On the justice of voting systems

What are the best voting systems in terms of utilitarianism? Or in terms of maximin, or maximax? We study these questions for the case of three alternatives and a class of structurally equivalent voting rules. We show that plurality, arguably the most widely used voting system, performs very poorly in terms of remarkable ideals of justice, such as utilitarianism or maximin, and yet is optimal in terms of maximax. Utilitarianism is bestapproached by a voting system converging to the Borda count, while the best way to achieve maximin is by means of a voting system converging to negative voting. We study the robustness of our results across different social cultures, measures of performance, and population sizes.

Emergence of Cooperation on Static and Dynamic Networks

Game theory is a branch of applied mathematics used to analyze situation where two or more agents are interacting. Originally it was developed as a model for conflicts and collaborations between rational and intelligent individuals. Now it finds applications in social sciences, eco- nomics, biology (particularly evolutionary biology and ecology), engineering, political science, international relations, computer science, and philosophy. Networks are an abstract representation of interactions, dependencies or relationships. Net- works are extensively used in all the fields mentioned above and in many more. Many useful informations about a system can be discovered by analyzing the current state of a network representation of such system. In this work we will apply some of the methods of game theory to populations of agents that are interconnected. A population is in fact represented by a network of players where one can only interact with another if there is a connection between them. In the first part of this work we will show that the structure of the underlying network has a strong influence on the strategies that the players will decide to adopt to maximize their utility. We will then introduce a supplementary degree of freedom by allowing the structure of the population to be modified along the simulations. This modification allows the players to modify the structure of their environment to optimize the utility that they can obtain.

Tree of Sex: A database of sexual systems

The vast majority of eukaryotic organisms reproduce sexually, yet the nature of the sexual system and the mechanism of sex determination often vary remarkably, even among closely related species. Some species of animals and plants change sex across their lifespan, some contain hermaphrodites as well as males and females, some determine sex with highly differentiated chromosomes, while others determine sex according to their environment. Testing evolutionary hypotheses regarding the causes and consequences of this diversity requires interspecific data placed in a phylogenetic context. Such comparative studies have been hampered by the lack of accessible data listing sexual systems and sex determination mechanisms across the eukaryotic tree of life. Here, we describe a database developed to facilitate access to sexual system and sex chromosome information, with data on sexual systems from 11,038 plant, 705 fish, 173 amphibian, 593 non-avian reptilian, 195 avian, 479 mammalian, and 11,556 invertebrate species.

Short and long-term effects of tillage systems and nutrient sources on soil physical properties of a Southern Brazilian Hapludox

Soil tillage promotes changes in soil structure. The magnitude of the changes varies with the nature of the soil, tillage system and soil water content and decreases over time after tillage. The objective of this study was to evaluate short-term (one year period) and long-term (nine year period) effects of soil tillage and nutrient sources on some physical properties of a very clayey Hapludox. Five tillage systems were evaluated: no-till (NT), chisel plow + one secondary disking (CP), primary + two (secondary) diskings (CT), CT with burning of crop residues (CTb), and CT with removal of crop residues from the field (CTr), in combination with five nutrient sources: control without nutrient application (C); mineral fertilizers, according to technical recommendations for each crop (MF); 5 Mg ha-1 yr-1 of poultry litter (wetmatter) (PL); 60 m³ ha-1 yr-1 of cattle slurry (CS) and; 40 m³ ha-1 yr-1 of swine slurry (SS). Bulk density (BD), total porosity (TP), and parameters related to the water retention curve (macroporosity, mesoporosity and microporosity) were determined after nine years and at five sampling dates during the tenth year of the experiment. Soil physical properties were tillage and time-dependent. Tilled treatments increased total porosity and macroporosity, and reduced bulk density in the surface layer (0.00-0.05 m), but this effect decreased over time after tillage operations due to natural soil reconsolidation, since no external stress was applied in this period. Changes in pore size distribution were more pronounced in larger and medium pore diameter classes. The bulk density was greatest in intermediate layers in all tillage treatments (0.05-0.10 and 0.12-0.17 m) and decreased down to the deepest layer (0.27-0.32 m), indicating a more compacted layer around 0.05-0.20 m. Nutrient sources did not significantly affect soil physical and hydraulic properties studied.

