Darboux invariants for planar polynomial differential systems having an invariant conic

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

The cohomological invariant E'(G,W) and some properties

Let G be a group, W a nonempty G-set and M a Z2G-module. Consider the restriction map resG W : H1(G,M) → Pi wi∈E H1(Gwi,M), [f] → (resGG wi [f])i∈I , where E = {wi, i ∈ I} is a set of orbit representatives in W and Gwi = {g ∈ G | gwi = wi} is the G-stabilizer subgroup (or isotropy subgroup) of wi, for each wi ∈ E. In this work we analyze some results presented in Andrade et al [5] about splittings and duality of groups, using the point of view of Dicks and Dunwoody [10] and the invariant E'(G,W) := 1+dimkerresG W, defined when Gwi is a subgroup of infinite index in G for all wi in E, andM = Z2 (where dim = dimZ2). We observe that the theory of splittings of groups (amalgamated free product and HNN-groups) is inserted in the combinatory theory of groups which has many applications in graph theory (see, for example, Serre [12] and Dicks and Dunwoody [10]).

A dual homological invariant and some properties

Based on the cohomology theory of groups, Andrade and Fanti defined in [1] an algebraic invariant, denoted by E(G,S, M), where G is a group, S is a family of subgroups of G with infinite index and M is a Z2G-module. In this work, by using the homology theory of groups instead of cohomology theory, we define an invariant ``dual'' to E(G, S, M), which we denote by E*(G, S, M). The purpose of this paper is, through the invariant E*(G, S, M), to obtain some results and applications in the theory of duality groups and group pairs, similar to those shown in Andrade and Fanti [2], and thus, providing an alternative way to get applications and properties of this theory.

Normal Forms for Polynomial Differential Systems in R-3 Having an Invariant Quadric and a Darboux Invariant

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Adolescents’ Occupational and Educational Aspirations and Expectations: Links to High School Activities and Adult Educational Attainment

This longitudinal study explored adolescents’ future-oriented cognitions, current activities, and later educational attainment using data from 317 adolescents (55% female; mean age = 14.98 years, SD = 0.85) followed into early adulthood. Aspirations and expectations regarding work and education showed modest stability from year to year. Exploration of the reciprocal relations between these cognitions and adolescents’ activities supported both unidirectional and bidirectional effects, with different patterns emerging for aspirations and expectations. In multiple regression analyses, future-oriented cognitions predicted adult educational attainment; follow- up analyses indicated that the effect of adolescents’ expectations was partially mediated by participation in extracurricular activities. These results suggest a potentially important influence of adolescents’ future-oriented cognitions on their current behavior and future attainments.

Emerging Marine Diseases: Climate Links and Anthropogenic Factors

Mass mortalities due to disease outbreaks have recently affected major taxa in the oceans. For closely monitored groups like corals and marine mammals, reports of the frequency of epidemics and the number of new diseases have increased recently. A dramatic global increase in the severity of coral bleaching in 1997-98 is coincident with high El Niño temperatures. Such climate-mediated, physiological stresses may compromise host resistance and increase frequency of opportunistic diseases. Where documented, new diseases typically have emerged through host or range shifts of known pathogens. Both climate and human activities may have also accelerated global transport of species, bringing together pathogens and previously unexposed host populations.

Invariant Solutions of Richards' Equation for Water Movement in Dissimilar Soils

Scaling methods allow a single solution to Richards' equation (RE) to suffice for numerous specific cases of water flow in unsaturated soils. During the past half-century, many such methods were developed for similar soils. In this paper, a new method is proposed for scaling RE for a wide range of dissimilar soils. Exponential-power (EP) functions are used to reduce the dependence of the scaled RE on the soil hydraulic properties. To evaluate the proposed method, the scaled RE was solved numerically considering two test cases: infiltration into relatively dry soils having initially uniform water content distributions, and gravity-dominant drainage occurring from initially wet soil profiles. Although the results for four texturally different soils ranging from sand to heavy clay (adopted from the UNSODA database) showed that the scaled solution were invariant for a wide range of flow conditions, slight deviations were observed when the soil profile was initially wet in the infiltration case or deeply wet in the drainage case. The invariance of the scaled RE makes it possible to generalize a single solution of RE to many dissimilar soils and conditions. Such a procedure reduces the numerical calculations and provides additional opportunities for solving the highly nonlinear RE for unsaturated water flow in soils.

