Step-up and step-down procedures controlling the number and proportion of false positives

In multiple hypotheses testing, it is important to control the probability of rejecting “true” null hypotheses. A standard procedure has been to control the family-wise error rate (FWER), the probability of rejecting at least one true null hypothesis.For large numbers of hypotheses, using FWER can result in very low power for testing single hypotheses. Recently, powerful multiple step FDR procedures have been proposed which control the “false discovery rate” (expected proportion of Type I errors). More recently, van der Laan et al. [Augmentation procedures for control of the generalized family-wise error rate and tail probabilities for the proportion of false positives. Statist. Appl. in Genetics and Molecular Biol. 3, 1-25] proposed controlling a generalized family-wise error rate k-FWER (also called gFWER(k)), defined as the probability of at least (k+1) Type I errors (k=0 for the usual FWER).Lehmann and Romano [Generalizations of the familywise error rate. Ann. Statist. 33(3), 1138-1154] suggested both a single-step and a step-down procedure for controlling the generalized FWER. They make no assumptions concerning the p-values of the individual tests. The step-down procedure is simple to apply, and cannot be improved without violation of control of the k-FWER.In this paper, by limiting the number of steps in step-down or step-up procedures, new procedures are developed to control k-FWER (and the proportion of false positives) PFP. Using data from the literature, the procedures are compared with those of Lehmann and Romano [Generalizations of the familywise error rate. Ann. Statist. 33(3), 1138-1154], and, under the assumption of a multivariate normal distribution of the test statistics, show considerable improvement in the reduction of the number and PFP.     

Biohashing: two factor authentication featuring fingerprint data and tokenised random number

Human authentication is the security task whose job is to limit access to physical locations or computer network only to those with authorisation. This is done by equipped authorised users with passwords, tokens or using their biometrics. Unfortunately, the first two suffer a lack of security as they are easy being forgotten and stolen; even biometrics also suffers from some inherent limitation and specific security threats. A more practical approach is to combine two or more factor authenticator to reap benefits in security or convenient or both. This paper proposed a novel two factor authenticator based on iterated inner products between tokenised pseudo-random number and the user specific fingerprint feature, which generated from the integrated wavelet and Fourier-Mellin transform, and hence produce a set of user specific compact code that coined as BioHashing. BioHashing highly tolerant of data capture offsets, with same user fingerprint data resulting in highly correlated bitstrings. Moreover, there is no deterministic way to get the user specific code without having both token with random data and user fingerprint feature. This would protect us for instance against biometric fabrication by changing the user specific credential, is as simple as changing the token containing the random data. The BioHashing has significant functional advantages over solely biometrics i.e. zero equal error rate point and clean separation of the genuine and imposter populations, thereby allowing elimination of false accept rates without suffering from increased occurrence of false reject rates.     

Volume discounting coordinates a supply chain effectively when demand is sensitive to both price and sales effort

In this paper, we use a simple and parsimonious model to investigate the performance of volume discounting schemes (hereafter “[VD]”) in a supply chain where the market demand is sensitive to both retail price “p” and sales effort “e” — hereafter called a “(p,e)-channel.” The problem is analyzed as a manufacturer-leading Stackelberg game. We first present, for the deterministic-system-parameter situation, contract-designing procedures under two contract formats; namely, a “regular” version of [VD] (hereafter “[RVD]”) and a “continuous” version of [VD] (hereafter “[CVD]”). Our solutions show that [RVD] cannot perfectly coordinate this (p,e)-sensitive channel; moreover, very often [RVD] leads to a lower channel efficiency than the simple price-only contract. In contrast, we show that [CVD] leads to perfect channel coordination — a significant result since most contract formats have been shown in the literature to be unable to coordinate a (p,e)-channel. Next, we consider the more realistic situations in which the manufacturer is uncertain about one of the system parameters — specifically, either the market size “a” or the effort cost “η”. Our results show that, if Manu is uncertain about a, [RVD] becomes useless but the manufacturer can still use [CVD] to benefit himself. When the manufacturer is uncertain about η, [CVD] remains useful (as expected); however, surprisingly, [RVD] can outperform [CVD] when both the mean value and the uncertainty of η are sufficient high. These results underline the necessity of evaluating a contract format under various forms of system-parameter uncertainties — often at the expense of analytical tractability.     

