Hausdorff dimension versus smoothness

There is a one-to-one correspondence between C1+H Cantor exchange systems that are C1+H fixed points of renormalization and C1+H diffeomorphisms f on surfaces with a codimension 1 hyperbolic attractor Λ that admit an invariant measure absolutely continuous with respect to the Hausdorff measure on Λ. However, there is no such C1+α Cantor exchange system with bounded geometry that is a C1+α fixed point of renormalization with regularity α greater than the Hausdorff dimension of its invariant Cantor set. The proof of the last result uses that the stable holonomies of a codimension 1 hyperbolic attractor Λ are not C1+θ for θ greater than the Hausdorff dimension of the stable leaves of f intersected with Λ.

A Methodology to measure shareholder value orientation and shareholder value creation aimed at providing a research basis to investigate the link between both magnitudes

Does shareholder value orientation lead to shareholder value creation? This article proposes methods to quantify both, shareholder value orientation and shareholder value creation. Through the application of these models it is possible to quantify both dimensions and examine statistically in how far shareholder value orientation explains shareholder value creation. The scoring model developed in this paper allows quantifying the orientation of managers towards the objective to maximize wealth of shareholders. The method evaluates information that comes from the companies and scores the value orientation in a scale from 0 to 10 points. Analytically the variable value orientation is operationalized expressing it as the general attitude of managers toward the objective of value creation, investment policy and behavior, flexibility and further eight value drivers. The value creation model works with market data such as stock prices and dividend payments. Both methods where applied to a sample of 38 blue chip companies: 32 firms belonged to the share index IBEX 35 on July 1st, 1999, one company represents the “new economy” listed in the Spanish New Market as per July 1st, 2001, and 5 European multinational groups formed part of the EuroStoxx 50 index also on July 1st, 2001. The research period comprised the financial years 1998, 1999, and 2000. A regression analysis showed that between 15.9% and 23.4% of shareholder value creation can be explained by shareholder value orientation.

Semidiscretization and long-time asymptotics of nonlinear diffusion equations

We review several results concerning the long time asymptotics of nonlinear diffusion models based on entropy and mass transport methods. Semidiscretization of these nonlinear diffusion models are proposed and their numerical properties analysed. We demonstrate the long time asymptotic results by numerical simulation and we discuss several open problems based on these numerical results. We show that for general nonlinear diffusion equations the long-time asymptotics can be characterized in terms of fixed points of certain maps which are contractions for the euclidean Wasserstein distance. In fact, we propose a new scaling for which we can prove that this family of fixed points converges to the Barenblatt solution for perturbations of homogeneous nonlinearities for values close to zero.

Bifurcations of homoclinic tangency in two-dimensional area-preserving and reversible maps

Report for the scientific sojourn at the Research Institute for Applied Mathematics and Cybernetics, Nizhny Novgorod, Russia, from July to September 2006. Within the project, bifurcations of orbit behavior in area-preserving and reversible maps with a homoclinic tangency were studied. Finitely smooth normal forms for such maps near saddle fixed points were constructed and it was shown that they coincide in the main order with the analytical Birkhoff-Moser normal form. Bifurcations of single-round periodic orbits for two-dimensional symplectic maps close to a map with a quadratic homoclinic tangency were studied. The existence of one- and two-parameter cascades of elliptic periodic orbits was proved.

Quality of life: a potentially useful measure to indicate subclinical flares in Crohn disease.

Background:  While quality of life (QoL) is a well-recognised outcome measure of Crohn disease (CD) activity, its influence on other outcome measures, including exacerbation of CD is poorly understood. If QoL measures were to be associated with intestinal inflammatory activity, they might be useful for early detection of subclinical flares. Aims:  We hypothesised that low QoL might be associated with subsequent CD flares. Methods:  A cohort of 318 adult CD patients was observed for 1 year after assessment of baseline characteristics. Data were collected in Swiss university hospitals, regional hospitals and private practices. At inclusion, patients completed the Inflammatory Bowel Disease QoL Questionnaire (gastrointestinal QoL; range: 32 to 224 points) and the Short Form-36 Health Survey (general QoL; range: 35 to 145 points). During follow up, flares were recorded. Binary logistic regression was performed to estimate the relation between QoL and the odds of subsequent flares. Results:  A twofold decrease in the odds of flares (99% CI: 1.1; 4.0) per standard deviation of gastrointestinal QoL and a threefold decrease (99% CI: 1.5; 6.2) per standard deviation of general QoL were observed. Conclusions:  The close association between QoL and subsequent flares suggests that QoL measures might be useful in detecting upcoming flares before they become clinically apparent.

Generic super-exponential stability of invariant tori in Hamiltonian systems

In this article, we consider solutions starting close to some linearly stable invariant tori in an analytic Hamiltonian system and we prove results of stability for a super-exponentially long interval of time, under generic conditions. The proof combines classical Birkhoff normal forms and a new method to obtain generic Nekhoroshev estimates developed by the author and L. Niederman in another paper. We will mainly focus on the neighbourhood of elliptic fixed points, the other cases being completely similar.

