Lightweight Formal Verification in Classroom Instruction of Reasoning about Functional Code

In college courses dealing with material that requires mathematical rigor, the adoption of a machine-readable representation for formal arguments can be advantageous. Students can focus on a specific collection of constructs that are represented consistently. Examples and counterexamples can be evaluated. Assignments can be assembled and checked with the help of an automated formal reasoning system. However, usability and accessibility do not have a high priority and are not addressed sufficiently well in the design of many existing machine-readable representations and corresponding formal reasoning systems. In earlier work [Lap09], we attempt to address this broad problem by proposing several specific design criteria organized around the notion of a natural context: the sphere of awareness a working human user maintains of the relevant constructs, arguments, experiences, and background materials necessary to accomplish the task at hand. We report on our attempt to evaluate our proposed design criteria by deploying within the classroom a lightweight formal verification system designed according to these criteria. The lightweight formal verification system was used within the instruction of a common application of formal reasoning: proving by induction formal propositions about functional code. We present all of the formal reasoning examples and assignments considered during this deployment, most of which are drawn directly from an introductory text on functional programming. We demonstrate how the design of the system improves the effectiveness and understandability of the examples, and how it aids in the instruction of basic formal reasoning techniques. We make brief remarks about the practical and administrative implications of the system’s design from the perspectives of the student, the instructor, and the grader.

Improved Tracking of Multiple Humans with Trajectory Prediction and Occlusion Modeling

A combined 2D, 3D approach is presented that allows for robust tracking of moving bodies in a given environment as observed via a single, uncalibrated video camera. Tracking is robust even in the presence of occlusions. Low-level features are often insufficient for detection, segmentation, and tracking of non-rigid moving objects. Therefore, an improved mechanism is proposed that combines low-level (image processing) and mid-level (recursive trajectory estimation) information obtained during the tracking process. The resulting system can segment and maintain the tracking of moving objects before, during, and after occlusion. At each frame, the system also extracts a stabilized coordinate frame of the moving objects. This stabilized frame is used to resize and resample the moving blob so that it can be used as input to motion recognition modules. The approach enables robust tracking without constraining the system to know the shape of the objects being tracked beforehand; although, some assumptions are made about the characteristics of the shape of the objects, and how they evolve with time. Experiments in tracking moving people are described.

Design and Implementation of Statistical Rate Monotonic Scheduling in KURT Linux

Statistical Rate Monotonic Scheduling (SRMS) is a generalization of the classical RMS results of Liu and Layland [LL73] for periodic tasks with highly variable execution times and statistical QoS requirements. The main tenet of SRMS is that the variability in task resource requirements could be smoothed through aggregation to yield guaranteed QoS. This aggregation is done over time for a given task and across multiple tasks for a given period of time. Similar to RMS, SRMS has two components: a feasibility test and a scheduling algorithm. SRMS feasibility test ensures that it is possible for a given periodic task set to share a given resource without violating any of the statistical QoS constraints imposed on each task in the set. The SRMS scheduling algorithm consists of two parts: a job admission controller and a scheduler. The SRMS scheduler is a simple, preemptive, fixed-priority scheduler. The SRMS job admission controller manages the QoS delivered to the various tasks through admit/reject and priority assignment decisions. In particular, it ensures the important property of task isolation, whereby tasks do not infringe on each other. In this paper we present the design and implementation of SRMS within the KURT Linux Operating System [HSPN98, SPH 98, Sri98]. KURT Linux supports conventional tasks as well as real-time tasks. It provides a mechanism for transitioning from normal Linux scheduling to a mixed scheduling of conventional and real-time tasks, and to a focused mode where only real-time tasks are scheduled. We overview the technical issues that we had to overcome in order to integrate SRMS into KURT Linux and present the API we have developed for scheduling periodic real-time tasks using SRMS.

