$E_{1}$-Formality of complex algebraic varieties

Let $X$ be a smooth complex algebraic variety. Morgan showed that the rational homotopy type of $X$ is a formal consequence of the differential graded algebra defined by the first term $E_{1}(X,W)$ of its weight spectral sequence. In the present work, we generalize this result to arbitrary nilpotent complex algebraic varieties (possibly singular and/or non-compact) and to algebraic morphisms between them. In particular, our results generalize the formality theorem of Deligne, Griffiths, Morgan and Sullivan for morphisms of compact Kähler varieties, filling a gap in Morgan"s theory concerning functoriality over the rationals. As an application, we study the Hopf invariant of certain algebraic morphisms using intersection theory.

Weight filtration on the cohomology of complex analytic spaces

We extend Deligne's weight filtration to the integer cohomology of complex analytic spaces (endowed with an equivalence class of compactifications). In general, the weight filtration that we obtain is not part of a mixed Hodge structure. Our purely geometric proof is based on cubical descent for resolution of singularities and Poincaré-Verdier duality. Using similar techniques, we introduce the singularity filtration on the cohomology of compactificable analytic spaces. This is a new and natural analytic invariant which does not depend on the equivalence class of compactifications and is related to the weight filtration.

Greek by Steven Berkoff (1980): The Risky Transformation of Sophocles’ Oedipus Rex into a Love Story

[eng] Can Sophocles’ Oedipus Rex really be transformed into a love story, as in Steven Berkoff’s drama entitled Greek? This article will show that, although Greek may be viewed by some critics as simply a provocative drama by no means intended to justify incest, directors, actors and critics in the end become enthralled by the powerful love story that ensues between Eddy and his wife and mother. This perspective reveals that Berkoff’s adaptation, intended to portray the social degradation of 1980s Great Britain, is in reality a quite risky proposition since it represents a flat denial of the tragic awareness of contemporary men and women. However, if this is the case, the audience, apart from enjoying the performance of Berkoff’s drama, might question, even from a non-fundamentalist perspective within the classical tradition, to what degree it makes sense to take inspiration from a text by Sophocles that precisely illustrates the great tragic awareness of the ancient Greeks.

Greek de Steven Berkoff (1980): L’arriscada conversió de l’Èdip rei de Sòfocles en una love story

[cat] ¿Podem convertir l’Èdip rei de Sòfocles en una història d’amor com ho fa Berkoff a Greek?. Tot i que alguns crítics llegeixen Greek només com un drama provocador que de cap manera intenta justificar l’incest, directors, actors i crítics resten finalment captivats per la impactant història d’amor entre Eddy i la seva esposa-mare. Això demostraria que l’adaptació de Berkoff, pensada per a il·lustrar la degradació social de la Gran Bretanya dels 80s, esdevé una proposta arriscada, car significa negar de fet la consciència tràgica dels homes i dones contemporanis. Tanmateix, si aquest és el cas, lectors i espectadors, a banda de l’indubtable plaer d’assistir a la representació de Greek, poden preguntar-se, fins i tot des d’una perspectiva no fonamentalista de la tradició clàssica, si té sentit inspirar-se en el text de Sòfocles, el qual mostra precisament la gran consciència tràgica dels grecs.

Analysis of a Plant Complex Resistance Gene Locus Underlying Immune-Related Hybrid Incompatibility and Its Occurrence in Nature

