Vanishing ideals over graphs and even cycles

Let X be an algebraic toric set in a projective space over a finite field. We study the vanishing ideal, I(X), of X and show some useful degree bounds for a minimal set of generators of I(X). We give an explicit description of a set of generators of I(X), when X is the algebraic toric set associated to an even cycle or to a connected bipartite graph with pairwise disjoint even cycles. In this case, a fomula for the regularity of I(X) is given. We show an upper bound for this invariant, when X is associated to a (not necessarily connected) bipartite graph. The upper bound is sharp if the graph is connected. We are able to show a formula for the length of the parameterized linear code associated with any graph, in terms of the number of bipartite and non-bipartite components

Regularity and algebraic properties of certain lattice ideals

We study the regularity and the algebraic properties of certain lattice ideals. We establish a map I --> I\~ between the family of graded lattice ideals in an N-graded polynomial ring over a field K and the family of graded lattice ideals in a polynomial ring with the standard grading. This map is shown to preserve the complete intersection property and the regularity of I but not the degree. We relate the Hilbert series and the generators of I and I\~. If dim(I)=1, we relate the degrees of I and I\~. It is shown that the regularity of certain lattice ideals is additive in a certain sense. Then, we give some applications. For finite fields, we give a formula for the regularity of the vanishing ideal of a degenerate torus in terms of the Frobenius number of a semigroup. We construct vanishing ideals, over finite fields, with prescribed regularity and degree of a certain type. Let X be a subset of a projective space over a field K. It is shown that the vanishing ideal of X is a lattice ideal of dimension 1 if and only if X is a finite subgroup of a projective torus. For finite fields, it is shown that X is a subgroup of a projective torus if and only if X is parameterized by monomials. We express the regularity of the vanishing ideal over a bipartie graph in terms of the regularities of the vanishing ideals of the blocks of the graph.Comment: Bull. Braz. Math. Soc. (N.S.), to appea

Consensus must be found on intravenous fluid therapy management in trauma patients

Introduction: Trauma is an important cause of death among young people and 30-40% of this mortality rate is due to hypovolemic shock, intensified by trauma's lethal triad: Hypothermia, Acidosis, and Coagulopathy. Nurses are responsible for managing fluid therapy administration in trauma victims. The purpose of this study is to analyse the reasons why intravenous fluid therapy is recommended for trauma patients' hemodynamic stabilization. Methods: This narrative literature review included published and unpublished studies in English, Spanish or Portuguese between 1994 and January 2019. The search results were analyzed by two independent reviewers. Inclusion criteria encompasses quantitative studies involving trauma victims aged over 18 who underwent fluid therapy in a prehospital assessment context. Results&Discussion: 11 quantitative studies were included. 9 involved the use of fluid therapy for hypotension treatment and 2 of the studies analyzed involved the use of warmed fluid therapy for hypothermia treatment. The analysis performed reveals that the administration of aggressive fluid therapy seems to be responsible for the worsening of the lethal triad. In the presence of traumatic brain injury, permissive hypotension is not allowed due to the negative impact on cerebral perfusion pressure. Used as warming measure, warmed fluid therapy does not seem to have a significant impact on body temperature. Conclusions: There is no consensus regarding the administration of fluid therapy to trauma patients. This conclusion clearly supports the need to develop more randomized controlled trials in order to understand the effectiveness of such measure when it comes to control hypovolemia and hypothermia.info:eu-repo/semantics/publishedVersio

Neel order in the two-dimensional S=1/2 Heisenberg Model

The existence of Neel order in the S=1/2 Heisenberg model on the square lattice at T=0 is shown using inequalities set up by Kennedy, Lieb and Shastry in combination with high precision Quantum Monte Carlo data.Comment: 4 pages, 1 figur

Deep-PRWIS: Periocular Recognition Without the Iris and Sclera Using Deep Learning Frameworks

This work is based on a disruptive hypothesisfor periocular biometrics: in visible-light data, the recognitionperformance is optimized when the components inside the ocularglobe (the iris and the sclera) are simply discarded, and therecogniser’s response is exclusively based in information fromthe surroundings of the eye. As major novelty, we describe aprocessing chain based on convolution neural networks (CNNs)that defines the regions-of-interest in the input data that should beprivileged in an implicit way, i.e., without masking out any areasin the learning/test samples. By using an ocular segmentationalgorithm exclusively in the learning data, we separate the ocularfrom the periocular parts. Then, we produce a large set of”multi-class” artificial samples, by interchanging the periocularand ocular parts from different subjects. These samples areused for data augmentation purposes and feed the learningphase of the CNN, always considering as label the ID of theperiocular part. This way, for every periocular region, the CNNreceives multiple samples of different ocular classes, forcing itto conclude that such regions should not be considered in itsresponse. During the test phase, samples are provided withoutany segmentation mask and the networknaturallydisregardsthe ocular components, which contributes for improvements inperformance. Our experiments were carried out in full versionsof two widely known data sets (UBIRIS.v2 and FRGC) and showthat the proposed method consistently advances the state-of-the-art performance in theclosed-worldsetting, reducing the EERsin about 82% (UBIRIS.v2) and 85% (FRGC) and improving theRank-1 over 41% (UBIRIS.v2) and 12% (FRGC).info:eu-repo/semantics/publishedVersio

Soft Biometrics: Globally Coherent Solutions for Hair Segmentation and Style Recognition based on Hierarchical MRFs

Markov Random Fields (MRFs) are a populartool in many computer vision problems and faithfully modela broad range of local dependencies. However, rooted in theHammersley-Clifford theorem, they face serious difficulties inenforcing the global coherence of the solutions without using toohigh order cliques that reduce the computational effectiveness ofthe inference phase. Having this problem in mind, we describea multi-layered (hierarchical) architecture for MRFs that isbased exclusively in pairwise connections and typically producesglobally coherent solutions, with 1) one layer working at the local(pixel) level, modelling the interactions between adjacent imagepatches; and 2) a complementary layer working at theobject(hypothesis) level pushing toward globally consistent solutions.During optimization, both layers interact into an equilibriumstate, that not only segments the data, but also classifies it.The proposed MRF architecture is particularly suitable forproblems that deal with biological data (e.g., biometrics), wherethe reasonability of the solutions can be objectively measured.As test case, we considered the problem of hair / facial hairsegmentation and labelling, which are soft biometric labels usefulfor human recognitionin-the-wild. We observed performancelevels close to the state-of-the-art at a much lower computationalcost, both in the segmentation and classification (labelling) tasksinfo:eu-repo/semantics/publishedVersio