0 there exists a large subset of a ∈ F×p such that for kl a,1,p : x → e((ax+x) / p) we have M(kla,1,p) ≥ (1−ε/√2π + o(1)) log log p, as p→∞. Finally, we prove a result on the growth of the moments of {M (kla,1,p)}a∈F×p. 2020 Mathematics Subject Classification: 11L03, 11T23 (Primary); 14F20, 60F10 (Secondary). AU - Bonolis, Dante ID - 9364 JF - Mathematical Proceedings of the Cambridge Philosophical Society SN - 03050041 TI - On the size of the maximum of incomplete Kloosterman sums ER - TY - JOUR AB - Shigella are pathogens originating within the Escherichia lineage but frequently classified as a separate genus. Shigella genomes contain numerous insertion sequences (ISs) that lead to pseudogenisation of affected genes and an increase of non-homologous recombination. Here, we study 414 genomes of E. coli and Shigella strains to assess the contribution of genomic rearrangements to Shigella evolution. We found that Shigella experienced exceptionally high rates of intragenomic rearrangements and had a decreased rate of homologous recombination compared to pathogenic and non-pathogenic E. coli. The high rearrangement rate resulted in independent disruption of syntenic regions and parallel rearrangements in different Shigella lineages. Specifically, we identified two types of chromosomally encoded E3 ubiquitin-protein ligases acquired independently by all Shigella strains that also showed a high level of sequence conservation in the promoter and further in the 5′-intergenic region. In the only available enteroinvasive E. coli (EIEC) strain, which is a pathogenic E. coli with a phenotype intermediate between Shigella and non-pathogenic E. coli, we found a rate of genome rearrangements comparable to those in other E. coli and no functional copies of the two Shigella-specific E3 ubiquitin ligases. These data indicate that the accumulation of ISs influenced many aspects of genome evolution and played an important role in the evolution of intracellular pathogens. Our research demonstrates the power of comparative genomics-based on synteny block composition and an important role of non-coding regions in the evolution of genomic islands. AU - Seferbekova, Zaira AU - Zabelkin, Alexey AU - Yakovleva, Yulia AU - Afasizhev, Robert AU - Dranenko, Natalia O. AU - Alexeev, Nikita AU - Gelfand, Mikhail S. AU - Bochkareva, Olga ID - 9380 JF - Frontiers in Microbiology TI - High rates of genome rearrangements and pathogenicity of Shigella spp. VL - 12 ER - TY - JOUR AB - A game of rock-paper-scissors is an interesting example of an interaction where none of the pure strategies strictly dominates all others, leading to a cyclic pattern. In this work, we consider an unstable version of rock-paper-scissors dynamics and allow individuals to make behavioural mistakes during the strategy execution. We show that such an assumption can break a cyclic relationship leading to a stable equilibrium emerging with only one strategy surviving. We consider two cases: completely random mistakes when individuals have no bias towards any strategy and a general form of mistakes. Then, we determine conditions for a strategy to dominate all other strategies. However, given that individuals who adopt a dominating strategy are still prone to behavioural mistakes in the observed behaviour, we may still observe extinct strategies. That is, behavioural mistakes in strategy execution stabilise evolutionary dynamics leading to an evolutionary stable and, potentially, mixed co-existence equilibrium. AU - Kleshnina, Maria AU - Streipert, Sabrina S. AU - Filar, Jerzy A. AU - Chatterjee, Krishnendu ID - 9381 IS - 4 JF - PLoS Computational Biology SN - 1553734X TI - Mistakes can stabilise the dynamics of rock-paper-scissors games VL - 17 ER - TY - CONF AB - Modern neural networks can easily fit their training set perfectly. Surprisingly, despite being “overfit” in this way, they tend to generalize well to future data, thereby defying the classic bias–variance trade-off of machine learning theory. Of the many possible explanations, a prevalent one is that training by stochastic gradient descent (SGD) imposes an implicit bias that leads it to learn simple functions, and these simple functions generalize well. However, the specifics of this implicit bias are not well understood. In this work, we explore the smoothness conjecture which states that SGD is implicitly biased towards learning functions that are smooth. We propose several measures to formalize the intuitive notion of smoothness, and we conduct experiments to determine whether SGD indeed implicitly optimizes for these measures. Our findings rule out the possibility that smoothness measures based on first-order derivatives are being implicitly enforced. They are supportive, though, of the smoothness conjecture for measures based on second-order derivatives. AU - Volhejn, Vaclav AU - Lampert, Christoph ID - 9210 SN - 03029743 T2 - 42nd German Conference on Pattern Recognition TI - Does SGD implicitly optimize for smoothness? VL - 12544 LNCS ER - TY - JOUR AB - A primary roadblock to our understanding of speciation is that it usually occurs over a timeframe that is too long to study from start to finish. The idea of a speciation continuum provides something of a solution to this problem; rather than observing the entire process, we can simply reconstruct it from the multitude of speciation events that surround us. But what do we really mean when we talk about the speciation continuum, and can it really help us understand speciation? We explored these questions using a literature review and online survey of speciation researchers. Although most researchers were familiar with the concept and thought it was useful, our survey revealed extensive disagreement about what the speciation continuum actually tells us. This is due partly to the lack of a clear definition. Here, we provide an explicit definition that is compatible with the Biological Species Concept. That is, the speciation continuum is a continuum of reproductive isolation. After outlining the logic of the definition in light of alternatives, we explain why attempts to reconstruct the speciation process from present‐day populations will ultimately fail. We then outline how we think the speciation continuum concept can continue to act as a foundation for understanding the continuum of reproductive isolation that surrounds us. AU - Stankowski, Sean AU - Ravinet, Mark ID - 9383 JF - Evolution SN - 00143820 TI - Defining the speciation continuum ER - TY - JOUR AU - Bolger-Munro, Madison AU - Choi, Kate AU - Cheung, Faith AU - Liu, Yi Tian AU - Dang-Lawson, May AU - Deretic, Nikola AU - Keane, Connor AU - Gold, Michael R. ID - 9379 JF - Frontiers in Cell and Developmental Biology KW - B cell KW - actin KW - immune synapse KW - cell spreading KW - cofilin KW - WDR1 (AIP1) KW - LIM domain kinase KW - B cell receptor (BCR) TI - The Wdr1-LIMK-Cofilin axis controls B cell antigen receptor-induced actin remodeling and signaling at the immune synapse VL - 9 ER - TY - JOUR AB - We report the complete analysis of a deterministic model of deleterious mutations and negative selection against them at two haploid loci without recombination. As long as mutation is a weaker force than selection, mutant alleles remain rare at the only stable equilibrium, and otherwise, a variety of dynamics are possible. If the mutation-free genotype is absent, generally the only stable equilibrium is the one that corresponds to fixation of the mutant allele at the locus where it is less deleterious. This result suggests that fixation of a deleterious allele that follows a click of the Muller’s ratchet is governed by natural selection, instead of random drift. AU - Khudiakova, Kseniia AU - Neretina, Tatiana Yu. AU - Kondrashov, Alexey S. ID - 9387 JF - Journal of Theoretical Biology KW - General Biochemistry KW - Genetics and Molecular Biology KW - Modelling and Simulation KW - Statistics and Probability KW - General Immunology and Microbiology KW - Applied Mathematics KW - General Agricultural and Biological Sciences KW - General Medicine SN - 0022-5193 TI - Two linked loci under mutation-selection balance and Muller’s ratchet VL - 524 ER - TY - JOUR AB - We consider the core algorithmic problems related to verification of systems with respect to three classical quantitative properties, namely, the mean-payoff, the ratio, and the minimum initial credit for energy property. The algorithmic problem given a graph and a quantitative property asks to compute the optimal value (the infimum value over all traces) from every node of the graph. We consider graphs with bounded treewidth—a class that contains the control flow graphs of most programs. Let n denote the number of nodes of a graph, m the number of edges (for bounded treewidth 𝑚=𝑂(𝑛)) and W the largest absolute value of the weights. Our main theoretical results are as follows. First, for the minimum initial credit problem we show that (1) for general graphs the problem can be solved in 𝑂(𝑛2⋅𝑚) time and the associated decision problem in 𝑂(𝑛⋅𝑚) time, improving the previous known 𝑂(𝑛3⋅𝑚⋅log(𝑛⋅𝑊)) and 𝑂(𝑛2⋅𝑚) bounds, respectively; and (2) for bounded treewidth graphs we present an algorithm that requires 𝑂(𝑛⋅log𝑛) time. Second, for bounded treewidth graphs we present an algorithm that approximates the mean-payoff value within a factor of 1+𝜖 in time 𝑂(𝑛⋅log(𝑛/𝜖)) as compared to the classical exact algorithms on general graphs that require quadratic time. Third, for the ratio property we present an algorithm that for bounded treewidth graphs works in time 𝑂(𝑛⋅log(|𝑎⋅𝑏|))=𝑂(𝑛⋅log(𝑛⋅𝑊)), when the output is 𝑎𝑏, as compared to the previously best known algorithm on general graphs with running time 𝑂(𝑛2⋅log(𝑛⋅𝑊)). We have implemented some of our algorithms and show that they present a significant speedup on standard benchmarks. AU - Chatterjee, Krishnendu AU - Ibsen-Jensen, Rasmus AU - Pavlogiannis, Andreas ID - 9393 JF - Formal Methods in System Design SN - 09259856 TI - Faster algorithms for quantitative verification in bounded treewidth graphs ER - TY - JOUR AB - Chromosomal inversions have long been recognized for their role in local adaptation. By suppressing recombination in heterozygous individuals, they can maintain coadapted gene complexes and protect them from homogenizing effects of gene flow. However, to fully understand their importance for local adaptation we need to know their influence on phenotypes under divergent selection. For this, the marine snail Littorina saxatilis provides an ideal study system. Divergent ecotypes adapted to wave action and crab predation occur in close proximity on intertidal shores with gene flow between them. Here, we used F2 individuals obtained from crosses between the ecotypes to test for associations between genomic regions and traits distinguishing the Crab‐/Wave‐adapted ecotypes including size, shape, shell thickness, and behavior. We show that most of these traits are influenced by two previously detected inversion regions that are divergent between ecotypes. We thus gain a better understanding of one important underlying mechanism responsible for the rapid and repeated formation of ecotypes: divergent selection acting on inversions. We also found that some inversions contributed to more than one trait suggesting that they may contain several loci involved in adaptation, consistent with the hypothesis that suppression of recombination within inversions facilitates differentiation in the presence of gene flow. AU - Koch, Eva L. AU - Morales, Hernán E. AU - Larsson, Jenny AU - Westram, Anja M AU - Faria, Rui AU - Lemmon, Alan R. AU - Lemmon, E. Moriarty AU - Johannesson, Kerstin AU - Butlin, Roger K. ID - 9394 JF - Evolution Letters TI - Genetic variation for adaptive traits is associated with polymorphic inversions in Littorina saxatilis ER - TY - DATA AB - This .zip File contains the transport data for "Non-topological zero bias peaks in full-shell nanowires induced by flux tunable Andreev states" by M. Valentini, et. al. The measurements were done using Labber Software and the data is stored in the hdf5 file format. Instructions of how to read the data are in "Notebook_Valentini.pdf". AU - Valentini, Marco ID - 9389 TI - Research data for "Non-topological zero bias peaks in full-shell nanowires induced by flux tunable Andreev states" ER - TY - JOUR AU - Stankowski, Sean AU - Ravinet, Mark ID - 9392 IS - 9 JF - Current Biology SN - 09609822 TI - Quantifying the use of species concepts VL - 31 ER - TY - JOUR AB - Direct and indirect reciprocity are key mechanisms for the evolution of cooperation. Direct reciprocity means that individuals use their own experience to decide whether to cooperate with another person. Indirect reciprocity means that they also consider the experiences of others. Although these two mechanisms are intertwined, they are typically studied in isolation. Here, we introduce a mathematical framework that allows us to explore both kinds of reciprocity simultaneously. We show that the well-known ‘generous tit-for-tat’ strategy of direct reciprocity has a natural analogue in indirect reciprocity, which we call ‘generous scoring’. Using an equilibrium analysis, we characterize under which conditions either of the two strategies can maintain cooperation. With simulations, we additionally explore which kind of reciprocity evolves when members of a population engage in social learning to adapt to their environment. Our results draw unexpected connections between direct and indirect reciprocity while highlighting important differences regarding their evolvability. AU - Schmid, Laura AU - Chatterjee, Krishnendu AU - Hilbe, Christian AU - Nowak, Martin A. ID - 9402 JF - Nature Human Behaviour TI - A unified framework of direct and indirect reciprocity ER - TY - CHAP AB - Optimal decision making requires individuals to know their available options and to anticipate correctly what consequences these options have. In many social interactions, however, we refrain from gathering all relevant