Search

We establish a strong form of Littlewood's conjecture with inhomogeneous shifts, for a full‐dimensional set of pairs of badly approximable numbers on a vertical line. We also prove a uniform assertion of this nature, generalising a strong form of a result of Haynes et al. Finally, we establish a similar result involving inhomogeneously badly approximable numbers, making progress towards a problem posed by Pollington et al. [ABSTRACT FROM AUTHOR]

This paper examines how a regime of penalties or sanctions for breaching public financial management (PFM) laws and regulations can be designed to increase compliance with these laws. Financial irregularities can be as high as five to eight percent of GDP or more in some poorly administered countries. If a sanctions regime is to be effective, it should meet the three core principles of impartiality, proportionality, and transparency. An empirical analysis of sanctions regimes and recovery rates in 26 countries suggests that excessive use of "harsh" sanctions could negatively affect the level of compliance. The design of a sanctions regime should include both "soft" and "harsh" measures which are proportionate to the severity of financial irregularities. The paper describes three institutional models ("financial police," "risk‐based," and "sanctions coordinator") that countries have used to implement a sanctions regime. An approach targeting expenditure that is highly vulnerable to irregularities tends to achieve a better recovery rate than a regime based on a "mass investigation, mass sanctions" approach. A tailored approach based on the third model may be appropriate for low‐capacity countries. [ABSTRACT FROM AUTHOR]

An intercalate in a Latin square is a 2 x 2 Latin subsquare. Let N be the number of intercalates in a uniformly random n x n Latin square. We prove that asymptotically almost surely N ≥ (1 - o(1)) n²/4, and that 피N ≤ (1 + o(1)) n²/2 (therefore asymptotically almost surely N ≤ fn² for any f → ∞). This significantly improves the previous best lower and upper bounds. We also give an upper tail bound for the number of intercalates in 2 fixed rows of a random Latin square. In addition, we discuss a problem of Linial and Luria on low-discrepancy Latin squares. [ABSTRACT FROM AUTHOR]

Fractional factorial (FF) designs are no doubt the most widely used designs in experimental investigations due to their efficient use of experimental runs. One price we pay for using FF designs is, clearly, our inability to obtain estimates of some important effects (main effects or second order interactions) that are separate from estimates of other effects (usually higher order interactions). When the estimate of an effect also includes the influence of one or more other effects the effects are said to be aliased. Folding over an FF design is a method for breaking the links between aliased effects in a design. The question is, how do we define the foldover structure for asymmetric FF designs, whether regular or nonregular? How do we choose the optimal foldover plan? How do we use optimal foldover plans to construct combined designs which have better capability of estimating lower order effects? The main objective of the present paper is to provide answers to these questions. Using the new results in this paper as benchmarks, we can implement a powerful and efficient algorithm for finding optimal foldover plans which can be used to break links between aliased effects. [ABSTRACT FROM AUTHOR]

In this paper, we study the effects of anomalies on the distribution of TCP flow interarrival time process. We show empirically that despite the variety of data networks in size, number of users, applications, and load, the interarrival times of normal flows comply with the Weibull distribution, whereas specific irregularities (anomalies) causes deviations from the distribution. We first estimate the scale and shape parameters and then check the discrepancy of the data from a Weibull distribution with the estimated parameters. We also utilize the Weibull counting model to recheck the conformance of small flow interarrival times with the distribution. We perform our experiments on a diverse variety of traffic data sets from backbone connections to endpoints of academic and commercial networks. Moreover, we propose a window-based anomaly detection method as a possible application of our findings in which we first estimate the Weibull parameters of interarrival times in each window and then check the discrepancy of the data with a Weibull distribution with the estimated parameters and set an alarm whenever the difference is significant. We apply this method on one of our data sets and present the results to clarify the idea and show its capability in detecting volume anomalies. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Mangarevan traditionally contained two numeration systems: a general one, which was highly regular, decimal, and extraordinarily extensive; and a specific one, which was restricted to specific objects, based on diverging counting units, and interspersed with binary steps. While most of these characteristics are shared by numeration systems in related languages in Oceania, the binary steps are unique. To account for these characteristics, this article draws on-and tries to integrate-insights from anthropology, archeology, linguistics, psychology, and cognitive science more generally. The analysis of mental arithmetic with these systems reveals that both types of systems entailed cognitive advantages and served important functions in the cultural context of their application. How these findings speak to more general questions revolving around the theoretical models and evolutionary trajectory of numerical cognition will be discussed in the Conclusion Most treatises of numerical achievements so far have focused-with rare exceptions (e.g., Mimica, ; Saxe, )-on systems in literate societies (e.g., Chemla, ; Katz, ; Pellatt, ) or in societies that at least developed notational systems (e.g., Ascher & Ascher, ; overview in Chrisomalis, ), and most investigations of performance in mental arithmetic have been even more confined to users of the Hindu-Arabic system in the West (see, e.g., references cited in Section , and most contributions to Campbell, ). The Mangarevan example presented here demonstrates how much insight and how many theoretical advances are to be gained if one widens the scope further. Not only does Mangarevan stand as representative of a widespread habit of using specific systems with enlarged counting units, which is worthy of investigation in its own right. The Mangarevan mixed system is also, to the best of our knowledge, the only system documented so far that involved binary steps at an advanced level-thereby attesting to the creativity with which numeration systems are adapted to the cultural context in which they are used.. [ABSTRACT FROM AUTHOR]

