TY - CONF AB - Pruning large language models (LLMs) from the BERT family has emerged as a standard compression benchmark, and several pruning methods have been proposed for this task. The recent “Sparsity May Cry” (SMC) benchmark put into question the validity of all existing methods, exhibiting a more complex setup where many known pruning methods appear to fail. We revisit the question of accurate BERT-pruning during fine-tuning on downstream datasets, and propose a set of general guidelines for successful pruning, even on the challenging SMC benchmark. First, we perform a cost-vs-benefits analysis of pruning model components, such as the embeddings and the classification head; second, we provide a simple-yet-general way of scaling training, sparsification and learning rate schedules relative to the desired target sparsity; finally, we investigate the importance of proper parametrization for Knowledge Distillation in the context of LLMs. Our simple insights lead to state-of-the-art results, both on classic BERT-pruning benchmarks, as well as on the SMC benchmark, showing that even classic gradual magnitude pruning (GMP) can yield competitive results, with the right approach. AU - Kurtic, Eldar AU - Hoefler, Torsten AU - Alistarh, Dan-Adrian ID - 15011 T2 - Proceedings of Machine Learning Research TI - How to prune your language model: Recovering accuracy on the "Sparsity May Cry" benchmark VL - 234 ER - TY - JOUR AB - Electrostatic correlations between ions dissolved in water are known to impact their transport properties in numerous ways, from conductivity to ion selectivity. The effects of these correlations on the solvent itself remain, however, much less clear. In particular, the addition of salt has been consistently reported to affect the solution’s viscosity, but most modeling attempts fail to reproduce experimental data even at moderate salt concentrations. Here, we use an approach based on stochastic density functional theory, which accurately captures charge fluctuations and correlations. We derive a simple analytical expression for the viscosity correction in concentrated electrolytes, by directly linking it to the liquid’s structure factor. Our prediction compares quantitatively to experimental data at all temperatures and all salt concentrations up to the saturation limit. This universal link between the microscopic structure and viscosity allows us to shed light on the nanoscale dynamics of water and ions under highly concentrated and correlated conditions. AU - Robin, Paul ID - 15024 IS - 6 JF - Journal of Chemical Physics SN - 0021-9606 TI - Correlation-induced viscous dissipation in concentrated electrolytes VL - 160 ER - TY - JOUR AB - We consider quadratic forms of deterministic matrices A evaluated at the random eigenvectors of a large N×N GOE or GUE matrix, or equivalently evaluated at the columns of a Haar-orthogonal or Haar-unitary random matrix. We prove that, as long as the deterministic matrix has rank much smaller than √N, the distributions of the extrema of these quadratic forms are asymptotically the same as if the eigenvectors were independent Gaussians. This reduces the problem to Gaussian computations, which we carry out in several cases to illustrate our result, finding Gumbel or Weibull limiting distributions depending on the signature of A. Our result also naturally applies to the eigenvectors of any invariant ensemble. AU - Erdös, László AU - McKenna, Benjamin ID - 15025 IS - 1B JF - Annals of Applied Probability SN - 1050-5164 TI - Extremal statistics of quadratic forms of GOE/GUE eigenvectors VL - 34 ER - TY - JOUR AB - The GNOM (GN) Guanine nucleotide Exchange Factor for ARF small GTPases (ARF-GEF) is among the best studied trafficking regulators in plants, playing crucial and unique developmental roles in patterning and polarity. The current models place GN at the Golgi apparatus (GA), where it mediates secretion/recycling, and at the plasma membrane (PM) presumably contributing to clathrin-mediated endocytosis (CME). The mechanistic basis of the developmental function of GN, distinct from the other ARF-GEFs including its closest homologue GNOM-LIKE1 (GNL1), remains elusive. Insights from this study largely extend the current notions of GN function. We show that GN, but not