Symmetries and fixed point stability of stochastic differential equations modeling self-organized criticality

A stochastic nonlinear partial differential equation is constructed for two different models exhibiting self-organized criticality: the Bak-Tang-Wiesenfeld (BTW) sandpile model [Phys. Rev. Lett. 59, 381 (1987); Phys. Rev. A 38, 364 (1988)] and the Zhang model [Phys. Rev. Lett. 63, 470 (1989)]. The dynamic renormalization group (DRG) enables one to compute the critical exponents. However, the nontrivial stable fixed point of the DRG transformation is unreachable for the original parameters of the models. We introduce an alternative regularization of the step function involved in the threshold condition, which breaks the symmetry of the BTW model. Although the symmetry properties of the two models are different, it is shown that they both belong to the same universality class. In this case the DRG procedure leads to a symmetric behavior for both models, restoring the broken symmetry, and makes accessible the nontrivial fixed point. This technique could also be applied to other problems with threshold dynamics.

Phenomenological approach to nonlinear Langevin equations

In this paper we address the problem of consistently constructing Langevin equations to describe fluctuations in nonlinear systems. Detailed balance severely restricts the choice of the random force, but we prove that this property, together with the macroscopic knowledge of the system, is not enough to determine all the properties of the random force. If the cause of the fluctuations is weakly coupled to the fluctuating variable, then the statistical properties of the random force can be completely specified. For variables odd under time reversal, microscopic reversibility and weak coupling impose symmetry relations on the variable-dependent Onsager coefficients. We then analyze the fluctuations in two cases: Brownian motion in position space and an asymmetric diode, for which the analysis based in the master equation approach is known. We find that, to the order of validity of the Langevin equation proposed here, the phenomenological theory is in agreement with the results predicted by more microscopic models

MAP/ERK kinase kinase 1 (MEKK1) mediates transcriptional repression by interacting with polycystic kidney disease-1 (PKD1) promoter-bound p53 tumor suppressor protein.

Mitogen-activated protein kinase (MAPK) cascades regulate a wide variety of cellular processes that ultimately depend on changes in gene expression. We have found a novel mechanism whereby one of the key MAP3 kinases, Mekk1, regulates transcriptional activity through an interaction with p53. The tumor suppressor protein p53 down-regulates a number of genes, including the gene most frequently mutated in autosomal dominant polycystic kidney disease (PKD1). We have discovered that Mekk1 translocates to the nucleus and acts as a co-repressor with p53 to down-regulate PKD1 transcriptional activity. This repression does not require Mekk1 kinase activity, excluding the need for an Mekk1 phosphorylation cascade. However, this PKD1 repression can also be induced by the stress-pathway stimuli, including TNFα, suggesting that Mekk1 activation induces both JNK-dependent and JNK-independent pathways that target the PKD1 gene. An Mekk1-p53 interaction at the PKD1 promoter suggests a new mechanism by which abnormally elevated stress-pathway stimuli might directly down-regulate the PKD1 gene, possibly causing haploinsufficiency and cyst formation.

Boundary between Soil and Saprolite in Alisols in the South of Brazil

Despite numerous studies conducted on the lower limit of soil and its contact with saprolite layers, a great deal of work is left to standardize identification and annotation of these variables in the field. In shallow soils, the appropriately noting these limits or contacts is essential for determining their behavior and potential use. The aims of this study were to identify and define the field contact and/or transition zone between soil and saprolite in profiles of an Alisol derived from fine sandstone and siltstone/claystone in subtropical southern Brazil and to subsequently validate the field observations through a multivariate analysis of laboratory analytical data. In the six Alisol profiles evaluated, the sequence of horizons found was A, Bt, C, and Cr, where C was considered part of the soil due to its pedogenetic structure, and Cr was considered saprolite due to its rock structure. The morphological properties that were determined in the field and that were different between the B and C horizons and the Cr layer were color, structure, texture, and fragments of saprolite. According to the test of means, the properties that support the inclusion of the C horizon as part of the soil are sand, clay, water-dispersible clay, silt/clay ratio, macroporosity, total porosity, resistance to penetration, cation exchange capacity, Fe extracted by DCB, Al, H+Al, and cation exchange capacity of clay. The properties that support the C horizon as a transition zone are silt, Ca, total organic C, and Fe extracted by ammonium oxalate. Discriminant analysis indicated differences among the three horizons evaluated.

