8 research outputs found
Isolated factorizations and their applications in simplicial affine semigroups
We introduce the concept of isolated factorizations of an element of a
commutative monoid and study its properties. We give several bounds for the
number of isolated factorizations of simplicial affine semigroups and numerical
semigroups. We also generalize -rectangular numerical semigroups to the
context of simplicial affine semigroups and study their isolated
factorizations. As a consequence of our results, we characterize those complete
intersection simplicial affine semigroups with only one Betti minimal element
in several ways. Moreover, we define Betti sorted and Betti divisible
simplicial affine semigroups and characterize them in terms of gluings and
their minimal presentations. Finally, we determine all the Betti divisible
numerical semigroups, which turn out to be those numerical semigroups that are
free for any arrangement of their minimal generators
A snapshot of image pre-processing for convolutional neural networks: case study of MNIST
In the last five years, deep learning methods and particularly Convolutional Neural Networks (CNNs) have exhibited excellent accuracies in many pattern classification problems. Most of the state-of-the-art models apply data-augmentation techniques at the training stage. This paper provides a brief tutorial on data preprocessing and shows its benefits by using the competitive MNIST handwritten digits classification problem. We show and analyze the impact of different preprocessing techniques on the performance of three CNNs, LeNet, Network3 and DropConnect, together with their ensembles. The analyzed transformations are, centering, elastic deformation, translation, rotation and different combinations of them. Our analysis demonstrates that data-preprocessing techniques, such as the combination of elastic deformation and rotation, together with ensembles have a high potential to further improve the state-of-the-art accuracy in MNIST classification.Spanish Government
TIN2014-524 57251-PAndalusian Research Plans
P11-TIC-7765Spanish Government
RYC-2015-1813
Fast sampling of satisfying assignments from random -SAT
We give a nearly linear-time algorithm to approximately sample satisfying
assignments in the random -SAT model when the density of the formula scales
exponentially with . The best previously known sampling algorithm for the
random -SAT model applies when the density of the formula is
less than and runs in time (Galanis,
Goldberg, Guo and Yang, SIAM J. Comput., 2021). Here is the number of
variables and is the number of clauses. Our algorithm achieves a
significantly faster running time of and samples satisfying
assignments up to density .
The main challenge in our setting is the presence of many variables with
unbounded degree, which causes significant correlations within the formula and
impedes the application of relevant Markov chain methods from the
bounded-degree setting (Feng, Guo, Yin and Zhang, J. ACM, 2021; Jain, Pham and
Vuong, 2021). Our main technical contribution is a bound of the
sum of influences in the -SAT model which turns out to be robust against the
presence of high-degree variables. This allows us to apply the spectral
independence framework and obtain fast mixing results of a uniform-block
Glauber dynamics on a carefully selected subset of the variables. The final key
ingredient in our method is to take advantage of the sparsity of
logarithmic-sized connected sets and the expansion properties of the random
formula, and establish relevant properties of the set of satisfying assignments
that enable the fast simulation of this Glauber dynamics.Comment: 47 page
Cyclotomic numerical semigroup polynomials with few irreducible factors
A numerical semigroup is cyclotomic if its semigroup polynomial is
a product of cyclotomic polynomials. The number of irreducible factors of
(with multiplicity) is the polynomial length of We show that a
cyclotomic numerical semigroup is complete intersection if . This
establishes a particular case of a conjecture of Ciolan, Garc\'{i}a-S\'{a}nchez
and Moree (2016) claiming that every cyclotomic numerical semigroup is complete
intersection. In addition, we investigate the relation between and
the embedding dimension of Comment: 14 page
Cyclotomic exponent sequences of numerical semigroups
We study the cyclotomic exponent sequence of a numerical semigroup and
we compute its values at the gaps of the elements of with unique
representations in terms of minimal generators, and the Betti elements
for which the set is totally
ordered with respect to (we write whenever
with ). This allows us to characterize certain semigroup families,
such as Betti-sorted or Betti-divisible numerical semigroups, as well as
numerical semigroups with a unique Betti element, in terms of their cyclotomic
exponent sequences. Our results also apply to cyclotomic numerical semigroups,
which are numerical semigroups with a finitely supported cyclotomic exponent