Sampling using a ‘bank’ of clues

An easy-to-implement form of the Metropolis Algorithm is described which, unlike most standard techniques, is well suited to sampling from multi-modal distributions on spaces with moderate numbers of dimensions (order ten) in environments typical of investigations into current constraints on Beyond-the-Standard-Model physics. The sampling technique makes use of pre-existing information (which can safely be of low or uncertain quality) relating to the distribution from which it is desired to sample. This information should come in the form of a “bank” or “cache” of parameter space points of which at least some may be expected to be near regions of interest in the desired distribution. In practical circumstances such “banks of clues” are easy to assemble from earlier work, aborted runs, discarded burn-in samples from failed sampling attempts, or from prior scouting investigations. The technique equilibrates between disconnected parts of the distribution without user input. The algorithm is not lead astray by “bad” clues, but there is no free lunch: performance gains will only be seen where clues are helpful.     

Optimization, block designs and No Free Lunch theorems

We study the precise conditions under which all optimization strategies for a given family of finite functions yield the same expected maximization performance, when averaged over a uniform distribution of the functions. In the case of bounded-length searches in a family of Boolean functions, we provide tight connections between such “No Free Lunch” conditions and the structure of t-designs and t-wise balanced designs for arbitrary values t. As a corollary, we obtain a nontrivial family of n-variate Boolean functions that satisfies the “No Free Lunch” condition with respect to searches of length Ω(n1/2/log1/2n). Modifying the construction, we also obtain nontrivial “No Free Lunch” families of functions with large ranges.     

Set Membership approximation theory for fast implementation of Model Predictive Control laws

In this paper, the use of Set Membership (SM) methodologies is investigated in the approximation of Model Predictive Control (MPC) laws for linear systems. Such approximated MPC laws are derived from a finite number ν of exact control moves computed off-line. Properties, in terms of guaranteed approximation error, closed-loop stability and performance, are derived assuming only the continuity of the exact predictive control law. These results are achieved by means of two main contributions. At first, it will be shown that if the approximating function enjoys two key properties (i.e. fulfillment of input constraints and explicit evaluation of a bound on the approximation error, which converges to zero as ν increases), then it is possible to guarantee the boundedness of the controlled state trajectories inside a compact set, their convergency to an arbitrary small neighborhood of the origin, and satisfaction of state constraints. Moreover, the guaranteed performance degradation, in terms of maximum state trajectory distance, can be explicitly computed and reduced to an arbitrary small value, by increasing ν. Then, two SM approximations are investigated, both enjoying the above key properties. The first one minimizes the guaranteed approximation error, but its on-line computational time increases with ν. The second one has higher approximation error, but lower on-line computational time which is constant with ν when the off-line computed moves are suitably chosen. The presented approximation techniques can be systematically employed to obtain an efficient MPC implementation for “fast” processes. The effectiveness of the proposed techniques is tested on two numerical examples.     

Round-off error in products

LetA ₁ andA ₂ be floating point numbers represented in arbitrary base β and randomly chosen from a logarithmic distribution. Letr denote the round-off error $$r = fl(A_1 * A_2 ) - (A_1 * A_2 )$$ where * is floating point multiplication and wherefl(A ₁*A ₂) denotes the normalizedN digit computer result of forming (A ₁*A ₂). This paper analyzes the mean and variance of both the actual round-off error and the fraction round-off error. This analysis relies upon sharp order estimates for the digit by digit deviation of logarithmically distributed numbers from uniformly distributed numbers. This completely resolves open questions of Kaneko and Liu and of Tsao. Also included is a generalization to arbitrary base (from binary) of an important round-off theorem of Henrici.     

Correcting MM estimates for “fat” data sets

Regression MM estimates require the estimation of the error scale, and the determination of a constant that controls the efficiency. These two steps are based on the asymptotic results that are derived assuming that the number of predictors p remains fixed while the number of observations n tends to infinity, which means assuming that the ratio p/n is “small”. However, many high-dimensional data sets have a “large” value of p/n (say, ≥0.2). It is shown that the standard asymptotic results do not hold if p/n is large; namely that (a) the estimated scale underestimates the true error scale, and (b) that even if the scale is correctly estimated, the actual efficiency can be much lower than the nominal one. To overcome these drawbacks simple corrections for the scale and for the efficiency controlling constant are proposed, and it is demonstrated that these corrections improve on the estimate’s performance under both normal and contaminated data.     

