A gibbad-satterthwaite theorem for public good economies

We study the properties of mechanisms for deciding upon the provision of public goods when the feasible set is exogenously given (by financial and/or technological constraints), and individuals' preferences are represented by continuous, increasing and concave utility functions, and we establish a result analog to the Gibbard-Satterthwaite Theorem: strategy-proof mechanisms are dictatorial. Further, efficient and strategy-proof mechanisms are strongly dictatorial (i.e., maximize the dictator's welfare on the entire feasible set.

Strategy-proof allocation mechanisms for economies with public goods

We show that strategy-proof allocation mechanisms for economies with public goods are dictatorial -- i.e., they always select an allocation in their range that maximizes the welfare of the same single individual (the dictator). Further, strategy-proof and efficient allocation mechanisms are strongly dictatorial -- i.e., they select the dictator's preferred allocation on the entire feasible set. Thus, our results reveal the extent to which the conflict between individual incentives and other properties that may be deemed desirable (e.g., fairness, equal treatment, distributive justice) pervades resource allocation problems.Allocation mechanisms, Public goods, Strategy-proofness, Dictatorship, Efficiency

A Gibbad-Satterthwaite Theorem for Public Good Economies

We study the properties of mechanisms for deciding upon the provision of public goods when the feasible set is exogenously given (by financial and/or technological constraints), and individuals' preferences are represented by continuous, increasing and concave utility functions, and we establish a result analog to the Gibbard-Satterthwaite Theorem: strategy-proof mechanisms are dictatorial. Further, efficient and strategy-proof mechanisms are strongly dictatorial (i.e., maximize the dictator's welfare on the entire feasible set.)

Strategy-proof allocation mechanisms for economies with public goods

We show that strategy-proof allocation mechanisms for economies with public goods are dictatorial -- i.e., they always select an allocation in their range that maximizes the welfare of the same single individual (the dictator). Further, strategy-proof and efficient allocation mechanisms are strongly dictatorial -- i.e., they select the dictator's preferred allocation on the entire feasible set. Thus, our results reveal the extent to which the conflict between individual incentives and other properties that may be deemed desirable (e.g., fairness, equal treatment, distributive justice) pervades resource allocation problems

An attempt to identify the issues underlying the lack of consistent conceptualisations in the field of student mathematics-related beliefs

This paper aims to clarify the inconsistencies present in the field of student mathematics-related beliefs. Despite the general agreement about the important role that beliefs play in the learning of mathematics, the study of student mathematics-related beliefs has resulted in a body of uncoordinated research. The lack of consensus on defining and classifying beliefs has generated much confusing terminology, preventing a consistent conceptualization of the phenomenon. To identify the problem underlying existing inconsistencies, we have undertaken a systematic review of the literature to analyse the belief conceptualisations proposed by the most cited authors in this field of research. Our analysis suggests that authors often fail to conceptualise beliefs in four important ways: existing theories related to the phenomenon under research are normally not considered; definitions are often too broad and do not clearly confine the construct under evaluation; and existing beliefs sub-constructs are rarely defined and thus not explicitly distinguished. Our study has also revealed that some of the scales developed to measure the belief constructs lack of content and internal validity. We believe that these findings open new lines of research that may help to clarify the field of student mathematics-related beliefs.This work was supported by Horizon 2020 (710577), Ministerio de Ciencia e Innovación (EDU2017-84979-R), Erasmus+ (2017-1-ES01-KA203-038491) and (2019-1-CZ01-KA201-061377), Ministerio de Ciencia e Innovación (PGC2018-100758-B-I00), RED8-Educación matemática y formación de profesores (EDU2016-81994-REDT) and Junta de Castilla y León (Q3718001E)S

Creating Realistic Mathematics Tasks Involving Authenticity, Cognitive Domains, and Openness Characteristics: A Study with Pre-Service Teachers

