Small Depth Quantum Circuits

Small depth quantum circuits have proved to be unexpectedly powerful in comparison to their classical counterparts. We survey some of the recent work on this and present some open problems.

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.

Swarming on optimized graphs for n-way broadcast

In an n-way broadcast application each one of n overlay nodes wants to push its own distinct large data file to all other n-1 destinations as well as download their respective data files. BitTorrent-like swarming protocols are ideal choices for handling such massive data volume transfers. The original BitTorrent targets one-to-many broadcasts of a single file to a very large number of receivers and thus, by necessity, employs an almost random overlay topology. n-way broadcast applications on the other hand, owing to their inherent n-squared nature, are realizable only in small to medium scale networks. In this paper, we show that we can leverage this scale constraint to construct optimized overlay topologies that take into consideration the end-to-end characteristics of the network and as a consequence deliver far superior performance compared to random and myopic (local) approaches. We present the Max-Min and MaxSum peer-selection policies used by individual nodes to select their neighbors. The first one strives to maximize the available bandwidth to the slowest destination, while the second maximizes the aggregate output rate. We design a swarming protocol suitable for n-way broadcast and operate it on top of overlay graphs formed by nodes that employ Max-Min or Max-Sum policies. Using trace-driven simulation and measurements from a PlanetLab prototype implementation, we demonstrate that the performance of swarming on top of our constructed topologies is far superior to the performance of random and myopic overlays. Moreover, we show how to modify our swarming protocol to allow it to accommodate selfish nodes.

Simultaneous Learning of Nonlinear Manifold and Dynamical Models for High-dimensional Time Series

The goal of this work is to learn a parsimonious and informative representation for high-dimensional time series. Conceptually, this comprises two distinct yet tightly coupled tasks: learning a low-dimensional manifold and modeling the dynamical process. These two tasks have a complementary relationship as the temporal constraints provide valuable neighborhood information for dimensionality reduction and conversely, the low-dimensional space allows dynamics to be learnt efficiently. Solving these two tasks simultaneously allows important information to be exchanged mutually. If nonlinear models are required to capture the rich complexity of time series, then the learning problem becomes harder as the nonlinearities in both tasks are coupled. The proposed solution approximates the nonlinear manifold and dynamics using piecewise linear models. The interactions among the linear models are captured in a graphical model. By exploiting the model structure, efficient inference and learning algorithms are obtained without oversimplifying the model of the underlying dynamical process. Evaluation of the proposed framework with competing approaches is conducted in three sets of experiments: dimensionality reduction and reconstruction using synthetic time series, video synthesis using a dynamic texture database, and human motion synthesis, classification and tracking on a benchmark data set. In all experiments, the proposed approach provides superior performance.

Entropy Loss is Maximal for Uniform Inputs

A secure sketch (defined by Dodis et al.) is an algorithm that on an input w produces an output s such that w can be reconstructed given its noisy version w' and s. Security is defined in terms of two parameters m and m˜ : if w comes from a distribution of entropy m, then a secure sketch guarantees that the distribution of w conditioned on s has entropy m˜ , where λ = m−m˜ is called the entropy loss. In this note we show that the entropy loss of any secure sketch (or, more generally, any randomized algorithm) on any distribution is no more than it is on the uniform distribution.

Hidden Type Variables and Conditional Extension for More Expressive Generic Programs

Generic object-oriented programming languages combine parametric polymorphism and nominal subtype polymorphism, thereby providing better data abstraction, greater code reuse, and fewer run-time errors. However, most generic object-oriented languages provide a straightforward combination of the two kinds of polymorphism, which prevents the expression of advanced type relationships. Furthermore, most generic object-oriented languages have a type-erasure semantics: instantiations of type parameters are not available at run time, and thus may not be used by type-dependent operations. This dissertation shows that two features, which allow the expression of many advanced type relationships, can be added to a generic object-oriented programming language without type erasure: 1. type variables that are not parameters of the class that declares them, and 2. extension that is dependent on the satisfiability of one or more constraints. We refer to the first feature as hidden type variables and the second feature as conditional extension. Hidden type variables allow: covariance and contravariance without variance annotations or special type arguments such as wildcards; a single type to extend, and inherit methods from, infinitely many instantiations of another type; a limited capacity to augment the set of superclasses after that class is defined; and the omission of redundant type arguments. Conditional extension allows the properties of a collection type to be dependent on the properties of its element type. This dissertation describes the semantics and implementation of hidden type variables and conditional extension. A sound type system is presented. In addition, a sound and terminating type checking algorithm is presented. Although designed for the Fortress programming language, hidden type variables and conditional extension can be incorporated into other generic object-oriented languages. Many of the same problems would arise, and solutions analogous to those we present would apply.

