@article{9301, abstract = {Electrodepositing insulating lithium peroxide (Li2O2) is the key process during discharge of aprotic Li–O2 batteries and determines rate, capacity, and reversibility. Current understanding states that the partition between surface adsorbed and dissolved lithium superoxide governs whether Li2O2 grows as a conformal surface film or larger particles, leading to low or high capacities, respectively. However, better understanding governing factors for Li2O2 packing density and capacity requires structural sensitive in situ metrologies. Here, we establish in situ small- and wide-angle X-ray scattering (SAXS/WAXS) as a suitable method to record the Li2O2 phase evolution with atomic to submicrometer resolution during cycling a custom-built in situ Li–O2 cell. Combined with sophisticated data analysis, SAXS allows retrieving rich quantitative structural information from complex multiphase systems. Surprisingly, we find that features are absent that would point at a Li2O2 surface film formed via two consecutive electron transfers, even in poorly solvating electrolytes thought to be prototypical for surface growth. All scattering data can be modeled by stacks of thin Li2O2 platelets potentially forming large toroidal particles. Li2O2 solution growth is further justified by rotating ring-disk electrode measurements and electron microscopy. Higher discharge overpotentials lead to smaller Li2O2 particles, but there is no transition to an electronically passivating, conformal Li2O2 coating. Hence, mass transport of reactive species rather than electronic transport through a Li2O2 film limits the discharge capacity. Provided that species mobilities and carbon surface areas are high, this allows for high discharge capacities even in weakly solvating electrolytes. The currently accepted Li–O2 reaction mechanism ought to be reconsidered.}, author = {Prehal, Christian and Samojlov, Aleksej and Nachtnebel, Manfred and Lovicar, Ludek and Kriechbaum, Manfred and Amenitsch, Heinz and Freunberger, Stefan Alexander}, issn = {1091-6490}, journal = {Proceedings of the National Academy of Sciences}, keywords = {small-angle X-ray scattering, oxygen reduction, disproportionation, Li-air battery}, number = {14}, publisher = {National Academy of Sciences}, title = {{In situ small-angle X-ray scattering reveals solution phase discharge of Li–O2 batteries with weakly solvating electrolytes}}, doi = {10.1073/pnas.2021893118}, volume = {118}, year = {2021}, } @article{9304, abstract = {The high processing cost, poor mechanical properties and moderate performance of Bi2Te3–based alloys used in thermoelectric devices limit the cost-effectiveness of this energy conversion technology. Towards solving these current challenges, in the present work, we detail a low temperature solution-based approach to produce Bi2Te3-Cu2-xTe nanocomposites with improved thermoelectric performance. Our approach consists in combining proper ratios of colloidal nanoparticles and to consolidate the resulting mixture into nanocomposites using a hot press. The transport properties of the nanocomposites are characterized and compared with those of pure Bi2Te3 nanomaterials obtained following the same procedure. In contrast with most previous works, the presence of Cu2-xTe nanodomains does not result in a significant reduction of the lattice thermal conductivity of the reference Bi2Te3 nanomaterial, which is already very low. However, the introduction of Cu2-xTe yields a nearly threefold increase of the power factor associated to a simultaneous increase of the Seebeck coefficient and electrical conductivity at temperatures above 400 K. Taking into account the band alignment of the two materials, we rationalize this increase by considering that Cu2-xTe nanostructures, with a relatively low electron affinity, are able to inject electrons into Bi2Te3, enhancing in this way its electrical conductivity. The simultaneous increase of the Seebeck coefficient is related to the energy filtering of charge carriers at energy barriers within Bi2Te3 domains associated with the accumulation of electrons in regions nearby a Cu2-xTe/Bi2Te3 heterojunction. Overall, with the incorporation of a proper amount of Cu2-xTe nanoparticles, we demonstrate a 250% improvement of the thermoelectric figure of merit of Bi2Te3.