@article{11340, abstract = {Like-charge attraction, driven by ionic correlations, challenges our understanding of electrostatics both in soft and hard matter. For two charged planar surfaces confining counterions and water, we prove that, even at relatively low correlation strength, the relevant physics is the ground-state one, oblivious of fluctuations. Based on this, we derive a simple and accurate interaction pressure that fulfills known exact requirements and can be used as an effective potential. We test this equation against implicit-solvent Monte Carlo simulations and against explicit-solvent simulations of cement and several types of clays. We argue that water destructuring under nanometric confinement drastically reduces dielectric screening, enhancing ionic correlations. Our equation of state at reduced permittivity therefore explains the exotic attractive regime reported for these materials, even in the absence of multivalent counterions.}, author = {Palaia, Ivan and Goyal, Abhay and Del Gado, Emanuela and Šamaj, Ladislav and Trizac, Emmanuel}, issn = {1520-5207}, journal = {Journal of Physical Chemistry B}, number = {16}, pages = {3143--3149}, publisher = {American Chemical Society}, title = {{Like-charge attraction at the nanoscale: Ground-state correlations and water destructuring}}, doi = {10.1021/acs.jpcb.2c00028}, volume = {126}, year = {2022}, } @article{11341, abstract = {Intragenic regions that are removed during maturation of the RNA transcript—introns—are universally present in the nuclear genomes of eukaryotes1. The budding yeast, an otherwise intron-poor species, preserves two sets of ribosomal protein genes that differ primarily in their introns2,3. Although studies have shed light on the role of ribosomal protein introns under stress and starvation4,5,6, understanding the contribution of introns to ribosome regulation remains challenging. Here, by combining isogrowth profiling7 with single-cell protein measurements8, we show that introns can mediate inducible phenotypic heterogeneity that confers a clear fitness advantage. Osmotic stress leads to bimodal expression of the small ribosomal subunit protein Rps22B, which is mediated by an intron in the 5′ untranslated region of its transcript. The two resulting yeast subpopulations differ in their ability to cope with starvation. Low levels of Rps22B protein result in prolonged survival under sustained starvation, whereas high levels of Rps22B enable cells to grow faster after transient starvation. Furthermore, yeasts growing at high concentrations of sugar, similar to those in ripe grapes, exhibit bimodal expression of Rps22B when approaching the stationary phase. Differential intron-mediated regulation of ribosomal protein genes thus provides a way to diversify the population when starvation threatens in natural environments. Our findings reveal a role for introns in inducing phenotypic heterogeneity in changing environments, and suggest that duplicated ribosomal protein genes in yeast contribute to resolving the evolutionary conflict between precise expression control and environmental responsiveness9.}, author = {Lukacisin, Martin and Espinosa-Cantú, Adriana and Bollenbach, Mark Tobias}, issn = {1476-4687}, journal = {Nature}, pages = {113--118}, publisher = {Springer Nature}, title = {{Intron-mediated induction of phenotypic heterogeneity}}, doi = {10.1038/s41586-022-04633-0}, volume = {605}, year = {2022}, } @article{11343, abstract = {Multistable systems are characterized by exhibiting domain coexistence, where each domain accounts for the different equilibrium states. In case these systems are described by vectorial fields, domains can be connected through topological defects. Vortices are one of the most frequent and studied topological defect points. Optical vortices are equally relevant for their fundamental features as beams with topological features and their applications in image processing, telecommunications, optical tweezers, and quantum information. A natural source of optical vortices is the interaction of light beams with matter vortices in liquid crystal cells. The rhythms that govern the emergence of matter vortices due to fluctuations are not established. Here, we investigate the nucleation mechanisms of the matter vortices in liquid crystal cells and establish statistical laws that govern them. Based on a stochastic amplitude equation, the law for the number of nucleated vortices as a function of anisotropy, voltage, and noise level intensity is set. Experimental observations in a nematic liquid crystal cell with homeotropic anchoring and a negative anisotropic dielectric constant under the influence of a transversal electric field show a qualitative agreement with the theoretical findings.