A Topological Approach to Fuzzy Sets

This thesis presents a topological approach to studying fuzzy setsby means of modifier operators. Modifier operators are mathematical models, e.g., for hedges, and we present briefly different approaches to studying modifier operators. We are interested in compositional modifier operators, modifiers for short, and these modifiers depend on binary relations. We show that if a modifier depends on a reflexive and transitive binary relation on U, then there exists a unique topology on U such that this modifier is the closure operator in that topology. Also, if U is finite then there exists a lattice isomorphism between the class of all reflexive and transitive relations and the class of all topologies on U. We define topological similarity relation "≈" between L-fuzzy sets in an universe U, and show that the class LU/ ≈ is isomorphic with the class of all topologies on U, if U is finite and L is suitable. We consider finite bitopological spaces as approximation spaces, and we show that lower and upper approximations can be computed by means of α-level sets also in the case of equivalence relations. This means that approximations in the sense of Rough Set Theory can be computed by means of α-level sets. Finally, we present and application to data analysis: we study an approach to detecting dependencies of attributes in data base-like systems, called information systems.

A note on the periodic orbits and topological entropy of graph maps

This paper deals with the relationship between the periodic orbits of continuous maps on graphs and the topological entropy of the map. We show that the topological entropy of a graph map can be approximated by the entropy of its periodic orbits.

Task complexity, the Cognition Hypothesis and second language learning and performance

In this paper we describe a taxonomy of task demands which distinguishes between Task Complexity, Task Condition and Task Difficulty. We then describe three theoretical claims and predictions of the Cognition Hypothesis (Robinson 2001, 2003b, 2005a) concerning the effects of task complexity on: (a) language production; (b) interaction and uptake of information available in the input to tasks; and (c) individual differences-task interactions. Finally we summarize the findings of the empirical studies in this special issue which all address one or more of these predictions and point to some directions for continuing, future research into the effects of task complexity on learning and performance.

A survey of transposable element classification systems--a call for a fundamental update to meet the challenge of their diversity and complexity.

The increase of publicly available sequencing data has allowed for rapid progress in our understanding of genome composition. As new information becomes available we should constantly be updating and reanalyzing existing and newly acquired data. In this report we focus on transposable elements (TEs) which make up a significant portion of nearly all sequenced genomes. Our ability to accurately identify and classify these sequences is critical to understanding their impact on host genomes. At the same time, as we demonstrate in this report, problems with existing classification schemes have led to significant misunderstandings of the evolution of both TE sequences and their host genomes. In a pioneering publication Finnegan (1989) proposed classifying all TE sequences into two classes based on transposition mechanisms and structural features: the retrotransposons (class I) and the DNA transposons (class II). We have retraced how ideas regarding TE classification and annotation in both prokaryotic and eukaryotic scientific communities have changed over time. This has led us to observe that: (1) a number of TEs have convergent structural features and/or transposition mechanisms that have led to misleading conclusions regarding their classification, (2) the evolution of TEs is similar to that of viruses by having several unrelated origins, (3) there might be at least 8 classes and 12 orders of TEs including 10 novel orders. In an effort to address these classification issues we propose: (1) the outline of a universal TE classification, (2) a set of methods and classification rules that could be used by all scientific communities involved in the study of TEs, and (3) a 5-year schedule for the establishment of an International Committee for Taxonomy of Transposable Elements (ICTTE).

Impact of model complexity on cross-temporal transferability in Maxent species distribution models: An assessment using paleobotanical data

Maximum entropy modeling (Maxent) is a widely used algorithm for predicting species distributions across space and time. Properly assessing the uncertainty in such predictions is non-trivial and requires validation with independent datasets. Notably, model complexity (number of model parameters) remains a major concern in relation to overfitting and, hence, transferability of Maxent models. An emerging approach is to validate the cross-temporal transferability of model predictions using paleoecological data. In this study, we assess the effect of model complexity on the performance of Maxent projections across time using two European plant species (Alnus giutinosa (L.) Gaertn. and Corylus avellana L) with an extensive late Quaternary fossil record in Spain as a study case. We fit 110 models with different levels of complexity under present time and tested model performance using AUC (area under the receiver operating characteristic curve) and AlCc (corrected Akaike Information Criterion) through the standard procedure of randomly partitioning current occurrence data. We then compared these results to an independent validation by projecting the models to mid-Holocene (6000 years before present) climatic conditions in Spain to assess their ability to predict fossil pollen presence-absence and abundance. We find that calibrating Maxent models with default settings result in the generation of overly complex models. While model performance increased with model complexity when predicting current distributions, it was higher with intermediate complexity when predicting mid-Holocene distributions. Hence, models of intermediate complexity resulted in the best trade-off to predict species distributions across time. Reliable temporal model transferability is especially relevant for forecasting species distributions under future climate change. Consequently, species-specific model tuning should be used to find the best modeling settings to control for complexity, notably with paleoecological data to independently validate model projections. For cross-temporal projections of species distributions for which paleoecological data is not available, models of intermediate complexity should be selected.

