Approval voting ion dichotomous preferences

The aim of this paper is to find normative foundations of Approval Voting. In order to show that Approval Voting is the only social choice function that satisfies anonymity, neutrality, strategy-proofness and strict monotonicity we rely on an intermediate result which relates strategy-proofness of a social choice function to the properties of Independence of Irrelevant Alternatives and monotonicity of the corresponding social welfare function. Afterwards we characterize Approval Voting by means of strict symmetry, neutrality and strict monotonicity and relate this result to May's Theorem. Finally, we show that it is possible to substitute the property of strict monotonicity by the one efficiency of in the second characterization.

Fair and efficient student placement with couples

We study situations of allocating positions or jobs to students or workers based on priorities. An example is the assignment of medical students to hospital residencies on the basis of one or several entrance exams. For markets without couples, e.g., for ``undergraduate student placement,'' acyclicity is a necessary and sufficient condition for the existence of a fair and efficient placement mechanism (Ergin, 2002). We show that in the presence of couples, which introduces complementarities into the students' preferences, acyclicity is still necessary, but not sufficient (Theorem 4.1). A second necessary condition (Theorem 4.2) is ``priority-togetherness'' of couples. A priority structure that satisfies both necessary conditions is called pt-acyclic. For student placement problems where all quotas are equal to one we characterize pt-acyclicity (Lemma 5.1) and show that it is a sufficient condition for the existence of a fair and efficient placement mechanism (Theorem 5.1). If in addition to pt-acyclicity we require ``reallocation-'' and ``vacancy-fairness'' for couples, the so-called dictator-bidictator placement mechanism is the unique fair and efficient placement mechanism (Theorem 5.2). Finally, for general student placement problems, we show that pt-acyclicity may not be sufficient for the existence of a fair and efficient placement mechanism (Examples 5.4, 5.5, and 5.6). We identify a sufficient condition such that the so-called sequential placement mechanism produces a fair and efficient allocation (Theorem 5.3).

A foundation model for marxian theories of the breakdown of capitalism

Marx and the writers that followed him have produced a number of theories of the breakdown of capitalism. The majority of these theories were based on the historical tendencies: the rise in the composition of capital and the share of capital and the fall in the rate of profit. However these theories were never modeled with main stream rigour. This paper presents a constant wage model, with capital, labour and land as factors of production, which reproduces the historical tendencies and so can be used as a foundation for the various theories. The use of Chaplygins theorem in the proof of the main result also gives the paper a technical interest.

Reflected Backward Stochastic Differential Equation with Jumps and RCLL Obstacle

In this paper we study one-dimensional reflected backward stochastic differential equation when the noise is driven by a Brownian motion and an independent Poisson point process when the solution is forced to stay above a right continuous left-hand limited obstacle. We prove existence and uniqueness of the solution by using a penalization method combined with a monotonic limit theorem.

Algebraic extensions in free groups

The aim of this paper is to unify the points of view of three recent and independent papers (Ventura 1997, Margolis, Sapir and Weil 2001 and Kapovich and Miasnikov 2002), where similar modern versions of a 1951 theorem of Takahasi were given. We develop a theory of algebraic extensions for free groups, highlighting the analogies and differences with respect to the corresponding classical fieldt heoretic notions, and we discuss in detail the notion of algebraic closure. We apply that theory to the study and the computation of certain algebraic properties of subgroups (e.g. being malnormal, pure, inert or compressed, being closed in certain profinite topologies) and the corresponding closure operators. We also analyze the closure of a subgroup under the addition of solutions of certain sets of equations.

Repeated games played in a network

Delayed perfect monitoring in an infinitely repeated discounted game is modelled by letting the players form a connected and undirected network. Players observe their immediate neighbors' behavior only, but communicate over time the repeated game's history truthfully throughout the network. The Folk Theorem extends to this setup, although for a range of discount factors strictly below 1, the set of sequential equilibria and the corresponding payoff set may be reduced. A general class of games is analyzed without imposing restrictions on the dimensionality of the payoff space. This and the bilateral communication structure allow for limited results under strategic communication only. As a by-product this model produces a network result; namely, the level of cooperation in this setup depends on the network's diameter, and not on its clustering coefficient as in other models.

The bogomolov conjecture for totally degenerate Abelian varieties

We prove the Bogomolov conjecture for a totally degenerate abelian variety A over a function field. We adapt Zhang's proof of the number field case replacing the complex analytic tools by tropical analytic geometry. A key step is the tropical equidistribution theorem for A at the totally degenerate place.

Semipurity of tempered Deligne cohomology

In this paper we define the formal and tempered Deligne cohomology groups, that are obtained by applying the Deligne complex functor to the complexes of formal differential forms and tempered currents respectively. We then prove the existence of a duality between them, a vanishing theorem for the former and a semipurity property for the latter. The motivation of this results comes from the study of covariant arithmetic Chow groups. The semi-purity property of tempered Deligne cohomology implies, in particular, that several definitions of covariant arithmetic Chow groups agree for projective arithmetic varieties.

Smith and Rawls share a room

We consider one-to-one matching (roommate) problems in which agents (students) can either be matched as pairs or remain single. The aim of this paper is twofold. First, we review a key result for roommate problems (the ``lonely wolf'' theorem) for which we provide a concise and elementary proof. Second, and related to the title of this paper, we show how the often incompatible concepts of stability (represented by the political economist Adam Smith) and fairness (represented by the political philosopher John Rawls) can be reconciled for roommate problems.

Corrigendum: stable matchings and preferences of couples

We correct an omission in the definition of the domain of weakly responsive preferences introduced in Klaus and Klijn (2005) or KK05 for short. The proof of the existence of stable matchings (KK05, Theorem 3.3) and a maximal domain result (KK05, Theorem 3.5) are adjusted accordingly.

