@unpublished{20572, abstract = {We present an elementary non-recursive formula for the multivariate moments of the Dirichlet distribution on the standard simplex, in terms of the pattern inventory of the moments' exponents. We obtain analog formulas for the multivariate moments of the Dirichlet-Ferguson and Gamma measures. We further introduce a polychromatic analogue of Ewens sampling formula on colored integer partitions, discuss its relation with suitable extensions of Hoppe's urn model and of the Chinese restaurant process, and prove that it satisfies an adapted notion of consistency in the sense of Kingman.}, author = {Dello Schiavo, Lorenzo and Quattrocchi, Filippo}, booktitle = {arXiv}, keywords = {Dirichlet distribution, Ewens sampling formula, Hoppe urn model, colored partitions}, title = {{Multivariate Dirichlet moments and a polychromatic Ewens sampling formula}}, doi = {10.48550/arXiv.2309.11292}, year = {2023}, } @unpublished{20624, abstract = {We describe a sequence of smooth quotients of the Deligne-Mumford moduli space ${\mathbb R}\overline{\mathcal M}_{0,\ell+1}$ of real rational curves with $\ell\!+\!1$ conjugate pairs of marked points that terminates at ${\mathbb R}\overline{\mathcal M}_{0,\ell}\!\times\!{\mathbb C}{\mathbb P}^1$. This produces an analogue of Keel's blowup construction of the Deligne-Mumford moduli spaces $\overline{\mathcal M}_{\ell+1}$ of rational curves with $\ell\!+\!1$ marked points, but with an explicit description of the intermediate spaces and the blowups of three different types. The same framework readily adapts to the real moduli spaces with real points. In a sequel, we use this inductive construction of ${\mathbb R}\overline{\mathcal M}_{0,\ell+1}$ to completely determine the rational (co)homology ring of ${\mathbb R}\overline{\mathcal M}_{0,\ell}$.}, author = {Chen, Xujia and Zinger, Aleksey}, booktitle = {arXiv}, title = {{Blowdowns of the Deligne-Mumford spaces of real rational curves}}, doi = {10.48550/ARXIV.2305.08811}, year = {2023}, } @unpublished{20625, abstract = {It is a long-established and heavily-used fact that the integral cohomology ring of the Deligne-Mumford moduli space of (complex) rational curves is the polynomial ring on the boundary divisors modulo the ideal generated by the obvious geometric relations between them. We show that the rational cohomology ring of the Deligne-Mumford moduli space of real rational curves with conjugate marked points only is the polynomial ring on certain (``complex") boundary divisors and real boundary hypersurfaces modulo the ideal generated by the obvious geometric relations between them and the geometric relation in positive dimension and codimension identified in a previous paper.}, author = {Chen, Xujia and Georgieva, Penka and Zinger, Aleksey}, booktitle = {arXiv}, title = {{The cohomology ring of the Deligne-Mumford moduli space of real rational curves with conjugate marked points}}, doi = {10.48550/ARXIV.2305.08798}, year = {2023}, } @unpublished{20626, abstract = {Kontsevich's characteristic classes are invariants of framed smooth fiber bundles with homology sphere fibers. It was shown by Watanabe that they can be used to distinguish smooth $S^4$-bundles that are all trivial as topological fiber bundles. In this article we show that this ability of Kontsevich's classes is a manifestation of the following principle: the ``real blow-up'' construction on a smooth manifold essentially depends on its smooth structure and thus, given a smooth manifold (or smooth fiber bundle) $M$, the topological invariants of spaces constructed from $M$ by real blow-ups could potentially differentiate smooth structures on $M$. The main theorem says that Kontsevich's characteristic classes of a smooth framed bundle $π$ are determined by the topology of the 2-point configuration space bundle of $π$ and framing data.}, author = {Chen, Xujia}, booktitle = {arXiv}, title = {{Kontsevich's characteristic classes as topological invariants of configuration space bundles}}, doi = {10.48550/ARXIV.2302.03021}, year = {2023}, } @article{20759, abstract = {Recent advances in single-atom insertion reactions have opened up new synthetic approaches for molecular diversification. Developing innovative strategies to directly transform biologically relevant molecules, without any prefunctionalization, is key to further expanding the scope and utility of such transformations. Herein, the direct access to quinazolines and pyrimidines from the corresponding unprotected 1H-indoles and 1H-pyrroles is reported, relying on the implementation of lithium bis(trimethylsilyl)amide (LiHMDS) as a novel nitrogen atom source in combination with commercially available hypervalent iodine reagents. Further application of this strategy in late-stage settings demonstrates its potential in lead structure diversification campaigns.