Integral form of Yang-Mills equations and its gauge invariant conserved charges

Despite the fact that the integral form of the equations of classical electrodynamics is well known, the same is not true for non-Abelian gauge theories. The aim of the present paper is threefold. First, we present the integral form of the classical Yang-Mills equations in the presence of sources and then use it to solve the long-standing problem of constructing conserved charges, for any field configuration, which are invariant under general gauge transformations and not only under transformations that go to a constant at spatial infinity. The construction is based on concepts in loop spaces and on a generalization of the non-Abelian Stokes theorem for two-form connections. The third goal of the paper is to present the integral form of the self-dual Yang-Mills equations and calculate the conserved charges associated with them. The charges are explicitly evaluated for the cases of monopoles, dyons, instantons and merons, and we show that in many cases those charges must be quantized. Our results are important in the understanding of global properties of non-Abelian gauge theories.

Invariant Natural Killer T Cell Agonist Modulates Experimental Focal and Segmental Glomerulosclerosis

A growing body of evidence demonstrates a correlation between Th2 cytokines and the development of focal and segmental glomerulosclerosis ( FSGS). Therefore, we hypothesized that GSL-1, a monoglycosylceramide from Sphingomonas ssp. with pro-Th1 activity on invariant Natural Killer T ( iNKT) lymphocytes, could counterbalance the Th2 profile and modulate glomerulosclerosis. Using an adriamycin( ADM)-based model of FSGS, we found that BALB/c mice presented albuminuria and glomerular degeneration in association with a Th2-like pro-fibrogenic profile; these mice also expressed a combination of inflammatory cytokines, such as IL-4, IL-1 alpha, IL-1 beta, IL-17, TNF-alpha, and chemokines, such as RANTES and eotaxin. In addition, we observed a decrease in the mRNA levels of GD3 synthase, the enzyme responsible for GD3 metabolism, a glycolipid associated with podocyte physiology. GSL-1 treatment inhibited ADM-induced renal dysfunction and preserved kidney architecture, a phenomenon associated with the induction of a Th1-like response, increased levels of GD3 synthase transcripts and inhibition of pro-fibrotic transcripts and inflammatory cytokines. TGF-beta analysis revealed increased levels of circulating protein and tissue transcripts in both ADM- and GSL-1-treated mice, suggesting that TGF-beta could be associated with both FSGS pathology and iNKT-mediated immunosuppression; therefore, we analyzed the kidney expression of phosphorylated SMAD2/3 and SMAD7 proteins, molecules associated with the deleterious and protective effects of TGF-beta, respectively. We found high levels of phosphoSMAD2/3 in ADM mice in contrast to the GSL-1 treated group in which SMAD7 expression increased. These data suggest that GSL-1 treatment modulates the downstream signaling of TGF-beta through a renoprotective pathway. Finally, GSL-1 treatment at day 4, a period when proteinuria was already established, was still able to improve renal function, preserve renal structure and inhibit fibrogenic transcripts. In conclusion, our work demonstrates that the iNKT agonist GSL-1 modulates the pathogenesis of ADM-induced glomerulosclerosis and may provide an alternative approach to disease management.

Evaluating links through spectral decomposition

Spectral decomposition has rarely been used to investigate complex networks. In this work we apply this concept in order to define two kinds of link-directed attacks while quantifying their respective effects on the topology. Several other kinds of more traditional attacks are also adopted and compared. These attacks had substantially diverse effects, depending on each specific network (models and real-world structures). It is also shown that the spectrally based attacks have special effects in affecting the transitivity of the networks.

