Abstract:
In order to compute the Schmidt decomposition of $A\in M_k\otimes M_m$, we must consider an associated self-adjoint map. Here, we show that if $A$ is positive under partial transposition (PPT) or symmetric with positive coefficients (SPC) or invariant under realignment then its associated self-adjoint map is completely reducible. We give applications of this fact in Quantum Information Theory. We recover some theorems recently proved for PPT and SPC matrices and we prove these theorems for matrices invariant under realignment using theorems of Perron-Frobenius theory. We also provide a new proof of the fact that if $\mathbb{C}^{k}$ contains $k$ mutually unbiased bases then $\mathbb{C}^{k}$ contains $k+1$. We search for other types of matrices that could have the same property. We consider a group of linear transformations acting on $M_k\otimes M_k$, which contains the partial transpositions and the realignment map. For each element of this group, we consider the set of matrices in $M_k\otimes M_k\simeq M_{k^2}$ that are positive and remain positive, or invariant, under the action of this element. Within this family of sets, we have the set of PPT matrices, the set of SPC matrices and the set of matrices invariant under realignment. We show that these three sets are the only sets of this family such that the associated self-adjoint map of each matrix is completely reducible. We also show that every matrix invariant under realignment is PPT in $M_2\otimes M_2$ and we present a counterexample in $M_k\otimes M_k$, $k\geq 3$.

Abstract:
Recently, in [1], the author proved that many results that are true for PPT matrices also hold for another class of matrices with a certain symmetry in their Hermitian Schmidt decompositions. These matrices were called SPC in [1] (definition 1.1). Before that, in [9], T\'oth and G\"uhne proved that if a state is symmetric then it is PPT if and only if it is SPC. A natural question appeared: What is the connection between SPC matrices and PPT matrices? Is every SPC matrix PPT? Here we show that every SPC matrix is PPT in $M_2\otimes M_2$ (theorem 4.3). This theorem is a consequence of the fact that every density matrix in $M_2\otimes M_m$, with tensor rank smaller or equal to 3, is separable (theorem 3.2). This theorem is a generalization of the same result found in [1] for tensor rank 2 matrices in $M_k\otimes M_m$. Although, in $M_3\otimes M_3$, there exists a SPC matrix with tensor rank 3 that is not PPT (proposition 5.2). We shall also provide a non trivial example of a family of matrices in $M_k\otimes M_k$, in which both, the SPC and PPT properties, are equivalent (proposition 6.2). Within this family, there exists a non trivial subfamily in which the SPC property is equivalent to separability (proposition 6.4).

Abstract:
This paper is devoted to the study of the separability problem in the field of Quantum information theory. We deal mainly with the bipartite finite dimensional case and with two types of matrices, one of them being the PPT matrices. We proved that many results holds for both types. If these matrices have specific Hermitian Schmidt decompositions then the matrices are separable in a very strong sense. We proved that both types have what we call split decompositions. We defined the notion of weak irreducible matrix, based on the concept of irreducible state defined recently. These split decomposition theorems together with the notion of weak irreducible matrix, imply that these matrices are weak irreducible or a sum of weak irreducible matrices of the same type. The separability problem for these types of matrices can be reduced to the set of weak irreducible matrices of the same type. We also provided a complete description of weak irreducible matrices of both types. Using the fact that every positive semidefinite Hermitian matrix with tensor rank 2 is separable, we found sharp inequalites providing separability for both types.

Abstract:
In this paper we introduce a new technique to prove the existence of closed subspaces of maximal dimension inside sets of topological vector sequence spaces. The results we prove cover some sequence spaces not studied before in the context of spaceability and settle some questions on classical sequence spaces that remained open.

Abstract:
Let $X$ be a sequence space and denote by $Z(X)$ the subset of $X$ formed by sequences having only a finite number of zero coordinates. We study algebraic properties of $Z(X)$ and show (among other results) that (for $p \in [1,\infty]$) $Z(\ell_p)$ does not contain infinite dimensional closed subspaces. This solves an open question originally posed by R. M. Aron and V. I. Gurariy in 2003 on the linear structure of $Z(\ell_\infty)$. In addition to this, we also give a thorough analysis of the existing algebraic structures within the set $X \setminus Z(X)$ and its algebraic genericity.

Abstract:
Objective. Recent evidence indicates that volatile anesthetics improve post-ischemic recovery. In a meta-analysis of 22 randomized studies, the use of volatile anesthetics was associated with significant reduction in myocardial infarction and mortality. All the studies in this meta-analysis included low risk patients undergoing isolated procedures (mostly isolated coronary artery bypass grafting). We want to confirm the cardioprotective effects of volatile anesthetics, in cardiac surgery, as indicated by a reduced intensive care unit stay and/or death in a high risk population of patients, undergoing combined valvular and coronary procedures. Methods. Four centres will randomize 200 patients to receive either total intravenous anesthesia with propofol or anesthesia with sevoflurane. All patients will receive a standard average dose of opiates. Perioperative management will be otherwise identical and standardized. Transfer out of the intensive care unit will follow standard criteria.Results. Reduced cardiac damage will probably translate into better tissue perfusion and faster recovery, as documented by a reduced intensive care unit stay. The study is powered to detect a reduction in the composite end point of prolonged intensive care unit stay (>2days) and/or death from 60% to 40%. Conclusions. This will be the first multicentre randomized controlled trial comparing the effects of volatile anesthetics and total intravenous anesthesia in high risk patients undergoing cardiac procedures. Our trial should help clarify whether or not volatile agents should be recommended in high risk patients undergoing cardiac surgery.