Effects of manipulating Task Complexity on self-repairs during L2 oral production

This paper analyses the effects of manipulating the cognitive complexity of L2 oral tasks on language production. It specifically focuses on self-repairs, which are taken as a measure of accuracy since they denote both attention to form and an attempt at being accurate. By means of a repeated measures de- sign, 42 lower-intermediate students were asked to perform three different tasks types (a narrative, and instruction-giving task, and a decision-making task) for which two degrees of cognitive complexity were established. The narrative task was manipulated along +/− Here-and-Now, an instruction-giving task ma- nipulated along +/− elements, and the decision-making task which is manipu- lated along +/− reasoning demands. Repeated measures ANOVAs are used for the calculation of differences between degrees of complexity and among task types. One-way ANOVA are used to detect potential differences between low- proficiency and high-proficiency participants. Results show an overall effect of Task Complexity on self-repairs behavior across task types, with different be- haviors existing among the three task types. No differences are found between the self-repair behavior between low and high proficiency groups. Results are discussed in the light of theories of cognition and L2 performance (Robin- son 2001a, 2001b, 2003, 2005, 2007), L1 and L2 language production models (Levelt 1989, 1993; Kormos 2000, 2006), and attention during L2 performance (Skehan 1998; Robinson, 2002).

Better-quasi-order : ideals and spaces

This thesis deals with combinatorics, order theory and descriptive set theory. The first contribution is to the theory of well-quasi-orders (wqo) and better-quasi-orders (bqo). The main result is the proof of a conjecture made by Maurice Pouzet in 1978 his thèse d'état which states that any wqo whose ideal completion remainder is bqo is actually bqo. Our proof relies on new results with both a combinatorial and a topological flavour concerning maps from a front into a compact metric space. The second contribution is of a more applied nature and deals with topological spaces. We define a quasi-order on the subsets of every second countable To topological space in a way that generalises the Wadge quasi-order on the Baire space, while extending its nice properties to virtually all these topological spaces. The Wadge quasi-order of reducibility by continuous functions is wqo on Borei subsets of the Baire space, this quasi-order is however far less satisfactory for other important topological spaces such as the real line, as Hertling, Ikegami and Schlicht notably observed. Some authors have therefore studied reducibility with respect to some classes of discontinuous functions to remedy this situation. We propose instead to keep continuity but to weaken the notion of function to that of relation. Using the notion of admissible representation studied in Type-2 theory of effectivity, we define the quasi-order of reducibility by relatively continuous relations. We show that this quasi-order both refines the classical hierarchies of complexity and is wqo on the Borei subsets of virtually every second countable To space - including every (quasi-)Polish space. -- Cette thèse se situe dans les domaines de la combinatoire, de la théorie des ordres et de la théorie descriptive. La première contribution concerne la théorie des bons quasi-ordres (wqo) et des meilleurs quasi-ordres (bqo). Le résultat principal est la preuve d'une conjecture, énoncée par Pouzet en 1978 dans sa thèse d'état, qui établit que tout wqo dont l'ensemble des idéaux non principaux ordonnés par inclusion forme un bqo est alors lui-même un bqo. La preuve repose sur de nouveaux résultats, qui allient la combinatoire et la topologie, au sujet des fonctions d'un front vers un espace métrique compact. La seconde contribution de cette thèse traite de la complexité topologique dans le cadre des espaces To à base dénombrable. Dans le cas de l'espace de Baire, le quasi-ordre de Wadge est un wqo sur les sous-ensembles Boréliens qui a suscité énormément d'intérêt. Cependant cette relation de réduction par fonctions continues s'avère bien moins satisfaisante pour d'autres espaces d'importance tels que la droite réelle, comme l'ont fait notamment remarquer Hertling, Schlicht et Ikegami. Nous proposons de conserver la continuité et d'affaiblir la notion de fonction pour celle de relation. Pour ce faire, nous utilisons la notion de représentation admissible étudiée en « Type-2 theory of effectivity » initiée par Weihrauch. Nous introduisons alors le quasi-ordre de réduction par relations relativement continues et montrons que celui-ci à la fois raffine les hiérarchies classiques de complexité topologique et forme un wqo sur les sous-ensembles Boréliens de chaque espace quasi-Polonais.

Controlling complexity: the clinical relevance of mouse complex genetics.

Experimental animal models are essential to obtain basic knowledge of the underlying biological mechanisms in human diseases. Here, we review major contributions to biomedical research and discoveries that were obtained in the mouse model by using forward genetics approaches and that provided key insights into the biology of human diseases and paved the way for the development of novel therapeutic approaches.