GNL1, localizes to the cell periphery at long-lived structures distinct from clathrin-coated pits, while CME and secretion proceed normally in gn knockouts. The functional GN mutant variant GNfewerroots, absent from the GA, suggests that the cell periphery is the major site of GN action responsible for its developmental function. Following inhibition by Brefeldin A, GN, but not GNL1, relocates to the PM likely on exocytic vesicles, suggesting selective molecular associations en route to the cell periphery. A study of GN-GNL1 chimeric ARF-GEFs indicates that all GN domains contribute to the specific GN function in a partially redundant manner. Together, this study offers significant steps toward the elucidation of the mechanism underlying unique cellular and development functions of GNOM. AU - Adamowski, Maciek AU - Matijevic, Ivana AU - Friml, Jiří ID - 15033 JF - eLife KW - General Immunology and Microbiology KW - General Biochemistry KW - Genetics and Molecular Biology KW - General Medicine KW - General Neuroscience SN - 2050-084X TI - Developmental patterning function of GNOM ARF-GEF mediated from the cell periphery VL - 13 ER - TY - JOUR AB - In animals, parasitic infections impose significant fitness costs.1,2,3,4,5,6 Infected animals can alter their feeding behavior to resist infection,7,8,9,10,11,12 but parasites can manipulate animal foraging behavior to their own benefits.13,14,15,16 How nutrition influences host-parasite interactions is not well understood, as studies have mainly focused on the host and less on the parasite.9,12,17,18,19,20,21,22,23 We used the nutritional geometry framework24 to investigate the role of amino acids (AA) and carbohydrates (C) in a host-parasite system: the Argentine ant, Linepithema humile, and the entomopathogenic fungus, Metarhizium brunneum. First, using 18 diets varying in AA:C composition, we established that the fungus performed best on the high-amino-acid diet 1:4. Second, we found that the fungus reached this optimal diet when given various diet pairings, revealing its ability to cope with nutritional challenges. Third, we showed that the optimal fungal diet reduced the lifespan of healthy ants when compared with a high-carbohydrate diet but had no effect on infected ants. Fourth, we revealed that infected ant colonies, given a choice between the optimal fungal diet and a high-carbohydrate diet, chose the optimal fungal diet, whereas healthy colonies avoided it. Lastly, by disentangling fungal infection from host immune response, we demonstrated that infected ants foraged on the optimal fungal diet in response to immune activation and not as a result of parasite manipulation. Therefore, we revealed that infected ant colonies chose a diet that is costly for survival in the long term but beneficial in the short term—a form of collective self-medication. AU - Csata, Eniko AU - Perez-Escudero, Alfonso AU - Laury, Emmanuel AU - Leitner, Hanna AU - Latil, Gerard AU - Heinze, Juerge AU - Simpson, Stephen AU - Cremer, Sylvia AU - Dussutour, Audrey ID - 14479 IS - 4 JF - Current Biology SN - 0960-9822 TI - Fungal infection alters collective nutritional intake of ant colonies VL - 34 ER - TY - JOUR AB - Coupling of orbital motion to a spin degree of freedom gives rise to various transport phenomena in quantum systems that are beyond the standard paradigms of classical physics. Here, we discuss features of spin-orbit dynamics that can be visualized using a classical model with two coupled angular degrees of freedom. Specifically, we demonstrate classical ‘spin’ filtering through our model and show that the interplay between angular degrees of freedom and dissipation can lead to asymmetric ‘spin’ transport. AU - Varshney, Atul AU - Ghazaryan, Areg AU - Volosniev, Artem ID - 15045 JF - Few-Body Systems KW - Atomic and Molecular Physics KW - and Optics SN - 1432-5411 TI - Classical ‘spin’ filtering with two degrees of freedom and dissipation VL - 65 ER - TY - JOUR AB - Atom-based quantum simulators have had many successes in tackling challenging quantum many-body problems, owing to the precise and dynamical control that they provide over the systems' parameters. They are, however, often optimized to address a specific type of problem. Here, we present the design and implementation