Oligocene CO2 decline promoted C4 photosynthesis in grasses.

C4 photosynthesis is an adaptation derived from the more common C3 photosynthetic pathway that confers a higher productivity under warm temperature and low atmospheric CO2 concentration [1, 2]. C4 evolution has been seen as a consequence of past atmospheric CO2 decline, such as the abrupt CO2 fall 32-25 million years ago (Mya) [3-6]. This relationship has never been tested rigorously, mainly because of a lack of accurate estimates of divergence times for the different C4 lineages [3]. In this study, we inferred a large phylogenetic tree for the grass family and estimated, through Bayesian molecular dating, the ages of the 17 to 18 independent grass C4 lineages. The first transition from C3 to C4 photosynthesis occurred in the Chloridoideae subfamily, 32.0-25.0 Mya. The link between CO2 decrease and transition to C4 photosynthesis was tested by a novel maximum likelihood approach. We showed that the model incorporating the atmospheric CO2 levels was significantly better than the null model, supporting the importance of CO2 decline on C4 photosynthesis evolvability. This finding is relevant for understanding the origin of C4 photosynthesis in grasses, which is one of the most successful ecological and evolutionary innovations in plant history.

Rare chromosome abnormalities, prevalence and prenatal diagnosis rates from population-based congenital anomaly registers in Europe.

The aim of this study is to quantify the prevalence and types of rare chromosome abnormalities (RCAs) in Europe for 2000-2006 inclusive, and to describe prenatal diagnosis rates and pregnancy outcome. Data held by the European Surveillance of Congenital Anomalies database were analysed on all the cases from 16 population-based registries in 11 European countries diagnosed prenatally or before 1 year of age, and delivered between 2000 and 2006. Cases were all unbalanced chromosome abnormalities and included live births, fetal deaths from 20 weeks gestation and terminations of pregnancy for fetal anomaly. There were 10,323 cases with a chromosome abnormality, giving a total birth prevalence rate of 43.8/10,000 births. Of these, 7335 cases had trisomy 21,18 or 13, giving individual prevalence rates of 23.0, 5.9 and 2.3/10,000 births, respectively (53, 13 and 5% of all reported chromosome errors, respectively). In all, 473 cases (5%) had a sex chromosome trisomy, and 778 (8%) had 45,X, giving prevalence rates of 2.0 and 3.3/10,000 births, respectively. There were 1,737 RCA cases (17%), giving a prevalence of 7.4/10,000 births. These included triploidy, other trisomies, marker chromosomes, unbalanced translocations, deletions and duplications. There was a wide variation between the registers in both the overall prenatal diagnosis rate of RCA, an average of 65% (range 5-92%) and the prevalence of RCA (range 2.4-12.9/10,000 births). In all, 49% were liveborn. The data provide the prevalence of families currently requiring specialised genetic counselling services in the perinatal period for these conditions and, for some, long-term care.

New perspectives in the use of ink evidence in forensic science: Part I. Development of a quality assurance process for forensic ink analysis by HPTLC

The level of information provided by ink evidence to the criminal and civil justice system is limited. The limitations arise from the weakness of the interpretative framework currently used, as proposed in the ASTM 1422-05 and 1789-04 on ink analysis. It is proposed to use the likelihood ratio from the Bayes theorem to interpret ink evidence. Unfortunately, when considering the analytical practices, as defined in the ASTM standards on ink analysis, it appears that current ink analytical practices do not allow for the level of reproducibility and accuracy required by a probabilistic framework. Such framework relies on the evaluation of the statistics of the ink characteristics using an ink reference database and the objective measurement of similarities between ink samples. A complete research programme was designed to (a) develop a standard methodology for analysing ink samples in a more reproducible way, (b) comparing automatically and objectively ink samples and (c) evaluate the proposed methodology in a forensic context. This report focuses on the first of the three stages. A calibration process, based on a standard dye ladder, is proposed to improve the reproducibility of ink analysis by HPTLC, when these inks are analysed at different times and/or by different examiners. The impact of this process on the variability between the repetitive analyses of ink samples in various conditions is studied. The results show significant improvements in the reproducibility of ink analysis compared to traditional calibration methods.

Finance and Balanced Growth

The Uzawa (1961) theorem applied to finance and growthsuggests that a long-run positive correlation between financial efficiency and depth is only present when variations in the extent of access to financial services are considered. Improvements in financial efficiency can lead to new capital augmenting technologies along the balanced path, but only improvements in financial efficiency directed towards labor can change the rate of growth in the long-run. These findings suggest ways to understand some of the more nuanced relationships between finance and growth observed in the data and point in a number of directions for future research.

Point-occurrence self-similarity in crackling-noise systems and in other complex systems

It has been recently found that a number of systems displaying crackling noise also show a remarkable behavior regarding the temporal occurrence of successive events versus their size: a scaling law for the probability distributions of waiting times as a function of a minimum size is fulfilled, signaling the existence on those systems of self-similarity in time-size. This property is also present in some non-crackling systems. Here, the uncommon character of the scaling law is illustrated with simple marked renewal processes, built by definition with no correlations. Whereas processes with a finite mean waiting time do not fulfill a scaling law in general and tend towards a Poisson process in the limit of very high sizes, processes without a finite mean tend to another class of distributions, characterized by double power-law waiting-time densities. This is somehow reminiscent of the generalized central limit theorem. A model with short-range correlations is not able to escape from the attraction of those limit distributions. A discussion on open problems in the modeling of these properties is provided.