EGOIST: Overlay Routing Using Selfish Neighbor Selection

A foundational issue underlying many overlay network applications ranging from routing to P2P file sharing is that of connectivity management, i.e., folding new arrivals into an existing overlay, and re-wiring to cope with changing network conditions. Previous work has considered the problem from two perspectives: devising practical heuristics for specific applications designed to work well in real deployments, and providing abstractions for the underlying problem that are analytically tractable, especially via game-theoretic analysis. In this paper, we unify these two thrusts by using insights gleaned from novel, realistic theoretic models in the design of Egoist – a prototype overlay routing system that we implemented, deployed, and evaluated on PlanetLab. Using measurements on PlanetLab and trace-based simulations, we demonstrate that Egoist's neighbor selection primitives significantly outperform existing heuristics on a variety of performance metrics, including delay, available bandwidth, and node utilization. Moreover, we demonstrate that Egoist is competitive with an optimal, but unscalable full-mesh approach, remains highly effective under significant churn, is robust to cheating, and incurs minimal overhead. Finally, we discuss some of the potential benefits Egoist may offer to applications.

An Energy-conscious Transport Protocol for Multi-hop Wireless Networks

We present a transport protocol whose goal is to reduce power consumption without compromising delivery requirements of applications. To meet its goal of energy efficiency, our transport protocol (1) contains mechanisms to balance end-to-end vs. local retransmissions; (2) minimizes acknowledgment traffic using receiver regulated rate-based flow control combined with selected acknowledgements and in-network caching of packets; and (3) aggressively seeks to avoid any congestion-based packet loss. Within a recently developed ultra low-power multi-hop wireless network system, extensive simulations and experimental results demonstrate that our transport protocol meets its goal of preserving the energy efficiency of the underlying network.

System F with Constraint Types

System F is a type system that can be seen as both a proof system for second-order propositional logic and as a polymorphic programming language. In this work we explore several extensions of System F by types which express subtyping constraints. These systems include terms which represent proofs of subtyping relationships between types. Given a proof that one type is a subtype of another, one may use a coercion term constructor to coerce terms from the first type to the second. The ability to manipulate type constraints as first-class entities gives these systems a lot of expressive power, including the ability to encode generalized algebraic data types and intensional type analysis. The main contributions of this work are in the formulation of constraint types and a proof of strong normalization for an extension of System F with constraint types.

TCP over CDMA2000 Networks: A Cross-Layer Measurement Study

Modern cellular channels in 3G networks incorporate sophisticated power control and dynamic rate adaptation which can have a significant impact on adaptive transport layer protocols, such as TCP. Though there exists studies that have evaluated the performance of TCP over such networks, they are based solely on observations at the transport layer and hence have no visibility into the impact of lower layer dynamics, which are a key characteristic of these networks. In this work, we present a detailed characterization of TCP behavior based on cross-layer measurement of transport, as well as RF and MAC layer parameters. In particular, through a series of active TCP/UDP experiments and measurement of the relevant variables at all three layers, we characterize both, the wireless scheduler in a commercial CDMA2000 network and its impact on TCP dynamics. Somewhat surprisingly, our findings indicate that the wireless scheduler is mostly insensitive to channel quality and sector load over short timescales and is mainly affected by the transport layer data rate. Furthermore, we empirically demonstrate the impact of the wireless scheduler on various TCP parameters such as the round trip time, throughput and packet loss rate.

On the Stable Paths Problem and a Restricted Variant

Interdomain routing on the Internet is performed using route preference policies specified independently, and arbitrarily by each Autonomous System in the network. These policies are used in the border gateway protocol (BGP) by each AS when selecting next-hop choices for routes to each destination. Conflicts between policies used by different ASs can lead to routing instabilities that, potentially, cannot be resolved no matter how long BGP is run. The Stable Paths Problem (SPP) is an abstract graph theoretic model of the problem of selecting nexthop routes for a destination. A stable solution to the problem is a set of next-hop choices, one for each AS, that is compatible with the policies of each AS. In a stable solution each AS has selected its best next-hop given that the next-hop choices of all neighbors are fixed. BGP can be viewed as a distributed algorithm for solving SPP. In this report we consider the stable paths problem, as well as a family of restricted variants of the stable paths problem, which we call F stable paths problems. We show that two very simple variants of the stable paths problem are also NP-complete. In addition we show that for networks with a DAG topology, there is an efficient centralized algorithm to solve the stable paths problem, and that BGP always efficiently converges to a stable solution on such networks.

