@article{7389,
abstract = {Recently Kloeckner described the structure of the isometry group of the quadratic Wasserstein space W_2(R^n). It turned out that the case of the real line is exceptional in the sense that there exists an exotic isometry flow. Following this line of investigation, we compute Isom(W_p(R)), the isometry group of the Wasserstein space
W_p(R) for all p \in [1,\infty) \setminus {2}. We show that W_2(R) is also exceptional regarding the
parameter p: W_p(R) is isometrically rigid if and only if p is not equal to 2. Regarding the underlying
space, we prove that the exceptionality of p = 2 disappears if we replace R by the compact
interval [0,1]. Surprisingly, in that case, W_p([0,1]) is isometrically rigid if and only if
p is not equal to 1. Moreover, W_1([0,1]) admits isometries that split mass, and Isom(W_1([0,1]))
cannot be embedded into Isom(W_1(R)).},
author = {Geher, Gyorgy Pal and Titkos, Tamas and Virosztek, Daniel},
issn = {10886850},
journal = {Transactions of the American Mathematical Society},
keywords = {Wasserstein space, isometric embeddings, isometric rigidity, exotic isometry flow},
number = {8},
pages = {5855--5883},
publisher = {American Mathematical Society},
title = {{Isometric study of Wasserstein spaces - the real line}},
doi = {10.1090/tran/8113},
volume = {373},
year = {2020},
}
@inbook{74,
abstract = {We study the Gromov waist in the sense of t-neighborhoods for measures in the Euclidean space, motivated by the famous theorem of Gromov about the waist of radially symmetric Gaussian measures. In particular, it turns our possible to extend Gromov’s original result to the case of not necessarily radially symmetric Gaussian measure. We also provide examples of measures having no t-neighborhood waist property, including a rather wide class
of compactly supported radially symmetric measures and their maps into the Euclidean space of dimension at least 2.
We use a simpler form of Gromov’s pancake argument to produce some estimates of t-neighborhoods of (weighted) volume-critical submanifolds in the spirit of the waist theorems, including neighborhoods of algebraic manifolds in the complex projective space. In the appendix of this paper we provide for reader’s convenience a more detailed explanation of the Caffarelli theorem that we use to handle not necessarily radially symmetric Gaussian
measures.},
author = {Akopyan, Arseniy and Karasev, Roman},
booktitle = {Geometric Aspects of Functional Analysis},
editor = {Klartag, Bo'az and Milman, Emanuel},
isbn = {9783030360191},
issn = {16179692},
pages = {1--27},
publisher = {Springer Nature},
title = {{Gromov's waist of non-radial Gaussian measures and radial non-Gaussian measures}},
doi = {10.1007/978-3-030-36020-7_1},
volume = {2256},
year = {2020},
}
@article{7416,
abstract = {Earlier, we demonstrated that transcript levels of METAL TOLERANCE PROTEIN2 (MTP2) and of HEAVY METAL ATPase2 (HMA2) increase strongly in roots of Arabidopsis upon prolonged zinc (Zn) deficiency and respond to shoot physiological Zn status, and not to the local Zn status in roots. This provided evidence for shoot-to-root communication in the acclimation of plants to Zn deficiency. Zn-deficient soils limit both the yield and quality of agricultural crops and can result in clinically relevant nutritional Zn deficiency in human populations. Implementing Zn deficiency during cultivation of the model plant Arabidopsis thaliana on agar-solidified media is difficult because trace element contaminations are present in almost all commercially available agars. Here, we demonstrate root morphological acclimations to Zn deficiency on agar-solidified medium following the effective removal of contaminants. These advancements allow reproducible phenotyping toward understanding fundamental plant responses to deficiencies of Zn and other essential trace elements.},
author = {Sinclair, Scott A and Krämer, U.},
issn = {1559-2324},
journal = {Plant Signaling & Behavior},
number = {1},
publisher = {Informa UK Limited},
title = {{Generation of effective zinc-deficient agar-solidified media allows identification of root morphology changes in response to zinc limitation}},
doi = {10.1080/15592324.2019.1687175},
volume = {15},
year = {2020},
}
@article{7417,
abstract = {Previously, we reported that the allelic de-etiolated by zinc (dez) and trichome birefringence (tbr) mutants exhibit photomorphogenic development in the dark, which is enhanced by high Zn. TRICHOME BIREFRINGENCE-LIKE proteins had been implicated in transferring acetyl groups to various hemicelluloses. Pectin O-acetylation levels were lower in dark-grown dez seedlings than in the wild type. We observed Zn-enhanced photomorphogenesis in the dark also in the reduced wall acetylation 2 (rwa2-3) mutant, which exhibits lowered O-acetylation levels of cell wall macromolecules including pectins and xyloglucans, supporting a role for cell wall macromolecule O-acetylation in the photomorphogenic phenotypes of rwa2-3 and dez. Application of very short oligogalacturonides (vsOGs) restored skotomorphogenesis in dark-grown dez and rwa2-3. Here we demonstrate that in dez, O-acetylation of non-pectin cell wall components, notably of xyloglucan, is enhanced. Our results highlight the complexity of cell wall homeostasis and indicate against an influence of xyloglucan O-acetylation on light-dependent seedling development.},
author = {Sinclair, Scott A and Gille, S. and Pauly, M. and Krämer, U.},
issn = {1559-2324},
journal = {Plant Signaling & Behavior},
number = {1},
publisher = {Informa UK Limited},
title = {{Regulation of acetylation of plant cell wall components is complex and responds to external stimuli}},
doi = {10.1080/15592324.2019.1687185},
volume = {15},
year = {2020},
}
@article{7426,
abstract = {This paper presents a novel abstraction technique for analyzing Lyapunov and asymptotic stability of polyhedral switched systems. A polyhedral switched system is a hybrid system in which the continuous dynamics is specified by polyhedral differential inclusions, the invariants and guards are specified by polyhedral sets and the switching between the modes do not involve reset of variables. A finite state weighted graph abstracting the polyhedral switched system is constructed from a finite partition of the state–space, such that the satisfaction of certain graph conditions, such as the absence of cycles with product of weights on the edges greater than (or equal) to 1, implies the stability of the system. However, the graph is in general conservative and hence, the violation of the graph conditions does not imply instability. If the analysis fails to establish stability due to the conservativeness in the approximation, a counterexample (cycle with product of edge weights greater than or equal to 1) indicating a potential reason for the failure is returned. Further, a more precise approximation of the switched system can be constructed by considering a finer partition of the state–space in the construction of the finite weighted graph. We present experimental results on analyzing stability of switched systems using the above method.},
author = {Garcia Soto, Miriam and Prabhakar, Pavithra},
issn = {1751570X},
journal = {Nonlinear Analysis: Hybrid Systems},
number = {5},
publisher = {Elsevier},
title = {{Abstraction based verification of stability of polyhedral switched systems}},
doi = {10.1016/j.nahs.2020.100856},
volume = {36},
year = {2020},
}