information, even if this information would help us make better decisions and is costless to obtain. This chapter examines several examples of “deliberate ignorance.” Two simple models are proposed to illustrate how ignorance can evolve among self-interested and payoff - maximizing individuals, and open problems are highlighted that lie ahead for future research to explore. AU - Schmid, Laura AU - Hilbe, Christian ED - Hertwig, Ralph ED - Engel, Christoph ID - 9403 SN - 978-0-262-04559-9 T2 - Deliberate Ignorance: Choosing Not To Know TI - The evolution of strategic ignorance in strategic interaction VL - 29 ER - TY - JOUR AB - We extend our recent result [22] on the central limit theorem for the linear eigenvalue statistics of non-Hermitian matrices X with independent, identically distributed complex entries to the real symmetry class. We find that the expectation and variance substantially differ from their complex counterparts, reflecting (i) the special spectral symmetry of real matrices onto the real axis; and (ii) the fact that real i.i.d. matrices have many real eigenvalues. Our result generalizes the previously known special cases where either the test function is analytic [49] or the first four moments of the matrix elements match the real Gaussian [59, 44]. The key element of the proof is the analysis of several weakly dependent Dyson Brownian motions (DBMs). The conceptual novelty of the real case compared with [22] is that the correlation structure of the stochastic differentials in each individual DBM is non-trivial, potentially even jeopardising its well-posedness. AU - Cipolloni, Giorgio AU - Erdös, László AU - Schröder, Dominik J ID - 9412 JF - Electronic Journal of Probability TI - Fluctuation around the circular law for random matrices with real entries VL - 26 ER - TY - JOUR AB - The dynamics of a triangular magnetocapillary swimmer is studied using the lattice Boltzmann method. We extend on our previous work, which deals with the self-assembly and a specific type of the swimmer motion characterized by the swimmer’s maximum velocity centred around the particle’s inverse viscous time. Here, we identify additional regimes of motion. First, modifying the ratio of surface tension and magnetic forces allows to study the swimmer propagation in the regime of significantly lower frequencies mainly defined by the strength of the magnetocapillary potential. Second, introducing a constant magnetic contribution in each of the particles in addition to their magnetic moment induced by external fields leads to another regime characterized by strong in-plane swimmer reorientations that resemble experimental observations. AU - Sukhov, Alexander AU - Hubert, Maxime AU - Grosjean, Galien M AU - Trosman, Oleg AU - Ziegler, Sebastian AU - Collard, Ylona AU - Vandewalle, Nicolas AU - Smith, Ana Sunčana AU - Harting, Jens ID - 9411 IS - 4 JF - European Physical Journal E SN - 12928941 TI - Regimes of motion of magnetocapillary swimmers VL - 44 ER - TY - JOUR AB - Microtubule plus-end depolymerization rate is a potentially important target of physiological regulation, but it has been challenging to measure, so its role in spatial organization is poorly understood. Here we apply a method for tracking plus ends based on time difference imaging to measure depolymerization rates in large interphase asters growing in Xenopus egg extract. We observed strong spatial regulation of depolymerization rates, which were higher in the aster interior compared with the periphery, and much less regulation of polymerization or catastrophe rates. We interpret these data in terms of a limiting component model, where aster growth results in lower levels of soluble tubulin and microtubule-associated proteins (MAPs) in the interior cytosol compared with that at the periphery. The steady-state polymer fraction of tubulin was ∼30%, so tubulin is not strongly depleted in the aster interior. We propose that the limiting component for microtubule assembly is a MAP that inhibits depolymerization, and that egg asters are tuned to low microtubule density. AU - Ishihara, Keisuke AU - Decker, Franziska AU - Dos Santos Caldas, Paulo R AU - Pelletier, James F. AU - Loose, Martin AU - Brugués, Jan AU - Mitchison, Timothy J. ID - 9414 IS - 9 JF - Molecular Biology of the Cell SN - 10591524 TI - Spatial variation of microtubule depolymerization in large asters VL - 32 ER - TY - CONF AB - Formal design of embedded and cyber-physical systems relies on mathematical modeling. In this paper, we consider the model class of hybrid automata whose dynamics are defined by affine differential equations. Given a set of time-series data, we present an algorithmic approach to synthesize a hybrid automaton exhibiting behavior that is close to the data, up to a specified precision, and changes in synchrony with the data. A fundamental problem in our synthesis algorithm is to check membership of a time series in a hybrid automaton. Our solution integrates reachability and optimization techniques for affine dynamical systems to obtain both a sufficient and a necessary condition for membership, combined in a refinement framework. The algorithm processes one time series at a time and hence can be interrupted, provide an intermediate result, and be resumed. We report experimental results demonstrating the applicability of our synthesis approach. AU - Garcia Soto, Miriam AU - Henzinger, Thomas A AU - Schilling, Christian ID - 9200 KW - hybrid automaton KW - membership KW - system identification SN - 9781450383394 T2 - HSCC '21: Proceedings of the 24th International Conference on Hybrid Systems: Computation and Control TI - Synthesis of hybrid automata with affine dynamics from time-series data ER - TY - JOUR AB - We present a computational design system that assists users to model, optimize, and fabricate quad-robots with soft skins. Our system addresses the challenging task of predicting their physical behavior by fully integrating the multibody dynamics of the mechanical skeleton and the elastic behavior of the soft skin. The developed motion control strategy uses an alternating optimization scheme to avoid expensive full space time-optimization, interleaving space-time optimization for the skeleton, and frame-by-frame optimization for the full dynamics. The output are motor torques to drive the robot to achieve a user prescribed motion trajectory. We also provide a collection of convenient engineering tools and empirical manufacturing guidance to support the fabrication of the designed quad-robot. We validate the feasibility of designs generated with our system through physics simulations and with a physically-fabricated prototype. AU - Feng, Xudong AU - Liu, Jiafeng AU - Wang, Huamin AU - Yang, Yin AU - Bao, Hujun AU - Bickel, Bernd AU - Xu, Weiwei ID - 9408 IS - 6 JF - IEEE Transactions on Visualization and Computer Graphics SN - 19410506 TI - Computational design of skinned Quad-Robots VL - 27 ER - TY - JOUR AB - Antibiotic concentrations vary dramatically in the body