An investigation of the distributional characteristics of 440 large-sample achievement and psychometric measures found all to be significantly nonnormal at the alpha .01 significance level. Several classes of contamination were found, including tail weights from the uniform to the double exponential, exponential-level asymmetry, severe digit preferences, multimodalities, and modes external to t...

We prove the “End Curve Theorem” which states that a normal surface singularity (X, o) with rational homology sphere link Σ is a splice-quotient singularity if and only if it has an end curve function for each leaf of a good resolution tree. An “end-curve function” is an analytic function (X, o) → (C, 0) whose zero set intersects Σ in the knot given by a meridian curve of the exceptional curve ...

In this paper, we proposed another new form of type-2 fuzzy data points(T2FDPs) that is perfectly normal type-2 data points(PNT2FDPs). These kinds of brand-new data were defined by using the existing type-2 fuzzy set theory(T2FST) and type-2 fuzzy number(T2FN) concept since we dealt with the problem of defining complex uncertainty data. Along with this restructuring, we included the fuzzificati...

In this paper we present an improved algorithm for counting points on elliptic curves over finite fields. It is mainly based on SatohSkjernaa-Taguchi algorithm [SST01], and uses a Gaussian Normal Basis (GNB) of small type t ≤ 4. In practice, about 42% (36% for prime N) of fields in cryptographic context (i.e., for p = 2 and 160 < N < 600) have such bases. They can be lifted from FpN to ZpN in a...

Despite the widespread popularity of growth curve analysis, few studies have investigated robust growth curve models. In this paper, the t distribution is applied to model heavy-tailed data and contaminated normal data with outliers for growth curve analysis. The derived robust growth curve models are estimated through Bayesian methods utilizing data augmentation and Gibbs sampling algorithms. ...

Let C ⊆ P denote the rational normal curve of order d. Its homogeneous defining ideal IC ⊆ Q[a0, . . . , ad] admits an SL2-stable filtration J2 ⊆ J4 ⊆ · · · ⊆ IC by sub-ideals such that the saturation of each J2q equals IC . Hence, one can associate to d a sequence of integers (α1, α2, . . . ) which encodes the degrees in which the successive inclusions in this filtration become trivial. In thi...

In this work we introduce a new dissimilarity measure for shape registration using the notion of normal cycles, a concept from geometric measure theory which allows to generalize curvature for non smooth subsets of the euclidean space. Our construction is based on the definition of kernel metrics on the space of normal cycles which take explicit expressions in a discrete setting. This approach ...

In this paper, we proposed a new form of type-2 fuzzy data points(T2FDPs) that is normal type-2 data points(NT2FDPs). These brand-new forms of data were defined by using the definition of normal type-2 triangular fuzzy number(NT2TFN). Then, we applied fuzzification(alpha-cut) and type-reduction processes towards NT2FDPs after they had been redefined based on the situation of NT2FDPs. Furthermor...