Sparse image reconstruction on the sphere: implications of a new sampling theorem.

We study the impact of sampling theorems on the fidelity of sparse image reconstruction on the sphere. We discuss how a reduction in the number of samples required to represent all information content of a band-limited signal acts to improve the fidelity of sparse image reconstruction, through both the dimensionality and sparsity of signals. To demonstrate this result, we consider a simple inpainting problem on the sphere and consider images sparse in the magnitude of their gradient. We develop a framework for total variation inpainting on the sphere, including fast methods to render the inpainting problem computationally feasible at high resolution. Recently a new sampling theorem on the sphere was developed, reducing the required number of samples by a factor of two for equiangular sampling schemes. Through numerical simulations, we verify the enhanced fidelity of sparse image reconstruction due to the more efficient sampling of the sphere provided by the new sampling theorem.

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.

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.

Is there a common factor for vision?

In cognition, common factors play a crucial role. For example, different types of intelligence are highly correlated, pointing to a common factor, which is often called g. One might expect that a similar common factor would also exist for vision. Surprisingly, no one in the field has addressed this issue. Here, we provide the first evidence that there is no common factor for vision. We tested 40 healthy students' performance in six basic visual paradigms: visual acuity, vernier discrimination, two visual backward masking paradigms, Gabor detection, and bisection discrimination. One might expect that performance levels on these tasks would be highly correlated because some individuals generally have better vision than others due to superior optics, better retinal or cortical processing, or enriched visual experience. However, only four out of 15 correlations were significant, two of which were nontrivial. These results cannot be explained by high intraobserver variability or ceiling effects because test-retest reliability was high and the variance in our student population is commensurate with that from other studies with well-sighted populations. Using a variety of tests (e.g., principal components analysis, Bayes theorem, test-retest reliability), we show the robustness of our null results. We suggest that neuroplasticity operates during everyday experience to generate marked individual differences. Our results apply only to the normally sighted population (i.e., restricted range sampling). For the entire population, including those with degenerate vision, we expect different results.

Endogenous steroid profiling in the athlete biological passport.

The Athlete Biological Passport (ABP) is an individual electronic document that collects data regarding a specific athlete that is useful in differentiating between natural physiologic variations of selected biomarkers and deviations caused by artificial manipulations. A subsidiary of the endocrine module of the ABP, that which here is called Athlete Steroidal Passport (ASP), collects data on markers of an altered metabolism of endogenous steroidal hormones measured in urine samples. The ASP aims to identify not only doping with anabolic-androgenic steroids, but also most indirect steroid doping strategies such as doping with estrogen receptor antagonists and aromatase inhibitors. Development of specific markers of steroid doping, use of the athlete's previous measurements to define individual limits, with the athlete becoming his or her own reference, the inclusion of heterogeneous factors such as the UDPglucuronosyltransferase B17 genotype of the athlete, the knowledge of potentially confounding effects such as heavy alcohol consumption, the development of an external quality control system to control analytical uncertainty, and finally the use of Bayesian inferential methods to evaluate the value of indirect evidence have made the ASP a valuable alternative to deter steroid doping in elite sports. The ASP can be used to target athletes for gas chromatography/combustion/ isotope ratio mass spectrometry (GC/C/IRMS) testing, to withdraw temporarily the athlete from competing when an abnormality has been detected, and ultimately to lead to an antidoping infraction if that abnormality cannot be explained by a medical condition. Although the ASP has been developed primarily to ensure fairness in elite sports, its application in endocrinology for clinical purposes is straightforward in an evidence-based medicine paradigm.