Abstract:
Angelino Julio Cariello,1 Paulo José Martins Bispo,2 Gabriela Freitas Pereira de Souza,3 Antonio Carlos Campos Pignatari,2 Marcelo Ganzarolli de Oliveira,3 Ana Luisa Hofling-Lima11Department of Ophthalmology, 2Division of Infectious Diseases, Federal University of S o Paulo, 3Institute of Chemistry, University of Campinas, Campinas, S o Paulo, BrazilBackground: The purpose of this study was to evaluate the antimicrobial activity of two nitric oxide donors, ie, S-nitrosoglutathione (GSNO) and S-nitroso-N-acetylcysteine (SNAC), against clinical isolates from patients with infectious keratitis.Methods: Reference broth microdilution assays were performed to determine the minimum inhibitory and bactericidal concentrations for GSNO and SNAC against four American Type Culture Collection strains and 52 clinical isolates from patients with infectious keratitis as follows: 14 (26.9%) Pseudomonas species; 13 (25.0%) coagulase-negative Staphylococci; 10 (19.2%) Staphylococcus aureus; nine (17.3%) Serratia marcescens; and six (11.5%) Enterobacter aerogenes. Sterility control and bacterial growth control were also performed.Results: SNAC showed lower minimum inhibitory and bactericidal concentrations than GSNO for all clinical isolates from patients with infectious keratitis. For Gram-positive bacteria, mean minimum inhibitory and bactericidal concentrations were 2.1 ± 1.3 and 8.6 ± 3.8 mM for SNAC and 4.6 ± 3.2 and 21.5 ± 12.5 mM for GSNO (P < 0.01). For Gram-negative bacteria, mean minimum inhibitory and bactericidal concentrations were 3.3 ± 1.4 and 6.1 ± 3.4 mM for SNAC and 12.4 ± 5.4 and 26.5 ± 10.1 mM for GSNO (P < 0.01). The minimum bactericidal to inhibitory concentration ratio was ≤8 in 100% of all isolates tested for SNAC and in 94.2% tested for GSNO.Conclusions: SNAC and GSNO had effective inhibitory and bactericidal effects against bacterial isolates from keratitis. SNAC showed greater antimicrobial activity than GSNO against all bacteria. Gram-positive bacteria were more susceptible to the inhibitory and bactericidal effects of the S-nitrosothiols.Keywords: antimicrobial activity, S-nitroso-N-acetylcysteine, S-nitrosoglutathione, nitric oxide donors, infectious keratitis

Abstract:
the following hypotheses were tested for groups of simultaneous hermaphrodites biomphalaria tenagophila: (a) snails that have low reproductive success during the process of self-fertilization do not increase their reproductive success after the end of grouping; (b) the copulation behaviour and the presence of one snail whose eggs have a low viability rate influence the partner's reproductive success by cross-fertilization. groups were constituted by a homozygous pigmented snail and two albinos: one with a viability rate higher than 70% ("good reproducers") and the other less than 10% ("bad reproducers"). all pigmented snails had viability rates higher than 70%. the "good" and "bad" reproducer albino snails had similar copulation behaviour. however, after the end of grouping, the "bad reproducers" continued to have viability rates less than 10% over 30 days. in 100% of the cases that pigmented snails copulated (performing either a male role or simultaneously male and female roles) exclusively with "good" reproducer albinos, they presented high reproductive success (producing, on average of 8.4 pigmented embryos/egg-mass). however, in 100% of the cases that pigmented snails copulated with both partners, the "good" reproducer albino snails produced none or very few embryos (the highest average was 2.2 pigmented embryos/egg-mass). therefore, the production of viable embryos by cross-fertilization was more influenced by self-fertilization performance than by copulation behaviour. the presence of a snail whose eggs have a low viability rate could decrease their partners reproductive success

Abstract:
purpose: to analyze the influence of botulinum toxin on the lacrimal function of patients with facial dystonias. methods: patients with the diagnosis of hemifacial spasm or benign essential blepharospasm were evaluated and invited to answer the ocular surface index disease (osid) questionnaire. all patients underwent schirmer i and basal tests; break-up time (but) test and lacrimal clearance evaluation. on the following day, the patients were treated with botulinum toxin. the ocular surface index disease questionnaire and all the initial tests were reapplied 30 days after the treatment by the same examiner. results: twenty-six patients were enrolled in this study, 15 (57.7%) with hemifacial spasm and 11 (42.3%) with benign essential blepharospasm. the mean age of patients with hemifacial spasm was 70.9 ± 13.3 years and the male:female ratio was 1:1.5. in the group of patients with benign essential blepharospasm, the mean age was 68.9 ± 8.4 years with a female preponderance (90.0%). after the treatment, the ocular surface index disease score, schirmer i and basal tests score decreased in both groups. the mean of break-up time test increased significantly in both groups. the lacrimal clearance evaluation showed a greater number of eyes that achieved a complete drainage of the tears after the treatment in both groups. conclusion: the treatment with botulinum toxin improved dry eye symptoms in patients with facial dystonia. despite of the aqueous portion of tear have decreased, blink modifications improved the tear stability and drainage.