This paper is about counting the number of distinct (scattered) subwords occurring in a given word. More precisely, we consider the generalization of the Pascal triangle to binomial coefficients of words and the sequence (S(n))n≥0 counting the number of positive entries on each row. By introducing a convenient tree structure, we provide a recurrence relation for (S(n))n≥0. This leads to a conne...

We analyze the performance of the top-down multiclass classification algorithm for decision tree learning called LOMtree, recently proposed in the literature Choromanska and Langford (2014) for solving efficiently classification problems with very large number of classes. The algorithm online optimizes the objective function which simultaneously controls the depth of the tree and its statistica...

The Practical Fat Tree Network(PFN) is proposed as an eecient intercon-nection structure for parallel processing computers using a butterry network. It satisses the concept of volume universality from Leiserson's theoretical fat tree network 1]. In the fat tree network, the locality of input traac is a very important factor because it has signiicant eeects on performance. The proposed performan...

Most of commercial CAD assembly modules are based on a geometric entities constraining. DOF between surfaces (or faces), axis alignments and point-to-point constraining are targeted to a final product digital mockup. The assembly components are not specifically time sequenced and ordered and the assembly simulation is targeted to improve and optimize the component interaction. The final assembl...

We analyze the polytope associated with a combinatorial problem that combines the Steiner tree problem and the uncapacitated facility location problem. The problem, called connected facility location problem, is motivated by a real-world application in the design of a telecommunication network, and concerns with deciding the facilities to open, the assignment of customers to open facilities, an...

This paper presents new single-layer, i.e., planar-embeddable, clock tree constructions with exact zero skew under either the linear or the Elmore delay model. Our method, called Planar-DME, consists of two parts. The rst algorithm, called Linear-Planar-DME, guarantees an optimal planar zero-skew clock tree (ZST) under the linear delay model. The second algorithm, called ElmorePlanar-DME, uses ...

We give a unified treatment of the limit, as the size tends to infinity, of simply generated random trees, including both the well-known result in the standard case of critical Galton–Watson trees and similar but less well-known results in the other cases (i.e., when no equivalent critical Galton–Watson tree exists). There is a well-defined limit in the form of an infinite random tree in all ca...

We present a novel data structure, the Bayes tree, that provides an algorithmic foundation enabling a better understanding of existing graphical model inference algorithms and their connection to sparse matrix factorization methods. Similar to a clique tree, a Bayes tree encodes a factored probability density, but unlike the clique tree it is directed and maps more naturally to the square root ...

The so-called binary perfect phylogeny with persistent characters has recently been thoroughly studied in computational biology as it is less restrictive than the well known binary perfect phylogeny. Here, we focus on the notion of (binary) persistent characters, i.e. characters that can be realized on a phylogenetic tree by at most one 0 → 1 transition followed by at most one 1 → 0 transition ...

Balanced minimum evolution (BME) is a statistically consistent distance-based method to reconstruct a phylogenetic tree from an alignment of molecular data. In 2000, Pauplin showed that the BME method is equivalent to optimizing a linear functional over the BME polytope, the convex hull of the BME vectors obtained from Pauplin's formula applied to all binary trees. The BME method is related to ...