@unpublished{18673, abstract = {Motivated by applications to crystalline materials, we generalize the merge tree and the related barcode of a filtered complex to the periodic setting in Euclidean space. They are invariant under isometries, changing bases, and indeed changing lattices. In addition, we prove stability under perturbations and provide an algorithm that under mild geometric conditions typically satisfied by crystalline materials takes O((n+m)logn) time, in which n and m are the numbers of vertices and edges in the quotient complex, respectively. }, author = {Edelsbrunner, Herbert and Heiss, Teresa}, booktitle = {arXiv}, title = {{Merge trees of periodic filtrations}}, doi = {10.48550/arXiv.2408.16575}, year = {2024}, } @unpublished{15091, abstract = {Motivated by applications in the medical sciences, we study finite chromatic sets in Euclidean space from a topological perspective. Based on the persistent homology for images, kernels and cokernels, we design provably stable homological quantifiers that describe the geometric micro- and macro-structure of how the color classes mingle. These can be efficiently computed using chromatic variants of Delaunay and alpha complexes, and code that does these computations is provided.}, author = {Cultrera di Montesano, Sebastiano and Draganov, Ondrej and Edelsbrunner, Herbert and Saghafian, Morteza}, booktitle = {arXiv}, title = {{Chromatic alpha complexes}}, doi = {10.48550/arXiv.2212.03128}, year = {2024}, } @article{18564, abstract = {The recently discovered Pa 30 nebula, the putative type Iax supernova remnant associated with the historical supernova of 1181 AD, shows puzzling characteristics that make it unique among known supernova remnants. In particular, Pa 30 exhibits a complex morphology, with a unique radial and filamentary structure, and it hosts a hot stellar remnant at its center, which displays oxygen-dominated, ultrafast winds. Because of the surviving stellar remnant and the lack of hydrogen and helium in its filaments, it has been suggested that Pa 30 is the product of a failed thermonuclear explosion in a near- or super-Chandrasekhar white dwarf, which created a subluminous transient, a rare subtype of the Ia class of supernovae called type Iax. We present here a detailed study of the 3D structure and velocities of a full radial section of the remnant. The Integral Field Unit observations, obtained with the new red channel of the Keck Cosmic Web Imager spectrograph, reveal that the ejecta are consistent with being ballistic, with velocities close to the free-expansion velocity. Additionally, we detect a large cavity inside the supernova remnant and a sharp inner edge to the filamentary structure, which coincides with the outer edge of a bright ring detected in infrared images. Finally, we detect a strong asymmetry in the amount of ejecta along the line of sight, which might hint at an asymmetric explosion. Our analysis provides strong confirmation that the explosion originated from SN 1181.}, author = {Cunningham, Tim and Caiazzo, Ilaria and Prusinski, Nikolaus Z. and Fuller, James and Raymond, John C. and Kulkarni, S. R. and Neill, James D. and Duffell, Paul and Martin, Chris and Toloza, Odette and Charbonneau, David and Kenyon, Scott J. and Lin, Zeren and Matuszewski, Mateusz and McGurk, Rosalie and Polin, Abigail and Yao, Philippe Z.}, issn = {2041-8213}, journal = {The Astrophysical Journal Letters}, number = {1}, publisher = {IOP Publishing}, title = {{Expansion properties of the young supernova type Iax remnant Pa 30 revealed}}, doi = {10.3847/2041-8213/ad713b}, volume = {975}, year = {2024}, } @article{18709, abstract = {We measure the mass distribution of main-sequence (MS) companions to hot subdwarf B stars (sdBs) in post-common envelope binaries (PCEBs). We carried out a spectroscopic survey of 14 eclipsing systems ("HW Vir binaries") with orbital periods of 3.8 < Porb < 12 hr, resulting in a well-understood selection function and a near-complete sample of HW Vir binaries with G < 16. We constrain companion masses from the radial velocity curves of the sdB stars. The companion mass distribution peaks at MMS ≈ 0.15 M⊙ and drops off at MMS > 0.2 M⊙, with only two systems hosting companions above the fully convective limit. There is no correlation between Porb and MMS within the sample. A similar drop-off in the companion mass distribution of white dwarf (WD) + MS PCEBs has been attributed to disrupted magnetic braking (MB) below the fully convective limit. We compare the sdB companion mass distribution to predictions of binary evolution simulations with a range of MB laws. Because sdBs have short lifetimes compared to WDs, explaining the lack of higher-mass MS companions to sdBs with disrupted MB requires MB to be boosted by a factor of 20–100 relative to MB laws inferred from the rotation evolution of single stars. We speculate that such boosting may be a result of irradiation-driven enhancement of the MS stars' winds. An alternative possibility is that common envelope evolution favors low-mass companions in short-period orbits, but the existence of massive WD companions to sdBs with similar periods disfavors this scenario.