@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{10564, abstract = {We study a class of polaron-type Hamiltonians with sufficiently regular form factor in the interaction term. We investigate the strong-coupling limit of the model, and prove suitable bounds on the ground state energy as a function of the total momentum of the system. These bounds agree with the semiclassical approximation to leading order. The latter corresponds here to the situation when the particle undergoes harmonic motion in a potential well whose frequency is determined by the corresponding Pekar functional. We show that for all such models the effective mass diverges in the strong coupling limit, in all spatial dimensions. Moreover, for the case when the phonon dispersion relation grows at least linearly with momentum, the bounds result in an asymptotic formula for the effective mass quotient, a quantity generalizing the usual notion of the effective mass. This asymptotic form agrees with the semiclassical Landau–Pekar formula and can be regarded as the first rigorous confirmation, in a slightly weaker sense than usually considered, of the validity of the semiclassical formula for the effective mass.}, author = {Mysliwy, Krzysztof and Seiringer, Robert}, issn = {1572-9613}, journal = {Journal of Statistical Physics}, number = {1}, publisher = {Springer Nature}, title = {{Polaron models with regular interactions at strong coupling}}, doi = {10.1007/s10955-021-02851-w}, volume = {186}, year = {2022}, } @article{10588, abstract = {We prove the Sobolev-to-Lipschitz property for metric measure spaces satisfying the quasi curvature-dimension condition recently introduced in Milman (Commun Pure Appl Math, to appear). We provide several applications to properties of the corresponding heat semigroup. In particular, under the additional assumption of infinitesimal Hilbertianity, we show the Varadhan short-time asymptotics for the heat semigroup with respect to the distance, and prove the irreducibility of the heat semigroup. These results apply in particular to large classes of (ideal) sub-Riemannian manifolds.}, author = {Dello Schiavo, Lorenzo and Suzuki, Kohei}, issn = {1432-1807}, journal = {Mathematische Annalen}, keywords = {quasi curvature-dimension condition, sub-riemannian geometry, Sobolev-to-Lipschitz property, Varadhan short-time asymptotics}, pages = {1815--1832}, publisher = {Springer Nature}, title = {{Sobolev-to-Lipschitz property on QCD- spaces and applications}}, doi = {10.1007/s00208-021-02331-2}, volume = {384}, year = {2022}, } @article{10602, abstract = {Transforming ω-automata into parity automata is traditionally done using appearance records. We present an efficient variant of this idea, tailored to Rabin automata, and several optimizations applicable to all appearance records. We compare the methods experimentally and show that our method produces significantly smaller automata than previous approaches.}, author = {Kretinsky, Jan and Meggendorfer, Tobias and Waldmann, Clara and Weininger, Maximilian}, issn = {1432-0525}, journal = {Acta Informatica}, keywords = {computer networks and communications, information systems, software}, pages = {585--618}, publisher = {Springer Nature}, title = {{Index appearance record with preorders}}, doi = {10.1007/s00236-021-00412-y}, volume = {59}, year = {2022}, } @article{10623, abstract = {We investigate the BCS critical temperature Tc in the high-density limit and derive an asymptotic formula, which strongly depends on the behavior of the interaction potential V on the Fermi-surface. Our results include a rigorous confirmation for the behavior of Tc at high densities proposed by Langmann et al. (Phys Rev Lett 122:157001, 2019) and identify precise conditions under which superconducting domes arise in BCS theory.}, author = {Henheik, Sven Joscha}, issn = {1572-9656}, journal = {Mathematical Physics, Analysis and Geometry}, keywords = {geometry and topology, mathematical physics}, number = {1}, publisher = {Springer Nature}, title = {{The BCS critical temperature at high density}}, doi = {10.1007/s11040-021-09415-0}, volume = {25}, year = {2022}, } @article{10704, abstract = {We define and study the existence of very stable Higgs bundles on Riemann surfaces, how it implies a precise formula for the multiplicity of the very stable components of the global nilpotent cone and its relationship to mirror symmetry. The main ingredients are the Bialynicki-Birula theory of C∗-actions on semiprojective varieties, C∗ characters of indices of C∗-equivariant coherent sheaves, Hecke transformation for Higgs bundles, relative Fourier–Mukai transform along the Hitchin fibration, hyperholomorphic structures on universal bundles and cominuscule Higgs bundles.