@inproceedings{17126, abstract = {Functional encryption (FE) is a primitive where the holder of a master secret key can control which functions a user can evaluate on encrypted data. It is a powerful primitive that even implies indistinguishability obfuscation (iO), given sufficiently compact ciphertexts (Ananth-Jain, CRYPTO’15 and Bitansky-Vaikuntanathan, FOCS’15). However, despite being extensively studied, there are FE schemes, such as function-hiding inner-product FE (Bishop-Jain-Kowalczyk, AC’15, Abdalla-Catalano-Fiore-Gay-Ursu, CRYPTO’18) and compact quadratic FE (Baltico-Catalano-Fiore-Gay, Lin, CRYPTO’17), that can be only realized using pairings. This raises the question if there are some mathematical barriers that hinder us from realizing these FE schemes from other assumptions. In this paper, we study the difficulty of constructing lattice-based compact FE. We generalize the impossibility results of Ünal (EC’20) for lattice-based function-hiding FE, and extend it to the case of compact FE. Concretely, we prove lower bounds for lattice-based compact FE schemes which meet some (natural) algebraic restrictions at encryption and decryption, and have ciphertexts of linear size and secret keys of minimal degree. We see our results as important indications of why it is hard to construct lattice-based FE schemes for new functionalities, and which mathematical barriers have to be overcome.}, author = {Tairi, Erkan and Ünal, Akin}, booktitle = {Advances in Cryptology – EUROCRYPT 2024}, isbn = {9783031587221}, issn = {1611-3349}, location = {Zurich, Switzerland}, pages = {249--279}, publisher = {Springer Nature}, title = {{Lower bounds for lattice-based compact functional encryption}}, doi = {10.1007/978-3-031-58723-8_9}, volume = {14652}, year = {2024}, } @article{17127, abstract = {Let P(x)∈Z[x] be a polynomial with at least two distinct complex roots. We prove that the number of solutions (x1,…,xk,y1,…,yk)∈[N]2k to the equation ∏1≤i≤kP(xi)=∏1≤j≤kP(yj)≠0 (for any k≥1 ) is asymptotically k!Nk as N→+∞. This solves a question first proposed and studied by Najnudel. The result can also be interpreted as saying that all even moments of random partial sums 1N√∑n≤Nf(P(n)) match standard complex Gaussian moments as N→+∞ , where f is the Steinhaus random multiplicative function.}, author = {Wang, Victor and Xu, Max Wenqiang}, issn = {1469-2120}, journal = {Bulletin of the London Mathematical Society}, number = {8}, pages = {2718--2726}, publisher = {London Mathematical Society}, title = {{Paucity phenomena for polynomial products}}, doi = {10.1112/blms.13095}, volume = {56}, year = {2024}, } @article{17128, abstract = {The onset of turbulence in pipe flow has defied detailed understanding ever since the first observations of the spatially heterogeneous nature of the transition. Recent theoretical studies and experiments in simpler, shear-driven flows suggest that the onset of turbulence is a directed-percolation non-equilibrium phase transition, but whether these findings are generic and also apply to open or pressure-driven flows is unknown. In pipe flow, the extremely long time scales near the transition make direct observations of critical behaviour virtually impossible. Here we find a technical solution to that limitation and show that the universality class of the transition is directed percolation, from which a jammed phase of puffs emerges above the critical point. Our method is to experimentally characterize all pairwise interactions between localized patches of turbulence puffs and use these interactions as input for renormalization group and computer simulations of minimal models that extrapolate to long length and time scales. The strong interactions in the jamming regime enable us to explicitly measure the turbulent fraction and confirm model predictions. Our work shows that directed-percolation scaling applies beyond simple closed shear flows and underscores how statistical mechanics can lead to profound, quantitative and predictive insights on turbulent flows and their phases.}, author = {Lemoult, Grégoire M and Vasudevan, Mukund and Shih, Hong Yan and Linga, Gaute and Mathiesen, Joachim and Goldenfeld, Nigel and Hof, Björn}, issn = {1745-2481}, journal = {Nature Physics}, pages = {1339--1345}, publisher = {Springer Nature}, title = {{Directed percolation and puff jamming near the transition to pipe turbulence}}, doi = {10.1038/s41567-024-02513-0}, volume = {20}, year = {2024}, } @article{17141, abstract = {The TIR1/AFB–Aux/IAA–ARF canonical auxin signaling pathway is widely accepted to (de)active transcriptional regulation, thus controlling auxin-associated developmental processes. However, the theme of a rapid auxin response has emerged since the 2018 Auxins and Cytokinin in Plant Development conference. To date, a few signaling components have been identified to mediate both slow and rapid auxin responses, which unveils the complexity of auxin signaling.