Exponential Explosion Research Articles

Optimal Energy and Delay Tradeoffs for Multiuser Wireless Downlinks

We consider the fundamental delay tradeoffs for minimizing energy expenditure in a multiuser wireless downlink with randomly varying channels. First, we extend the Berry-Gallager bound to a multiuser context, demonstrating that any algorithm that yields average power within <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> (1/ <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</i> ) of the minimum power required for network stability must also have an average queueing delay greater than or equal to Omega(radic <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</i> ). We then develop a class of algorithms, parameterized by <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</i> , that come within a logarithmic factor of achieving this fundamental tradeoff. The algorithms overcome an exponential state-space explosion, and can be implemented in real time without <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">priori</i> knowledge of traffic rates or channel statistics. Further, we discover a ldquosuperfastrdquo scheduling mode that beats the Berry-Gallager bound in the exceptional case when power functions are piecewise linear.

A concise proof of the Kronecker polynomial system solver from scratch

Nowadays polynomial system solvers are involved in sophisticated computations in algebraic geometry as well as in practical engineering. The most popular algorithms are based on Gröbner bases, resultants, Macaulay matrices, or triangular decompositions. In all these algorithms, multivariate polynomials are expanded in a monomial basis, and the computations mainly reduce to linear algebra. The major drawback of these techniques is the exponential explosion of the size of the polynomials needed to represent highly positive dimensional solution sets. Alternatively, the “Kronecker solver” uses data structures to represent the input polynomials as the functions that compute their values at any given point. In this paper, we present the first self-contained and student friendly version of the Kronecker solver, with a substantially simplified proof of correctness. In addition, we enhance the solver in order to compute the multiplicities of the zeros without any extra cost.

Planar detonation structure for chain-branching kinetics with large activation energy and small initiation rate

The structure of the steady planar detonation wave is analyzed for three-step chain-branching kinetics consistent with hydrogen–air chemistry. The initiation and chain-branching steps are described by an Arrhenius rate. Both are thermally neutral, so that heat release is due to termination. The initiation rate is typically very low and very stiff. As a result, a small fraction of the reactant is consumed in the initiation region, which is very long but ends in an exponential chain-branching explosion. Next, the reactant is rapidly converted into chain-branching radicals, within a very thin zone, which ends when the concentration of the chain-branching radical reaches a peak, because of reactant depletion. Finally, the termination step consumes the chain-branching radicals and releases heat within a region thicker than the peak zone, but much thinner than the initiation region. The analysis is based upon two assumptions: that the chain-branching activation energy is high and that initiation is slow. The structure of the initiation and chain-branching zones is different for post-shock states within or outside the explosion region in the chain-branching diagram. In the former situation, chain-branching is already stronger than termination at the von Neumann point, and vice versa. In the no-explosion case, the initiation zone becomes very long, while the little chain-branching specie produced by initiation is directly converted into product by the termination step. Temperature increases slowly until reaching the explosion curve, when chain-branching becomes stronger than termination. The subsequent structure is similar to the explosion case.

Perineural Infusion of Local Anesthetics

Perineural Infusion of Local Anesthetics

A hybrid supervisory control approach for virtual production systems

With the development of computer technology, the anticipated extensive use of virtual production systems (VPSs) in the future has encouraged its intensive research recently. However, a limited amount of research has been made on its efficient control. In this paper, a hybrid supervisory control approach based on autonomy and coordination is proposed for VPSs to enhance the efficiency of control. Its three primary advantages are: (1) application of supervisory control theory, which can efficiently obtain the desired property through closed-loop feedback; (2) use of hybrid control structure combining hierarchical and distributed ones, which can avoid the exponential explosion of state space due to synthesis of models; and (3) utilization of autonomous and coordination mechanisms, which can keep the balance of local quick response and global optimization. A case study is used to illustrate how to implement the proposed approach, and is finally analyzed and simulated by an integrated tool named UPPAAL.