An AdS/QCD model from tachyon condensation: II

A simple holographic model is presented and analyzed that describes chiral symmetry breaking and the physics of the meson sector in QCD. This is a bottom-up model that incorporates string theory ingredients like tachyon condensation which is expected to be the main manifestation of chiral symmetry breaking in the holographic context. As a model for glue the Kuperstein-Sonnenschein background is used. The structure of the flavor vacuum is analyzed in the quenched approximation. Chiral symmetry breaking is shown at zero temperature. Above the deconfinement transition chiral symmetry is restored. A complete holographic renormalization is performed and the chiral condensate is calculated for different quark masses both at zero and non-zero temperatures. The 0++, 0¿+, 1++, 1¿¿ meson trajectories are analyzed and their masses and decay constants are computed. The asymptotic trajectories are linear. The model has one phenomenological parameter beyond those of QCD that affects the 1++, 0¿+ sectors. Fitting this parameter we obtain very good agreement with data. The model improves in several ways the popular hard-wall and soft wall bottom-up models.

SPATIAL DEPENDENCE OF ELECTRICAL CONDUCTIVITY AND CHEMICAL PROPERTIES OF THE SOIL BY ELECTROMAGNETIC INDUCTION

Brazilian soils have natural high chemical variability; thus, apparent electrical conductivity (ECa) can assist interpretation of crop yield variations. We aimed to select soil chemical properties with the best linear and spatial correlations to explain ECa variation in the soil using a Profiler sensor (EMP-400). The study was carried out in Sidrolândia, MS, Brazil. We analyzed the following variables: electrical conductivity - EC (2, 7, and 15 kHz), organic matter, available K, base saturation, and cation exchange capacity (CEC). Soil ECa was measured with the aid of an all-terrain vehicle, which crossed the entire area in strips spaced at 0.45 m. Soil samples were collected at the 0-20 cm depth with a total of 36 samples within about 70 ha. Classical descriptive analysis was applied to each property via SAS software, and GS+ for spatial dependence analysis. The equipment was able to simultaneously detect ECa at the different frequencies. It was also possible to establish site-specific management zones through analysis of correlation with chemical properties. We observed that CEC was the property that had the best correlation with ECa at 15 kHz.

Remote Synchronization Reveals Network Symmetries and Functional Modules

We study a Kuramoto model in which the oscillators are associated with the nodes of a complex network and the interactions include a phase frustration, thus preventing full synchronization. The system organizes into a regime of remote synchronization where pairs of nodes with the same network symmetry are fully synchronized, despite their distance on the graph. We provide analytical arguments to explain this result, and we show how the frustration parameter affects the distribution of phases. An application to brain networks suggests that anatomical symmetry plays a role in neural synchronization by determining correlated functional modules across distant locations.

Collineations of a symmetric 2-covariant tensor: Ricci collineations

The infinitesimal transformations that leave invariant a two-covariant symmetric tensor are studied. The interest of these symmetry transformations lays in the fact that this class of tensors includes the energy-momentum and Ricci tensors. We find that in most cases the class of infinitesimal generators of these transformations is a finite dimensional Lie algebra, but in some cases exhibiting a higher degree of degeneracy, this class is infinite dimensional and may fail to be a Lie algebra. As an application, we study the Ricci collineations of a type B warped spacetime.

Valence-bond treatment of distortions in polyacene polymers

Distortions of polyacene polymers are studied within a many-body valence-bond framework using a powerful transfer-matrix technique for the valence-bond (or Heisenberg) model of the system. The computations suggest that the ground-state geometry is either totally symmetric or possibly exhibits a slight (A2 or B2 symmetry) bond-alternation distortion. The lowest-energy (nonsymmetric, in-plane) distortions are the A2 and B2 modes, which, within our approximations, are degenerate.