}, author = {Aguilera, Esteban and Clerc, Marcel G. and Zambra, Valeska}, issn = {1573-269X}, journal = {Nonlinear Dynamics}, keywords = {Electrical and Electronic Engineering, Applied Mathematics, Mechanical Engineering, Ocean Engineering, Aerospace Engineering, Control and Systems Engineering}, pages = {3209--3218}, publisher = {Springer Nature}, title = {{Vortices nucleation by inherent fluctuations in nematic liquid crystal cells}}, doi = {10.1007/s11071-022-07396-5}, volume = {108}, year = {2022}, } @article{11344, abstract = {Until recently, Shigella and enteroinvasive Escherichia coli were thought to be primate-restricted pathogens. The base of their pathogenicity is the type 3 secretion system (T3SS) encoded by the pINV virulence plasmid, which facilitates host cell invasion and subsequent proliferation. A large family of T3SS effectors, E3 ubiquitin-ligases encoded by the ipaH genes, have a key role in the Shigella pathogenicity through the modulation of cellular ubiquitination that degrades host proteins. However, recent genomic studies identified ipaH genes in the genomes of Escherichia marmotae, a potential marmot pathogen, and an E. coli extracted from fecal samples of bovine calves, suggesting that non-human hosts may also be infected by these strains, potentially pathogenic to humans. We performed a comparative genomic study of the functional repertoires in the ipaH gene family in Shigella and enteroinvasive Escherichia from human and predicted non-human hosts. We found that fewer than half of Shigella genomes had a complete set of ipaH genes, with frequent gene losses and duplications that were not consistent with the species tree and nomenclature. Non-human host IpaH proteins had a diverse set of substrate-binding domains and, in contrast to the Shigella proteins, two variants of the NEL C-terminal domain. Inconsistencies between strains phylogeny and composition of effectors indicate horizontal gene transfer between E. coli adapted to different hosts. These results provide a framework for understanding of ipaH-mediated host-pathogens interactions and suggest a need for a genomic study of fecal samples from diseased animals.}, author = {Dranenko, NO and Tutukina, MN and Gelfand, MS and Kondrashov, Fyodor and Bochkareva, Olga}, issn = {2045-2322}, journal = {Scientific Reports}, publisher = {Springer Nature}, title = {{Chromosome-encoded IpaH ubiquitin ligases indicate non-human enteroinvasive Escherichia}}, doi = {10.1038/s41598-022-10827-3}, volume = {12}, year = {2022}, } @article{11351, abstract = {One hallmark of plant cells is their cell wall. They protect cells against the environment and high turgor and mediate morphogenesis through the dynamics of their mechanical and chemical properties. The walls are a complex polysaccharidic structure. Although their biochemical composition is well known, how the different components organize in the volume of the cell wall and interact with each other is not well understood and yet is key to the wall’s mechanical properties. To investigate the ultrastructure of the plant cell wall, we imaged the walls of onion (Allium cepa) bulbs in a near-native state via cryo-focused ion beam milling (cryo-FIB milling) and cryo-electron tomography (cryo-ET). This allowed the high-resolution visualization of cellulose fibers in situ. We reveal the coexistence of dense fiber fields bathed in a reticulated matrix we termed “meshing,” which is more abundant at the inner surface of the cell wall. The fibers adopted a regular bimodal angular distribution at all depths in the cell wall and bundled according to their orientation, creating layers within the cell wall. Concomitantly, employing homogalacturonan (HG)-specific enzymatic digestion, we observed changes in the meshing, suggesting that it is—at least in part—composed of HG pectins. We propose the following model for the construction of the abaxial epidermal primary cell wall: the cell deposits successive layers of cellulose fibers at −45° and +45° relative to the cell’s long axis and secretes the surrounding HG-rich meshing proximal to the plasma membrane, which then migrates to more distal regions of the cell wall.}, author = {Nicolas, William J. and Fäßler, Florian and Dutka, Przemysław and Schur, Florian KM and Jensen, Grant and Meyerowitz, Elliot}, issn = {0960-9822}, journal = {Current Biology}, keywords = {General Agricultural and Biological Sciences, General Biochemistry, Genetics and Molecular Biology}, number = {11}, pages = {P2375--2389}, publisher = {Elsevier}, title = {{Cryo-electron tomography of the onion cell wall shows bimodally oriented cellulose fibers and reticulated homogalacturonan networks}}, doi = {10.1016/j.cub.2022.04.024}, volume = {32}, year = {2022}, } @article{11354, abstract = {We construct a recurrent diffusion process with values in the space of probability measures over an arbitrary closed Riemannian manifold of dimension d≥2. The process is associated with the Dirichlet form defined by integration of the Wasserstein gradient w.r.t. the Dirichlet–Ferguson measure, and is the counterpart on multidimensional base spaces to the modified massive Arratia flow over the unit interval described in V. Konarovskyi and M.