastian and Taylor, Verdon and Schachtrup, Kristina and Uhlenhaut, N Henriette and Schachtrup, Christian}, journal = {Development}, pages = {3917 -- 3931}, publisher = {Company of Biologists}, title = {{The E2A splice variant E47 regulates the differentiation of projection neurons via p57(KIP2) during cortical development}}, doi = {10.1242/dev.145698}, volume = {144}, year = {2017}, } @article{822, abstract = {Polymicrobial infections constitute small ecosystems that accommodate several bacterial species. Commonly, these bacteria are investigated in isolation. However, it is unknown to what extent the isolates interact and whether their interactions alter bacterial growth and ecosystem resilience in the presence and absence of antibiotics. We quantified the complete ecological interaction network for 72 bacterial isolates collected from 23 individuals diagnosed with polymicrobial urinary tract infections and found that most interactions cluster based on evolutionary relatedness. Statistical network analysis revealed that competitive and cooperative reciprocal interactions are enriched in the global network, while cooperative interactions are depleted in the individual host community networks. A population dynamics model parameterized by our measurements suggests that interactions restrict community stability, explaining the observed species diversity of these communities. We further show that the clinical isolates frequently protect each other from clinically relevant antibiotics. Together, these results highlight that ecological interactions are crucial for the growth and survival of bacteria in polymicrobial infection communities and affect their assembly and resilience. }, author = {De Vos, Marjon and Zagórski, Marcin P and Mcnally, Alan and Bollenbach, Mark Tobias}, issn = {0027-8424}, journal = {PNAS}, number = {40}, pages = {10666 -- 10671}, publisher = {National Academy of Sciences}, title = {{Interaction networks, ecological stability, and collective antibiotic tolerance in polymicrobial infections}}, doi = {10.1073/pnas.1713372114}, volume = {114}, year = {2017}, } @article{823, abstract = {The resolution of a linear system with positive integer variables is a basic yet difficult computational problem with many applications. We consider sparse uncorrelated random systems parametrised by the density c and the ratio α=N/M between number of variables N and number of constraints M. By means of ensemble calculations we show that the space of feasible solutions endows a Van-Der-Waals phase diagram in the plane (c, α). We give numerical evidence that the associated computational problems become more difficult across the critical point and in particular in the coexistence region.}, author = {Colabrese, Simona and De Martino, Daniele and Leuzzi, Luca and Marinari, Enzo}, issn = {1742-5468}, journal = { Journal of Statistical Mechanics: Theory and Experiment}, number = {9}, publisher = {IOP Publishing}, title = {{Phase transitions in integer linear problems}}, doi = {10.1088/1742-5468/aa85c3}, volume = {2017}, year = {2017}, } @article{824, abstract = {In shear flows at transitional Reynolds numbers, localized patches of turbulence, known as puffs, coexist with the laminar flow. Recently, Avila et al. (Phys. Rev. Lett., vol. 110, 2013, 224502) discovered two spatially localized relative periodic solutions for pipe flow, which appeared in a saddle-node bifurcation at low Reynolds number. Combining slicing methods for continuous symmetry reduction with Poincaré sections for the first time in a shear flow setting, we compute and visualize the unstable manifold of the lower-branch solution and show that it extends towards the neighbourhood of the upper-branch solution. Surprisingly, this connection even persists far above the bifurcation point and appears to mediate the first stage of the puff generation: amplification of streamwise localized fluctuations. When the state-space trajectories on the unstable manifold reach the vicinity of the upper branch, corresponding fluctuations expand in space and eventually take the usual shape of a puff.}, author = {Budanur, Nazmi B and Hof, Björn}, issn = {0022-1120}, journal = {Journal of Fluid Mechanics}, publisher = {Cambridge University Press}, title = {{Heteroclinic path to spatially localized chaos in pipe flow}}, doi = {10.1017/jfm.2017.516}, volume = {827}, year = {2017}, } @inproceedings{833, abstract = {We present an efficient algorithm to compute Euler characteristic curves of gray scale images of arbitrary dimension. In various applications the Euler characteristic curve is used as a descriptor of an image. Our algorithm is the first streaming algorithm for Euler characteristic curves. The usage of streaming removes the necessity to store the entire image in RAM. Experiments show that our implementation handles terabyte scale images on commodity hardware. Due to lock-free parallelism, it scales well with the number of processor cores. Additionally, we put the concept of the Euler characteristic curve in the wider context of computational topology. In particular, we explain the connection with persistence diagrams.