}, author = {Blomberg, Lisa and El-Badry, Kareem and Breivik, Katelyn and Caiazzo, Ilaria and Nagarajan, Pranav and Rodriguez, Antonio and Van Roestel, Jan and Vanderbosch, Zachary P. and Yamaguchi, Natsuko}, issn = {0004-6280}, journal = {Publications of the Astronomical Society of the Pacific}, number = {12}, publisher = {IOP Publishing}, title = {{The companion mass distribution of post common envelope hot subdwarf binaries: Evidence for boosted and disrupted magnetic braking?}}, doi = {10.1088/1538-3873/ad94a2}, volume = {136}, year = {2024}, } @article{15372, abstract = {CRISPR-Cas9 is a powerful tool for genome editing, but the strict requirement for an NGG protospacer-adjacent motif (PAM) sequence immediately next to the DNA target limits the number of editable genes. Recently developed Cas9 variants have been engineered with relaxed PAM requirements, including SpG-Cas9 (SpG) and the nearly PAM-less SpRY-Cas9 (SpRY). However, the molecular mechanisms of how SpRY recognizes all potential PAM sequences remains unclear. Here, we combine structural and biochemical approaches to determine how SpRY interrogates DNA and recognizes target sites. Divergent PAM sequences can be accommodated through conformational flexibility within the PAM-interacting region, which facilitates tight binding to off-target DNA sequences. Nuclease activation occurs ~1000-fold slower than for Streptococcus pyogenes Cas9, enabling us to directly visualize multiple on-pathway intermediate states. Experiments with SpG position it as an intermediate enzyme between Cas9 and SpRY. Our findings shed light on the molecular mechanisms of PAMless genome editing.}, author = {Hibshman, Grace N. and Bravo, Jack Peter Kelly and Hooper, Matthew M. and Dangerfield, Tyler L. and Zhang, Hongshan and Finkelstein, Ilya J. and Johnson, Kenneth A. and Taylor, David W.}, issn = {2041-1723}, journal = {Nature Communications}, publisher = {Springer Nature}, title = {{Unraveling the mechanisms of PAMless DNA interrogation by SpRY-Cas9}}, doi = {10.1038/s41467-024-47830-3}, volume = {15}, year = {2024}, } @article{17442, abstract = {Although eukaryotic Argonautes have a pivotal role in post-transcriptional gene regulation through nucleic acid cleavage, some short prokaryotic Argonaute variants (pAgos) rely on auxiliary nuclease factors for efficient foreign DNA degradation1. Here we reveal the activation pathway of the DNA defence module DdmDE system, which rapidly eliminates small, multicopy plasmids from the Vibrio cholerae seventh pandemic strain (7PET)2. Through a combination of cryo-electron microscopy, biochemistry and in vivo plasmid clearance assays, we demonstrate that DdmE is a catalytically inactive, DNA-guided, DNA-targeting pAgo with a distinctive insertion domain. We observe that the helicase-nuclease DdmD transitions from an autoinhibited, dimeric complex to a monomeric state upon loading of single-stranded DNA targets. Furthermore, the complete structure of the DdmDE–guide–target handover complex provides a comprehensive view into how DNA recognition triggers processive plasmid destruction. Our work establishes a mechanistic foundation for how pAgos utilize ancillary factors to achieve plasmid clearance, and provides insights into anti-plasmid immunity in bacteria. }, author = {Bravo, Jack Peter Kelly and Ramos, Delisa A. and Fregoso Ocampo, Rodrigo and Ingram, Caiden and Taylor, David W.}, issn = {1476-4687}, journal = {Nature}, number = {8018}, pages = {961--967}, publisher = {Springer Nature}, title = {{Plasmid targeting and destruction by the DdmDE bacterial defence system}}, doi = {10.1038/s41586-024-07515-9}, volume = {630}, year = {2024}, } @article{17494, author = {Bravo, Jack Peter Kelly}, issn = {1746-0921}, journal = {Future Microbiology}, number = {15}, pages = {1269--1272}, publisher = {Taylor & Francis}, title = {{Anti-plasmid immunity: A key to pathogen success?