-K. von Renesse (Comm. Pure Appl. Math. 72 (2019) 764–800). Together with two different constructions of the process, we discuss its ergodicity, invariant sets, finite-dimensional approximations, and Varadhan short-time asymptotics.}, author = {Dello Schiavo, Lorenzo}, issn = {2168-894X}, journal = {Annals of Probability}, number = {2}, pages = {591--648}, publisher = {Institute of Mathematical Statistics}, title = {{The Dirichlet–Ferguson diffusion on the space of probability measures over a closed Riemannian manifold}}, doi = {10.1214/21-AOP1541}, volume = {50}, year = {2022}, } @inproceedings{11355, abstract = {Contract-based design is a promising methodology for taming the complexity of developing sophisticated systems. A formal contract distinguishes between assumptions, which are constraints that the designer of a component puts on the environments in which the component can be used safely, and guarantees, which are promises that the designer asks from the team that implements the component. A theory of formal contracts can be formalized as an interface theory, which supports the composition and refinement of both assumptions and guarantees. Although there is a rich landscape of contract-based design methods that address functional and extra-functional properties, we present the first interface theory that is designed for ensuring system-wide security properties. Our framework provides a refinement relation and a composition operation that support both incremental design and independent implementability. We develop our theory for both stateless and stateful interfaces. We illustrate the applicability of our framework with an example inspired from the automotive domain.}, author = {Bartocci, Ezio and Ferrere, Thomas and Henzinger, Thomas A and Nickovic, Dejan and Da Costa, Ana Oliveira}, booktitle = {Fundamental Approaches to Software Engineering}, isbn = {9783030994280}, issn = {1611-3349}, location = {Munich, Germany}, pages = {3--22}, publisher = {Springer Nature}, title = {{Information-flow interfaces}}, doi = {10.1007/978-3-030-99429-7_1}, volume = {13241}, year = {2022}, } @article{11356, author = {Chang, Cheng and Qin, Bingchao and Su, Lizhong and Zhao, Li Dong}, issn = {2095-9281}, journal = {Science Bulletin}, number = {11}, pages = {1105--1107}, publisher = {Elsevier}, title = {{Distinct electron and hole transports in SnSe crystals}}, doi = {10.1016/j.scib.2022.04.007}, volume = {67}, year = {2022}, } @article{11379, abstract = {Bernal-stacked multilayer graphene is a versatile platform to explore quantum transport phenomena and interaction physics due to its exceptional tunability via electrostatic gating. For instance, upon applying a perpendicular electric field, its band structure exhibits several off-center Dirac points (so-called Dirac gullies) in each valley. Here, the formation of Dirac gullies and the interaction-induced breakdown of gully coherence is explored via magnetotransport measurements in high-quality Bernal-stacked (ABA) trilayer graphene. At zero magnetic field, multiple Lifshitz transitions indicating the formation of Dirac gullies are identified. In the quantum Hall regime, the emergence of Dirac gullies is evident as an increase in Landau level degeneracy. When tuning both electric and magnetic fields, electron–electron interactions can be controllably enhanced until, beyond critical electric and magnetic fields, the gully degeneracy is eventually lifted. The arising correlated ground state is consistent with a previously predicted nematic phase that spontaneously breaks the rotational gully symmetry.}, author = {Winterer, Felix and Seiler, Anna M. and Ghazaryan, Areg and Geisenhof, Fabian R. and Watanabe, Kenji and Taniguchi, Takashi and Serbyn, Maksym and Weitz, R. Thomas}, issn = {1530-6992}, journal = {Nano Letters}, number = {8}, pages = {3317--3322}, publisher = {American Chemical Society}, title = {{Spontaneous gully-polarized quantum hall states in ABA trilayer graphene}}, doi = {10.1021/acs.nanolett.2c00435}, volume = {22}, year = {2022}, } @article{11400, abstract = {By varying the concentration of molecules in the cytoplasm or on the membrane, cells can induce the formation of condensates and liquid droplets, similar to phase separation. Their thermodynamics, much studied, depends on the mutual interactions between microscopic constituents. Here, we focus on the kinetics and size control of 2D clusters, forming on membranes. Using molecular dynamics of patchy colloids, we model a system of two species of proteins, giving origin to specific heterotypic bonds. We find that concentrations, together with valence and bond strength, control both the size and the growth time rate of the clusters. In particular, if one species is in large excess, it gradually saturates the binding sites of the other species; the system then becomes kinetically arrested and cluster coarsening slows down or stops, thus yielding effective size selection. This phenomenology is observed both in solid and fluid clusters, which feature additional generic homotypic interactions and are reminiscent of the ones observed on biological membranes.