The Dynamics of Power laws: Fitness and Aging in Preferential Attachment Trees

Continuous-time branching processes describe the evolution of a population whose individuals generate a random number of children according to a birth process. Such branching processes can be used to understand preferential attachment models in which the birth rates are linear functions. We are motivated by citation networks, where power-law citation counts are observed as well as aging in the citation patterns. To model this, we introduce fitness and age-dependence in these birth processes. The multiplicative fitness moderates the rate at which children are born, while the aging is integrable, so that individuals receives a finite number of children in their lifetime. We show the existence of a limiting degree distribution for such processes. In the preferential attachment case, where fitness and aging are absent, this limiting degree distribution is known to have power-law tails. We show that the limiting degree distribution has exponential tails for bounded fitnesses in the presence of integrable aging, while the power-law tail is restored when integrable aging is combined with fitness with unbounded support with at most exponential tails. In the absence of integrable aging, such processes are explosive.     

Enzyme-catalyzed modification of PES surfaces: reduction in adsorption of BSA, dextrin and tannin

The effect of pH on the build-up of polyelectrolyte multilayers, PEMs, composed by poly-L-lysine and heparin onto two different substrates, silica and gold, has been studied by means of ellipsometry and quartz crystal microbalance with dissipation, QCM-D. Ellipsometry results indicate that the dry mass grows exponentially with the number of layers, and that this amount is larger as the pH values are raised. From QCM-D data the viscoelastic properties of the multilayered structure have been obtained. These data reflect that PEMs become more viscoelastic as the pH values are increased for silica substrates, while for gold the highest viscoelastic behavior is obtained at neutral pH and the elastic behavior becomes dominant as the pH is further increased or decreased. By combining these two surface techniques it has been also possible to determine the solvent content in the multilayers and reach a deeper understanding of the internal structure.     

Profiling of erythropoietin products by capillary electrophoresis with native fluorescence detection

The potential of CE with native fluorescence detection (Flu) for the profiling of the therapeutic protein erythropoietin (EPO) was studied. EPO is a highly heterogeneous glycoprotein comprising a large number of isoforms. CE was applied to induce separation among the various glycoforms. Native Flu of EPO provided high detection selectivity yielding good signal‐to‐noise ratios and stable baselines, particularly when compared to conventional UV absorbance detection. In order to enhance EPO isoform resolution, CE was performed using a capillary with a neutral coating in combination with a simple BGE of 2.0 M acetic acid (pH 2.1). CE‐Flu analysis of the EPO biological reference preparation of the European Pharmacopeia resulted in a highly detailed glycoform profile. Migration time RSDs for selected EPO isoforms were less than 0.22% and 0.80% for intraday and interday repeatability, respectively. RSDs for relative peak intensity of the major EPO isoforms were less than 3%. The achieved resolution, migration time stability, and sensitivity allowed discrimination of different EPO products (EPO‐α and EPO‐β) based on the recorded glycoform pattern. The developed CE‐Flu method is relatively straightforward, and shows potential for quality control in biopharmaceutical production.     

The historical development of classical stability concepts: Lagrange, Poisson and Lyapunov stability

A brief historical overview is given which discusses the development of classical stability concepts, starting in the seventeenth century and finally leading to the concept of Lyapunov stability at the beginning of the twentieth century. The aim of the paper is to find out how various scientists thought about stability and to which extent their work is related to the stability concepts bearing their names, i.e. Lagrange, Poisson and Lyapunov stability. To this end, excerpts of original texts are discussed in detail. Furthermore, the relationship between the various works is addressed.     

Offense Control Taking into Account Heterogeneity of Age

This paper studies the optimal tradeoff between the benefits and costs of preventing offenses and treating offenders. Based on a flexible age-structured epidemiological framework, a two-state compartment model is analyzed to reduce the prevalence of offending such as illicit drug consumption or violence. It turns out that, even in this highly simplified model, multiple stationary states exist. In particular, three different kinds of equilibria are identified, i.e., law and order, conservative, and liberal. The optimal mix of the control instruments is calculated providing interesting insight into the structure of the paths minimizing the discounted stream of social costs and expenditures for prevention and treatment.It can happen that a Skiba point exists. This implies that, for an initially small number of offenders, saddle-point convergence to a law-and-order equilibrium (boundary solution with no offenders) or to a conservative equilibrium (with few offenders) occurs, while if the number of offenders is large, the effects of prevention and treatment are too low or too expensive so that a liberal equilibrium (with many offenders) occurs.     

Dynamic effects on j-couplings across hydrogen bonds in proteins

We combine molecular dynamics simulation (MD) with density functional theory (DFT)/finite perturbation theory (FPT) to obtain the Fermi contact contributions to the 3hJNC' couplings in the SMN Tudor domain. Our results show that the effect of conformational motion needs to be considered for the accurate prediction of these scalar couplings. For hydrogen bonds in the beta-sheet regions, the calculated cumulative J-coupling averages remain constant after the first 200 ps. In the more flexible regions at the edges of the beta-sheets, the cumulative J-coupling averages vary over the 500-ps trajectory, providing a qualitative insight into the degree of conformational motion in different regions of the protein.     

Diameter in ultra‐small scale‐free random graphs

It is well known that many random graphs with infinite variance degrees are ultra‐small. More precisely, for configuration models and preferential attachment models where the proportion of vertices of degree at least k is approximately k^{?(τ ? 1)} with τ ∈ (2,3), typical distances between pairs of vertices in a graph of size n are asymptotic to and , respectively. In this paper, we investigate the behavior of the diameter in such models. We show that the diameter is of order precisely when the minimal forward degree d_fwd of vertices is at least 2. We identify the exact constant, which equals that of the typical distances plus . Interestingly, the proof for both models follows identical steps, even though the models are quite different in nature.