Interactive Epistemology and Reasoning: On the Foundations of Game Theory

Game theory describes and analyzes strategic interaction. It is usually distinguished between static games, which are strategic situations in which the players choose only once as well as simultaneously, and dynamic games, which are strategic situations involving sequential choices. In addition, dynamic games can be further classified according to perfect and imperfect information. Indeed, a dynamic game is said to exhibit perfect information, whenever at any point of the game every player has full informational access to all choices that have been conducted so far. However, in the case of imperfect information some players are not fully informed about some choices. Game-theoretic analysis proceeds in two steps. Firstly, games are modelled by so-called form structures which extract and formalize the significant parts of the underlying strategic interaction. The basic and most commonly used models of games are the normal form, which rather sparsely describes a game merely in terms of the players' strategy sets and utilities, and the extensive form, which models a game in a more detailed way as a tree. In fact, it is standard to formalize static games with the normal form and dynamic games with the extensive form. Secondly, solution concepts are developed to solve models of games in the sense of identifying the choices that should be taken by rational players. Indeed, the ultimate objective of the classical approach to game theory, which is of normative character, is the development of a solution concept that is capable of identifying a unique choice for every player in an arbitrary game. However, given the large variety of games, it is not at all certain whether it is possible to device a solution concept with such universal capability. Alternatively, interactive epistemology provides an epistemic approach to game theory of descriptive character. This rather recent discipline analyzes the relation between knowledge, belief and choice of game-playing agents in an epistemic framework. The description of the players' choices in a given game relative to various epistemic assumptions constitutes the fundamental problem addressed by an epistemic approach to game theory. In a general sense, the objective of interactive epistemology consists in characterizing existing game-theoretic solution concepts in terms of epistemic assumptions as well as in proposing novel solution concepts by studying the game-theoretic implications of refined or new epistemic hypotheses. Intuitively, an epistemic model of a game can be interpreted as representing the reasoning of the players. Indeed, before making a decision in a game, the players reason about the game and their respective opponents, given their knowledge and beliefs. Precisely these epistemic mental states on which players base their decisions are explicitly expressible in an epistemic framework. In this PhD thesis, we consider an epistemic approach to game theory from a foundational point of view. In Chapter 1, basic game-theoretic notions as well as Aumann's epistemic framework for games are expounded and illustrated. Also, Aumann's sufficient conditions for backward induction are presented and his conceptual views discussed. In Chapter 2, Aumann's interactive epistemology is conceptually analyzed. In Chapter 3, which is based on joint work with Conrad Heilmann, a three-stage account for dynamic games is introduced and a type-based epistemic model is extended with a notion of agent connectedness. Then, sufficient conditions for backward induction are derived. In Chapter 4, which is based on joint work with Jérémie Cabessa, a topological approach to interactive epistemology is initiated. In particular, the epistemic-topological operator limit knowledge is defined and some implications for games considered. In Chapter 5, which is based on joint work with Jérémie Cabessa and Andrés Perea, Aumann's impossibility theorem on agreeing to disagree is revisited and weakened in the sense that possible contexts are provided in which agents can indeed agree to disagree.

DNA evidence, probabilistic evaluation and collaborative tests.

Forensic scientists working in 12 state or private laboratories participated in collaborative tests to improve the reliability of the presentation of DNA data at trial. These tests were motivated in response to the growing criticism of the power of DNA evidence. The experts' conclusions in the tests are presented and discussed in the context of the Bayesian approach to interpretation. The use of a Bayesian approach and subjective probabilities in trace evaluation permits, in an easy and intuitive manner, the integration into the decision procedure of any revision of the measure of uncertainty in the light of new information. Such an integration is especially useful with forensic evidence. Furthermore, we believe that this probabilistic model is a useful tool (a) to assist scientists in the assessment of the value of scientific evidence, (b) to help jurists in the interpretation of judicial facts and (c) to clarify the respective roles of scientists and of members of the court. Respondents to the survey were reluctant to apply this methodology in the assessment of DNA evidence.

Large multi-gene phylogenetic trees of the grasses (Poaceae): progress towards complete tribal and generic level sampling.

