Unlabeled document collections are becoming increasingly common and available; mining such data sets represents a major contemporary challenge. Using words as features, text documents are often represented as high dimensional and sparse vectorsa few thousand dimensions is typical. Practical approaches to clustering such document vectors use an iterative procedure (e.g. k-means, EM) that is know...

The different time-dependent distances of two arbitrarily close quantum or classical-statistical states to a third fixed state are shown to imply an experimentally relevant notion of state sensitivity to initial conditions. A quantitative classification scheme of quantum states by their sensitivity and instability in state space is given that reduces to the one performed by classicalmechanical ...

In the study of Markov chain mixing times, analysis has centered on the performance from a worst-case starting state. Here, in the context of Glauber dynamics for the one-dimensional Ising model, we show how new ideas from information percolation can be used to establish mixing times from other starting states. At high temperatures we show that the alternating initial condition is asymptoticall...

Critical initial conditions for thermal ignition are calculated numerically for planar, cylindrical and spherical geometries. In each case a comparison is made on the bifurcation diagram with the intermediate steady state(s). It is clearly seen that the actual critical initial condition which depends upon the initial temperature proÐle, is partly below the intermediate steady state(s). The vari...

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...

We present a description of the early-stage dynamics in relativistic heavy ion collisions, where the free-streaming (FS) of partons is followed by a sudden equilibration (SE) to a thermalized phase, providing initial conditions for the subsequent hydrodynamic evolution. This FS+SE approximation has been proposed by Kolb, Sollfrank, and Heinz [1]. It has been further discussed in the context of ...

Population dynamics are almost inevitably associated with two predominant sources of variation: the first, demographic variability, a consequence of chance in progenitive and deleterious events; the second, initial state uncertainty, a consequence of partial observability and reporting delays and errors. Here we outline a general method for incorporating random initial conditions in population ...

Properties of reaction zones resulting from A + B → C type reaction-diffusion processes are investigated by analytical and numerical methods. The reagents A and B are separated initially and, in addition, there is an initial macroscopic inhomogeneity in the distribution of the B species. For simple two-dimensional geometries, exact analytical results are presented for the time-evolution of the ...

The standard procedure to generate initial conditions in numerical simulations of structure formation is to use the Zel’dovich approximation (ZA). Although the ZA correctly reproduces the linear growing modes of density and velocity perturbations, non-linear growth is inaccurately represented, particularly for velocity perturbations because of the ZA failure to conserve momentum. This implies t...