Creating mathematics tasks provide opportunities for students to develop their thinking, reasoning, communication, and creativity. This paper presents a study on teaching pre-service teachers to create realistic mathematics tasks in real contexts and amending them through an iterative process of analysis and refinement. The study was undertaken with pre-service teachers from two university training courses in Spain, undergraduate students from a primary teacher training course, and graduate students from an educational Master’s course. The students worked in groups to collaborate in the creation of the requested tasks and improvement of them based on critical thinking and creativity. The tasks were not only evaluated concerning their level of realism, but also regarding their level of authenticity, the cognitive domains involved, and their openness characteristic. These are the key characteristics related to environmental and sustainability aspects. The outcomes confirmed that the creation of realistic mathematics tasks was a challenge for future primary teachers; however, they were able to create tasks with high levels of cognitive domain, authenticity, and openness. This evidences, on the one hand, the difficulty that future teachers have in understanding the realism of a mathematics task, and, on the other, the possibilities offered by the task’s creation and the revision activity, which has educational implications and opens paths for future researchThis work was partially supported by the Project Science, Innovation and University Ministry, Spain [PGC2018-100758-B-100]; Project Junta de Castilla-León, Spain [SA050G19]; Project University of Salamanca, Spain [MODELGEO-CEI 18.K133]; FEDER/Ministerio de Ciencia, Innovación y Universidades–Agencia Estatal de Investigación/Proyect EDU2017-84979-R; Mathematics EduLarp (EDUMATH) [2019-1-CZ01-KA201-061377]S

Clarification on Host Range of Didymella pinodes the Causal Agent of Pea Ascochyta Blight

Didymella pinodes is the principal causal agent of ascochyta blight, one of the most important fungal diseases of pea (Pisum sativum) worldwide. Understanding its host specificity has crucial implications in epidemiology and management; however, this has not been clearly delineated yet. In this study we attempt to clarify the host range of D. pinodes and to compare it with that of other close Didymella spp. D. pinodes was very virulent on pea accessions, although differences in virulence were identified among isolates. On the contrary, studied isolates of D. fabae, D. rabiei, and D. lentil showed a reduced ability to infect pea not causing macroscopically visible symptoms on any of the pea accessions tested. D. pinodes isolates were also infective to some extend on almost all species tested including species such as Hedysarum coronarium, Lathyrus sativus, Lupinus albus, Medicago spp., Trifolium spp., Trigonella foenum-graecum, and Vicia articulata which were not mentioned before as hosts of D. pinodes. On the contrary, D. lentil and D. rabiei were more specific, infecting only lentil and chickpea, respectively. D. fabae was intermediate, infecting mainly faba bean, but also slightly other species such as Glycine max, Phaseolus vulgaris, Trifolium spp., Vicia sativa, and V. articulata. DNA sequence analysis of the nuclear ribosomal internal transcribed spacer region (ITS) was performed to confirm identity of the isolates studies and to determine phylogenetic relationship among the Didymella species, revealing the presence of two clearly distinct clades. Clade one was represented by two supported subclusters including D. fabae isolates as well as D. rabiei with D. lentil isolates. Clade two was the largest and included all the D. pinodes isolates as well as Phoma medicaginis var. pinodella. Genetic distance between D. pinodes and the other Didymella spp. isolates was not correlated with overall differences in pathogenicity. Based on evidences presented here, D. pinodes is not specialized on pea and its host range is larger than that of D. fabae, D. lentil, and D. rabiei. This has relevant implications in epidemiology and control as these species might act as alternative hosts for D. pinodes.This work was supported by Spanish project AGL2014-52871-R. EB was granted by a contract founded by the Spanish JAEdoc program and MC by the Spanish Juan de la Cierva program.Peer reviewe