For the uniform random regular directed graph we prove concentration inequalities for (1) codegrees and (2) the number of edges passing from one set of vertices to another. As a consequence, we can deduce discrepancy properties for the distribution of edges essentially matching results for Erdős-Rényi digraphs obtained from Chernoff-type bounds. The proofs make use of the method of exchangeable pairs, developed for concentration of measure by Chatterjee in (Chatterjee, Probab Theory and Relat Fields 138 (2007), 305-321). Exchangeable pairs are constructed using two involutions on the set of regular digraphs: a well-known 'simple switching' operation, as well as a novel 'reflection' operation. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 50, 23-58, 2017 [ABSTRACT FROM AUTHOR]

Answering in a strong form a question posed by Bollobás and Scott, in this paper we determine the discrepancy between two random k-uniform hypergraphs, up to a constant factor depending solely on k. © 2013 Wiley Periodicals, Inc. Random Struct. Alg., 47, 147-162, 2015 [ABSTRACT FROM AUTHOR]

Crystallographic least squares are a fundamental tool for crystal structure analysis. In this paper their properties are derived from functions estimating the degree of similarity between two electron-density maps. The new approach leads also to modifications of the standard least-squares procedures, potentially able to improve their efficiency. The role of the scaling factor between observed and model amplitudes is analysed: the concept of unlocated model is discussed and its scattering contribution is combined with that arising from the located model. Also, the possible use of an ancillary parameter, to be associated with the classical weight related to the variance of the observed amplitudes, is studied. The crystallographic discrepancy factors, basic tools often combined with least-squares procedures in phasing approaches, are analysed. The mathematical approach here described includes, as a special case, the so-called vector refinement, used when accurate estimates of the target phases are available. [ABSTRACT FROM AUTHOR]

SUMMARY This paper introduces a new strategy for setting the regularization parameter when solving large-scale discrete ill-posed linear problems by means of the Arnoldi-Tikhonov method. This new rule is essentially based on the discrepancy principle, although no initial knowledge of the norm of the error that affects the right-hand side is assumed; an increasingly more accurate approximation of this quantity is recovered during the Arnoldi algorithm. Some theoretical estimates are derived in order to motivate our approach. Many numerical experiments performed on classical test problems as well as image deblurring problems are presented. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY This paper presents a new method to construct a decentralized nonlinear robust H ∞ controller for a class of large-scale nonlinear uncertain systems. The admissible uncertainties and nonlinearities in the system satisfy integral quadratic constraints and global Lipschitz conditions, respectively. The decentralized controller, which is required to be stable, is capable of exploiting known nonlinearities and interconnections between subsystems without treating them as uncertainties. Instead, additional uncertainties are introduced because of the discrepancies between nondecentralized and decentralized nonlinear output feedback controllers. The H ∞ control objective is to achieve an absolutely stable closed-loop system with a specified disturbance attenuation level. A solution to this control problem involves stabilizing solutions to algebraic Riccati equations parametrized by scaling constants corresponding to the uncertainties and nonlinearities. This formulation is nonconvex; hence, an evolutionary optimization method is applied to solve the control problem considered. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We study the set of all strongly irregular points of a Brouwer homeomorphism f which is embeddable in a flow. We prove that this set is equal to the first prolongational limit set of any flow containing f. We also give a sufficient condition for a class of flows of Brouwer homeomorphisms to be topologically conjugate. [ABSTRACT FROM AUTHOR]