A Performance Evaluation of Hyper Text Transfer Protocols

Version 1.1 of the Hyper Text Transfer Protocol (HTTP) was principally developed as a means for reducing both document transfer latency and network traffic. The rationale for the performance enhancements in HTTP/1.1 is based on the assumption that the network is the bottleneck in Web transactions. In practice, however, the Web server can be the primary source of document transfer latency. In this paper, we characterize and compare the performance of HTTP/1.0 and HTTP/1.1 in terms of throughput at the server and transfer latency at the client. Our approach is based on considering a broader set of bottlenecks in an HTTP transfer; we examine how bottlenecks in the network, CPU, and in the disk system affect the relative performance of HTTP/1.0 versus HTTP/1.1. We show that the network demands under HTTP/1.1 are somewhat lower than HTTP/1.0, and we quantify those differences in terms of packets transferred, server congestion window size and data bytes per packet. We show that when the CPU is the bottleneck, there is relatively little difference in performance between HTTP/1.0 and HTTP/1.1. Surprisingly, we show that when the disk system is the bottleneck, performance using HTTP/1.1 can be much worse than with HTTP/1.0. Based on these observations, we suggest a connection management policy for HTTP/1.1 that can improve throughput, decrease latency, and keep network traffic low when the disk system is the bottleneck.

3D Trajectory Recovery for Tracking Multiple Objects and Trajectory Guided Recognition of Actions

A mechanism is proposed that integrates low-level (image processing), mid-level (recursive 3D trajectory estimation), and high-level (action recognition) processes. It is assumed that the system observes multiple moving objects via a single, uncalibrated video camera. A novel extended Kalman filter formulation is used in estimating the relative 3D motion trajectories up to a scale factor. The recursive estimation process provides a prediction and error measure that is exploited in higher-level stages of action recognition. Conversely, higher-level mechanisms provide feedback that allows the system to reliably segment and maintain the tracking of moving objects before, during, and after occlusion. The 3D trajectory, occlusion, and segmentation information are utilized in extracting stabilized views of the moving object. Trajectory-guided recognition (TGR) is proposed as a new and efficient method for adaptive classification of action. The TGR approach is demonstrated using "motion history images" that are then recognized via a mixture of Gaussian classifier. The system was tested in recognizing various dynamic human outdoor activities; e.g., running, walking, roller blading, and cycling. Experiments with synthetic data sets are used to evaluate stability of the trajectory estimator with respect to noise.

Recognition of Human Action Using Moment-Based Feature

The performance of different classification approaches is evaluated using a view-based approach for motion representation. The view-based approach uses computer vision and image processing techniques to register and process the video sequence. Two motion representations called Motion Energy Images and Motion History Image are then constructed. These representations collapse the temporal component in a way that no explicit temporal analysis or sequence matching is needed. Statistical descriptions are then computed using moment-based features and dimensionality reduction techniques. For these tests, we used 7 Hu moments, which are invariant to scale and translation. Principal Components Analysis is used to reduce the dimensionality of this representation. The system is trained using different subjects performing a set of examples of every action to be recognized. Given these samples, K-nearest neighbor, Gaussian, and Gaussian mixture classifiers are used to recognize new actions. Experiments are conducted using instances of eight human actions (i.e., eight classes) performed by seven different subjects. Comparisons in the performance among these classifiers under different conditions are analyzed and reported. Our main goals are to test this dimensionality-reduced representation of actions, and more importantly to use this representation to compare the advantages of different classification approaches in this recognition task.

Load Balancing a Cluster of Web Servers using Distributed Packet Rewriting

In this paper, we propose and evaluate an implementation of a prototype scalable web server. The prototype consists of a load-balanced cluster of hosts that collectively accept and service TCP connections. The host IP addresses are advertised using the Round Robin DNS technique, allowing any host to receive requests from any client. Once a client attempts to establish a TCP connection with one of the hosts, a decision is made as to whether or not the connection should be redirected to a different host---namely, the host with the lowest number of established connections. We use the low-overhead Distributed Packet Rewriting (DPR) technique to redirect TCP connections. In our prototype, each host keeps information about connections in hash tables and linked lists. Every time a packet arrives, it is examined to see if it has to be redirected or not. Load information is maintained using periodic broadcasts amongst the cluster hosts.

