TY - JOUR A1 - Hedayat Mahmoudi, Mahdi A1 - Schulze, Bert-Wolfgang T1 - Corner boundary value problems JF - Asian-European journal of mathematics N2 - The paper develops some crucial steps in extending the first-order cone or edge calculus to higher singularity orders. We focus here on order 2, but the ideas are motivated by an iterative approach for higher singularities. KW - Mellin operators KW - Mellin oscillatory integrals KW - exit calculus KW - weighted Sobolev spaces Y1 - 2016 U6 - https://doi.org/10.1142/S1793557117500541 SN - 1793-5571 SN - 1793-7183 VL - 10 IS - 1 PB - World Scientific CY - Singapore ER - TY - JOUR A1 - Cseh, Agnes A1 - Faenza, Yuri A1 - Kavitha, Telikepalli A1 - Powers, Vladlena T1 - Understanding popular matchings via stable matchings JF - SIAM journal on discrete mathematics N2 - An instance of the marriage problem is given by a graph G = (A boolean OR B, E), together with, for each vertex of G, a strict preference order over its neighbors. A matching M of G is popular in the marriage instance if M does not lose a head-to-head election against any matching where vertices are voters. Every stable matching is a min-size popular matching; another subclass of popular matchings that always exists and can be easily computed is the set of dominant matchings. A popular matching M is dominant if M wins the head-to-head election against any larger matching. Thus, every dominant matching is a max-size popular matching, and it is known that the set of dominant matchings is the linear image of the set of stable matchings in an auxiliary graph. Results from the literature seem to suggest that stable and dominant matchings behave, from a complexity theory point of view, in a very similar manner within the class of popular matchings. The goal of this paper is to show that there are instead differences in the tractability of stable and dominant matchings and to investigate further their importance for popular matchings. First, we show that it is easy to check if all popular matchings are also stable; however, it is co-NP hard to check if all popular matchings are also dominant. Second, we show how some new and recent hardness results on popular matching problems can be deduced from the NP-hardness of certain problems on stable matchings, also studied in this paper, thus showing that stable matchings can be employed to show not only positive results on popular matchings (as is known) but also most negative ones. Problems for which we show new hardness results include finding a min-size (resp., max-size) popular matching that is not stable (resp., dominant). A known result for which we give a new and simple proof is the NP-hardness of finding a popular matching when G is nonbipartite. KW - popular matching KW - stable matching KW - complexity KW - dominant matching Y1 - 2022 U6 - https://doi.org/10.1137/19M124770X SN - 0895-4801 SN - 1095-7146 VL - 36 IS - 1 SP - 188 EP - 213 PB - Society for Industrial and Applied Mathematics CY - Philadelphia ER - TY - THES A1 - Khalil, Sara T1 - Boundary Value Problems on Manifolds with Singularities T1 - Randwertprobleme auf Mannigfaltigkeiten mit Singularitäten N2 - In the thesis there are constructed new quantizations for pseudo-differential boundary value problems (BVPs) on manifolds with edge. The shape of operators comes from Boutet de Monvel’s calculus which exists on smooth manifolds with boundary. The singular case, here with edge and boundary, is much more complicated. The present approach simplifies the operator-valued symbolic structures by using suitable Mellin quantizations on infinite stretched model cones of wedges with boundary. The Mellin symbols themselves are, modulo smoothing ones, with asymptotics, holomorphic in the complex Mellin covariable. One of the main results is the construction of parametrices of elliptic elements in the corresponding operator algebra, including elliptic edge conditions. N2 - In der Dissertation wurden neue Quantisierungen konstruiert für pseudo-differentielle Randwertprobleme auf Mannigfaltigkeiten mit Kanten-Singularitäten. Die Gestalt der hier behandelten Operatoren ist motiviert durch