TY - JOUR
AB - We give a Wong-Zakai type characterisation of the solutions of quasilinear heat equations driven by space-time white noise in 1 + 1 dimensions. In order to show that the renormalisation counterterms are local in the solution, a careful arrangement of a few hundred terms is required. The main tool in this computation is a general ‘integration by parts’ formula that provides a number of linear identities for the renormalisation constants.
AU - Gerencser, Mate
ID - 7388
JF - Annales de l'Institut Henri Poincaré C, Analyse non linéaire
SN - 0294-1449
TI - Nondivergence form quasilinear heat equations driven by space-time white noise
ER -
TY - JOUR
AB - 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)).
AU - Geher, Gyorgy Pal
AU - Titkos, Tamas
AU - Virosztek, Daniel
ID - 7389
IS - 8
JF - Transactions of the American Mathematical Society
KW - Wasserstein space
KW - isometric embeddings
KW - isometric rigidity
KW - exotic isometry flow
SN - 00029947
TI - Isometric study of Wasserstein spaces - the real line
VL - 373
ER -
TY - CHAP
AB - 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.
AU - Akopyan, Arseniy
AU - Karasev, Roman
ED - Klartag, Bo'az
ED - Milman, Emanuel
ID - 74
SN - 00758434
T2 - Geometric Aspects of Functional Analysis
TI - Gromov's waist of non-radial Gaussian measures and radial non-Gaussian measures
VL - 2256
ER -
TY - JOUR
AB - 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.
AU - Sinclair, Scott A
AU - Krämer, U.
ID - 7416
IS - 1
JF - Plant Signaling & Behavior
SN - 1559-2324
TI - Generation of effective zinc-deficient agar-solidified media allows identification of root morphology changes in response to zinc limitation
VL - 15
ER -
TY - JOUR
AB - 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.
AU - Sinclair, Scott A
AU - Gille, S.
AU - Pauly, M.
AU - Krämer, U.
ID - 7417
IS - 1
JF - Plant Signaling & Behavior
SN - 1559-2324
TI - Regulation of acetylation of plant cell wall components is complex and responds to external stimuli
VL - 15
ER -