}, author = {Reisenbauer, Julia and Paschke, Ann-Sophie K. and Krizic, Jelena and Botlik, Bence B. and Finkelstein, Patrick and Morandi, Bill}, issn = {1523-7052}, journal = {Organic Letters}, number = {47}, pages = {8419--8423}, publisher = {American Chemical Society}, title = {{Direct access to quinazolines and pyrimidines from unprotected indoles and pyrroles through nitrogen atom insertion}}, doi = {10.1021/acs.orglett.3c03264}, volume = {25}, year = {2023}, } @article{20760, abstract = {The implementation of HCN-free transfer hydrocyanation reactions on laboratory scales has recently been achieved by using HCN donor reagents under nickel- and Lewis acid co-catalysis. More recently, malononitrile-based HCN donor reagents were shown to undergo the C(sp3)–CN bond activation by the nickel catalyst in the absence of Lewis acids. However, there is a lack of detailed mechanistic understanding of the challenging C(sp3)–CN bond cleavage step. In this work, in-depth kinetic and computational studies using alkynes as substrates were used to elucidate the overall reaction mechanism of this transfer hydrocyanation, with a particular focus on the activation of the C(sp3)–CN bond to generate the active H–Ni–CN transfer hydrocyanation catalyst. Comparisons of experimentally and computationally derived 13C kinetic isotope effect data support a direct oxidative addition mechanism of the nickel catalyst into the C(sp3)–CN bond facilitated by the coordination of the second nitrile group to the nickel catalyst.}, author = {Reisenbauer, Julia and Finkelstein, Patrick and Ebert, Marc-Olivier and Morandi, Bill}, issn = {2155-5435}, journal = {ACS Catalysis}, number = {17}, pages = {11548--11555}, publisher = {American Chemical Society}, title = {{Mechanistic investigation of the nickel-catalyzed transfer hydrocyanation of alkynes}}, doi = {10.1021/acscatal.3c02977}, volume = {13}, year = {2023}, } @article{20761, abstract = {We report a convenient protocol for a nitrogen atom insertion into indenes to afford isoquinolines. The reaction uses a combination of commercially available phenyliodine(III) diacetate (PIDA) and ammonium carbamate as the nitrogen source to furnish a wide range of isoquinolines. Various substitution patterns and commonly used functional groups are well tolerated. The operational simplicity renders this protocol broadly applicable and has been successfully extended towards the direct interconversion of cyclopentadienes into the corresponding pyridines. Furthermore, this strategy enables the facile synthesis of 15N labelled isoquinolines, using 15NH4Cl as a commercial 15N source.}, author = {Finkelstein, Patrick and Reisenbauer, Julia and Botlik, Bence B. and Green, Ori and Florin, Andri and Morandi, Bill}, issn = {2041-6539}, journal = {Chemical Science}, number = {11}, pages = {2954--2959}, publisher = {Royal Society of Chemistry}, title = {{Nitrogen atom insertion into indenes to access isoquinolines}}, doi = {10.1039/d2sc06952k}, volume = {14}, year = {2023}, } @article{20762, abstract = {A metal-free deaminative coupling of non-prefunctionalised benzylamines and arylboronic acids is reported. In this operationally simple reaction, a primary amine in benzylamine is converted into a good leaving group in situ using inexpensive and commercially available isoamyl nitrite as a nitrosating reagent. Lewis-acidic arylboronic acids are shown to replace mineral acids such as HCl or HBF4 that are conventionally used in the preparation of aryl diazonium salts. This unlocked the formation of the corresponding diarylmethanes by forging a new C–C bond in good yields. }, author = {Sirvinskaite, Giedre and Reisenbauer, Julia and Morandi, Bill}, issn = {2041-6539}, journal = {Chemical Science}, number = {7}, pages = {1709--1714}, publisher = {Royal Society of Chemistry}, title = {{Deaminative coupling of benzylamines and arylboronic acids}}, doi = {10.1039/d2sc06055h}, volume = {14}, year = {2023}, } @article{10145, abstract = {We study direct integrals of quadratic and Dirichlet forms. We show that each quasi-regular Dirichlet space over a probability space admits a unique representation as a direct integral of irreducible Dirichlet spaces, quasi-regular for the same underlying topology. The same holds for each quasi-regular strongly local Dirichlet space over a metrizable Luzin σ-finite Radon measure space, and admitting carré du champ operator. In this case, the representation is only projectively unique.