}}, doi = {10.1080/17460913.2024.2389720}, volume = {19}, year = {2024}, } @article{13318, abstract = {Bohnenblust–Hille inequalities for Boolean cubes have been proven with dimension-free constants that grow subexponentially in the degree (Defant et al. in Math Ann 374(1):653–680, 2019). Such inequalities have found great applications in learning low-degree Boolean functions (Eskenazis and Ivanisvili in Proceedings of the 54th annual ACM SIGACT symposium on theory of computing, pp 203–207, 2022). Motivated by learning quantum observables, a qubit analogue of Bohnenblust–Hille inequality for Boolean cubes was recently conjectured in Rouzé et al. (Quantum Talagrand, KKL and Friedgut’s theorems and the learnability of quantum Boolean functions, 2022. arXiv preprint arXiv:2209.07279). The conjecture was resolved in Huang et al. (Learning to predict arbitrary quantum processes, 2022. arXiv preprint arXiv:2210.14894). In this paper, we give a new proof of these Bohnenblust–Hille inequalities for qubit system with constants that are dimension-free and of exponential growth in the degree. As a consequence, we obtain a junta theorem for low-degree polynomials. Using similar ideas, we also study learning problems of low degree quantum observables and Bohr’s radius phenomenon on quantum Boolean cubes.}, author = {Volberg, Alexander and Zhang, Haonan}, issn = {1432-1807}, journal = {Mathematische Annalen}, pages = {1657--1676}, publisher = {Springer Nature}, title = {{Noncommutative Bohnenblust–Hille inequalities}}, doi = {10.1007/s00208-023-02680-0}, volume = {389}, year = {2024}, } @article{17282, abstract = {Let X be a vector field and Y be a co-vector field on a smooth manifold M. Does there exist a smooth Riemannian metric gαβ on M such that Yβ=gαβXα ? The main result of this note gives necessary and sufficient conditions for this to be true. As an application of this result we show that a finite-dimensional ergodic Lindblad equation admits a gradient flow structure for the von Neumann relative entropy if and only if the condition of BKM-detailed balance holds.}, author = {Brooks, Morris and Maas, Jan}, issn = {1432-0835}, journal = {Calculus of Variations and Partial Differential Equations}, number = {6}, publisher = {Springer Nature}, title = {{Characterisation of gradient flows for a given functional}}, doi = {10.1007/s00526-024-02755-z}, volume = {63}, year = {2024}, } @article{17143, abstract = {This paper deals with local criteria for the convergence to a global minimiser for gradient flow trajectories and their discretisations. To obtain quantitative estimates on the speed of convergence, we consider variations on the classical Kurdyka–Łojasiewicz inequality for a large class of parameter functions. Our assumptions are given in terms of the initial data, without any reference to an equilibrium point. The main results are convergence statements for gradient flow curves and proximal point sequences to a global minimiser, together with sharp quantitative estimates on the speed of convergence. These convergence results apply in the general setting of lower semicontinuous functionals on complete metric spaces, generalising recent results for smooth functionals on Rn. While the non-smooth setting covers very general spaces, it is also useful for (non)-smooth functionals on Rn. .}, author = {Dello Schiavo, Lorenzo and Maas, Jan and Pedrotti, Francesco}, issn = {1088-6850}, journal = {Transactions of the American Mathematical Society}, number = {6}, pages = {3779--3804}, publisher = {American Mathematical Society}, title = {{Local conditions for global convergence of gradient flows and proximal point sequences in metric spaces}}, doi = {10.1090/tran/9156}, volume = {377}, year = {2024}, } @article{13271, abstract = {In this paper, we prove the convexity of trace functionals (A,B,C)↦Tr|BpACq|s, for parameters (p, q, s) that are best possible, where B and C are any n-by-n positive-definite matrices, and A is any n-by-n matrix. We also obtain the monotonicity versions of trace functionals of this type. As applications, we extend some results in Carlen et al. (Linear Algebra Appl 490:174–185, 2016), Hiai and Petz (Publ Res Inst Math Sci 48(3):525-542, 2012) and resolve a conjecture in Al-Rashed and Zegarliński (Infin Dimens Anal Quantum Probab Relat Top 17(4):1450029, 2014) in the matrix setting. Other conjectures in Al-Rashed and Zegarliński (Infin Dimens Anal Quantum Probab Relat Top 17(4):1450029, 2014) will also be discussed. We also show that some related trace functionals are not concave in general. Such concavity results were expected to hold in different problems.}, author = {Zhang, Haonan}, issn = {1424-0637}, journal = {Annales Henri Poincare}, pages = {2087--2106}, publisher = {Springer Nature}, title = {{Some convexity and monotonicity results of trace functionals}}, doi = {10.1007/s00023-023-01345-7}, volume = {25}, year = {2024}, } @article{15252, abstract = {A measurable map between measure spaces is shown to have bounded compression if and only if its image via the measure-algebra functor is Lipschitz-continuous w.r.t. the measure-algebra distances. This provides a natural interpretation of maps of bounded compression/deformation by means of the measure-algebra functor and corrobo-rates the assertion that maps of bounded deformation are a natural class of morphisms for the category of complete and separable metric measure spaces.