Boutet de Monvels Kalkül, der auf glatten Mannigfaltigkeiten mit Rand bekannt ist. Der singuläre Fall, hier mit Kanten und Rand, ist weitaus komplizierter. Der gegenwärtige Zugang vereinfacht die operatarwertigen Symbolstrukturen unter Verwendung geeigneter Mellin-Quantisierungen auf unendlichen gestreckten Modell- Kegeln, die entsprechenden Keilen mit Rand zugeordnet sind. Die Mellin-Symbole selbst sind holomorph in der komplexen Mellin Kovariablen bis auf glättende Restglieder mit Asymptotiken. Zu den Hauptresultaten gehört die Konstruktion von Parametrices elliptischer Elemente in der erzeugten Operator-Algebra, einschließlich elliptischer Kanten-Bedingungen. KW - manifolds with singularities KW - boundary value problems KW - pseudo-differential equation KW - manifolds with edge KW - Boutet de Monvel's calculus KW - edge boundary value problems KW - Mannigfaltigkeiten mit Singularitäten KW - Randwertprobleme KW - pseudo-differentielle Gleichungen KW - Mannigfaltigkeiten mit Kante KW - Boutet de Monvels Kalkül KW - Kanten-Randwertprobleme Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-419018 ER - TY - JOUR A1 - Chang, Der-Chen A1 - Khalil, Sara A1 - Schulze, Bert-Wolfgang T1 - Analysis on regular corner spaces JF - The journal of geometric analysis N2 - We establish a new approach of treating elliptic boundary value problems (BVPs) on manifolds with boundary and regular corners, up to singularity order 2. Ellipticity and parametrices are obtained in terms of symbols taking values in algebras of BVPs on manifolds of corresponding lower singularity orders. Those refer to Boutet de Monvel's calculus of operators with the transmission property, see Boutet de Monvel (Acta Math 126:11-51, 1971) for the case of smooth boundary. On corner configuration operators act in spaces with multiple weights. We mainly study the case of upper left entries in the respective 2 x 2 operator block-matrices of such a calculus. Green operators in the sense of Boutet de Monvel (Acta Math 126:11-51, 1971) analogously appear in singular cases, and they are complemented by contributions of Mellin type. We formulate a result on ellipticity and the Fredholm property in weighted corner spaces, with parametrices of analogous kind. KW - Boutet de Monvel's calculus KW - Pseudo-differential operators KW - Singular cones KW - Mellin symbols with values in the edge calculus KW - Parametrices of elliptic operators KW - Kegel space Y1 - 2021 U6 - https://doi.org/10.1007/s12220-021-00614-3 SN - 1050-6926 SN - 1559-002X VL - 31 IS - 9 SP - 9199 EP - 9240 PB - Springer CY - New York ER - TY - THES A1 - Mauerberger, Stefan T1 - Correlation based Bayesian modeling T1 - Korrelationsbasierte Bayesianische Modellierung BT - with applications in travel time tomography, seismic source inversion and magnetic field modeling BT - mit Anwendungen in der Laufzeittomographie, Seismischer Quellinversion und Magnetfeldmodellierung N2 - The motivation for this work was the question of reliability and robustness of seismic tomography. The problem is that many earth models exist which can describe the underlying ground motion records equally well. Most algorithms for reconstructing earth models provide a solution, but rarely quantify their variability. If there is no way to verify the imaged structures, an interpretation is hardly reliable. The initial idea was to explore the space of equivalent earth models using Bayesian inference. However, it quickly became apparent that the rigorous quantification of tomographic uncertainties could not be accomplished within the scope of a dissertation. In order to maintain the fundamental concept of statistical inference, less complex problems from the geosciences are treated instead. This dissertation aims to anchor Bayesian inference more deeply in the geosciences and to transfer knowledge from applied mathematics. The underlying idea is to use well-known methods and techniques from statistics to quantify the uncertainties of inverse problems in the geosciences. This work is divided into three parts: Part I introduces the necessary mathematics and should be understood as a kind of toolbox. With