@article{DereudreHoudebert2018,
  author    = {Dereudre, David and Houdebert, Pierre},
  title     = {Sharp phase transition for the continuum Widom-Rowlinson model},
  series = {Annales de l'Institut Henri Poincar{\´e}. B, Probability and statistics},
  volume    = {57},
  journal   = {Annales de l'Institut Henri Poincar{\´e}. B, Probability and statistics},
  number    = {1},
  publisher = {Association des Publications de l'Institut Henri Poincar{\´e}},
  address   = {Bethesda, Md.},
  issn      = {0246-0203},
  doi       = {10.1214/20-AIHP1082},
  pages     = {387 -- 407},
  year      = {2018},
  abstract  = {The Widom-Rowlinson model (or the Area-interaction model) is a Gibbs point process in R-d with the formal Hamiltonian defined as the volume of Ux epsilon omega B1(x), where. is a locally finite configuration of points and B-1(x) denotes the unit closed ball centred at x. The model is also tuned by two other parameters: the activity z > 0 related to the intensity of the process and the inverse temperature beta >= 0 related to the strength of the interaction. In the present paper we investigate the phase transition of the model in the point of view of percolation theory and the liquid-gas transition. First, considering the graph connecting points with distance smaller than 2r > 0, we show that for any beta >= 0, there exists 0 <(similar to a)(zc) (beta, r) < +infinity such that an exponential decay of connectivity at distance n occurs in the subcritical phase (i.e. z <(similar to a)(zc) (beta, r)) and a linear lower bound of the connection at infinity holds in the supercritical case (i.e. z >(similar to a)(zc) (beta, r)). These results are in the spirit of recent works using the theory of randomised tree algorithms (Probab. Theory Related Fields 173 (2019) 479-490, Ann. of Math. 189 (2019) 75-99, Duminil-Copin, Raoufi and Tassion (2018)). Secondly we study a standard liquid-gas phase transition related to the uniqueness/non-uniqueness of Gibbs states depending on the parameters z, beta. Old results (Phys. Rev. Lett. 27 (1971) 1040-1041, J. Chem. Phys. 52 (1970) 1670-1684) claim that a non-uniqueness regime occurs for z = beta large enough and it is conjectured that the uniqueness should hold outside such an half line ( z = beta >= beta(c) > 0). We solve partially this conjecture in any dimension by showing that for beta large enough the non-uniqueness holds if and only if z = beta. We show also that this critical value z = beta corresponds to the percolation threshold (similar to a)(zc) (beta, r) = beta for beta large enough, providing a straight connection between these two notions of phase transition.},
  language  = {en}
}
@article{ChangSchulze2018,
  author    = {Chang, Der-Chen and Schulze, Bert-Wolfgang},
  title     = {Corner spaces and Mellin quantization},
  series = {Journal of nonlinear and convex analysis : an international journal},
  volume    = {19},
  journal   = {Journal of nonlinear and convex analysis : an international journal},
  number    = {2},
  publisher = {Yokohama Publishers},
  address   = {Yokohama},
  issn      = {1345-4773},
  pages     = {179 -- 195},
  year      = {2018},
  abstract  = {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.},
  language  = {en}
}
@article{GomezHartung2018,
  author    = {Gomez, Christophe and Hartung, Niklas},
  title     = {Stochastic and deterministic models for the metastatic emission process},
  series = {Cancer Systems Biology},
  volume    = {1711},
  journal   = {Cancer Systems Biology},
  publisher = {Humana Press Inc.},
  address   = {Totowa},
  isbn      = {978-1-4939-7493-1},
  issn      = {1064-3745},
  doi       = {10.1007/978-1-4939-7493-1_10},
  pages     = {193 -- 224},
  year      = {2018},
  abstract  = {Although the detection of metastases radically changes prognosis of and treatment decisions for a cancer patient, clinically undetectable micrometastases hamper a consistent classification into localized or metastatic disease. This chapter discusses mathematical modeling efforts that could help to estimate the metastatic risk in such a situation. We focus on two approaches: (1) a stochastic framework describing metastatic emission events at random times, formalized via Poisson processes, and (2) a deterministic framework describing the micrometastatic state through a size-structured density function in a partial differential equation model. Three aspects are addressed in this chapter. First, a motivation for the Poisson process framework is presented and modeling hypotheses and mechanisms are introduced. Second, we extend the Poisson model to account for secondary metastatic emission. Third, we highlight an inherent crosslink between the stochastic and deterministic frameworks and discuss its implications. For increased accessibility the chapter is split into an informal presentation of the results using a minimum of mathematical formalism and a rigorous mathematical treatment for more theoretically interested readers.},