Three-dimensional multi-probe analysis of the galaxy cluster A1689

arXiv:1503.01482v2.-- et al.We perform a three-dimensional multi-probe analysis of the rich galaxy cluster A1689, one of the most powerful known lenses on the sky, by combining improved weak-lensing data from new wide-field ${{BVR}}_{{\rm C}}i\prime z\prime$ Subaru/Suprime-Cam observations with strong-lensing, X-ray, and Sunyaev–Zel'dovich effect (SZE) data sets. We reconstruct the projected matter distribution from a joint weak-lensing analysis of two-dimensional shear and azimuthally integrated magnification constraints, the combination of which allows us to break the mass-sheet degeneracy. The resulting mass distribution reveals elongation with an axis ratio of ~0.7 in projection, aligned well with the distributions of cluster galaxies and intracluster gas. When assuming a spherical halo, our full weak-lensing analysis yields a projected halo concentration of ${c}_{200{\rm c}}^{2{\rm D}}=8.9\pm 1.1$ (${c}_{\mathrm{vir}}^{2{\rm D}}\sim 11$), consistent with and improved from earlier weak-lensing work. We find excellent consistency between independent weak and strong lensing in the region of overlap. In a parametric triaxial framework, we constrain the intrinsic structure and geometry of the matter and gas distributions, by combining weak/strong lensing and X-ray/SZE data with minimal geometric assumptions. We show that the data favor a triaxial geometry with minor–major axis ratio 0.39±0.15 and major axis closely aligned with the line of sight (22°±10°). We obtain a halo mass ${M}_{200{\rm c}}=(1.2\pm 0.2)\times {10}^{15}\;{M}_{\odot }\;{h}^{-1}$ and a halo concentration ${c}_{200{\rm c}}=8.4\pm 1.3$, which overlaps with the $\gtrsim 1\sigma$ tail of the predicted distribution. The shape of the gas is rounder than the underlying matter but quite elongated with minor–major axis ratio 0.60 ± 0.14. The gas mass fraction within 0.9 Mpc is ${10}_{-2}^{+3}\%$, a typical value for high-mass clusters. The thermal gas pressure contributes to ~60% of the equilibrium pressure, indicating a significant level of non-thermal pressure support. When compared to Planck's hydrostatic mass estimate, our lensing measurements yield a spherical mass ratio of MPlanck/MGL = 0.70 ± 0.15 and 0.58 ± 0.10 with and without corrections for lensing projection effects, respectively.The work is partially supported by the Ministry of Science and Technology of Taiwan under the grant MOST 103-2112-M-001-030-MY3. M. S. acknowledges financial contributions from contracts ASI/INAF I/023/12/0, by the PRIN MIUR 2010–2011 “The dark universe and the cosmic evolution of baryons: from current surveys to Euclid” and by the PRIN INAF 2012 “The universe in the box: multiscale simulations of cosmic structure.” M. N. acknowledges financial support from PRIN INAF 2014. J. M. D. acknowledges support of the consolider project CSD2010-00064 and AYA2012-39475-C02-01 funded by the Ministerio de Economia y Competitividad. N. O. is supported by a Grant-in-Aid from the Ministry of Education, Culture, Sports, Science, and Technology of Japan (26800097). This work was partially supported by “World Premier International Research Center Initiative (WPI Initiative)” and the Funds for the Development of Human Resources in Science and Technology under MEXT, Japan.Peer Reviewe

Fluctuations and Instabilities of Ferromagnetic Domain Wall pairs in an External Magnetic Field

Soliton excitations and their stability in anisotropic quasi-1D ferromagnets are analyzed analytically. In the presence of an external magnetic field, the lowest lying topological excitations are shown to be either soliton-soliton or soliton-antisoliton pairs. In ferromagnetic samples of macro- or mesoscopic size, these configurations correspond to twisted or untwisted pairs of Bloch walls. It is shown that the fluctuations around these configurations are governed by the same set of operators. The soliton-antisoliton pair has exactly one unstable mode and thus represents a critical nucleus for thermally activated magnetization reversal in effectively one-dimensional systems. The soliton-soliton pair is stable for small external fields but becomes unstable for large magnetic fields. From the detailed expression of this instability threshold and an analysis of nonlocal demagnetizing effects it is shown that the relative chirality of domain walls can be detected experimentally in thin ferromagnetic films. The static properties of the present model are equivalent to those of a nonlinear sigma-model with anisotropies. In the limit of large hard-axis anisotropy the model reduces to a double sine-Gordon model.Comment: 15 pages RevTex 3.0 (twocolumn), 9 figures available on request, to appear in Phys Rev B, Dec (1994