In this paper we included a very broad representation of grass family diversity (84% of tribes and 42% of genera). Phylogenetic inference was based on three plastid DNA regions rbcL, matK and trnL-F, using maximum parsimony and Bayesian methods. Our results resolved most of the subfamily relationships within the major clades (BEP and PACCMAD), which had previously been unclear, such as, among others the: (i) BEP and PACCMAD sister relationship, (ii) composition of clades and the sister-relationship of Ehrhartoideae and Bambusoideae + Pooideae, (iii) paraphyly of tribe Bambuseae, (iv) position of Gynerium as sister to Panicoideae, (v) phylogenetic position of Micrairoideae. With the presence of a relatively large amount of missing data, we were able to increase taxon sampling substantially in our analyses from 107 to 295 taxa. However, bootstrap support and to a lesser extent Bayesian inference posterior probabilities were generally lower in analyses involving missing data than those not including them. We produced a fully resolved phylogenetic summary tree for the grass family at subfamily level and indicated the most likely relationships of all included tribes in our analysis.

Detection of nandrolone metabolites in urine after a football game in professional and amateur players: a Bayesian comparison.

Nandrolone (19-nortestosterone) is a widely used anabolic steroid in sports where strength plays an essential role. Once nandrolone has been metabolised, two major metabolites are excreted in urine, 19-norandrosterone (NA) and 19-noretiocholanolone (NE). In 1997, in France, quite a few sportsmen had concentrations of 19-norandrosterone very close to the IOC cut off limit (2ng/ml). At that time, a debate took place about the capability of the human male body to produce by itself these metabolites without any intake of nandrolone or related compounds. The International Football Federation (FIFA) was very concerned with this problematic, especially because the World Cup was about to start in France. In this respect, a statistical study was held with all football players from the first and second divisions of the Swiss Football National League. All players gave a urine sample after effort and around 6% of them showed traces of 19-norandrosterone. These results were compared with amateur football players (control group) and around 6% of them had very small amounts of 19-norandrosterone and/or 19-noretiocholanolone in urine after effort, whereas none of them had detectable traces of one or the other metabolite before effort. The origin of these compounds in urine after a strenuous physical activity is still unknown, but three hypotheses can be put forward. First, an endogenous production of nandrolone metabolites takes place. Second, nandrolone metabolites are released from the fatty tissues after an intake of nandrolone, some related compounds or some contaminated nutritive supplements. Finally, the sportsmen may have taken something during or just before the football game.

The complex history of the olive tree: from Late Quaternary diversification of Mediterranean lineages to primary domestication in the northern Levant.

The location and timing of domestication of the olive tree, a key crop in Early Mediterranean societies, remain hotly debated. Here, we unravel the history of wild olives (oleasters), and then infer the primary origins of the domesticated olive. Phylogeography and Bayesian molecular dating analyses based on plastid genome profiling of 1263 oleasters and 534 cultivated genotypes reveal three main lineages of pre-Quaternary origin. Regional hotspots of plastid diversity, species distribution modelling and macrofossils support the existence of three long-term refugia; namely the Near East (including Cyprus), the Aegean area and the Strait of Gibraltar. These ancestral wild gene pools have provided the essential foundations for cultivated olive breeding. Comparison of the geographical pattern of plastid diversity between wild and cultivated olives indicates the cradle of first domestication in the northern Levant followed by dispersals across the Mediterranean basin in parallel with the expansion of civilizations and human exchanges in this part of the world.

The likelihood approach to compare populations : a study on DNA evidence and pitfalls of intuitions

The paper follows on from earlier work [Taroni F and Aitken CGG. Probabilistic reasoning in the law, Part 1: assessment of probabilities and explanation of the value of DNA evidence. Science & Justice 1998; 38: 165-177]. Different explanations of the value of DNA evidence were presented to students from two schools of forensic science and to members of fifteen laboratories all around the world. The responses were divided into two groups; those which came from a school or laboratory identified as Bayesian and those which came from a school or laboratory identified as non-Bayesian. The paper analyses these responses using a likelihood approach. This approach is more consistent with a Bayesian analysis than one based on a frequentist approach, as was reported by Taroni F and Aitken CGG. [Probabilistic reasoning in the law, Part 1: assessment of probabilities and explanation of the value of DNA evidence] in Science & Justice 1998.