Although a complete dynamic model includes the equations of motion as well as the initial conditions, many of the learning dynamics in the literature do not entail a serious theory of initial conditions. This paper explores and evaluates five approaches to complete learning models with a theory of initial conditions. We find that (1) the initial period’s fit is sensitive to the model of initial...

We present a model with an infinite volume bulk in which a braneworld with a cosmological constant evolves to a static, 4-dimensional Minkowski spacetime. This evolution occurs for a generic class of initial conditions with positive energy densities. The metric everywhere outside the brane is that of a 5-dimensional Minkowski spacetime, where the effect of the brane is the creation of a frame w...

This paper is concerned with the boundedness of the following symmetric system of max-type difference equations 1 1 1 1 max{ , }, max{ , }, , p p n n n n q q n n y x 0 x c y c n x y + + − − = = N ∈ where , the parameters and the initial conditions { } 0 0 N N = ∪ , , (0, ) c p q ∈ ∞ 1 0 1 0 , , , x x y y − − are arbitrary positive real numbers.

We focus on a Cauchy problem for impulsive integrodifferential equations involving nonlocal initial conditions, where the linear part is a generator of a solution operator on a complex Banach space. A suitable mild solution for the Cauchy problem is introduced. The existence and uniqueness of mild solutions for the Cauchy problem, under various criterions, are proved. In the last part of the pa...

A cart with two independent inverted pendula, called a dual-inverted-pendulum system, is analyzed and compared to the single-inverted-pendulum system using classical linear methods. Using only the angles of the pendula and the position of the cart, a classical controller is designed that stabilizes the pendula in the inverted position with the cart at the center of the track. Simulations of the...

In studies of perturbation dynamics in physical systems certain specification of the governing perturbation dynamical system is generally lacking, either because the perturbation system is imperfectly known or because its specification is intrinsically uncertain, while a statistical characterization of the perturbation dynamical system is often available. In this report exact and asymptotically...

We show that the scale of the inflationary potential may be the electroweak scale or even lower, while still generating an acceptable spectrum of primordial density perturbations. Thermal effects readily lead to the initial conditions necessary for low scale inflation to occur, and even the moduli problem can be evaded if there is such an inflationary period. We discuss how low scale inflationa...

We prove that the continuous-time discrete-agent system studied in [1] admits a unique solution for almost all initial conditions. We consider the following continuous-time model: each of n agents, labeled 1, . . . , n, maintains a real number xi(t), which is a continuous function of time, and evolves according to xi(t) = xi(0) + ∫ t

For gas spheres with masses of 104M0'"'-'1020Me, the hydro dynamical evolution, beginning from a state where the objects have become opaque, is calculated by means of an electronic computer. The effects of general relativity is included, but energy transport is neglected. The mechanism of bounce, crush and collapse is discussed qualitatively. It is shown that gas spheres with mass greater than ...

Given a branching Markov process on a tree, the goal of the reconstruction (or “broadcast”) problem is to guess the initial condition at the root, given the states of the leaves. In this essay, we evaluate the performance of some algorithms, new and old, for solving the reconstruction problem.