of a 6Li-based quantum gas platform that provides wide-ranging capabilities and is able to address a variety of quantum many-body problems. Our two-chamber architecture relies on a robust combination of gray molasses and optical transport from a laser-cooling chamber to a glass cell with excellent optical access. There, we first create unitary Fermi superfluids in a three-dimensional axially symmetric harmonic trap and characterize them using in situ thermometry, reaching temperatures below 20 nK. This allows us to enter the deep superfluid regime with samples of extreme diluteness, where the interparticle spacing is sufficiently large for direct single-atom imaging. Second, we generate optical lattice potentials with triangular and honeycomb geometry in which we study diffraction of molecular Bose-Einstein condensates, and show how going beyond the Kapitza-Dirac regime allows us to unambiguously distinguish between the two geometries. With the ability to probe quantum many-body physics in both discrete and continuous space, and its suitability for bulk and single-atom imaging, our setup represents an important step towards achieving a wide-scope quantum simulator. AU - Jin, Shuwei AU - Dai, Kunlun AU - Verstraten, Joris AU - Dixmerias, Maxime AU - Al Hyder, Ragheed AU - Salomon, Christophe AU - Peaudecerf, Bruno AU - de Jongh, Tim AU - Yefsah, Tarik ID - 15053 IS - 1 JF - Physical Review Research KW - General Physics and Astronomy SN - 2643-1564 TI - Multipurpose platform for analog quantum simulation VL - 6 ER - TY - JOUR AB - Embryogenesis results from the coordinated activities of different signaling pathways controlling cell fate specification and morphogenesis. In vertebrate gastrulation, both Nodal and BMP signaling play key roles in germ layer specification and morphogenesis, yet their interplay to coordinate embryo patterning with morphogenesis is still insufficiently understood. Here, we took a reductionist approach using zebrafish embryonic explants to study the coordination of Nodal and BMP signaling for embryo patterning and morphogenesis. We show that Nodal signaling triggers explant elongation by inducing mesendodermal progenitors but also suppressing BMP signaling activity at the site of mesendoderm induction. Consistent with this, ectopic BMP signaling in the mesendoderm blocks cell alignment and oriented mesendoderm intercalations, key processes during explant elongation. Translating these ex vivo observations to the intact embryo showed that, similar to explants, Nodal signaling suppresses the effect of BMP signaling on cell intercalations in the dorsal domain, thus allowing robust embryonic axis elongation. These findings suggest a dual function of Nodal signaling in embryonic axis elongation by both inducing mesendoderm and suppressing BMP effects in the dorsal portion of the mesendoderm. AU - Schauer, Alexandra AU - Pranjic-Ferscha, Kornelija AU - Hauschild, Robert AU - Heisenberg, Carl-Philipp J ID - 15048 IS - 4 JF - Development SN - 0950-1991 TI - Robust axis elongation by Nodal-dependent restriction of BMP signaling VL - 151 ER - TY - COMP AU - Hauschild, Robert ID - 14926 TI - Matlab script for analysis of clone dispersal ER - TY - JOUR AB - Tropical precipitation extremes and their changes with surface warming are investigated using global storm resolving simulations and high-resolution observations. The simulations demonstrate that the mesoscale organization of convection, a process that cannot be physically represented by conventional global climate models, is important for the variations of tropical daily accumulated precipitation extremes. In both the simulations and observations, daily precipitation extremes increase in a more organized state, in association with larger, but less frequent, storms. Repeating the simulations for a warmer climate results in a robust increase in monthly-mean daily precipitation extremes. Higher precipitation percentiles have a greater sensitivity to convective organization, which is predicted to increase with warming. Without changes in organization, the strongest daily precipitation extremes over the tropical oceans increase at a rate close to Clausius-Clapeyron (CC) scaling. Thus, in a future warmer state with increased organization, the strongest daily