}, author = {Zhang, Zilin and Chen, Huihuang and Peng, Shuaiying and Han, Huibin}, issn = {0022-0957}, journal = {Journal of Experimental Botany}, number = {18}, publisher = {Oxford University Press}, title = {{Slow and rapid auxin responses in Arabidopsis}}, doi = {10.1093/jxb/erae246}, volume = {75}, year = {2024}, } @article{17142, abstract = {Despite the diverse genetic origins of autism spectrum disorders (ASDs), affected individuals share strikingly similar and correlated behavioural traits that include perceptual and sensory processing challenges. Notably, the severity of these sensory symptoms is often predictive of the expression of other autistic traits. However, the origin of these perceptual deficits remains largely elusive. Here, we show a recurrent impairment in visual threat perception that is similarly impaired in 3 independent mouse models of ASD with different molecular aetiologies. Interestingly, this deficit is associated with reduced avoidance of threatening environments—a nonperceptual trait. Focusing on a common cause of ASDs, the Setd5 gene mutation, we define the molecular mechanism. We show that the perceptual impairment is caused by a potassium channel (Kv1)-mediated hypoexcitability in a subcortical node essential for the initiation of escape responses, the dorsal periaqueductal grey (dPAG). Targeted pharmacological Kv1 blockade rescued both perceptual and place avoidance deficits, causally linking seemingly unrelated trait deficits to the dPAG. Furthermore, we show that different molecular mechanisms converge on similar behavioural phenotypes by demonstrating that the autism models Cul3 and Ptchd1, despite having similar behavioural phenotypes, differ in their functional and molecular alteration. Our findings reveal a link between rapid perception controlled by subcortical pathways and appropriate learned interactions with the environment and define a nondevelopmental source of such deficits in ASD.}, author = {Burnett, Laura and Koppensteiner, Peter and Symonova, Olga and Masson, Tomas and Vega Zuniga, Tomas A and Contreras, Ximena and Rülicke, Thomas and Shigemoto, Ryuichi and Novarino, Gaia and Jösch, Maximilian A}, issn = {1545-7885}, journal = {PLoS Biology}, publisher = {Public Library of Science}, title = {{Shared behavioural impairments in visual perception and place avoidance across different autism models are driven by periaqueductal grey hypoexcitability in Setd5 haploinsufficient mice}}, doi = {10.1371/journal.pbio.3002668}, volume = {22}, year = {2024}, } @inproceedings{17144, abstract = {We prove that the medial axis of closed sets is Hausdorff stable in the following sense: Let 𝒮 ⊆ ℝ^d be a fixed closed set that contains a bounding sphere. That is, the bounding sphere is part of the set 𝒮. Consider the space of C^{1,1} diffeomorphisms of ℝ^d to itself, which keep the bounding sphere invariant. The map from this space of diffeomorphisms (endowed with a Banach norm) to the space of closed subsets of ℝ^d (endowed with the Hausdorff distance), mapping a diffeomorphism F to the closure of the medial axis of F(𝒮), is Lipschitz. This extends a previous stability result of Chazal and Soufflet on the stability of the medial axis of C² manifolds under C² ambient diffeomorphisms.}, author = {Kourimska, Hana and Lieutier, André and Wintraecken, Mathijs}, booktitle = {40th International Symposium on Computational Geometry}, isbn = {9783959773164}, issn = {1868-8969}, location = {Athens, Greece}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{The medial axis of any closed bounded set Is Lipschitz stable with respect to the Hausdorff distance Under ambient diffeomorphisms}}, doi = {10.4230/LIPIcs.SoCG.2024.69}, volume = {293}, year = {2024}, } @inproceedings{17145, abstract = {Grid peeling is the process of repeatedly removing the convex hull vertices of the grid points that lie inside a given convex curve. It has been conjectured that, for a more and more refined grid, grid peeling converges to a continuous process, the affine curve-shortening flow, which deforms the curve based on the curvature. We prove this conjecture for one class of curves, parabolas with a vertical axis, and we determine the value of the constant factor in the formula that relates the two processes.}, author = {Rote, Günter and Rüber, Moritz and Saghafian, Morteza}, booktitle = {40th International Symposium on Computational Geometry}, isbn = {9783959773164}, issn = {1868-8969}, location = {Athens, Greece}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Grid peeling of parabolas}}, doi = {10.4230/LIPIcs.SoCG.2024.76}, volume = {293}, year = {2024}, } @inproceedings{17146, abstract = {The Upper Bound Theorem for convex polytopes implies that the p-th Betti number of the Čech complex of any set of N points in ℝ^d and any radius satisfies β_p = O(N^m), with m = min{p+1, ⌈d/2⌉}. We construct sets in even and odd dimensions, which prove that this upper bound is asymptotically tight. For example, we describe a set of N = 2(n+1) points in ℝ³ and two radii such that the first Betti number of the Čech complex at one radius is (n+1)² - 1, and the second Betti number of the Čech complex at the other radius is n². In particular, there is an arrangement of n contruent balls in ℝ³ that enclose a quadratic number of voids, which answers a long-standing open question in computational geometry.