Mechanisms underlying speciation in plants include detrimental (incompatible) genetic interactions between parental alleles that incur a fitness cost in hybrids. We reported on recessive hybrid incompatibility between an Arabidopsis thaliana strain from Poland, Landsberg erecta (Ler), and many Central Asian A. thaliana strains. The incompatible interaction is determined by a polymorphic cluster of Toll/interleukin-1 receptor-nucleotide binding-leucine rich repeat (TNL) RPP1 (Recognition of Peronospora parasitica1)-like genes in Ler and alleles of the receptor-like kinase Strubbelig Receptor Family 3 (SRF3) in Central Asian strains Kas-2 or Kond, causing temperature-dependent autoimmunity and loss of growth and reproductive fitness. Here, we genetically dissected the RPP1-like Ler locus to determine contributions of individual RPP1-like Ler (R1R8) genes to the incompatibility. In a neutral background, expression of most RPP1-like Ler genes, except R3, has no effect on growth or pathogen resistance. Incompatibility involves increased R3 expression and engineered R3 overexpression in a neutral background induces dwarfism and sterility. However, no individual RPP1-like Ler gene is sufficient for incompatibility between Ler and Kas-2 or Kond, suggesting that co-action of at least two RPP1-like members underlies this epistatic interaction. We find that the RPP1-like Ler haplotype is frequent and occurs with other Ler RPP1-like alleles in a local population in Gorzów Wielkopolski (Poland). Only Gorzów individuals carrying the RPP1-like Ler haplotype are incompatible with Kas-2 and Kond, whereas other RPP1-like alleles in the population are compatible. Therefore, the RPP1-like Ler haplotype has been maintained in genetically different individuals at a single site, allowing exploration of forces shaping the evolution of RPP1-like genes at local and regional population scales.

Fuzzy subgroups, algebraic and topological points of view and complex analysis

Fuzzy subsets and fuzzy subgroups are basic concepts in fuzzy mathematics. We shall concentrate on fuzzy subgroups dealing with some of their algebraic, topological and complex analytical properties. Explorations are theoretical belonging to pure mathematics. One of our ideas is to show how widely fuzzy subgroups can be used in mathematics, which brings out the wealth of this concept. In complex analysis we focus on Möbius transformations, combining them with fuzzy subgroups in the algebraic and topological sense. We also survey MV spaces with or without a link to fuzzy subgroups. Spectral space is known in MV algebra. We are interested in its topological properties in MV-semilinear space. Later on, we shall study MV algebras in connection with Riemann surfaces. In fact, the Riemann surface as a concept belongs to complex analysis. On the other hand, Möbius transformations form a part of the theory of Riemann surfaces. In general, this work gives a good understanding how it is possible to fit together different fields of mathematics.

DWI and complex brain network analysis predicts vascular cognitive impairment in spontaneous hypertensive rats undergoing executive function tests

The identification of biomarkers of vascular cognitive impairment is urgent for its early diagnosis. The aim of this study was to detect and monitor changes in brain structure and connectivity, and to correlate them with the decline in executive function. We examined the feasibility of early diagnostic magnetic resonance imaging (MRI) to predict cognitive impairment before onset in an animal model of chronic hypertension: Spontaneously Hypertensive Rats. Cognitive performance was tested in an operant conditioning paradigm that evaluated learning, memory, and behavioral flexibility skills. Behavioral tests were coupled with longitudinal diffusion weighted imaging acquired with 126 diffusion gradient directions and 0.3 mm(3) isometric resolution at 10, 14, 18, 22, 26, and 40 weeks after birth. Diffusion weighted imaging was analyzed in two different ways, by regional characterization of diffusion tensor imaging (DTI) indices, and by assessing changes in structural brain network organization based on Q-Ball tractography. Already at the first evaluated times, DTI scalar maps revealed significant differences in many regions, suggesting loss of integrity in white and gray matter of spontaneously hypertensive rats when compared to normotensive control rats. In addition, graph theory analysis of the structural brain network demonstrated a significant decrease of hierarchical modularity, global and local efficacy, with predictive value as shown by regional three-fold cross validation study. Moreover, these decreases were significantly correlated with the behavioral performance deficits observed at subsequent time points, suggesting that the diffusion weighted imaging and connectivity studies can unravel neuroimaging alterations even overt signs of cognitive impairment become apparent.

One, two, or many mechanisms? The brain's processing of complex words

The heated debate over whether there is only a single mechanism or two mechanisms for morphology has diverted valuable research energy away from the more critical questions about the neural computations involved in the comprehension and production of morphologically complex forms. Cognitive neuroscience data implicate many brain areas. All extant models, whether they rely on a connectionist network or espouse two mechanisms, are too underspecified to explain why more than a few brain areas differ in their activity during the processing of regular and irregular forms. No one doubts that the brain treats regular and irregular words differently, but brain data indicate that a simplistic account will not do. It is time for us to search for the critical factors free from theoretical blinders.