Schedulability analysis of fixed-priority systems using timed automata

In classic scheduling theory, real-time tasks are usually assumed to be periodic, i.e. tasks are released and computed with fixed rates periodically. To relax the stringent constraints on task arrival times, we propose to use timed automata to describe task arrival patterns. In a previous work, it is shown that the general schedulability checking problem for such models is a reachability problem for a decidable class of timed automata extended with subtraction. Unfortunately, the number of clocks needed in the analysis is proportional to the maximal number of schedulable task instances associated with a model, which is in many cases huge. In this paper, we show that for fixed-priority scheduling strategy, the schedulability checking problem can be solved using standard timed automata with two extra clocks in addition to the clocks used in the original model to describe task arrival times. The analysis can be done in a similar manner to response time analysis in classic Rate-Monotonic Analysis (RMA). The result is further extended to systems with data-dependent control, in which the release time of a task may depend on the time-point at which other tasks finish their execution. For the case when the execution times of tasks are constants, we show that the schedulability problem can be solved using n + 1 extra clocks, where n is the number of tasks. The presented analysis techniques have been implemented in the Times tool. For systems with only periodic tasks, the performance of the tool is comparable with tools implementing the classic RMA technique based on equation-solving, without suffering from the exponential explosion in the number of tasks.

A false negative approach to mining frequent itemsets from high speed transactional data streams

Mining frequent itemsets from transactional data streams is challenging due to the nature of the exponential explosion of itemsets and the limit memory space required for mining frequent itemsets. Given a domain of I unique items, the possible number of itemsets can be up to 2 I − 1. When the length of data streams approaches to a very large number N, the possibility of an itemset to be frequent becomes larger and difficult to track with limited memory. The existing studies on finding frequent items from high speed data streams are false-positive oriented. That is, they control memory consumption in the counting processes by an error parameter ϵ, and allow items with support below the specified minimum support s but above s − ϵ counted as frequent ones. However, such false-positive oriented approaches cannot be effectively applied to frequent itemsets mining for two reasons. First, false-positive items found increase the number of false-positive frequent itemsets exponentially. Second, minimization of the number of false-positive items found, by using a small ϵ, will make memory consumption large. Therefore, such approaches may make the problem computationally intractable with bounded memory consumption. In this paper, we developed algorithms that can effectively mine frequent item(set)s from high speed transactional data streams with a bound of memory consumption. Our algorithms are based on Chernoff bound in which we use a running error parameter to prune item(set)s and use a reliability parameter to control memory. While our algorithms are false-negative oriented, that is, certain frequent itemsets may not appear in the results, the number of false-negative itemsets can be controlled by a predefined parameter so that desired recall rate of frequent itemsets can be guaranteed. Our extensive experimental studies show that the proposed algorithms have high accuracy, require less memory, and consume less CPU time. They significantly outperform the existing false-positive algorithms.

I Have the Answer, Now What's the Question?: Why Metaanalyses Do Not Provide Definitive Solutions