}, author = {Zhang, Yu and Xing, Congcong and Liu, Yu and Li, Mengyao and Xiao, Ke and Guardia, Pablo and Lee, Seungho and Han, Xu and Moghaddam, Ahmad and Roa, Joan J and Arbiol, Jordi and Ibáñez, Maria and Pan, Kai and Prato, Mirko and Xie, Ying and Cabot, Andreu}, issn = {1385-8947}, journal = {Chemical Engineering Journal}, number = {8}, publisher = {Elsevier}, title = {{Influence of copper telluride nanodomains on the transport properties of n-type bismuth telluride}}, doi = {10.1016/j.cej.2021.129374}, volume = {418}, year = {2021}, } @article{9305, abstract = {Copper chalcogenides are outstanding thermoelectric materials for applications in the medium-high temperature range. Among different chalcogenides, while Cu2−xSe is characterized by higher thermoelectric figures of merit, Cu2−xS provides advantages in terms of low cost and element abundance. In the present work, we investigate the effect of different dopants to enhance the Cu2−xS performance and also its thermal stability. Among the tested options, Pb-doped Cu2−xS shows the highest improvement in stability against sulfur volatilization. Additionally, Pb incorporation allows tuning charge carrier concentration, which enables a significant improvement of the power factor. We demonstrate here that the introduction of an optimal additive amount of just 0.3% results in a threefold increase of the power factor in the middle-temperature range (500–800 K) and a record dimensionless thermoelectric figure of merit above 2 at 880 K.}, author = {Zhang, Yu and Xing, Congcong and Liu, Yu and Spadaro, Maria Chiara and Wang, Xiang and Li, Mengyao and Xiao, Ke and Zhang, Ting and Guardia, Pablo and Lim, Khak Ho and Moghaddam, Ahmad Ostovari and Llorca, Jordi and Arbiol, Jordi and Ibáñez, Maria and Cabot, Andreu}, issn = {2211-2855}, journal = {Nano Energy}, number = {7}, publisher = {Elsevier}, title = {{Doping-mediated stabilization of copper vacancies to promote thermoelectric properties of Cu2-xS}}, doi = {10.1016/j.nanoen.2021.105991}, volume = {85}, year = {2021}, } @article{9306, abstract = {Assemblies of actin and its regulators underlie the dynamic morphology of all eukaryotic cells. To understand how actin regulatory proteins work together to generate actin-rich structures such as filopodia, we analyzed the localization of diverse actin regulators within filopodia in Drosophila embryos and in a complementary in vitro system of filopodia-like structures (FLSs). We found that the composition of the regulatory protein complex where actin is incorporated (the filopodial tip complex) is remarkably heterogeneous both in vivo and in vitro. Our data reveal that different pairs of proteins correlate with each other and with actin bundle length, suggesting the presence of functional subcomplexes. This is consistent with a theoretical framework where three or more redundant subcomplexes join the tip complex stochastically, with any two being sufficient to drive filopodia formation. We provide an explanation for the observed heterogeneity and suggest that a mechanism based on multiple components allows stereotypical filopodial dynamics to arise from diverse upstream signaling pathways.}, author = {Dobramysl, Ulrich and Jarsch, Iris Katharina and Inoue, Yoshiko and Shimo, Hanae and Richier, Benjamin and Gadsby, Jonathan R. and Mason, Julia and Szałapak, Alicja and Ioannou, Pantelis Savvas and Correia, Guilherme Pereira and Walrant, Astrid and Butler, Richard and Hannezo, Edouard B and Simons, Benjamin D. and Gallop, Jennifer L.