Axioms for the coincidence index of maps between manifolds of the same dimension

We study the coincidence theory of maps between two manifolds of the same dimension from an axiomatic viewpoint. First we look at coincidences of maps between manifolds where one of the maps is orientation true, and give a set of axioms such that characterizes the local index (which is an integer valued function). Then we consider coincidence theory for arbitrary pairs of maps between two manifolds. Similarly we provide a set of axioms which characterize the local index, which in this case is a function with values in Z circle plus Z(2). We also show in each setting that the group of values for the index (either Z or Z circle plus Z(2)) is determined by the axioms. Finally, for the general case of coincidence theory for arbitrary pairs of maps between two manifolds we provide a set of axioms which characterize the local Reidemeister trace which is an element of an abelian group which depends on the pair of functions. These results extend known results for coincidences between orientable differentiable manifolds. (C) 2012 Elsevier B.V. All rights reserved.

Wecken type problems for self-maps of the Klein bottle

We consider various problems regarding roots and coincidence points for maps into the Klein bottle . The root problem where the target is and the domain is a compact surface with non-positive Euler characteristic is studied. Results similar to those when the target is the torus are obtained. The Wecken property for coincidences from to is established, and we also obtain the following 1-parameter result. Families which are coincidence free but any homotopy between and , , creates a coincidence with . This is done for any pair of maps such that the Nielsen coincidence number is zero. Finally, we exhibit one such family where is the constant map and if we allow for homotopies of , then we can find a coincidence free pair of homotopies.

Self-Organizing Maps of Molecular Descriptors for Sesquiterpene Lactones and Their Application to the Chemotaxonomy of the Asteraceae Family

The Asteraceae, one of the largest families among angiosperms, is chemically characterised by the production of sesquiterpene lactones (SLs). A total of 1,111 SLs, which were extracted from 658 species, 161 genera, 63 subtribes and 15 tribes of Asteraceae, were represented and registered in two dimensions in the SISTEMATX, an in-house software system, and were associated with their botanical sources. The respective 11 block of descriptors: Constitutional, Functional groups, BCUT, Atom-centred, 2D autocorrelations, Topological, Geometrical, RDF, 3D-MoRSE, GETAWAY and WHIM were used as input data to separate the botanical occurrences through self-organising maps. Maps that were generated with each descriptor divided the Asteraceae tribes, with total index values between 66.7% and 83.6%. The analysis of the results shows evident similarities among the Heliantheae, Helenieae and Eupatorieae tribes as well as between the Anthemideae and Inuleae tribes. Those observations are in agreement with systematic classifications that were proposed by Bremer, which use mainly morphological and molecular data, therefore chemical markers partially corroborate with these classifications. The results demonstrate that the atom-centred and RDF descriptors can be used as a tool for taxonomic classification in low hierarchical levels, such as tribes. Descriptors obtained through fragments or by the two-dimensional representation of the SL structures were sufficient to obtain significant results, and better results were not achieved by using descriptors derived from three-dimensional representations of SLs. Such models based on physico-chemical properties can project new design SLs, similar structures from literature or even unreported structures in two-dimensional chemical space. Therefore, the generated SOMs can predict the most probable tribe where a biologically active molecule can be found according Bremer classification.

Proteinuria predicts relapse in adolescent and adult minimal change disease

OBJECTIVE: This study sought to outline the clinical and laboratory characteristics of minimal change disease in adolescents and adults and establish the clinical and laboratory characteristics of relapsing and non-relapsing patients. METHODS: We retrospectively evaluated patients with confirmed diagnoses of minimal change disease by renal biopsy from 1979 to 2009; the patients were aged >13 years and had minimum 1-year follow-ups. RESULTS: Sixty-three patients with a median age (at diagnosis) of 34 (23-49) years were studied, including 23 males and 40 females. At diagnosis, eight (12.7%) patients presented with microscopic hematuria, 17 (27%) with hypertension and 17 (27%) with acute kidney injury. After the initial treatment, 55 (87.3%) patients showed complete remission, six (9.5%) showed partial remission and two (3.1%) were nonresponders. Disease relapse was observed in 34 (54%) patients who were initial responders (n = 61). In a comparison between the relapsing patients (n = 34) and the non-relapsing patients (n = 27), only proteinuria at diagnosis showed any significant difference (8.8 (7.1-12.0) vs. 6.0 (3.6-7.3) g/day, respectively, p = 0.001). Proteinuria greater than 7 g/day at the initial screening was associated with relapsing disease. CONCLUSIONS: In conclusion, minimal change disease in adults may sometimes present concurrently with hematuria, hypertension, and acute kidney injury. The relapsing pattern in our patients was associated with basal proteinuria over 7 g/day.

