We consider a flow-level model of a network operating under an α-fair bandwidth sharing policy (with α > 0) proposed by Roberts and Massoulié (2000). This is a probabilistic model that captures the long-term aspects of bandwidth sharing between users or flows in a communication network. We study the transient properties as well as the steady-state distribution of the model. In particular, for α...

We consider sequential and concurrent probabilistic processes and propose a general notion of fairness with respect to probabilistic choice, which allows to express various notions of fairness such as process fairness and event fairness. We show the soundness of proving the validity of qualitative properties of probabilistic processes under fairness constraints in the sense that whenever all fa...

Frequently expert systems are being developed to operate in dynamic environments where they must reason about time-varying information and generate hypotheses, conclusions, and process inputs that can drastically influence the environment within which they operate. For instance, expert systems used for fault diagnosis and fault accomodation in nuclear power plants reason over sensor data and op...

The Dirac equation for a massive spin-12 field in a central potential V in three dimensions is studied without fixing a priori the functional form of V . The second-order equations for the radial parts of the spinor wave function are shown to involve a squared Dirac operator for the free case, whose essential self-adjointness is proved by using the Weyl limit point-limit circle criterion, and a...

We investigate the Baire category of I-convergent subsequences and rearrangements of a divergent sequence s = (sn) of reals, if I is an ideal on N having the Baire property. We also discuss the measure of the set of I-convergent subsequences for some classes of ideals on N. Our results generalize theorems due to H. Miller and C. Orhan (2001).

We study a class of Piecewise Deterministic Markov Processes with state space R d × E where E is a finite set. The continuous component evolves according to a smooth vector field that is switched at the jump times of the discrete coordinate. The jump rates may depend on the whole position of the process. Working under the general assumption that the process stays in a compact set, we detail a p...

Perceptual experience seems to involve distinct intentional and qualitative features. Inasmuch as one can visually perceive that there is a Coke can in front of one, perceptual experience must be intentional. But such experiences seem to differ from paradigmatic intentional states in having introspectible qualitative character. Peacocke (1983) argues that a perceptual experience s qualitative c...