RECOVERY OF AN OXISOL DEGRADED BY THE CONSTRUCTION OF A HYDROELECTRIC POWER PLANT

ABSTRACT The removal of thick layers of soil under native scrubland (Cerrado) on the right bank of the Paraná River in Selvíria (State of Mato Grosso do Sul, Brazil) for construction of the Ilha Solteira Hydroelectric Power Plant caused environmental damage, affecting the revegetation process of the stripped soil. Over the years, various kinds of land use and management systems have been tried, and the aim of this study was to assess the effects of these attempts to restore the structural quality of the soil. The experiment was conducted considering five treatments and thirty replications. The following treatments were applied: stripped soil without anthropic intervention and total absence of plant cover; stripped soil treated with sewage sludge and planted to eucalyptus and grass a year ago; stripped soil developing natural secondary vegetation (capoeira) since 1969; pastureland since 1978, replacing the native vegetation; and soil under native vegetation (Cerrado). In the 0.00-0.20 m layer, the soil was chemically characterized for each experimental treatment. A 30-point sampling grid was used to assess soil porosity and bulk density, and to assess aggregate stability in terms of mean weight diameter (MWD) and geometric mean diameter (GMD). Aggregate stability was also determined using simulated rainfall. The results show that using sewage sludge incorporated with a rotary hoe improved the chemical fertility of the soil and produced more uniform soil pore size distribution. Leaving the land to develop secondary vegetation or turning it over to pastureland produced an intermediate level of structural soil quality, and these two treatments produced similar results. Stripped soil without anthropic intervention was of the lowest quality, with the lowest values for cation exchange capacity (CEC) and macroporosity, as well as the highest values of soil bulk density and percentage of aggregates with diameter size <0.50 mm, corroborated by its lower organic matter content. However, the percentage of larger aggregates was higher in the native vegetation treatment, which boosted MWD and GMD values. Therefore, assessment of some land use and management systems show that even decades after their implementation to mitigate the degenerative effects resulting from the installation of the Hydroelectric Plant, more efficient approaches are still required to recover the structural quality of the soil.

Electrical Conductivity and Chemical Composition of Soil Solution: Comparison of Solution Samplers in Tropical Soils

ABSTRACT Soil solution samplers may have the same working principle, but they differ in relation to chemical and physical characteristics, cost and handling, and these aspects exert influence on the chemical composition of the soil solution obtained. This study was carried out to evaluate, over time, the chemical composition of solutions extracted by Suolo Acqua, with the hydrophilic membrane (HM) as a standard, using soils with contrasting characteristics, and to determine the relationship between electrical conductivity (EC) and concentration of ions and pH of soil solution samples. This study was carried out under laboratory conditions, using three soils samples with different clay and organic matter (OM) contents. Soil solution contents of F−, Cl−, NO−3, Br−, SO42−, Na+, NH4+, K+, Mg2+, Ca2+, were analyzed, as well as inorganic, organic, and total C contents, pH, and EC, in four successive sampling times. Soil solution chemical composition extracted by the Suolo Acqua sampler is similar to that collected by the HM, but the Suolo Acqua extracted more Na+ and soluble organic C than the HM solution. Solution EC, cation and anion concentrations, and soluble C levels are higher in the soil with greater clay and OM contents (Latossolo and Cambissolo in this case). Soil solution composition varied over time, with considerable changes in pH, EC, and nutrient concentrations, especially associated with soil OM. Thus, single and isolated sampling of the soil solution must be avoided, otherwise composition of the soil solution may not be correctly evaluated. Soil solution EC was regulated by pH, as well as the sum of cation and anion concentrations, and the C contents determined in the soil liquid phase.

Extraction and concentration of vapors from fire debris for forensic purposes: evaluation of the use of Radiello Passive Air Sampler

The Radiello Passive Air Sampler is one of the latest innovations developed for the sampling of pollutants in the air by passive headspace. It has been reported that its properties allow an enhanced sensitivity, reproducibility and adsorption capacity. It therefore appears to be of interest in the extraction of potential residues of ignitable liquids present in fire debris when arson is suspected. A theoretical approach and several laboratory tests have made it possible to precisely characterize in a forensic perspective the potential of the device in extracting and concentrating the vapors of ignitable liquids found in fire debris. Despite some advantages, the Radiello device appears to be less efficient than traditional axial symmetry samplers.

Sperm velocity in an Alpine whitefish: effects of age, size, condition, fluctuating asymmetry and gonad abnormalities

The relationship between sperm velocity and individual age, size, body condition and fluctuating asymmetry was investigated in Alpine whitefish Coregonus fatioi. The fish analysed belonged to one among several sympatric whitefish populations of Lake Thun, Switzerland, which are characterized by a high prevalence of gonad alterations. Therefore, sperm velocity data were also tested for a link between gonad deformation and sperm swimming speed. Sperm velocity was significantly lower in larger-grown individuals and in individuals of higher body condition. As expected, sperm velocity was higher in males with higher levels of fluctuating asymmetry, but it did not significantly vary with male age. Moreover, variation in sperm velocity was found to be significantly higher in individuals showing some types of gonad alterations but it did not significantly correlate with the presence of other types of alterations. (C) 2007 The Authors Journal compilation (C) 2007 The Fisheries Society of the British Isles.

Aggregate monotonic stable single-valued solutions for cooperative games

[cat] En aquest treball caracteritzem les solucions puntuals de jocs cooperatius d'utilitat transferible que compleixen selecció del core i monotonia agregada. També mostrem que aquestes dues propietats són compatibles amb la individualitat racional, la propietat del jugador fals i la propietat de simetria. Finalment, caracteritzem les solucions puntuals que compleixen les cinc propietats a l'hora.