}, author = {Heiss, Teresa and Wagner, Hubert}, editor = {Felsberg, Michael and Heyden, Anders and Krüger, Norbert}, issn = {0302-9743}, location = {Ystad, Sweden}, pages = {397 -- 409}, publisher = {Springer}, title = {{Streaming algorithm for Euler characteristic curves of multidimensional images}}, doi = {10.1007/978-3-319-64689-3_32}, volume = {10424}, year = {2017}, } @article{834, abstract = {Thermal and many-body localized phases are separated by a dynamical phase transition of a new kind. We analyze the distribution of off-diagonal matrix elements of local operators across this transition in two different models of disordered spin chains. We show that the behavior of matrix elements can be used to characterize the breakdown of thermalization and to extract the many-body Thouless energy. We find that upon increasing the disorder strength the system enters a critical region around the many-body localization transition. The properties of the system in this region are: (i) the Thouless energy becomes smaller than the level spacing, (ii) the matrix elements show critical dependence on the energy difference, and (iii) the matrix elements, viewed as amplitudes of a fictitious wave function, exhibit strong multifractality. This critical region decreases with the system size, which we interpret as evidence for a diverging correlation length at the many-body localization transition. Our findings show that the correlation length becomes larger than the accessible system sizes in a broad range of disorder strength values and shed light on the critical behavior near the many-body localization transition.}, author = {Serbyn, Maksym and Zlatko, Papic and Abanin, Dmitry}, issn = {2469-9950}, journal = {Physical Review B - Condensed Matter and Materials Physics}, number = {10}, publisher = {American Physical Society}, title = {{Thouless energy and multifractality across the many-body localization transition}}, doi = {10.1103/PhysRevB.96.104201}, volume = {96}, year = {2017}, } @inproceedings{836, abstract = {Recent research has examined how to study the topological features of a continuous self-map by means of the persistence of the eigenspaces, for given eigenvalues, of the endomorphism induced in homology over a field. This raised the question of how to select dynamically significant eigenvalues. The present paper aims to answer this question, giving an algorithm that computes the persistence of eigenspaces for every eigenvalue simultaneously, also expressing said eigenspaces as direct sums of “finite” and “singular” subspaces.}, author = {Ethier, Marc and Jablonski, Grzegorz and Mrozek, Marian}, booktitle = {Special Sessions in Applications of Computer Algebra}, isbn = {978-331956930-7}, location = {Kalamata, Greece}, pages = {119 -- 136}, publisher = {Springer}, title = {{Finding eigenvalues of self-maps with the Kronecker canonical form}}, doi = {10.1007/978-3-319-56932-1_8}, volume = {198}, year = {2017}, } @inbook{84, abstract = {The advent of high-throughput technologies and the concurrent advances in information sciences have led to a data revolution in biology. This revolution is most significant in molecular biology, with an increase in the number and scale of the “omics” projects over the last decade. Genomics projects, for example, have produced impressive advances in our knowledge of the information concealed into genomes, from the many genes that encode for the proteins that are responsible for most if not all cellular functions, to the noncoding regions that are now known to provide regulatory functions. Proteomics initiatives help to decipher the role of post-translation modifications on the protein structures and provide maps of protein-protein interactions, while functional genomics is the field that attempts to make use of the data produced by these projects to understand protein functions. The biggest challenge today is to assimilate the wealth of information provided by these initiatives into a conceptual framework that will help us decipher life. For example, the current views of the relationship between protein structure and function remain fragmented. We know of their sequences, more and more about their structures, we have information on their biological activities, but we have difficulties connecting this dotted line into an informed whole. We lack the experimental and computational tools for directly studying protein structure, function, and dynamics at the molecular and supra-molecular levels. In this chapter, we review some of the current developments in building the computational tools that are needed, focusing on the role that geometry and topology play in these efforts. One of our goals is to raise the general awareness about the importance of geometric methods in elucidating the mysterious foundations of our very existence. Another goal is the broadening of what we consider a geometric algorithm. There is plenty of valuable no-man’s-land between combinatorial and numerical algorithms, and it seems opportune to explore this land with a computational-geometric frame of mind.}, author = {Edelsbrunner, Herbert and Koehl, Patrice}, booktitle = {Handbook of Discrete and Computational Geometry, Third Edition}, editor = {Toth, Csaba and O'Rourke, Joseph and Goodman, Jacob}, pages = {1709 -- 1735}, publisher = {Taylor & Francis}, title = {{Computational topology for structural molecular biology}}, doi = {10.1201/9781315119601}, year = {2017}, } @article{909, abstract = {We study the lengths of curves passing through a fixed number of points on the boundary of a convex shape in the plane. We show that, for any convex shape K, there exist four points on the boundary of K such that the length of any curve passing through these points is at least half of the perimeter of K. It is also shown that the same statement does not remain valid with the additional constraint that the points are extreme points of K. Moreover, the factor ½ cannot be achieved with any fixed number of extreme points. We conclude the paper with a few other inequalities related to the perimeter of a convex shape.}, author = {Akopyan, Arseniy and Vysotsky, Vladislav}, issn = {0002-9890}, journal = {The American Mathematical Monthly}, number = {7}, pages = {588 -- 596}, publisher = {Mathematical Association of America}, title = {{On the lengths of curves passing through boundary points of a planar convex shape}}, doi = {10.4169/amer.math.monthly.124.7.588}, volume = {124}, year = {2017}, }