Worst-case Analyses Research Articles

Average-Case Performance of the Apriori Algorithm

The failure rate of the Apriori Algorithm is studied analytically for the case of random shoppers. The time needed by the Apriori Algorithm is determined by the number of item sets that are output (successes: item sets that occur in at least k baskets) and the number of item sets that are counted but not output (failures: item sets where all subsets of the item set occur in at least k baskets but the full set occurs in less than k baskets). The number of successes is a property of the data; no algorithm that is required to output each success can avoid doing work associated with the successes. The number of failures is a property of both the algorithm and the data.We find that under a wide range of conditions the performance of the Apriori Algorithm is almost as bad as is permitted under sophisticated worst-case analyses. In particular, there is usually a bad level with two properties: (1) it is the level where nearly all of the work is done, and (2) nearly all item sets counted are failures. Let l be the...

The Ordered Open-End Bin-Packing Problem

We study a variant of the classical bin-packing problem, the ordered open-end bin-packing problem, where first a bin can be filled to a level above 1 as long as the removal of the last piece brings the bin's level back to below 1 and second, the last piece is the largest-indexed piece among all pieces in the bin. We conduct both worst-case and average-case analyses for the problem. In the worst-case analysis, pieces of size 1 play distinct roles and render the analysis more difficult with their presence. We give lower bounds for the performance ratio of any online algorithm for cases both with and without the 1-pieces, and in the case without the 1-pieces, identify an online algorithm whose worst-case performance ratio is less than 2 and an offline algorithm with good worst-case performance. In the average-case analysis, assuming that pieces are independently and uniformly drawn from [0, 1], we find the optimal asymptotic average ratio of the number of occupied bins over the number of pieces. We also introduce other online algorithms and conduct simulation study on the average-case performances of all the proposed algorithms.

Zonisamide add-on for drug-resistant partial epilepsy.

The majority of people with epilepsy have a good prognosis and their seizures can be well controlled with the use of a single antiepileptic agent, but up to 30 per cent develop refractory epilepsy, especially those with partial seizures. In this review we summarize the current evidence regarding zonisamide, when used as an add-on treatment for drug-resistant partial epilepsy. To evaluate the effects of zonisamide when used as an add-on treatment for people with drug -resistant partial epilepsy. We searched the Cochrane Epilepsy Group trial register (14/12/01), the Cochrane Controlled Trials Register (Cochrane Library Issue 4, 2001). In addition, we contacted Dainippon and Elan Pharma (makers and licensees of zonisamide) and experts in the field to seek any ongoing studies or unpublished studies. Randomized placebo controlled add-on trials of zonisamide in people with drug-resistant partial epilepsy. Two reviewers independently selected trials for inclusion and extracted relevant data. Outcomes were: (a) fifty per cent or greater reduction in total seizure frequency; (b) treatment withdrawal (any reason); (c) adverse events. Primary analyses were intention to treat. Summary odds ratios (ORs) were estimated for each outcome. Three trials (499 participants) were included. The overall odds ratio (OR, 95% Confidence Interval (CI)) for 50 per cent reduction in seizure frequency compared to placebo was 2.07(1.36 to 3.15) for a 400mg/day dose of zonisamide. When the full treatment period of 12 weeks was considered for all three trials including varied rates of titration to 400mg/day the OR compared to placebo was 2.72(95% CI 1.74 to 4.25). There was insufficient evidence to support a dose response relationship for this outcome. The OR for treatment withdrawal was 1.74(95% CI 1.03 to 2.95). The 99% CI for the following side effects indicate that they are significantly associated with zonisamide: ataxia 3.94(1.23 to 12.57); somnolence 2.11(1.11 to 3.98); agitation 3.52(1.26 to 9.68); agitation and irritability 2.43(1.04 to 5.66) and anorexia 2.98(1.38 to 6.42). Zonisamide has efficacy as an add-on treatment in people with drug-resistant partial epilepsy. Minimum effective and maximum tolerated doses cannot be identified. The trials reviewed were of 12 week duration and results cannot be used to confirm longer periods of effectiveness in seizure control. The results cannot be extrapolated to monotherapy or to people with other seizure types or epilepsy syndromes.