}, author = {Dello Schiavo, Lorenzo}, issn = {1572-929X}, journal = {Potential Analysis}, pages = {573--615}, publisher = {Springer Nature}, title = {{Ergodic decomposition of Dirichlet forms via direct integrals and applications}}, doi = {10.1007/s11118-021-09951-y}, volume = {58}, year = {2023}, } @article{10173, abstract = {We study the large scale behavior of elliptic systems with stationary random coefficient that have only slowly decaying correlations. To this aim we analyze the so-called corrector equation, a degenerate elliptic equation posed in the probability space. In this contribution, we use a parabolic approach and optimally quantify the time decay of the semigroup. For the theoretical point of view, we prove an optimal decay estimate of the gradient and flux of the corrector when spatially averaged over a scale R larger than 1. For the numerical point of view, our results provide convenient tools for the analysis of various numerical methods.}, author = {Clozeau, Nicolas}, issn = {2194-0401}, journal = {Stochastics and Partial Differential Equations: Analysis and Computations}, pages = {1254–1378}, publisher = {Springer Nature}, title = {{Optimal decay of the parabolic semigroup in stochastic homogenization for correlated coefficient fields}}, doi = {10.1007/s40072-022-00254-w}, volume = {11}, year = {2023}, } @article{10174, abstract = {Quantitative stochastic homogenization of linear elliptic operators is by now well-understood. In this contribution we move forward to the nonlinear setting of monotone operators with p-growth. This first work is dedicated to a quantitative two-scale expansion result. Fluctuations will be addressed in companion articles. By treating the range of exponents 2≤p<∞ in dimensions d≤3, we are able to consider genuinely nonlinear elliptic equations and systems such as −∇⋅A(x)(1+|∇u|p−2)∇u=f (with A random, non-necessarily symmetric) for the first time. When going from p=2 to p>2, the main difficulty is to analyze the associated linearized operator, whose coefficients are degenerate, unbounded, and depend on the random input A via the solution of a nonlinear equation. One of our main achievements is the control of this intricate nonlinear dependence, leading to annealed Meyers' estimates for the linearized operator, which are key to the quantitative two-scale expansion result.}, author = {Clozeau, Nicolas and Gloria, Antoine}, issn = {1432-0673}, journal = {Archive for Rational Mechanics and Analysis }, number = {4}, publisher = {Springer Nature}, title = {{Quantitative nonlinear homogenization: Control of oscillations}}, doi = {10.1007/s00205-023-01895-4}, volume = {247}, year = {2023}, } @article{10405, abstract = {We consider large non-Hermitian random matrices X with complex, independent, identically distributed centred entries and show that the linear statistics of their eigenvalues are asymptotically Gaussian for test functions having 2+ϵ derivatives. Previously this result was known only for a few special cases; either the test functions were required to be analytic [72], or the distribution of the matrix elements needed to be Gaussian [73], or at least match the Gaussian up to the first four moments [82, 56]. We find the exact dependence of the limiting variance on the fourth cumulant that was not known before. The proof relies on two novel ingredients: (i) a local law for a product of two resolvents of the Hermitisation of X with different spectral parameters and (ii) a coupling of several weakly dependent Dyson Brownian motions. These methods are also the key inputs for our analogous results on the linear eigenvalue statistics of real matrices X that are presented in the companion paper [32]. }, author = {Cipolloni, Giorgio and Erdös, László and Schröder, Dominik J}, issn = {1097-0312}, journal = {Communications on Pure and Applied Mathematics}, number = {5}, pages = {946--1034}, publisher = {Wiley}, title = {{Central limit theorem for linear eigenvalue statistics of non-Hermitian random matrices}}, doi = {10.1002/cpa.22028}, volume = {76}, year = {2023}, } @article{10550, abstract = {The global existence of renormalised solutions and convergence to equilibrium for reaction-diffusion systems with non-linear diffusion