}, author = {Palaia, Ivan and Šarić, Anđela}, issn = {1089-7690}, journal = {The Journal of Chemical Physics}, keywords = {Physical and Theoretical Chemistry, General Physics and Astronomy}, number = {19}, publisher = {AIP Publishing}, title = {{Controlling cluster size in 2D phase-separating binary mixtures with specific interactions}}, doi = {10.1063/5.0087769}, volume = {156}, year = {2022}, } @article{11401, abstract = {Tin selenide (SnSe) is considered a robust candidate for thermoelectric applications due to its very high thermoelectric figure of merit, ZT, with values of 2.6 in p-type and 2.8 in n-type single crystals. Sn has been replaced with various lower group dopants to achieve successful p-type doping in SnSe with high ZT values. A known, facile, and powerful alternative way to introduce a hole carrier is to use a natural single Sn vacancy, VSn. Through transport and scanning tunneling microscopy studies, we discovered that VSn are dominant in high-quality (slow cooling rate) SnSe single crystals, while multiple vacancies, Vmulti, are dominant in low-quality (high cooling rate) single crystals. Surprisingly, both VSn and Vmulti help to increase the power factors of SnSe, whereas samples with dominant VSn have superior thermoelectric properties in SnSe single crystals. Additionally, the observation that Vmulti are good p-type sources observed in relatively low-quality single crystals is useful in thermoelectric applications because polycrystalline SnSe can be used due to its mechanical strength; this substance is usually fabricated at very high cooling speeds.}, author = {Nguyen, Van Quang and Trinh, Thi Ly and Chang, Cheng and Zhao, Li Dong and Nguyen, Thi Huong and Duong, Van Thiet and Duong, Anh Tuan and Park, Jong Ho and Park, Sudong and Kim, Jungdae and Cho, Sunglae}, issn = {1884-4057}, journal = {NPG Asia Materials}, publisher = {Springer Nature}, title = {{Unidentified major p-type source in SnSe: Multivacancies}}, doi = {10.1038/s41427-022-00393-5}, volume = {14}, year = {2022}, } @article{11402, abstract = {Fixed-horizon planning considers a weighted graph and asks to construct a path that maximizes the sum of weights for a given time horizon T. However, in many scenarios, the time horizon is not fixed, but the stopping time is chosen according to some distribution such that the expected stopping time is T. If the stopping-time distribution is not known, then to ensure robustness, the distribution is chosen by an adversary as the worst-case scenario. A stationary plan for every vertex always chooses the same outgoing edge. For fixed horizon or fixed stopping-time distribution, stationary plans are not sufficient for optimality. Quite surprisingly we show that when an adversary chooses the stopping-time distribution with expected stopping-time T, then stationary plans are sufficient. While computing optimal stationary plans for fixed horizon is NP-complete, we show that computing optimal stationary plans under adversarial stopping-time distribution can be achieved in polynomial time.}, author = {Chatterjee, Krishnendu and Doyen, Laurent}, issn = {1090-2724}, journal = {Journal of Computer and System Sciences}, pages = {1--21}, publisher = {Elsevier}, title = {{Graph planning with expected finite horizon}}, doi = {10.1016/j.jcss.2022.04.003}, volume = {129}, year = {2022}, } @article{11403, author = {Stöllner, Andrea}, issn = {2662-138X}, journal = {Nature Reviews Earth and Environment}, number = {6}, pages = {360}, publisher = {Springer Nature}, title = {{Measuring airborne nanoplastics using aerosol physics}}, doi = {10.1038/s43017-022-00302-y}, volume = {3}, year = {2022}, } @article{11417, abstract = {Over the past few years, the field of quantum information science has seen tremendous progress toward realizing large-scale quantum computers. With demonstrations of quantum computers outperforming classical computers for a select range of problems,1–3 we have finally entered the noisy, intermediate-scale quantum (NISQ) computing era. While the quantum computers of today are technological marvels, they are not yet error corrected, and it is unclear whether any system will scale beyond a few hundred logical qubits without significant changes to architecture and control schemes. Today's quantum systems are analogous to the ENIAC (Electronic