824 research outputs found
New bounds for circulant Johnson-Lindenstrauss embeddings
This paper analyzes circulant Johnson-Lindenstrauss (JL) embeddings which, as
an important class of structured random JL embeddings, are formed by
randomizing the column signs of a circulant matrix generated by a random
vector. With the help of recent decoupling techniques and matrix-valued
Bernstein inequalities, we obtain a new bound
for Gaussian circulant JL embeddings.
Moreover, by using the Laplace transform technique (also called Bernstein's
trick), we extend the result to subgaussian case. The bounds in this paper
offer a small improvement over the current best bounds for Gaussian circulant
JL embeddings for certain parameter regimes and are derived using more direct
methods.Comment: 11 pages; accepted by Communications in Mathematical Science
Characterization of potato plants overexpressing plastidic transporters involved in starch metabolism
Kurzfassung in English Potato is one of the most important crops in the world. Starch is the most important carbohydrate used for food and feed purposes and represents the major resource for our diet. Potato tubers represent typical starch-storing storage sinks that accumulate high levels of starch in the amyloplasts. For starch synthesis in potato tubers, amyloplasts depend on the import of carbon and energy. Carbon enters the amyloplasts in form of glucose-6-phosphate via the GPT, and energy is imported as ATP via the NTT. The impact of increasing Glc6P and ATP import into amyloplasts of potato tubers on starch synthesis as well as tuber yield was analyzed. Overexpressing GPT or NTT solely under the control of either CaMV 35S promoter or patatin promoter B33 (EW, BG and BA plants) did not lead to an increase of starch of tubers as well as yield. However, GPT overexpression under control of the CaMV 35S promoter (EW plants) resulted in an increase of leaf starch content. Overexpression of the GPT under control of the CaMV 35S promoter or of the patatin promoter B33 in NTT overexpressor (JT62) plants also did not show increased tuber starch and yield. However, starch amount in tubers and tuber yield were increased when GPT and NTT were overexpressed together under control of the patatin promoter B33. Heterologously synthesized transporter proteins from pea and Arabidopsis were functionally integrated into the plastid envelope of potato tubers. These results suggest that GPT and NTT co-limit starch synthesis in potato tubers. To obtain an increased starch content and tuber yield, increased carbon and energy import into amyloplasts should be in balance. A bidirectionalized patatin promoter B33 was constructed. This construct, however, was not suitable to drive gene expression in two directions simultaneously in potato tubers
Bregman Proximal Gradient Algorithm with Extrapolation for a class of Nonconvex Nonsmooth Minimization Problems
In this paper, we consider an accelerated method for solving nonconvex and
nonsmooth minimization problems. We propose a Bregman Proximal Gradient
algorithm with extrapolation(BPGe). This algorithm extends and accelerates the
Bregman Proximal Gradient algorithm (BPG), which circumvents the restrictive
global Lipschitz gradient continuity assumption needed in Proximal Gradient
algorithms (PG). The BPGe algorithm has higher generality than the recently
introduced Proximal Gradient algorithm with extrapolation(PGe), and besides,
due to the extrapolation step, BPGe converges faster than BPG algorithm.
Analyzing the convergence, we prove that any limit point of the sequence
generated by BPGe is a stationary point of the problem by choosing parameters
properly. Besides, assuming Kurdyka-{\'L}ojasiewicz property, we prove the
whole sequences generated by BPGe converges to a stationary point. Finally, to
illustrate the potential of the new method BPGe, we apply it to two important
practical problems that arise in many fundamental applications (and that not
satisfy global Lipschitz gradient continuity assumption): Poisson linear
inverse problems and quadratic inverse problems. In the tests the accelerated
BPGe algorithm shows faster convergence results, giving an interesting new
algorithm.Comment: Preprint submitted for publication, February 14, 201
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