}, author = {Hausel, Tamás and Hitchin, Nigel}, issn = {1432-1297}, journal = {Inventiones Mathematicae}, pages = {893--989}, publisher = {Springer Nature}, title = {{Very stable Higgs bundles, equivariant multiplicity and mirror symmetry}}, doi = {10.1007/s00222-021-01093-7}, volume = {228}, year = {2022}, } @article{10758, abstract = {5-Carboxycytosine (5caC) is a rare epigenetic modification found in nucleic acids of all domains of life. Despite its sparse genomic abundance, 5caC is presumed to play essential regulatory roles in transcription, maintenance and base-excision processes in DNA. In this work, we utilize nuclear magnetic resonance (NMR) spectroscopy to address the effects of 5caC incorporation into canonical DNA strands at multiple pH and temperature conditions. Our results demonstrate that 5caC has a pH-dependent global destabilizing and a base-pair mobility enhancing local impact on dsDNA, albeit without any detectable influence on the ground-state B-DNA structure. Measurement of hybridization thermodynamics and kinetics of 5caC-bearing DNA duplexes highlighted how acidic environment (pH 5.8 and 4.7) destabilizes the double-stranded structure by ∼10–20 kJ mol–1 at 37 °C when compared to the same sample at neutral pH. Protonation of 5caC results in a lower activation energy for the dissociation process and a higher barrier for annealing. Studies on conformational exchange on the microsecond time scale regime revealed a sharply localized base-pair motion involving exclusively the modified site and its immediate surroundings. By direct comparison with canonical and 5-formylcytosine (5fC)-edited strands, we were able to address the impact of the two most oxidized naturally occurring cytosine derivatives in the genome. These insights on 5caC’s subtle sensitivity to acidic pH contribute to the long-standing questions of its capacity as a substrate in base excision repair processes and its purpose as an independent, stable epigenetic mark.}, author = {Dubini, Romeo C. A. and Korytiaková, Eva and Schinkel, Thea and Heinrichs, Pia and Carell, Thomas and Rovo, Petra}, issn = {2694-2445}, journal = {ACS Physical Chemistry Au}, number = {3}, pages = {237--246}, publisher = {American Chemical Society}, title = {{1H NMR chemical exchange techniques reveal local and global effects of oxidized cytosine derivatives}}, doi = {10.1021/acsphyschemau.1c00050}, volume = {2}, year = {2022}, } @article{11478, abstract = {Cerebral organoids differentiated from human-induced pluripotent stem cells (hiPSC) provide a unique opportunity to investigate brain development. However, organoids usually lack microglia, brain-resident immune cells, which are present in the early embryonic brain and participate in neuronal circuit development. Here, we find IBA1+ microglia-like cells alongside retinal cups between week 3 and 4 in 2.5D culture with an unguided retinal organoid differentiation protocol. Microglia do not infiltrate the neuroectoderm and instead enrich within non-pigmented, 3D-cystic compartments that develop in parallel to the 3D-retinal organoids. When we guide the retinal organoid differentiation with low-dosed BMP4, we prevent cup development and enhance microglia and 3D-cysts formation. Mass spectrometry identifies these 3D-cysts to express mesenchymal and epithelial markers. We confirmed this microglia-preferred environment also within the unguided protocol, providing insight into microglial behavior and migration and offer a model to study how they enter and distribute within the human brain.}, author = {Bartalska, Katarina and Hübschmann, Verena and Korkut, Medina and Cubero, Ryan J and Venturino, Alessandro and Rössler, Karl and Czech, Thomas and Siegert, Sandra}, issn = {2589-0042}, journal = {iScience}, number = {7}, publisher = {Elsevier}, title = {{A systematic characterization of microglia-like cell occurrence during retinal organoid differentiation}}, doi = {10.1016/j.isci.2022.104580}, volume = {25}, year = {2022}, } @article{7791, abstract = {Extending a result of Milena Radnovic and Serge Tabachnikov, we establish conditionsfor two different non-symmetric norms to define the same billiard reflection law.}, author = {Akopyan, Arseniy and Karasev, Roman}, issn = {2199-6768}, journal = {European Journal of Mathematics}, number = {4}, pages = {1309 -- 1312}, publisher = {Springer Nature}, title = {{When different norms lead to same billiard trajectories?