}, author = {Dello Schiavo, Lorenzo}, issn = {1848-8013}, journal = {Mathematical Communications}, number = {1}, pages = {137--142}, publisher = {Udruga Matematicara Osijek}, title = {{A characterization of maps of bounded compression}}, volume = {29}, year = {2024}, } @article{18490, abstract = {For large classes of even-dimensional Riemannian manifolds (Formula presented.), we construct and analyze conformally invariant random fields. These centered Gaussian fields (Formula presented.), called co-polyharmonic Gaussian fields, are characterized by their covariance kernels k which exhibit a precise logarithmic divergence: (Formula presented.). They share a fundamental quasi-invariance property under conformal transformations. In terms of the co-polyharmonic Gaussian field (Formula presented.), we define the Liouville Quantum Gravity measure, a random measure on (Formula presented.), heuristically given as (Formula presented.) and rigorously obtained as almost sure weak limit of the right-hand side with (Formula presented.) replaced by suitable regular approximations (Formula presented.). In terms on the Liouville Quantum Gravity measure, we define the Liouville Brownian motion on (Formula presented.) and the random GJMS operators. Finally, we present an approach to a conformal field theory in arbitrary even dimension with an ansatz based on Branson's (Formula presented.) -curvature: we give a rigorous meaning to the Polyakov–Liouville measure (Formula presented.) and we derive the corresponding conformal anomaly. The set of admissible manifolds is conformally invariant. It includes all compact 2-dimensional Riemannian manifolds, all compact non-negatively curved Einstein manifolds of even dimension, and large classes of compact hyperbolic manifolds of even dimension. However, not every compact even-dimensional Riemannian manifold is admissible. Our results concerning the logarithmic divergence of the kernel (Formula presented.) rely on new sharp estimates for heat kernels and higher order Green kernels on arbitrary closed manifolds. }, author = {Dello Schiavo, Lorenzo and Herry, Ronan and Kopfer, Eva and Sturm, Karl Theodor}, issn = {1469-7750}, journal = {Journal of the London Mathematical Society}, number = {5}, publisher = {London Mathematical Society}, title = {{Conformally invariant random fields, Liouville quantum gravity measures, and random Paneitz operators on Riemannian manifolds of even dimension}}, doi = {10.1112/jlms.70003}, volume = {110}, year = {2024}, } @article{15350, abstract = {We extend three related results from the analysis of influences of Boolean functions to the quantum setting, namely the KKL theorem, Friedgut’s Junta theorem and Talagrand’s variance inequality for geometric influences. Our results are derived by a joint use of recently studied hypercontractivity and gradient estimates. These generic tools also allow us to derive generalizations of these results in a general von Neumann algebraic setting beyond the case of the quantum hypercube, including examples in infinite dimensions relevant to quantum information theory such as continuous variables quantum systems. Finally, we comment on the implications of our results as regards to noncommutative extensions of isoperimetric type inequalities, quantum circuit complexity lower bounds and the learnability of quantum observables.}, author = {Rouzé, Cambyse and Wirth, Melchior and Zhang, Haonan}, issn = {1432-0916}, journal = {Communications in Mathematical Physics}, number = {4}, publisher = {Springer Nature}, title = {{Quantum Talagrand, KKL and Friedgut’s theorems and the learnability of quantum boolean functions}}, doi = {10.1007/s00220-024-04981-0}, volume = {405}, year = {2024}, } @article{18158, abstract = {We study the geometry of Poisson point processes from the point of view of optimal transport and Ricci lower bounds. We construct a Riemannian structure on the space of point processes and the associated distance W that corresponds to the Benamou–Brenier variational formula. Our main tool is a non-local continuity equation formulated with the difference operator. The closure of the domain of the relative entropy is a complete geodesic space, when endowed with W. The geometry of this non-local infinite-dimensional space is analogous to that of spaces with positive Ricci curvature. Among others: (a) the Ornstein–Uhlenbeck semi-group is the gradient flow of the relative entropy; (b) the Poisson space has an entropic Ricci curvature bounded from below by 1; (c) W satisfies an HWI inequality.