are investigated. The system is assumed to have quasi-positive non-linearities and to satisfy an entropy inequality. The difficulties in establishing global renormalised solutions caused by possibly degenerate diffusion are overcome by introducing a new class of weighted truncation functions. By means of the obtained global renormalised solutions, we study the large-time behaviour of complex balanced systems arising from chemical reaction network theory with non-linear diffusion. When the reaction network does not admit boundary equilibria, the complex balanced equilibrium is shown, by using the entropy method, to exponentially attract all renormalised solutions in the same compatibility class. This convergence extends even to a range of non-linear diffusion, where global existence is an open problem, yet we are able to show that solutions to approximate systems converge exponentially to equilibrium uniformly in the regularisation parameter.}, author = {Fellner, Klemens and Fischer, Julian L and Kniely, Michael and Tang, Bao Quoc}, issn = {1432-1467}, journal = {Journal of Nonlinear Science}, publisher = {Springer Nature}, title = {{Global renormalised solutions and equilibration of reaction-diffusion systems with non-linear diffusion}}, doi = {10.1007/s00332-023-09926-w}, volume = {33}, year = {2023}, } @article{10551, abstract = {The Dean–Kawasaki equation—a strongly singular SPDE—is a basic equation of fluctuating hydrodynamics; it has been proposed in the physics literature to describe the fluctuations of the density of N independent diffusing particles in the regime of large particle numbers N≫1. The singular nature of the Dean–Kawasaki equation presents a substantial challenge for both its analysis and its rigorous mathematical justification. Besides being non-renormalisable by the theory of regularity structures by Hairer et al., it has recently been shown to not even admit nontrivial martingale solutions. In the present work, we give a rigorous and fully quantitative justification of the Dean–Kawasaki equation by considering the natural regularisation provided by standard numerical discretisations: We show that structure-preserving discretisations of the Dean–Kawasaki equation may approximate the density fluctuations of N non-interacting diffusing particles to arbitrary order in N−1 (in suitable weak metrics). In other words, the Dean–Kawasaki equation may be interpreted as a “recipe” for accurate and efficient numerical simulations of the density fluctuations of independent diffusing particles.}, author = {Cornalba, Federico and Fischer, Julian L}, issn = {1432-0673}, journal = {Archive for Rational Mechanics and Analysis}, number = {5}, publisher = {Springer Nature}, title = {{The Dean-Kawasaki equation and the structure of density fluctuations in systems of diffusing particles}}, doi = {10.1007/s00205-023-01903-7}, volume = {247}, year = {2023}, } @article{10770, abstract = {Mathematical models often aim to describe a complicated mechanism in a cohesive and simple manner. However, reaching perfect balance between being simple enough or overly simplistic is a challenging task. Frequently, game-theoretic models have an underlying assumption that players, whenever they choose to execute a specific action, do so perfectly. In fact, it is rare that action execution perfectly coincides with intentions of individuals, giving rise to behavioural mistakes. The concept of incompetence of players was suggested to address this issue in game-theoretic settings. Under the assumption of incompetence, players have non-zero probabilities of executing a different strategy from the one they chose, leading to stochastic outcomes of the interactions. In this article, we survey results related to the concept of incompetence in classic as well as evolutionary game theory and provide several new results. We also suggest future extensions of the model and argue why it is important to take into account behavioural mistakes when analysing interactions among players in both economic and biological settings.}, author = {Graham, Thomas and Kleshnina, Maria and Filar, Jerzy A.