@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}, } @unpublished{17352, abstract = {We prove upper bounds on the $L^\infty$-Wasserstein distance from optimal transport between strongly log-concave probability densities and log-Lipschitz perturbations. In the simplest setting, such a bound amounts to a transport-information inequality involving the $L^\infty$-Wasserstein metric and the relative $L^\infty$-Fisher information. We show that this inequality can be sharpened significantly in situations where the involved densities are anisotropic. Our proof is based on probabilistic techniques using Langevin dynamics. As an application of these results, we obtain sharp exponential rates of convergence in Fisher's infinitesimal model from quantitative genetics, generalising recent results by Calvez, Poyato, and Santambrogio in dimension 1 to arbitrary dimensions.}, author = {Khudiakova, Kseniia and Maas, Jan and Pedrotti, Francesco}, booktitle = {arXiv}, title = {{L∞-optimal transport of anisotropic log-concave measures and exponential convergence in Fisher's infinitesimal model}}, doi = {10.48550/arXiv.2402.04151}, year = {2024}, } @book{18899, abstract = {The flourishing theory of classical optimal transport concerns mass transportation at minimal cost. This book introduces the reader to optimal transport on quantum structures, i.e., optimal transportation between quantum states and related non-commutative concepts of mass transportation. It contains lecture notes on classical optimal transport and Wasserstein gradient flows dynamics and quantum optimal transport quantum couplings and many-body problems quantum channels and qubits These notes are based on lectures given by the authors at the "Optimal Transport on Quantum Structures" School held at the Erdös Center in Budapest in the fall of 2022. The lecture notes are complemented by two survey chapters presenting the state of the art in different research areas of non-commutative optimal transport.}, editor = {Maas, Jan and Rademacher, Simone Anna Elvira and Titkos, Tamás and Virosztek, Daniel}, isbn = {9783031504655}, issn = {2947-9460}, publisher = {Springer Nature}, title = {{Optimal Transport on Quantum Structures}}, doi = {10.1007/978-3-031-50466-2}, volume = {29}, year = {2024}, } @unpublished{17353, abstract = {In this paper we derive estimates for the Hessian of the logarithm (log-Hessian) for solutions to the heat equation. For initial data in the form of log-Lipschitz perturbation of strongly log-concave measures, the log-Hessian admits an explicit, uniform (in space) lower bound. This yields a new estimate for the Lipschitz constant of a transport map pushing forward the standard Gaussian to a measure in this class. Further connections are discussed with score-based diffusion models and improved Gaussian logarithmic Sobolev inequalities. Finally, we show that assuming only fast decay of the tails of the initial datum does not suffice to guarantee uniform log-Hessian upper bounds.}, author = {Brigati, Giovanni and Pedrotti, Francesco}, booktitle = {arXiv}, title = {{Heat flow, log-concavity, and Lipschitz transport maps}}, doi = {10.48550/arXiv.2404.15205}, year = {2024}, } @article{14251, abstract = {The phytohormone auxin and its directional transport through tissues play a fundamental role in development of higher plants. This polar auxin transport predominantly relies on PIN-FORMED (PIN) auxin exporters. Hence, PIN polarization is crucial for development, but its evolution during the rise of morphological complexity in land plants remains unclear. Here, we performed a cross-species investigation by observing the trafficking and localization of endogenous and exogenous PINs in two bryophytes, Physcomitrium patens and Marchantia polymorpha, and in the flowering plant Arabidopsis thaliana. We confirmed that the GFP fusion did not compromise the auxin export function of all examined PINs by using radioactive auxin export assay and by observing the phenotypic changes in transgenic bryophytes. Endogenous PINs polarize to filamentous apices, while exogenous Arabidopsis PINs distribute symmetrically on the membrane in both bryophytes. In Arabidopsis root epidermis, bryophytic PINs show no defined polarity. Pharmacological interference revealed a strong cytoskeleton dependence of bryophytic but not Arabidopsis PIN polarization. The divergence of PIN polarization and trafficking is also observed within the bryophyte clade and between tissues of individual species. These results collectively reveal a divergence of PIN trafficking and polarity mechanisms throughout land plant evolution and a co-evolution of PIN sequence-based and cell-based polarity mechanisms.