a physical application in mind, this section provides a compact summary of all methods and techniques used. The introduction of Bayesian inference makes the beginning. Then, as a special case, the focus is on regression with Gaussian processes under linear transformations. The chapters on the derivation of covariance functions and the approximation of non-linearities are discussed in more detail. Part II presents two proof of concept studies in the field of seismology. The aim is to present the conceptual application of the introduced methods and techniques with moderate complexity. The example about traveltime tomography applies the approximation of non-linear relationships. The derivation of a covariance function using the wave equation is shown in the example of a damped vibrating string. With these two synthetic applications, a consistent concept for the quantification of modeling uncertainties has been developed. Part III presents the reconstruction of the Earth's archeomagnetic field. This application uses the whole toolbox presented in Part I and is correspondingly complex. The modeling of the past 1000 years is based on real data and reliably quantifies the spatial modeling uncertainties. The statistical model presented is widely used and is under active development. The three applications mentioned are intentionally kept flexible to allow transferability to similar problems. The entire work focuses on the non-uniqueness of inverse problems in the geosciences. It is intended to be of relevance to those interested in the concepts of Bayesian inference. N2 - Die Motivation für diese Arbeit war die Frage nach Verlässlichkeit und Belastbarkeit der seismischen Tomographie. Das Problem besteht darin, dass sehr viele Erdmodelle existieren welche die zugrundeliegenden seismischen Aufzeichnungen gleich gut beschreiben können. Die meisten Algorithmen zur Rekonstruktion von Erdmodellen liefern zwar eine Lösung, quantifizierten jedoch kaum deren Variabilität. Wenn es keine Möglichkeit gibt die abgebildeten Strukturen zu verifizieren, so ist eine Interpretation kaum verlässlich. Der ursprüngliche Gedanke war den Raum äquivalenter Erdmodelle mithilfe Bayesianische Inferenz zu erkunden. Es stellte sich jedoch schnell heraus, dass die vollständige Quantifizierung tomographischer Unsicherheiten im Rahmen einer Promotion nicht zu bewältigen ist. Um das wesentliche Konzept der statistischen Inferenz beizubehalten werden stattdessen weniger komplexe Problemstellungen aus den Geowissenschaften behandelt. Diese Dissertation hat das Ziel die Bayesianische Inferenz tiefer in den Geowissenschaften zu verankern und Wissen aus der angewandten Mathematik zu transferieren. Die zugrundeliegende Idee besteht darin auf bekannte Methoden und Techniken der Statistik zurückzugreifen um die Unsicherheiten inverser Probleme in den Geowissenschaften zu quantifizieren. Diese Arbeit gliedert sich in drei Teile: Teil I führt die notwendige Mathematik ein und soll als eine Art Werkzeugkasten verstanden werden. In Hinblick auf eine physikalische Anwendung bietet dieser Abschnitt eine kompakte Zusammenfassung aller eingesetzter Methoden und Techniken. Den Anfang macht die Einführung der Bayesianische Inferenz. Danach steht als Spezialfall die Regression mit Gauß-Prozessen unter linearen Transformationen im Vordergrund. Die Kapitel zur Herleitung von Kovarianzfunktionen und die Approximation von Nichtlinearitäten gehen etwas weiter in die Tiefe. Teil II präsentiert zwei Konzeptstudien aus dem Bereich der Seismologie. Ziel ist es bei moderater Komplexität die prinzipielle Anwendung der eingeführten Methoden und Techniken zu präsentieren. Das Beispiel zur Laufzeittomographie wendet die Näherungs\-methoden für nichtlineare Zusammenhänge an. Die Herleitung einer Kovarianzfunktion mithilfe der Wellengleichung ist am Beispiel der gedämpften Saitenschwingung gezeigt. Mit diesen beiden synthetischen Anwendungen wurde ein konsistentes Konzept zur Quantifizierung von Modellierungsunsicherheiten erarbeitet. Teil III präsentiert die Rekonstruktion des archeomagnetischen Feldes unserer Erde. Diese Anwendung nutzt den gesamten