Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

Part I. Foundations: 1. Random variables 2. Probability measures 3. Stochastic processes 4. The stochastic integral Part II. Existence and Uniqueness: 5. Linear equations with additive noise 6. Linear equations with multiplicative noise 7. Existence and uniqueness for nonlinear equations 8. Martingale solutions Part III. Properties of Solutions: 9. Markov properties and Kolmogorov equations 10. Absolute continuity and Girsanov's theorem 11. Large time behaviour of solutions 12. Small noise asymptotic.

Stochastic Equations in Infinite Dimensions

We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of its infinitesimal generator.

Stochastic Differential Equations

Stochastic equations in infinite dimensions

Stochastic differential equations and diffusion processes

Mobility traces of people and vehicles have been collected and published to assist the design and evaluation of mobilee networks, such as large-scale urban sensing networks. Although the published traces are often made anonymous in that the true identities of nodes are replaced by random identifiers, the privacy concern remains. This is because in real life, nodes are open to observations in public spaces, or they may voluntarily or inadvertently disclose partial knowledge of their whereabouts. Thus, snapshots of nodes' location information can be learned by interested third parties, e.g., directly through chance/engineered meetings between the nodes and their observers, or indirectly through casual conversations or other information sources about people. In this paper, we investigate how an adversary, when equipped with a small amount of the snapshot information termed as side information, can infer an extended view of the whereabouts of a victim node appearing in an anonymous trace. Our results quantify the loss of victim nodes' privacy as a function of the nodal mobility (captured in both real and synthetic traces), the inference strategies of adversaries, and any noise that may appear in the trace or the side information. Generally, our results indicate that the privacy concern is significant in that a relatively small amount of side information is sufficient for the adversary to infer the true identity (either uniquely or with high probability) of a victim in a set of anonymous traces.

Privacy vulnerability of published anonymous mobility traces

Mobility traces of people and vehicles have been collected and published to assist the design and evaluation of mobile networks, such as large-scale urban sensing networks. Although the published traces are often made anonymous in that the true identities of nodes are replaced by random identifiers, the privacy concern remains. This is because in real life, nodes are open to observations in public spaces, or they may voluntarily or inadvertently disclose partial knowledge of their whereabouts. Thus, snapshots of nodes' location information can be learned by interested third parties, e.g., directly through chance/engineered meetings between the nodes and their observers, or indirectly through casual conversations or other information sources about people. In this paper, we investigate how an adversary, when equipped with a small amount of the snapshot information termed as side information, can infer an extended view of the whereabouts of a victim node appearing in an anonymous trace. Our results quantify the loss of victim nodes' privacy as a function of the nodal mobility, the inference strategies of adversaries, and any noise that may appear in the trace or the side information. Generally, our results indicate that the privacy concern is significant in that a relatively small amount of side information is sufficient for the adversary to infer the true identity (either uniquely or with high probability) of a victim in a set of anonymous traces. For instance, an adversary is able to identify the trace of 30%-50% of the victims when she has collected 10 pieces of side information about a victim.

A mobile sensor is used to cover a number of points of interest (PoIs), where dynamic events appear and disappear according to the given random processes. The sensor, which is of sensing range r, visits the PoIs in a cyclic schedule and gains information about any event that falls within its range. We consider the temporal dimension of the sensing as given by a utility function, which specifies how much information is gained about an event as a function of the cumulative sensing or observation time. The quality of monitoring (QoM), i.e., the fraction of information captured about all events, depends on the speed of the sensor and has been analyzed in an earlier paper for different utility functions. The prior work, however, does not consider the energy of motion, which is an important constraint for mobile sensor coverage. In this paper, we analyze the expected Information captured Per unit of Energy consumption (IPE) as a function of the event type (in terms of the utility function), the event dynamics, and the speed of the mobile sensor. Our analysis uses a realistic energy model of motion, and it allows the sensor speed to be optimized for information capture. The case of multiple sensors will also be discussed. Extensive simulation results verify and illustrate the analytical results.

On Optimal Information Capture by Energy-Constrained Mobile Sensors

We study a recently demonstrated AC electrokinetic technique for manipulation and concentration of colloidal particles on an electrode surface. The technique uses indium tin oxide (ITO)-based parallel-plate electrodes on which highly localized infrared (1064 nm) laser illumination is shone. We show that the highly localized laser illumination leads to a highly nonuniform heating of the electrode substrate, which in turn drives an electrothermal microvortex resulting in a rapid transport of particles toward the illuminated site. Hundreds of polystyrene particles, with diameters ranging from 2.0 to 0.1 μm, suspended in a low conductivity solution (2.0 mS/m) could be aggregated at selected locations on the electrode by activating the laser illumination at suitable AC frequencies. Subsequent deactivation of the laser illumination causes the particles to scatter, and we explore this dynamical behavior for 1.0 μm particles using Delaunay tessellations and high-speed videography. We establish that drag from the ...

/pdf/optically-modulated-electrokinetic-manipulation-and-2aid1ldmw8.pdf

Optically modulated electrokinetic manipulation and concentration of colloidal particles near an electrode surface.

This paper investigates the pinning and de-pinning phenomena of some evolutionary partial differential equations which arise in the modelling of the propagation of phase boundaries in materials under the combined effects of an external driving force F and an underlying heterogeneous environment. The phenomenology is the existence of pinning states—stationary solutions—for small values of F, and the appearance of genuine motion whenF is above some threshold value. In the case of a periodic medium, we characterise quantitatively, near the transition regime, the scaling behaviour of the interface velocity as a function of F . The results are proved for a class of semilinear and reaction-diffusion equations.

/pdf/pinning-and-de-pinning-phenomena-in-front-propagation-in-wh94xlqfqr.pdf

Nung Kwan Yip

Papers

Privacy vulnerability of published anonymous mobility traces

Privacy vulnerability of published anonymous mobility traces

On Optimal Information Capture by Energy-Constrained Mobile Sensors

Optically modulated electrokinetic manipulation and concentration of colloidal particles near an electrode surface.

Pinning and de-pinning phenomena in front propagation in heterogeneous media