797 research outputs found
On the fast computation of the weight enumerator polynomial and the value of digital nets over finite abelian groups
In this paper we introduce digital nets over finite abelian groups which
contain digital nets over finite fields and certain rings as a special case. We
prove a MacWilliams type identity for such digital nets. This identity can be
used to compute the strict -value of a digital net over finite abelian
groups. If the digital net has points in the dimensional unit cube
, then the -value can be computed in
operations and the weight enumerator polynomial can be computed in
operations, where operations mean arithmetic of
integers. By precomputing some values the number of operations of computing the
weight enumerator polynomial can be reduced further
Eigenvalue Estimates for submanifolds of with locally bounded mean curvature
We give lower bounds for the fundamental tone of open sets in submanifolds
with locally bounded mean curvature in , where is an
-dimensional complete Riemannian manifold with radial sectional curvature
. When the immersion is minimal our estimates are sharp. We
also show that cylindrically bounded minimal surfaces has positive fundamental
tone.Comment: 9 page
The prime at infinity and the rank of the class group in global function fields
AbstractIn this paper we construct, for any integers m and n, and 2â©œgâ©œm-1, infinitely many function fields K of degree m over F(T) such that the prime at infinity splits into exactly g primes in K and the ideal class group of K contains a subgroup isomorphic to (Z/nZ)m-g. This extends previous results of the author and Lee for the cases g=1 and g=m
Collective discussions for the development of Interpretative Knowledge in Mathematics Teacher Education
We start from the assumption that teachers need a deep and broad mathematical knowledge âcalled Interpretative Knowledge (IK)âthat allows them to support students in building their mathematical knowledge from their own reasoning and productions. In the present study, we aimed to ascertain how collective discussions focusing on the interpretation of studentsâ productions engage Prospective Teachers (PTs) and impact their IK development. In particular, we observe how this form of collaborative work among PTs allows for the emergence of novel insights into the mathematical aspects of studentsâ productions that were not considered during previous individual work, and produce changes in PTsâ attitudes towards studentsâ productions
Effect of obesity and metabolic syndrome on plasma oxysterols and fatty acids in human
BACKGROUND:
Obesity and the related entity metabolic syndrome are characterized by altered lipid metabolism and associated with increased morbidity risk for cardiovascular disease and cancer. Oxysterols belong to a large family of cholesterol-derived molecules known to play crucial role in many signaling pathways underlying several diseases. Little is known on the potential effect of obesity and metabolic syndrome on oxysterols in human.
OBJECTIVES:
In this work, we questioned whether circulating oxysterols might be significantly altered in obese patients and in patients with metabolic syndrome. We also tested the potential correlation between circulating oxysterols and fatty acids.
METHODS:
60 obese patients and 75 patients with metabolic syndrome were enrolled in the study along with 210 age- and sex-matched healthy subjects, used as control group. Plasma oxysterols were analyzed by isotope dilution GC/MS, and plasma fatty acids profiling was assessed by gas chromatography coupled with flame ionization detection.
RESULTS:
We found considerable differences in oxysterols profiling in the two disease groups that were gender-related. Compared to controls, males showed significant differences only in 4α- and 4ÎČ-hydroxycholesterol levels in obese and metabolic syndrome patients. In contrast, females showed consistent differences in 7-oxocholesterol, 4α-hydroxycholesterol, 25-hydroxycholesterol and triol. Concerning fatty acids, we found minor differences in the levels of these variables in males of the three groups. Significant changes were observed in plasma fatty acid profile of female patients with obesity or metabolic syndrome. We found significant correlations between various oxysterols and fatty acids. In particular, 4ÎČ-hydroxycholesterol, which is reduced in obesity and metabolic syndrome, correlated with a number of saturated and mono-unsaturated fatty acids that are end-products of de novo lipogenesis.
CONCLUSIONS:
Our data provide the first evidence that obesity and metabolic syndrome are associated with major, gender-specific, changes in circulating oxysterols and fatty acids. These findings suggest a metabolic link between oxysterols and fatty acids, and that oxysterols may contribute to the epidemic diseases associated with obesity and metabolic syndrome in female
On submanifolds with tamed second fundamental form
We show that a complete submanifold with tamed second fundamental form in
a complete Riemannian manifold with sectional curvature are proper, (compact if is compact). In addition, if is
Hadamard then has finite topology. We also show that the fundamental tone
is an obstruction for a Riemannian manifold to be realized as submanifold with
tamed second fundamental form of a Hadamard manifold with sectional curvature
bounded below.Comment: 10 page
Efeito de fĂłsforo e potĂĄssio no desenvolvimento de bandarra (Schizolobium amazonicum (Hub) Ducke) em solo de baixa fertilidade no Estado de RondĂŽnia.
Este trabalho avaliou os nĂveis crescentes de P e K com e sem a correção do solo em condiçÔes de plantio no campo em um Latossolo Amarelo argiloso aos 14 meses de idade.bitstream/item/42533/1/Cot291-bandarra.pd
Universal mean-field upper bound for the generalization gap of deep neural networks
Modern deep neural networks (DNNs) represent a formidable challenge for theorists: according to the commonly accepted probabilistic framework that describes their performance, these architectures should overfit due to the huge number of parameters to train, but in practice they do not. Here we employ results from replica mean field theory to compute the generalization gap of machine learning models with quenched features, in the teacher-student scenario and for regression problems with quadratic loss function. Notably, this framework includes the case of DNNs where the last layer is optimized given a specific realization of the remaining weights. We show how these results-combined with ideas from statistical learning theory-provide a stringent asymptotic upper bound on the generalization gap of fully trained DNN as a function of the size of the dataset P. In particular, in the limit of large P and N-out (where N-out is the size of the last layer) and N-out << P, the generalization gap approaches zero faster than 2N(out)/P, for any choice of both architecture and teacher function. Notably, this result greatly improves existing bounds from statistical learning theory. We test our predictions on a broad range of architectures, from toy fully connected neural networks with few hidden layers to state-of-the-art deep convolutional neural networks
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