Trajectory Guided Tracking and Recognition of Actions

A combined 2D, 3D approach is presented that allows for robust tracking of moving people and recognition of actions. It is assumed that the system observes multiple moving objects via a single, uncalibrated video camera. Low-level features are often insufficient for detection, segmentation, and tracking of non-rigid moving objects. Therefore, an improved mechanism is proposed that integrates low-level (image processing), mid-level (recursive 3D trajectory estimation), and high-level (action recognition) processes. A novel extended Kalman filter formulation is used in estimating the relative 3D motion trajectories up to a scale factor. The recursive estimation process provides a prediction and error measure that is exploited in higher-level stages of action recognition. Conversely, higher-level mechanisms provide feedback that allows the system to reliably segment and maintain the tracking of moving objects before, during, and after occlusion. The 3D trajectory, occlusion, and segmentation information are utilized in extracting stabilized views of the moving object that are then used as input to action recognition modules. Trajectory-guided recognition (TGR) is proposed as a new and efficient method for adaptive classification of action. The TGR approach is demonstrated using "motion history images" that are then recognized via a mixture-of-Gaussians classifier. The system was tested in recognizing various dynamic human outdoor activities: running, walking, roller blading, and cycling. Experiments with real and synthetic data sets are used to evaluate stability of the trajectory estimator with respect to noise.

Fast, Reliable Head Tracking under Varying Illumination: An Approach Based on Registration of Texture-Mapped 3D Model

An improved technique for 3D head tracking under varying illumination conditions is proposed. The head is modeled as a texture mapped cylinder. Tracking is formulated as an image registration problem in the cylinder's texture map image. The resulting dynamic texture map provides a stabilized view of the face that can be used as input to many existing 2D techniques for face recognition, facial expressions analysis, lip reading, and eye tracking. To solve the registration problem in the presence of lighting variation and head motion, the residual error of registration is modeled as a linear combination of texture warping templates and orthogonal illumination templates. Fast and stable on-line tracking is achieved via regularized, weighted least squares minimization of the registration error. The regularization term tends to limit potential ambiguities that arise in the warping and illumination templates. It enables stable tracking over extended sequences. Tracking does not require a precise initial fit of the model; the system is initialized automatically using a simple 2D face detector. The only assumption is that the target is facing the camera in the first frame of the sequence. The formulation is tailored to take advantage of texture mapping hardware available in many workstations, PC's, and game consoles. The non-optimized implementation runs at about 15 frames per second on a SGI O2 graphic workstation. Extensive experiments evaluating the effectiveness of the formulation are reported. The sensitivity of the technique to illumination, regularization parameters, errors in the initial positioning and internal camera parameters are analyzed. Examples and applications of tracking are reported.

Combinations of Deformable Shape Prototypes

We propose to investigate a model-based technique for encoding non-rigid object classes in terms of object prototypes. Objects from the same class can be parameterized by identifying shape and appearance invariants of the class to devise low-level representations. The approach presented here creates a flexible model for an object class from a set of prototypes. This model is then used to estimate the parameters of low-level representation of novel objects as combinations of the prototype parameters. Variations in the object shape are modeled as non-rigid deformations. Appearance variations are modeled as intensity variations. In the training phase, the system is presented with several example prototype images. These prototype images are registered to a reference image by a finite element-based technique called Active Blobs. The deformations of the finite element model to register a prototype image with the reference image provide the shape description or shape vector for the prototype. The shape vector for each prototype, is then used to warp the prototype image onto the reference image and obtain the corresponding texture vector. The prototype texture vectors, being warped onto the same reference image have a pixel by pixel correspondence with each other and hence are "shape normalized". Given sufficient number of prototypes that exhibit appropriate in-class variations, the shape and the texture vectors define a linear prototype subspace that spans the object class. Each prototype is a vector in this subspace. The matching phase involves the estimation of a set of combination parameters for synthesis of the novel object by combining the prototype shape and texture vectors. The strengths of this technique lie in the combined estimation of both shape and appearance parameters. This is in contrast with the previous approaches where shape and appearance parameters were estimated separately.

Optimal Scheduling of Secondary Content for Aggregation in Video-on-Demand Systems

Dynamic service aggregation techniques can exploit skewed access popularity patterns to reduce the costs of building interactive VoD systems. These schemes seek to cluster and merge users into single streams by bridging the temporal skew between them, thus improving server and network utilization. Rate adaptation and secondary content insertion are two such schemes. In this paper, we present and evaluate an optimal scheduling algorithm for inserting secondary content in this scenario. The algorithm runs in polynomial time, and is optimal with respect to the total bandwidth usage over the merging interval. We present constraints on content insertion which make the overall QoS of the delivered stream acceptable, and show how our algorithm can satisfy these constraints. We report simulation results which quantify the excellent gains due to content insertion. We discuss dynamic scenarios with user arrivals and interactions, and show that content insertion reduces the channel bandwidth requirement to almost half. We also discuss differentiated service techniques, such as N-VoD and premium no-advertisement service, and show how our algorithm can support these as well.