Étude du mécanisme de transport des cations par la Na, K-ATPase et de son implication dans la migraine familiale hémiplégique de type 2

Résumé La Na,K-ATPase est une protéine transmembranaire, présente dans toutes les cellules de mammifères et indispensable à la viabilité cellulaire. Elle permet le maintien des gradients sodiques et potassiques à l'origine du potentiel membranaire en transportant 3 Na+ en dehors de la cellule contre 2 K+, grâce à l'énergie fournie par l'hydrolyse d'une molécule d'ATP. Le potentiel membranaire est indispensable au maintien de l'excitabilité cellulaire et à la transmission de l'influx nerveux. Il semblerait que la Na,K-ATPase soit liée à l'hypertension et à certains troubles neurologiques comme la Migraine Familiale Hémiplégique (1VIFH). La MFH est une forme de migraine avec aura, qui se caractérise par une hémiparésie. Cette forme de migraine est très rare. Elle se transmet génétiquement sur un mode autosomique dominant. Plusieurs mutations localisées dans le gène de la Na,K-ATPase ont été identifiées durant ces 3 dernières années. C'est la première fois qu'une maladie génétique est associée au gène de la Na,K-ATPase. La compréhension du fonctionnement de cette protéine peut donner des informations sur les mécanismes conduisant à ces pathologies. On sait que la fonction d'une protéine est liée à sa structure. L'étude de sa fonction nécessite donc l'étude de sa structure. Alors que la structure de la SERCA a été déterminée à haute résolution, par cristallographie, celle de la Na,K-ATPase ne l'est toujours pas. Mais ces 2 ATPases présentent une telle homologie qu'un modèle de la Na,K-ATPase a pu être élaboré à partir de la structure de la SERCA. Les objectifs de cette étude sont d'une part, de comprendre le contrôle de l'accessibilité du K+ extracellulaire àses sites de liaison. Pour cela, nous avons ciblé cette étude sur la 2ìème et la 31eme boucle extracellulaire, qui relient respectivement les segments transmembranaires (STM) 3-4 et 5-6. Le choix s'est porté sur ces 2 boucles car elles bordent le canal des cations formés des 4ième' Sième et 6'ème hélices. D'autre part, nous avons également essayer de comprendre les effets des mutations, liées à la Migraine Familiale Hémiplégique de type 2 (MFH2), sur la fonctionnalité de la Na,K-ATPase. Alors que les STM et les domaines cytoplasmiques sont relativement proches entre la Na,KATPase et la SERCA, les boucles extracellulaires présentent des différences. Le modèle n'est donc pas une approche fiable pour déterminer la structure et la fonction des régions extracellulaires. Nous avons alors utilisé une approche fonctionnelle faisant appel à la mutation dirigée puis à l'étude de l'activité fonctionnelle de la Na,K ATPase par électrophysiologie sur des ovocytes de Xenopus. En conclusion, nous pouvons dire que la troisième boucle extracellulaire participerait à la structure de la voie d'entrée des cations et que la deuxième boucle extracellulaire semble impliquée dans le contrôle de l'accessibilité des ions K+àses sites de liaison. Concernant les mutations associées à la MFH2, nos résultats ont montré une forte diminution de l'activité fonctionnelle de la pompe Na,K, inférieure aux conditions physiologiques de fonctionnement, et pour une des mutations nous avons observés une diminution de l'affmité apparente au K+ externe. Nous poumons faire l'hypothèse que l'origine pathologique de la migraine est liée à une diminution de l'activité de la pompe à Na+. Summary The Na,K-ATPase is a transmembrane protein, present in all mammalian cells and is necessary for the viability of the cells. It maintains the gradients of Na+ and K+ involved in the membrane potential, by transporting 3Na+ out the cell, and 2K+ into the cell, using the energy providing from one ATP molecule hydrolysis. The membrane potential is necessary for the cell excitability and for the transmission of the nervous signal. Some evidence show that Na,K-ATPase is involved in hypertension and neurological disorders like the Familial Hemiplegic Migraine (FHM). La FHM is a rare form of migraine characterised by aura and hemiparesis and an autosomal dominant transmission. Several mutations linked to the Na,KATPase gene have been identified during these 3 last years. It's the first genetic disorder associated with the Na,K-ATPase gene. Understand the function of this protein is important to elucidate the mechanisms implicated in these pathologies. The function of a protein is linked with its structure. Thus, to know the function of a protein, we need to know its structure. While the Ca-ATPase (SERCA) has been crystallised with a high resolution, the structure of the Na,K-ATPase is not known. Because of the great homology between