Werkzeugkasten aus Teil I und ist entsprechend umfangreich. Die Modellierung der vergangenen 1000 Jahre basiert auf echten Daten und quantifiziert zuverlässig die räumlichen Modellierungsunsicherheiten. Das präsentierte statistische Modell findet breite Anwendung und wird aktiv weiter entwickelt. Die drei genannten Anwendungen sind bewusst flexibel gehalten um die Übertragbarkeit auf ähnliche Problemstellungen zu ermöglichen. Die gesamte Arbeit legt den Fokus auf die nicht-Eindeutigkeit inverser Probleme in den Geowissenschaften. Sie will für all Jene von Relevanz sein, die sich für die Konzepte der Bayesianischen Inferenz interessieren. KW - statistical inference KW - Bayesian inversion KW - travel time tomography KW - seismic source inversion KW - magnetic field modeling KW - mit Anwendungen in der Laufzeittomographie, Seismischer Quellinversion und Magnetfeldmodellierung KW - Magnetfeldmodellierung KW - seismische Quellinversion KW - statistische Inferenz KW - Laufzeittomographie Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-537827 ER - TY - JOUR A1 - Eckert, Silvia A1 - Herden, Jasmin A1 - Stift, Marc A1 - Durka, Walter A1 - Kleunen, Mark van A1 - Joshi, Jasmin Radha T1 - Traces of genetic but not epigenetic adaptation in the invasive goldenrod Solidago canadensis despite the absence of population structure JF - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - Biological invasions may result from multiple introductions, which might compensate for reduced gene pools caused by bottleneck events, but could also dilute adaptive processes. A previous common-garden experiment showed heritable latitudinal clines in fitness-related traits in the invasive goldenrod Solidago canadensis in Central Europe. These latitudinal clines remained stable even in plants chemically treated with zebularine to reduce epigenetic variation. However, despite the heritability of traits investigated, genetic isolation-by-distance was non-significant. Utilizing the same specimens, we applied a molecular analysis of (epi)genetic differentiation with standard and methylation-sensitive (MSAP) AFLPs. We tested whether this variation was spatially structured among populations and whether zebularine had altered epigenetic variation. Additionally, we used genome scans to mine for putative outlier loci susceptible to selection processes in the invaded range. Despite the absence of isolation-by-distance, we found spatial genetic neighborhoods among populations and two AFLP clusters differentiating northern and southern Solidago populations. Genetic and epigenetic diversity were significantly correlated, but not linked to phenotypic variation. Hence, no spatial epigenetic patterns were detected along the latitudinal gradient sampled. Applying genome-scan approaches (BAYESCAN, BAYESCENV, RDA, and LFMM), we found 51 genetic and epigenetic loci putatively responding to selection. One of these genetic loci was significantly more frequent in populations at the northern range. Also, one epigenetic locus was more frequent in populations in the southern range, but this pattern was lost under zebularine treatment. Our results point to some genetic, but not epigenetic adaptation processes along a large-scale latitudinal gradient of S. canadensis in its invasive range. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1271 KW - AFLP KW - MSAP KW - cytosine methylation KW - spatial autocorrelation KW - genome scan Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-566758 SN - 1866-8372 SP - 1 EP - 17 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - GEN A1 - Böckmann, Christine A1 - Ritter, Christoph A1 - Cappelletti, David T1 - Mathematical tool for a closure study of aerosol microphysical property retrieval using lidar and photometer data T2 - IGARSS 2018 - 2018 IEEE International Geoscience and Remote Sensing Symposium N2 - We present a project combining lidar, photometer and particle counter data with a regularization software tool for a closure study of aerosol microphysical property retrieval. In a first step only lidar data are used to retrieve the particle size distribution (PSD). Secondly, photometer