Numerical Integrator And Computer) and EDVAC (Electronic Discrete Variable Automatic Computer) systems of the 1940s, which ran on vacuum tubes. These machines were built on a solid, nominally scalable architecture and when they were developed, nobody could have predicted the development of the transistor and the impact of the resulting semiconductor industry. Simply put, the computers of today are nothing like the early computers of the 1940s. We believe that the qubits of future fault-tolerant quantum systems will look quite different from the qubits of the NISQ machines in operation today. This Special Topic issue is devoted to new and emerging quantum systems with a focus on enabling technologies that can eventually lead to the quantum analog to the transistor. We have solicited both research4–18 and perspective articles19–21 to discuss new and emerging qubit systems with a focus on novel materials, encodings, and architectures. We are proud to present a collection that touches on a wide range of technologies including superconductors,7–13,21 semiconductors,15–17,19 and individual atomic qubits.18 }, author = {Sigillito, Anthony J. and Covey, Jacob P. and Fink, Johannes M and Petersson, Karl and Preble, Stefan}, issn = {0003-6951}, journal = {Applied Physics Letters}, number = {19}, publisher = {American Institute of Physics}, title = {{Emerging qubit systems: Guest editorial}}, doi = {10.1063/5.0097339}, volume = {120}, year = {2022}, } @article{11418, abstract = {We consider the quadratic form of a general high-rank deterministic matrix on the eigenvectors of an N×N Wigner matrix and prove that it has Gaussian fluctuation for each bulk eigenvector in the large N limit. The proof is a combination of the energy method for the Dyson Brownian motion inspired by Marcinek and Yau (2021) and our recent multiresolvent local laws (Comm. Math. Phys. 388 (2021) 1005–1048).}, author = {Cipolloni, Giorgio and Erdös, László and Schröder, Dominik J}, issn = {2168-894X}, journal = {Annals of Probability}, number = {3}, pages = {984--1012}, publisher = {Institute of Mathematical Statistics}, title = {{Normal fluctuation in quantum ergodicity for Wigner matrices}}, doi = {10.1214/21-AOP1552}, volume = {50}, year = {2022}, } @article{11419, abstract = {Elevation of soluble wild-type (WT) tau occurs in synaptic compartments in Alzheimer’s disease. We addressed whether tau elevation affects synaptic transmission at the calyx of Held in slices from mice brainstem. Whole-cell loading of WT human tau (h-tau) in presynaptic terminals at 10–20 µM caused microtubule (MT) assembly and activity-dependent rundown of excitatory neurotransmission. Capacitance measurements revealed that the primary target of WT h-tau is vesicle endocytosis. Blocking MT assembly using nocodazole prevented tau-induced impairments of endocytosis and neurotransmission. Immunofluorescence imaging analyses revealed that MT assembly by WT h-tau loading was associated with an increased MT-bound fraction of the endocytic protein dynamin. A synthetic dodecapeptide corresponding to dynamin 1-pleckstrin-homology domain inhibited MT-dynamin interaction and rescued tau-induced impairments of endocytosis and neurotransmission. We conclude that elevation of presynaptic WT tau induces de novo assembly of MTs, thereby sequestering free dynamins. As a result, endocytosis and subsequent vesicle replenishment are impaired, causing activity-dependent rundown of neurotransmission.}, author = {Hori, Tetsuya and Eguchi, Kohgaku and Wang, Han Ying and Miyasaka, Tomohiro and Guillaud, Laurent and Taoufiq, Zacharie and Mahapatra, Satyajit and Yamada, Hiroshi and Takei, Kohji and Takahashi, Tomoyuki}, issn = {2050-084X}, journal = {eLife}, publisher = {eLife Sciences Publications}, title = {{Microtubule assembly by tau impairs endocytosis and neurotransmission via dynamin sequestration in Alzheimer's disease synapse model}}, doi = {10.7554/eLife.73542}, volume = {11}, year = {2022}, } @inproceedings{11428, abstract = {The medial axis of a set consists of the points in the ambient space without a unique closest point on the original set. Since its introduction, the medial axis has been used extensively in many applications as a method of computing a topologically equivalent skeleton. Unfortunately, one limiting factor in the use of the medial axis of a smooth manifold is that it is not necessarily topologically stable under small perturbations of the manifold. To counter these instabilities various prunings of the medial axis have been proposed. Here, we examine one type of pruning, called burning. Because of the good experimental results, it was hoped that the burning method of simplifying the medial axis would be stable. In this work we show a simple example that dashes such hopes based on Bing’s house with two rooms, demonstrating an isotopy of a shape where the medial axis goes from collapsible to non-collapsible.