The Discrepancy and Gain Coefficients of Scrambled Digital Nets

Digital sequences and nets are among the most popular kinds of low discrepancy sequences and sets and are often used for quasi-Monte Carlo quadrature rules. Several years ago Owen proposed a method of scrambling digital sequences and recently Faure and Tezuka have proposed another method. This article considers the discrepancy of digital nets under these scramblings. The first main result of this article is a formula for the discrepancy of a scrambled digital (λ, t, m, s)-net in base b with n=λbm points that requires only O(n) operations to evaluate. The second main result is exact formulas for the gain coefficients of a digital (t, m, s)-net in terms of its generator matrices. The gain coefficients, as defined by Owen, determine both the worst-case and random-case analyses of quadrature error.

Vagus nerve stimulation for partial seizures.

Vagus nerve stimulation (VNS) has recently been introduced as an adjunct for treating patients with seizures. The aim of this systematic review was to overview the current evidence for the effects of vagus nerve stimulation, when used as an adjunctive treatment for patients with drug-resistant partial epilepsy. To determine the effects of VNS high-level stimulation compared to low-level (presumed subtherapeutic dose) stimulation. We searched the Cochrane Epilepsy Group trials register, MEDLINE (January 1966 to October 2000) and The Cochrane Controlled Trials Register (Cochrane Library Issue 4, 2000). Randomized, double-blind controlled trials of VNS comparing high and low stimulation paradigms. Studies in adults or children with drug-resistant partial seizures. Two reviewers independently selected trials for inclusion and extracted data. The following outcomes were assessed: (a) 50% or greater reduction in total seizure frequency; (b) treatment withdrawal (any reason); (c) side effects. Primary analyses were intention to treat. Sensitivity best and worst case analyses were also undertaken. Summary odds ratios (ORs) were estimated for each outcome. Results of the overall efficacy analysis show that VNS stimulation using the high stimulation paradigm was significantly better than low stimulation. The overall OR (95% Confidence Interval (CI)) for 50% responders across all studies is 1.93 (1.1,3.3). This effect did not vary substantially and remained statistically significant for both the best and worst case scenarios. Results for the outcome "withdrawal of allocated treatment" suggest that VNS is well tolerated as no significant difference was found between the high and low stimulation groups, and withdrawals were rare. Statistically significant adverse effects associated with implantation (low versus baseline) were hoarseness, cough, pain and paresthesia. Statistically significant adverse effects associated with stimulation (high versus low) were hoarseness and dyspnea, suggesting the implantation is associated with hoarseness, but the stimulation produces additional hoarseness. VNS for partial seizures appears to be an effective and well tolerated treatment. Adverse effects of hoarseness, cough, pain, paresthesias and dyspnea are associated with the treatment but appear to be reasonably well tolerated as dropouts were rare. Typical central nervous system adverse effects of antiepileptic drugs such as ataxia, dizziness, fatigue, nausea and somnolence were not statistically significantly associated with VNS treatment.

Optimisation of electromagnetic devices with uncertain parameters and tolerances in the design variables

The common approach to continuous and discrete optimisation problems in electromagnetics does not take into account uncertainties and variations of the design variables. Local sensitivity analysis is usually performed only after the optimisation run to study the behaviour of the objective function in the neighbourhood of the optimum. However, this procedure may prove inefficient if the optimum has to be rejected due to sensitivity considerations and a new run has then to be performed. In this paper an alternative approach, which takes into account uncertainties in the design variables and physical data, is presented, and an analytical function is used to highlight the features of the proposed method. The essence of the technique is to couple the optimisation with a series of worst case analyses which are embedded in the optimisation loop. The method is fully general and can be applied to any optimisation method. The additional computational costs associated with the procedure maybe relatively high, but in the authors’ opinion the obtained gains in user confidence in the solution and the computational savings in some cases far offset the possible drawbacks of the method.

Levetiracetam add-on for drug-resistant localization related (partial) epilepsy.