these 2 ATPases, a model of the Na,K-ATPase was realised by comparing with the structure of the SERCA. The aim of this study is on one side, understand the control of the extracellular K+ accessibility to their binding sites. Because of theirs closed proximity with the cation pathway, located between the 4th, 5th and 6th helices, we have targeted this study on the 2nd and the 3rd extracellular loops linking respectively the transmembrane segment (TMS) 3 and 4, and the TMS 5 and 6. And on the other side, we have tried to understand the functional effects of mutations linked with the Familial Hemiplegic Migraine Type 2 (FHM2). In contrast with the transmembrane segments and the cytoplasmic domains, the extracellular loops show lots of difference between Na,K-ATPase and SERCA, the model is not a good approach to know the structure and the function of the extracellular loops. Thus, we have used a functional approach consisting in directed mutagenesis and the study of the functional activity of the Na,K-ATPase by electrophysiological techniques with Xenopus oocytes. In conclusion, we have demonstrated that the third extracellular loop could participate in the structure of the entry of the cations pathway and that the second extracellular loop could control the K+ accessibility to their binding sites. Concerning the mutations associated with the FHM2, our results showed a strong decrease in the functional activity of the Na,K-pump under physiological conditions and for one of mutations, induce a decrease in the apparent external K+ affinity. We could make the hypothesis that the pathogenesis of migraine is related to the decrease in Na,K-pump activity. Résumé au large publique De la même manière que l'assemblage des mots forme des phrases et que l'assemblage des phrases forme des histoires, l'assemblage des cellules forme des organes et l'ensemble des organes constitue les êtres vivants. La fonction d'une cellule dans le corps humain peut se rapprocher de celle d'une usine hydroélectrique. La matière première apportée est l'eau, l'usine électrique va ensuite convertir l'eau en énergie hydraulique pour fournir de l'électricité. Le fonctionnement de base d'une cellule suit le même processus. La cellule a besoin de matières premières (oxygène, nutriments, eau...) pour produire une énergie sous forme chimique, l'ATP. Cette énergie est utilisée par exemple pour contracter les muscles et permet donc à l'individu de se déplacer. Morphologiquement la cellule est une sorte de petit sac rempli de liquide (milieu intracellulaire) baignant elle-même dans le liquide (milieu extracellulaire) composant le corps humain (un adulte est constitué environ de 65 % d'eau). La composition du milieu intracellulaire est différente de celle du milieu extracellulaire. Cette différence doit être maintenue pour que l'organisme fonctionne correctement. Une des différences majeures est la quantité de sodium. En effet il y a beaucoup plus de sodium à l'extérieur qu'à l'intérieur de la cellule. Bien que l'intérieur de la cellule soit isolé de l'extérieur par une membrane, le sodium arrive à passer à travers cette membrane, ce qui a tendance à augmenter la quantité de sodium dans la cellule et donc à diminuer sa différence de concentration entre le milieu extracellulaire et le milieu intracellulaire. Mais dans les membranes, il existe des pompes qui tournent et dont le rôle est de rejeter le sodium de la cellule. Ces pompes sont des protéines connues sous le nom de pompe à sodium ou Na,K-ATPase. On lui attribue le nom de Na,K-ATPase car en réalité elle rejette du sodium (Na) et en échange elle fait entrer dans la cellule du potassium (K), et pour fonctionner elle a besoin d'énergie (ATP). Lorsque les pompes à sodium ne fonctionnent pas bien, cela peut conduire à des maladies. En effet la Migraine Familiale Hémiplégique de type 2, est une migraine très rare qui se caractérise par l'apparition de la paralysie de la moitié d'un corps avant l'apparition du mal de tête. C'est une maladie génétique (altération qui modifie la fonction d'une protéine) qui touche la pompe à sodium située dans le cerveau. On a découvert que certaines altérations (mutations) empêchent les pompes à sodium de fonctionner correctement. On pense alors que le développement des migraines est en partie dû au fait que ces pompes fonctionnent moins bien. Il est important de bien connaître la fonction de ces pompes car cela permet de comprendre des mécanismes pouvant conduire à certaines maladies, comme les migraines. En biologie, la fonction d'une protéine est étudiée à travers sa structure. C'est pourquoi l'objectif de cette thèse a été d'étudier la structure de la Na,K-ATPase afin de mieux comprendre son mécanisme d'action.