N-dimensional dynamical systems exploiting instabilities in full

We report experimental and numerical results showing how certain N-dimensional dynamical systems are able to exhibit complex time evolutions based on the nonlinear combination of N-1 oscillation modes. The experiments have been done with a family of thermo-optical systems of effective dynamical dimension varying from 1 to 6. The corresponding mathematical model is an N-dimensional vector field based on a scalar-valued nonlinear function of a single variable that is a linear combination of all the dynamic variables. We show how the complex evolutions appear associated with the occurrence of successive Hopf bifurcations in a saddle-node pair of fixed points up to exhaust their instability capabilities in N dimensions. For this reason the observed phenomenon is denoted as the full instability behavior of the dynamical system. The process through which the attractor responsible for the observed time evolution is formed may be rather complex and difficult to characterize. Nevertheless, the well-organized structure of the time signals suggests some generic mechanism of nonlinear mode mixing that we associate with the cluster of invariant sets emerging from the pair of fixed points and with the influence of the neighboring saddle sets on the flow nearby the attractor. The generation of invariant tori is likely during the full instability development and the global process may be considered as a generalized Landau scenario for the emergence of irregular and complex behavior through the nonlinear superposition of oscillatory motions

Quantifying urban attractiveness from the distribution and density of digital footprints

In the past, sensors networks in cities have been limited to fixed sensors, embedded in particular locations, under centralised control. Today, new applications can leverage wireless devices and use them as sensors to create aggregated information. In this paper, we show that the emerging patterns unveiled through the analysis of large sets of aggregated digital footprints can provide novel insights into how people experience the city and into some of the drivers behind these emerging patterns. We particularly explore the capacity to quantify the evolution of the attractiveness of urban space with a case study of in the area of the New York City Waterfalls, a public art project of four man-made waterfalls rising from the New York Harbor. Methods to study the impact of an event of this nature are traditionally based on the collection of static information such as surveys and ticket-based people counts, which allow to generate estimates about visitors’ presence in specific areas over time. In contrast, our contribution makes use of the dynamic data that visitors generate, such as the density and distribution of aggregate phone calls and photos taken in different areas of interest and over time. Our analysis provides novel ways to quantify the impact of a public event on the distribution of visitors and on the evolution of the attractiveness of the points of interest in proximity. This information has potential uses for local authorities, researchers, as well as service providers such as mobile network operators.

The population genetics of clonal and partially clonal diploids.

The consequences of variable rates of clonal reproduction on the population genetics of neutral markers are explored in diploid organisms within a subdivided population (island model). We use both analytical and stochastic simulation approaches. High rates of clonal reproduction will positively affect heterozygosity. As a consequence, nearly twice as many alleles per locus can be maintained and population differentiation estimated as F(ST) value is strongly decreased in purely clonal populations as compared to purely sexual ones. With increasing clonal reproduction, effective population size first slowly increases and then points toward extreme values when the reproductive system tends toward strict clonality. This reflects the fact that polymorphism is protected within individuals due to fixed heterozygosity. Contrarily, genotypic diversity smoothly decreases with increasing rates of clonal reproduction. Asexual populations thus maintain higher genetic diversity at each single locus but a lower number of different genotypes. Mixed clonal/sexual reproduction is nearly indistinguishable from strict sexual reproduction as long as the proportion of clonal reproduction is not strongly predominant for all quantities investigated, except for genotypic diversities (both at individual loci and over multiple loci).

Effects of small surface tension in Hele-Shaw multifinger dynamics: an analytical and numerical study

We study the singular effects of vanishingly small surface tension on the dynamics of finger competition in the Saffman-Taylor problem, using the asymptotic techniques described by Tanveer [Philos. Trans. R. Soc. London, Ser. A 343, 155 (1993)] and Siegel and Tanveer [Phys. Rev. Lett. 76, 419 (1996)], as well as direct numerical computation, following the numerical scheme of Hou, Lowengrub, and Shelley [J. Comput. Phys. 114, 312 (1994)]. We demonstrate the dramatic effects of small surface tension on the late time evolution of two-finger configurations with respect to exact (nonsingular) zero-surface-tension solutions. The effect is present even when the relevant zero-surface-tension solution has asymptotic behavior consistent with selection theory. Such singular effects, therefore, cannot be traced back to steady state selection theory, and imply a drastic global change in the structure of phase-space flow. They can be interpreted in the framework of a recently introduced dynamical solvability scenario according to which surface tension unfolds the structurally unstable flow, restoring the hyperbolicity of multifinger fixed points.

Surface tension and dynamics of fingering patterns

We study the minimal class of exact solutions of the Saffman-Taylor problem with zero surface tension, which contains the physical fixed points of the regularized (nonzero surface tension) problem. New fixed points are found and the basin of attraction of the Saffman-Taylor finger is determined within that class. Specific features of the physics of finger competition are identified and quantitatively defined, which are absent in the zero surface tension case. This has dramatic consequences for the long-time asymptotics, revealing a fundamental role of surface tension in the dynamics of the problem. A multifinger extension of microscopic solvability theory is proposed to elucidate the interplay between finger widths, screening and surface tension.