(Can J Psychiatry 2005;50:829-831) It ain't so much the things we don't know that get us in trouble. It's the things we know that just ain't so. -Artemus Ward In a recent issue of the British Medical Journal, Moncrieff and Kirsch (1 ) concluded that Recent meta-analyses show selective serotonin reuptake inhibitors [SSRIs] have no clinically meaningful advantage over placebo and that Methodological artefacts may account for the small degree of superiority shown over placebo. Needless to say, this article generated a large number of letters to the editor, citing everything from despair about the lack of available alternatives to charges that the authors overlooked or ignored evidence about the positive effects of SSRIs, that they misinterpreted the findings and recommendations of the National Institute for Health and Clinical Excellence (NICE), that both the authors and NICE used inappropriate criteria to evaluate improvement, that the authors made erroneous assumptions about the distribution of depression, and so on. This editorial does not aim to critique the article by Moncrieff and Kirsch. Rather, it tries to explain why different people with honourable intentions can come to different conclusions regarding metaanalyses. Suffice it to say for now that their summary and recommendations are by no means accepted by all. Other metaanalyses (for example, 2-4), including one coauthored by Moncrieff (5), have supported the use of SSRIs; this article has merely brought the controversy to a head. The fact is that Moncrieff and Kirsch' s conclusions should not come as a surprise. Fourteen years ago, Greenberg and others (6) came to similar conclusions regarding the effectiveness (or rather, the lack thereof) of the older class of tricyclic antidepressants (TCAs). What some may find strange is why this debate (and similar ones regarding the effectiveness of interventions ranging from screening for breast cancer to the use of cholinesterase inhibitors in Alzheimer's disease) is still going on. After all, weren't we promised that metaanalyses would provide definitive answers to questions such as these? Metaanalysis is predicated on the assumption (or it may be more a belief and hope) that objectivity regarding the criteria used for conducting literature searches, selecting the articles to include or exclude, and abstracting and summarizing the findings would result in unbiased and unequivocal answers. In some hierarchies of evidence, metaanalyses are at the top, trumping even very large randomized controlled trials (7). Since Smith and Glass's pioneering 1977 metaanalysis of psychotherapy (8), there has been an exponential explosion in the number published in the medical and psychological literature. Doing a simple Medline and PsycLit search, using just the keyword metaanalysis, I found that there were 3 published in 1981, 422 in 1991, and 1712 in 2003. Indeed, there are international organizations, such as the Cochrane Collaboration in medicine and the Campbell Collaboration in the social sciences, devoted exclusively to conducting and publishing metaanalyses. Further, there are regularly published compendia of treatment recommendations based on their results (9). The fact is, though, that disagreements among metaanalyses of the same topic are quite common. Oxman and Guyatt found that 5 reviews about the need to treat mild hypertension all resulted in different recommendations (10), and Munsinger (11) and Kamin (12), reviewing the same articles about environmental effects on intelligence, came to diametrically opposite conclusions. Indeed, our review of the effectiveness of TCAs (13) disagreed with Greenberg and others' findings (6). The reality is that, despite the claims of true believers, metaanalysis is neither a purely objective, mechanical process nor a panacea for answering all questions. There are 2 major reasons why metaanalyses may differ with regard to the conclusions they draw: methodological considerations and interpretation. …

Modular Fault Diagnosis Based on Discrete Event Systems

An awareness of failure type and location is an indispensable requirement for the establishment of adequate recovery strategies and the maintenance of Factory Automation and Process Control systems. The failure diagnosis methodology presented in this paper is based on Discrete Event Systems models and in the diagnoser concept, which enable the off-line and on-line analysis of systems failures. We present an approach for models and associated diagnosers based on a modular decomposition of the global system, with the aim of avoiding problems of exponential explosion in the number of states and computational complexity of the diagnosis process.

3D reconstruction and visualization [Guest Editors' Introduction

We have entered an era where the acquisition of 3D data is ubiquitous, continuous, and massive. These data come from multiple sources including high-resolution, geo-corrected imagery from aerial photography and satellites; ground-based close-up images of buildings and urban features; 3D point clouds from airborne laser rangefinding systems, such as Lidar; imagery from synthetic aperture radar; and other sources. To make these data really useful, they should be employed to model the real world, and the model should then be available for interactive exploration and analysis. However, the modeling aspect is not straightforward since almost all the collected data has holes (due to obstructions or poor acquisition conditions), and no single acquisition mode is likely to produce complete models. The overall modeling problem is then one of fusing multisource data consistently and accurately. As acquisition modes are automated and models are produced, there will be an exponential explosion in the amount of data available for analysis and exploration. Based on these needs and issues, we formulated this special issue, which provides a sampling of the latest and most interesting research in several of these areas. The articles included are briefly summarized.

Free access to information challenged by filtering techniques

The exponential growth and explosion of information on the Internet has given rise to several questions of a sociological, economic, political and legal nature, especially as regards the issue of free access to information and possible limitations to this free use. Since the Internet is a global operating network exceeding national territories, the problem of universal jurisdiction arises when conflicts emerge. Filtering techniques have been introduced to deal with this problem. However the use of filtering techniques poses several difficulties as well and can therefore clearly have a chilling effect on free speech. In the following article the author will highlight some of the problems with reference to the experiences of the information portal Yahoo!.

