SELLING SHARES TO RETAIL INVESTORS: AUCTION VS. FIXED PRICE

We analyze the problem of selling shares of a divisible good to a large number of buyers when demand is uncertain. We characterize equilibria of two popular mechanisms, a fixed price mechanism and a uniform price auction, and compare the revenues. While in the auction truthful bidding is a dominant strategy, we find that bidders have an incentive to overstate their demand in the fixed price mechanism. For some parameter values this yields the surprising result that the fixed price mechanism outperforms the auction.IPO, Uniform Price Auction, Open Offer, Proportional Rationing.

Coherent exciton transport in dendrimers and continuous-time quantum walks

We model coherent exciton transport in dendrimers by continuous-time quantum walks (CTQWs). For dendrimers up to the second generation the coherent transport shows perfect recurrences, when the initial excitation starts at the central node. For larger dendrimers, the recurrence ceases to be perfect, a fact which resembles results for discrete quantum carpets. Moreover, depending on the initial excitation site we find that the coherent transport to certain nodes of the dendrimer has a very low probability. When the initial excitation starts from the central node, the problem can be mapped onto a line which simplifies the computational effort. Furthermore, the long time average of the quantum mechanical transition probabilities between pairs of nodes show characteristic patterns and allow to classify the nodes into clusters with identical limiting probabilities. For the (space) average of the quantum mechanical probability to be still or again at the initial site, we obtain, based on the Cauchy-Schwarz inequality, a simple lower bound which depends only on the eigenvalue spectrum of the Hamiltonian.Comment: 8 pages, 8 figures, accepted for publication in J. Chem. Phy

Deterministic and stochastic descriptions of gene expression dynamics

A key goal of systems biology is the predictive mathematical description of gene regulatory circuits. Different approaches are used such as deterministic and stochastic models, models that describe cell growth and division explicitly or implicitly etc. Here we consider simple systems of unregulated (constitutive) gene expression and compare different mathematical descriptions systematically to obtain insight into the errors that are introduced by various common approximations such as describing cell growth and division by an effective protein degradation term. In particular, we show that the population average of protein content of a cell exhibits a subtle dependence on the dynamics of growth and division, the specific model for volume growth and the age structure of the population. Nevertheless, the error made by models with implicit cell growth and division is quite small. Furthermore, we compare various models that are partially stochastic to investigate the impact of different sources of (intrinsic) noise. This comparison indicates that different sources of noise (protein synthesis, partitioning in cell division) contribute comparable amounts of noise if protein synthesis is not or only weakly bursty. If protein synthesis is very bursty, the burstiness is the dominant noise source, independent of other details of the model. Finally, we discuss two sources of extrinsic noise: cell-to-cell variations in protein content due to cells being at different stages in the division cycles, which we show to be small (for the protein concentration and, surprisingly, also for the protein copy number per cell) and fluctuations in the growth rate, which can have a significant impact.Comment: 23 pages, 5 figures; Journal of Statistical physics (2012

Selling shares to retail investors: auction vs. fixed price

We analyze the problem of selling shares of a divisible good to a large number of buyers when demand is uncertain. We characterize equilibria of two popular mechanisms, a fixed price mechanism and a uniform price auction, and compare the revenues. While in the auction truthful bidding is a dominant strategy, we find that bidders have an incentive to overstate their demand in the fixed price mechanism. For some parameter values this yields the surprising result that the fixed price mechanism outperforms the auction

Selling shares to retail investors: auction vs. fixed price

IPO, Uniform price auction, Open offer, Proportional rationing, D44, D45, G32,

Dwell Time Distributions of the Molecular Motor Myosin V

<div><p>The dwell times between two successive steps of the two-headed molecular motor myosin V are governed by non-exponential distributions. These distributions have been determined experimentally for various control parameters such as nucleotide concentrations and external load force. First, we use a simplified network representation to determine the dwell time distributions of myosin V, with the associated dynamics described by a Markov process on networks with absorbing boundaries. Our approach provides a direct relation between the motor’s chemical kinetics and its stepping properties. In the absence of an external load, the theoretical distributions quantitatively agree with experimental findings for various nucleotide concentrations. Second, using a more complex branched network, which includes ADP release from the leading head, we are able to elucidate the motor’s gating effect. This effect is caused by an asymmetry in the chemical properties of the leading and the trailing head of the motor molecule. In the case of an external load acting on the motor, the corresponding dwell time distributions reveal details about the motor’s backsteps.</p> </div

(a) Root mean square deviation RMSD between the experimental data (green bars in Fig. 3 (c, d)) and the simulated dwell time distributions for the three-cycle network as a function of the gating parameter for [ATP] = 10 (crosses) and [ATP] = 2 (circles).

<p>A lower deviation indicates an improved agreement between the experimental values and the distributions that result from the three-cycle network. For both concentrations, the RMSD decreases with increasing , until it saturates for , as indicated by the dashed line. The fluctuations for large values of arise from the variance in the simulations. The solid lines serve as a guide to the eye. (b) In case of a variable ATP binding rate , the agreement between the simulated dwell time distributions (symbols) and the experimental data (green bars) is further improved. The agreement is optimal for (red crosses), and is significantly improved in contrast to the distribution based on the experimental value of (red circles). The inset shows the RMSD as a function of , illustrating the minimal deviation for </p

(a–d) Dwell time distributions for different concentrations of ATP and ADP, with [P] = as discussed in the text.

<p>Comparison of distributions calculated using the uni-cycle network in Fig. 2(a) (blue solid lines) with experimental data (green bars) from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0055366#pone.0055366-Rief1" target="_blank">[4]</a>. Insets: Concentrations that apply to both experimental data theoretical curves are shown in the gray panels, while parameters specific to the theoretical results are given in the framed panels. In (a), (c–d), the experimental concentration of ADP is believed to be negligible. For saturating [ATP], (a,b) the dwell time distributions for the uni-cycle network (blue line) agree with those for the network shown in 2(b), for all gating parameters (data not shown). The symbols show simulated data for the network in 2(b) without gating (green circles) and gating with a 10-fold decelerated ADP release from the motor’s leading head (red circles).</p