}, author = {Edelsbrunner, Herbert and Pach, János}, booktitle = {40th International Symposium on Computational Geometry}, isbn = {9783959773164}, issn = {1868-8969}, location = {Athens, Greece}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Maximum Betti numbers of Čech complexes}}, doi = {10.4230/LIPIcs.SoCG.2024.53}, volume = {293}, year = {2024}, } @inproceedings{17147, abstract = {Efficient utilization of large-scale biobank data is crucial for inferring the genetic basis of disease and predicting health outcomes from the DNA. Yet we lack efficient, accurate methods that scale to data where electronic health records are linked to whole genome sequence information. To address this issue, our paper develops a new algorithmic paradigm based on Approximate Message Passing (AMP), which is specifically tailored for genomic prediction and association testing. Our method yields comparable out-of-sample prediction accuracy to the state of the art on UK Biobank traits, whilst dramatically improving computational complexity, with a 8x-speed up in the run time. In addition, AMP theory provides a joint association testing framework, which outperforms the currently used REGENIE method, in roughly a third of the compute time. This first, truly large-scale application of the AMP framework lays the foundations for a far wider range of statistical analyses for hundreds of millions of variables measured on millions of people.}, author = {Depope, Al and Mondelli, Marco and Robinson, Matthew Richard}, booktitle = {2024 IEEE International Conference on Acoustics, Speech, and Signal Processing}, isbn = {9798350344851}, issn = {1520-6149}, location = {Seoul, Korea}, pages = {13151--13155}, publisher = {IEEE}, title = {{Inference of genetic effects via approximate message passing}}, doi = {10.1109/ICASSP48485.2024.10447198}, year = {2024}, } @article{17161, abstract = {Dynamic processes in molecules can occur on a wide range of timescales, and it is important to understand which timescales of motion contribute to different parameters used in dynamics measurements. For spin relaxation, this can easily be understood from the sampling frequencies of the spectral-density function by different relaxation-rate constants. In addition to data from relaxation measurements, determining dynamically averaged anisotropic interactions in magic-angle spinning (MAS) solid-state NMR allows for better quantification of the amplitude of molecular motion. For partially averaged anisotropic interactions, the relevant timescales of motion are not so clearly defined. Whether the averaging depends on the experimental methods (e.g., pulse sequences) or conditions (e.g., MAS frequency, magnitude of anisotropic interaction, radio-frequency field amplitudes) is not fully understood. To investigate these questions, we performed numerical simulations of dynamic systems based on the stochastic Liouville equation using several experiments for recoupling the dipolar coupling, chemical-shift anisotropy or quadrupolar coupling. As described in the literature, the transition between slow motion, where parameters characterizing the anisotropic interaction are not averaged, and fast motion, where the tensors are averaged leading to a scaled anisotropic quantity, occurs over a window of motional rate constants that depends mainly on the strength of the interaction. This transition region can span 2 orders of magnitude in exchange-rate constants (typically in the microsecond range) but depends only marginally on the employed recoupling scheme or sample spinning frequency. The transition region often coincides with a fast relaxation of coherences, making precise quantitative measurements difficult. Residual couplings in off-magic-angle experiments, however, average over longer timescales of motion. While in principle one may gain information on the timescales of motion from the transition area, extracting such information is hampered by low signal-to-noise ratio in experimental spectra due to fast relaxation that occurs in the same region.