Motivated by the problem of zero-error broadcasting, we introduce a new notion of graph capacity, termed ρ-capacity, that generalizes the Shannon capacity of a graph. We derive upper and lower bounds on the ρ-capacity of arbitrary graphs, and provide a Lovász-type upper bound for regular graphs. We study the behavior of the ρ-capacity under two graph operations: the strong product and the disjo...

This paper presents a scheme for separately characterizing computational algorithms and characterizing computing hardware, and then combining those analyses to find the suitability of a piece of hardware for a scientific algorithm. The analysis of the algorithm concentrates on a continuous computational density function, ρ, that characterizes the loss of efficiency of computation as a function ...

We present high-resolution optical spectra of 15 objects near or below the sub-stellar limit in the Upper Scorpius and ρ Ophiuchus star-forming regions. These spectra, obtained with the HIRES instrument on the Keck I telescope, are used to investigate disk accretion, rotation and activity in young very low mass objects. We report the detection of a broad, asymmetric Hα emission line in the ρ Op...

In time-frequency analysis Hilbert transformation is used to define analytic signals based on which meaningful instantaneous amplitude and instantaneous frequency are defined. In relation to this background we study characteristic properties of the real-valued measurable functions ρ(t) and θ(t), t ∈ R, such that H(ρ(·) cos θ(·))(t) = ρ(t) sin θ(t), ρ(t) ≥ 0, where H is the Hilbert transformatio...

The subject of this thesis is learning and testing properties of mixed quantum states. A mixed state is described by a density matrix ρ ∈ Cd×d. In the standard model, one is given access to many identical copies of the mixed state, and the goal is to perform measurements on the copies to infer some information about ρ. In our problem, each copy of ρ plays a role analogous to a sample drawn from...

A vote-buying mechanism is such that each agent chooses a quantity of votes x to cast for an alternative at a cost c(x), and the outcome is determined by the total number of votes cast for each alternative. In the context of binary decisions, we prove that the welfare optima that can be implemented by vote-buying mechanisms in large societies are parameterized by a positive parameter ρ, which m...

In a previous paper we studied a two-stage group sequential procedure (GSP) for testing primary and secondary endpoints where the primary endpoint serves as a gatekeeper for the secondary endpoint. We assumed a simple setup of a bivariate normal distribution for the two endpoints with the correlation coefficient ρ between them being either an unknown nuisance parameter or a known constant. Unde...