data are added, which results in a good consistency of the retrieved PSDs. Finally, those retrieved PSDs may be compared with the measured PSD from a particle counter. The data here were taken in Ny Alesund, Svalbard, as an example. KW - Aerosol KW - Raman lidar KW - photometer KW - inversion KW - regularization KW - particle microphysics Y1 - 2018 SN - 978-1-5386-7150-4 U6 - https://doi.org/10.1109/IGARSS.2018.8518674 SN - 2153-6996 SP - 5575 EP - 5578 PB - IEEE CY - New York ER - TY - JOUR A1 - Dube, Jonas A1 - Böckmann, Christine A1 - Ritter, Christoph T1 - Lidar-Derived Aerosol Properties from Ny-Ålesund, Svalbard during the MOSAiC Spring 2020 JF - Remote sensing / Molecular Diversity Preservation International (MDPI) N2 - In this work, we present Raman lidar data (from a Nd:YAG operating at 355 nm, 532 nm and 1064 nm) from the international research village Ny-Alesund for the time period of January to April 2020 during the Arctic haze season of the MOSAiC winter. We present values of the aerosol backscatter, the lidar ratio and the backscatter Angstrom exponent, though the latter depends on wavelength. The aerosol polarization was generally below 2%, indicating mostly spherical particles. We observed that events with high backscatter and high lidar ratio did not coincide. In fact, the highest lidar ratios (LR > 75 sr at 532 nm) were already found by January and may have been caused by hygroscopic growth, rather than by advection of more continental aerosol. Further, we performed an inversion of the lidar data to retrieve a refractive index and a size distribution of the aerosol. Our results suggest that in the free troposphere (above approximate to 2500 m) the aerosol size distribution is quite constant in time, with dominance of small particles with a modal radius well below 100 nm. On the contrary, below approximate to 2000 m in altitude, we frequently found gradients in aerosol backscatter and even size distribution, sometimes in accordance with gradients of wind speed, humidity or elevated temperature inversions, as if the aerosol was strongly modified by vertical displacement in what we call the "mechanical boundary layer". Finally, we present an indication that additional meteorological soundings during MOSAiC campaign did not necessarily improve the fidelity of air backtrajectories. KW - aerosol KW - Arctic haze KW - lidar KW - microphysical properties KW - backtrajectories; KW - Ny-Alesund KW - Svalbard KW - MOSAiC KW - aerosol-boundary layer interactions Y1 - 2022 U6 - https://doi.org/10.3390/rs14112578 SN - 2072-4292 VL - 14 IS - 11 PB - MDPI CY - Basel ER - TY - JOUR A1 - Pornsawad, Pornsarp A1 - Sapsakul, Nantawan A1 - Böckmann, Christine T1 - A modified asymptotical regularization of nonlinear ill-posed problems JF - Mathematics N2 - In this paper, we investigate the continuous version of modified iterative Runge–Kutta-type methods for nonlinear inverse ill-posed problems proposed in a previous work. The convergence analysis is proved under the tangential cone condition, a modified discrepancy principle, i.e., the stopping time T is a solution of ∥𝐹(𝑥𝛿(𝑇))−𝑦𝛿∥=𝜏𝛿+ for some 𝛿+>𝛿, and an appropriate source condition. We yield the optimal rate of convergence. KW - nonlinear operator KW - regularization KW - discrepancy principle KW - asymptotic method KW - optimal rate Y1 - 2019 U6 - https://doi.org/10.3390/math7050419 SN - 2227-7390 VL - 7 PB - MDPI CY - Basel, Schweiz ET - 5 ER - TY - INPR A1 - Pornsawad, Pornsarp A1 - Böckmann, Christine T1 - Modified iterative Runge-Kutta-type methods for nonlinear ill-posed problems N2 - This work is devoted to the convergence analysis of a modified Runge-Kutta-type iterative regularization method for solving nonlinear ill-posed problems under a priori and a posteriori stopping rules. The convergence rate results of the proposed method can be obtained under Hölder-type source-wise condition if the Fréchet derivative is properly scaled and locally Lipschitz continuous. Numerical results are achieved by using the Levenberg-Marquardt and Radau methods. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 3 (2014) 7 KW - ill-posed problems KW - Runge-Kutta methods KW - regularization methods KW - Hölder-type source condition KW - stopping rules Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-70834 SN - 2193-6943 VL - 3 IS - 7 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - JOUR A1 - Pornsawad, Pornsarp A1 - Böckmann, Christine A1 - Panitsupakamon, Wannapa T1 - The Levenberg–Marquardt regularization for the backward heat equation with fractional derivative JF - Electronic transactions on numerical analysis - ETNA N2 - The backward heat problem with time-fractional derivative in Caputo's sense is studied. The inverse problem is severely ill-posed in the case when the fractional order is close to unity. A Levenberg-Marquardt method with a new a posteriori stopping rule is investigated. We show that optimal order can be obtained for the proposed method under a Hölder-type source condition. Numerical examples for one and two dimensions are provided. KW - ill-posed problems KW - time-fractional derivative KW - backward heat problem KW - Levenberg-Marquardt method KW - a posteriori stopping rule KW - optimal order Y1 - 2022 SN - 978-3-7001-8258-0 U6 - https://doi.org/10.1553/etna_vol57s67 SN - 1068-9613 VL - 57 SP - 67 EP - 79 PB - Kent State University CY - Kent ER - TY - GEN A1 - Perera, Upeksha A1 - Böckmann, Christine T1 - Solutions of direct and inverse even-order Sturm-Liouville problems using Magnus expansion T2 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - In this paper Lie group method in combination with Magnus expansion is utilized to develop a universal method applicable to solving a Sturm–Liouville problem (SLP) of any order with arbitrary boundary conditions. It is shown that the method has ability to solve direct regular (and some singular) SLPs of even orders (tested for up to eight), with a mix of (including non-separable and finite singular endpoints) boundary conditions, accurately and efficiently. The present technique is successfully applied to overcome the difficulties in finding suitable sets of eigenvalues so that the inverse SLP problem can be effectively solved. The inverse SLP algorithm proposed by Barcilon (1974) is utilized in combination with the Magnus method so that a direct SLP of any (even) order and an inverse SLP of order two can be solved effectively. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1336 KW - higher-order Sturm–Liouville problems KW - inverse Sturm–Liouville problems KW - Magnus expansion Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-473414 SN - 1866-8372 IS - 1336 ER - TY - GEN A1 - Pornsawad, Pornsarp A1 - Sapsakul, Nantawan A1 - Böckmann, Christine T1 - A modified asymptotical regularization of nonlinear ill-posed problems T2 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - In this paper, we investigate the continuous version of modified iterative Runge–Kutta-type methods for nonlinear inverse ill-posed problems proposed in a previous work. The convergence analysis is proved under the tangential cone condition, a modified discrepancy principle, i.e., the stopping time T is a solution of ∥𝐹(𝑥𝛿(𝑇))−𝑦𝛿∥=𝜏𝛿+ for some 𝛿+>𝛿, and an appropriate source condition. We yield the optimal rate of convergence. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1335 KW - nonlinear operator KW - regularization KW - discrepancy principle KW - asymptotic method KW - optimal rate Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-473433 SN - 1866-8372 IS - 1335 ER - TY - JOUR A1 - Wormell, Caroline L. A1 - Reich, Sebastian T1 - Spectral convergence of diffusion maps BT - Improved error bounds and an alternative normalization JF - SIAM journal on numerical analysis / Society for Industrial and Applied Mathematics N2 - Diffusion maps is a manifold learning algorithm widely used for dimensionality reduction. Using a sample from a distribution, it approximates the eigenvalues and eigenfunctions of associated Laplace-Beltrami operators. Theoretical bounds on the approximation error are, however, generally much weaker than the rates that are seen in practice. This paper uses new approaches to improve the error bounds in the model case where the