tions. Bootstrap has found many applications in engineering field, including artificial neural networks, biomedical engineering, environmental engineering, image processing, and radar and sonar signal processing. Basic concepts of the bootstrap are summarized in each section as a step-by-step algorithm for ease of implementation. Most of the applications are taken from the signal processing literature. The principles of the bootstrap are introduced in Chapter 2. Both the nonparametric and parametric bootstrap procedures are explained. Babu and Singh (1984) have demonstrated that in general, these two procedures behave similarly for pivotal (Studentized) statistics. The fact that the bootstrap is not the solution for all of the problems has been known to statistics community for a long time; however, this fact is rarely touched on in the manuscripts meant for practitioners. It was first observed by Babu (1984) that the bootstrap does not work in the infinite variance case. Bootstrap Techniques for Signal Processing explains the limitations of bootstrap method with an example. I especially liked the presentation style. The basic results are stated without proofs; however, the application of each result is presented as a simple step-by-step process, easy for nonstatisticians to follow. The bootstrap procedures, such as moving block bootstrap for dependent data, along with applications to autoregressive models and for estimation of power spectral density, are also presented in Chapter 2. Signal detection in the presence of noise is generally formulated as a testing of hypothesis problem. Chapter 3 introduces principles of bootstrap hypothesis testing. The topics are introduced with interesting real life examples. Flow charts, typical in engineering literature, are used to aid explanations of the bootstrap hypothesis testing procedures. The bootstrap leads to second-order correction due to pivoting; this improvement in the results due to pivoting is also explained. In the second part of Chapter 3, signal processing is treated as a regression problem. The performance of the bootstrap for matched filters as well as constant false-alarm rate matched filters is also illustrated. Chapters 2 and 3 focus on estimation problems. Chapter 4 introduces bootstrap methods used in model selection. Due to the inherent structure of the subject matter, this chapter may be difficult for nonstatisticians to follow. Chapter 5 is the most impressive chapter in the book, especially from the standpoint of statisticians. It provides real data bootstrap applications to illustrate the theory covered in the earlier chapters. These include applications to optimal sensor placement for knock detection and land-mine detection. The authors also provide a MATLAB toolbox comprising frequently used routines. Overall, this is a very useful handbook for engineers, especially those working in signal processing.

Probability and Random Processes

The uniform spanning tree (UST) and the loop-erased random walk (LERW) are strongly related probabilistic processes. We consider the limits of these models on a fine grid in the plane, as the mesh goes to zero. Although the existence of scaling limits is still unproven, subsequential scaling limits can be defined in various ways, and do exist. We establish some basic a.s. properties of these subsequential scaling limits in the plane. It is proved that any LERW subsequential scaling limit is a simple path, and that the trunk of any UST subsequential scaling limit is a topological tree, which is dense in the plane.

Scaling Limits of Loop-Erased Random Walks and Uniform Spanning Trees

This survey covers hard real-time scheduling algorithms and schedulability analysis techniques for homogeneous multiprocessor systems. It reviews the key results in this field from its origins in the late 1960s to the latest research published in late 2009. The survey outlines fundamental results about multiprocessor real-time scheduling that hold independent of the scheduling algorithms employed. It provides a taxonomy of the different scheduling methods, and considers the various performance metrics that can be used for comparison purposes. A detailed review is provided covering partitioned, global, and hybrid scheduling algorithms, approaches to resource sharing, and the latest results from empirical investigations. The survey identifies open issues, key research challenges, and likely productive research directions.

/pdf/a-survey-of-hard-real-time-scheduling-for-multiprocessor-313o35g6ho.pdf

A survey of hard real-time scheduling for multiprocessor systems

In this Note we study critical site percolation on triangular lattice. We introduce harmonic conformal invariants as scaling limits of certain probabilities and calculate their values. As a corollary we obtain conformal invariance of the crossing probabilities (conjecture attributed to Aizenman by Langlands, Pouliot, and Saint-Aubin in [7]) and find their values (predicted by Cardy in [4], we discuss simpler representation found by Carleson). Then we discuss existence, uniqueness, and conformal invariance of the continuum scaling limit. The detailed proofs appear in [10].

http://www.unige.ch/%7Esmirnov/papers/percras-j.pdf

Critical percolation in the plane: conformal invariance, Cardy's formula, scaling limits