}, issn = {15408140}, journal = {Journal of Cell Biology}, number = {4}, publisher = {Rockefeller University Press}, title = {{Stochastic combinations of actin regulatory proteins are sufficient to drive filopodia formation}}, doi = {10.1083/jcb.202003052}, volume = {220}, year = {2021}, } @article{9307, abstract = {We establish finite time extinction with probability one for weak solutions of the Cauchy–Dirichlet problem for the 1D stochastic porous medium equation with Stratonovich transport noise and compactly supported smooth initial datum. Heuristically, this is expected to hold because Brownian motion has average spread rate O(t12) whereas the support of solutions to the deterministic PME grows only with rate O(t1m+1). The rigorous proof relies on a contraction principle up to time-dependent shift for Wong–Zakai type approximations, the transformation to a deterministic PME with two copies of a Brownian path as the lateral boundary, and techniques from the theory of viscosity solutions.}, author = {Hensel, Sebastian}, issn = {2194-041X}, journal = {Stochastics and Partial Differential Equations: Analysis and Computations}, pages = {892–939}, publisher = {Springer Nature}, title = {{Finite time extinction for the 1D stochastic porous medium equation with transport noise}}, doi = {10.1007/s40072-021-00188-9}, volume = {9}, year = {2021}, } @article{9315, abstract = {We consider inertial iteration methods for Fermat–Weber location problem and primal–dual three-operator splitting in real Hilbert spaces. To do these, we first obtain weak convergence analysis and nonasymptotic O(1/n) convergence rate of the inertial Krasnoselskii–Mann iteration for fixed point of nonexpansive operators in infinite dimensional real Hilbert spaces under some seemingly easy to implement conditions on the iterative parameters. One of our contributions is that the convergence analysis and rate of convergence results are obtained using conditions which appear not complicated and restrictive as assumed in other previous related results in the literature. We then show that Fermat–Weber location problem and primal–dual three-operator splitting are special cases of fixed point problem of nonexpansive mapping and consequently obtain the convergence analysis of inertial iteration methods for Fermat–Weber location problem and primal–dual three-operator splitting in real Hilbert spaces. Some numerical implementations are drawn from primal–dual three-operator splitting to support the theoretical analysis.}, author = {Iyiola, Olaniyi S. and Shehu, Yekini}, issn = {1420-9012}, journal = {Results in Mathematics}, number = {2}, publisher = {Springer Nature}, title = {{New convergence results for inertial Krasnoselskii–Mann iterations in Hilbert spaces with applications}}, doi = {10.1007/s00025-021-01381-x}, volume = {76}, year = {2021}, } @article{9316, abstract = {Embryo morphogenesis is impacted by dynamic changes in tissue material properties, which have been proposed to occur via processes akin to phase transitions (PTs). Here, we show that rigidity percolation provides a simple and robust theoretical framework to predict material/structural PTs of embryonic tissues from local cell connectivity. By using percolation theory, combined with directly monitoring dynamic changes in tissue rheology and cell contact mechanics, we demonstrate that the zebrafish blastoderm undergoes a genuine rigidity PT, brought about by a small reduction in adhesion-dependent cell connectivity below a critical value. We quantitatively predict and experimentally verify hallmarks of PTs, including power-law exponents and associated discontinuities of macroscopic observables. Finally, we show that this uniform PT depends on blastoderm cells undergoing meta-synchronous divisions causing random and, consequently, uniform changes in cell connectivity. Collectively, our theoretical and experimental findings reveal the structural basis of material PTs in an organismal context.}, author = {Petridou, Nicoletta and Corominas-Murtra, Bernat and Heisenberg, Carl-Philipp J and Hannezo, Edouard B}, issn = {10974172}, journal = {Cell}, number = {7}, pages = {1914--1928.e19}, publisher = {Elsevier}, title = {{Rigidity percolation uncovers a structural basis for embryonic tissue phase transitions}}, doi = {10.1016/j.cell.2021.02.017}, volume = {184}, year = {2021}, } @article{9317, abstract = {Given a locally finite X⊆Rd and a radius r≥0, the k-fold cover of X and r consists of all points in Rd that have k or more points of X within distance r. We consider two filtrations—one in scale obtained by fixing k and increasing r, and the other in depth obtained by fixing r and decreasing k—and we compute the persistence diagrams of both. While standard methods suffice for the filtration in scale, we need novel geometric and topological concepts for the filtration in depth. In particular, we introduce a rhomboid tiling in Rd+1 whose horizontal integer slices are the order-k Delaunay mosaics of X, and construct a zigzag module of Delaunay mosaics that is isomorphic to the persistence module of the multi-covers.