precipitation extremes over oceans increase at a faster rate than CC scaling. AU - Bao, Jiawei AU - Stevens, Bjorn AU - Kluft, Lukas AU - Muller, Caroline J ID - 15047 IS - 8 JF - Science Advances TI - Intensification of daily tropical precipitation extremes from more organized convection VL - 10 ER - TY - JOUR AB - The superior colliculus (SC) in the mammalian midbrain is essential for multisensory integration and is composed of a rich diversity of excitatory and inhibitory neurons and glia. However, the developmental principles directing the generation of SC cell-type diversity are not understood. Here, we pursued systematic cell lineage tracing in silico and in vivo, preserving full spatial information, using genetic mosaic analysis with double markers (MADM)-based clonal analysis with single-cell sequencing (MADM-CloneSeq). The analysis of clonally related cell lineages revealed that radial glial progenitors (RGPs) in SC are exceptionally multipotent. Individual resident RGPs have the capacity to produce all excitatory and inhibitory SC neuron types, even at the stage of terminal division. While individual clonal units show no pre-defined cellular composition, the establishment of appropriate relative proportions of distinct neuronal types occurs in a PTEN-dependent manner. Collectively, our findings provide an inaugural framework at the single-RGP/-cell level of the mammalian SC ontogeny. AU - Cheung, Giselle T AU - Pauler, Florian AU - Koppensteiner, Peter AU - Krausgruber, Thomas AU - Streicher, Carmen AU - Schrammel, Martin AU - Özgen, Natalie Y AU - Ivec, Alexis AU - Bock, Christoph AU - Shigemoto, Ryuichi AU - Hippenmeyer, Simon ID - 12875 IS - 2 JF - Neuron SN - 0896-6273 TI - Multipotent progenitors instruct ontogeny of the superior colliculus VL - 112 ER - TY - JOUR AB - Poxviruses are among the largest double-stranded DNA viruses, with members such as variola virus, monkeypox virus and the vaccination strain vaccinia virus (VACV). Knowledge about the structural proteins that form the viral core has remained sparse. While major core proteins have been annotated via indirect experimental evidence, their structures have remained elusive and they could not be assigned to individual core features. Hence, which proteins constitute which layers of the core, such as the palisade layer and the inner core wall, has remained enigmatic. Here we show, using a multi-modal cryo-electron microscopy (cryo-EM) approach in combination with AlphaFold molecular modeling, that trimers formed by the cleavage product of VACV protein A10 are the key component of the palisade layer. This allows us to place previously obtained descriptions of protein interactions within the core wall into perspective and to provide a detailed model of poxvirus core architecture. Importantly, we show that interactions within A10 trimers are likely generalizable over members of orthopox- and parapoxviruses. AU - Datler, Julia AU - Hansen, Jesse AU - Thader, Andreas AU - Schlögl, Alois AU - Bauer, Lukas W AU - Hodirnau, Victor-Valentin AU - Schur, Florian KM ID - 14979 JF - Nature Structural & Molecular Biology KW - Molecular Biology KW - Structural Biology SN - 1545-9993 TI - Multi-modal cryo-EM reveals trimers of protein A10 to form the palisade layer in poxvirus cores ER - TY - JOUR AB - Contraction and flow of the actin cell cortex have emerged as a common principle by which cells reorganize their cytoplasm and take shape. However, how these cortical flows interact with adjacent cytoplasmic components, changing their form and localization, and how this affects cytoplasmic organization and cell shape remains unclear. Here we show that in ascidian oocytes, the cooperative activities of cortical actomyosin flows and deformation of the adjacent mitochondria-rich myoplasm drive oocyte cytoplasmic reorganization and shape changes following fertilization. We show that vegetal-directed cortical actomyosin flows, established upon oocyte fertilization, lead to both the accumulation of cortical actin at the vegetal pole of the zygote and compression and local buckling of the adjacent elastic solid-like myoplasm layer due to friction forces generated at their interface. Once cortical flows have ceased, the multiple myoplasm buckles resolve into one larger