distribution is supported on a hypertorus. For the data sampling (variance) component of the error we make spatially localized compact embedding estimates on certain Hardy spaces; we study the deterministic (bias) component as a perturbation of the Laplace-Beltrami operator's associated PDE and apply relevant spectral stability results. Using these approaches, we match long-standing pointwise error bounds for both the spectral data and the norm convergence of the operator discretization. We also introduce an alternative normalization for diffusion maps based on Sinkhorn weights. This normalization approximates a Langevin diffusion on the sample and yields a symmetric operator approximation. We prove that it has better convergence compared with the standard normalization on flat domains, and we present a highly efficient rigorous algorithm to compute the Sinkhorn weights. KW - diffusion maps KW - graph Laplacian KW - Sinkhorn problem KW - kernel methods Y1 - 2021 U6 - https://doi.org/10.1137/20M1344093 SN - 0036-1429 SN - 1095-7170 VL - 59 IS - 3 SP - 1687 EP - 1734 PB - Society for Industrial and Applied Mathematics CY - Philadelphia ER - TY - JOUR A1 - Keller, Matthias A1 - Liu, Shiping A1 - Peyerimhoff, Norbert T1 - A note on eigenvalue bounds for non-compact manifolds JF - Mathematische Nachrichten N2 - In this article we prove upper bounds for the Laplace eigenvalues lambda(k) below the essential spectrum for strictly negatively curved Cartan-Hadamard manifolds. Our bound is given in terms of k(2) and specific geometric data of the manifold. This applies also to the particular case of non-compact manifolds whose sectional curvature tends to -infinity, where no essential spectrum is present due to a theorem of Donnelly/Li. The result stands in clear contrast to Laplacians on graphs where such a bound fails to be true in general. KW - Cheeger inequality KW - eigenvalues KW - Laplacian KW - negative curvature KW - Riemannian manifold Y1 - 2021 U6 - https://doi.org/10.1002/mana.201900209 SN - 0025-584X SN - 1522-2616 VL - 294 IS - 6 SP - 1134 EP - 1139 PB - Wiley-VCH CY - Weinheim ER - TY - JOUR A1 - Peng, Junhao A1 - Sandev, Trifce A1 - Kocarev, Ljupco T1 - First encounters on Bethe lattices and Cayley trees JF - Communications in nonlinear science & numerical simulation N2 - In this work we consider the first encounter problems between a fixed and/or mobile target A and a moving trap B on Bethe lattices and Cayley trees. The survival probabilities (SPs) of the target A on the both kinds of structures are considered analytically and compared. On Bethe lattices, the results show that the fixed target will still prolong its survival time, whereas, on Cayley trees, there are some initial positions where the target should move to prolong its survival time. The mean first encounter time (MFET) for mobile target A is evaluated numerically and compared with the mean first passage time (MFPT) for the fixed target A. Different initial settings are addressed and clear boundaries are obtained. These findings are helpful for optimizing the strategy to prolong the survival time of the target or to speed up the search process on Cayley trees, in relation to the target's movement and the initial position configuration of the two walkers. We also present a new method, which uses a small amount of memory, for simulating random walks on Cayley trees. (C) 2020 Elsevier B.V. All rights reserved. KW - Random walks KW - Survival probability KW - Mean first encounter time KW - Bethe KW - lattices KW - Cayley trees Y1 - 2021 U6 - https://doi.org/10.1016/j.cnsns.2020.105594 SN - 1007-5704 SN - 1878-7274 VL - 95 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Andjelkovic, Marko A1 - Simevski, Aleksandar A1 - Chen, Junchao A1 - Schrape, Oliver A1 - Stamenkovic, Zoran A1 - Krstić, Miloš A1 - Ilic, Stefan A1 - Ristic, Goran A1 - Jaksic, Aleksandar A1 - Vasovic, Nikola A1 - Duane, Russell A1 - Palma, Alberto J. A1 - Lallena, Antonio M. A1 - Carvajal, Miguel A. T1 - A design concept for radiation hardened RADFET readout system for space applications JF - Microprocessors and microsystems N2 - Instruments