sequence. We show that cyclotomic numerical semigroups with certain cyclotomic
exponent sequences are complete intersections, thereby making progress towards
proving the conjecture of Ciolan, Garc\'ia-S\'anchez and Moree (2016) stating
that is cyclotomic if and only if it is a complete intersection.Comment: 25 page
Cyclotomic exponent sequences of numerical semigroups
Part of the work on this paper was done during an internship in the Fall of 2016 carried out by
the third author at the Max Planck Institute for Mathematics in Bonn and during a one-week visit
in April 2019. He would like to thank the fourth author for the invitation and the institute staff
for their hospitality and support. The project was completed during a stay of the first author at
the same institute. Substantial progress on this paper was made in February 2017, when the first
and the fourth author were invited by the second and third author for one week to the University
of Granada. They are grateful for the hospitality, for the inspiring and cheerful atmosphere and,
last but not least, for the excellent tapas and wine!We study the cyclotomic exponent sequence of a numerical semigroup S, and we compute its values at the gaps of S, the elements of S with unique representations in terms of minimal generators, and the Betti elements b∈S for which the set {a∈Betti(S):a≤Sb} is totally ordered with respect to ≤S (we write a≤Sb whenever a−b∈S, with a,b∈S). This allows us to characterize certain semigroup families, such as Betti-sorted or Betti-divisible numerical semigroups, as well as numerical semigroups with a unique Betti element, in terms of their cyclotomic exponent sequences. Our results also apply to cyclotomic numerical semigroups, which are numerical semigroups with a finitely supported cyclotomic exponent sequence. We show that cyclotomic numerical semigroups with certain cyclotomic exponent sequences are complete intersections, thereby making progress towards proving the conjecture of Ciolan, García-Sánchez and Moree (2016) stating that S is cyclotomic if and only if it is a complete intersection
Subcutaneous anti-COVID-19 hyperimmune immunoglobulin for prevention of disease in asymptomatic individuals with SARS-CoV-2 infection: a double-blind, placebo-controlled, randomised clinical trialResearch in context
Summary: Background: Anti-COVID-19 hyperimmune immunoglobulin (hIG) can provide standardized and controlled antibody content. Data from controlled clinical trials using hIG for the prevention or treatment of COVID-19 outpatients have not been reported. We assessed the safety and efficacy of subcutaneous anti-COVID-19 hyperimmune immunoglobulin 20% (C19-IG20%) compared to placebo in preventing development of symptomatic COVID-19 in asymptomatic individuals with SARS-CoV-2 infection. Methods: We did a multicentre, randomized, double-blind, placebo-controlled trial, in asymptomatic unvaccinated adults (≥18 years of age) with confirmed SARS-CoV-2 infection within 5 days between April 28 and December 27, 2021. Participants were randomly assigned (1:1:1) to receive a blinded subcutaneous infusion of 10 mL with 1 g or 2 g of C19-IG20%, or an equivalent volume of saline as placebo. The primary endpoint was the proportion of participants who remained asymptomatic through day 14 after infusion. Secondary endpoints included the proportion of individuals who required oxygen supplementation, any medically attended visit, hospitalisation, or ICU, and viral load reduction and viral clearance in nasopharyngeal swabs. Safety was assessed as the proportion of patients with adverse events. The trial was terminated early due to a lack of potential benefit in the target population in a planned interim analysis conducted in December 2021. ClinicalTrials.gov registry: NCT04847141. Findings: 461 individuals (mean age 39.6 years [SD 12.8]) were randomized and received the intervention within a mean of 3.1 (SD 1.27) days from a positive SARS-CoV-2 test. In the prespecified modified intention-to-treat analysis that included only participants who received a subcutaneous infusion, the primary outcome occurred in 59.9% (91/152) of participants receiving 1 g C19-IG20%, 64.7% (99/153) receiving 2 g, and 63.5% (99/156) receiving placebo (difference in proportions 1 g C19-IG20% vs. placebo, −3.6%; 95% CI -14.6% to 7.3%, p = 0.53; 2 g C19-IG20% vs placebo, 1.1%; −9.6% to 11.9%, p = 0.85). None of the secondary clinical efficacy endpoints or virological endpoints were significantly different between study groups. Adverse event rate was similar between groups, and no severe or life-threatening adverse events related to investigational product infusion were reported. Interpretation: Our findings suggested that administration of subcutaneous human hyperimmune immunoglobulin C19-IG20% to asymptomatic individuals with SARS-CoV-2 infection was safe but did not prevent development of symptomatic COVID-19. Funding: Grifols