To generalize simple bead-linker model of swimmers to higher dimensions and to demonstrate the chemotaxis ability of such swimmers, here we introduce a low-Reynolds predator, using a two-dimensional triangular bead-spring model. Two-state linkers as mechanochemical enzymes expand as a result of interaction with particular activator substances in the environment, causing the whole body to translate and rotate. The concentration of the chemical stimulator controls expansion versus the contraction rate of each arm and so affects the ability of the body for diffusive movements; also the variation of activator substance's concentration in the environment breaks the symmetry of linkers' preferred state, resulting in the drift of the random walker along the gradient of the density of activators. External food or danger sources may attract or repel the body by producing or consuming the chemical activators of the organism's enzymes, inducing chemotaxis behavior. Generalization of the model to three dimensions is straightforward.
Permutation approach is suggested as a method to investigate financial time series in micro scales. The method is used to see how high frequency trading in recent years has affected the micro patterns which may be seen in financial time series. Tick to tick exchange rates are considered as examples. It is seen that variety of patterns evolve through time; and that the scale over which the target markets have no dominant patterns, have decreased steadily over time with the emergence of higher frequency trading. 1
What is the connection between financing constraints and the equity premium? To answer this question, we build a model with inalienable human capital, in which investors finance individuals who can potentially become skilled. Though investment in skill is always optimal, it does not take place in some states of the world, due to moral hazard. In other states of the world, individuals acquire skill; however outside investors and individuals inefficiently share risk. We show that this simple moral hazard problem and the resultant financing friction leads to a realistic equity premium, a low riskfree rate, and severe negative consequences for distribution of wealth and for welfare. When investment fails to take place, the economy enters an endogenous disaster state. We show that the possibility of these disaster states distorts risk prices, even under calibrations in which they never occur in equilibrium.
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