}, author = {Aebischer, Kathrin and Becker, Lea Marie and Schanda, Paul and Ernst, Matthias}, issn = {2699-0016}, journal = {Magnetic Resonance}, number = {1}, pages = {69--86}, publisher = {Copernicus Publications}, title = {{Evaluating the motional timescales contributing to averaged anisotropic interactions in MAS solid-state NMR}}, doi = {10.5194/mr-5-69-2024}, volume = {5}, year = {2024}, } @article{17162, abstract = {Cost analysis, also known as resource usage analysis, is the task of finding bounds on the total cost of a program and is a well-studied problem in static analysis. In this work, we consider two classical quantitative problems in cost analysis for probabilistic programs. The first problem is to find a bound on the expected total cost of the program. This is a natural measure for the resource usage of the program and can also be directly applied to average-case runtime analysis. The second problem asks for a tail bound, i.e. ‍given a threshold t the goal is to find a probability bound p such that ℙ[total cost ≥ t] ≤ p. Intuitively, given a threshold t on the resource, the problem is to find the likelihood that the total cost exceeds this threshold. First, for expectation bounds, a major obstacle in previous works on cost analysis is that they can handle only non-negative costs or bounded variable updates. In contrast, we provide a new variant of the standard notion of cost martingales, that allows us to find expectation bounds for a class of programs with general positive or negative costs and no restriction on the variable updates. More specifically, our approach is applicable as long as there is a lower bound on the total cost incurred along every path. Second, for tail bounds, all previous methods are limited to programs in which the expected total cost is finite. In contrast, we present a novel approach, based on a combination of our martingale-based method for expectation bounds with a quantitative safety analysis, to obtain a solution to the tail bound problem that is applicable even to programs with infinite expected cost. Specifically, this allows us to obtain runtime tail bounds for programs that do not terminate almost-surely. In summary, we provide a novel combination of martingale-based cost analysis and quantitative safety analysis that is able to find expectation and tail cost bounds for probabilistic programs, without the restrictions of non-negative costs, bounded updates, or finiteness of the expected total cost. Finally, we provide experimental results showcasing that our approach can solve instances that were beyond the reach of previous methods.}, author = {Chatterjee, Krishnendu and Goharshady, Amir Kafshdar and Meggendorfer, Tobias and Zikelic, Dorde}, issn = {2475-1421}, journal = {Proceedings of the ACM on Programming Languages}, number = {OOPSLA1}, publisher = {Association for Computing Machinery}, title = {{Quantitative bounds on resource usage of probabilistic programs}}, doi = {10.1145/3649824}, volume = {8}, year = {2024}, } @inproceedings{17170, abstract = {In this article we extend and strengthen the seminal work by Niyogi, Smale, and Weinberger on the learning of the homotopy type from a sample of an underlying space. In their work, Niyogi, Smale, and Weinberger studied samples of C² manifolds with positive reach embedded in ℝ^d. We extend their results in the following ways: - As the ambient space we consider both ℝ^d and Riemannian manifolds with lower bounded sectional curvature. - In both types of ambient spaces, we study sets of positive reach - a significantly more general setting than C² manifolds - as well as general manifolds of positive reach. - The sample P of a set (or a manifold) 𝒮 of positive reach may be noisy. We work with two one-sided Hausdorff distances - ε and δ - between P and 𝒮. We provide tight bounds in terms of ε and δ, that guarantee that there exists a parameter r such that the union of balls of radius r centred at the sample P deformation-retracts to 𝒮. We exhibit their tightness by an explicit construction. We carefully distinguish the roles of δ and ε. This is not only essential to achieve tight bounds, but also sensible in practical situations, since it allows one to adapt the bound according to sample density and the amount of noise present in the sample separately.}, author = {Attali, Dominique and Kourimska, Hana and Fillmore, Christopher D and Ghosh, Ishika and Lieutier, André and Stephenson, Elizabeth R and Wintraecken, Mathijs}, booktitle = {40th International Symposium on Computational Geometry}, isbn = {9783959773164}, issn = {1868-8969}, location = {Athens, Greece}, pages = {11:1--11:19}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Tight bounds for the learning of homotopy à la Niyogi, Smale, and Weinberger for subsets of euclidean spaces and of Riemannian manifolds}}, doi = {10.4230/LIPIcs.SoCG.2024.11}, volume = {293}, year = {2024}, } @article{17188, abstract = {In a delegation problem, a principal P with commitment power tries to pick one out of 𝑛 options. Each option is drawn independently from a known distribution. Instead of inspecting the options herself, P delegates the information acquisition to a rational and self-interested agent A. After inspection, A proposes one of the options, and P can accept or reject. Delegation