We prove that there are 2א0 many H-degrees in the random reals.

Let I be the toric ideal defined by a 2× n matrix of integers,

Experiments are presented in which a random dot pattern moved vertically upwards (velocity vector V(1)) and then abruptly changed its direction of motion by the angle alpha (velocity vector V(2)), either to the left or to the right, without changing the speed. Subjects performed simple reactions to the direction change, disregarding its sign. In another experiment choice reactions to the same s...

For privacy and security professionals following the news, the incidents reveal a wide span of provider philosophy and response regarding breaches. Facilities demonstrate varied degrees of access control management, differing stringency of enforcement policy, and inconsistent application of employee sanctions. Sanctions have ranged from gentle reminders to unspecified disciplinary action to ter...

We study the grand-canonical ensemble with a fluctuating number of degrees of freedom in the context of generalized thermostatistics. Several choices of grand-canonical entropy functional are considered. The ideal gas is taken as an example.

Research degrees have been changing radically in the last twenty years, with an extensive body of work accumulated on improving the practice of research degrees and on developing skills for independent researchers. However, most of this work focuses on full-time residential research degrees, and little attention has been paid to part-time research degrees at a distance. This paper presents a no...

The existence of symmetry in chaotic dynamical systems often leads to one or several low-dimensional invariant subspaces in the phase space. We demonstrate that complex behaviors can arise when the dynamics in the invariant subspace is Hamiltonian but the full system is dissipative. In particular, an infinite number of distinct attractors can coexist. These attractors can be quasiperiodic, stra...

The validity of the fluctuation theorem for entropy production as deduced from the observation of trajectories implicitly requires that all slow degrees of freedom are accessible. We experimentally investigate the role of hidden slow degrees of freedom in a system of two magnetically coupled driven colloidal particles. The apparent entropy production based on the observation of just one particl...

Real-space renormalization approaches for quantum lattice systems generate certain hierarchical classes of states that are subsumed by the multiscale entanglement renormalization Ansatz (MERA). It is shown that, with the exception of one spatial dimension, MERA states are actually states with finite correlations, i.e., projected entangled pair states (PEPS) with a bond dimension independent of ...

We construct an approximate renormalization transformation that combines Kolmogorov-Arnol'd-Moser and renormalization-group techniques, to analyze instabilities in Hamiltonian systems with three degrees of freedom. This scheme is implemented both for isoenergetically nondegenerate and for degenerate Hamiltonians. For the spiral mean frequency vector, we find numerically that the iterations of t...