}, issn = {2153-0793}, journal = {Dynamic Games and Applications}, pages = {231--264}, publisher = {Springer Nature}, title = {{Where do mistakes lead? A survey of games with incompetent players}}, doi = {10.1007/s13235-022-00425-3}, volume = {13}, year = {2023}, } @unpublished{17351, abstract = {Contractive coupling rates have been recently introduced by Conforti as a tool to establish convex Sobolev inequalities (including modified log-Sobolev and Poincar\'{e} inequality) for some classes of Markov chains. In this work, we show how contractive coupling rates can also be used to prove stronger inequalities, in the form of curvature lower bounds for Markov chains and geodesic convexity of entropic functionals. We illustrate this in several examples discussed by Conforti, where in particular, after appropriately choosing a parameter function, we establish positive curvature in the entropic and (discrete) Bakry--\'{E}mery sense. In addition, we recall and give straightforward generalizations of some notions of coarse Ricci curvature, and we discuss some of their properties and relations with the concepts of couplings and coupling rates: as an application, we show exponential contraction of the $p$-Wasserstein distance for the heat flow in the aforementioned examples.}, author = {Pedrotti, Francesco}, booktitle = {arXiv}, title = {{Contractive coupling rates and curvature lower bounds for Markov chains}}, doi = {10.48550/arXiv.2308.00516}, year = {2023}, } @inproceedings{17378, abstract = {Generative Pre-trained Transformer models, known as GPT or OPT, set themselves apart through breakthrough performance across complex language modelling tasks, but also by their extremely high computational and storage costs. Specifically, due to their massive size, even inference for large, highly-accurate GPT models may require multiple performant GPUs, which limits the usability of such models. While there is emerging work on relieving this pressure via model compression, the applicability and performance of existing compression techniques is limited by the scale and complexity of GPT models. In this paper, we address this challenge, and propose OPTQ, a new one-shot weight quantization method based on approximate second-order information, that is both highly-accurate and highly-efficient. Specifically, OPTQ can quantize GPT models with 175 billion parameters in approximately four GPU hours, reducing the bitwidth down to 3 or 4 bits per weight, with negligible accuracy degradation relative to the uncompressed baseline. Our method more than doubles the compression gains relative to previously-proposed one-shot quantization methods, preserving accuracy, allowing us for the first time to execute an 175 billion-parameter model inside a single GPU for generative inference. Moreover, we also show that our method can still provide reasonable accuracy in the extreme quantization regime, in which weights are quantized to 2-bit or even ternary quantization levels. We show experimentally that these improvements can be leveraged for end-to-end inference speedups over FP16, of around 3.25x when using high-end GPUs (NVIDIA A100) and 4.5x when using more cost-effective ones (NVIDIA A6000). The implementation is available at https://github.com/IST-DASLab/gptq.}, author = {Frantar, Elias and Ashkboos, Saleh and Hoefler, Torsten and Alistarh, Dan-Adrian}, booktitle = {11th International Conference on Learning Representations }, location = {Kigali, Rwanda}, publisher = {International Conference on Learning Representations}, title = {{OPTQ: Accurate post-training quantization for generative pre-trained transformers}}, year = {2023}, } @article{17379, abstract = {We introduce a computational pipeline for simulating and designing C-shells, a new class of planar-to-spatial deployable linkage structures. A C-shell is composed of curved flexible beams connected at rotational joints that can be assembled in a stress-free planar configuration. When actuated, the elastic beams deform and the assembly deploys towards the target 3D shape. We propose two alternative computational design approaches for C-shells: (i) Forward exploration simulates the deployed shape from a planar beam layout provided by the user. Once a satisfactory overall shape is found, a subsequent design optimization adapts the beam geometry to reduce the elastic energy of the linkage while preserving the target shape. (ii) Inverse design is facilitated by a new geometric flattening method that takes a design surface as input and computes an initial layout of piecewise straight linkage beams. Our design optimization algorithm then calculates the smooth curved beams to best reproduce the target shape at minimal elastic energy. We find that C-shells offer a rich space for design and show several studies that highlight new shape topologies that cannot be achieved with existing deployable linkage structures.