Wireless and Physical Security via Embedded Sensor Networks

Wireless Intrusion Detection Systems (WIDS) monitor 802.11 wireless frames (Layer-2) in an attempt to detect misuse. What distinguishes a WIDS from a traditional Network IDS is the ability to utilize the broadcast nature of the medium to reconstruct the physical location of the offending party, as opposed to its possibly spoofed (MAC addresses) identity in cyber space. Traditional Wireless Network Security Systems are still heavily anchored in the digital plane of "cyber space" and hence cannot be used reliably or effectively to derive the physical identity of an intruder in order to prevent further malicious wireless broadcasts, for example by escorting an intruder off the premises based on physical evidence. In this paper, we argue that Embedded Sensor Networks could be used effectively to bridge the gap between digital and physical security planes, and thus could be leveraged to provide reciprocal benefit to surveillance and security tasks on both planes. Toward that end, we present our recent experience integrating wireless networking security services into the SNBENCH (Sensor Network workBench). The SNBENCH provides an extensible framework that enables the rapid development and automated deployment of Sensor Network applications on a shared, embedded sensing and actuation infrastructure. The SNBENCH's extensible architecture allows an engineer to quickly integrate new sensing and response capabilities into the SNBENCH framework, while high-level languages and compilers allow novice SN programmers to compose SN service logic, unaware of the lower-level implementation details of tools on which their services rely. In this paper we convey the simplicity of the service composition through concrete examples that illustrate the power and potential of Wireless Security Services that span both the physical and digital plane.

An Information Theoretic Framework for Field Monitoring Using Autonomously Mobile Sensors

We consider a mobile sensor network monitoring a spatio-temporal field. Given limited cache sizes at the sensor nodes, the goal is to develop a distributed cache management algorithm to efficiently answer queries with a known probability distribution over the spatial dimension. First, we propose a novel distributed information theoretic approach in which the nodes locally update their caches based on full knowledge of the space-time distribution of the monitored phenomenon. At each time instant, local decisions are made at the mobile nodes concerning which samples to keep and whether or not a new sample should be acquired at the current location. These decisions account for minimizing an entropic utility function that captures the average amount of uncertainty in queries given the probability distribution of query locations. Second, we propose a different correlation-based technique, which only requires knowledge of the second-order statistics, thus relaxing the stringent constraint of having a priori knowledge of the query distribution, while significantly reducing the computational overhead. It is shown that the proposed approaches considerably improve the average field estimation error by maintaining efficient cache content. It is further shown that the correlation-based technique is robust to model mismatch in case of imperfect knowledge of the underlying generative correlation structure.

Detour-Based Mobility Coordination in DTNs

Commonly, research work in routing for delay tolerant networks (DTN) assumes that node encounters are predestined, in the sense that they are the result of unknown, exogenous processes that control the mobility of these nodes. In this paper, we argue that for many applications such an assumption is too restrictive: while the spatio-temporal coordinates of the start and end points of a node's journey are determined by exogenous processes, the specific path that a node may take in space-time, and hence the set of nodes it may encounter could be controlled in such a way so as to improve the performance of DTN routing. To that end, we consider a setting in which each mobile node is governed by a schedule consisting of a ist of locations that the node must visit at particular times. Typically, such schedules exhibit some level of slack, which could be leveraged for DTN message delivery purposes. We define the Mobility Coordination Problem (MCP) for DTNs as follows: Given a set of nodes, each with its own schedule, and a set of messages to be exchanged between these nodes, devise a set of node encounters that minimize message delivery delays while satisfying all node schedules. The MCP for DTNs is general enough that it allows us to model and evaluate some of the existing DTN schemes, including data mules and message ferries. In this paper, we show that MCP for DTNs is NP-hard and propose two detour-based approaches to solve the problem. The first (DMD) is a centralized heuristic that leverages knowledge of the message workload to suggest specific detours to optimize message delivery. The second (DNE) is a distributed heuristic that is oblivious to the message workload, and which selects detours so as to maximize node encounters. We evaluate the performance of these detour-based approaches using extensive simulations based on synthetic workloads as well as real schedules obtained from taxi logs in a major metropolitan area. Our evaluation shows that our centralized, workload-aware DMD approach yields the best performance, in terms of message delay and delivery success ratio, and that our distributed, workload-oblivious DNE approach yields favorable performance when compared to approaches that require the use of data mules and message ferries.

Universal Quantum Circuits

We define and construct efficient depth universal and almost size universal quantum circuits. Such circuits can be viewed as general purpose simulators for central classes of quantum circuits and can be used to capture the computational power of the circuit class being simulated. For depth we construct universal circuits whose depth is the same order as the circuits being simulated. For size, there is a log factor blow-up in the universal circuits constructed here. We prove that this construction is nearly optimal. Our results apply to a number of well-studied quantum circuit classes.