}, author = {Dello Schiavo, Lorenzo and Herry, Ronan and Suzuki, Kohei}, issn = {2270-518X}, journal = {Journal de l'Ecole Polytechnique - Mathematiques}, pages = {957--1010}, publisher = {Ecole Polytechnique}, title = {{Wasserstein geometry and Ricci curvature bounds for Poisson spaces}}, doi = {10.5802/jep.270}, volume = {11}, year = {2024}, } @article{14934, abstract = {We study random perturbations of a Riemannian manifold (M, g) by means of so-called Fractional Gaussian Fields, which are defined intrinsically by the given manifold. The fields h• : ω → hω will act on the manifold via the conformal transformation g → gω := e2hω g. Our focus will be on the regular case with Hurst parameter H > 0, the critical case H = 0 being the celebrated Liouville geometry in two dimensions. We want to understand how basic geometric and functional-analytic quantities like diameter, volume, heat kernel, Brownian motion, spectral bound, or spectral gap change under the influence of the noise. And if so, is it possible to quantify these dependencies in terms of key parameters of the noise? Another goal is to define and analyze in detail the Fractional Gaussian Fields on a general Riemannian manifold, a fascinating object of independent interest.}, author = {Dello Schiavo, Lorenzo and Kopfer, Eva and Sturm, Karl Theodor}, issn = {1572-929X}, journal = {Potential Analysis}, pages = {501--553}, publisher = {Springer Nature}, title = {{A discovery tour in random Riemannian geometry}}, doi = {10.1007/s11118-023-10118-0}, volume = {61}, year = {2024}, } @article{15317, abstract = {We consider the open symmetric exclusion (SEP) and inclusion (SIP) processes on a bounded Lipschitz domain Ω, with both fast and slow boundary. For the random walks on Ω dual to SEP/SIP we establish: a functional-CLT-type convergence to the Brownian motion on Ω with either Neumann (slow boundary), Dirichlet (fast boundary), or Robin (at criticality) boundary conditions; the discrete-to-continuum convergence of the corresponding harmonic profiles. As a consequence, we rigorously derive the hydrodynamic and hydrostatic limits for SEP/SIP on Ω, and analyze their stationary nonequilibrium fluctuations. All scaling limit results for SEP/SIP concern finite-dimensional distribution convergence only, as our duality techniques do not require to establish tightness for the fields associated to the particle systems.}, author = {Dello Schiavo, Lorenzo and Portinale, Lorenzo and Sau, Federico}, issn = {1050-5164}, journal = {Annals of Applied Probability}, number = {2}, pages = {1789--1845}, publisher = {Institute of Mathematical Statistics}, title = {{Scaling limits of random walks, harmonic profiles, and stationary nonequilibrium states in Lipschitz domains}}, doi = {10.1214/23-AAP2007}, volume = {34}, year = {2024}, } @article{15373, abstract = {In this article we prove a refined version of the Christensen–Evans theorem for generators of uniformly continuous GNS-symmetric quantum Markov semigroups. We use this result to show the existence of GNS-symmetric extensions of GNS-symmetric quantum Markov semigroups. In particular, this implies that the generators of GNS-symmetric quantum Markov semigroups on finite-dimensional von Neumann algebra can be written in the form specified by Alicki's theorem.}, author = {Wirth, Melchior}, issn = {1096-0783}, journal = {Journal of Functional Analysis}, number = {3}, publisher = {Elsevier}, title = {{Christensen–Evans theorem and extensions of GNS-symmetric quantum Markov semigroups}}, doi = {10.1016/j.jfa.2024.110475}, volume = {287}, year = {2024}, } @article{17277, abstract = {This paper is devoted to stability results for the Gaussian logarithmic Sobolev inequality, with explicit stability constants. }, author = {Brigati, Giovanni and Dolbeault, Jean and Simonov, Nikita}, issn = {1096-0783}, journal = {Journal of Functional Analysis}, number = {8}, publisher = {Elsevier}, title = {{Stability for the logarithmic Sobolev inequality}}, doi = {10.1016/j.jfa.2024.110562}, volume = {287}, year = {2024}, } @article{18900, abstract = {We prove that certain closable derivations on the GNS Hilbert space associated with a non-tracial weight on a von Neumann algebra give rise to GNS-symmetric semigroups of contractive completely positive maps on the von Neumann algebra.}, author = {Wirth, Melchior}, issn = {1687-0247}, journal = {International Mathematics Research Notices}, number = {14}, pages = {10597--10614}, publisher = {Oxford University Press}, title = {{Modular completely Dirichlet forms as squares of derivations}}, doi = {10.1093/imrn/rnae092}, volume = {2024}, year = {2024}, }