7,946 research outputs found
On Hopf algebras of dimension
We discuss some general results on finite-dimensional Hopf algebras over an
algebraically closed field k of characteristic zero and then apply them to Hopf
algebras H of dimension p^{3} over k. There are 10 cases according to the
group-like elements of H and H^{*}. We show that in 8 of the 10 cases, it is
possible to determine the structure of the Hopf algebra. We give also a partial
classification of the quasitriangular Hopf algebras of dimension p^{3} over k,
after studying extensions of a group algebra of order p by a Taft algebra of
dimension p^{2}. In particular, we prove that every ribbon Hopf algebra of
dimension p^{3} over k is either a group algebra or a Frobenius-Lusztig kernel.
Finally, using some previous results on bounds for the dimension of the first
term H_{1} in the coradical filtration of H, we give the complete
classification of the quasitriangular Hopf algebras of dimension 27.Comment: 27 pages, minor changes. Accepted for publication in the Tsukuba
Journal of Mathematic
Parkinsons Disease Detection by using Isosurfaces with Convolutional Neural Networks
Computer aided diagnosis systems based on brain imaging are an important tool
to assist in the diagnosis of Parkinson’s disease. The ultimate goal would be detec-
tion by automatic recognizing of patterns that characterize the disease. In recent
times Convolutional Neural Networks (CNN) have proved to be amazingly useful
for that task. The drawback, however, is that 3D brain images contains a huge
amount of information that leads to complex CNN architectures. When these
architectures become too complex, classification performances often degrades be-
cause the limitations of the training algorithm and overfitting. Thus, this paper
proposes the use of isosurfaces as a way to reduce such amount of data while
keeping the most relevant information. These isosurfaces are then used to im-
plement a classification system which uses two of the most well-known CNN
architectures to classify DaTScan images with an average
accuracy of 95.1% and AUC=97%, obtaining comparable (slightly better) values
to those obtained for most of the recently proposed systems. It can be concluded
therefore that the computation of isosurfaces reduces the complexity of the inputs
significantly, resulting in high classification accuracies with reduced computa-
tional burden.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech
The microbiological effect of ozone and chlorine treatments on minimally processed lettuce
Chlorine is an effective sanitizer against many foodborne microorganisms. However, it may cause the formation of carcinogenic trihalomethane compounds. Ozone is an effective disinfectant having greater oxidation potential than chlorine. Limited studies have been done to determine the optimum concentration and contact time for ozone and if there is a synergistic interaction with chlorine when treating minimally processed produce.
Our objective was to determine the sanitizing efficacy of ozone and chlorine, alone or in combination on microbial reduction on fresh-cut lettuce and to develop data that was of used for the ready-to-eat salad industry based on the sensory characteristics and shelf-life of these products.
Iceberg lettuce was cut into 2 by 5 cm strips and inoculated with log 8 CFU/g of a mixture of natural microflora strains isolated from cut lettuce stored at 10°C. 100 g samples were treated with 1 L distilled water solutions containing combinations of 0, 100, 150 or 200 ppm chlorine and 0, 2.5, 5.0 or 7.5 ppm ozone for a total of 16 treatments. Lettuce-water solutions were stirred constantly for 10 min and then lettuce was sampled for Aerobic Plate Counts (APC) and Psychrotrophic Plate Counts (PPC), four repetitions were used in this study. Commercially processed salads treated with chlorine, ozone or an ozone-chlorine mixture were evaluated for shelf-life using visual inspection by an untrained panel (n=30). Water samples were also analyzed for UV-Vis and total solids to determine the effect of the treatments in the processing water.
Lettuce treated with only chlorine had reductions in APC up to 1.38 Logs and 1.71 Logs for PYS. Samples treated with ozone decreased in APC up to 1.12 Logs and 2.00 Logs for PPC. Lettuce treated with the combinations of chlorine and ozone had the greatest reduction in APC up to 2.5 Logs and 1.91 Logs for PPC. Sensory evaluation showed that the commercially processed samples treated with chlorine were least desirable having the shortest shelf-life with product decay after 16 days of treatment. Samples treated with ozone alone had a shelf-life of at least 20 days. Lettuce treated with the combination had the longest shelf-life retaining good visual sensory characteristics until at least 25 days after treatment.
Results suggest that washing fresh-cut salads with an ozone-chlorine sanitation treatment can improve and extend the shelf-life of these products compared to either ozone or chlorine solutions individually
Multiparameter quantum groups at roots of unity
We address the problem of studying multiparameter quamtum groups (=MpQG's) at
roots of unity, namely quantum universal enveloping algebras depending on a matrix of parameters . This is performed
via the construction of quantum root vectors and suitable "integral forms" of , a restricted one - generated by
quantum divided powers and quantum binomial coefficients - and an unrestricted
one - where quantum root vectors are suitably renormalized. The specializations
at roots of unity of either forms are the "MpQG's at roots of unity" we are
investigating. In particular, we study special subalgebras and quotients of our
MpQG's at roots of unity - namely, the multiparameter version of small quantum
groups - and suitable associated quantum Frobenius morphisms, that link the
(specializations of) MpQG's at roots of 1 with MpQG's at 1, the latter being
classical Hopf algebras bearing a well precise Poisson-geometrical content. A
key point in the discussion - often at the core of our strategy - is that every
MpQG is actually a 2-cocycle deformation of the algebra structure of (a lift
of) the "canonical" one-parameter quantum group by Jimbo-Lusztig, so that we
can often rely on already established results available for the latter. On the
other hand, depending on the chosen multiparameter our
quantum groups yield (through the choice of integral forms and their
specialization) different semiclassical structures, namely different Lie
coalgebra structures and Poisson structures on the Lie algebra and algebraic
group underlying the canonical one-parameter quantum group.Comment: 84 pages. New version slightly re-edited and streamlined: the content
only is affected in Sec. 3.1, but page flushing occurs in the sequel as well
(overall, the text is now one page shorter
Deformation by cocycles of pointed Hopf algebras over non-abelian groups
We introduce a method to construct explicitly multiplicative 2-cocycles for
bosonizations of Nichols algebras B(V) over Hopf algebras H. These cocycles
arise as liftings of H-invariant linear functionals on V tensor V and give a
close formula to deform braided commutator-type relations.
Using this construction, we show that all known finite dimensional pointed
Hopf algebras over the dihedral groups D_m with m=4t > 11, over the symmetric
group S_3 and some families over S_4 are cocycle deformations of bosonizations
of Nichols algebras.Comment: 20 pages. This version: extended version following the referee's
suggestions. Intended for non-expert
Classifying Hopf algebras of a given dimension
Classifying all Hopf algebras of a given finite dimension over the complex
numbers is a challenging problem which remains open even for many small
dimensions, not least because few general approaches to the problem are known.
Some useful techniques include counting the dimensions of spaces related to
the coradical filtration, studying sub- and quotient Hopf algebras, especially
those sub-Hopf algebras generated by a simple subcoalgebra, working with the
antipode, and studying Hopf algebras in Yetter-Drinfeld categories to help to
classify Radford biproducts. In this paper, we add to the classification tools
in our previous work [arXiv:1108.6037v1] and apply our results to Hopf algebras
of dimension rpq and 8p where p,q,r are distinct primes.
At the end of this paper we summarize in a table the status of the
classification for dimensions up to 100 to date.Comment: This version of the paper contains a correction on the published
version. The statement and proof of Proposition 2.17 are changed and the
proof of the results that follow from it are corrected accordingly. We thank
H.-S. Ng for kindly communicating the gap to us and for the careful reading
of our pape
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