}}, doi = {10.1007/s40879-020-00405-0}, volume = {8}, year = {2022}, } @article{10211, abstract = {We study the problem of recovering an unknown signal 𝑥𝑥 given measurements obtained from a generalized linear model with a Gaussian sensing matrix. Two popular solutions are based on a linear estimator 𝑥𝑥^L and a spectral estimator 𝑥𝑥^s. The former is a data-dependent linear combination of the columns of the measurement matrix, and its analysis is quite simple. The latter is the principal eigenvector of a data-dependent matrix, and a recent line of work has studied its performance. In this paper, we show how to optimally combine 𝑥𝑥^L and 𝑥𝑥^s. At the heart of our analysis is the exact characterization of the empirical joint distribution of (𝑥𝑥,𝑥𝑥^L,𝑥𝑥^s) in the high-dimensional limit. This allows us to compute the Bayes-optimal combination of 𝑥𝑥^L and 𝑥𝑥^s, given the limiting distribution of the signal 𝑥𝑥. When the distribution of the signal is Gaussian, then the Bayes-optimal combination has the form 𝜃𝑥𝑥^L+𝑥𝑥^s and we derive the optimal combination coefficient. In order to establish the limiting distribution of (𝑥𝑥,𝑥𝑥^L,𝑥𝑥^s), we design and analyze an approximate message passing algorithm whose iterates give 𝑥𝑥^L and approach 𝑥𝑥^s. Numerical simulations demonstrate the improvement of the proposed combination with respect to the two methods considered separately.}, author = {Mondelli, Marco and Thrampoulidis, Christos and Venkataramanan, Ramji}, issn = {1615-3383}, journal = {Foundations of Computational Mathematics}, keywords = {Applied Mathematics, Computational Theory and Mathematics, Computational Mathematics, Analysis}, publisher = {Springer}, title = {{Optimal combination of linear and spectral estimators for generalized linear models}}, doi = {10.1007/s10208-021-09531-x}, year = {2021}, } @article{10221, abstract = {We prove that any deterministic matrix is approximately the identity in the eigenbasis of a large random Wigner matrix with very high probability and with an optimal error inversely proportional to the square root of the dimension. Our theorem thus rigorously verifies the Eigenstate Thermalisation Hypothesis by Deutsch (Phys Rev A 43:2046–2049, 1991) for the simplest chaotic quantum system, the Wigner ensemble. In mathematical terms, we prove the strong form of Quantum Unique Ergodicity (QUE) with an optimal convergence rate for all eigenvectors simultaneously, generalizing previous probabilistic QUE results in Bourgade and Yau (Commun Math Phys 350:231–278, 2017) and Bourgade et al. (Commun Pure Appl Math 73:1526–1596, 2020).}, author = {Cipolloni, Giorgio and Erdös, László and Schröder, Dominik J}, issn = {1432-0916}, journal = {Communications in Mathematical Physics}, number = {2}, pages = {1005–1048}, publisher = {Springer Nature}, title = {{Eigenstate thermalization hypothesis for Wigner matrices}}, doi = {10.1007/s00220-021-04239-z}, volume = {388}, year = {2021}, } @article{10806, abstract = {Ligands are a fundamental part of nanocrystals. They control and direct nanocrystal syntheses and provide colloidal stability. Bound ligands also affect the nanocrystals’ chemical reactivity and electronic structure. Surface chemistry is thus crucial to understand nanocrystal properties and functionality. Here, we investigate the synthesis of metal oxide nanocrystals (CeO2-x, ZnO, and NiO) from metal nitrate precursors, in the presence of oleylamine ligands. Surprisingly, the nanocrystals are capped exclusively with a fatty acid instead of oleylamine. Analysis of the reaction mixtures with nuclear magnetic resonance spectroscopy revealed several reaction byproducts and intermediates that are common to the decomposition of Ce, Zn, Ni, and Zr nitrate precursors. Our evidence supports the oxidation of alkylamine and formation of a carboxylic acid, thus unraveling this counterintuitive surface chemistry.}, author = {Calcabrini, Mariano and Van den Eynden, Dietger and Sanchez Ribot, Sergi and Pokratath, Rohan and Llorca, Jordi and De Roo, Jonathan and Ibáñez, Maria}, issn = {2691-3704}, journal = {JACS Au}, keywords = {general medicine}, number = {11}, pages = {1898--1903}, publisher = {American Chemical Society}, title = {{Ligand conversion in nanocrystal synthesis: The oxidation of alkylamines to fatty acids by nitrate}}, doi = {10.1021/jacsau.1c00349}, volume = {1}, year = {2021}, } @article{7901, abstract = {We derive rigorously the leading order of the correlation energy of a Fermi gas in a scaling regime of high density and weak interaction. The result verifies the prediction of the random-phase approximation. Our proof refines the method of collective bosonization in three dimensions. We approximately diagonalize an effective Hamiltonian describing approximately bosonic collective excitations around the Hartree–Fock state, while showing that gapless and non-collective excitations have only a negligible effect on the ground state energy.