}, author = {Becker, Quentin and Suzuki, Seiichi and Ren, Yingying and Pellis, Davide and Panetta, Julian and Pauly, Mark}, issn = {1557-7368}, journal = {ACM Transactions on Graphics}, number = {6}, publisher = {Association for Computing Machinery}, title = {{C-shells: Deployable gridshells with curved beams}}, doi = {10.1145/3618366}, volume = {42}, year = {2023}, } @inbook{17380, abstract = {Deployable gridshells are a class of planar-to-spatial structures that achievea 3D curved geometry by inducing bending on a flat grid of elastic beams. However, theslender nature of these beams often conflicts with the structure’s load-bearing capacity.To address this issue, multiple layers are typically stacked to enhance out-of-planestiffness and prevent stability issues. The primary challenge then lies in deploying suchmulti-layered systems globally, as it requires significant shaping forces for actuation.This paper presents an alternative design approach that involves strategically connect-ing compact-to-volumetric gridshell components using weaving principles to shape athick segmented shell. This innovative approach allows for an incremental construc-tion process based entirely on deployable modules with volumetric configurations thatlocally provide the necessary structural depth for the entire system. To demonstrate thisprinciple, we present the realization of BamX, a research pavilion constructed usingdeployable cylindrical components made from raw bamboo slats. These componentsare interconnected at carefully optimized interlocking woven nodes, resulting in abending-active structural frame that is both strong and exceptionally lightweight. Todetermine the optimal topology and geometry of the pavilion, we employ an integrativecomputational approach that leverages advanced numerical optimization techniques.Our method incorporates a physics-based simulation of the bending and twisting be-havior of the bamboo ribbons. By finding the ideal locations for ribbon crossings, weensure that all external and internal forces are in global equilibrium while minimizingthe mechanical stress experienced by each ribbon. BamX exemplifies how a symbiosisof refined weaving craft and advanced computational modeling enables fascinatingnew opportunities for rethinking deployability in architecture.}, author = {Suzuki, Seiichi and Martin, Alison and Ren, Yingying and Chen, Tzu-Ying and Parascho, Stefana and Pauly, Mark}, booktitle = {Advances in Architectural Geometry 2023}, editor = {Dörfler, Kathrin and Knippers, Jan and Menges, Achim and Parascho, Stefana and Pottmann, Helmut and Wortmann, Thomas}, isbn = {9783111160115}, publisher = {De Gruyter}, title = {{BamX: Rethinking Deployability in Architecture through Weaving}}, doi = {10.1515/9783111162683-016}, year = {2023}, } @article{17381, abstract = {We present an algorithmic approach to discover, study, and design multistable elastic knots. Elastic knots are physical realizations of closed curves embedded in 3-space. When endowed with the material thickness and bending resistance of a physical wire, these knots settle into equilibrium states that balance the forces induced by elastic deformation and self-contacts of the wire. In general, elastic knots can have many distinct equilibrium states, i.e. they are multistable mechanical systems. We propose a computational pipeline that combines randomized spatial sampling and physics simulation to efficiently find stable equilibrium states of elastic knots. Leveraging results from knot theory, we run our pipeline on thousands of different topological knot types to create an extensive data set of multistable knots. By applying a series of filters to this data, we discover new transformable knots with interesting geometric and physical properties. A further analysis across knot types reveals geometric and topological patterns, yielding constructive principles that generalize beyond the currently tabulated knot types. We show how multistable elastic knots can be used to design novel deployable structures and engaging recreational puzzles. Several physical prototypes at different scales highlight these applications and validate our simulation.}, author = {Vidulis, Michele and Ren, Yingying and Panetta, Julian and Grinspun, Eitan and Pauly, Mark}, issn = {1557-7368}, journal = {ACM Transactions on Graphics}, number = {4}, publisher = {Association for Computing Machinery}, title = {{Computational exploration of multistable elastic knots}}, doi = {10.1145/3592399}, volume = {42}, year = {2023}, }