Estimation and Prediction of Evolving Color Distributions for Skin Segmentation Under Varying Illumination

A novel approach for real-time skin segmentation in video sequences is described. The approach enables reliable skin segmentation despite wide variation in illumination during tracking. An explicit second order Markov model is used to predict evolution of the skin color (HSV) histogram over time. Histograms are dynamically updated based on feedback from the current segmentation and based on predictions of the Markov model. The evolution of the skin color distribution at each frame is parameterized by translation, scaling and rotation in color space. Consequent changes in geometric parameterization of the distribution are propagated by warping and re-sampling the histogram. The parameters of the discrete-time dynamic Markov model are estimated using Maximum Likelihood Estimation, and also evolve over time. Quantitative evaluation of the method was conducted on labeled ground-truth video sequences taken from popular movies.

Recursive Estimation of Motion and Planar Structure

A specialized formulation of Azarbayejani and Pentland's framework for recursive recovery of motion, structure and focal length from feature correspondences tracked through an image sequence is presented. The specialized formulation addresses the case where all tracked points lie on a plane. This planarity constraint reduces the dimension of the original state vector, and consequently the number of feature points needed to estimate the state. Experiments with synthetic data and real imagery illustrate the system performance. The experiments confirm that the specialized formulation provides improved accuracy, stability to observation noise, and rate of convergence in estimation for the case where the tracked points lie on a plane.

On the Complexity of Quantum ACC

For any q > 1, let MOD_q be a quantum gate that determines if the number of 1's in the input is divisible by q. We show that for any q,t > 1, MOD_q is equivalent to MOD_t (up to constant depth). Based on the case q=2, Moore has shown that quantum analogs of AC^(0), ACC[q], and ACC, denoted QAC^(0)_wf, QACC[2], QACC respectively, define the same class of operators, leaving q > 2 as an open question. Our result resolves this question, implying that QAC^(0)_wf = QACC[q] = QACC for all q. We also prove the first upper bounds for QACC in terms of related language classes. We define classes of languages EQACC, NQACC (both for arbitrary complex amplitudes) and BQACC (for rational number amplitudes) and show that they are all contained in TC^(0). To do this, we show that a TC^(0) circuit can keep track of the amplitudes of the state resulting from the application of a QACC operator using a constant width polynomial size tensor sum. In order to accomplish this, we also show that TC^(0) can perform iterated addition and multiplication in certain field extensions.

On the Origin of Power Laws in Internet Topologies

Recent empirical studies have shown that Internet topologies exhibit power laws of the form for the following relationships: (P1) outdegree of node (domain or router) versus rank; (P2) number of nodes versus outdegree; (P3) number of node pairs y = x^α within a neighborhood versus neighborhood size (in hops); and (P4) eigenvalues of the adjacency matrix versus rank. However, causes for the appearance of such power laws have not been convincingly given. In this paper, we examine four factors in the formation of Internet topologies. These factors are (F1) preferential connectivity of a new node to existing nodes; (F2) incremental growth of the network; (F3) distribution of nodes in space; and (F4) locality of edge connections. In synthetically generated network topologies, we study the relevance of each factor in causing the aforementioned power laws as well as other properties, namely diameter, average path length and clustering coefficient. Different kinds of network topologies are generated: (T1) topologies generated using our parametrized generator, we call BRITE; (T2) random topologies generated using the well-known Waxman model; (T3) Transit-Stub topologies generated using GT-ITM tool; and (T4) regular grid topologies. We observe that some generated topologies may not obey power laws P1 and P2. Thus, the existence of these power laws can be used to validate the accuracy of a given tool in generating representative Internet topologies. Power laws P3 and P4 were observed in nearly all considered topologies, but different topologies showed different values of the power exponent α. Thus, while the presence of power laws P3 and P4 do not give strong evidence for the representativeness of a generated topology, the value of α in P3 and P4 can be used as a litmus test for the representativeness of a generated topology. We also find that factors F1 and F2 are the key contributors in our study which provide the resemblance of our generated topologies to that of the Internet.