is a classic setting in economic information design with many prominent applications, but the computational problems are only poorly understood. In this paper, we study a natural online variant of delegation, in which the agent searches through the options in an online fashion. For each option, he has to irrevocably decide if he wants to propose the current option or discard it, before seeing information on the next option(s). How can we design algorithms for P that approximate the utility of her best option in hindsight? We show that in general P can obtain a Θ(1∕𝑛)-approximation and extend this result to ratios of Θ(𝑘∕𝑛) in case (1) A has a lookahead of 𝑘 rounds, or (2) A can propose up to 𝑘 different options. We provide fine-grained bounds independent of 𝑛 based on three parameters. If the ratio of maximum and minimum utility for A is bounded by a factor 𝛼, we obtain an Ω(loglog 𝛼∕ log 𝛼)- approximation algorithm, and we show that this is best possible. Additionally, if P cannot distinguish options with the same value for herself, we show that ratios polynomial in 1∕𝛼 cannot be avoided. If there are at most 𝛽 different utility values for A, we show a Θ(1∕𝛽)-approximation. If the utilities of P and A for each option are related by a factor 𝛾, we obtain an Ω(1∕ log 𝛾)- approximation, where 𝑂(log log 𝛾∕ log 𝛾) is best possible.}, author = {Braun, Pirmin and Hahn, Niklas and Hoefer, Martin and Schecker, Conrad}, issn = {0004-3702}, journal = {Artificial Intelligence}, publisher = {Elsevier}, title = {{Delegated online search}}, doi = {10.1016/j.artint.2024.104171}, volume = {334}, year = {2024}, } @article{17189, abstract = {Supergranules, which are solar flow features with a lateral scale of 30,000–40,000 km and a lifetime of ~24 h, form a prominent component of the Sun’s convective spectrum. However, their internal flows, which can be probed only by helioseismology, are not well understood. We analyse dopplergrams recorded by the Solar Dynamics Observatory satellite to identify and characterize ~23,000 supergranules. We find that the vertical flows peak at a depth of ~10,000 km, and remain invariant over the full range of lateral supergranular scales, contrary to numerical predictions. We also infer that, within the local seismic resolution (≳5,000 km), downflows are ~40% weaker than upflows, indicating an apparent mass-flux imbalance. This may imply that the descending flows also comprise plumes, which maintain the mass balance but are simply too small to be detected by seismic waves. These results challenge the widely used mixing-length description of solar convection.}, author = {Hanson, Chris S. and Das, Srijan B and Mani, Prasad and Hanasoge, Shravan and Sreenivasan, Katepalli R.}, issn = {2397-3366}, journal = {Nature Astronomy}, pages = {1088--1101}, publisher = {Springer Nature}, title = {{Supergranular-scale solar convection not explained by mixing-length theory}}, doi = {10.1038/s41550-024-02304-w}, volume = {8}, year = {2024}, } @article{17190, abstract = {For a locally finite set, 𝐴⊆ℝ𝑑 , the 𝑘 th Brillouin zone of 𝑎∈𝐴 is the region of points 𝑥∈ℝ𝑑 for which ‖𝑥−𝑎‖ is the 𝑘 th smallest among the Euclidean distances between 𝑥 and the points in 𝐴 . If 𝐴 is a lattice, the 𝑘 th Brillouin zones of the points in 𝐴 are translates of each other, and together they tile space. Depending on the value of 𝑘 , they express medium- or long-range order in the set. We study fundamental geometric and combinatorial properties of Brillouin zones, focusing on the integer lattice and its perturbations. Our results include the stability of a Brillouin zone under perturbations, a linear upper bound on the number of chambers in a zone for lattices in ℝ2 , and the convergence of the maximum volume of a chamber to zero for the integer lattice.}, author = {Edelsbrunner, Herbert and Garber, Alexey and Ghafaris, Mohadese and Heiss, Teresa and Saghafiant, Morteza and Wintraecken, Mathijs}, issn = {0895-4801}, journal = {SIAM Journal on Discrete Mathematics}, number = {2}, pages = {1784--1807}, publisher = {Society for Industrial and Applied Mathematics}, title = {{Brillouin zones of integer lattices and their perturbations}}, doi = {10.1137/22M1489071}, volume = {38}, year = {2024}, } @article{17191, abstract = {Dendritic cells migrate to and from lymph nodes in response to chemokine gradients.Data now show that steady-state migration of these cells can be triggered by a mechanosensitive pathway.