Rotation-discriminating template matching based on Fourier coefficients of radial projections with robustness to scaling and partial occlusion

We consider brightness/contrast-invariant and rotation-discriminating template matching that searches an image to analyze A for a query image Q. We propose to use the complex coefficients of the discrete Fourier transform of the radial projections to compute new rotation-invariant local features. These coefficients can be efficiently obtained via FFT. We classify templates in “stable” and “unstable” ones and argue that any local feature-based template matching may fail to find unstable templates. We extract several stable sub-templates of Q and find them in A by comparing the features. The matchings of the sub-templates are combined using the Hough transform. As the features of A are computed only once, the algorithm can find quickly many different sub-templates in A, and it is suitable for finding many query images in A, multi-scale searching and partial occlusion-robust template matching.     

Smart PAC-learners

The PAC-learning model is distribution-independent in the sense that the learner must reach a learning goal with a limited number of labeled random examples without any prior knowledge of the underlying domain distribution. In order to achieve this, one needs generalization error bounds that are valid uniformly for every domain distribution. These bounds are (almost) tight in the sense that there is a domain distribution which does not admit a generalization error being significantly smaller than the general bound. Note however that this leaves open the possibility to achieve the learning goal faster if the underlying distribution is “simple”. Informally speaking, we say a PAC-learner L is “smart” if, for a “vast majority” of domain distributions D, L does not require significantly more examples to reach the “learning goal” than the best learner whose strategy is specialized to D. In this paper, focusing on sample complexity and ignoring computational issues, we show that smart learners do exist. This implies (at least from an information-theoretical perspective) that full prior knowledge of the domain distribution (or access to a huge collection of unlabeled examples) does (for a vast majority of domain distributions) not significantly reduce the number of labeled examples required to achieve the learning goal.     

Unbounded-error quantum computation with small space bounds

We prove the following facts about the language recognition power of quantum Turing machines (QTMs) in the unbounded error setting: QTMs are strictly more powerful than probabilistic Turing machines for any common space bound s satisfying s(n)=o(loglogn). For “one-way” Turing machines, where the input tape head is not allowed to move left, the above result holds for s(n)=o(logn). We also give a characterization for the class of languages recognized with unbounded error by real-time quantum finite automata (QFAs) with restricted measurements. It turns out that these automata are equal in power to their probabilistic counterparts, and this fact does not change when the QFA model is augmented to allow general measurements and mixed states. Unlike the case with classical finite automata, when the QFA tape head is allowed to remain stationary in some steps, more languages become recognizable. We define and use a QTM model that generalizes the other variants introduced earlier in the study of quantum space complexity.     

Constructive linear-time temporal logic: Proof systems and Kripke semantics

In this paper we study a version of constructive linear-time temporal logic (LTL) with the “next” temporal operator. The logic is originally due to Davies, who has shown that the proof system of the logic corresponds to a type system for binding-time analysis via the Curry-Howard isomorphism. However, he did not investigate the logic itself in detail; he has proved only that the logic augmented with negation and classical reasoning is equivalent to (the “next” fragment of) the standard formulation of classical linear-time temporal logic. We give natural deduction, sequent calculus and Hilbert-style proof systems for constructive LTL with conjunction, disjunction and falsehood, and show that the sequent calculus enjoys cut elimination. Moreover, we also consider Kripke semantics and prove soundness and completeness. One distinguishing feature of this logic is that distributivity of the “next” operator over disjunction “?(A∨B)⊃?A∨?B” is rejected in view of a type-theoretic interpretation.     

Required extra capacity: A comparative estimation of overprovisioning needed for a classless IP backbone

The benefit of Class-of-Service (CoS) is an important topic in the “Network Neutrality” debate. As part of the debate, it has been suggested that over-provisioning is a viable strategy to meet performance targets of future applications, and that there is no need for to worry about provisioning differentiated services in an IP backbone for a small fraction of users needing better-than-best-effort service. In this paper, we quantify the extra capacity requirement for an over-provisioned classless (i.e., best-effort) network compared to a CoS network providing the same delay or loss performance for premium traffic. We first develop a link model that quantifies the required extra capacity (REC). To illustrate key parameters involved in analytically quantifying REC, we start with simple traffic distributions. Then, for more bursty traffic distributions (e.g., long-range dependent), we find the REC using ns-2 simulations of CoS and classless links. We, then, use these link models to quantify the REC for network topologies (obtained from Rocketfuel) under various scenarios including situations with “closed loop” traffic generated by many TCP sources that adapt to the available capacity. We also study the REC under link and node failures. We show that REC can still be significant even when the proportion of premium traffic requiring performance assurances is small, a situation often considered benign for the over-provisioning alternative. We also show that the impact of CoS on best-effort (BE) traffic is relatively small while still providing the desired performance for premium traffic.     