CID: an efficient complexity-invariant distance for time series

The ubiquity of time series data across almost all human endeavors has produced a great interest in time series data mining in the last decade. While dozens of classification algorithms have been applied to time series, recent empirical evidence strongly suggests that simple nearest neighbor classification is exceptionally difficult to beat. The choice of distance measure used by the nearest neighbor algorithm is important, and depends on the invariances required by the domain. For example, motion capture data typically requires invariance to warping, and cardiology data requires invariance to the baseline (the mean value). Similarly, recent work suggests that for time series clustering, the choice of clustering algorithm is much less important than the choice of distance measure used.In this work we make a somewhat surprising claim. There is an invariance that the community seems to have missed, complexity invariance. Intuitively, the problem is that in many domains the different classes may have different complexities, and pairs of complex objects, even those which subjectively may seem very similar to the human eye, tend to be further apart under current distance measures than pairs of simple objects. This fact introduces errors in nearest neighbor classification, where some complex objects may be incorrectly assigned to a simpler class. Similarly, for clustering this effect can introduce errors by “suggesting” to the clustering algorithm that subjectively similar, but complex objects belong in a sparser and larger diameter cluster than is truly warranted.We introduce the first complexity-invariant distance measure for time series, and show that it generally produces significant improvements in classification and clustering accuracy. We further show that this improvement does not compromise efficiency, since we can lower bound the measure and use a modification of triangular inequality, thus making use of most existing indexing and data mining algorithms. We evaluate our ideas with the largest and most comprehensive set of time series mining experiments ever attempted in a single work, and show that complexity-invariant distance measures can produce improvements in classification and clustering in the vast majority of cases.

Nonlinear/electromagnetic co-simulation of microwaves and millimeter-waves links

The Ph.D. thesis describes the simulations of different microwave links from the transmitter to the receiver intermediate-frequency ports, by means of a rigorous circuit-level nonlinear analysis approach coupled with the electromagnetic characterization of the transmitter and receiver front ends. This includes a full electromagnetic computation of the radiated far field which is used to establish the connection between transmitter and receiver. Digitally modulated radio-frequency drive is treated by a modulation-oriented harmonic-balance method based on Krylov-subspace model-order reduction to allow the handling of large-size front ends. Different examples of links have been presented: an End-to-End link simulated by making use of an artificial neural network model; the latter allows a fast computation of the link itself when driven by long sequences of the order of millions of samples. In this way a meaningful evaluation of such link performance aspects as the bit error rate becomes possible at the circuit level. Subsequently, a work focused on the co-simulation an entire link including a realistic simulation of the radio channel has been presented. The channel has been characterized by means of a deterministic approach, such as Ray Tracing technique. Then, a 2x2 multiple-input multiple-output antenna link has been simulated; in this work near-field and far-field coupling between radiating elements, as well as the environment factors, has been rigorously taken into account. Finally, within the scope to simulate an entire ultra-wideband link, the transmitting side of an ultrawideband link has been designed, and an interesting Front-End co-design technique application has been setup.

Nonlinear / electromagnetic co-simulation and co-design of microwave links in highly polluted and / or strongly inhomogeneous environments

The objective of the Ph.D. thesis is to put the basis of an all-embracing link analysis procedure that may form a general reference scheme for the future state-of-the-art of RF/microwave link design: it is basically meant as a circuit-level simulation of an entire radio link, with – generally multiple – transmitting and receiving antennas examined by EM analysis. In this way the influence of mutual couplings on the frequency-dependent near-field and far-field performance of each element is fully accounted for. The set of transmitters is treated as a unique nonlinear system loaded by the multiport antenna, and is analyzed by nonlinear circuit techniques. In order to establish the connection between transmitters and receivers, the far-fields incident onto the receivers are evaluated by EM analysis and are combined by extending an available Ray Tracing technique to the link study. EM theory is used to describe the receiving array as a linear active multiport network. Link performances in terms of bit error rate (BER) are eventually verified a posteriori by a fast system-level algorithm. In order to validate the proposed approach, four heterogeneous application contexts are provided. A complete MIMO link design in a realistic propagation scenario is meant to constitute the reference case study. The second one regards the design, optimization and testing of various typologies of rectennas for power generation by common RF sources. Finally, the project and implementation of two typologies of radio identification tags, at X-band and V-band respectively. In all the cases the importance of an exhaustive nonlinear/electromagnetic co-simulation and co-design is demonstrated to be essential for any accurate system performance prediction.