buckle, which again drives the formation of the contraction pole—a protuberance of the zygote’s vegetal pole where maternal mRNAs accumulate. Thus, our findings reveal a mechanism where cortical actomyosin network flows determine cytoplasmic reorganization and cell shape by deforming adjacent cytoplasmic components through friction forces. AU - Caballero Mancebo, Silvia AU - Shinde, Rushikesh AU - Bolger-Munro, Madison AU - Peruzzo, Matilda AU - Szep, Gregory AU - Steccari, Irene AU - Labrousse Arias, David AU - Zheden, Vanessa AU - Merrin, Jack AU - Callan-Jones, Andrew AU - Voituriez, Raphaël AU - Heisenberg, Carl-Philipp J ID - 14846 JF - Nature Physics SN - 1745-2473 TI - Friction forces determine cytoplasmic reorganization and shape changes of ascidian oocytes upon fertilization ER - TY - THES AB - This thesis consists of four distinct pieces of work within theoretical biology, with two themes in common: the concept of optimization in biological systems, and the use of information-theoretic tools to quantify biological stochasticity and statistical uncertainty. Chapter 2 develops a statistical framework for studying biological systems which we believe to be optimized for a particular utility function, such as retinal neurons conveying information about visual stimuli. We formalize such beliefs as maximum-entropy Bayesian priors, constrained by the expected utility. We explore how such priors aid inference of system parameters with limited data and enable optimality hypothesis testing: is the utility higher than by chance? Chapter 3 examines the ultimate biological optimization process: evolution by natural selection. As some individuals survive and reproduce more successfully than others, populations evolve towards fitter genotypes and phenotypes. We formalize this as accumulation of genetic information, and use population genetics theory to study how much such information can be accumulated per generation and maintained in the face of random mutation and genetic drift. We identify the population size and fitness variance as the key quantities that control information accumulation and maintenance. Chapter 4 reuses the concept of genetic information from Chapter 3, but from a different perspective: we ask how much genetic information organisms actually need, in particular in the context of gene regulation. For example, how much information is needed to bind transcription factors at correct locations within the genome? Population genetics provides us with a refined answer: with an increasing population size, populations achieve higher fitness by maintaining more genetic information. Moreover, regulatory parameters experience selection pressure to optimize the fitness-information trade-off, i.e. minimize the information needed for a given fitness. This provides an evolutionary derivation of the optimization priors introduced in Chapter 2. Chapter 5 proves an upper bound on mutual information between a signal and a communication channel output (such as neural activity). Mutual information is an important utility measure for biological systems, but its practical use can be difficult due to the large dimensionality of many biological channels. Sometimes, a lower bound on mutual information is computed by replacing the high-dimensional channel outputs with decodes (signal estimates). Our result provides a corresponding upper bound, provided that the decodes are the maximum posterior estimates of the signal. AU - Hledik, Michal ID - 15020 KW - Theoretical biology KW - Optimality KW - Evolution KW - Information SN - 2663 - 337X TI - Genetic information and biological optimization ER - TY - GEN AB - Eva Benkova received a PhD in Biophysics at the Institute of Biophysics of the Czech Academy of Sciences in 1998. After working as a postdoc at the Max Planck Institute in Cologne and the Center for Plant Molecular Biology (ZMBP) in Tübingen, she became a group leader at the Plant Systems Biology Department of the Vlaams Instituut voor Biotechnologie (VIB) in Gent. In 2012, she transitioned to an Assistant Professor position at the Institute of Science and Technology Austria (ISTA) where she was later promoted to Professor. Since 2021, she has served as the Dean of the ISTA Graduate School. As a plant developmental biologist, she