Comparison of averages of flows and maps

It is shown that in transient chaos there is no direct relation between averages in a continuos time dynamical system (flow) and averages using the analogous discrete system defined by the corresponding Poincare map. In contrast to permanent chaos, results obtained from the Poincare map can even be qualitatively incorrect. The reason is that the return time between intersections on the Poincare surface becomes relevant. However, after introducing a true-time Poincare map, quantities known from the usual Poincare map, such as conditionally invariant measure and natural measure, can be generalized to this case. Escape rates and averages, e.g. Liapunov exponents and drifts can be determined correctly using these novel measures. Significant differences become evident when we compare with results obtained from the usual Poincare map.Comment: 4 pages in Revtex with 2 included postscript figures, submitted to Phys. Rev.

Excitable media in open and closed chaotic flows

We investigate the response of an excitable medium to a localized perturbation in the presence of a two-dimensional smooth chaotic flow. Two distinct types of flows are numerically considered: open and closed. For both of them three distinct regimes are found, depending on the relative strengths of the stirring and the rate of the excitable reaction. In order to clarify and understand the role of the many competing mechanisms present, simplified models of the process are introduced. They are one-dimensional baker-map models for the flow and a one-dimensional approximation for the transverse profile of the filaments.Comment: 14 pages, 16 figure

Fast flowing populations are not well mixed

In evolutionary dynamics, well-mixed populations are almost always associated with all-to-all interactions; mathematical models are based on complete graphs. In most cases, these models do not predict fixation probabilities in groups of individuals mixed by flows. We propose an analytical description in the fast-flow limit. This approach is valid for processes with global and local selection, and accurately predicts the suppression of selection as competition becomes more local. It provides a modelling tool for biological or social systems with individuals in motion.Comment: 19 pages, 8 figure

Learning valued relations from data

Driven by a large number of potential applications in areas like bioinformatics, information retrieval and social network analysis, the problem setting of inferring relations between pairs of data objects has recently been investigated quite intensively in the machine learning community. To this end, current approaches typically consider datasets containing crisp relations, so that standard classification methods can be adopted. However, relations between objects like similarities and preferences are in many real-world applications often expressed in a graded manner. A general kernel-based framework for learning relations from data is introduced here. It extends existing approaches because both crisp and valued relations are considered, and it unifies existing approaches because different types of valued relations can be modeled, including symmetric and reciprocal relations. This framework establishes in this way important links between recent developments in fuzzy set theory and machine learning. Its usefulness is demonstrated on a case study in document retrieval

The effect of iterative model reconstruction on coronary artery calcium quantification

Coronary artery calcium (CAC) scoring with computed tomography (CT) is an established tool for quantifying calcified atherosclerotic plaque burden. Despite the widespread use of novel image reconstruction techniques in CT, the effect of iterative model reconstruction on CAC score remains unclear. We sought to assess the impact of iterative model based reconstruction (IMR) on coronary artery calcium quantification as compared to the standard filtered back projection (FBP) algorithm and hybrid iterative reconstruction (HIR). In addition, we aimed to simulate the impact of iterative reconstruction techniques on calcium scoring based risk stratification of a larger asymptomatic population. We studied 63 individuals who underwent CAC scoring. Images were reconstructed with FBP, HIR and IMR and CAC scores were measured. We estimated the cardiovascular risk reclassification rate of IMR versus HIR and FBP in a larger asymptomatic population (n = 504). The median CAC scores were 147.7 (IQR 9.6-582.9), 107.0 (IQR 5.9-526.6) and 115.1 (IQR 9.3-508.3) for FBP, HIR and IMR, respectively. The HIR and IMR resulted in lower CAC scores as compared to FBP (both p < 0.001), however there was no difference between HIR and IMR (p = 0.855). The CAC score decreased by 7.2 % in HIR and 7.3 % in IMR as compared to FBP, resulting in a risk reclassification rate of 2.4 % for both HIR and IMR. The utilization of IMR for CAC scoring reduces the measured calcium quantity. However, the CAC score based risk stratification demonstrated modest reclassification in IMR and HIR versus FBP

Acute hyperglycemia abolishes cardioprotection by remote ischemic perconditioning