Dynamic Partitioning in Linear Relation Analysis: Application to the Verification of Reactive Systems

We apply linear relation analysis (P. Cousot and N. Halbwachs, in 5th ACM Symposium on Principles of Programming Languages, POPL'78, Tucson (Arizona), January 1978s N. Halbwachs, Y.E. Proy, and P. Roumanoff, Formal Methods in System Design, Vol. 11, No. 2, pp. 157–185, 1997) to the verification of declarative synchronous programs (N. Halbwachs, Science of Computer Programming, Special Issue on SAS'94, Vol. 31, No. 1, 1998). In this approach, state partitioning plays an important role: on one hand the precision of the results highly depends on the fineness of the partitionings on the other hand, a too much detailed partitioning may result in an exponential explosion of the analysis. In this paper, we propose to dynamically select a suitable partitioning according to the property to be proved. The presented approach is quite general and can be applied to other abstract interpretations.

An assume-guarantee rule for checking simulation

The simulation preorder on state transition systems is widely accepted as a useful notion of refinement, both in its own right and as an efficiently checkable sufficient condition for trace containment. For composite systems, due to the exponential explosion of the state space, there is a need for decomposing a simulation check of the form P ≤ s Q , denoting " P is simulated by Q ," into simpler simulation checks on the components of P and Q . We present an assume-guarantee rule that enables such a decomposition. To the best of our knowledge, this is the first assume-guarantee rule that applies to a refinement relation different from trace containment. Our rule is circular, and its soundness proof requires induction on trace trees. The proof is constructive: given simulation relations that witness the simulation preorder between corresponding components of P and Q , we provide a procedure for constructing a witness relation for P ≤ s Q . We also extend our assume-guarantee rule to account for fairness constraints on transition systems.

Automatic analysis of consistency between requirements and designs

Writing requirements in a formal notation permits automatic assessment of such properties as ambiguity, consistency, and completeness. However, verifying that the properties expressed in requirements are preserved in other software life cycle artifacts remains difficult. The existing techniques either require substantial manual effort and skill or suffer from exponential explosion of the number of states in the generated state spaces. "Light-weight" formal methods is an approach to achieve scalability in fully automatic verification by checking an abstraction of the system for only certain properties. We describe light-weight techniques for automatic analysis of consistency between software requirements (expressed in SCR) and detailed designs in low-degree-polynomial time, achieved at the expense of using imprecise data-flow analysis techniques. A specification language SCR describes the systems as state machines with event-driven transitions. We define detailed designs to be consistent with their SCR requirements if they contain exactly the same transitions. We have developed a language for specifying detailed designs, an analysis technique to create a model of a design through data-flow analysis of the language constructs, and a method to automatically generate and check properties derived from requirements to ensure a design's consistency with them. These ideas are implemented in a tool named CORD, which we used to uncover errors in designs of some existing systems.

The shape of fuzzy sets in adaptive function approximation

The shape of if-part fuzzy sets affects how well feedforward fuzzy systems approximate continuous functions. We explore a wide range of candidate if-part sets and derive supervised learning laws that tune them. Then we test how well the resulting adaptive fuzzy systems approximate a battery of test functions. No one shape emerges as the best. The sine function often does well and has tractable learning, but its undulating side-lobes may have no linguistic meaning. This suggests that function-approximation accuracy may sometimes have to outweigh linguistic or philosophical interpretations. We divide the if-part sets into two large classes. The first consists of n-dimensional joint sets that factor into n scalar sets. These sets ignore the correlations among input vector components. Fuzzy systems suffer in general from exponential rule explosion in high dimensions when they blindly approximate functions. The factorable fuzzy sets themselves also suffer from a curse of dimensionality: they tend to become binary spikes in high dimension. The second class consists of the more general but less common n-dimensional joint sets that do not factor into n scalar fuzzy sets. We present a method for constructing such unfactorable joint sets from scalar distance measures. Fuzzy systems that use unfactorable sets need not suffer from exponential rule explosion but their increased complexity may lead to intractable learning and inscrutable if-then rules. We prove that some of these sets still suffer from spikiness.