and the environment. Hence, understanding the dynamics of resistance evolution along antibiotic concentration gradients is critical for predicting and slowing the emergence and spread of resistance. While it has been shown that increasing the concentration of an antibiotic slows resistance evolution, how adaptation to one antibiotic concentration correlates with fitness at other points along the gradient has not received much attention. Here, we selected populations of Escherichia coli at several points along a concentration gradient for three different antibiotics, asking how rapidly resistance evolved and whether populations became specialized to the antibiotic concentration they were selected on. Populations selected at higher concentrations evolved resistance more slowly but exhibited equal or higher fitness across the whole gradient. Populations selected at lower concentrations evolved resistance rapidly, but overall fitness in the presence of antibiotics was lower. However, these populations readily adapted to higher concentrations upon subsequent selection. Our results indicate that resistance management strategies must account not only for the rates of resistance evolution but also for the fitness of evolved strains. AU - Lagator, Mato AU - Uecker, Hildegard AU - Neve, Paul ID - 9410 IS - 5 JF - Biology letters TI - Adaptation at different points along antibiotic concentration gradients VL - 17 ER - TY - JOUR AB - This paper presents a method for designing planar multistable compliant structures. Given a sequence of desired stable states and the corresponding poses of the structure, we identify the topology and geometric realization of a mechanism—consisting of bars and joints—that is able to physically reproduce the desired multistable behavior. In order to solve this problem efficiently, we build on insights from minimally rigid graph theory to identify simple but effective topologies for the mechanism. We then optimize its geometric parameters, such as joint positions and bar lengths, to obtain correct transitions between the given poses. Simultaneously, we ensure adequate stability of each pose based on an effective approximate error metric related to the elastic energy Hessian of the bars in the mechanism. As demonstrated by our results, we obtain functional multistable mechanisms of manageable complexity that can be fabricated using 3D printing. Further, we evaluated the effectiveness of our method on a large number of examples in the simulation and fabricated several physical prototypes. AU - Zhang, Ran AU - Auzinger, Thomas AU - Bickel, Bernd ID - 9376 JF - ACM Transactions on Graphics KW - multistability KW - mechanism KW - computational design KW - rigidity TI - Computational design of planar multistable compliant structures ER - TY - JOUR AB - We derive rigorously the leading order of the correlation energy of a Fermi gas in a scaling regime of high density and weak interaction. The result verifies the prediction of the random-phase approximation. Our proof refines the method of collective bosonization in three dimensions. We approximately diagonalize an effective Hamiltonian describing approximately bosonic collective excitations around the Hartree–Fock state, while showing that gapless and non-collective excitations have only a negligible effect on the ground state energy. AU - Benedikter, Niels P AU - Nam, Phan Thành AU - Porta, Marcello AU - Schlein, Benjamin AU - Seiringer, Robert ID - 7901 JF - Inventiones Mathematicae SN - 00209910 TI - Correlation energy of a weakly interacting Fermi gas ER - TY - JOUR AB - The synaptic connection from medial habenula (MHb) to interpeduncular nucleus (IPN) is critical for emotion-related behaviors and uniquely expresses R-type Ca2+ channels (Cav2.3) and auxiliary GABAB receptor (GBR) subunits, the K+-channel tetramerization domain-containing proteins (KCTDs). Activation of GBRs facilitates or inhibits transmitter release from MHb terminals depending on the IPN subnucleus, but the role of KCTDs is unknown. We therefore examined the localization and function of Cav2.3, GBRs, and KCTDs in this pathway in mice. We show in heterologous cells that KCTD8 and KCTD12b directly bind to Cav2.3 and that KCTD8 potentiates Cav2.3 currents in the absence of GBRs. In the rostral IPN, KCTD8, KCTD12b, and Cav2.3 co-localize at the presynaptic active zone. Genetic deletion indicated a bidirectional modulation of Cav2.3-mediated release by these KCTDs with a compensatory increase of KCTD8 in the active zone in KCTD12b-deficient mice. The interaction of Cav2.3 with KCTDs therefore scales synaptic strength independent of GBR activation. AU - Bhandari, Pradeep AU - Vandael, David H AU - Fernández-Fernández, Diego AU - Fritzius, Thorsten AU - Kleindienst, David AU - Önal, Hüseyin C AU - Montanaro-Punzengruber, Jacqueline-Claire AU - Gassmann, Martin AU - Jonas, Peter M AU - Kulik, Akos AU - Bettler, Bernhard AU - Shigemoto, Ryuichi AU - Koppensteiner, Peter ID - 9437 JF - eLife TI - GABAB receptor auxiliary subunits modulate Cav2.3-mediated release from medial habenula terminals VL - 10 ER - TY - JOUR AB - The ability to adapt to changes in stimulus statistics is a hallmark of sensory systems. Here, we developed a theoretical framework that can account for the dynamics of adaptation from an information processing perspective. We use this framework to optimize and analyze adaptive sensory codes, and we show that codes optimized for stationary environments can suffer from prolonged periods of poor performance when the environment changes. To mitigate the adversarial effects of these environmental changes, sensory systems must navigate tradeoffs between the ability to accurately encode incoming stimuli and the ability to rapidly detect and adapt to changes in the distribution of these stimuli. We derive families of codes that balance these objectives, and we demonstrate their close match to experimentally observed neural dynamics during mean and variance adaptation. Our results provide a unifying perspective on adaptation across a range of sensory systems, environments, and sensory tasks. AU - Mlynarski, Wiktor F AU - Hermundstad, Ann M. ID - 9439 JF - Nature Neuroscience SN - 10976256 TI - Efficient and adaptive sensory codes ER - TY - GEN AB - For any given positive integer l, we prove that every plane deformation of a circlewhich preserves the 1/2and 1/ (2l + 1) -rational caustics is trivial i.e. the deformationconsists only of similarities (rescalings and isometries). AU - Kaloshin, Vadim AU - Koudjinan, Edmond ID - 9435 TI - Non co-preservation of the 1/2 and 1/(2l+1)-rational caustics along deformations of circles ER - TY - JOUR AB - Rigorous investigation of synaptic transmission requires analysis of unitary synaptic events by simultaneous recording from presynaptic terminals and postsynaptic target neurons. However, this has been achieved at only a limited number of model synapses, including the squid giant synapse and the mammalian calyx of Held. Cortical presynaptic