A relatively recent development in nonparametric regression is the representation of spline-based smoothers as mixed model fits. In particular, generalized nonparametric regression (e.g. smoothingwith a binary response) corresponds to fitting a generalized linear mixedmodel. Automation, or data-driven smoothing parameter selection, can be achieved via (restricted) maximum likelihood estimation ...

In computer graphics, modeling the geometry of hair and hair-like patterns such as grass and fur remains a significant challenge. Hair strands can exist in an extensive variety of arrangements and the choice of an appropriate representation for tasks such as hair synthesis, fitting, editing, or reconstruction from samples, is non-trivial. To support such applications we present a novel mathemat...

Quantum algorithms for factoring and finding discrete logarithms have previously been generalized to finding hidden subgroups of finite Abelian groups. This paper explores the possibility of extending this general viewpoint to finding hidden subgroups of noncommutative groups. We present a quantum algorithm for the special case of dihedral groups which determines the hidden subgroup in a linear...

A subgroup H of a finite group G is said to be W -S-permutable in G if there is a subgroup K of G such that G = HK and H ∩K is a nearly S-permutable subgroup of G. In this article, we analyse the structure of a finite group G by using the properties of W -S-permutable subgroups and obtain some new characterizations of finite p-nilpotent groups and finite supersolvable groups. Some known results...

Geometric methods proposed by Stallings [13] for treating finitely generated subgroups of free groups were successfully used to solve a wide collection of decision problems for free groups and their subgroups [1, 5, 9, 10, 16]. In the present paper we employ the generalized Stallings’ folding method developed in [11] to introduce a procedure, which given a subgroup H of a free product of finite...

In this paper, we introduce two new flexible families of unimodal circular distributions obtained by wrapping onto the unit circle two recently explored heavytailed distributions defined on the real line. The first, the four-parameter wrapped normal–Laplace distribution, is nested within the second, the five-parameter wrapped generalized normal–Laplace distribution. Both families contain the wr...

The "leapfrog" hybrid Monte Carlo algorithm is a simple and effective MCMC method for fitting Bayesian generalized linear models with canonical link. The algorithm leads to large trajectories over the posterior and a rapidly mixing Markov chain, having superior performance over conventional methods in difficult problems like logistic regression with quasicomplete separation. This method offers ...

Strategy-proof social choice functions are characterized for societies where the space of alternatives is any full dimensional compact subset of a Euclidean space and all voters have generalized single-peaked preferences. Our results build upon and extend those obtained for cartesian product ranges by Border and Jordan (1983). By admitting a large set of non-Cartesian ranges, we give a partial ...

Geometric methods proposed by Stallings [17] for treating finitely generated subgroups of free groups were successfully used to solve a wide collection of decision problems for free groups and their subgroups [1, 6, 10, 11, 15, 16, 20]. In the present paper we employ the generalized Stallings’ folding method developed in [12] to introduce a procedure, which given a subgroup H of a free product ...

Let M be the moduli space of generalized parabolic bundles (GPBs) of rank r and degree d on a smooth curve X . Let ML̄ be the closure of its subset consisting of GPBs with fixed determinant L̄. We define a moduli functor for which ML̄ is the coarse moduli scheme. Using the correspondence between GPBs on X and torsion-free sheaves on a nodal curve Y of which X is a desingularization, we show that M...