Hydration and anomalous solubility of the Bell-Lavis model as solvent

We address the investigation of the solvation properties of the minimal orientational model for water originally proposed by [Bell and Lavis, J. Phys. A 3, 568 (1970)]. The model presents two liquid phases separated by a critical line. The difference between the two phases is the presence of structure in the liquid of lower density, described through the orientational order of particles. We have considered the effect of a small concentration of inert solute on the solvent thermodynamic phases. Solute stabilizes the structure of solvent by the organization of solvent particles around solute particles at low temperatures. Thus, even at very high densities, the solution presents clusters of structured water particles surrounding solute inert particles, in a region in which pure solvent would be free of structure. Solute intercalates with solvent, a feature which has been suggested by experimental and atomistic simulation data. Examination of solute solubility has yielded a minimum in that property, which may be associated with the minimum found for noble gases. We have obtained a line of minimum solubility (TmS) across the phase diagram, accompanying the line of maximum density. This coincidence is easily explained for noninteracting solute and it is in agreement with earlier results in the literature. We give a simple argument which suggests that interacting solute would dislocate TmS to higher temperatures.

Minimal residual disease in cerebrospinal fluid at diagnosis: a more intensive treatment protocol was able to eliminate the adverse prognosis in children with acute lymphoblastic leukemia

We analyzed cerebrospinal fluid (CSF) samples from 65 consecutive children with acute lymphoblastic leukemia (ALL) treated according to two different treatment protocols (GBTLI-ALL-93 and -99) with no puncture accident for minimal residual disease (MRD) in the central nervous system (CNS). Minimal residual disease was detected by polymerase chain reaction (PCR) with homo/heteroduplex analysis using consensus primers to IgH and TCR genes. MRD in the CSF at diagnosis was detected by PCR in 46.8% of children with no puncture accident or morphological involvement. In patients treated with GBTLI-ALL-93 a significantly lower 5-year event-free survival (EFS) was demonstrated for those with CSF involvement, in univariate (p = 0.01) and multivariate (p = 0.04) analysis. This observation was not true for patients treated with the more intensive protocol GBTLI-ALL-99 (p = 0.81). These findings suggest that MRD detection in the CSF is a common event in children with ALL. Treatment intensification provided by the GBTLI-ALL-99 apparently overcomes the detrimental effect of CNS minimal residual disease at diagnosis.

Bourgin-Yang version of the Borsuk-Ulam theorem for Z(pk)-equivariant maps

Let G = Z(pk) be a cyclic group of prime power order and let V and W be orthogonal representations of G with V-G = W-G = W-G = {0}. Let S(V) be the sphere of V and suppose f: S(V) -> W is a G-equivariant mapping. We give an estimate for the dimension of the set f(-1){0} in terms of V and W. This extends the Bourgin-Yang version of the Borsuk-Ulam theorem to this class of groups. Using this estimate, we also estimate the size of the G-coincidences set of a continuous map from S(V) into a real vector space W'.

Minimal processing of jucara's heart palm packed in brine acidified

The jucara's palm (Euterpe edulis), native to the Atlantic Forest is one of the palms most exploited for the removal of heart palm and the tree was removed in large areas. The aim of this study was to examine the feasibility of the methodology of "minimally processed" in jucara's palm. The raw material was obtained by COOPERAGUA, Sete Barras (SP) through a Sustainable Management Plan culminating in a permit issued by IBAMA, Forestry Foundation and DPRN. The process began with the withdrawal of external sheaths and cut, with subsequent immersion in a solution of sodium metabisulphite (Na2S2O5 - 200 ppm), sanitize with a chlorine solution and soak in brine acidified to wait until the filling. The cuttings were placed in polyethylene bags containing acidified solution at concentrations A 0.225%, B 0.375%, C 0.6%, D 0.825% determined by titration curve. The staining became clearer in treatments C and D, due to more acidity, resulting in higher inactivation of enzymes. Even with these positive results, were concluded that minimal processing of jucara is not effective due to the blackout, preventing its commercialization. To stop it requires the bleaching step, which does not characterize it as minimally processed.

On the existence of G-equivariant maps

Let G be a compact Lie group. Let X, Y be free G-spaces. In this paper, by using the numerical index i (X; R), under cohomological conditions on the spaces X and Y, we consider the question of the existence of G-equivariant maps f: X -> Y.

