@article{13129, abstract = {We study the representative volume element (RVE) method, which is a method to approximately infer the effective behavior ahom of a stationary random medium. The latter is described by a coefficient field a(x) generated from a given ensemble ⟨⋅⟩ and the corresponding linear elliptic operator −∇⋅a∇. In line with the theory of homogenization, the method proceeds by computing d=3 correctors (d denoting the space dimension). To be numerically tractable, this computation has to be done on a finite domain: the so-called representative volume element, i.e., a large box with, say, periodic boundary conditions. The main message of this article is: Periodize the ensemble instead of its realizations. By this, we mean that it is better to sample from a suitably periodized ensemble than to periodically extend the restriction of a realization a(x) from the whole-space ensemble ⟨⋅⟩. We make this point by investigating the bias (or systematic error), i.e., the difference between ahom and the expected value of the RVE method, in terms of its scaling w.r.t. the lateral size L of the box. In case of periodizing a(x), we heuristically argue that this error is generically O(L−1). In case of a suitable periodization of ⟨⋅⟩ , we rigorously show that it is O(L−d). In fact, we give a characterization of the leading-order error term for both strategies and argue that even in the isotropic case it is generically non-degenerate. We carry out the rigorous analysis in the convenient setting of ensembles ⟨⋅⟩ of Gaussian type, which allow for a straightforward periodization, passing via the (integrable) covariance function. This setting has also the advantage of making the Price theorem and the Malliavin calculus available for optimal stochastic estimates of correctors. We actually need control of second-order correctors to capture the leading-order error term. This is due to inversion symmetry when applying the two-scale expansion to the Green function. As a bonus, we present a stream-lined strategy to estimate the error in a higher-order two-scale expansion of the Green function.}, author = {Clozeau, Nicolas and Josien, Marc and Otto, Felix and Xu, Qiang}, issn = {1615-3383}, journal = {Foundations of Computational Mathematics}, publisher = {Springer Nature}, title = {{Bias in the representative volume element method: Periodize the ensemble instead of its realizations}}, doi = {10.1007/s10208-023-09613-y}, year = {2023}, } @misc{13124, abstract = {This dataset comprises all data shown in the figures of the submitted article "Tunable directional photon scattering from a pair of superconducting qubits" at arXiv:2205.03293. Additional raw data are available from the corresponding author on reasonable request.}, author = {Redchenko, Elena and Poshakinskiy, Alexander and Sett, Riya and Zemlicka, Martin and Poddubny, Alexander and Fink, Johannes M}, publisher = {Zenodo}, title = {{Tunable directional photon scattering from a pair of superconducting qubits}}, doi = {10.5281/ZENODO.7858567}, year = {2023}, } @misc{13122, abstract = {Data for submitted article "Entangling microwaves with light" at arXiv:2301.03315v1}, author = {Sahu, Rishabh}, publisher = {Zenodo}, title = {{Entangling microwaves with light}}, doi = {10.5281/ZENODO.7789417}, year = {2023}, } @article{13166, abstract = {Brachyury, a member of T-box gene family, is widely known for its major role in mesoderm specification in bilaterians. It is also present in non-bilaterian metazoans, such as cnidarians, where it acts as a component of an axial patterning system. In this study, we present a phylogenetic analysis of Brachyury genes within phylum Cnidaria, investigate differential expression and address a functional framework of Brachyury paralogs in hydrozoan Dynamena pumila. Our analysis indicates two duplication events of Brachyury within the cnidarian lineage. The first duplication likely appeared in the medusozoan ancestor, resulting in two copies in medusozoans, while the second duplication arose in the hydrozoan ancestor, resulting in three copies in hydrozoans. Brachyury1 and 2 display a conservative expression pattern marking the oral pole of the body axis in D. pumila. On the contrary, Brachyury3 expression was detected in scattered presumably nerve cells of the D. pumila larva. Pharmacological modulations indicated that Brachyury3 is not under regulation of cWnt signaling in contrast to the other two Brachyury genes. Divergence in expression patterns and regulation suggest neofunctionalization of Brachyury3 in hydrozoans.}, author = {Vetrova, Alexandra A. and Kupaeva, Daria M. and Kizenko, Alena and Lebedeva, Tatiana S. and Walentek, Peter and Tsikolia, Nikoloz and Kremnyov, Stanislav V.}, issn = {2045-2322}, journal = {Scientific Reports}, publisher = {Springer Nature}, title = {{The evolutionary history of Brachyury genes in Hydrozoa involves duplications, divergence, and neofunctionalization}}, doi = {10.1038/s41598-023-35979-8}, volume = {13}, year = {2023}, } @article{13138, abstract = {We consider the spin- 1 2 Heisenberg chain (XXX model) weakly perturbed away from integrability by an isotropic next-to-nearest neighbor exchange interaction. Recently, it was conjectured that this model possesses an infinite tower of quasiconserved integrals of motion (charges) [D. Kurlov et al., Phys. Rev. B 105, 104302 (2022)]. In this work we first test this conjecture by investigating how the norm of the adiabatic gauge potential (AGP) scales with the system size, which is known to be a remarkably accurate measure of chaos. We find that for the perturbed XXX chain the behavior of the AGP norm corresponds to neither an integrable nor a chaotic regime, which supports the conjectured quasi-integrability of the model. We then prove the conjecture and explicitly construct the infinite set of quasiconserved charges. Our proof relies on the fact that the XXX chain perturbed by next-to-nearest exchange interaction can be viewed as a truncation of an integrable long-range deformation of the Heisenberg spin chain.}, author = {Orlov, Pavel and Tiutiakina, Anastasiia and Sharipov, Rustem and Petrova, Elena and Gritsev, Vladimir and Kurlov, Denis V.}, issn = {2469-9969}, journal = {Physical Review B}, number = {18}, publisher = {American Physical Society}, title = {{Adiabatic eigenstate deformations and weak integrability breaking of Heisenberg chain}}, doi = {10.1103/PhysRevB.107.184312}, volume = {107}, year = {2023}, }