The majority of patients with epilepsy have a good prognosis and their seizures are well controlled by a single antiepileptic drug. However, up to 30% develop refractory seizures, particularly those with partial seizures. In this review, we summarise the current evidence regarding a new antiepileptic drug, levetiracetam, when used as an add-on treatment for drug-resistant localization related (partial) epilepsy. To evaluate the effects of levetiracetam on seizures, side effects, quality of life and cognition, when used as an add-on treatment for patients with a drug-resistant localization related (partial) epilepsy. We searched the Cochrane Epilepsy Group trials register, the Cochrane Controlled Trials Register (Cochrane Library Issue 2, 2000). In addition, we contacted UCB SA (makers of levetiracetam) and experts in the field to seek any ongoing studies or unpublished studies. Randomized placebo controlled add-on trials of levetiracetam in patients with a drug-resistant localization related (partial) epilepsy. Two reviewers independently selected trials for inclusion and extracted relevant data. The following outcomes were assessed: (a) 50% or greater reduction in total seizure frequency; (b) treatment withdrawal (any reason); (c) side effects; (d) cognitive effects; (e) quality of life. Primary analyses were intention to treat. Sensitivity best and worst case analyses were also undertaken. Summary odds ratios (ORs) were estimated for each outcome. Dose response was evaluated in regression models. Four trials (1023 patients) were included. All four trials had data for treatment withdrawal and side effect outcomes. Three trials (904 patients) had data for 50% or greater reduction in seizure frequency. Three trials (595 patients) had data for quality of life and cognitive outcomes. The overall Odds Ratio (OR) (95% Confidence Interval (CI)) for 50% or greater reduction in total seizure frequency outcome was 3.81 (2.78,5.22). Dose regression analysis shows clear evidence that levetiracetam reduces seizure frequency with an increase in efficacy with increasing dose of levetiracetam. Approximately 15% of patients taking 1000 mg and 20-30% of patients taking 3000 mg levetiracetam per day have a 50% or greater reduction in seizure frequency. Patients were not significantly more likely to have levetiracetam withdrawn, OR (95% CI) 1.25 (0.87,1.80). The following side effects were significantly associated with levetiracetam: dizziness 2.36 (1.21, 4.61) and infection 1.82 (1.05, 3.14) whereas accidental injury was significantly associated with placebo 0.55 (0.32, 0.93). Quality of life and cognitive effect outcomes suggest that levetiracetam has a positive effect on cognition and some aspects of quality of life. Levetiracetam reduces seizure frequency when used as an add-on treatment for patients with a drug-resistant localization related (partial) epilepsy, and seems well tolerated. Minimum effective and maximum tolerated doses have not been identified. The trials reviewed were of 16-24 weeks duration and results cannot be used to confirm longer term effects. Our results cannot be extrapolated to monotherapy or to patients with other seizure types or epilepsy syndromes. Great care should also be taken with any attempt to apply these results to children.

The asymptotic efficiency of randomized nets for quadrature

An L 2 -type discrepancy arises in the average- and worst-case error analyses for multidimensional quadrature rules. This discrepancy is uniquely defined by K(x,y), which serves as the covariance kernel for the space of random functions in the average-case analysis and a reproducing kernel for the space of functions in the worst-case analysis. This article investigates the asymptotic order of the root mean square discrepancy for randomized (0,m,s)-nets in base b. For moderately smooth K(x,y) the discrepancy is O(N -1 [log(N)] (s-1)/2 ), and for K(x,y) with greater smoothness the discrepancy is O(N-3/2[log(N)] (s-1)/2 ), where N = b m is the number of points in the net. Numerical experiments indicate that the (t,m,s)-nets of Faure, Niederreiter and Sobol' do not necessarily attain the higher order of decay for sufficiently smooth kernels. However, Niederreiter nets may attain the higher order for kernels corresponding to spaces of periodic functions.

Gabapentin add-on for drug-resistant partial epilepsy.