}, author = {Edelsbrunner, Herbert and Osang, Georg F}, issn = {1432-0444}, journal = {Discrete and Computational Geometry}, pages = {1296–1313}, publisher = {Springer Nature}, title = {{The multi-cover persistence of Euclidean balls}}, doi = {10.1007/s00454-021-00281-9}, volume = {65}, year = {2021}, } @article{9318, abstract = {We consider a system of N bosons in the mean-field scaling regime for a class of interactions including the repulsive Coulomb potential. We derive an asymptotic expansion of the low-energy eigenstates and the corresponding energies, which provides corrections to Bogoliubov theory to any order in 1/N.}, author = {Bossmann, Lea and Petrat, Sören P and Seiringer, Robert}, issn = {20505094}, journal = {Forum of Mathematics, Sigma}, publisher = {Cambridge University Press}, title = {{Asymptotic expansion of low-energy excitations for weakly interacting bosons}}, doi = {10.1017/fms.2021.22}, volume = {9}, year = {2021}, } @misc{9323, abstract = {This .zip File contains the data for figures presented in the main text and supplementary material of "A singlet triplet hole spin qubit in planar Ge" by D. Jirovec, et. al. The measurements were done using Labber Software and the data is stored in the hdf5 file format. The files can be opened using either the Labber Log Browser (https://labber.org/overview/) or Labber Python API (http://labber.org/online-doc/api/LogFile.html). A single file is acquired with QCodes and features the corresponding data type. XRD data are in .dat format and a code to open the data is provided. The code for simulations is as well provided in Python.}, author = {Jirovec, Daniel}, publisher = {Institute of Science and Technology Austria}, title = {{Research data for "A singlet-triplet hole spin qubit planar Ge"}}, doi = {10.15479/AT:ISTA:9323}, year = {2021}, } @misc{9327, abstract = {This archive contains the missing sweater mesh animations and displacement models for the code of "Mechanics-Aware Deformation of Yarn Pattern Geometry" Code Repository: https://git.ist.ac.at/gsperl/MADYPG}, author = {Sperl, Georg and Narain, Rahul and Wojtan, Christopher J}, publisher = {IST Austria}, title = {{Mechanics-Aware Deformation of Yarn Pattern Geometry (Additional Animation/Model Data)}}, doi = {10.15479/AT:ISTA:9327}, year = {2021}, } @article{9329, abstract = {Background: To understand information coding in single neurons, it is necessary to analyze subthreshold synaptic events, action potentials (APs), and their interrelation in different behavioral states. However, detecting excitatory postsynaptic potentials (EPSPs) or currents (EPSCs) in behaving animals remains challenging, because of unfavorable signal-to-noise ratio, high frequency, fluctuating amplitude, and variable time course of synaptic events. New method: We developed a method for synaptic event detection, termed MOD (Machine-learning Optimal-filtering Detection-procedure), which combines concepts of supervised machine learning and optimal Wiener filtering. Experts were asked to manually score short epochs of data. The algorithm was trained to obtain the optimal filter coefficients of a Wiener filter and the optimal detection threshold. Scored and unscored data were then processed with the optimal filter, and events were detected as peaks above threshold. Results: We challenged MOD with EPSP traces in vivo in mice during spatial navigation and EPSC traces in vitro in slices under conditions of enhanced transmitter release. The area under the curve (AUC) of the receiver operating characteristics (ROC) curve was, on average, 0.894 for in vivo and 0.969 for in vitro data sets, indicating high detection accuracy and efficiency. Comparison with existing methods: When benchmarked using a (1 − AUC)−1 metric, MOD outperformed previous methods (template-fit, deconvolution, and Bayesian methods) by an average factor of 3.13 for in vivo data sets, but showed comparable (template-fit, deconvolution) or higher (Bayesian) computational efficacy. Conclusions: MOD may become an important new tool for large-scale, real-time analysis of synaptic activity.