Non-Uniform Reductions

We study properties of non-uniform reductions and related completeness notions. We strengthen several results of Hitchcock and Pavan and give a trade-off between the amount of advice needed for a reduction and its honesty on NEXP. We construct an oracle relative to which this trade-off is optimal. We show, in a more systematic study of non-uniform reductions, that among other things non-uniformity can be removed at the cost of more queries. In line with Post's program for complexity theory we connect such 'uniformization' properties to the separation of complexity classes.

HEATING IN VASCULAR TISSUE AND FLOW-THROUGH TISSUE PHANTOMS INDUCED BY FOCUSED ULTRASOUND

High intensity focused ultrasound (HIFU) can be used to control bleeding, both from individual blood vessels as well as from gross damage to the capillary bed. This process, called acoustic hemostasis, is being studied in the hope that such a method would ultimately provide a lifesaving treatment during the so-called "golden hour", a brief grace period after a severe trauma in which prompt therapy can save the life of an injured person. Thermal effects play a major role in occlusion of small vessels and also appear to contribute to the sealing of punctures in major blood vessels. However, aggressive ultrasound-induced tissue heating can also impact healthy tissue and can lead to deleterious mechanical bioeffects. Moreover, the presence of vascularity can limit one’s ability to elevate the temperature of blood vessel walls owing to convective heat transport. In an effort to better understand the heating process in tissues with vascular structure we have developed a numerical simulation that couples models for ultrasound propagation, acoustic streaming, ultrasound heating and blood cooling in Newtonian viscous media. The 3-D simulation allows for the study of complicated biological structures and insonation geometries. We have also undertaken a series of in vitro experiments, in non-uniform flow-through tissue phantoms, designed to provide a ground truth verification of the model predictions. The calculated and measured results were compared over a range of values for insonation pressure, insonation time, and flow rate; we show good agreement between predictions and measurements. We then conducted a series of simulations that address two limiting problems of interest: hemostasis in small and large vessels. We employed realistic human tissue properties and considered more complex geometries. Results show that the heating pattern in and around a blood vessel is different for different vessel sizes, flow rates and for varying beam orientations relative to the flow axis. Complete occlusion and wall- puncture sealing are both possible depending on the exposure conditions. These results concur with prior clinical observations and may prove useful for planning of a more effective procedure in HIFU treatments.

Geometric Generalizations of the Power of Two Choices

A well-known paradigm for load balancing in distributed systems is the``power of two choices,''whereby an item is stored at the less loaded of two (or more) random alternative servers. We investigate the power of two choices in natural settings for distributed computing where items and servers reside in a geometric space and each item is associated with the server that is its nearest neighbor. This is in fact the backdrop for distributed hash tables such as Chord, where the geometric space is determined by clockwise distance on a one-dimensional ring. Theoretically, we consider the following load balancing problem. Suppose that servers are initially hashed uniformly at random to points in the space. Sequentially, each item then considers d candidate insertion points also chosen uniformly at random from the space,and selects the insertion point whose associated server has the least load. For the one-dimensional ring, and for Euclidean distance on the two-dimensional torus, we demonstrate that when n data items are hashed to n servers,the maximum load at any server is log log n / log d + O(1) with high probability. While our results match the well-known bounds in the standard setting in which each server is selected equiprobably, our applications do not have this feature, since the sizes of the nearest-neighbor regions around servers are non-uniform. Therefore, the novelty in our methods lies in developing appropriate tail bounds on the distribution of nearest-neighbor region sizes and in adapting previous arguments to this more general setting. In addition, we provide simulation results demonstrating the load balance that results as the system size scales into the millions.

Amorphous Placement and Informed Diffusion for Timely Monitoring by Autonomous, Resource-Constrained, Mobile Sensors

Personal communication devices are increasingly equipped with sensors for passive monitoring of encounters and surroundings. We envision the emergence of services that enable a community of mobile users carrying such resource-limited devices to query such information at remote locations in the field in which they collectively roam. One approach to implement such a service is directed placement and retrieval (DPR), whereby readings/queries about a specific location are routed to a node responsible for that location. In a mobile, potentially sparse setting, where end-to-end paths are unavailable, DPR is not an attractive solution as it would require the use of delay-tolerant (flooding-based store-carry-forward) routing of both readings and queries, which is inappropriate for applications with data freshness constraints, and which is incompatible with stringent device power/memory constraints. Alternatively, we propose the use of amorphous placement and retrieval (APR), in which routing and field monitoring are integrated through the use of a cache management scheme coupled with an informed exchange of cached samples to diffuse sensory data throughout the network, in such a way that a query answer is likely to be found close to the query origin. We argue that knowledge of the distribution of query targets could be used effectively by an informed cache management policy to maximize the utility of collective storage of all devices. Using a simple analytical model, we show that the use of informed cache management is particularly important when the mobility model results in a non-uniform distribution of users over the field. We present results from extensive simulations which show that in sparsely-connected networks, APR is more cost-effective than DPR, that it provides extra resilience to node failure and packet losses, and that its use of informed cache management yields superior performance.