Tuning the structural and magnetic properties of Sr 2 FeReO 6 by substituting Fe and Re with valence invariant metals

In the course of this work the effect of metal substitution on the structural and magnetic properties of the double perovskites Sr2MM’O6 (M = Fe, substituted by Cr, Zn and Ga; M’ = Re, substituted by Sb) was explored by means of X-ray diffraction, magnetic measurements, band structure calculations, Mößbauer spectroscopy and conductivity measurements. The focus of this study was the determination of (i) the kind and structural boundary conditions of the magnetic interaction between the M and M’ cations and (ii) the conditions for the principal application of double perovskites as spintronic materials by means of the band model approach. Strong correlations between the electronic, structural and magnetic properties have been found during the study of the double perovskites Sr2Fe1-xMxReO6 (0 < x < 1, M = Zn, Cr). The interplay between van Hove-singularity and Fermi level plays a crucial role for the magnetic properties. Substitution of Fe by Cr in Sr2FeReO6 leads to a non-monotonic behaviour of the saturation magnetization (MS) and an enhancement for substitution levels up to 10 %. The Curie temperatures (TC) monotonically increase from 401 to 616 K. In contrast, Zn substitution leads to a continuous decrease of MS and TC. The diamagnetic dilution of the Fe-sublattice by Zn leads to a transition from an itinerant ferrimagnetic to a localized ferromagnetic material. Thus, Zn substitution inhibits the long-range ferromagnetic interaction within the Fe-sublattice and preserves the long-range ferromagnetic interaction within the Re-sublattice. Superimposed on the electronic effects is the structural influence which can be explained by size effects modelled by the tolerance factor t. In the case of Cr substitution, a tetragonal – cubic transformation for x > 0.4 is observed. For Zn substituted samples the tetragonal distortion linearly increases with increasing Zn content. In order to elucidate the nature of the magnetic interaction between the M and M’ cations, Fe and Re were substituted by the valence invariant main group metals Ga and Sb, respectively. X-ray diffraction reveals Sr2FeRe1-xSbxO6 (0 < x < 0.9) to crystallize without antisite disorder in the tetragonal distorted perovskite structure (space group I4/mmm). The ferrimagnetic behaviour of the parent compound Sr2FeReO6 changes to antiferromagnetic upon Sb substitution as determined by magnetic susceptibility measurements. Samples up to a doping level of 0.3 are ferrimagnetic, while Sb contents higher than 0.6 result in an overall antiferromagnetic behaviour. 57Fe Mößbauer results show a coexistence of ferri- and antiferromagnetic clusters within the same perovskite-type crystal structure in the Sb substitution range 0.3 < x < 0.8, whereas Sr2FeReO6 and Sr2FeRe0.9Sb0.1O6 are “purely” ferrimagnetic and Sr2FeRe0.1Sb0.9O6 contains antiferromagnetically ordered Fe sites only. Consequently, a replacement of the Re atoms by a nonmagnetic main group element such as Sb blocks the double exchange pathways Fe–O–Re(Sb)–O–Fe along the crystallographic axis of the perovskite unit cell and destroys the itinerant magnetism of the parent compound. The structural and magnetic characterization of Sr2Fe1-xGaxReO6 (0 < x < 0.7) exhibit a Ga/Re antisite disorder which is unexpected because the parent compound Sr2FeReO6 shows no Fe/Re antisite disorder. This antisite disorder strongly depends on the Ga content of the sample. Although the X-ray data do not hint at a phase separation, sample inhomogeneities caused by a demixing are observed by a combination of magnetic characterization and Mößbauer spectroscopy. The 57Fe Mößbauer data suggest the formation of two types of clusters, ferrimagnetic Fe- and paramagnetic Ga-based ones. Below 20 % Ga content, Ga statistically dilutes the Fe–O–Re–O–Fe double exchange pathways. Cluster formation begins at x = 0.2, for 0.2 < x < 0.4 the paramagnetic Ga-based clusters do not contain any Fe. Fe containing Ga-based clusters which can be detected by Mößbauer spectroscopy firstly appear for x = 0.4.