The majority of patients with epilepsy have a good prognosis and their seizures are well controlled by a single antiepileptic drug, but up to 30% develop refractory epilepsy, especially those with partial seizures. In this review we summarise the current evidence regarding a new antiepileptic drug, gabapentin, when used as an add-on treatment for drug-resistant partial epilepsy. To evaluate the efficacy and tolerability of gabapentin when used as an add-on treatment for patients with drug-resistant partial epilepsy. We searched the Cochrane Epilepsy Group's trial register, the Cochrane Controlled Trials Register (The Cochrane Library Issue 1, 2000). In addition, we contacted Parke Davis (manufacturers of gabapentin) and experts in the field to seek any ongoing studies or unpublished studies. Randomized placebo controlled double blind add-on trials of gabapentin in patients with drug-resistant partial epilepsy. Two reviewers independently selected trials for inclusion and extracted the relevant data. The following outcomes were assessed: (a) 50% or greater reduction in seizure frequency; (b) treatment withdrawal (any reason); (c) side effects. Primary analyses were intention to treat. Sensitivity best and worst case analyses were also undertaken. Summary odds ratios were estimated for each outcome. Dose response was evaluated in regression models, and Number Needed to Treat (NNTs) were calculated for individual doses. Five trials were included representing 997 randomized patients. Overall odds ratio (OR) (95% Confidence Interval (CI)) for 50% or greater reduction in seizure frequency compared to placebo was 1.93 (1.37 - 2.71). Dose regression analysis shows increasing efficacy with increasing dose, with 28.5% (21.5 - 36.7) of patients responding to 1800mg of gabapentin compared to placebo, NNT 6.7 (3.0 - 10.5). Treatment withdrawal OR (95% CI) compared to placebo 1.05 (0.68 - 1.61); Side effects: OR (99% CI) compared to placebo. Dizziness 2.22 (1.28 - 3. 85); fatigue 2.28 (1.15 - 4.52); somnolence 2.01 (1.24 - 3.28) were significantly associated with gabapentin. Gabapentin has efficacy as an add-on treatment in patients with drug-resistant partial epilepsy. However, trials reviewed were of relatively short duration, and provide no evidence for the long term efficacy of gabapentin. Results cannot be extrapolated to monotherapy or patients with other epilepsy types.

Some results of the worst-case analysis for flow shop scheduling

Known approximation algorithms recommended for the permutation flow-shop problem with the weighted sum of completion times have a worst-case performance ratio which is unknown, or known but unlimited. We propose new algorithms with this ratio equal to [ m k]ϱ k , where ϱ k is the worst-case performance ratio of an algorithm which solves an auxiliary k -machine problem. Worst-case analyses of other approximation algorithms for the mean completion time and the makespan criteria are also presented.

Exploiting ellipsoidal parameter set estimates in H robust control design

The focus of this investigation is the exploitation of knowledge of an ellipsoidal bound on system parameters for the identification of modeling uncertainty information vital to the H robust control designer, a time to frequency domain uncertainty transformation. The characterizations of parametric uncertainty as coprime factor and additive perturbations to a nominal plant model are addressed in worst-case analyses. A Kharitonov type analysis provides sufficient conditions for the use of an additive plant perturbation uncertainty characterization. Original optimization results for the coprime factor perturbation enable the essential task of loopshaping to be conducted in the control design phase. A novel scheme is introduced to interpolate magnitude samples of the perturbation bounding function and is further developed into a technique for identification of reduced-order perturbation weightings, vital for practical control design. An example serves to illustrate the success of the developed techniques.

Worst-case analyses, linear programming and the bin-packing problem

In this paper we consider the familiar bin-packing problem and its associated set-partitioning formulation. We show that the optimal solution to the bin-packing problem can be no larger than 4/3 ⌈ZLP⌉, whereZLP is the optimal solution value of the linear programming relaxation of the set-partitioning formulation. An example is provided to show that the bound is tight. A by-product of our analysis is a new worst-case bound on the performance of the well studied First Fit Decreasing and Best Fit Decreasing heuristics.

Probabilistic Stability Robustness of Structural Systems

Model uncertainty, if ignored, can seriously degrade the performance of an otherwise well-designed control system. If the level of this uncertainty is extreme, the system may even be driven to instability. In the context of structural control, performance degradation and instability imply excessive vibration or even structural failure. Robust control has typically been applied to the issue of model uncertainty through worst-case analyses. These traditional methods include the use of the structured singular value, as applied to the small gain condition, to provide estimates of controller robustness. However, this emphasis on the worst-case scenario has not allowed a probabilistic understanding of robust control. In this paper an attempt to view controller robustness as a probability measure is presented. The probability of failure due to parametric uncertainty is estimated using first-order reliability methods (FORM). It is demonstrated that FORM can provide quite accurate results on the probability of fai...

