Computing congruences of modular forms and Galois representations modulo prime powers

This article starts a computational study of congruences of modular forms and modular Galoisrepresentations modulo prime powers. Algorithms are described that compute the maximum integermodulo which two monic coprime integral polynomials have a root in common in a sensethat is defined. These techniques are applied to the study of congruences of modular forms andmodular Galois representations modulo prime powers. Finally, some computational results withimplications on the (non-)liftability of modular forms modulo prime powers and possible generalisationsof level raising are presented.

Ignoring information in binary choice with continuous variables: When is less 'more'?

When can a single variable be more accurate in binary choice than multiple sources of information? We derive analytically the probability that a single variable (SV) will correctly predict one of two choices when both criterion and predictor are continuous variables. We further provide analogous derivations for multiple regression (MR) and equal weighting (EW) and specify the conditions under which the models differ in expected predictive ability. Key factors include variability in cue validities, intercorrelation between predictors, and the ratio of predictors to observations in MR. Theory and simulations are used to illustrate the differential effects of these factors. Results directly address why and when one-reason decision making can be more effective than analyses that use more information. We thus provide analytical backing to intriguing empirical results that, to date, have lacked theoretical justification. There are predictable conditions for which one should expect less to be more.

The meiosis-specific recombinase hDmc1 forms ring structures and interacts with hRad51.

Eukaryotic cells encode two homologs of Escherichia coli RecA protein, Rad51 and Dmc1, which are required for meiotic recombination. Rad51, like E.coli RecA, forms helical nucleoprotein filaments that promote joint molecule and heteroduplex DNA formation. Electron microscopy reveals that the human meiosis-specific recombinase Dmc1 forms ring structures that bind single-stranded (ss) and double-stranded (ds) DNA. The protein binds preferentially to ssDNA tails and gaps in duplex DNA. hDmc1-ssDNA complexes exhibit an irregular, often compacted structure, and promote strand-transfer reactions with homologous duplex DNA. hDmc1 binds duplex DNA with reduced affinity to form nucleoprotein complexes. In contrast to helical RecA/Rad51 filaments, however, Dmc1 filaments are composed of a linear array of stacked protein rings. Consistent with the requirement for two recombinases in meiotic recombination, hDmc1 interacts directly with hRad51.

Galois representations, embedding problems and modular forms

To an odd irreducible 2-dimensional complex linear representation of the absolute Galois group of the field Q of rational numbers, a modular form of weight 1 is associated (modulo Artin's conjecture on the L-series of the representation in the icosahedral case). In addition, linear liftings of 2-dimensional projective Galois representations are related to solutions of certain Galois embedding problems. In this paper we present some recent results on the existence of liftings of projective representations and on the explicit resolution of embedding problems associated to orthogonal Galois representations, and explain how these results can be used to construct modular forms.

Arithmetical problems in number fields, abelian varieties and modular forms

Number theory, a fascinating area in mathematics and one of the oldest, has experienced spectacular progress in recent years. The development of a deep theoretical background and the implementation of algorithms have led to new and interesting interrelations with mathematics in general which have paved the way for the emergence of major theorems in the area. This report summarizes the contribution to number theory made by the members of the Seminari de Teoria de Nombres (UB-UAB-UPC) in Barcelona. These results are presented in connection with the state of certain arithmetical problems, and so this monograph seeks to provide readers with a glimpse of some specific lines of current mathematical research.

Phosphate forms in plant and their internal buffering in five soybean cultivars

Differences among plants in their ability to support nutritional stress periods may be caused by a differential vacuole capacity of ion storage and release and may also depend on the intensity of nutrient re-translocation under such conditions. In five soybean cultivars, submitted to eight days of P deprivation, the dry matter production and the contents of three phosphorus (P) forms - inorganic (Pi), organic (Po), and acid-soluble total (Pts) of different plant organs were determined. Pi release velocity (RSPi) was estimated as the tangent to the equations obtained for Pi f(t) at the point t = 2 days (the mean point in the period of greatest Pi decrease), considering that -deltaPi/deltat expresses the rate of Pi release. The internal Pi buffering capacity (IBCPi) was calculated as the inverse of the RSPi. Cultivars' differences in size of the non-metabolic Pi pool, RSPi, and the ability to transport Pi from less to more actively metabolizing regions were evaluated. The preferential Pi source and sink compartments under limited P absorption conditions were also evaluated. The cultivar Santa Rosa showed the highest Pi storage ability when the external supply was high, and a more intensive release under low P supply conditions than IAC8 and UFV1. The cultivar Uberaba was superior to Doko in its ability to store and use Pi. In all cultivars, upper leaves and roots were the main sink of Pi stored in the middle and lower leaves. Roots and upper leaves showed larger RSPi and lower IBCPi values than middle and lower leaves.