Topological phases in small quantum Hall samples

Topological order has proven a useful concept to describe quantum phase transitions which are not captured by the Ginzburg-Landau type of symmetry-breaking order. However, lacking a local order parameter, topological order is hard to detect. One way to detect it is via direct observation of anyonic properties of excitations which are usually discussed in the thermodynamic limit, but so far has not been realized in macroscopic quantum Hall samples. Here we consider a system of few interacting bosons subjected to the lowest Landau level by a gauge potential, and theoretically investigate vortex excitations in order to identify topological properties of different ground states. Our investigation demonstrates that even in surprisingly small systems anyonic properties are able to characterize the topological order. In addition, focusing on a system in the Laughlin state, we study the robustness of its anyonic behavior in the presence of tunable finite-range interactions acting as a perturbation. A clear signal of a transition to a different state is reflected by the system's anyonic properties.

Identity, non-identity, and near-identity: Addressing the complexity of coreference

This article examines the mainstream categorical definition of coreference as "identity of reference." It argues that coreference is best handled when identity is treated as a continuum, ranging from full identity to non-identity, with room for near-identity relations to explain currently problematic cases. This middle ground is needed to account for those linguistic expressions in real text that stand in relations that are neither full coreference nor non-coreference, a situation that has led to contradictory treatment of cases in previous coreference annotation efforts. We discuss key issues for coreference such as conceptual categorization, individuation, criteria of identity, and the discourse model construct. We redefine coreference as a scalar relation between two (or more) linguistic expressions that refer to discourse entities considered to be at the same granularity level relevant to the linguistic and pragmatic context. We view coreference relations in terms of mental space theory and discuss a large number of real life examples that show near-identity at different degrees.

Estimation of reference curves for the urinary steroid metabolome in the first year of life in healthy children : Tracing the complexity of human postnatal steroidogenesis.

CONTEXT: Complex steroid disorders such as P450 oxidoreductase deficiency or apparent cortisone reductase deficiency may be recognized by steroid profiling using chromatographic mass spectrometric methods. These methods are highly specific and sensitive, and provide a complete spectrum of steroid metabolites in a single measurement of one sample which makes them superior to immunoassays. The steroid metabolome during the fetal-neonatal transition is characterized by (a) the metabolites of the fetal-placental unit at birth, (b) the fetal adrenal androgens until its involution 3-6 months postnatally, and (c) the steroid metabolites produced by the developing endocrine organs. All these developmental events change the steroid metabolome in an age- and sex-dependent manner during the first year of life. OBJECTIVE: The aim of this study was to provide normative values for the urinary steroid metabolome of healthy newborns at short time intervals in the first year of life. METHODS: We conducted a prospective, longitudinal study to measure 67 urinary steroid metabolites in 21 male and 22 female term healthy newborn infants at 13 time-points from week 1 to week 49 of life. Urine samples were collected from newborn infants before discharge from hospital and from healthy infants at home. Steroid metabolites were measured by gas chromatography-mass spectrometry (GC-MS) and steroid concentrations corrected for urinary creatinine excretion were calculated. RESULTS: 61 steroids showed age and 15 steroids sex specificity. Highest urinary steroid concentrations were found in both sexes for progesterone derivatives, in particular 20α-DH-5α-DH-progesterone, and for highly polar 6α-hydroxylated glucocorticoids. The steroids peaked at week 3 and decreased by ∼80% at week 25 in both sexes. The decline of progestins, androgens and estrogens was more pronounced than of glucocorticoids whereas the excretion of corticosterone and its metabolites and of mineralocorticoids remained constant during the first year of life. CONCLUSION: The urinary steroid profile changes dramatically during the first year of life and correlates with the physiologic developmental changes during the fetal-neonatal transition. Thus detailed normative data during this time period permit the use of steroid profiling as a powerful diagnostic tool.

Complexity of the Paradigms Present in Quality Criteria of Qualitative Research Grids

With qualitative methods being increasingly used in health science fields, numerous grids proposing criteria to evaluate the quality of this type of research have been produced. Expert evaluators deem that there is a lack of consensual tools to evaluate qualitative research. Based on the review of 133 quality criteria grids for qualitative research in health sciences, the authors present the results of a computerized lexicometric analysis, which confirms the variety of intra- and inter-grid constructions, including within the same field. This variety is linked to the authors' paradigmatic references underlying the criteria proposed. These references seem to be built intuitively, reflecting internal representations of qualitative research, thus making the grids and their criteria hard to compare. Consequently, the consensus on the definitions and the number of criteria becomes problematic. The paradigmatic and theoretical references of the grids should be specified so that users could better assess their contributions and limitations.

The influence of decision-maker effort and case complexity on appealed rulings subject to multi-categorical selection

This study extends the standard econometric treatment of appellate court outcomes by 1) considering the role of decision-maker effort and case complexity, and 2) adopting a multi-categorical selection process of appealed cases. We find evidence of appellate courts being affected by both the effort made by first-stage decision makers and case complexity. This illustrates the value of widening the narrowly defined focus on heterogeneity in individual-specific preferences that characterises many applied studies on legal decision-making. Further, the majority of appealed cases represent non-random sub-samples and the multi-categorical selection process appears to offer advantages over the more commonly used dichotomous selection models.