terminals have been largely inaccessible to direct presynaptic recording, due to their small size. Here, we describe a protocol for improved subcellular patch-clamp recording in rat and mouse brain slices, with the synapse in a largely intact environment. Slice preparation takes ~2 h, recording ~3 h and post hoc morphological analysis 2 d. Single presynaptic hippocampal mossy fiber terminals are stimulated minimally invasively in the bouton-attached configuration, in which the cytoplasmic content remains unperturbed, or in the whole-bouton configuration, in which the cytoplasmic composition can be precisely controlled. Paired pre–postsynaptic recordings can be integrated with biocytin labeling and morphological analysis, allowing correlative investigation of synapse structure and function. Paired recordings can be obtained from mossy fiber terminals in slices from both rats and mice, implying applicability to genetically modified synapses. Paired recordings can also be performed together with axon tract stimulation or optogenetic activation, allowing comparison of unitary and compound synaptic events in the same target cell. Finally, paired recordings can be combined with spontaneous event analysis, permitting collection of miniature events generated at a single identified synapse. In conclusion, the subcellular patch-clamp techniques detailed here should facilitate analysis of biophysics, plasticity and circuit function of cortical synapses in the mammalian central nervous system. AU - Vandael, David H AU - Okamoto, Yuji AU - Borges Merjane, Carolina AU - Vargas Barroso, Victor M AU - Suter, Benjamin AU - Jonas, Peter M ID - 9438 IS - 6 JF - Nature Protocols SN - 17542189 TI - Subcellular patch-clamp techniques for single-bouton stimulation and simultaneous pre- and postsynaptic recording at cortical synapses VL - 16 ER - TY - JOUR AB - Embryo morphogenesis is impacted by dynamic changes in tissue material properties, which have been proposed to occur via processes akin to phase transitions (PTs). Here, we show that rigidity percolation provides a simple and robust theoretical framework to predict material/structural PTs of embryonic tissues from local cell connectivity. By using percolation theory, combined with directly monitoring dynamic changes in tissue rheology and cell contact mechanics, we demonstrate that the zebrafish blastoderm undergoes a genuine rigidity PT, brought about by a small reduction in adhesion-dependent cell connectivity below a critical value. We quantitatively predict and experimentally verify hallmarks of PTs, including power-law exponents and associated discontinuities of macroscopic observables. Finally, we show that this uniform PT depends on blastoderm cells undergoing meta-synchronous divisions causing random and, consequently, uniform changes in cell connectivity. Collectively, our theoretical and experimental findings reveal the structural basis of material PTs in an organismal context. AU - Petridou, Nicoletta AU - Corominas-Murtra, Bernat AU - Heisenberg, Carl-Philipp J AU - Hannezo, Edouard B ID - 9316 IS - 7 JF - Cell SN - 00928674 TI - Rigidity percolation uncovers a structural basis for embryonic tissue phase transitions VL - 184 ER - TY - JOUR AB - The inverse problem of designing component interactions to target emergent structure is fundamental to numerous applications in biotechnology, materials science, and statistical physics. Equally important is the inverse problem of designing emergent kinetics, but this has received considerably less attention. Using recent advances in automatic differentiation, we show how kinetic pathways can be precisely designed by directly differentiating through statistical physics models, namely free energy calculations and molecular dynamics simulations. We consider two systems that are crucial to our understanding of structural self-assembly: bulk crystallization and small nanoclusters. In each case, we are able to assemble precise dynamical features. Using gradient information, we manipulate interactions among constituent particles to tune the rate at which these systems yield specific structures of interest. Moreover, we use this approach to learn nontrivial features about the high-dimensional design space, allowing us to accurately predict when multiple kinetic features can be simultaneously and independently controlled. These results provide a concrete and generalizable foundation for studying nonstructural self-assembly, including kinetic properties as well as other complex emergent properties, in a vast array of systems. AU - Goodrich, Carl Peter AU - King, Ella M. AU - Schoenholz, Samuel S. AU - Cubuk, Ekin D. AU - Brenner, Michael P. ID - 9257 IS - 10 JF - Proceedings of the National Academy of Sciences SN - 0027-8424 TI - Designing self-assembling kinetics with differentiable statistical physics models VL - 118 ER - TY - JOUR AB - Electrodepositing insulating lithium peroxide (Li2O2) is the key process during discharge of aprotic Li–O2 batteries and determines rate, capacity, and reversibility. Current understanding states that the partition between surface adsorbed and dissolved lithium superoxide governs whether Li2O2 grows as a conformal surface film or larger particles, leading to low or high capacities, respectively. However, better understanding governing factors for Li2O2 packing density and capacity requires structural sensitive in situ metrologies. Here, we establish in situ small- and wide-angle X-ray scattering (SAXS/WAXS) as a suitable method to record the Li2O2 phase evolution with atomic to submicrometer resolution during cycling a custom-built in situ Li–O2 cell. Combined with sophisticated data analysis, SAXS allows retrieving rich quantitative structural information from complex multiphase systems. Surprisingly, we find that features are absent that would point at a Li2O2 surface film formed via two consecutive electron transfers, even in poorly solvating electrolytes thought to be prototypical for surface growth. All scattering data can be modeled by stacks of thin Li2O2 platelets potentially forming large toroidal particles. Li2O2 solution growth is further justified by rotating ring-disk electrode measurements and electron microscopy. Higher discharge overpotentials lead to smaller Li2O2 particles, but there is no transition to an electronically passivating, conformal Li2O2 coating. Hence, mass transport of reactive species rather than electronic transport through a Li2O2 film limits the discharge capacity. Provided that species mobilities and carbon surface areas are high, this allows for high discharge capacities even in weakly solvating electrolytes. The currently accepted Li–O2 reaction mechanism ought to be reconsidered. AU - Prehal, Christian AU - Samojlov, Aleksej AU - Nachtnebel, Manfred AU - Lovicar, Ludek AU - Kriechbaum, Manfred AU - Amenitsch, Heinz AU - Freunberger, Stefan Alexander ID - 9301 IS - 14 JF - Proceedings of the National Academy of Sciences KW - small-angle X-ray scattering KW - oxygen reduction KW - disproportionation KW - Li-air battery SN - 0027-8424 TI - In situ small-angle X-ray scattering reveals solution phase discharge of Li–O2 batteries with weakly solvating electrolytes VL - 118 ER - TY - CONF AB - Modeling a crystal as a periodic point set, we present a fingerprint consisting of density functionsthat facilitates the efficient search for new materials and material properties. We prove invarianceunder isometries, continuity, and completeness in the generic case, which are necessary featuresfor the reliable comparison of crystals. The proof of continuity integrates methods from discretegeometry and lattice theory, while the proof of generic completeness combines techniques fromgeometry with analysis. The fingerprint has a fast algorithm based on Brillouin zones and relatedinclusion-exclusion formulae. We have implemented the algorithm and describe its application tocrystal structure prediction. AU - Edelsbrunner, Herbert AU - Heiss, Teresa AU - Kurlin , Vitaliy AU - Smith, Philip AU - Wintraecken, Mathijs ID - 9345 SN - 1868-8969 T2 - 37th International Symposium on Computational Geometry (SoCG 2021) TI - The density fingerprint of a periodic point set VL - 189 ER - TY - CONF AB - Isomanifolds are the generalization of isosurfaces to arbitrary dimension and codimension, i.e. submanifolds of ℝ^d defined as the zero set of some multivariate multivalued smooth function f: ℝ^d → ℝ^{d-n}, where n is the intrinsic dimension of the manifold. A natural way to approximate a smooth isomanifold M is to consider its Piecewise-Linear (PL) approximation M̂ based on a triangulation 𝒯 of the ambient space ℝ^d. In this paper, we describe a simple algorithm to trace isomanifolds from a given starting point. The algorithm works for arbitrary dimensions n and d, and any precision D. Our main result is that, when f (or M) has bounded complexity, the complexity of the algorithm is polynomial in d and δ = 1/D (and unavoidably exponential in n). Since it is known that for δ = Ω (d^{2.5}), M̂ is O(D²)-close and isotopic to M, our algorithm produces a faithful PL-approximation of isomanifolds of bounded complexity in time polynomial in d. Combining this algorithm with dimensionality reduction techniques, the dependency on d in the size of M̂ can be completely removed with high probability. We also show that the algorithm can handle isomanifolds with boundary and, more generally, isostratifolds. The algorithm for isomanifolds with boundary has been implemented and experimental results are reported, showing that it is practical and can handle cases that are far ahead of the state-of-the-art. AU - Boissonnat, Jean-Daniel AU - Kachanovich, Siargey AU - Wintraecken, Mathijs ID - 9441 SN - 1868-8969 T2 - 37th International Symposium on Computational Geometry (SoCG 2021) TI - Tracing isomanifolds in Rd in time polynomial in d using Coxeter-Freudenthal-Kuhn triangulations VL - 189 ER - TY - JOUR AB - Endoplasmic reticulum–plasma membrane contact sites (ER–PM CS) play fundamental roles in all eukaryotic cells. Arabidopsis thaliana mutants lacking the ER–PM protein tether synaptotagmin1 (SYT1) exhibit decreased PM integrity under multiple abiotic stresses, such as freezing, high salt, osmotic stress, and mechanical damage. Here, we show that, together with SYT1, the stress-induced SYT3 is an ER–PM tether that also functions in maintaining PM integrity. The ER–PM CS localization of SYT1 and SYT3 is dependent on PM phosphatidylinositol-4-phosphate and is regulated by abiotic stress. Lipidomic analysis revealed that cold stress increased the accumulation of diacylglycerol at the PM in a syt1/3 double mutant relative to wild-type while the levels of most glycerolipid species remain unchanged. In addition, the SYT1-green fluorescent protein fusion preferentially binds diacylglycerol in vivo with little affinity for polar glycerolipids. Our work uncovers a SYT-dependent mechanism of stress adaptation counteracting the detrimental accumulation of diacylglycerol at the PM produced during episodes of abiotic stress. AU - Ruiz-Lopez, N AU - Pérez-Sancho, J AU - Esteban Del Valle, A AU - Haslam, RP AU - Vanneste, S AU - Catalá, R AU - Perea-Resa, C AU - Van Damme, D AU - García-Hernández, S AU - Albert, A AU - Vallarino, J AU - Lin, J AU - Friml, Jiří AU - Macho, AP AU - Salinas, J AU - Rosado, A AU - Napier, JA AU - Amorim-Silva, V AU - Botella, MA ID - 9443 JF - Plant Cell SN - 1040-4651 TI - Synaptotagmins at the endoplasmic reticulum-plasma membrane contact sites maintain diacylglycerol homeostasis during abiotic stress ER - TY - JOUR AB - Lithium bis(trifluoromethylsulfonyl)imide (LiTFSI) based water-in-salt electrolytes (WiSEs) has recently emerged as a new promising class of electrolytes, primarily owing to their wide electrochemical stability windows (~3–4 V), that by far exceed the thermodynamic stability window of water (1.23 V). Upon increasing the salt concentration towards superconcentration the onset of the oxygen evolution reaction (OER) shifts more significantly than the hydrogen evolution reaction (HER) does. The OER shift has been explained by the accumulation of hydrophobic anions blocking water access to the electrode surface, hence by double layer theory. Here we demonstrate that the processes during oxidation are much more complex, involving OER, carbon and salt decomposition by OER intermediates, and salt precipitation upon local oversaturation. The positive shift in the onset potential of oxidation currents was elucidated by combining several advanced analysis techniques: rotating ring-disk electrode voltammetry, online electrochemical mass spectrometry, and X-ray photoelectron spectroscopy, using both dilute and superconcentrated electrolytes. The results demonstrate the importance of reactive OER intermediates and surface films for electrolyte and electrode stability and motivate further studies of the nature of the electrode. AU - Maffre, Marion AU - Bouchal, Roza AU - Freunberger, Stefan Alexander AU - Lindahl, Niklas AU - Johansson, Patrik AU - Favier, Frédéric AU - Fontaine, Olivier AU - Bélanger, Daniel ID - 9447 IS - 5 JF - Journal of The Electrochemical Society KW - Renewable Energy KW - Sustainability and the Environment KW - Electrochemistry KW - Materials Chemistry KW - Electronic KW - Optical and Magnetic Materials KW - Surfaces KW - Coatings and Films KW - Condensed Matter Physics SN - 0013-4651 TI - Investigation of electrochemical and chemical processes occurring at positive potentials in “Water-in-Salt” electrolytes VL - 168 ER - TY - JOUR AB - Spin qubits are considered to be among the most promising candidates for building a quantum processor. Group IV hole spin qubits have moved into the focus of interest due to the ease of operation and compatibility with Si technology. In addition, Ge offers the option for monolithic superconductor-semiconductor integration. Here we demonstrate a hole spin qubit operating at fields below 10 mT, the critical field of Al, by exploiting the large