258 research outputs found
How degenerate is the parametrization of neural networks with the ReLU activation function?
Neural network training is usually accomplished by solving a non-convex
optimization problem using stochastic gradient descent. Although one optimizes
over the networks parameters, the main loss function generally only depends on
the realization of the neural network, i.e. the function it computes. Studying
the optimization problem over the space of realizations opens up new ways to
understand neural network training. In particular, usual loss functions like
mean squared error and categorical cross entropy are convex on spaces of neural
network realizations, which themselves are non-convex. Approximation
capabilities of neural networks can be used to deal with the latter
non-convexity, which allows us to establish that for sufficiently large
networks local minima of a regularized optimization problem on the realization
space are almost optimal. Note, however, that each realization has many
different, possibly degenerate, parametrizations. In particular, a local
minimum in the parametrization space needs not correspond to a local minimum in
the realization space. To establish such a connection, inverse stability of the
realization map is required, meaning that proximity of realizations must imply
proximity of corresponding parametrizations. We present pathologies which
prevent inverse stability in general, and, for shallow networks, proceed to
establish a restricted space of parametrizations on which we have inverse
stability w.r.t. to a Sobolev norm. Furthermore, we show that by optimizing
over such restricted sets, it is still possible to learn any function which can
be learned by optimization over unrestricted sets.Comment: Accepted at NeurIPS 201
Begrenzte Heterotrophie bei Amphidinium (Dinoflagellata)
An bakterienfreien Kulturen von Amphidinium höfleri in vollsynthetischem NÀhrmedium konnte mit dem Coulter-Counter gezeigt werden, daà gelöste AminosÀuren in Konzentrationen von 50 mg/l eine Erhöhung des Zellvolumens der Population um 6,1% bewirken. Eine Beeinflussung der Generationszeit konnte nicht festgestellt werden. Wurden die AminosÀuren in Konzentrationen von 200 ”g/l, also in Konzentrationen, wie sie im Pelagial des Meeres vorkommen, geboten, so konnte keine Förderung des Wachstums nachgewiesen werden.
With axenic cultures of Amphidinium höfleri it was shown by using the Coulter-Counter, that dissolved amino-acids in concentrations of 50 mg/l will increase the cellvolume by 6.1%. There was no effect on the generation time. If the aminoacids were added in concentrations of 200 ”g/l - the concentration of natural sea water - then there was no effect
To be or not to be: On the usefulness of infraspecific names in Heterocapsa steinii (Heterocapsaceae, Peridiniales)
Hydrographic, chemical and planktological data from the north-west African upwelling area obtained from February to April 1983 : ("Ostatlantik-Biozirkel")
A Gordian knot: Nomenclature and taxonomy of Heterocapsa triquetra (Peridiniales: Heterocapsaceae)
In the course of polyphasic taxonomic work in the dinophytes, we became aware of a fundamental misapplication
of the name Glenodinium triquetrum (now represented conceptually by a species of Kryptoperidinium), when Stein assigned it to Heterocapsa. Possible solutions involve a conflict between retaining Ehrenbergâs epithet in its correct application in the interest of priority and preserving current usage of Heterocapsa. However, we do not achieve a consensus on how to disentangle this Gordian knot, underlining that this is not a regular case of taxonomic confusion. We intend to stimulate a more general discussion about best practices in such cases, balancing between the interest of nomenclatural practicability and the respectful acknowledgement of scientific work, even if it was conducted many years ago
Sexual reproduction and two different encystment strategies of Lingulodinium polyedrum (Dinophyceae) in culture
Unreported aspects in the sexual cycle of the marine dinoflagellate Lingulodinium polyedrum (Stein) Dodge were described. Our observations included the description of two types of hypnozygote formation, because culture planozygotes were observed to encyst in two different ways: an ecdysal sexual stage or a spiny resting cyst. Phosphate deficiency was the main nutritional condition required for fusing gamete pairs to form resting cysts, whereas replete conditions prevented their appearance and favored the formation of ecdysal sexual forms. Mating experiments revealed the existence of two sexual types (+/â), which were enough to explain resting cyst appearance (simple heterothallism). Morphological aspects and timing of gamete mating, fusion, and the efficiency of encystment under different external levels of nitrate and phosphate were analyzed after isolating and monitoring individual pairs of fusing gametes. The staining of sexual stages showed that nuclear fusion was completed at the same time as the cytoplasmic fusion. After 1 to 2 h, the planozygotes presented one quadrolobulated nucleus. Germination of ecdysal sexual stages occurred after <24â72 h, whereas excystment of resting cysts was dependent on the studied parental cross and took place after 2â4 months. Newly germinated cells from both types of cysts had a similar, big, U-shaped nucleus. Twenty-four to 48 h after excystment, the germlings divided by desmoschisis, a process before which enlargement of the nucleus was observed.Postprin
An Updated List of Generic Names in the Thoracosphaeraceae
Calcareous dinophytes produce exoskeletal calcified structures during their life history (a unique character among the alveolates) and are subsumed under the Thoracosphaeraceae as part of the Peridiniales. We provide a brief synopsis about the taxonomic history of the group, from the first descriptions of fossils in the 19th century through to the results of molecular phylogenetics studies undertaken during the past two decades. Delimitation and circumscription of the Thoracosphaeraceae are challenging, as they comprise both phototrophic (presumably including endosymbiotic) as well as heterotrophic (and even parasitic) dinophytes from marine and freshwater environments, respectively. However, calcareous structures are not known from all members of the Thoracosphaeraceae, and the corresponding species and groups are considered to have lost the capacity to calcify. Five years ago, a taxonomic list of 99 generic names assigned to the Thoracosphaeraceae was published, and we update this compendium with 19 additional names based on recent studies
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