Screening LCA for large numbers of products

CIBA’s Textile Dyes and Chemicals divisions use screening LCAs for their 1700 sales products to improve portfolio management and ecological process development. Material flow, energy, and waste data for in-house manufacturing processes are extracted from our company databases into our LCA system ECOSYS. For meaningful comparisons of whole life cycles, we must include LCA estimates for over 4000 raw materials from other suppliers. Even crude estimates are preferable to the frequently practiced omission of unknown process steps since they allow worst-case or sensitivity analyses. Sources for mass flows are (decreasing order of reliability): process literature (SRI-PEP Yearbook, Ullmann, Kirk-Othmer, patents), yields of analogous processes, theoretical stoichiometry. Energy demands come from literature, or from a set of standard operation estimates developed by our process engineers. Wastes/emissions, if not published, are derived from yields and elemental balances, estimated emissions of energy carriers (BUWAL-132), and typical end-of-pipe measures in CIBA. These data sets are kept as “added-burden modules” (ABM) in our system, each with a set of “inherent burdens”, which are transformed to step-specific burden estimates by a “propagation” program, before the overall burdens of the whole process tree are cumulated. This program checks every process for actually measured burdens, before applying the attached ABM estimates to fill the gaps. Centralization of estimates as ABM with inherent burdens facilitates maintenance and adaptation. At present, well over 250 important intermediates were estimated and used in our product trees; many more follow rapidly. This article is an example of how industry is using LCA to address environmental issues.

Probability-Based Stability Robustness Assessment of Controlled Structures

Model uncertainty, if ignored, can seriously degrade the performance of an otherwise well-designed control system. If the level of this uncertainty is extreme, the system may even be driven to instability. In the context of structural control, performance degradation and instability imply excessive vibration or even structural failure. Robust control has typically been applied to the issue of model uncertainty through worst-case analyses. These traditional methods include the use of the structured singular value, as applied to the small gain condition, to provide estimates of controller robustness. However, this emphasis on the worst-case scenario has not allowed a probabilistic understanding of robust control. In this paper an attempt to view controller robustness as a probability measure is presented. The probability of failure due to parametric uncertainty is estimated using first-order reliability methods (FORM). It is demonstrated that this method can provide quite accurate results on the probability of failure of actively controlled structures. Moreover, a comparison of this method to a suitably modified structured singular value robustness analysis in a probabilistic framework is performed. It is shown that FORM is the superior analysis technique when applied to a controlled three degree-of-freedorn structure. In addition, the robustness qualities of various active control design schemes such as LQR, H2, H∞ and μ -synthesis are discussed in order to provide some design guidelines.

Randomised controlled trial of single-dose antibiotic prophylaxis in surgical treatment of closed fractures: the Dutch Trauma Trial

SummaryBackground The efficacy of prophylactic antibiotics in fracture surgery remains controversial for lack of well-documented prospective studies. We report here the findings of the Dutch Trauma Trial, a prospective, randomised, double-blind, placebo-controlled study of antibiotic prophylaxis in the primary operative treatment of limb fractures. Ceftriaxone was chosen because of its broad spectrum of activity and because its pharmacokinetic profile, including high serum levels, high tissue penetration, and long elimination half-life, makes it suitable for single-dose prophylaxis.Methods Patients aged 18 years or more, attending one of fourteen Dutch centres for acute treatment of closed fractures, were randomly allocated to a single preoperative dose of ceftriaxone 2 g or placebo, and evaluated for development of wound infection and nosocomial infection at 10 days, 30 days, and 120 days. To assess the effects of drop-outs and withdrawals, best-case and worst-case analyses were performed.Findings A total of 2195 patients were included. The incidence of superficial and deep wound infections after placebo was 8·3%, compared with 3·6% in the ceftriaxone group (p<0·001, Pearson X2-test). The rate of nosocomial infection in the first month was 10·2% with placebo and 2·3% with ceftriaxone (p<0·001, Pearson χ2-test). Gram-positive bacteria were found in 74·5% of wound infections and 13·4% of nosocomial infections.Interpretation Adequate single-dose prophylaxis with a long-acting broad-spectrum antibiotic substantially reduces the incidence of wound infection and early nosocomial infection after surgery for closed fractures.