for measuring the absorbed dose and dose rate under radiation exposure, known as radiation dosimeters, are indispensable in space missions. They are composed of radiation sensors that generate current or voltage response when exposed to ionizing radiation, and processing electronics for computing the absorbed dose and dose rate. Among a wide range of existing radiation sensors, the Radiation Sensitive Field Effect Transistors (RADFETs) have unique advantages for absorbed dose measurement, and a proven record of successful exploitation in space missions. It has been shown that the RADFETs may be also used for the dose rate monitoring. In that regard, we propose a unique design concept that supports the simultaneous operation of a single RADFET as absorbed dose and dose rate monitor. This enables to reduce the cost of implementation, since the need for other types of radiation sensors can be minimized or eliminated. For processing the RADFET's response we propose a readout system composed of analog signal conditioner (ASC) and a self-adaptive multiprocessing system-on-chip (MPSoC). The soft error rate of MPSoC is monitored in real time with embedded sensors, allowing the autonomous switching between three operating modes (high-performance, de-stress and fault-tolerant), according to the application requirements and radiation conditions. KW - RADFET KW - Radiation hardness KW - Absorbed dose KW - Dose rate KW - Self-adaptive MPSoC Y1 - 2022 U6 - https://doi.org/10.1016/j.micpro.2022.104486 SN - 0141-9331 SN - 1872-9436 VL - 90 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Chang, Der-Chen A1 - Schulze, Bert-Wolfgang T1 - Corner spaces and Mellin quantization JF - Journal of nonlinear and convex analysis : an international journal N2 - Manifolds with corners in the present investigation are non-smooth configurations - specific stratified spaces - with an incomplete metric such as cones, manifolds with edges, or corners of piecewise smooth domains in Euclidean space. We focus here on operators on such "corner manifolds" of singularity order <= 2, acting in weighted corner Sobolev spaces. The corresponding corner degenerate pseudo-differential operators are formulated via Mellin quantizations, and they also make sense on infinite singular cones. KW - Mellin quantizations KW - operator-valued symbols KW - weighted edge and corner spaces Y1 - 2018 SN - 1345-4773 SN - 1880-5221 VL - 19 IS - 2 SP - 179 EP - 195 PB - Yokohama Publishers CY - Yokohama ER - TY - JOUR A1 - Chang, Der-Chen A1 - Schulze, Bert-Wolfgang T1 - Ellipticity on spaces with higher singularities JF - Science China Mathematics N2 - We study corner-degenerate pseudo-differential operators of any singularity order and develop ellipticity based on the principal symbolic hierarchy, associated with the stratification of the underlying space. We construct parametrices within the calculus and discuss the aspect of additional trace and potential conditions along lower-dimensional strata. KW - pseudo-differential operators KW - operator-valued symbols KW - Fourier and Mellin transforms Y1 - 2017 U6 - https://doi.org/10.1007/s11425-016-0519-9 SN - 1674-7283 SN - 1869-1862 VL - 60 IS - 11 SP - 2053 EP - 2076 PB - Science China Press CY - Beijing ER - TY - JOUR A1 - Khalil, Sara A1 - Schulze, Bert-Wolfgang T1 - Boundary problems on a manifold with edge JF - Asian-European Journal of Mathematics N2 - We establish a calculus of boundary value problems (BVPs) on a manifold N with boundary and edge, based on Boutet de Monvel’s theory of BVPs in the case of a smooth boundary and on the edge calculus, where in the present case the model cone has a base which is a compact manifold with boundary. The corresponding calculus with boundary and edge is a unification of both structures and controls different operator-valued symbolic structures, in order to obtain ellipticity and parametrices. KW - manifolds with edge and boundary KW - distribution with asymptotics KW - ellipticity KW - Fredholm property Y1 - 2017 U6 - https://doi.org/10.1142/S1793557117500875 SN - 1793-5571 SN - 1793-7183 VL - 10 IS - 2 PB - World Scientific CY - Singapore ER -