Soil water dynamics related to the degree of compaction of two brazilian oxisols under no-tillage

Soil water properties are related to crop growth and environmental aspects and are influenced by the degree of soil compaction. The objective of this study was to determine the water infiltration and hydraulic conductivity of saturated soil under field conditions in terms of the compaction degree of two Oxisols under a no-tillage (NT). Two commercial fields were studied in the state of Rio Grande do Sul, Brazil: one a Haplortox after 14 years under NT; the other a Hapludox after seven years under NT. Maps (50 x 30 m) of the levels of mechanical penetration resistance (PR) were drawn based on the kriging method, differentiating three compaction degrees (CD): high, intermediate and low. In each CD area, the infiltration rate (initial and steady-state) and cumulative water infiltration were measured using concentric rings, with six replications, and the saturated hydraulic conductivity (K(θs)) was determined using the Guelph permeameter. Statistical evaluation was performed based on a randomized design, using the least significant difference (LSD) test and regression analysis. The steady-state infiltration rate was not influenced by the compaction degree, with mean values of 3 and 0.39 cm h-1 in the Haplortox and the Hapludox, respectively. In the Haplortox, saturated soil hydraulic conductivity was 26.76 cm h-1 at a low CD and 9.18 cm h-1 at a high CD, whereas in the Hapludox, this value was 5.16 cm h-1 and 1.19 cm h-1 for the low and high CD, respectively. The compaction degree did not affect the initial and steady-state water infiltration rate, nor the cumulative water infiltration for either soil type, although the values were higher for the Haplortox than the Hapludox.

Critical behavior of a system with orientational and positional degrees of freedom: A Monte Carlo simulation study

The critical behavior of a system constituted by molecules with a preferred symmetry axis is studied by means of a Monte Carlo simulation of a simplified two-dimensional model. The system exhibits two phase transitions, associated with the vanishing of the positional order of the center of mass of the molecules and with the orientational order of the symmetry axis. The evolution of the order parameters and the specific heat is also studied. The transition associated with the positional degrees of freedom is found to change from a second-order to a first-order behavior when the two phase transitions are close enough, due to the coupling with the orientational degrees of freedom. This fact is qualitatively compared with similar results found in pure liquid crystals and liquid-crystal mixtures.

Wave-vector dependence of spin and density multipole excitations in quantum dots

We have employed time-dependent local-spin density-functional theory to analyze the multipole spin and charge density excitations in GaAs-AlxGa1-xAs quantum dots. The on-plane transferred momentum degree of freedom has been taken into account, and the wave-vector dependence of the excitations is discussed. In agreement with previous experiments, we have found that the energies of these modes do not depend on the transferred wave vector, although their intensities do. Comparison with a recent resonant Raman scattering experiment [C. Schüller et al., Phys. Rev. Lett. 80, 2673 (1998)] is made. This allows us to identify the angular momentum of several of the observed modes as well as to reproduce their energies

Exact lower bounds to the ground-state energy of spin systems: The two-dimensional S=1/2 antiferromagnetic Heisenberg model

We present a very simple but fairly unknown method to obtain exact lower bounds to the ground-state energy of any Hamiltonian that can be partitioned into a sum of sub-Hamiltonians. The technique is applied, in particular, to the two-dimensional spin-1/2 antiferromagnetic Heisenberg model. Reasonably good results are easily obtained and the extension of the method to other systems is straightforward.

Effects of tillage systems on physical properties of a cohesive yellow argisol in the northern state of Espírito Santo, Brazil

Tillage systems are a key element of the technology of crop production, both with a view to crop yield and from the perspective of soil conservation and sustainability of the production system. The aim of this paper was to evaluate the effects of five tillage systems on the physical properties of a cohesive Yellow Argisol. The experiment was installed in the field on January 21, 2011 and lasted 260 days, in an area previously used as pasture with Brachiaria grass without liming or fertilization, but irrigated by a low pressure spray system. The treatments, in five replications and in a randomized block design, consisted of: 1) disk plow (twice) + disk harrow + ridge-furrow tillage (raising a ridge along the planting row), 135 days after transplanting (DP + RID); 2) disk plow (twice) + disk harrow (DP no RID); 3) subsoiler (SB); 4) disk plow (twice) + disk harrow + scarification with three shanks along the plant row (DP + SPR); and 5) disk plow (twice) + disk harrow + scarification with three shanks in the total area (DP + STA). In all tillage systems, furrows were mechanically opened for the papaya plants. After the treatments, the mechanical resistance to penetration was determined, followed by soil moisture, mean weight diameter (MWD), geometric mean diameter (GMD), bulk density (BD), macroporosity (Ma), microporosity (Mi), and number of fruits per plant. There were differences in penetration resistance (PR) between treatments. The subsoiler was more effective to decrease RP to a distance of 0.35 m from the plants, perpendicular to the plant row. The scarifier resulted in a lower PR than DP or SB, even at the depth of 0.40 m, and it was more effective at greater distances perpendicular to the plant. All tillage systems induced a PR between 2.0 and 3.0 MPa at the depth with the highest concentration of papaya tree roots (0-0.25 m), improving the physical conditions to this depth. There was no statistical difference among the treatments for BD, Ma, Mi, MWD, and GMD at a depth of 0.20 m. The disk plow changed the physical properties of the soil most intensely to a depth of 0.20 m. The use of scarification, reduced tillage with a forest subsoiler, or ridge-furrow tillage did not improve the physical properties in the rhizosphere. Reduced tillage with a forest subsoiler resulted in a lower number of fruits per plant than all other treatments, which did not differ from each other.