}, author = {Zhang, Xiaomin and Schlögl, Alois and Vandael, David H and Jonas, Peter M}, issn = {1872-678X}, journal = {Journal of Neuroscience Methods}, number = {6}, publisher = {Elsevier}, title = {{MOD: A novel machine-learning optimal-filtering method for accurate and efficient detection of subthreshold synaptic events in vivo}}, doi = {10.1016/j.jneumeth.2021.109125}, volume = {357}, year = {2021}, } @article{9330, abstract = {In nerve cells the genes encoding for α2δ subunits of voltage-gated calcium channels have been linked to synaptic functions and neurological disease. Here we show that α2δ subunits are essential for the formation and organization of glutamatergic synapses. Using a cellular α2δ subunit triple-knockout/knockdown model, we demonstrate a failure in presynaptic differentiation evidenced by defective presynaptic calcium channel clustering and calcium influx, smaller presynaptic active zones, and a strongly reduced accumulation of presynaptic vesicle-associated proteins (synapsin and vGLUT). The presynaptic defect is associated with the downscaling of postsynaptic AMPA receptors and the postsynaptic density. The role of α2δ isoforms as synaptic organizers is highly redundant, as each individual α2δ isoform can rescue presynaptic calcium channel trafficking and expression of synaptic proteins. Moreover, α2δ-2 and α2δ-3 with mutated metal ion-dependent adhesion sites can fully rescue presynaptic synapsin expression but only partially calcium channel trafficking, suggesting that the regulatory role of α2δ subunits is independent from its role as a calcium channel subunit. Our findings influence the current view on excitatory synapse formation. First, our study suggests that postsynaptic differentiation is secondary to presynaptic differentiation. Second, the dependence of presynaptic differentiation on α2δ implicates α2δ subunits as potential nucleation points for the organization of synapses. Finally, our results suggest that α2δ subunits act as transsynaptic organizers of glutamatergic synapses, thereby aligning the synaptic active zone with the postsynaptic density.}, author = {Schöpf, Clemens L. and Ablinger, Cornelia and Geisler, Stefanie M. and Stanika, Ruslan I. and Campiglio, Marta and Kaufmann, Walter and Nimmervoll, Benedikt and Schlick, Bettina and Brockhaus, Johannes and Missler, Markus and Shigemoto, Ryuichi and Obermair, Gerald J.}, issn = {1091-6490}, journal = {PNAS}, number = {14}, publisher = {National Academy of Sciences}, title = {{Presynaptic α2δ subunits are key organizers of glutamatergic synapses}}, doi = {10.1073/pnas.1920827118}, volume = {118}, year = {2021}, } @article{9331, abstract = {Quantum entanglement has been generated and verified in cold-atom experiments and used to make atom-interferometric measurements below the shot-noise limit. However, current state-of-the-art cold-atom devices exploit separable (i.e., unentangled) atomic states. This perspective piece asks the question: can entanglement usefully improve cold-atom sensors, in the sense that it gives new sensing capabilities unachievable with current state-of-the-art devices? We briefly review the state-of-the-art in precision cold-atom sensing, focusing on clocks and inertial sensors, identifying the potential benefits entanglement could bring to these devices, and the challenges that need to be overcome to realize these benefits. We survey demonstrated methods of generating metrologically useful entanglement in cold-atom systems, note their relative strengths and weaknesses, and assess their prospects for near-to-medium term quantum-enhanced cold-atom sensing.