  language  = {en}
}
@article{deWiljesReichStannat2018,
  author    = {de Wiljes, Jana and Reich, Sebastian and Stannat, Wilhelm},
  title     = {Long-Time stability and accuracy of the ensemble Kalman-Bucy Filter for fully observed processes and small measurement noise},
  series = {SIAM Journal on Applied Dynamical Systems},
  volume    = {17},
  journal   = {SIAM Journal on Applied Dynamical Systems},
  number    = {2},
  publisher = {Society for Industrial and Applied Mathematics},
  address   = {Philadelphia},
  issn      = {1536-0040},
  doi       = {10.1137/17M1119056},
  pages     = {1152 -- 1181},
  year      = {2018},
  abstract  = {The ensemble Kalman filter has become a popular data assimilation technique in the geosciences. However, little is known theoretically about its long term stability and accuracy. In this paper, we investigate the behavior of an ensemble Kalman-Bucy filter applied to continuous-time filtering problems. We derive mean field limiting equations as the ensemble size goes to infinity as well as uniform-in-time accuracy and stability results for finite ensemble sizes. The later results require that the process is fully observed and that the measurement noise is small. We also demonstrate that our ensemble Kalman-Bucy filter is consistent with the classic Kalman-Bucy filter for linear systems and Gaussian processes. We finally verify our theoretical findings for the Lorenz-63 system.},
  language  = {en}
}
@article{BourneCushingLiuetal.2018,
  author    = {Bourne, D. P. and Cushing, D. and Liu, S. and M{\"u}nch, Florentin and Peyerimhoff, Norbert},
  title     = {Ollivier-Ricci idleness functions of graphs},
  series = {SIAM Journal on Discrete Mathematics},
  volume    = {32},
  journal   = {SIAM Journal on Discrete Mathematics},
  number    = {2},
  publisher = {Society for Industrial and Applied Mathematics},
  address   = {Philadelphia},
  issn      = {0895-4801},
  doi       = {10.1137/17M1134469},
  pages     = {1408 -- 1424},
  year      = {2018},
  abstract  = {We study the Ollivier-Ricci curvature of graphs as a function of the chosen idleness. We show that this idleness function is concave and piecewise linear with at most three linear parts, and at most two linear parts in the case of a regular graph. We then apply our result to show that the idleness function of the Cartesian product of two regular graphs is completely determined by the idleness functions of the factors.},
  language  = {en}
}
@article{WangLiZhangetal.2018,
  author    = {Wang, Guang and Li, Pei-zhi and Zhang, Shi-yao and Zhong, Shan and Chu, Chang and Zeng, Shufei and Yan, Yu and Cheng, Xin and Chuai, Manli and Hocher, Berthold and Yang, Xuesong},
  title     = {Lipopolysaccharides (LPS) Induced Angiogenesis During Chicken Embryogenesis is Abolished by Combined ETA/ETB Receptor Blockade},
  series = {Cellular physiology and biochemistry : international journal of experimental cellular physiology, biochemistry and pharmacology},
  volume    = {48},
  journal   = {Cellular physiology and biochemistry : international journal of experimental cellular physiology, biochemistry and pharmacology},
  number    = {5},
  publisher = {Karger},
  address   = {Basel},
  issn      = {1015-8987},
  doi       = {10.1159/000492547},
  pages     = {2084 -- 2090},
  year      = {2018},
  abstract  = {Background/Aims: Angiogenesis plays a key role during embryonic development. The vascular endothelin (ET) system is involved in the regulation of angiogenesis. Lipopolysaccharides (LPS) could induce angiogenesis. The effects of ET blockers on baseline and LPS-stimulated angiogenesis during embryonic development remain unknown so far. Methods: The blood vessel density (BVD) of chorioallantoic membranes (CAMs), which were treated with saline (control), LPS, and/or BQ123 and the ETB blocker BQ788, were quantified and analyzed using an IPP 6.0 image analysis program. Moreover, the expressions of ET-1, ET-2, ET3, ET receptor A (ETRA), ET receptor B (ETRB) and VEGFR2 mRNA during embryogenesis were analyzed by semi-quantitative RT-PCR. Results: All components of the ET system are detectable during chicken embryogenesis. LPS increased angiogenesis substantially. This process was completely blocked by the treatment of a combination of the ETA receptor blockers-BQ123 and the ETB receptor blocker BQ788. This effect was accompanied by a decrease in ETRA, ETRB, and VEGFR2 gene expression. However, the baseline angiogenesis was not affected by combined ETA/ETB receptor blockade. Conclusion: During chicken embryogenesis, the LPS-stimulated angiogenesis, but not baseline angiogenesis, is sensitive to combined ETA/ETB receptor blockade.},