}, author = {Lembo, Sergio and Sixt, Michael K}, issn = {1529-2916}, journal = {Nature Immunology}, pages = {1131–1132 }, publisher = {Springer Nature}, title = {{Nuclear squeezing wakes up dendritic cells}}, doi = {10.1038/s41590-024-01881-2}, volume = {25}, year = {2024}, } @article{17203, abstract = {The behavior of a rigid body primarily depends on its mass moments, which consist of the mass, center of mass, and moments of inertia. It is possible to manipulate these quantities without altering the geometric appearance of an object by introducing cavities in its interior. Algorithms that find cavities of suitable shapes and sizes have enabled the computational design of spinning tops, yo-yos, wheels, buoys, and statically balanced objects. Previous work is based, for example, on topology optimization on voxel grids, which introduces a large number of optimization variables and box constraints, or offset surface computation, which cannot guarantee that solutions to a feasible problem will always be found. In this work, we provide a mathematical analysis of constrained topology optimization problems that depend only on mass moments. This class of problems covers, among others, all applications mentioned above. Our main result is to show that no matter the outer shape of the rigid body to be optimized or the optimization objective and constraints considered, the optimal solution always features a quadric-shaped interface between material and cavities. This proves that optimal interfaces are always ellipsoids, hyperboloids, paraboloids, or one of a few degenerate cases, such as planes. This insight lets us replace a difficult topology optimization problem with a provably equivalent non-linear equation system in a small number (<10) of variables, which represent the coefficients of the quadric. This system can be solved in a few seconds for most examples, provides insights into the geometric structure of many specific applications, and lets us describe their solution properties. Finally, our method integrates seamlessly into modern fabrication workflows because our solutions are analytical surfaces that are native to the CAD domain.}, author = {Hafner, Christian and Ly, Mickaël and Wojtan, Christopher J}, issn = {1557-7368}, journal = {Transactions on Graphics}, keywords = {Topology Optimization, Mass Moments, Computational Geometry}, location = {Denver, Colorado}, number = {4}, publisher = {Association for Computing Machinery}, title = {{Spin-it faster: Quadrics solve all topology optimization problems that depend only on mass moments}}, doi = {10.1145/3658194}, volume = {43}, year = {2024}, } @article{17207, author = {Fouqueau, Louise and Polechova, Jitka}, issn = {1420-9101}, journal = {Journal of evolutionary biology}, number = {6}, pages = {579--587}, publisher = {Oxford University Press}, title = {{Eco-evolutionary dynamics in changing environments: Integrating theory with data}}, doi = {10.1093/jeb/voae067}, volume = {37}, year = {2024}, } @inproceedings{17214, abstract = {Current numerical algorithms for simulating friction fall in one of two camps: smooth solvers sacrifice the stable treatment of static friction in exchange for fast convergence, and non-smooth solvers accurately compute friction at convergence rates that are often prohibitive for large graphics applications. We introduce a novel bridge between these two ideas that computes static and dynamic friction stably and efficiently. Our key idea is to convert the highly constrained non-smooth problem into an unconstrained smooth problem using logarithmic barriers that converges to the exact solution as accuracy increases. We phrase the problem as an interior point primal-dual problem that can be solved efficiently with Newton iteration. We observe quadratic convergence despite the non-smooth nature of the original problem, and our method is well-suited for large systems of tightly packed objects with many contact points. We demonstrate the efficacy of our method with stable piles of grains and stacks of objects, complex granular flows, and robust interlocking assemblies of rigid bodies.}, author = {Chen, Yi-Lu and Ly, Mickaël and Wojtan, Christopher J}, booktitle = {Special Interest Group on Computer Graphics and Interactive Techniques Conference Conference Papers '24}, isbn = {9798400705250}, keywords = {physical simulation, frictional contact, rigid body mechanics, non-smooth dynamics}, location = {Denver, United States}, publisher = {Association for Computing Machinery}, title = {{Primal-dual non-smooth friction for rigid body animation}}, doi = {10.1145/3641519.3657485}, year = {2024}, } @article{17231, abstract = {In the class of projective billiards, which contains the usual billiards, we exhibit counter-examples to Ivrii's conjecture, which states that in any planar billiard with smooth boundary the set of periodic orbits has zero measure. The counter-examples are polygons admitting a 2-parameters family of n-periodic orbits, with n being either 3 or any even integer greater than 4.}, author = {Fiorebe, Corentin}, issn = {1553-5231}, journal = {Discrete and Continuous Dynamical Systems- Series A}, number = {11}, pages = {3287--3301}, publisher = {American Institute of Mathematical Sciences}, title = {{Examples of projective billiards with open sets of periodic orbits}}, doi = {10.3934/dcds.2024059}, volume = {44}, year = {2024}, }