Minimal change disease associated with type 1 and type 2 diabetes mellitus

A 19-year-old female with type 1 diabetes for four years, and a 73-year-old female with type 2 diabetes for twenty years developed sudden-onset nephrotic syndrome. Examination by light microscopy, immunofluorescence, and electron microscopy (in one case) identified minimal change disease (MCD) in both cases. There was a potential causative drug (meloxicam) for the 73-year-old patient. Both patients were treated with prednisone and responded with complete remission. The patient with type 1 diabetes showed complete remission without relapse, and the patient with type 2 diabetes had two relapses; complete remission was sustained after associated treatment with cyclophosphamide and prednisone. Both patients had two years of follow-up evaluation after remission. We discuss the outcomes of both patients and emphasize the role of kidney biopsy in diabetic patients with an atypical proteinuric clinical course, because patients with MCD clearly respond to corticotherapy alone or in conjunction with other immunosuppressive agents. Arq Bras Endocrinol Metab. 2012;56(5):331-5

Minimally invasive mastectomy: minimal incisions for better aesthetic quality of breast reconstruction

Background: Women with a family history of breast cancer who develop this disease are confronted with important situations regarding the increased risk for development of a second cancer in the contralateral breast. Prophylactic contralateral mastectomy (PCM) reduces by approximately 95% the risk for contralateral breast cancer. In spite of an increase in indications for PCM, the technical difficulties are many regarding the accomplishment of these procedures. The aim of this study is to describe the technique of mastectomy with preservation of the nipple-areola complex and a small incision, reducing surgical difficulties and complications attributed to this technique, thus allowing better aesthetic results in breast reconstruction. Methods: Forty-six patients with indications for PCM (28 bilateral) were submitted to minimally invasive mastectomy from March 2005 to November 2007. A small incision in the superior pole of the areola, sufficient to pass a liposuction 4 mm cannula is made. With the help of this cannula, detachment of the skin from the gland tissue is performed. Then a 3.5 to 4.5-cm long incision in the inframammary fold is made. Glandular detachment is completed using cautery in the sub,glandular portion and scissors in the upper breast portion cutting the restraints left by the cannula. The mammary gland tissue is removed through this incision. Results: Seventy-four breasts were operated on. The resected breast mass ranged from 285 g to 475 g. All 43 patients were reconstructed with prostheses. There was no necrosis of the nipple-areola complex or of the skin. Conclusions: This technique is an option for cases of patients with indications for PCM.

Secondary nontwist phenomena in area-preserving maps

Phenomena as reconnection scenarios, periodic-orbit collisions, and primary shearless tori have been recognized as features of nontwist maps. Recently, these phenomena and secondary shearless tori were analytically predicted for generic maps in the neighborhood of the tripling bifurcation of an elliptic fixed point. In this paper, we apply a numerical procedure to find internal rotation number profiles that highlight the creation of periodic orbits within islands of stability by a saddle-center bifurcation that emerges out a secondary shearless torus. In addition to the analytical predictions, our numerical procedure applied to the twist and nontwist standard maps reveals that the atypical secondary shearless torus occurs not only near a tripling bifurcation of the fixed point but also near a quadrupling bifurcation. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4750040]

Nontwist symplectic maps in tokamaks

We review symplectic nontwist maps that we have introduced to describe Lagrangian transport properties in magnetically confined plasmas in tokamaks. These nontwist maps are suitable to describe the formation and destruction of transport barriers in the shearless region (i.e., near the curve where the twist condition does not hold). The maps can be used to investigate two kinds of problems in plasmas with non-monotonic field profiles: the first is the chaotic magnetic field line transport in plasmas with external resonant perturbations. The second problem is the chaotic particle drift motion caused by electrostatic drift waves. The presented analytical maps, derived from plasma models with equilibrium field profiles and control parameters that are commonly measured in plasma discharges, can be used to investigate long-term transport properties. (C) 2011 Elsevier B.V. All rights reserved.

Flow Visualization with Quantified Spatial and Temporal Errors Using Edge Maps

Robust analysis of vector fields has been established as an important tool for deriving insights from the complex systems these fields model. Traditional analysis and visualization techniques rely primarily on computing streamlines through numerical integration. The inherent numerical errors of such approaches are usually ignored, leading to inconsistencies that cause unreliable visualizations and can ultimately prevent in-depth analysis. We propose a new representation for vector fields on surfaces that replaces numerical integration through triangles with maps from the triangle boundaries to themselves. This representation, called edge maps, permits a concise description of flow behaviors and is equivalent to computing all possible streamlines at a user defined error threshold. Independent of this error streamlines computed using edge maps are guaranteed to be consistent up to floating point precision, enabling the stable extraction of features such as the topological skeleton. Furthermore, our representation explicitly stores spatial and temporal errors which we use to produce more informative visualizations. This work describes the construction of edge maps, the error quantification, and a refinement procedure to adhere to a user defined error bound. Finally, we introduce new visualizations using the additional information provided by edge maps to indicate the uncertainty involved in computing streamlines and topological structures.

BANACH SPACES WITHOUT MINIMAL SUBSPACES - EXAMPLES

We analyse several examples of separable Banach spaces, some of them new, and relate them to several dichotomies obtained in [11], by classifying them according to which side of the dichotomies they fall.