Projecting the self to past and future in mental time

Introduction: Human experience takes place in the line of mental-time (MT) created through imagination of oneself in different time-points in past or future (self-projection in time). Here we manipulated self-projection in MT not only with respect to one's life-events but also with respect to one's faces from different past and future time-points. Methods: We here compared MTT with respect to one's facial images from different time points in past and future (study 1: MT-faces) as well as with respect to different past and future life events (study 2: MT-events). Participants were asked to make judgments about past and future face images and past and future events from three different time-points: the present (Now), eight years earlier (Past) or eight years later (Future). In addition, as a control task participants were asked to make recognition judgments with respect to faces and memory-related judgments with respect to events without changing their habitual self-location in time. Behavioral measures and functional magnetic resonance imaging (fMRI) activity after subtraction of recognition and memory related activities show both absolute MT and relative MT effects for faces and events, signifying a fundamental brain mechanism of MT, disentangled from episodic memory functions. Results: Behavioural and event-related fMRI activity showed three independent effects characterized by (1) similarity between past recollection and future imagination, (2) facilitation of judgments related to the future as compared to the past, and (3) facilitation of judgments related to time-points distant from the present. These effects were found with respect to faces and events suggesting that the brain mechanisms of MT are independent of whether actual life episodes have to be re-/pre-experienced and recruited a common cerebral network including the medial-temporal, precuneus, inferior-frontal, temporo-parietal, and insular cortices. Conclusions: These behavioural and neural data suggest that self-projection in time is a crucial aspect of MT, relying on neural structures encoding memory, mental imagery, and self. Furthermore our results emphasize the idea that mental temporal processing is more strongly directed to future prediction than to past recollection.

An index to identify stroke-related vs incidental patent foramen ovale in cryptogenic stroke.

OBJECTIVE: We aimed to create an index to stratify cryptogenic stroke (CS) patients with patent foramen ovale (PFO) by their likelihood that the stroke was related to their PFO. METHODS: Using data from 12 component studies, we used generalized linear mixed models to predict the presence of PFO among patients with CS, and derive a simple index to stratify patients with CS. We estimated the stratum-specific PFO-attributable fraction and stratum-specific stroke/TIA recurrence rates. RESULTS: Variables associated with a PFO in CS patients included younger age, the presence of a cortical stroke on neuroimaging, and the absence of these factors: diabetes, hypertension, smoking, and prior stroke or TIA. The 10-point Risk of Paradoxical Embolism score is calculated from these variables so that the youngest patients with superficial strokes and without vascular risk factors have the highest score. PFO prevalence increased from 23% (95% confidence interval [CI]: 19%-26%) in those with 0 to 3 points to 73% (95% CI: 66%-79%) in those with 9 or 10 points, corresponding to attributable fraction estimates of approximately 0% to 90%. Kaplan-Meier estimated stroke/TIA 2-year recurrence rates decreased from 20% (95% CI: 12%-28%) in the lowest Risk of Paradoxical Embolism score stratum to 2% (95% CI: 0%-4%) in the highest. CONCLUSION: Clinical characteristics identify CS patients who vary markedly in PFO prevalence, reflecting clinically important variation in the probability that a discovered PFO is likely to be stroke-related vs incidental. Patients in strata more likely to have stroke-related PFOs have lower recurrence risk.

Subjective mental time: the functional architecture of projecting the self to past and future.

Abstract Human experience takes place in the line of mental time (MT) created through 'self-projection' of oneself to different time-points in the past or future. Here we manipulated self-projection in MT not only with respect to one's life events but also with respect to one's faces from different past and future time-points. Behavioural and event-related functional magnetic resonance imaging activity showed three independent effects characterized by (i) similarity between past recollection and future imagination, (ii) facilitation of judgements related to the future as compared with the past, and (iii) facilitation of judgements related to time-points distant from the present. These effects were found with respect to faces and events, and also suggest that brain mechanisms of MT are independent of whether actual life episodes have to be re-experienced or pre-experienced, recruiting a common cerebral network including the anteromedial temporal, posterior parietal, inferior frontal, temporo-parietal and insular cortices. These behavioural and neural data suggest that self-projection in time is a fundamental aspect of MT, relying on neural structures encoding memory, mental imagery and self.

The use of insulin to improve fertility of timed-inseminated postpartum suckled beef cows

The objective of this work was to evaluate the effect of insulin alone or in association with equine chorionic gonadotropin (eCG) on the fertility of postpartum beef cows subjected to synchronization. A total of 340 cows was subjected to fixed time artificial insemination. In the trial 1, the cows were subjected to temporary weaning (TW), while in the trial 2 the same protocol was tested without TW. The addition of an insulin injection to a progesterone/eCG-based protocol without TW increased the pregnancy rate of beef cows with body condition score (BCS) equal to or lower than 2.5. Insulin had no effect on cows submitted to TW or with BCS equal to or higher than 3.0.