This paper utilizes advanced methods from Fourier analysis in order to describe periodicities in financial ultrahigh frequency foreign exchange data. The Lomb-Scargle Fourier transform is used to take into account the irregularity in spacing in the time domain. It provides a natural framework for the power spectra of different inhomogeneous time-series processes to be easily and quickly estimated. Furthermore, an event-based approach in intrinsic time based on a power-law relationship is employed using different event thresholds to filter the foreign exchange tick-data. The calculated spectral density demonstrates that the price process in intrinsic time contains different periodic components for directional changes, especially in the medium-long term, implying the existence of stylized facts of ultrahigh frequency data in the frequency domain. [ABSTRACT FROM AUTHOR]

Two-dimensional point sets derived from pairs of quasirandom numbers generated by the bit-reversal method introduced by van der Corput exhibit features well known from the quasiperiodic binary substitution tilings derived from the rhombic tilings of Penrose and Ammann-Beenker. The concept of geometric discrepancy, a measure describing the uniformity of distribution of quasirandom sequences or point sets, is discussed from the perspective of structural chemistry. [ABSTRACT FROM AUTHOR]

Let S be a minimal complex surface of general type with irregularity q ≥ 2 and let C ⊂ S be an irreducible curve of geometric genus g. Assume that C is Albanese defective, that is, that the image of C via the Albanese map does not generate the Albanese variety Alb(S); we obtain a linear upper bound in terms of K2S and g for the canonical degree KSC of C. As a corollary, we obtain a bound for the canonical degree of curves with g ≤ q−1, thereby generalizing and sharpening the main result of Lu [‘On surfaces of general type with maximal Albanese dimension’, J. reine angew. Math. 641 (2010) 163–175.]. [ABSTRACT FROM PUBLISHER]

With regard to the nonlinearity and irregularity along with implicit seasonality and trend in the context of air passenger traffic forecasting, this study proposes an ensemble empirical mode decomposition (EEMD) based support vector machines (SVMs) modeling framework incorporating a slope-based method to restrain the end effect issue occurring during the shifting process of EEMD, which is abbreviated as EEMD-Slope-SVMs. Real monthly air passenger traffic series including six selected airlines in USA and UK were collected to test the effectiveness of the proposed approach. Empirical results demonstrate that the proposed decomposition and ensemble modeling framework outperform the selected counterparts such as single SVMs (straightforward application of SVMs), Holt-Winters, and ARIMA in terms of RMSE, MAPE, GMRAE, and DS. Additional evidence is also shown to highlight the improved performance while compared with EEMD-SVM model not restraining the end effect. [ABSTRACT FROM AUTHOR]

A vertex irregular total k-labeling of a graph G with vertex set V and edge set E is an assignment of positive integer labels {1, 2, . . . , k} to both vertices and edges so that the weights calculated at vertices are distinct. The total vertex irregularity strength of G, denoted by tvs(G) is the minimum value of the largest label k over all such irregular assignment. In this paper, we consider the total vertex irregularity strengths of disjoint union of s isomorphic sun graphs, tvs(sMn), disjoint union of s consecutive nonisomorphic sun graphs, tvs(∪si=1 Mi+2), and disjoint union of any two nonisomorphic sun graphs tvs(Mk ∪ Mn). [ABSTRACT FROM AUTHOR]

This paper proposes a new wavelet-based method for deconvolving a density. The estimator combines the ideas of non-linear wavelet thresholding with periodized Meyer wavelets and estimation by information projection. It is guaranteed to be in the class of density functions, in particular it is positive everywhere by construction. The asymptotic optimality of the estimator is established in terms of the rate of convergence of the Kullback–Leibler discrepancy over Besov classes. Finite sample properties are investigated in detail, and show the excellent empirical performance of the estimator, compared with other recently introduced estimators. [ABSTRACT FROM AUTHOR]

Les auteurs s'intéressent au problème d'estimation des fonctions de régression qui présentent des discontinuités dans la première dérivée. Ils analysent le biais de l'estimateur de régression linéaire locale et de ses versions à noyau unilatéral droite et gauche afin de proposer une procédure d'estimation améliorée, fondée sur la sélection automatique du meilleur estimateur basé sur la somme des résidus carrés. Les auteurs fournissent des résultats théoriques ainsi qu'une étude numérique sur des données simulées et réelles. La revue canadienne de statistique 37: 453-475; 2009 © 2009 Société statistique du Canada [ABSTRACT FROM AUTHOR]