}, author = {Szigeti, Stuart S. and Hosten, Onur and Haine, Simon A.}, issn = {00036951}, journal = {Applied Physics Letters}, number = {14}, publisher = {AIP Publishing}, title = {{Improving cold-atom sensors with quantum entanglement: Prospects and challenges}}, doi = {10.1063/5.0050235}, volume = {118}, year = {2021}, } @article{9332, abstract = {Lateral root (LR) formation is an example of a plant post-embryonic organogenesis event. LRs are issued from non-dividing cells entering consecutive steps of formative divisions, proliferation and elongation. The chromatin remodeling protein PICKLE (PKL) negatively regulates auxin-mediated LR formation through a mechanism that is not yet known. Here we show that PKL interacts with RETINOBLASTOMA-RELATED 1 (RBR1) to repress the LATERAL ORGAN BOUNDARIES-DOMAIN 16 (LBD16) promoter activity. Since LBD16 function is required for the formative division of LR founder cells, repression mediated by the PKL–RBR1 complex negatively regulates formative division and LR formation. Inhibition of LR formation by PKL–RBR1 is counteracted by auxin, indicating that, in addition to auxin-mediated transcriptional responses, the fine-tuned process of LR formation is also controlled at the chromatin level in an auxin-signaling dependent manner.}, author = {Ötvös, Krisztina and Miskolczi, Pál and Marhavý, Peter and Cruz-Ramírez, Alfredo and Benková, Eva and Robert, Stéphanie and Bakó, László}, issn = {1422-0067}, journal = {International Journal of Molecular Sciences}, number = {8}, publisher = {MDPI}, title = {{Pickle recruits retinoblastoma related 1 to control lateral root formation in arabidopsis}}, doi = {10.3390/ijms22083862}, volume = {22}, year = {2021}, } @article{9333, abstract = {We revise a previous result about the Fröhlich dynamics in the strong coupling limit obtained in Griesemer (Rev Math Phys 29(10):1750030, 2017). In the latter it was shown that the Fröhlich time evolution applied to the initial state φ0⊗ξα, where φ0 is the electron ground state of the Pekar energy functional and ξα the associated coherent state of the phonons, can be approximated by a global phase for times small compared to α2. In the present note we prove that a similar approximation holds for t=O(α2) if one includes a nontrivial effective dynamics for the phonons that is generated by an operator proportional to α−2 and quadratic in creation and annihilation operators. Our result implies that the electron ground state remains close to its initial state for times of order α2, while the phonon fluctuations around the coherent state ξα can be described by a time-dependent Bogoliubov transformation.}, author = {Mitrouskas, David Johannes}, issn = {15730530}, journal = {Letters in Mathematical Physics}, publisher = {Springer Nature}, title = {{A note on the Fröhlich dynamics in the strong coupling limit}}, doi = {10.1007/s11005-021-01380-7}, volume = {111}, year = {2021}, } @article{9335, abstract = {Various degenerate diffusion equations exhibit a waiting time phenomenon: depending on the “flatness” of the compactly supported initial datum at the boundary of the support, the support of the solution may not expand for a certain amount of time. We show that this phenomenon is captured by particular Lagrangian discretizations of the porous medium and the thin film equations, and we obtain sufficient criteria for the occurrence of waiting times that are consistent with the known ones for the original PDEs. For the spatially discrete solution, the waiting time phenomenon refers to a deviation of the edge of support from its original position by a quantity comparable to the mesh width, over a mesh-independent time interval. Our proof is based on estimates on the fluid velocity in Lagrangian coordinates. Combining weighted entropy estimates with an iteration technique à la Stampacchia leads to upper bounds on free boundary propagation. Numerical simulations show that the phenomenon is already clearly visible for relatively coarse discretizations.