An online tutoring system for language translation

Our interactive intelligent language tutoring system acquires Japanese-English technical translations over the Internet. The system consists of an augmented transition network-based template, a global-matching algorithm embedded in the template structure, a parts-of-speech tagged parser, and a visual interface authoring tool. Acquiring key English patterns greatly simplifies the template structure, which effectively controls an exponential explosion in the number of possible combinations inherent in many natural language applications.

Simple, fast and flexible pricing of Asian options

The author describes a modified binomial method that provides a simple and unified framework for the valuation of various kinds of Asian options (American or European, arithmetic or geometric, fixed or floating strike, discrete or continuous sampling and dividends, and partial Asians). The greeks can also be calculated accurately and stably. The method is a refinement of that of Hull and White (1993), where at each node of a standard binomial tree one also considers a table of possible values of the average. To avoid the exponential explosion of the size of this table in the arithmetic average case, one considers a smaller set of representative values for the average, interpolates when necessary, and otherwise uses standard backward recursion to value the option. In this paper, an efficient implementation of this idea is presented. In particular, option values are insured to be smooth as a function of the number N of binomial time periods, so that Richardson extrapolation can be applied to eliminate 1/N (and sometimes higher-order) corrections, dramatically increasing the speed of the method. Detailed checks and illustrations are provided, showing that this approach can achieve any desired level of accuracy for convection- or diffusion-dominated regimes and for long or short maturities. It is typically much faster than standard PDE and Monte Carlo approaches.

Dynamic Partitioning in Linear Relation Analysis. Application to the Verification of Synchronous Programs

&lt;p&gt;We apply linear relation analysis [CH78, HPR97] to the verification&lt;br /&gt;of declarative synchronous programs [Hal98]. In this approach,&lt;br /&gt;state partitioning plays an important role: on one hand the precision of the results highly depends on the fineness of the partitioning; on the other hand, a too much detailed partitioning may result in an exponential explosion of the analysis. In this paper we propose to consider very general partitions of the state space and to dynamically select a suitable partitioning according to the property to be proved. The presented approach is quite general and can be applied to other abstract interpretations.&lt;/p&gt;&lt;p&gt;Keywords and Phrases: Abstract Interpretation, Partitioning,&lt;br /&gt;Linear Relation Analysis, Reactive Systems, Program Verification&lt;/p&gt;

Waiting for the millennium: some thoughts on being elected President of the Library Association for the year 2000

Everyone needs milestones in their lives and the millennium provides one, whatever we think of the event personally. Librarians and information workers are facing major changes as this date approaches. Despite having little history, the skills of the professional will be crucial in managing the exponential explosion of information and creativity. The needs of users will focus as much on leisure as academic study, which may be a challenge to some people. Libraries will be points of access, not physical collections which require different psychology for users and professionals alike. The costs of information provision may need to be moved from the institution to the user, with special provision for those with particular social needs. This raises social and ethical issues. The millennium has a spiritual dimension, which may require many people to question the direction in which the profession is going.

CRITICAL CARE AND THE WORLD WIDE WEB

The Internet was created in 1969, when the Advanced Research Projects Agency of the United States Department of Defense fired up an experimental network consisting of only four computers. Over the past five years there has been an exponential explosion in the number of computers added to this network. It is estimated that Internet traffic doubles every 100 days with more than 100 million people worldwide now on-line. The Internet is so vast that practically every aspect of human interest is represented is some form or fashion. From recreation to applied science and technology, and from Critical Care Medicine case scenarios to digitized radiology images and pathology specimens, the Internet has become increasingly useful for critical care practitioners. To date, no resource is better equipped to assist critical care providers in many of their daily tasks. This article presents some of the historical developments of the Internet as well as common applications that are useful for critical care practitioners.