BACKGROUND: Remote ischemic perconditioning (RIPerC) has a promising therapeutic insight to improve the prognosis of acute myocardial infarction. Chronic comorbidities such as diabetes are known to interfere with conditioning interventions by modulating cardioprotective signaling pathways, such as e.g., mTOR pathway and autophagy. However, the effect of acute hyperglycemia on RIPerC has not been studied so far. Therefore, here we investigated the effect of acute hyperglycemia on cardioprotection by RIPerC. METHODS: Wistar rats were divided into normoglycemic (NG) and acute hyperglycemic (AHG) groups. Acute hyperglycemia was induced by glucose infusion to maintain a serum glucose concentration of 15-20 mM throughout the experimental protocol. NG rats received mannitol infusion of an equal osmolarity. Both groups were subdivided into an ischemic (Isch) and a RIPerC group. Each group underwent reversible occlusion of the left anterior descending coronary artery (LAD) for 40 min in the presence or absence of acute hyperglycemia. After the 10-min LAD occlusion, RIPerC was induced by 3 cycles of 5-min unilateral femoral artery and vein occlusion and 5-min reperfusion. After 120 min of reperfusion, infarct size was measured by triphenyltetrazolium chloride staining. To study underlying signaling mechanisms, hearts were harvested for immunoblotting after 35 min in both the NG and AHG groups. RESULTS: Infarct size was significantly reduced by RIPerC in NG, but not in the AHG group (NG + Isch: 46.27 +/- 5.31 % vs. NG + RIPerC: 24.65 +/- 7.45 %, p < 0.05; AHG + Isch: 54.19 +/- 4.07 % vs. 52.76 +/- 3.80 %). Acute hyperglycemia per se did not influence infarct size, but significantly increased the incidence and duration of arrhythmias. Acute hyperglycemia activated mechanistic target of rapamycine (mTOR) pathway, as it significantly increased the phosphorylation of mTOR and S6 proteins and the phosphorylation of AKT. In spite of a decreased LC3II/LC3I ratio, other markers of autophagy, such as ATG7, ULK1 phopsphorylation, Beclin 1 and SQSTM1/p62, were not modulated by acute hyperglycemia. Furthermore, acute hyperglycemia significantly elevated nitrative stress in the heart (0.87 +/- 0.01 vs. 0.50 +/- 0.04 microg 3-nitrotyrosine/mg protein, p < 0.05). CONCLUSIONS: This is the first demonstration that acute hypreglycemia deteriorates cardioprotection by RIPerC. The mechanism of this phenomenon may involve an acute hyperglycemia-induced increase in nitrative stress and activation of the mTOR pathway

The Evolution of Enzyme Specificity in the Metabolic Replicator Model of Prebiotic Evolution

The chemical machinery of life must have been catalytic from the outset. Models of the chemical origins have attempted to explain the ecological mechanisms maintaining a minimum necessary diversity of prebiotic replicator enzymes, but little attention has been paid so far to the evolutionary initiation of that diversity. We propose a possible first step in this direction: based on our previous model of a surface-bound metabolic replicator system we try to explain how the adaptive specialization of enzymatic replicator populations might have led to more diverse and more efficient communities of cooperating replicators with two different enzyme activities. The key assumptions of the model are that mutations in the replicator population can lead towards a) both of the two different enzyme specificities in separate replicators: efficient “specialists” or b) a “generalist” replicator type with both enzyme specificities working at less efficiency, or c) a fast-replicating, non-enzymatic “parasite”. We show that under realistic trade-off constraints on the phenotypic effects of these mutations the evolved replicator community will be usually composed of both types of specialists and of a limited abundance of parasites, provided that the replicators can slowly migrate on the mineral surface. It is only at very weak trade-offs that generalists take over in a phase-transition-like manner. The parasites do not seriously harm the system but can freely mutate, therefore they can be considered as pre-adaptations to later, useful functions that the metabolic system can adopt to increase its own fitness

Periodic decomposition of integer valued functions

We study those functions that can be written as a finite sum of periodic integer valued functions. On &#8484; we give three different characterizations of these functions. For this we prove that the existence of a real valued periodic decomposition of a &#8484; &#8594; &#8484; function implies the existence of an integer valued periodic decomposition with the same periods. This result depends on the representation of the greatest common divisor of certain polynomials with integer coefficients as a linear combination of the given polynomials where the coefficients also belong to &#8484;[x]. We give an example of an &#8484; &#8594; {0, 1} function that has a bounded real valued periodic decomposition but does not have a bounded integer valued periodic decomposition with the same periods. It follows that the class of bounded &#8484; &#8594; &#8484; functions has the decomposition property as opposed to the class of bounded &#8477; &#8594; &#8484; functions. If the periods are pairwise commensurable or not prescribed, then we get more general results