focuses on unraveling the molecular mechanisms and principles that underlie hormonal interactions in plants. In her current work, she explores the intricate connections between hormones and regulatory pathways that mediate the perception of environmental stimuli, including abiotic stress and nitrate availability. AU - Benková, Eva ID - 14842 IS - 1 T2 - Current Biology TI - Eva Benkova VL - 34 ER - TY - JOUR AB - GABAB receptor (GBR) activation inhibits neurotransmitter release in axon terminals in the brain, except in medial habenula (MHb) terminals, which show robust potentiation. However, mechanisms underlying this enigmatic potentiation remain elusive. Here, we report that GBR activation on MHb terminals induces an activity-dependent transition from a facilitating, tonic to a depressing, phasic neurotransmitter release mode. This transition is accompanied by a 4.1-fold increase in readily releasable vesicle pool (RRP) size and a 3.5-fold increase of docked synaptic vesicles (SVs) at the presynaptic active zone (AZ). Strikingly, the depressing phasic release exhibits looser coupling distance than the tonic release. Furthermore, the tonic and phasic release are selectively affected by deletion of synaptoporin (SPO) and Ca 2+ -dependent activator protein for secretion 2 (CAPS2), respectively. SPO modulates augmentation, the short-term plasticity associated with tonic release, and CAPS2 retains the increased RRP for initial responses in phasic response trains. The cytosolic protein CAPS2 showed a SV-associated distribution similar to the vesicular transmembrane protein SPO, and they were colocalized in the same terminals. We developed the “Flash and Freeze-fracture” method, and revealed the release of SPO-associated vesicles in both tonic and phasic modes and activity-dependent recruitment of CAPS2 to the AZ during phasic release, which lasted several minutes. Overall, these results indicate that GBR activation translocates CAPS2 to the AZ along with the fusion of CAPS2-associated SVs, contributing to persistency of the RRP increase. Thus, we identified structural and molecular mechanisms underlying tonic and phasic neurotransmitter release and their transition by GBR activation in MHb terminals. AU - Koppensteiner, Peter AU - Bhandari, Pradeep AU - Önal, Hüseyin C AU - Borges Merjane, Carolina AU - Le Monnier, Elodie AU - Roy, Utsa AU - Nakamura, Yukihiro AU - Sadakata, Tetsushi AU - Sanbo, Makoto AU - Hirabayashi, Masumi AU - Rhee, JeongSeop AU - Brose, Nils AU - Jonas, Peter M AU - Shigemoto, Ryuichi ID - 15084 IS - 8 JF - Proceedings of the National Academy of Sciences SN - 0027-8424 TI - GABAB receptors induce phasic release from medial habenula terminals through activity-dependent recruitment of release-ready vesicles VL - 121 ER - TY - JOUR AB - Direct reciprocity is a powerful mechanism for cooperation in social dilemmas. The very logic of reciprocity, however, seems to require that individuals are symmetric, and that everyone has the same means to influence each others’ payoffs. Yet in many applications, individuals are asymmetric. Herein, we study the effect of asymmetry in linear public good games. Individuals may differ in their endowments (their ability to contribute to a public good) and in their productivities (how effective their contributions are). Given the individuals’ productivities, we ask which allocation of endowments is optimal for cooperation. To this end, we consider two notions of optimality. The first notion focuses on the resilience of cooperation. The respective endowment distribution ensures that full cooperation is feasible even under the most adverse conditions. The second notion focuses on efficiency. The corresponding endowment distribution maximizes group welfare. Using analytical methods, we fully characterize these two endowment distributions. This analysis reveals that both optimality notions favor some endowment inequality: More productive players ought to get higher endowments. Yet the two notions disagree on how unequal endowments are supposed to be. A focus on resilience results in less inequality. With additional simulations, we show that the optimal endowment allocation needs to account for both the resilience and the efficiency of cooperation. AU - Hübner, Valentin