Reliable autofocusing is a critical part of any automated microscopy system: by precisely positioning the sample in the focal plane, the acquired images are sharp and can be accurately segmented and quantified. The three main components of an autofocus algorithm are a contrast function, an optimization algorithm and a sampling strategy. The latter has not been given much attention in the literature. It is however a very important part of the autofocusing algorithm, especially in high content and high throughput image-based screening. It deals with the problem of sampling the focus surface as sparsely as possible to reduce bleaching and computation time while with sufficient detail as to permit a faithful interpolation. We propose a new strategy that has higher performance compared to the classical square grid or the hexagonal lattice, which is based on the concept of low discrepancy point sets and in particular on the Halton point set. We tested the new algorithm on nine different focus surfaces, each under 24 different combinations of Signal-to-Noise ratio (SNR) and sampling rate, obtaining that in 88% of the tested conditions, Halton sampling outperforms its counterparts. [ABSTRACT FROM AUTHOR]

Functional analyses that were conducted in two settings (playground and classroom) indicated that problem behavior was sensitive to adult attention on the playground and tangible items in the classroom. Attention- and tangible-based interventions were designed based on the results from each of the assessment environments and were compared. The attention-based intervention was more effective on the playground, and the tangible-based intervention was more effective in the classroom. Findings are discussed in regards to the generality of functional analysis results across environments. [ABSTRACT FROM AUTHOR]

The present work focuses on extensions of the posterior predictive p-value (ppp-value) for models with hierarchical structure, designed for testing assumptions made on underlying processes. The ppp-values are popular as tools for model criticism, yet their lack of a common interpretation limit their practical use. We discuss different extensions of ppp-values to hierarchical models, allowing for discrepancy measures that can be used for checking properties of the model at all stages. Through analytical derivations and simulation studies on simple models, we show that similar to the standard ppp-values, these extensions are typically far from uniformly distributed under the model assumptions and can give poor power in a hypothesis testing framework. We propose a calibration of the p-values, making the resulting calibrated p-values uniformly distributed under the model conditions. Illustrations are made through a real example of multinomial regression to age distributions of fish. [ABSTRACT FROM AUTHOR]

Rudas, Clogg, and Lindsay (RCL) proposed a new index of fit for contingency table analysis. Using the overparametrized two-component mixture, where the first component with weight 1 2 w represents the model to be tested and the second component with weight w is unstructured, the mixture index of fit was defined to be the smallest w compatible with the saturated two-component mixture. This index of fit, which is insensitive to sample size, is applied to the problem of assessing the fit of the Rasch model. In this application, use is made of the equivalence of the semi-parametric version of the Rasch model to specifically restricted latent class models. Therefore, the Rasch model can be represented by the structured component of the RCL mixture, with this component itself consisting of two or more subcomponents corresponding to the classes, and the unstructured component capturing the discrepancies between the data and the model. An empirical example demonstrates the application of this approach. Based on four-item data, the one- and two-class unrestricted latent class models and the one- to three-class models restricted according to the Rasch model are considered, with respect to both their chi-squared statistics and their mixture fit indices. [ABSTRACT FROM AUTHOR]

For discrete distributions, the standard method of producing a two-sided confidence interval generates an interval that is exact but conservative. This paper proposes a new algorithm to produce a short exact geometric confidence interval with proven properties, and compares the new interval with the standard interval. [ABSTRACT FROM AUTHOR]

A three-pole ceramic monoblock filter is analysed using HFSS. The numerical results are compared with the measurements, and possible reasons for disagreement between the measured and simulated results are investigated. The development of new techniques to minimise this discrepancy is also presented. [ABSTRACT FROM AUTHOR]

The purpose of this article is to propose and highlight a statistical estimation procedure for joint identification of irregularities in population distribution in urban areas having a directional dimension, and the estimation of the parameters of the model's separate regimes. The method we propose here is an application of the switching regimes regression technique developed by Quandt (1958, 1960) for identifying the most likely allocation of n observations into two separate regimes, each associated with a different mechanism that generates its own set of observations. A subsequent purpose is to apply empirically the switching regimes method to the city of Tel-Aviv – Yafo, and discern possible regimes where population densities are generated by different processes. [ABSTRACT FROM AUTHOR]

Let ℬ2 denote the family of all circular discs in the plane. It is proved that the discrepancy for the family {B1 × B2 ∶ B1, B2 ∈ ℬ2} in R4 is O(n1/4+ε) for an arbitrarily small constant ε > 0, that is, it is essentially the same as that for the family ℬ2 itself. The result is established for the combinatorial discrepancy, and consequently it holds for the discrepancy with respect to the Lebesgue measure as well. This answers a question of Beck and Chen. More generally, we prove an upper bound for the discrepancy for a family {Πi=1k Ai∶ Ai ∈ Ai, i = 1,2,...,k}, where each Ai is a family in Rdi, each of whose sets is described by a bounded number of polynomial inequalities of bounded degree. The resulting discrepancy bound is determined by the 'worst' of the families Ai, and it depends on the existence of certain decompositions into constant-complexity cells for arrangements of surfaces bounding the sets of Ai. The proof uses Beck's partial coloring method and decomposition techniques developed for the range-searching problem in computational geometry. [ABSTRACT FROM AUTHOR]