}, author = {Benedikter, Niels P and Nam, Phan Thành and Porta, Marcello and Schlein, Benjamin and Seiringer, Robert}, issn = {1432-1297}, journal = {Inventiones Mathematicae}, pages = {885--979}, publisher = {Springer}, title = {{Correlation energy of a weakly interacting Fermi gas}}, doi = {10.1007/s00222-021-01041-5}, volume = {225}, year = {2021}, } @article{7905, abstract = {We investigate a sheaf-theoretic interpretation of stratification learning from geometric and topological perspectives. Our main result is the construction of stratification learning algorithms framed in terms of a sheaf on a partially ordered set with the Alexandroff topology. We prove that the resulting decomposition is the unique minimal stratification for which the strata are homogeneous and the given sheaf is constructible. In particular, when we choose to work with the local homology sheaf, our algorithm gives an alternative to the local homology transfer algorithm given in Bendich et al. (Proceedings of the 23rd Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 1355–1370, ACM, New York, 2012), and the cohomology stratification algorithm given in Nanda (Found. Comput. Math. 20(2), 195–222, 2020). Additionally, we give examples of stratifications based on the geometric techniques of Breiding et al. (Rev. Mat. Complut. 31(3), 545–593, 2018), illustrating how the sheaf-theoretic approach can be used to study stratifications from both topological and geometric perspectives. This approach also points toward future applications of sheaf theory in the study of topological data analysis by illustrating the utility of the language of sheaf theory in generalizing existing algorithms.}, author = {Brown, Adam and Wang, Bei}, issn = {1432-0444}, journal = {Discrete and Computational Geometry}, pages = {1166--1198}, publisher = {Springer Nature}, title = {{Sheaf-theoretic stratification learning from geometric and topological perspectives}}, doi = {10.1007/s00454-020-00206-y}, volume = {65}, year = {2021}, } @article{7925, abstract = {In this paper, we introduce a relaxed CQ method with alternated inertial step for solving split feasibility problems. We give convergence of the sequence generated by our method under some suitable assumptions. Some numerical implementations from sparse signal and image deblurring are reported to show the efficiency of our method.}, author = {Shehu, Yekini and Gibali, Aviv}, issn = {1862-4480}, journal = {Optimization Letters}, pages = {2109--2126}, publisher = {Springer Nature}, title = {{New inertial relaxed method for solving split feasibilities}}, doi = {10.1007/s11590-020-01603-1}, volume = {15}, year = {2021}, } @article{7939, abstract = {We design fast deterministic algorithms for distance computation in the Congested Clique model. Our key contributions include: A (2+ϵ)-approximation for all-pairs shortest paths in O(log2n/ϵ) rounds on unweighted undirected graphs. With a small additional additive factor, this also applies for weighted graphs. This is the first sub-polynomial constant-factor approximation for APSP in this model. A (1+ϵ)-approximation for multi-source shortest paths from O(n−−√) sources in O(log2n/ϵ) rounds on weighted undirected graphs. This is the first sub-polynomial algorithm obtaining this approximation for a set of sources of polynomial size. Our main techniques are new distance tools that are obtained via improved algorithms for sparse matrix multiplication, which we leverage to construct efficient hopsets and shortest paths. Furthermore, our techniques extend to additional distance problems for which we improve upon the state-of-the-art, including diameter approximation, and an exact single-source shortest paths algorithm for weighted undirected graphs in O~(n1/6) rounds. }, author = {Censor-Hillel, Keren and Dory, Michal and Korhonen, Janne and Leitersdorf, Dean}, issn = {1432-0452}, journal = {Distributed Computing}, pages = {463--487}, publisher = {Springer Nature}, title = {{Fast approximate shortest paths in the congested clique}}, doi = {10.1007/s00446-020-00380-5}, volume = {34}, year = {2021}, } @article{8196, abstract = {This paper aims to obtain a strong convergence result for a Douglas–Rachford splitting method with inertial extrapolation step for finding a zero of the sum of two set-valued maximal monotone operators without any further assumption of uniform monotonicity on any of the involved maximal monotone operators. Furthermore, our proposed method is easy to implement and the inertial factor in our proposed method is a natural choice. Our method of proof is of independent interest. Finally, some numerical implementations are given to confirm the theoretical analysis.