Solutions of fuzzy relation equations based on continuous t-norms

This study is concerned with fuzzy relation equations with continuous t-norms in the form ATR = B, where A and B are the fuzzy subsets of X and Y, respectively; R ⊂ X × Y is a fuzzy relation, and T is a continuous t-norm. The problem is how to determine A from R and B. First, an “if and only if” condition of being solvable is presented. Novel algorithms are then presented for determining minimal solutions when X and Y are finite. The proposed algorithms generate all minimal solutions for the equations, making them efficient solving procedures.     

The effect of an information ethics course on the information ethics values of students - A Chinese guanxi culture perspective

The development of information technology has a significant influence on social structure and norms, and also impacts upon human behavior. In order to achieve stability and social harmony, people need to respect various norms, and have their rights protected. Students’ information ethics values are of critical and radical importance in achieving this goal. Using qualitative approach, the present study utilizes Kohlberg’s CMD model to measure improvement in students’ “information ethics values” through “technology mediated learning (TML)” models, and to assess the extent to which it is influenced by gender and Chinese guanxi culture. We find that while e-learning improves female students’ “respect rules,” “privacy,” “accessibility” and “intellectual property” values more than male students, the percentages relating to “intellectual property” for females in the higher stages remain lower than for males. Moreover, these results are interpreted from a Chinese guanxi culture perspective. In light of these results, educators should take account of such improvements when designing effective teaching methods and incentives.     

Comments on “Generalised finite Radon transform for N × N images”

In Kingston and Svalbe [1], a generalized finite Radon transform (FRT) that applied to square arrays of arbitrary size N × N was defined and the Fourier slice theorem was established for the FRT. Kingston and Svalbe asserted that “the original definition by Matúš and Flusser was restricted to apply only to square arrays of prime size,” and “Hsung, Lun and Siu developed an FRT that also applied to dyadic square arrays,” and “Kingston further extended this to define an FRT that applies to prime-adic arrays”. It should be said that the presented generalized FRT together with the above FRT definitions repeated the known concept of tensor representation, or tensor transform of images of size N × N which was published earlier by Artyom Grigoryan in 1984-1991 in the USSR. The above mentioned “Fourier slice theorem” repeated the known tensor transform-based algorithm of 2-D DFT [5-11], which was developed for any order N₁ × N₂ of the transformation, including the cases of N × N, when N = 2^r, (r > 1), and N = L^r, (r ≥ 1), where L is an odd prime. The problem of “over-representation” of the two-dimensional discrete Fourier transform in tensor representation was also solved by means of the paired representation in Grigoryan [6-9].     

A generalization of the 0-1 principle for sorting

The traditional zero-one principle for sorting networks states that “if a network with n input lines sorts alln² binary sequences into nondecreasing order, then it will sort any arbitrary sequence of n numbers into nondecreasing order”. We generalize this to the situation when a network sorts almost all binary sequences and relate it to the behavior of the sorting network on arbitrary inputs. We also present an application to mesh sorting.     

Performance evaluation of spectral vegetation indices using a statistical sensitivity function

A great number of spectral vegetation indices (VIs) have been developed to estimate biophysical parameters of vegetation. Traditional techniques for evaluating the performance of VIs are regression-based statistics, such as the coefficient of determination and root mean square error. These statistics, however, are not capable of quantifying the detailed relationship between VIs and biophysical parameters because the sensitivity of a VI is usually a function of the biophysical parameter instead of a constant. To better quantify this relationship, we developed a “sensitivity function” for measuring the sensitivity of a VI to biophysical parameters. The sensitivity function is defined as the first derivative of the regression function, divided by the standard error of the dependent variable prediction. The function elucidates the change in sensitivity over the range of the biophysical parameter. The Student's t- or z-statistic can be used to test the significance of VI sensitivity. Additionally, we developed a “relative sensitivity function” that compares the sensitivities of two VIs when the biophysical parameters are unavailable.