out-of-plane hole g-factors in planar Ge and by encoding the qubit into the singlet-triplet states of a double quantum dot. We observe electrically controlled X and Z-rotations with tunable frequencies exceeding 100 MHz and dephasing times of 1μs which we extend beyond 15μs with echo techniques. These results show that Ge hole singlet triplet qubits outperform their electronic Si and GaAs based counterparts in speed and coherence, respectively. In addition, they are on par with Ge single spin qubits, but can be operated at much lower fields underlining their potential for on chip integration with superconducting technologies. AU - Jirovec, Daniel AU - Hofmann, Andrea C AU - Ballabio, Andrea AU - Mutter, Philipp M. AU - Tavani, Giulio AU - Botifoll, Marc AU - Crippa, Alessandro AU - Kukucka, Josip AU - Sagi, Oliver AU - Martins, Frederico AU - Saez Mollejo, Jaime AU - Prieto Gonzalez, Ivan AU - Borovkov, Maksim AU - Arbiol, Jordi AU - Chrastina, Daniel AU - Isella, Giovanni AU - Katsaros, Georgios ID - 8909 JF - Nature Materials SN - 1476-1122 TI - A singlet triplet hole spin qubit in planar Ge ER - TY - DATA AB - This .zip File contains the data for figures presented in the main text and supplementary material of "A singlet triplet hole spin qubit in planar Ge" by D. Jirovec, et. al. The measurements were done using Labber Software and the data is stored in the hdf5 file format. The files can be opened using either the Labber Log Browser (https://labber.org/overview/) or Labber Python API (http://labber.org/online-doc/api/LogFile.html). A single file is acquired with QCodes and features the corresponding data type. XRD data are in .dat format and a code to open the data is provided. The code for simulations is as well provided in Python. AU - Jirovec, Daniel ID - 9323 TI - Research data for "A singlet-triplet hole spin qubit planar Ge" ER - TY - JOUR AB - Given a locally finite set 𝑋⊆ℝ𝑑 and an integer 𝑘≥0, we consider the function 𝐰𝑘:Del𝑘(𝑋)→ℝ on the dual of the order-k Voronoi tessellation, whose sublevel sets generalize the notion of alpha shapes from order-1 to order-k (Edelsbrunner et al. in IEEE Trans Inf Theory IT-29:551–559, 1983; Krasnoshchekov and Polishchuk in Inf Process Lett 114:76–83, 2014). While this function is not necessarily generalized discrete Morse, in the sense of Forman (Adv Math 134:90–145, 1998) and Freij (Discrete Math 309:3821–3829, 2009), we prove that it satisfies similar properties so that its increments can be meaningfully classified into critical and non-critical steps. This result extends to the case of weighted points and sheds light on k-fold covers with balls in Euclidean space. AU - Edelsbrunner, Herbert AU - Nikitenko, Anton AU - Osang, Georg F ID - 9465 IS - 1 JF - Journal of Geometry SN - 00472468 TI - A step in the Delaunay mosaic of order k VL - 112 ER - TY - CONF AB - In this work, we apply the dynamical systems analysis of Hanrot et al. (CRYPTO’11) to a class of lattice block reduction algorithms that includes (natural variants of) slide reduction and block-Rankin reduction. This implies sharper bounds on the polynomial running times (in the query model) for these algorithms and opens the door to faster practical variants of slide reduction. We give heuristic arguments showing that such variants can indeed speed up slide reduction significantly in practice. This is confirmed by experimental evidence, which also shows that our variants are competitive with state-of-the-art reduction algorithms. AU - Walter, Michael ID - 9466 SN - 03029743 TI - The convergence of slide-type reductions VL - 12710 ER - TY - CONF AB - We firstly introduce the self-assembled growth of highly uniform Ge quantum wires with controllable position, distance and length on patterned Si (001) substrates. We then present the electrically tunable strong spin-orbit coupling, the first Ge hole spin qubit and ultrafast operation of hole spin qubit in the Ge/Si quantum wires. AU - Gao, Fei AU - Zhang, Jie Yin AU - Wang, Jian Huan AU - Ming, Ming AU - Wang, Tina AU - Zhang, Jian Jun AU - Watzinger, Hannes AU - Kukucka, Josip AU - Vukušić, Lada AU - Katsaros, Georgios AU - Wang, Ke AU - Xu, Gang AU - Li, Hai Ou AU - Guo, Guo Ping ID - 9464 SN - 9781728181769 T2 - 2021 5th IEEE Electron Devices Technology and Manufacturing Conference, EDTM 2021 TI - Ge/Si quantum wires for quantum computing ER - TY - JOUR AB - In this paper, we consider reflected three-operator splitting methods for monotone inclusion problems in real Hilbert spaces. To do this, we first obtain weak convergence analysis and nonasymptotic O(1/n) convergence rate of the reflected Krasnosel'skiĭ-Mann iteration for finding a fixed point of nonexpansive mapping in real Hilbert spaces under some seemingly easy to implement conditions on the iterative parameters. We then apply our results to three-operator splitting for the monotone inclusion problem and consequently obtain the corresponding convergence analysis. Furthermore, we derive reflected primal-dual algorithms for highly structured monotone inclusion problems. Some numerical implementations are drawn from splitting methods to support the theoretical analysis. AU - Iyiola, Olaniyi S. AU - Enyi, Cyril D. AU - Shehu, Yekini ID - 9469 JF - Optimization Methods and Software SN - 10556788 TI - Reflected three-operator splitting method for monotone inclusion problem ER - TY - JOUR AB - A key step in understanding the genetic basis of different evolutionary outcomes (e.g., adaptation) is to determine the roles played by different mutation types (e.g., SNPs, translocations and inversions). To do this we must simultaneously consider different mutation types in an evolutionary framework. Here, we propose a research framework that directly utilizes the most important characteristics of mutations, their population genetic effects, to determine their relative evolutionary significance in a given scenario. We review known population genetic effects of different mutation types and show how these may be connected to different evolutionary outcomes. We provide examples of how to implement this framework and pinpoint areas where more data, theory and synthesis are needed. Linking experimental and theoretical approaches to examine different mutation types simultaneously is a critical step towards understanding their evolutionary significance. AU - Berdan, Emma L. AU - Blanckaert, Alexandre AU - Slotte, Tanja AU - Suh, Alexander AU - Westram, Anja M AU - Fragata, Inês ID - 9470 IS - 12 JF - Molecular Ecology SN - 09621083 TI - Unboxing mutations: Connecting mutation types with evolutionary consequences VL - 30 ER - TY - JOUR AB - Turbulence in the flow of fluid through a pipe can be suppressed by buoyancy forces. As the suppression of turbulence leads to severe heat transfer deterioration, this is an important and undesirable phenomenon in both heating and cooling applications. Vertical flow is often considered, as the axial buoyancy force can help drive the flow. With heating measured by the buoyancy