}, author = {Tang, Han and Lu, KJ and Zhang, Y and Cheng, YL and Tu, SL and Friml, Jiří}, issn = {2590-3462}, journal = {Plant Communications}, number = {1}, publisher = {Elsevier}, title = {{Divergence of trafficking and polarization mechanisms for PIN auxin transporters during land plant evolution}}, doi = {10.1016/j.xplc.2023.100669}, volume = {5}, year = {2024}, } @article{14447, abstract = {Auxin belongs among major phytohormones and governs multiple aspects of plant growth and development. The establishment of auxin concentration gradients, determines, among other processes, plant organ positioning and growth responses to environmental stimuli. Herein we report the synthesis of new NBD- or DNS-labelled IAA derivatives and the elucidation of their biological activity, fluorescence properties and subcellular accumulation patterns in planta. These novel compounds did not show auxin-like activity, but instead antagonized physiological auxin effects. The DNS-labelled derivatives FL5 and FL6 showed strong anti-auxin activity in roots and hypocotyls, which also occurred at the level of gene transcription as confirmed by quantitative PCR analysis. The auxin antagonism of our derivatives was further demonstrated in vitro using an SPR-based binding assay. The NBD-labelled compound FL4 with the best fluorescence properties proved to be unsuitable to study auxin accumulation patterns in planta. On the other hand, the strongest anti-auxin activity possessing compounds FL5 and FL6 could be useful to study binding mechanisms to auxin receptors and for manipulations of auxin-regulated processes.}, author = {Bieleszová, Kristýna and Hladík, Pavel and Kubala, Martin and Napier, Richard and Brunoni, Federica and Gelová, Zuzana and Fiedler, Lukas and Kulich, Ivan and Strnad, Miroslav and Doležal, Karel and Novák, Ondřej and Friml, Jiří and Žukauskaitė, Asta}, issn = {1573-5087}, journal = {Plant Growth Regulation}, pages = {589--602}, publisher = {Springer Nature}, title = {{New fluorescent auxin derivatives: Anti-auxin activity and accumulation patterns in Arabidopsis thaliana}}, doi = {10.1007/s10725-023-01083-0}, volume = {102}, year = {2024}, } @article{17048, abstract = {A key mechanism employed by plants to adapt to salinity stress involves maintaining ion homeostasis via the actions of ion transporters. While the function of cation transporters in maintaining ion homeostasis in plants has been extensively studied, little is known about the roles of their anion counterparts in this process. Here, we describe a mechanism of salt adaptation in plants. We characterized the chloride channel (CLC) gene AtCLCf, whose expression is regulated by WRKY transcription factor under salt stress in Arabidopsis thaliana. Loss-of-function atclcf seedlings show increased sensitivity to salt, whereas AtCLCf overexpression confers enhanced resistance to salt stress. Salt stress induces the translocation of GFP-AtCLCf fusion protein to the plasma membrane (PM). Blocking AtCLCf translocation using the exocytosis inhibitor brefeldin-A or mutating the small GTPase gene AtRABA1b/BEX5 (RAS GENES FROM RAT BRAINA1b homolog) increases salt sensitivity in plants. Electrophysiology and liposome-based assays confirm the Cl−/H+ antiport function of AtCLCf. Therefore, we have uncovered a mechanism of plant adaptation to salt stress involving the NaCl-induced translocation of AtCLCf to the PM, thus facilitating Cl− removal at the roots, and increasing the plant’s salinity tolerance.}, author = {Rajappa, Sivamathini and Krishnamurthy, Pannaga and Huang, Hua and Yu, Dejie and Friml, Jiří and Xu, Jian and Kumar, Prakash P.}, issn = {2041-1723}, journal = {Nature Communications}, publisher = {Springer Nature}, title = {{The translocation of a chloride channel from the Golgi to the plasma membrane helps plants adapt to salt stress}}, doi = {10.1038/s41467-024-48234-z}, volume = {15}, year = {2024}, }