The high computational complexity required for performing an exact schedulability analysis of fixed priority systems has led the research community to investigate new feasibility tests which are less complex than exact tests, but still provide a reasonable performance in terms of acceptance ratio. The performance of a test is typically evaluated by generating a huge number of synthetic task sets and then computing the fraction of those that pass the test with respect to the total number of feasible ones. The resulting ratio, however, depends on the metrics used for evaluating the performance and on the method for generating random task parameters. In particular, an important factor that affects the overall result of the simulation is the probability density function of the random variables used to generate the task set parameters. In this paper we discuss and compare three different metrics that can be used for evaluating the performance of schedulability tests. Then, we investigate how the random generation procedure can bias the simulation results of some specific scheduling algorithm. Finally, we present an efficient method for generating task sets with uniform distribution in a given space, and show how some intuitive solutions typically used for task set generation can bias the simulation results.

/pdf/measuring-the-performance-of-schedulability-tests-yr1og35xbk.pdf

Measuring the Performance of Schedulability Tests

Optimal scheduling of real-time tasks on multiprocessor systems is known to be computationally intractable for large task sets. Any practical scheduling algorithm for assigning real-time tasks to a multiprocessor system presents a trade-off between its computational complexity and its performance. In this study, new schedulability conditions are presented for homogeneous multiprocessor systems where individual processors execute the rate-monotonic scheduling algorithm. The conditions are used to develop new strategies for assigning real-time tasks to processors. The performance of the new strategies is shown to be significantly better than suggested by the existing literature. Under the realistic assumption that the load of each real-time task is small compared to the processing speed of each processor, it is shown that the processors can be almost fully utilized.

New Strategies for Assigning Re;al-Time Tasks to Multimocessor Svstems

New strategies for assigning real-time tasks to multiprocessor systems

Random systems of curves exhibiting fluctuating features on arbitrarily small scales (δ) are often encountered in critical models. For such systems it is shown that scale-invariant bounds on the probabilities of crossing events imply that typically all the realized curves admit Holder continuous parametrizations with a common exponent and a common random prefactor, which in the scaling limit (δ → 0) remains stochastically bounded. The regularity is used for the construction of scaling limits, formulated in terms of probability measures on the space of closed sets of curves. Under the hypotheses presented here the limiting measures are supported on sets of curves which are Holder continuous but not rectifiable, and have Hausdorff dimensions strictly greater than one. The hypotheses are known to be satisfied in certain two dimensional percolation models. Other potential applications are also mentioned.

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.237.6859&rep=rep1&type=pdf

Holder Regularity and Dimension Bounds for Random Curves

This paper establishes a link between two principal tools for the analysis of network traffic, namely, effective bandwidth and network calculus. It is shown that a general version of effective bandwidth can be expressed within the framework of a probabilistic version of the network calculus, where both arrivals and service are specified in terms of probabilistic bounds. By formulating well-known effective bandwidth expressions in terms of probabilistic envelope functions, the developed network calculus can be applied to a wide range of traffic types, including traffic that has self-similar characteristics. As applications, probabilistic lower bounds are presented on the service given by three different scheduling algorithms: static priority, earliest deadline first, and generalized processor sharing. Numerical examples show the impact of specific traffic models and scheduling algorithms on the multiplexing gain in a network.

/pdf/a-network-calculus-with-effective-bandwidth-1ra6s6pad8.pdf

A network calculus with effective bandwidth

Network services for the most demanding advanced networked applications which require absolute, per-flow service assurances can be deterministic or statistical. By exploiting the statistical properties of traffic, statistical assurances can extract more capacity from a network than deterministic assurances. We consider statistical service assurances for traffic scheduling algorithms. We present functions, so-called effective envelopes, which are, with high certainty, upper bounds of multiplexed traffic. Effective envelopes can be used to obtain bounds on the amount of traffic on a link that can be provisioned with statistical service assurances. We show that our bounds can be applied to a variety of traffic scheduling algorithms. In fact, one can reuse existing admission control functions for scheduling algorithms with deterministic assurances. We present numerical examples which compare the number of flows with statistical assurances that can be admitted with our effective envelope approach to those achieved with existing methods.

/pdf/statistical-service-assurances-for-traffic-scheduling-43ryfwi0kl.pdf

Almut Burchard

Papers

New Strategies for Assigning Re;al-Time Tasks to Multimocessor Svstems

New strategies for assigning real-time tasks to multiprocessor systems

Holder Regularity and Dimension Bounds for Random Curves

A network calculus with effective bandwidth

Statistical service assurances for traffic scheduling algorithms