For A,B subsets of an additive group Z, we define A + B to be the sumset {a + b : a ∈ A, b ∈ B}, and kA to be the k-fold sum A + A + · · · + A of A. We also let A−B = {a−b : a ∈ A, b ∈ B} and b+A = {b}+A for a single element set {b}, a translate of A. Note that A − A is not 0 unless |A| = 1. We let k ⋄ A = {ka : a ∈ A}, a dilate of A. There are many obvious properties of “+” that can be checked...

A notion of additive dilogarithm for a field k is introduced, based on the K-theory and higher Chow groups of the affine line relative to 2(0). Analogues of the K2-regulator, the polylogarithm Lie algebra, and the `-adic realization of the dilogarithm motive are discussed. The higher Chow groups of 0-cycles in this theory are identified with the Kähler differential forms Ωk. It is hoped that th...

A d d i t i v e AND/OR graphs are de f ined as AND/ /ORgraphs w i t hou t c i r c u i t s , which can be cons idered as fo lded AND/OR t r e e s ; i . e . the cost of a common subproblem is added to the cost as many t imes as the subproblem occurs , but i t is computed on ly once. A d d i t i v e AND/OR graphs are n a t u r a l l y obta ined by r e i n t e r p r e t i n g the dy namic programmi...

We revisit the additive model learning literature and adapt a penalized spline formulation due to Eilers and Marx [4], to train additive classifiers efficiently. We also propose two new embeddings based two classes of orthogonal basis with orthogonal derivatives, which can also be used to efficiently learn additive classifiers. This paper follows the popular theme in the current literature wher...

We consider the problem of predicting an outcome variable using p covariates that are measured on n independent observations, in a setting in which additive, flexible, and interpretable fits are desired. We propose the fused lasso additive model (FLAM), in which each additive function is estimated to be piecewise constant with a small number of adaptively-chosen knots. FLAM is the solution to a...

Living organisms such as bacteria are able to grow, respond to stimuli, and divide as part of their life cycle. Designing smart three-dimensional (3D) materials that are able to perform such feats, i.e., continue on-demand growth and respond to external stimuli, is always a challenge for polymer and material scientists. At present, Johnson and co-workers have made a significant step forward in ...

The paper presents some models involving a pair of actors that aim at bartering the goods from two privately owned pools of heterogeneous goods. In the models we discuss in the paper the barter can occur only once and can involve either a single good or a basket of goods from each actor/player. In the paper we examine both the basic symmetric model (one-to-one barter) as well as some other vers...

We propose a new sparsity-smoothness penalty for high-dimensional generalized additive models. The combination of sparsity and smoothness is crucial for mathematical theory as well as performance for finite-sample data. We present a computationally efficient algorithm, with provable numerical convergence properties, for optimizing the penalized likelihood. Furthermore, we provide oracle results...

The generalized additive model is extended to handle negative binomial responses. The extension is complicated by the fact that the negative binomial distribution has two parameters and is not in the exponential family. The methodology is applied to data involving DNA adduct counts and smoking variables among ex-smokers with lung cancer. A more detailed investigation is made of the parametric r...