AU - Staab, Manuel AU - Hilbe, Christian AU - Chatterjee, Krishnendu AU - Kleshnina, Maria ID - 15083 IS - 10 JF - Proceedings of the National Academy of Sciences SN - 0027-8424 TI - Efficiency and resilience of cooperation in asymmetric social dilemmas VL - 121 ER - TY - GEN AB - in the research article "Efficiency and resilience of cooperation in asymmetric social dilemmas" (by Valentin Hübner, Manuel Staab, Christian Hilbe, Krishnendu Chatterjee, and Maria Kleshnina). We used different implementations for the case of two and three players, both described below. AU - Hübner, Valentin AU - Kleshnina, Maria ID - 15108 TI - Computer code for "Efficiency and resilience of cooperation in asymmetric social dilemmas" ER - TY - JOUR AB - Global storm-resolving models (GSRMs) use strongly refined horizontal grids compared with the climate models typically used in the Coupled Model Intercomparison Project (CMIP) but employ comparable vertical grid spacings. Here, we study how changes in the vertical grid spacing and adjustments to the integration time step affect the basic climate quantities simulated by the ICON-Sapphire atmospheric GSRM. Simulations are performed over a 45 d period for five different vertical grids with between 55 and 540 vertical layers and maximum tropospheric vertical grid spacings of between 800 and 50 m, respectively. The effects of changes in the vertical grid spacing are compared with the effects of reducing the horizontal grid spacing from 5 to 2.5 km. For most of the quantities considered, halving the vertical grid spacing has a smaller effect than halving the horizontal grid spacing, but it is not negligible. Each halving of the vertical grid spacing, along with the necessary reductions in time step length, increases cloud liquid water by about 7 %, compared with an approximate 16 % decrease for halving the horizontal grid spacing. The effect is due to both the vertical grid refinement and the time step reduction. There is no tendency toward convergence in the range of grid spacings tested here. The cloud ice amount also increases with a refinement in the vertical grid, but it is hardly affected by the time step length and does show a tendency to converge. While the effect on shortwave radiation is globally dominated by the altered reflection due to the change in the cloud liquid water content, the effect on longwave radiation is more difficult to interpret because changes in the cloud ice concentration and cloud fraction are anticorrelated in some regions. The simulations show that using a maximum tropospheric vertical grid spacing larger than 400 m would increase the truncation error strongly. Computing time investments in a further vertical grid refinement can affect the truncation errors of GSRMs similarly to comparable investments in horizontal refinement, because halving the vertical grid spacing is generally cheaper than halving the horizontal grid spacing. However, convergence of boundary layer cloud properties cannot be expected, even for the smallest maximum tropospheric grid spacing of 50 m used in this study. AU - Schmidt, Hauke AU - Rast, Sebastian AU - Bao, Jiawei AU - Cassim, Amrit AU - Fang, Shih Wei AU - Jimenez-De La Cuesta, Diego AU - Keil, Paul AU - Kluft, Lukas AU - Kroll, Clarissa AU - Lang, Theresa AU - Niemeier, Ulrike AU - Schneidereit, Andrea AU - Williams, Andrew I.L. AU - Stevens, Bjorn ID - 15097 IS - 4 JF - Geoscientific Model Development SN - 1991-959X TI - Effects of vertical grid spacing on the climate simulated in the ICON-Sapphire global storm-resolving model VL - 17 ER - TY - JOUR AB - In this note, we prove a formula for the cancellation exponent kv,n between division polynomials ψn and ϕn associated with a sequence {nP}n∈N of points on an elliptic curve E defined over a discrete valuation field K. The formula greatly generalizes the previously known special cases and treats also the case of non-standard Kodaira types for non-perfect residue fields. AU - Naskręcki, Bartosz AU - Verzobio, Matteo ID - 12311 JF - Proceedings of the Royal Society of Edinburgh Section A: Mathematics KW - Elliptic curves KW - Néron models KW - division polynomials KW - height functions KW - discrete valuation rings SN - 0308-2105 TI - Common valuations of division polynomials ER -