}, author = {Chambers, Erin and Fillmore, Christopher D and Stephenson, Elizabeth R and Wintraecken, Mathijs}, booktitle = {38th International Symposium on Computational Geometry}, editor = {Goaoc, Xavier and Kerber, Michael}, isbn = {978-3-95977-227-3}, issn = {1868-8969}, location = {Berlin, Germany}, pages = {66:1--66:9}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{A cautionary tale: Burning the medial axis is unstable}}, doi = {10.4230/LIPIcs.SoCG.2022.66}, volume = {224}, year = {2022}, } @book{11429, abstract = {This book constitutes the refereed proceedings of the 18th International Symposium on Web and Wireless Geographical Information Systems, W2GIS 2022, held in Konstanz, Germany, in April 2022. The 7 full papers presented together with 6 short papers in the volume were carefully reviewed and selected from 16 submissions. The papers cover topics that range from mobile GIS and Location-Based Services to Spatial Information Retrieval and Wireless Sensor Networks.}, editor = {Karimipour, Farid and Storandt, Sabine}, isbn = {9783031062445}, issn = {1611-3349}, pages = {153}, publisher = {Springer Nature}, title = {{Web and Wireless Geographical Information Systems}}, doi = {10.1007/978-3-031-06245-2}, volume = {13238}, year = {2022}, } @article{11432, abstract = {This paper proposes a method for simulating liquids in large bodies of water by coupling together a water surface wave simulator with a 3D Navier-Stokes simulator. The surface wave simulation uses the equivalent sources method (ESM) to efficiently animate large bodies of water with precisely controllable wave propagation behavior. The 3D liquid simulator animates complex non-linear fluid behaviors like splashes and breaking waves using off-the-shelf simulators using FLIP or the level set method with semi-Lagrangian advection. We combine the two approaches by using the 3D solver to animate localized non-linear behaviors, and the 2D wave solver to animate larger regions with linear surface physics. We use the surface motion from the 3D solver as boundary conditions for 2D surface wave simulator, and we use the velocity and surface heights from the 2D surface wave simulator as boundary conditions for the 3D fluid simulation. We also introduce a novel technique for removing visual artifacts caused by numerical errors in 3D fluid solvers: we use experimental data to estimate the artificial dispersion caused by the 3D solver and we then carefully tune the wave speeds of the 2D solver to match it, effectively eliminating any differences in wave behavior across the boundary. To the best of our knowledge, this is the first time such a empirically driven error compensation approach has been used to remove coupling errors from a physics simulator. Our coupled simulation approach leverages the strengths of each simulation technique, animating large environments with seamless transitions between 2D and 3D physics.}, author = {Schreck, Camille and Wojtan, Christopher J}, issn = {1467-8659}, journal = {Computer Graphics Forum}, number = {2}, pages = {343--353}, publisher = {Wiley}, title = {{Coupling 3D liquid simulation with 2D wave propagation for large scale water surface animation using the equivalent sources method}}, doi = {10.1111/cgf.14478}, volume = {41}, year = {2022}, } @article{11435, abstract = {We introduce a new variant of quantitative Helly-type theorems: the minimal homothetic distance of the intersection of a family of convex sets to the intersection of a subfamily of a fixed size. As an application, we establish the following quantitative Helly-type result for the diameter. If $K$ is the intersection of finitely many convex bodies in $\mathbb{R}^d$, then one can select $2d$ of these bodies whose intersection is of diameter at most $(2d)^3{diam}(K)$. The best previously known estimate, due to Brazitikos [Bull. Hellenic Math. Soc., 62 (2018), pp. 19--25], is $c d^{11/2}$. Moreover, we confirm that the multiplicative factor $c d^{1/2}$ conjectured by Bárány, Katchalski, and Pach [Proc. Amer. Math. Soc., 86 (1982), pp. 109--114] cannot be improved. The bounds above follow from our key result that concerns sparse approximation of a convex polytope by the convex hull of a well-chosen subset of its vertices: Assume that $Q \subset {\mathbb R}^d$ is a polytope whose centroid is the origin. Then there exist at most 2d vertices of $Q$ whose convex hull $Q^{\prime \prime}$ satisfies $Q \subset - 8d^3 Q^{\prime \prime}.$}, author = {Ivanov, Grigory and Naszodi, Marton}, issn = {0895-4801}, journal = {SIAM Journal on Discrete Mathematics}, number = {2}, pages = {951--957}, publisher = {Society for Industrial and Applied Mathematics}, title = {{A quantitative Helly-type theorem: Containment in a homothet}}, doi = {10.1137/21M1403308}, volume = {36}, year = {2022}, }