  language  = {en}
}
@misc{BlanchardScott2018,
  author    = {Blanchard, Gilles and Scott, Clayton},
  title     = {Corrigendum to: Classification with asymmetric label noise},
  series = {Electronic journal of statistics},
  volume    = {12},
  journal   = {Electronic journal of statistics},
  number    = {1},
  publisher = {Institute of Mathematical Statistics},
  address   = {Cleveland},
  issn      = {1935-7524},
  doi       = {10.1214/18-EJS1422},
  pages     = {1779 -- 1781},
  year      = {2018},
  abstract  = {We point out a flaw in Lemma 15 of [1]. We also indicate how the main results of that section are still valid using a modified argument.},
  language  = {en}
}
@article{MeraStepanenkoTarkhanov2018,
  author    = {Mera, Azal and Stepanenko, Vitaly A. and Tarkhanov, Nikolai Nikolaevich},
  title     = {Successive approximation for the inhomogeneous burgers equation},
  series = {Journal of Siberian Federal University : Mathematics \& Physics},
  volume    = {11},
  journal   = {Journal of Siberian Federal University : Mathematics \& Physics},
  number    = {4},
  publisher = {Siberian Federal University},
  address   = {Krasnoyarsk},
  issn      = {1997-1397},
  doi       = {10.17516/1997-1397-2018-11-4-519-531},
  pages     = {519 -- 531},
  year      = {2018},
  abstract  = {The inhomogeneous Burgers equation is a simple form of the Navier-Stokes equations. From the analytical point of view, the inhomogeneous form is poorly studied, the complete analytical solution depending closely on the form of the nonhomogeneous term.},
  language  = {en}
}
@article{BlanchardHoffmannReiss2018,
  author    = {Blanchard, Gilles and Hoffmann, Marc and Reiss, Markus},
  title     = {Optimal adaptation for early stopping in statistical inverse problems},
  series = {SIAM/ASA Journal on Uncertainty Quantification},
  volume    = {6},
  journal   = {SIAM/ASA Journal on Uncertainty Quantification},
  number    = {3},
  publisher = {Society for Industrial and Applied Mathematics},
  address   = {Philadelphia},
  issn      = {2166-2525},
  doi       = {10.1137/17M1154096},
  pages     = {1043 -- 1075},
  year      = {2018},
  abstract  = {For linear inverse problems Y = A mu + zeta, it is classical to recover the unknown signal mu by iterative regularization methods ((mu) over cap,(m) = 0,1, . . .) and halt at a data-dependent iteration tau using some stopping rule, typically based on a discrepancy principle, so that the weak (or prediction) squared-error parallel to A((mu) over cap (()(tau)) - mu)parallel to(2) is controlled. In the context of statistical estimation with stochastic noise zeta, we study oracle adaptation (that is, compared to the best possible stopping iteration) in strong squared- error E[parallel to((mu) over cap (()(tau)) - mu)parallel to(2)]. For a residual-based stopping rule oracle adaptation bounds are established for general spectral regularization methods. The proofs use bias and variance transfer techniques from weak prediction error to strong L-2-error, as well as convexity arguments and concentration bounds for the stochastic part. Adaptive early stopping for the Landweber method is studied in further detail and illustrated numerically.},
  language  = {en}
}
@misc{BoeckmannRitterCappelletti2018,
  author    = {B{\"o}ckmann, Christine and Ritter, Christoph and Cappelletti, David},
  title     = {Mathematical tool for a closure study of aerosol microphysical property retrieval using lidar and photometer data},
  series = {IGARSS 2018 - 2018 IEEE International Geoscience and Remote Sensing Symposium},
  journal   = {IGARSS 2018 - 2018 IEEE International Geoscience and Remote Sensing Symposium},
  publisher = {IEEE},
  address   = {New York},
  isbn      = {978-1-5386-7150-4},
  issn      = {2153-6996},
  doi       = {10.1109/IGARSS.2018.8518674},
  pages     = {5575 -- 5578},
  year      = {2018},
  abstract  = {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.},
  language  = {en}
}