}, author = {Shehu, Yekini and Dong, Qiao-Li and Liu, Lu-Lu and Yao, Jen-Chih}, issn = {1573-2924}, journal = {Optimization and Engineering}, pages = {2627--2653}, publisher = {Springer Nature}, title = {{New strong convergence method for the sum of two maximal monotone operators}}, doi = {10.1007/s11081-020-09544-5}, volume = {22}, year = {2021}, } @article{8286, abstract = {We consider the following dynamic load-balancing process: given an underlying graph G with n nodes, in each step t≥ 0, one unit of load is created, and placed at a randomly chosen graph node. In the same step, the chosen node picks a random neighbor, and the two nodes balance their loads by averaging them. We are interested in the expected gap between the minimum and maximum loads at nodes as the process progresses, and its dependence on n and on the graph structure. Variants of the above graphical balanced allocation process have been studied previously by Peres, Talwar, and Wieder [Peres et al., 2015], and by Sauerwald and Sun [Sauerwald and Sun, 2015]. These authors left as open the question of characterizing the gap in the case of cycle graphs in the dynamic case, where weights are created during the algorithm’s execution. For this case, the only known upper bound is of 𝒪(n log n), following from a majorization argument due to [Peres et al., 2015], which analyzes a related graphical allocation process. In this paper, we provide an upper bound of 𝒪 (√n log n) on the expected gap of the above process for cycles of length n. We introduce a new potential analysis technique, which enables us to bound the difference in load between k-hop neighbors on the cycle, for any k ≤ n/2. We complement this with a "gap covering" argument, which bounds the maximum value of the gap by bounding its value across all possible subsets of a certain structure, and recursively bounding the gaps within each subset. We provide analytical and experimental evidence that our upper bound on the gap is tight up to a logarithmic factor. }, author = {Alistarh, Dan-Adrian and Nadiradze, Giorgi and Sabour, Amirmojtaba}, issn = {1432-0541}, journal = {Algorithmica}, location = {Virtual, Online; Germany}, publisher = {Springer Nature}, title = {{Dynamic averaging load balancing on cycles}}, doi = {10.1007/s00453-021-00905-9}, year = {2021}, } @article{8601, abstract = {We consider large non-Hermitian real or complex random matrices X with independent, identically distributed centred entries. We prove that their local eigenvalue statistics near the spectral edge, the unit circle, coincide with those of the Ginibre ensemble, i.e. when the matrix elements of X are Gaussian. This result is the non-Hermitian counterpart of the universality of the Tracy–Widom distribution at the spectral edges of the Wigner ensemble.}, author = {Cipolloni, Giorgio and Erdös, László and Schröder, Dominik J}, issn = {14322064}, journal = {Probability Theory and Related Fields}, publisher = {Springer Nature}, title = {{Edge universality for non-Hermitian random matrices}}, doi = {10.1007/s00440-020-01003-7}, year = {2021}, } @article{8816, abstract = {Area-dependent quantum field theory is a modification of two-dimensional topological quantum field theory, where one equips each connected component of a bordism with a positive real number—interpreted as area—which behaves additively under glueing. As opposed to topological theories, in area-dependent theories the state spaces can be infinite-dimensional. We introduce the notion of regularised Frobenius algebras in Hilbert spaces and show that area-dependent theories are in one-to-one correspondence to commutative regularised Frobenius algebras. We also provide a state sum construction for area-dependent theories. Our main example is two-dimensional Yang–Mills theory with compact gauge group, which we treat in detail.}, author = {Runkel, Ingo and Szegedy, Lorant}, issn = {14320916}, journal = {Communications in Mathematical Physics}, number = {1}, pages = {83–117}, publisher = {Springer Nature}, title = {{Area-dependent quantum field theory}}, doi = {10.1007/s00220-020-03902-1}, volume = {381}, year = {2021}, }