}, author = {Fischer, Julian L and Matthes, Daniel}, issn = {0036-1429}, journal = {SIAM Journal on Numerical Analysis}, number = {1}, pages = {60--87}, publisher = {Society for Industrial and Applied Mathematics}, title = {{The waiting time phenomenon in spatially discretized porous medium and thin film equations}}, doi = {10.1137/19M1300017}, volume = {59}, year = {2021}, } @article{9336, abstract = {Mentorship is experience and/or knowledge‐based guidance. Mentors support, sponsor and advocate for mentees. Having one or more mentors when you seek advice can significantly influence and improve your research endeavours, well‐being and career development. Positive mentee–mentor relationships are vital for maintaining work–life balance and success in careers. Early‐career researchers (ECRs), in particular, can benefit from mentorship to navigate challenges in academic and nonacademic life and careers. Yet, strategies for selecting mentors and maintaining interactions with them are often underdiscussed within research environments. In this Words of Advice, we provide recommendations for ECRs to seek and manage mentorship interactions. Our article draws from our experiences as ECRs and published work, to provide suggestions for mentees to proactively promote beneficial mentorship interactions. The recommended practices highlight the importance of identifying mentorship needs, planning and selecting multiple and diverse mentors, setting goals, and maintaining constructive, and mutually beneficial working relationships with mentors.}, author = {Sarabipour, Sarvenaz and Hainer, Sarah J. and Arslan, Feyza N and De Winde, Charlotte M. and Furlong, Emily and Bielczyk, Natalia and Jadavji, Nafisa M. and Shah, Aparna P. and Davla, Sejal}, issn = {1742-4658}, journal = {FEBS Journal}, publisher = {Wiley}, title = {{Building and sustaining mentor interactions as a mentee}}, doi = {10.1111/febs.15823}, year = {2021}, } @inproceedings{9345, abstract = {Modeling a crystal as a periodic point set, we present a fingerprint consisting of density functionsthat facilitates the efficient search for new materials and material properties. We prove invarianceunder isometries, continuity, and completeness in the generic case, which are necessary featuresfor the reliable comparison of crystals. The proof of continuity integrates methods from discretegeometry and lattice theory, while the proof of generic completeness combines techniques fromgeometry with analysis. The fingerprint has a fast algorithm based on Brillouin zones and relatedinclusion-exclusion formulae. We have implemented the algorithm and describe its application tocrystal structure prediction.}, author = {Edelsbrunner, Herbert and Heiss, Teresa and Kurlin , Vitaliy and Smith, Philip and Wintraecken, Mathijs}, booktitle = {37th International Symposium on Computational Geometry (SoCG 2021)}, issn = {1868-8969}, location = {Virtual}, pages = {32:1--32:16}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{The density fingerprint of a periodic point set}}, doi = {10.4230/LIPIcs.SoCG.2021.32}, volume = {189}, year = {2021}, } @article{9348, abstract = {We consider the stochastic quantization of a quartic double-well energy functional in the semiclassical regime and derive optimal asymptotics for the exponentially small splitting of the ground state energy. Our result provides an infinite-dimensional version of some sharp tunneling estimates known in finite dimensions for semiclassical Witten Laplacians in degree zero. From a stochastic point of view it proves that the L2 spectral gap of the stochastic one-dimensional Allen-Cahn equation in finite volume satisfies a Kramers-type formula in the limit of vanishing noise. We work with finite-dimensional lattice approximations and establish semiclassical estimates which are uniform in the dimension. Our key estimate shows that the constant separating the two exponentially small eigenvalues from the rest of the spectrum can be taken independently of the dimension.}, author = {Brooks, Morris and Di Gesù, Giacomo}, issn = {1096-0783}, journal = {Journal of Functional Analysis}, number = {3}, publisher = {Elsevier}, title = {{Sharp tunneling estimates for a double-well model in infinite dimension}}, doi = {10.1016/j.jfa.2021.109029}, volume = {281}, year = {2021}, }