On the binary nature of the γ-ray sources AGL J2241+4454 (= MWC 656) and HESS J0632+057 (= MWC 148)

We present optical spectroscopy of MWC 656 and MWC 148, the proposed optical counterparts of the gamma-ray sources AGL J2241+4454 and HESS J0632+0 57, respectively. The main parameters of the Halpha emission line (EW, FWHM and centroid velocity) in these stars are modulated on the proposed orbital periods of 60.37 and 321 days, respectively. These modulations are likely produced by the resonant interaction of the Be discs with compact stars in eccentric orbits. We also present radial velocity curves of the optical stars folded on the above periods and obtain the first orbital elements of the two gamma-ray sources thus confirming their binary nature. Our orbital solution support eccentricities e~0.4 and 0.83+-0.08 for MWC 656 and MWC 148, respectively. Further, our orbital elements imply that the X-ray outbursts in HESS J0632+057/MWC 148 are delayed ~0.3 orbital phases after periastron passage, similarly to the case of LS I +61 303. In addition, the optical photometric light curve maxima in AGL J2241+4454/MWC 656 occur ~0.25 phases passed periastron, similar to what is seen in LS I +61 303. We also find that the orbital eccentricity is correlated with orbital period for the known gamma-ray binaries. This is explained by the fact that small stellar separations are required for the efficient triggering of VHE radiation. Another correlation between the EW of Halpha and orbital period is also observed, similarly to the case of Be/X-ray binaries. These correlations are useful to provide estimates of the key orbital parameters Porb and e from the Halpha line in future Be gamma-ray binary candidates.

Persuasion, binary choice, and the costs of dishonesty

We study the strategic interaction between a decision maker who needs to take a binary decision but is uncertain about relevant facts and an informed expert who can send a message to the decision maker but has a preference over the decision.We show that the probability that the expert can persuade the decision maker to take the expert's preferred decision is a hump-shaped function of his costs of sending dishonest messages.

Phosphorous forms in cultivated indian black earth (anthrosols) of varying texture in the brazilian Amazon

Despite the agricultural importance of Indian Black Earth (IBE) in the Amazon region, there are few studies that report on the relation between soil texture and chemical fertility of IBE. These soils of pre-Colombian origin, with high contents of P, Ca and other nutrients are found across the Amazon valley. IBE profiles were studied to evaluate the total contents of P, its primary chemical forms and the P transformation phases in areas with IBE soils of variable texture and in adjacent reference soils. The soil texture strongly influenced soil fertility, changing in terms of transformation of the primary P forms and, consequently, predominant P forms in IBE. Soils with texture varying between clay and heavy clay had higher total P contents and primary Ca-P forms. Highest P-Al and lowest total P amounts were observed at the site Rio Preto da Eva, where texture varies from sandy loam to sandy clay loam. In the IBE with clay texture the amounts of soluble P, extracted with NH4Cl were highest, although different from Mehlich 1-extractable amounts.

Mobility of inorganic and organic phosphorus forms under different levels of phosphate and poultry litter fertilization in soils

The eutrophication of aquifers is strongly linked to the mobility of P in soils. Although P mobility was considered irrelevant in a more distant past, more recent studies have shown that P, both in organic (Po) and inorganic forms (Pi), can be lost by leaching and eluviation through the soil profile, particularly in less weathered and/or sandier soils with low P adsorption capacity. The purpose of this study was to determine losses of P forms by leaching and eluviation from soil columns. Each column consisted of five PVC rings (diameter 5 cm, height 10 cm), filled with two soil types: a clayey Red-Yellow Latosol and a sandy loam Red-Yellow Latosol, which were exposed to water percolation. The soils were previously treated with four P rates (as KH2PO4 ) to reach 0, 12.5, 25.0 and 50 % of the maximum P adsorption capacity (MPAC). The P source was homogenized with the whole soil volume and incubated for 60 days. After this period the soils were placed in the columns; the soil of the top ring was mixed with five poultry litter rates of 0, 20, 40, 80, and 160 t ha-1 (dry weight basis). Treatments consisted of a 4 x 5 x 2 factorial scheme corresponding to four MPAC levels, five poultry litter rates, two soils, with three replications, arranged in a completely randomized block design. Deionized water was percolated through the columns 10 times in 35 days to simulate about 1,200 mm rainfall. In the leachate of each column the inorganic P (reactive P, Pi) and organic P forms (unreactive P, Po) were determined. At the end of the experiment, the columns were disassembled and P was extracted with the extractants Mehlich-1 (HCl 0.05 mol L-1 and H2SO4 0.0125 mol L-1) and Olsen (NaHCO3 0.5 mol L-1; pH 8.5) from the soil of each ring. The Pi and Po fractions were measured by the Olsen extractant. It was found that under higher poultry litter rates the losses of unreactive P (Po) were 6.4 times higher than of reactive P (Pi). Both the previous P fertilization and increasing poultry litter rates caused a vertical movement of P down the soil columns, as verified by P concentrations extracted by Mehlich-1 and NaHCO3 (Olsen). The environmental critical level (ECL), i.e., the P soil concentration above which P leaching increases exponentially, was 100 and 150 mg dm-3 by Mehlich-1 and 40 and 60 mg dm-3 by Olsen, for the sandy loam and clay soils, respectively. In highly weathered soils, where residual P is accumulated by successive crops, P leaching through the profile can be significant, particularly when poultry litter is applied as fertilizer.