parameter 𝐶, our direct numerical simulations show that shear-driven turbulence may either be completely laminarised or it transitions to a relatively quiescent convection-driven state. Buoyancy forces cause a flattening of the base flow profile, which in isothermal pipe flow has recently been linked to complete suppression of turbulence (Kühnen et al., Nat. Phys., vol. 14, 2018, pp. 386–390), and the flattened laminar base profile has enhanced nonlinear stability (Marensi et al., J. Fluid Mech., vol. 863, 2019, pp. 50–875). In agreement with these findings, the nonlinear lower-branch travelling-wave solution analysed here, which is believed to mediate transition to turbulence in isothermal pipe flow, is shown to be suppressed by buoyancy. A linear instability of the laminar base flow is responsible for the appearance of the relatively quiescent convection driven state for 𝐶≳4 across the range of Reynolds numbers considered. In the suppression of turbulence, however, i.e. in the transition from turbulence, we find clearer association with the analysis of He et al. (J. Fluid Mech., vol. 809, 2016, pp. 31–71) than with the above dynamical systems approach, which describes better the transition to turbulence. The laminarisation criterion He et al. propose, based on an apparent Reynolds number of the flow as measured by its driving pressure gradient, is found to capture the critical 𝐶=𝐶𝑐𝑟(𝑅𝑒) above which the flow will be laminarised or switch to the convection-driven type. Our analysis suggests that it is the weakened rolls, rather than the streaks, which appear to be critical for laminarisation. AU - Marensi, Elena AU - He, Shuisheng AU - Willis, Ashley P. ID - 9467 JF - Journal of Fluid Mechanics SN - 00221120 TI - Suppression of turbulence and travelling waves in a vertical heated pipe VL - 919 ER - TY - JOUR AB - Motivated by the successful application of geometry to proving the Harary--Hill conjecture for “pseudolinear” drawings of $K_n$, we introduce “pseudospherical” drawings of graphs. A spherical drawing of a graph $G$ is a drawing in the unit sphere $\mathbb{S}^2$ in which the vertices of $G$ are represented as points---no three on a great circle---and the edges of $G$ are shortest-arcs in $\mathbb{S}^2$ connecting pairs of vertices. Such a drawing has three properties: (1) every edge $e$ is contained in a simple closed curve $\gamma_e$ such that the only vertices in $\gamma_e$ are the ends of $e$; (2) if $e\ne f$, then $\gamma_e\cap\gamma_f$ has precisely two crossings; and (3) if $e\ne f$, then $e$ intersects $\gamma_f$ at most once, in either a crossing or an end of $e$. We use properties (1)--(3) to define a pseudospherical drawing of $G$. Our main result is that for the complete graph, properties (1)--(3) are equivalent to the same three properties but with “precisely two crossings” in (2) replaced by “at most two crossings.” The proof requires a result in the geometric transversal theory of arrangements of pseudocircles. This is proved using the surprising result that the absence of special arcs (coherent spirals) in an arrangement of simple closed curves characterizes the fact that any two curves in the arrangement have at most two crossings. Our studies provide the necessary ideas for exhibiting a drawing of $K_{10}$ that has no extension to an arrangement of pseudocircles and a drawing of $K_9$ that does extend to an arrangement of pseudocircles, but no such extension has all pairs of pseudocircles crossing twice. AU - Arroyo Guevara, Alan M AU - Richter, R. Bruce AU - Sunohara, Matthew ID - 9468 IS - 2 JF - SIAM Journal on Discrete Mathematics SN - 08954801 TI - Extending drawings of complete graphs into arrangements of pseudocircles VL - 35 ER - TY - JOUR AB - Brain neurons arise from relatively few progenitors generating an enormous diversity of neuronal types. Nonetheless, a cardinal feature of mammalian brain neurogenesis is thought to be that excitatory and inhibitory neurons derive from separate, spatially segregated progenitors. Whether bi-potential progenitors with an intrinsic capacity to generate both lineages exist and how such a fate decision may be regulated are unknown. Using cerebellar development as a model, we discover that individual progenitors can give rise to both inhibitory and excitatory lineages. Gradations of Notch activity determine the fates of the progenitors and their daughters. Daughters with the highest levels of Notch activity retain the progenitor fate, while intermediate levels of Notch activity generate inhibitory neurons, and daughters with very low levels of Notch signaling adopt the excitatory fate. Therefore, Notch-mediated binary cell fate choice is a mechanism for regulating the ratio of excitatory to inhibitory neurons from common progenitors. AU - Zhang, Tingting AU - Liu, Tengyuan AU - Mora, Natalia AU - Guegan, Justine AU - Bertrand, Mathilde AU - Contreras, Ximena AU - Hansen, Andi H AU - Streicher, Carmen AU - Anderle, Marica AU - Danda, Natasha AU - Tiberi, Luca AU - Hippenmeyer, Simon AU - Hassan, Bassem A. ID - 8546 IS - 10 JF - Cell Reports TI - Generation of excitatory and inhibitory neurons from common progenitors via Notch signaling in the cerebellum VL - 35 ER - TY - JOUR AB - We prove that the energy of any eigenvector of a sum of several independent large Wigner matrices is equally distributed among these matrices with very high precision. This shows a particularly strong microcanonical form of the equipartition principle for quantum systems whose components are modelled by Wigner matrices. AU - Bao, Zhigang AU - Erdös, László AU - Schnelli, Kevin ID - 9550 JF - Forum of Mathematics, Sigma TI - Equipartition principle for Wigner matrices VL - 9 ER - TY - JOUR AB - We extend the notion of the minimal volume ellipsoid containing a convex body in Rd to the setting of logarithmically concave functions. We consider a vast class of logarithmically concave functions whose superlevel sets are concentric ellipsoids. For a fixed function from this class, we consider the set of all its “affine” positions. For any log-concave function f on Rd, we consider functions belonging to this set of “affine” positions, and find the one with the minimal integral under the condition that it is pointwise greater than or equal to f. We study the properties of existence and uniqueness of the solution to this problem. For any s∈[0,+∞), we consider the construction dual to the recently defined John s-function (Ivanov and Naszódi in Functional John ellipsoids. arXiv preprint: arXiv:2006.09934, 2020). We prove that such a construction determines a unique function and call it the Löwner s-function of f. We study the Löwner s-functions as s tends to zero and to infinity. Finally, extending the notion of the outer volume ratio, we define the outer integral ratio of a log-concave function and give an asymptotically tight bound on it. AU - Ivanov, Grigory AU - Tsiutsiurupa, Igor ID - 9548 JF - Journal of Geometric Analysis SN - 10506926 TI - Functional Löwner ellipsoids ER -