1 Nat-Bijection: Bijections between natural numbers and other types 13 1.1 Type nat × nat . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.2 Type nat + nat . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.3 Type int . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.4 Type nat list . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.5 Finite sets of naturals...

In this short note, we develop a local approximation for the log-ratio of multivariate hypergeometric probability mass function over corresponding multinomial function. conjunction with bounds from Carter (Ann Stat 30(3):708–730, 2002) and Ouimet (J Plan Inference 215:218–233, 2021) on total variation between law vector jittered by uniform $$(-\,1/2,1/2)^d$$ normal distribution, expansion is th...

A Multivariate Public-Key Cryptosystem (MPKC) is a public-key cryptosystem where the public map P, or trapdoor one-way function, is given as a set of m polynomial of a small degree d equations over n variables in a finite field F . Usually d = 2, hence the alternate name “Multivariate Quadratic” (MQ). To decrypt, authenticate or sign digitally, a user must, for a given m-tuple z = (z1, . . . , ...

As the name indicates, multivariate analysis comprises a set of techniques dedicated to the analysis of data sets with more than one variable. Several of these techniques were developed recently in part because they require the computational capabilities of modern computers. Also, because most of them are recent, these techniques are not always unified in their presentation, and the choice of t...

The purpose of this article is to introduce a new scheme for robust multivariate ranking by making use of a not so familiar notion called monotonicity. Under this scheme, as in the case of classical outward ranking, we get an increasing sequence of regions diverging away from a central region (may be a single point) as nucleus. The nuclear region may be deened as the median region.

EEcient data mining algorithms are crucial for eeective knowledge discovery. We present the Multi-Stream Dependency Detection (msdd) data mining algorithm that performs a systematic search for structure in multivariate time series of categorical data. The systematicity of msdd's search makes implementation of both parallel and distributed versions straightforward. Distributing the search for st...

BACKGROUND This population-based study investigated the different forms, magnitude and risk factors of men's violence against women in intimate relationships in a rural part of northern Vietnam and whether a difference in risk factors were at hand for the different forms of violence. Vietnam has undergone a rapid transition in the last 20 years, moving towards a more equal situation for men and...