Computing GCDs of Polynomials over Algebraic Number Fields

Modular methods for computing the gcd of two univariate polynomials over an algebraic number field require a priori knowledge about the denominators of the rational numbers in the representation of the gcd. A multiplicative bound for these denominators is derived without assuming that the number generating the field is an algebraic integer. Consequently, the gcd algorithm of Langemyr and McCallum [ J. Symbolic Computation 8, 429 - 448, 1989] can now be applied directly to polynomials that are not necessarily represented in terms of an algebraic integer. Worst-case analyses and experiments with an implementation show that by avoiding a conversion of representation the reduction in computing time can be significant. A further improvement is achieved by using an algorithm for reconstructing a rational number from its modular residue so that the denominator bound need not be explicitly computed. Experiments and analyses suggest that this is a good practical alternative.

Upper and Lower Bound Distributions That Give Simultaneous Confidence Intervals for Quantiles

Abstract We propose a new method for constructing parametric confidence intervals for quantiles of an unknown distribution. These confidence intervals are constructed so that the joint probability that all intervals simultaneously contain their respective percentiles is at least a preset value. Thus we may also use the set of either upper or lower confidence limits to define an upper (or lower) bound distribution function, which we call an upper (or lower) tolerance distribution because this distribution may also be used to construct tolerance intervals for the unknown distribution. We derive tolerance distributions with exact coverage probability for iid samples from distributions in the location-scale family. Tolerance distributions can also be used for best- and worst-case analyses, as we illustrate by considering bounds on the distribution of the time interval between the onset of infectiousness and development of detectable antibody in individuals newly infected with the human immunodeficiency virus ...

Performance Guarantees for Approximation Algorithms Depending on Parametrized Triangle Inequalities

The worst-case analyses of heuristics in combinatorial optimization are often far too pessimistic when confronted with performance on real-world problems. One approach to partially overcome this discrepancy is to resort to average-case analyses by stipulating realistic distributions of input data. Another way is to incorporate a priori information on the potential domain of the input data, for instance, assuming the triangle inequality for input matrices is in some cases instrumental for establishing approximation algorithms with fixed performance guarantee. Now, a parametrized form of the triangle inequality has a considerably larger range of applicability and allows the prediction of the heuristics performance, where otherwise no bound could be provided. For example, it is interesting to observe that two well-known approximation algorithms for the Traveling Salesman Problem (TSP), assuming the triangle inequality, behave differently when one relaxes the imposed triangle inequality. The double-spanning-tree heuristic can be adjusted (by suitably extracting a Hamilton circuit from a Eulerian walk) to yield an approximation algorithm with performance guarantee increasing quadratically with the parameter governing the relaxed triangle inequality. The Christofides algorithm cannot be modified in this way and hence does not tolerate a relaxation of the standard triangle inequality without loosing the bound on its relative performance.

Thek-server dual and loose competitiveness for paging

This paper has two results. The first is based on the surprising observation that the well-known ``least-recently-used'' paging algorithm and the ``balance'' algorithm for weighted caching are linear-programming primal-dual algorithms. This observation leads to a strategy (called ``Greedy-Dual'') that generalizes them both and has an optimal performance guarantee for weighted caching. For the second result, the paper presents empirical studies of paging algorithms, documenting that in practice, on ``typical'' cache sizes and sequences, the performance of paging strategies are much better than their worst-case analyses in the standard model suggest. The paper then presents theoretical results that support and explain this. For example: on any input sequence, with almost all cache sizes, either the performance guarantee of least-recently-used is O(log k) or the fault rate (in an absolute sense) is insignificant. Both of these results are strengthened and generalized in``On-line File Caching'' (1998).