Cet article présente des tables du test des rangs de Friedman pour l'analyse de variance à deux facteurs. Ces tables sont plus précises que celles présentées dans la littérature. A l'aide d'un grand nombre de simulations, nous avons remarqué pour certaines valeurs critiques quelques contradictions avec les tables publiées par d'autres auteurs. Les tables présentées dans cet article sont également plus exhaustives que celles disponibles actuellement. [ABSTRACT FROM AUTHOR]

The article presents research which examined the deficiencies in relation to the minimum discrepancy estimators. The researcher applied multinomial parameters in assessing the estimator which can be used for minimizing the discrepancy function. The study concluded that the least deficient estimators are impossible to exist in general uniform functions.

Suppose that 5 is a distribution of N points in the unit square U=[0, 1]2. For every x=(x1, x2)U, let B(x)=[0, x1]×[0, x2] denote the aligned rectangle containing all points y=(y1, y2)U satisfying 0dy1dx1 and 0dy2dx2. Denote by Z[5; B(x)] the number of points of 5 that lie in B(x), and consider the discrepancy functionD[5; B(x)]=Z[5; B(x)]N¼(B(x)),where ¼ denotes the usual area measure. [ABSTRACT FROM AUTHOR]

This paper proposes two consistent one-sided specification tests for parametric regression models, one based on the sample covariance between the residual from the parametric model and the discrepancy between the parametric and nonparametric fitted values; the other based on the difference in sums of squared residuals between the parametric and nonparametric models. We estimate the nonparametric model by series regression. The new test statistics converge in distribution to a unit normal under correct specification and grow to infinity faster than the parametric rate (n[sup -1/2]) under misspecification, while avoiding weighting, sample splitting, and non-nested testing procedures used elsewhere in the literature. Asymptotically, our tests can be viewed as a test of the joint hypothesis that the true parameters of a series regression model are zero, where the dependent variable is the residual from the parametric model, and the series terms are functions of the explanatory variables, chosen so as to support nonparametric estimation of a conditional expectation. We specifically consider Fourier series and regression splines, and present a Monte Carlo study of the finite sample performance of the new tests in comparison to consistent tests of Bierens (1990), Eubank and Spiegelman (1990), Jayasuriya (1990), Wooldridge (1992), and Yatchew (1992); the results show the new tests have good power, performing quite well in some situations. We suggest a joint Bonferroni procedure that combines a new test with those of Bierens and Wooldridge to capture the best features of the three approaches. [ABSTRACT FROM AUTHOR]

The Berlekamp-Massey (BM) algorithm is a well-known decoding approach for solving the key equation in Reed-Solomon decoding. Many efficient BM-based algorithms and architectures have been presented in recent years. Introduced are different initial settings of the BM algorithm that can reduce cost and power consumption for VLSI implementation. In addition, the new initialisation scheme eliminates one iteration of the algorithm, thus lowering computational complexity. [ABSTRACT FROM AUTHOR]

The article offers a study on the discrepancies in human platelet alloantigens (HPA) genotyping based on the frequency of glycoprotein IIIa (GPIIIa) variants. The study involves DNA samples from the donated blood at the International Society of Blood Transfusion (ISBT). Furthermore, it compares the frequency, particularly +28G>A variant, obtained from polymerized chain reaction with sequence-specific primers (PCR-SSP), among the unrelated blood donors in Germany.

The article presents the author's insights on his sentiments over an article showing the discrepancy between the perceived performance and the national bowel cancer audit programme (NBOCAP) of a small colorectal unit.

Benfords law (to base B) for an infinite sequence {xk : k = 1} of positive quantities xk is the assertion that {logB xk : k = 1} is uniformly distributed (mod 1). The 3x + 1 function T(n) is given by T(n) = (3n + 1)/2 if n is odd, and T(n) = n/2 if n is even. This paper studies the initial iterates xk = T(k)(x0) for 1 = k = N of the 3x + 1 function, where N is fixed. It shows that for most initial values x0, such sequences approximately satisfy Benfords law, in the sense that the discrepancy of the finite sequence {logB xk : 1 = k = N} is small. [ABSTRACT FROM AUTHOR]