Physical quality of an Oxisol after different periods of management systems

Management systems may lead to a loss of soil physical quality as a result of removal of the plant cover and excessive agricultural mechanization. The hypothesis of this study was that the soil aggregate stability, bulk density, macro- and microporosity, and the S index and saturated hydraulic conductivity may be used as indicators of the soil physical quality. The aim was to study the effects of different periods and managements on the physical attributes of a medium-textured Red Oxisol under soybean and corn for two growing seasons, and determine which layers are most susceptible to variations. A completely randomized experimental design was used with split plots (five treatments and four layers), with four replications. The treatments in 2008/09 consisted of: five years of no-tillage (NTS5), seven years of no-tillage (NTS7), nine years of no-tillage (NTS9), conventional tillage (CTS) and an adjacent area of native forest (NF). The treatments were extended for another year, identified in 2009/10 as: NTS6, NTS8, NTS10, CTS and NF. The soil layers 0-0.05, 0.05-0.10, 0.10-0.20 and 0.20-0.30 m were sampled. The highest S index values were observed in the treatment CTS in the 0-0.05 m layer (0.106) and the 0.05-0.10 m layer (0.099) in 2008/09, and in the 0-0.05 m layer (0.066) in 2009/10. This fact may be associated with soil turnover, resulting in high macroporosity in this treatment. In contrast, in the NTS, limiting macroporosity values were observed in some layers (below 0.10 m³ m-3). Highest aggregate stability as well as the highest saturated hydraulic conductivity (Kθ) values were observed in NF in relation to the other treatments. In 2009/10, the Kθ in NF differed only from NTS10. This study showed that the use of the S index alone cannot be recommended as an absolute indicator of the soil physical quality, even at values greater than 0.035.

Design of Optical Systems With Extended Depth of Field: an Educational Approach to Wavefront Coding Techniques

A practical activity designed to introduce wavefront coding techniques as a method to extend the depth of field in optical systems is presented. The activity is suitable for advanced undergraduate students since it combines different topics in optical engineering such as optical system design, aberration theory, Fourier optics, and digital image processing. This paper provides the theoretical background and technical information for performing the experiment. The proposed activity requires students able to develop a wide range of skills since they are expected to deal with optical components, including spatial light modulators, and develop scripts to perform some calculations.

Crystal defects and spin tunneling in single crystals of Mn12 clusters

The question addressed in this paper is that of the influence of the density of dislocations on the spin tunneling in Mn12 clusters. We have determined the variation in the mosaicity of fresh and thermally treated single crystals of Mn12 by analyzing the widening of low angle x-ray diffraction peaks. It has also been well established from both isothermal magnetization and relaxation experiments that there is a broad distribution of tunneling rates which is shifted to higher rates when the density of dislocations increases.

Effect of management systems and cover crops on organic matter dynamics of soil under vegetables

Vegetable production in conservation tillage has increased in Brazil, with positive effects on the soil quality. Since management systems alter the quantity and quality of organic matter, this study evaluated the influence of different management systems and cover crops on the organic matter dynamics of a dystrophic Red Latosol under vegetables. The treatments consisted of the combination of three soil tillage systems: no-tillage (NT), reduced tillage (RT) and conventional tillage (CT) and of two cover crops: maize monoculture and maize-mucuna intercrop. Vegetables were grown in the winter and the cover crops in the summer for straw production. The experiment was arranged in a randomized block design with four replications. Soil samples were collected between the crop rows in three layers (0.0-0.05, 0.05-0.10, and 0.10-0.30 m) twice: in October, before planting cover crops for straw, and in July, during vegetable cultivation. The total organic carbon (TOC), microbial biomass carbon (MBC), oxidizable fractions, and the carbon fractions fulvic acid (C FA), humic acid (C HA) and humin (C HUM) were determined. The main changes in these properties occurred in the upper layers (0.0-0.05 and 0.05-0.10 m) where, in general, TOC levels were highest in NT with maize straw. The MBC levels were lowest in CT systems, indicating sensitivity to soil disturbance. Under mucuna, the levels of C HA were lower in RT than NT systems, while the C FA levels were lower in RT than CT. For vegetable production, the C HUM values were lowest in the 0.05-0.10 m layer under CT. With regard to the oxidizable fractions, the tillage systems differed only in the most labile C fractions, with higher levels in NT than CT in the 0.0-0.05 m layer in both summer and winter, with no differences between these systems in the other layers. The cabbage yield was not influenced by the soil management system, but benefited from the mulch production of the preceding maize-mucuna intercrop as cover plant.