The love marriage : challenging Victorian myths in Anne Brontë’s 'The Tenant of Wildfell Hall'

La tesina analitza com Anne Brontë desafia el mite del casament romàntic a la novel·la The Tenant of Wildfell Hall. Argumento que aquesta crítica es fa mostrant les conseqüències nefastes d’un matrimoni (entre l’Arthur i l’Helen) basat en l’atracció i en la idea que una dona pot salvar un home de mala vida. Malgrat que la novel·la acaba amb un altre casament (entre l’Helen i en Gilbert), si s’analitza en detall es pot veure que presenta elements subversius. Per exemple, la seva unió està basada en igualtat intel·lectual i compatibilitat de caràcters, enlloc d’igualtat econòmica i social

Phase diagram and complex patterns in the modeling of the bromate-oxalic acid-Ce-acetone oscillating reaction

Simulations have been carried out on the bromate - oxalic acid - Ce(IV) - acetone oscillating reaction, under flow conditions, using Field and Boyd's model (J. Phys. Chem. 1985, 89, 3707). Many different complex dynamic behaviors were found, including simple periodic oscillations, complex periodic oscillations, quasiperiodicity and chaos. Some of these complex oscillations can be understood as belonging to a Farey sequence. The many different behaviors were systematized in a phase diagram which shows that some regions of complex patterns were nested with one inside the other. The existence of almost all known dynamic behavior for this system allows the suggestion that it can be used as a model for some very complex phenomena that occur in biological systems.

Human disease and drug pharmacology, complex as real life

In the past decades drug discovery practice has escaped from the complexity of the formerly used phenotypic screening in animals to focus on assessing drug effects on isolated protein targets in the search for drugs that exclusively and potently hit one selected target, thought to be critical for a given disease, while not affecting at all any other target to avoid the occurrence of side-effects. However, reality does not conform to these expectations, and, conversely, this approach has been concurrent with increased attrition figures in late-stage clinical trials, precisely due to lack of efficacy and safety. In this context, a network biology perspective of human disease and treatment has burst into the drug discovery scenario to bring it back to the consideration of the complexity of living organisms and particularly of the (patho)physiological environment where protein targets are (mal)functioning and where drugs have to exert their restoring action. Under this perspective, it has been found that usually there is not one but several disease-causing genes and, therefore, not one but several relevant protein targets to be hit, which do not work on isolation but in a highly interconnected manner, and that most known drugs are inherently promiscuous. In this light, the rationale behind the currently prevailing single-target-based drug discovery approach might even seem a Utopia, while, conversely, the notion that the complexity of human disease must be tackled with complex polypharmacological therapeutic interventions constitutes a difficult-torefuse argument that is spurring the development of multitarget therapies.

4 Love Sonnets

Digitoitu 16. 10. 2008.

Synthesis, characterization, DFT and Td-dfT study of the [Fe(mnt)(L)(t-BuNC) 2] octahedral complex (L = phen, bipy)

FeBr2 has reacted with an equivalent of mnt2- (mnt = cis-1,2-dicyanoethylene-1,2-dithiolate) and the α-diimine L (L = 1,10'-phenantroline, 2,2'-bipyridine) in THF solution, and followed by adding of t-butyl-isocyanide to give [Fe(mnt)(L)(t-BuNC)2] neutral compound. The products were characterized by infrared, UV-visible and Mössbauer spectroscopy, besides thermogravimetric and conductivity data. The geometry in the equilibrium was calculated by the density functional theory and the electronic spectrum by the time-dependent. The experimental and theoretical results in good agreement have defined an octahedral geometry with two isocyanide neighbours. The π→π* intraligand electronic transition was not observed for cis-isomers in the near-IR spectral region.

Selective and non-extractive spectrophotometric determination of cefdinir in formulations based on donor-acceptor complex formation

Cefdinir has broad spectrum of activity and high prescription rates, hence its counterfeiting seems imminent. We have proposed a simple, fast, selective and non-extractive spectrophotometric method for the content assay of cefdinir in formulations. The method is based on complexation of cefdinir and Fe under reducing condition in a buffered medium (pH 11) to form a magenta colored donor-acceptor complex (λ max = 550 nm; apparent molar absorptivity = 3720 L mol-1 cm-1). No other cephalosporins, penicillins and common excipients interfere under the test conditions. The Beer's law is followed in the concentration range 8-160 µg mL-1.